Didier Fass
email: didier.fass@loria.fr

Dominique Méry
email: dominique.mery@loria.fr

Keywords: Medical devices, modelling, system engineering, human system integration, bio-CPS, bio-compatibility, bio-integration, correctness by construction

come

Introduction

Developing and producing medical devices and healthcare systems is a crucial issue, both for the economy and for providing safe advances in healthcare delivery. Medical devices become smaller in physical terms (see for instance the new pacemaker implanted inside the ventricular) but larger in software-based elements, the design, testing, validation, and eventual authority device approval is becoming expensive for medical device manufacturers both in terms of time and cost. The increase of alarming rate leads to recalling failing devices. Recalling failing devices is increasing cost and gives a very negative feeling to patients as well as physicians; it leads to consider both forensic and medical issues. Questions on costs should not hide safety and security problems that are now stated in this new generation of software systems. Moreover, safety problems are related to requirements that are either related to technical elements or related to human body -both anatomical and physiological, features. As claims by Dines Bjoerner [START_REF] Bjørner | Domain engineering: A software engineering discipline in need of research[END_REF][START_REF] Bjørner | SOFSEM 2000: Theory and Practice of Informatics: 27th Conference on Current Trends in Theory and Practice of Informat-ics Milovy[END_REF][START_REF] Bjørner | Domain Engineering -Technology Management[END_REF] "Before software can be developed its requirements must be stated. Before requirements can be expressed the application domain must be understood". Since main healthcare system domain is life and health (biology and its two sub-domains: anatomy and physiology), medical devices require integration within or on the body -living system, it leads to modeling bio-compatible and bio-integrative medical devices. That needs to take into account information that is not necessarily explicit in the list of requirements and in the definition of domains such as nature of interactions and time representation. Systems under investigation are often called cyber-physical systems, for short CPS, and necessitate medical human-machine systems design integration, validation and certification. We propose a taxonomy of medical human-machine systems and define classes of healthcare applications for identifying a number of approaches and to overcome difficulties of bio-compatibility and bio-integration. Using the pacemaker case study, we sketch our Event-B-based methodology, which did not consider bio-compatibility and bio-integration and we show how we intend to take into account these new ideas in a correct-byconstruction approach.

. Categorisation of medical devices

Our aim is to focus primarily on the application of software and systems engineering to software-based medical devices used for patients. However, we classify medical devices or healthcare systems into categories corresponding to the use and to the bio-integration of these systems in the life of a patient.

A first class of medical devices is defined as devices which are permanently implanted in the body of a patient, as pacemakers, artificial heart. It requires a clear and as complete as possible statement for the environment. The challenge is to develop models for environment as well as tools. Moreover, when considering the artificial heart, we are facing questions of biocompatibility and bio-integration.

A second class of medical devices is defined as devices which are permanently used by patients but not implanted in the body of a patient, as the hemodialysis. The model for environment is yet a challenge because the global system is integrating several organs and regulations rules for glucose. It is then clear that models for environment necessitates to express flows of fluid in the body of the patient and rate of sugars in the blood. The system is used on a regular and periodic period.

A third class of medical devices is defined as devices which are temporary used for helping somebody to reach a given target state in intensive care, as for instance the extracorporeal membrane oxygenation (ECMO) [START_REF] Abrams | What's new in extra-corporeal mem-brane oxygenation for cardiac failure and cardiac arrest in adults?[END_REF]. It may happen after a heart attack, when the patient's heart requires a minimal activity, or / and during a pulmonary insufficiency (i.e. severe state with H1N1 flu) [START_REF] Kimmoun | Improving blood oxygenation during venovenous ecmo for heartsr[END_REF]. The system supports one or more functionalities and assists the patient. Still in this case we have to integrate bio-compatibility and bio-integration. Currently, implantable or wearable medical devices are designed by abstraction with a reductionist and functionalist approach. Thus living systems are reduced to their physical properties and logical models. Therefore developed and implemented algorithms result from functional analysis methods -abstraction and digitalization, and skills (knowledge and understanding) of the designers.

Mockups and prototypes are validated firstly by technical tests for ensuring technological regulatory standards and secondly by experimental and clinical test before their wide distribution and marketing. However, certification of medical devices , as in aerospace and nuclear industry, remains a challenge.

Medical devices require original, sound and reliable validation methods [START_REF] Jetley | A formal method approach to medical device review[END_REF][START_REF] Lee | High confidence medical device software and systems[END_REF][START_REF] Méry | Trustable formal specification for software certification[END_REF] based on scientifically validated modeling methods and tools (model-based engineering) and grounded on theoretical biology, medical knowledge and clinical evidences, and physicians expertise (evidence-based medicine).

We show how medical devices design, and more generally human-machine system concepts and epistemology, depend on our skills to think and conceptualize generally human system integration. We claim that it is necessary reclaiming these concepts for ensuring correctness by construction medical devices bio-compatibility and bio-integrative properties from the early stage of the design process grounding on both theoretical integrative physiology principles and trustable formal method. Next, we describe the correct-by-construction approach that was used by Méry and Singh [START_REF] Méry | Trustable formal specification for software certification[END_REF], when considering the pacemaker challenge using the Event-B modeling language.

Model-based Design of Medical Devices

Formal methods have emerged as a complementary approach to ensuring quality and correctness of high-confidence medical systems, overcoming limitations of traditional validation techniques such as simulation and testing. In [START_REF] Méry | Trustable formal specification for software certification[END_REF], authors propose a new methodology to obtain certification assurance for complex medical systems design, based on the use of formal methods. The methodology consists of five main phases: first, informal requirements, resulting in a structured version of the requirements, where each fragment is classified according to a fixed taxonomy. In the second phase, informal requirements are represented in formal modelling language, with a precise semantics, and enriched with invariants and temporal constraints. The third phase consists of refinement-based formal verification to test the internal consistency and correctness of the specifications. The fourth phase is the process of determining the degree to which a formal model is an accurate representation of the real world from the perspective of the intended uses of the model using model-checker. Last phase provides an animation framework for the formal model with real-time data set instead of toy-data, and offers a simple way for specifiers to build a domain specific visualization that can be used by domain experts to check whether a formal specification corresponds to their expectations. Fig. 1 sketches the methodology based on the refinement process providing possible feedbacks in the design of a system following a correct by construction process and producing a trustable formal model from the informal requirements. As we have mentioned in the previous lines, the animation phase is a way to integrate the domain experts in the design process. We have to warn the reader that the model of the pacemaker is a formal expression in a formal modelling language based on set theory and on the notion of generalized substitution. The link between knowledge of experts and the formal expressions are very critical to elaborate. Our point of view is that we are facing the question of validation of the formal model with respect to the informal requirements and the integration of physiological information or expert knowledge. A possible solution is to exploit domain ontologies combined with formal modelling language as proposed by Aït-Ameur and Mery [START_REF] Aït-Ameur | Making explicit domain knowl-edge in formal system development[END_REF]. However, it remains to consider how to model physiological features and to validate the resulting model. Event-B is a formal method for system-level modelling and analysis using set theory. In Fig. 1, this phase also gives the feedback to the formalization phase in case of unexpected behaviours of the system. The feedback approach is allowed to modify the formal model and verify it using any theorem prover tool and finally validate it using a model checker tool. The verification, validation and real-time animation processes are applied continue until not to find the correct formal model according to the expected system behaviour. In this phase of the formal development, most of errors are discovered by the domain experts. The real time animation is a key tool for helping the communication with domain experts.

Model

An Event-B model expresses a state property called invariant which is defining the set of possible states of the model. A state is a mapping relating each variable to a given value. The value of a variable is in a given domain which can be either codable in a programming language or member of a domain which is representing possible values. It means that an Event-B model can have variables and state variables modifiable by a finite list of events which are modelling the possible modifications of variables. An event of an Event-B model is not executed but observed, when its guard is true. Only one event may be observed at any time. An Event-B model is discrete and does not express any liveness or fairness property, even if there some extensions of the original Event-B models. Moreover, an Event-B model is based on a logical theory based on set-theoretical or predicate calculus notations. It means that the design of an Event-B model requires specific checking of well typing or verification conditions validating the invariant property. Questions are related to what properties over medical devices can we express and how tractable are these properties? In Event-B, we can express, first, invariant properties defining a stability condition of the system under consideration, or safety properties stating that nothing bad will happen. For instance, the pacemaker should not pace in the red zone and can pace in the green zone. Fig. 2 is containing the annotated ECG as well as the text of the invariant.

Figure 2: Example of a relation between an invariant and an ECG-based state

When validating an Event-B model, one should prove that each event maintain invariant and safety properties and this operation is done by the underlying proof assistant. The underlying proof process is adding trust to the resulting model and guide the designer when following the incremental refinement-based process for constructing formal models from informal requirements. The formality of Event-B models is helping to get a trustable model but we need to have modalities for communicating to the domain experts.

The choice of the Event-B modelling language is mainly guided by the simplicity of the basic concepts and the existence of a toolset namely Rodin [7]. Others modelling techniques can be used for developing models and the most important feature is the methodology of correct by construction development using the refinement. The refinement allows us to play with levels of abstraction. In next section, we sketch the methodology used for developing a closed-loop model for the pacemaker and we will give more details on the example of the pacemaker. We illustrate what authors were able to handle using Event-B and what we have validated and then we state questions on bio-compatibility and bio-integration in medical design devices.

Example of the Pacemaker

The pacemaker is a medical device which is implanted in the body of the patient. It is related to the heart by leads and it interacts with the heart according to modes defined by the physician. It is an example of a device which is supposed to remain for a long time in the body. Moreover, it augments the functionalities of the heart by helping it and the heart is evolving with the presence of the pacemaker. Consequently, the function of pumping is supported not only by the heart itself but also by the pacemaker. The heart is, after a while, working only with the pacemaker. In previous works, Mery and Singh [START_REF] Méry | Formalization of heart models based on the conduction of electrical impulses and cellular automata[END_REF] developed a discrete model of the pacemaker and the heart was modelled implicitly by records of ECG. We obtain a validation by off-line records.

In a second step, we should test the model with respect to a heart model called the electrical heart model developed by physicians. We summarize the electrical model. The heart consists of four chambers: right atrial, right ventricle, left atrial and left ventricle, which contract and relax periodically. The natural heart's system requires an electrical stimulus, which is generated by the small mass of specialized tissue located in the right atrium called the sinus node. This electrical stimulus travels down through the conduction pathways and causes the heart's chambers to contract and pump out blood. Each contraction of the ventricles represents one heartbeat. The atrial contract for a fraction of a second before the ventricles, so their blood empties into the ventricles before the ventricles contract. The electrical current flows progressively in the heart muscle using special conduction cells. In previous works, we developed a discrete model based on the electrical conduction flow according to the points A, B, C, D, E, F, G ,H. We obtain a closed-loop model of the pumping function, since the heart was no more considered as the environment of the pacemaker but as a part of the model itself. The closedloop model is used for studying the behaviour of the pacemaker in situ and it takes into account possible dysfunction of heart. Real time animation of formal models is a possible mean for communicating with physicians for instance in clinical experiences. Figure 4 describes the platform for animating Event-B models using a database of ECGs and plugins as Brama for feeding models. The platform is based on the Rodin tool which is offering functionalities for designing, verifying and animating models. An extra work has been done by N. Singh for making visual communications possible. In the last step, we have got a more trustable model for the pacemaker. However, we have not completely dealt with questions of bio-compatibility and bio-integration. These two extrapoints can be considered with the proposed methodology. However, they require to extend the methodology by considering expertise domains and by improving communication between physicians, designers and patients. Expertise domains require to integrate biology models. Finally, we summarize our position on the two concepts bio-compatibility and biointegration in the final section.

Concluding Remarks and Future Directions

Medical devices belong to the class of cyber-physical systems, since they must be integrated within or on the human body generating integrated wholes, human machine systems. They are made up of two main categories of systems. These two kinds of systems differ in their nature: their fundamental organization, complexity and behaviour. The first category, the traditional one, includes technical or artifactual systems that could be engineered. The second category includes biological systems: the human that could not be engineered. Thus, integrating human and cyber-physical systems in design is to couple and integrate in a structural (anatomical) and dynamical or functional (physiological) coherent way, a biological system (the human) with a technical and artifactual system in the same isomorphic framework. So medical devices engineering needs to model the organ or the part of the human body and its behaviour on the one hand, the cyber-physical system physical and computational components and its behaviour on the other hand, as well as their dynamical relation (interaction or coupling) to test and validate human machine reliability and human systems integration [START_REF] Fass | Augmented Human Engineering: A Theoretical and Experimental Approach to Human Systems Integration[END_REF].

Bio -Cyber-Physical Systems (Bio-CPS)

Traditional medical device design methods rely on analytic and reductionist concepts based on a mechanical or computational metaphor. The aim of making human and medical CPS "working" together is to assist a dysfunctional organ, transiently or permanently, to maintain the whole living system (a person) in stable condition or in a recovered "normal" condition. We call bio-CPS the whole and functional "living human artefact system" resulting from human medical CPS coupling and integration. The challenge is the design of medical CPS that ensure the correct integrative coupling by construction in spite of their different nature of interactions and the time representation.cf. table 1.

Medical CPS domain engineering

Using Bjoerner's framework we can ask the issue of medical devices domain to highlight its fundamental properties, which could satisfy human systems integration requirements. Bjoener's framework [START_REF] Bjørner | Domain Engineering -Technology Management[END_REF] based on the triptych: D, S -> R, where D is the domain of the problem and where requirements R are satisfied by the relation ->, which intends to mean entailment; so, S is a model of our system built or expressed from D. The domain provides a way to express properties and facts of the environment of the system under construction.

Bio CPS must help organ and the body (a person) to recover a stable state (invariant) compatible with survivability in intensive care or a physiological normal quality of life for implantable system like heart pacemaker despite pathology or illness. Consequently, Bio CPS specifications or model (S) must satisfy human system integration and integrative physiology requirements (R) [START_REF] Fass | Augmented Human Engineering: A Theoretical and Experimental Approach to Human Systems Integration[END_REF] and theoretical principles [16] [17] [18]. This especially concerns the artificial biological interface system and the behavioral monitoring and assisting computerized system and its algorithms. Their domain engineering (D) is biointegrative engineering. By consequence we can say that an "artificial" medical CPS that satisfied human system integration properties must present two fundamental properties: biocompatibility and "bio-integrability". For modelling biological system and biocompatible and biointegrable artificial systems -medical devices, we propose an isomorphic framework. This conceptual framework describes three categories of required main system dimension: structural elements, shapes or forms and dynamics. Taking into account two by two this main classes of system variables, one can describe three specification plan: architecture (structural elements to shape or form specify geometrical structure or system architecture), behaviour (shape or form to dynamics specify analytical functions or functionally analysed) and evolution (structural elements to dynamics specify three main types of functional interactions: physical Φ, logical Λ , biological Ψ). If we assume that a function does not exist by itself but is the emerging result of integrative organization, this framework grounds our bio-integrative model based Bio-CPS engineering. The schema extends clearly our methodology.

Bio CPS Methodology

We have first described a methodology based on a formal notation namely Event-B, which has been used for developing a closed-loop model for the pacemaker. The methodology is described by Fig 1 and is not restricted to Event-B. We have to address questions on the extension of the expressivity of the assertion language that should be able to state properties of the medical domain. Moreover, modelling CPS using Event-B or another formal method is a real challenge because we have to be able to manage hybrid medical models. Hybrid medical models are mathematical objects integrating discrete and continuous features of medical system under consideration.

Figure 1 :

 1 Figure 1: Design of Correct by Construction Medical Devices

inv 2 : 3 :

 23 Refinement-based Development of Medical Devices Case Study : Cardiac Pacemaker One and Two-Electrode Pacemaker First Refinement (Threshold): Sensor Activity in DDD inv 1 : Thr A 2 N 1 ^Thr V 2 N 1 Pace Int flag = FALSE ^sp > VRP ^sp < Pace Int FixedAV ) PM Sensor V = ON inv Pace Int flag = FALSE ^sp > Pace Int FixedAV ^sp < Pace Int ^AV Count STATE = TRUE ) PM Sensor A = OFF ^PM Sensor V = ON ^PM Actuator A = OFF Méry Dagstuhl Schloss, January 27-February1, 2013 18 / 25

Figure 3 :

 3 Figure 3: Different elements of the heart and the points defining the electrical conduction model of the heart.

Figure 4 :

 4 Figure 4 : Implementation of proposed functional architecture on the single electrode cardiac pacemaker case study

Figure 5 :

 5 Figure 5: Challenging human-machine system -bio-compatible and biointegrative medical devices, design and organization is modeling an heterogeneous system of systems (different by nature). That requires a proven and validate epistemic framework fitted to hybrid system, challenging the question of human machine system nature, correctness-by-construction and ensuring human systems integration reliability.

Table 1 : Classification of systems considering the nature of the interactions and the time rep- resentation [15]

 1


Jennie Lioris
email: jennie.lioris@enpc.fr

Adaptive level lane estimation policy of automotive systems moving within arbitrary road networks

Keywords: Highly Automated Driving Functions (HADF), lane identification, real time path and target tracking control, data mining, road navigation, autopilot perception, environment perception, adaptive policy for smart sensor utilization

The problem of a Vehicle Positioning System (VPS) is addressed. A specifically developed approach based on the cause-and-effect principle defines a closed-loop policy determining the lane level location of a sensor equipped vehicle moving within arbitrary road networks. After exploration of processed data provided by a smart camera and a laser detector appropriate information is routed to the decision making scheme. Based on identification of particular mobile objects circulating within the current and/or opposite flow the vehicle lane level location is determined when the car circulates within highway stretches or urban areas. Contrary to other schemes no additional investment on costly devices and complementary tools is required. The reduced computational complexity makes the deployment of the suggested methodology efficient for embedded technologies and can be utilized independently or as a complementary tool. Major restrictions of previous works of the same authors requiring divided freeway infrastructures are now overcome. A first appraisal of the system effectiveness is achieved though realistic simulation data fed by complex real recordings. Multiple drawbacks involved with information collected by professional driver behavior are minimized. Three case study scenarios, associated with different traffic and light intensity, resulting to a varying sensor behavioral functioning are considered. Adequate metrics appraise the efficiency of the suggested methodology.

I. INTRODUCTION

Smart decision making and control skills significantly contribute to efficient performance of any automotive structure. Advanced Vehicle Control System (AVCS), Advanced Driver-Assistance Systems (ADAS), Car Navigation System (CNS), Advanced Highway System (AHS) all contribute to optimal decisions for autonomous car driving and safety, requiring multiple information involving vehicle positioning. Additionally, fields of traffic estimation and control necessitate similar information. Connected vehicles can be used as mobile sensors and communicate information on traffic [START_REF] Bekiaris-Liberis | Highway traffic state estimation per lane in the presence of connected vehicles[END_REF], [START_REF] Papadopoulou | Microscopic simulation-based validation of a per-lane traffic state estimation scheme for highways with connected vehicles[END_REF]. Precise pathtracking control may influence vehicle itineraries, reduce travel times and positively impacting traffic management policies. Given a series of observations, simultaneous localization and mapping (SLAM) methods constructing or updating a map are often associated with increased computational power [START_REF] Magnabosco | Cross-spectral visual simultaneous localization and mapping (slam) with sensor handover[END_REF]. Consequently, embedded systems cannot fully implement SLAM. Recent studies on vehicle assistance guidance are employing expensive HD map approaches [START_REF] Seif | Autonomous driving in the icity, hd maps as a key challenge of the automotive industry[END_REF], [START_REF] Li | Lane-level map-matching with integrity on high-definition maps[END_REF] which should be additionally updated with every infrastructure modification. Other assistance systems utilizing dual frequency carrier phase differential GPS (DGPS) in association with HD maps [START_REF] Liu | Generating enhanced intersection maps for lane level vehicle positioning based applications[END_REF], [START_REF] Du | Next-generation automated vehicle location systems: Positioning at the lane level[END_REF], [START_REF] Samper | Ppp for advanced precise positioning applications including reliability bound[END_REF]. Nevertheless, multiple errors may interfere originated to satellite dysfunctions. There is no possibility of correcting the carrier phase ambiguities which need to be always approximated [START_REF] Leandro | Wide area based precise point positioning[END_REF]. The initialization time of about 20 minutes need for the float position to be converged into centimeter accuracy limits performance of GNSS/GPS data in systems involving real time data. Error mitigation approaches are developed in [START_REF] Hosseinyalamdary | Lane level localization; using images and hd maps to mitigate the lateral error[END_REF], [START_REF] Yu | Road curbs detection based on laser radar[END_REF] the performance of which depends upon the HD map quality. Radio frequency identification schemes (RFID) [START_REF] Wang | Rfid-based vehicle positioning and its applications in connected vehicles[END_REF], [START_REF] Bevilacqua | Vehicle positioning system using rfid technology and its use in the design of a rear-end collision avoidance system[END_REF], lane detection algorithms based on Hough transform [START_REF] Ran | Vision-based lane detection algorithm in urban traffic scenes[END_REF], [START_REF] Goldbeck | Lane following combining vision and dgps[END_REF], [START_REF] Wijesoma | Laser and vision sensing for road detection and reconstruction[END_REF] aiming at lane identification are also associated with increased complexity and errors. A lane estimation approach for urban areas is presented in [START_REF] Rabe | Ego-lane estimation for lane-level navigation in urban scenarios[END_REF] employing visual lane marking detection, radar, and GPS, and a digital map describing road geometry and topology.

This paper addresses the spatio-temporal problem of dynamic lane level identification of a sensor equipped vehicle moving within arbitrary road networks. The suggested policy makes use of minimal information available by a laser detector and a smart camera. The total number of lanes associated with the related road segment is provided by a GPS cartography. Furthermore, the proposed scheme is significantly advanced regarding previous works as in [START_REF] Lioris | Real time level lane decision algorithm based on autonomous vehicle sensors data[END_REF] where an elementary approach is presented requiring the existence of a physical road separator between the two opposite traffic directions. The new approach covers any type of freeway and arterial infrastructure. Despite the increased flexibility and contrary to various similar approaches frequently associated with complicated structures, low computations are now required due to the reduced complexity of each conceived algorithm. Consequently, the new decision-making scheme would be appropriate for embedded applications, employed independently and/or as a complementary decision approach operating in association with other methods. Furthermore, the proposed methodology is appraised by means of realistic simulation data based on real recordings. As a result, the multiple biases introduced by ideal driving behavior provided when drivers are aware of trip registrations are now significantly diminished.

The remainder of the paper is organized as follows. The problem to resolve is introduced in §II. The principle and mathematical model of the lane decision policy are defined in §III. §IV appraises the performance of the lane detection algorithm. The employed data and considered scenarios are discussed. Quantitative and qualitative statistical analysis measurements are evaluated. Finally, §V resumes the main findings and contributions of the research.

II. PROBLEM FORMULATION

Aiming at defining the lane level of a vehicle within any time t and position p(t) of the related trajectory a first approach of an adaptive feedback policy is going to be introduced. Sensors reveal a wealth of information on the tracked objects and vehicle state. At observation instant t a laser sensor scans multiple mobile and immobile objects within a multiplane and long range vision angle. Each detected entity is associated with an ordered pair of lateral and longitudinal coordinates with respect to the current position of the reference vehicle where the system origin is located at detection time t.

Let N (t) describe the number of all captured observations at time t, then the set of the relative reference points O can be determined at time t.

O(t) = {p i (t) = (x i (t), y i (t)), i = 1, . . . , N (t)}. (1) card(O(t)) = > 0, if N (t) > 0 0, otherwise. (2)
Eq. ( 2) underlines that set O may become very large or even empty. As laser sensors are associated with a long and wide detection range number N (t) can be very big or become zero depending upon the present environmental context of the car, sensor failures etc. Data fusion techniques (employing available information from complementary technologies) or missing signal estimation schemes for noisy and irregular data are some alternatives for an efficient handing of an empty observation set O at a time t. A signal estimation model based on artificial neural network programing is under development but it is not presented in this work. Additionally, disturbing objects may imply misleading results. An intelligently determined observation set comprised of well selected objects contributes to the performance of the lane identification algorithm.

A set of qualitative and quantitive constraints can be associated with each detected object allowing a finest definition of the observation set. Hence, if Q and Q denote the number of the considered qualitative and quantitative constraints, then sets C, C can be determined C = {c q , q = 1, . . . , Q}.

(3)

C = {c q , q = 1, . . . , Q }. (4)
As a result a restricted detection set can be constructed

O 1 (t) = {p(t) ∈ O(t) s.t c(p(t)) satisfied ∀c ∈ C ∪ C }. ( 5
)
Let p r denote the reference point of the considered vehicle, that is p r (t) = (0, 0) for any time instant t, v(p(t)) the speed of detection object p at time t. Furthermore, if (D 1 , d 1 ) and (D 2 , d 2) two ordered pairs where 1 , 2 can be any desired positive numbers,

D 1 ⊂ O, D 2 ⊂ O and d 1 , d 2 are metrics on D 1 , D 2 then D 1 (t) = {p(t) ∈ O(t) such that d 1 (p(t), p r (t)) ≤ 1 and v ( p(t)) > 0}. (6) D 2 (t) = {p(t) ∈ O(t) such that d 2 (p(t), p r (t)) ≤ 2 and v ( p(t)) < 0}. (7)
Equations ( 6) and ( 7) describe detections located within a desired area in a neighborhood of the reference vehicle moving either within the same traffic flow or following the opposite direction. Parameters 1 and 2 can be appropriately adjusted from one time t to another so as sets D 1 (t), D 2 (t) become neither empty nor very large.

Let m d denote the total number of lanes in the direction of the considered car (ego vehicle), j the candidate lane where the system origin is placed with 1 ≤ j ≤ m d , y l i,j (t) the y-coordinate of the left boundary of lane i regarding lane j at time t and y r i,j (t) the y-coordinate of the right boundary of lane i regarding lane j at time t, for any i, j such that 1 ≤ i ≤ j ≤ m d . Allow w to denote the lane width and d l , d r the distance between the ego vehicle and the left and right lane boundaries respectively. Hence, the values of y l i,j and y r i,j at time t can be computed by the following equations

y l i,j (t) = d l (t) + (j -i) × w, if i < j -(d r (t) + (i -j -1) × w), otherwise. (8)
y r i,j (t) = d l (t) + (j -i -1) × w, if i < j -(d r (t) + (i -j) × w), otherwise. (9)
Remark 1: For simplicity a fixed value of the lane width is considered equal for all lanes within the related road segment. If each lane i is associated with its proper width w i , it suffices to replace w by w i in Equations ( 8) and (11). Let s 1 denote the distance between the left boundary of the first lanes within the two opposite traffic flow directions (see also Fig. 1), with s 1 any positive number. If m o denotes the total number of lanes in the opposite direction of the ego vehicle, then the lane boundaries of the opposite road segment y l i ,j and y r i ,j at any time t can be computed regarding the candidate lane j from the following equations:

y l i ,j (t) = y l 1,j (t) + s 1 + (i -1) × w ∀i = 1, 2, . . . m o , ∀j = 1, 2, . . . m d . (10)
y r i ,j (t) = y l i +1,j (t) ∀i = 1, 2, . . . m o , ∀j = 1, 2, . . . m d . (11)
Remark 2: The distance s 1 between the two opposite flows may become a number close to zero especially in urban areas.

III. LANE LEVEL ALGORITHM -STRICT APPROACH

A strict policy determining the level lane position of the ego vehicle is proposed by detecting appropriate mobile entities. Three complementary approaches are employed regarding the vehicle followed direction. Thus, objects moving within the opposite traffic flow and/or current direction of the ego vehicle are utilized. Some common cases where the later two choices are privileged concern one way road infrastructures, decision instants related to missing information due to inadequate sensor information or traffic context or when multiple feasible responses are provided by the former scheme.

Denote p d M and p dm the largest and smallest elements of set D 2 , that is

p d M (t) = (x d M (t), y d M (t) ) = arg max y(t) D 2 (t). (12)
p dm (t) = (x dm (t), y dm )(t)

= arg min

y(t) D 2 (t). (13)
A candidate lane j will be considered if points p d M and p dm satisfy the following two equations

y r 1,j (t) -y l mo,j (t) -σ 1 < |y d M (t) -y dm (t)| ( 14
)
|y d M (t) -y dm (t)| < y l 1,j (t) -y r mo,j (t) + σ 2 (15)
where parameters σ 1 0 and σ 2 0 represent small positive numbers.

Remark 1: The term strict has the sense that the suggested methodology utilizes only object detections without any use of other approaches such as lane change observations which could considerably improve the resulting performance of the algorithm. The main purpose of this study is to examine the potential of the introduced methodology regarding reliability and robustness. In a final project it would be wiser to associate multiple approaches not presented in this paper. Remark 3: Parameters σ 1 and σ 2 are required for computational precisions due to sensor sensitive behavior in particular environmental contexts. Furthermore, parameter σ 1 allows perceptible movements within the the two last lanes of the opposite flow to be considered. Equivalently, parameter σ 2 represents movements within the boundary lanes of the two opposite flows when no road separator exists within the related road infrastructure.

Consider now reference points p d M and p dm such that

p d M (t) = (x d M (t), y d M (t) ) = arg max y(t) D 1 (t). (16)
p dm (t) = (x dm (t), y dm )(t)

= arg min

y(t) D 1 (t). (17)
If σ 3 0, σ 4 0 and σ 5 0 represent small positive numbers then candidate lane j will be considered if both equations are satisfied

y d M (t) ∈ [y l 1,j (t) -σ 3 , y r 1,j (t) + σ 4 ] (18)
y dm(t) ∈ [y l m d ,j (t) -σ 5 , y r m d ,j (t)]. (19)
Remark 4: Parameters σ 3 , σ 4 , σ 5 allow vehicle movements within related neighbor lanes to be taken into consideration.

Another criterion for considering candidate lane j involves reference points p d M and p dm . If ( 14) and ( 19) are simultaneously satisfied by the y coordinate of observations p d M and p dm respectively at time t then lane j can be considered as candidate.

IV. PERFORMANCE ASSESSMENT A. Case Study

The lane level algorithm described in §II estimating the current vehicle lane position is going to be evaluated. Within this goal, detailed simulation data fed by multiple real recordings are going to be utilized. Professional drivers being aware of the realized registrations present unrealistic behavior which often results to untruthful information. Moreover, frequently occurring irregular situations are missing. Appropriate data treatment is necessary for obtaining rational driving contexts.

A trajectory starting at Paris, Rue de l'Université, reaching Versailles and then returning back to Paris at Charles de Gaulle-Étoile is considered as depicted in Fig. 2. The trip is consisted of urban road segments as well highway stretches involving rich road infrastructure and complex traffic conditions. Three different scenarios are considered the duration of each is 68 minutes (4, 080 seconds). The first scenario occurs in the afternoon from 14.53 to 16.01, the second one is also realized within the same time period but under different meteorological and traffic conditions involving lower sunlight intensity and resulting to a different sensor functioning. Finally, the third scenario realized later from 17.53 to 19.01 is associated with decreased light of different nature and slightly increased traffic density allowing the trip to have the same duration as in the two previous scenarios. Each case will be separately appraised.

B. Measuring Accuracy

Within every sensor detection (related frequency of 25Hz) the previously introduced lane level identification policy is called estimating the lane position of the ego vehicle. Figs. 3,4 and 5 depict the estimated and real value of the followed lane id over time for the three considered scenarios. One observes that for the majority of the trip duration the real value (green plot) coincides with the calculated one (red curve for the first two scenarios and cyan plot for the third one). A deeper analysis implies that most of the erroneous responses are due to imprecise sensor information. Consequently, the relatively small mistakes on observations as provided by the laser sensor (LIDAR) affect the involved computations returning neighbor adjacent lanes as the current vehicle position. In case of important inaccurate information returned by the laser detector distant lanes could have been responded by the decision scheme. However, this situation can be handled by improving the laser technology requiring increased precision on information process and by adopting complementary decision policies. Thus, a lane change policy would have detected that the lane level of the considered car wouldn't have changed. However, as previously discussed no alternative estimation scheme is employed in this work. The main purpose of this study is to evaluate independently the presented methodology.

C. Sensor Information Quantification

With a laser sensor frequency of 25Hz, during the 4, 080 seconds of trip duration, 102, 000 times detected observations are returned. The suggested decision approach is employed only when the utilized information corresponds to valid signals. Table I illustrates the total number of times where valid detections are returned by the laser sensor, for each one of the three scenarios. One sees that the best performance is obtained Figs. 6, 7 and 8 present a classification of invalid information according to the type of the sensor. As the proposed decision approach utilizes laser and camera detections, the percentage of erroneous data is presented for each scenario and for both the laser sensor and smart camera. At a first sight one could affirm the camera sensitivity to sunlight as well the laser dependence upon the traffic density. However, the corresponding statistics concern the three considered case study configurations and it would be preferable if no definite conclusions are drawn at the current stage of the work.

D. Response Frequency and Error Quantification

Within every sensor detection utilized data are analyzed and if they considered valid they are next provided to the decision making policy for determining the lane level position of the ego vehicle. The current version of the suggested lane identification scheme provides a response when the sensor functioning is judged as acceptable as well a unique feasible response results. Moreover, the present methodology may provide no response if values 1 , 2 do not exist such that the arg min and arg max elements of sets D 1 and D 2 satisfy ( 14) and ( 15), ( 18) and (19,) ( 14) and (19). Figs. 9, 10 and 11 illustrate the response frequency of the employed lane identification policy for each one of the three considered scenarios. Thus, for the first scenario where 90% of the detection time was associated with valid information, the involved error of the ego-vehicle lane estimation is of 5.1%. The second case study was associated with valid information during 92.15% of the total travel time and for which 4% of the returned responses were mistaken. Finally, for the last scenario, a wrong lane id was computed during 3% within valid sensor functioning (95%). Similarly to previous statistical results, at this stage of the study the presented numbers should not lead to final conclusions as much more cases need to be further examined. A first appraisal of the suggested scheme is presented, applied on three scenarios created by simulation data feb by real recordings. Thus, multiple biases generated by drivers being aware of the registration procedures (adequately adapting their behavior) are reduced and consequently realistic information is now available. Each one of the three considered case studies corresponds to a different sensor functioning allowing the appraisal of the developed policy within various contexts. The same journey is considered in all scenarios, starting at Paris, arriving at Versailles and then returning back to Paris. A different trajectory path consists each one of the two way trip. A rich road infrastructure is involved as well varying and complex traffic conditions during the entire journey. A profound statistical analysis measures the response frequency and accuracy of the employed decision approach while a data qualification and classification is presented per employed sensor type. Nevertheless, it should be accentuated that at the present stage of work, no definite conclusions should be drawn regarding the provided numerical values quantifying the system performance. More scenarios are under considerarion involving various trajectories, traffic contexts and thus a representative sensor functioning.

4 Fig. 1 .

 41 Fig. 1. Vehicle environment

Remark 2 :

 2 If set D 2 (t) = ∅ then sets arg max y(t) D 2 (t) and arg min y(t) D 2 (t) are also nonempty and bounded. Hence points p d M (t), p dm (t) exist.

Fig. 2 .

 2 Fig. 2. Vehicle trajectory.

Fig. 3 . 1 Fig. 4 .

 314 Fig. 3. Vehicle lane trajectory-scenario 1

Fig. 5 .

 5 Fig. 5. Vehicle lane trajectory-scenario 3

Fig. 6 . 1 Fig. 7 .

 617 Fig. 6. Invalid data classification-scenario 1

Fig. 8 .

 8 Fig. 8. Invalid data classification-scenario 3

Fig. 9 .

 9 Fig. 9. Responce frequency-scenario 1

Fig. 10 . 2 Fig. 11 .

 10211 Fig. 10. Responce frequency-scenario 2

TABLE I

 I

		VALID SENSOR INFORMATION
	Scenario ID	Valid Detections %	Number Valid Detections
	1	85.8	87, 516
	2	92	93, 840
	3	94	95, 880


Bassem Fleifel

Osman I Or

Osman Bay

Abū Al-Mulūk Al-Sulṭān Al-Ghāzī Fakhr Al-Dīn

Qaraʻuthmān Khān Al-Awwal Bin Ertuğrul Bin Sulaymān

Sultan Osman I Osman Gazi

Shāh al-qayawi al-Turkumānī), was the leader of the Kayı Turkic clan, one of the border

Although the exact date of Osman's birth is unspecified, some sources indicate that he was born in 656 AH / 1258 CE, to Emir Ertuğrul Gazi, one of the border governors for the Sultanate of Rûm, and Halime Hatun. It so happened that Osman was born on the same day that the Mongols invaded Baghdad, [START_REF] Armağan | al-tārīkh al-sirrī lil-Imbarāṭūrīyah al-ʻUthmānīyah; Jawānib ghayr Maʻrūfa min ḥayāt Salāṭīn Banī ʻUthmān [The Secret History of the Ottoman Empire: Unrecognized Aspects of the Life of the Ottoman Sultans[END_REF] the capital of the Abbasid Islamic caliphate. The events were dramatically linked by the subsequent Ottoman and Muslim historians. Osman became Emir and the leader of the Kayı clan after the death of his father. He remained loyal to the Seljuk Sultanate of Rûm, despite the turmoil and dangers threatening it by that time.

In 1295 CE, Osman began attacking the Byzantine forts in the name of the Seljuk Sultan and Abbasid Caliph. He conquered several forts leading his clan north and west towards the coasts of the Marmara and Black Seas. When the Mongols overcame the Sultanate of Rûm and made it a sovereign state, Osman declared his independence from the Seljuks, and thus became the founder of a new Turkic state named after him: the Osmanic or ʻUthmānic State, Anglicized as the Ottoman Empire. Osman continued to rule his new state as an independent Emir until 1326. During this year, his son Orhan conquered the city of Bursa, and Osman fell sick. Soon later, he died. His body was transferred and buried in Bursa, this gave the city a great symbolism in the eyes of later Ottomans. Osman's successors followed his example and continued the campaigns he started until the mid-seventeenth century, they successfully transformed the principality that he laid its foundations into a global empire spanning three continents. [START_REF] Quataert | The Ottoman Empire, 1700-1922[END_REF] Figure 1 | Sultan Osman (ʻUthmān) Han I. Konstantin Kapıdağlı/PD-old Although Osman is called "Sultan" or "Padişah" in many sources, he did not hold that title during his lifetime. However, he was to be called so, subsequently for establishing the dynasty of the Ottoman Sultans, thus he was titled Abū al-mulūk (father of kings). Osman was renowned for his simple way of living, being influenced by the beliefs of Sufi Dervishes. He maintained the old Turkic traditions that govern the relationship between the leader and clan members, which pre-dates Islam's arrival among the Turks, as long as they did not contradict sharia law. [START_REF] Armağan | al-tārīkh al-sirrī lil-Imbarāṭūrīyah al-ʻUthmānīyah; Jawānib ghayr Maʻrūfa min ḥayāt Salāṭīn Banī ʻUthmān [The Secret History of the Ottoman Empire: Unrecognized Aspects of the Life of the Ottoman Sultans[END_REF] Historical Background Most sources agree that the Ottoman Turks belonged to the Kayı Oghuz Turkic clan, who, according to Ottoman traditions, fled their native homeland in central Asia, during the early 13 th century, due to the Mongol invasions. The clan settled in Anatolia, in a region belonging to the Seljuk Sultanate of Rûm. [START_REF] Efendi | Tâcü't-Tevârih [The Crown of Histories[END_REF] Other sources claim that the Kayı clan moved to Anatolia two centuries earlier than the previously mentioned date, alongside the Seljuks, when they left Transoxiana to Khurasan around 1040 CE to reside near the city of Merv. Then, the Kayı clan moved towards eastern Anatolia after 1071 CE, [START_REF] Yılmaz | Mawsūʻat tārīkh al-Imbarāṭūrīyah al-ʻUthmānīyah al-siyāsī wa-al-ʻaskarī wa-al-ḥaḍārī [Encyclopedia of the political, military and cultural history of the Ottoman Empire[END_REF] where it displaced alongside other turkic clans. Later, it became involved in the army of Sultan Alâeddin Kayqubad II and fought against the Khwarizmians, Mongols and Byzantines, who were raiding Seljuk lands. According to several sources, the Kayı warriors were known for filling first lines in battles, and their fighting skills and bravery were among the major factors the Seljuks were victorious in many battles. This fact prompted Sultan Kayqubad to appoint Ertuğrul, the clan's Emir, as a Moqaddam (Lieutenant), and to reward the Kayıs some fertile lands near Ankara, where they settled and remained in the service of the Sultan for several years. [START_REF] Farīd | Tārīkh al-Dawlah al-ʻAlīyah al-ʻUthmānīyah [History of the Exalted Ottoman State[END_REF] [START_REF] Qaramani | Tārīkh salāṭīn Āl ʻUthmān [History of the Ottoman Sultans[END_REF] Later, Ertuğrul was granted dominion over the town of Söğüt in northwestern Anatolia on the Byzantine frontier. [8] He also Obtained the title of Uç beyliği or Uç bey (literally: marcher-lord). Granting this title was in line with the traditions of the Seljuk Sultanate, which is rewarding any clan chieftain who rises to power and is joined by a number of smaller clans, the title of marcher-lord. However, Ertuğrul had far-reaching political ambitions. He sought to expand beyond the lands rewarded to him. Thus, he started raiding the Byzantine possessions in the name of the Sultan successfully conquering several towns and villages, and slowly expanding his dominion during the half of the century he spent as a Seljuk governor. In 680 AH / 1281 CE, Ertuğrul passed aways at nearly 90 years of age. [START_REF] Ṭaqqūsh | Tārīkh al-ʻuthmānīyīn min qiyām al-Dawlah ilá al-inqilāb ʻalá al-khilāfah [History of the Ottomans: from the rise of the Empire to the coup against the caliphate[END_REF] Osman's lineage Although the exact date of Osman's birth is unspecified, some sources indicate that he was born on 8 Safar 656 AH / 13 February 1258 CE, the exact same day the Mongol hordes invaded Baghdad, killing its inhabitants and ravaging its landmarks. [START_REF] Armağan | al-tārīkh al-sirrī lil-Imbarāṭūrīyah al-ʻUthmānīyah; Jawānib ghayr Maʻrūfa min ḥayāt Salāṭīn Banī ʻUthmān [The Secret History of the Ottoman Empire: Unrecognized Aspects of the Life of the Ottoman Sultans[END_REF] Other Sources, such as 16 th century Ottoman historian Kemalpaşazâde, says that Osman was most likely born around the middle of the 13 th century, possibly in 1254/5 CE. [START_REF] Murphey | Exploring Ottoman Sovereignty: Tradition, Image, and Practice in the Ottoman Imperial Household[END_REF] Information related to the early life of Osman is limited. However, the few available sources agree that he was born in the town of Söğüt, which his father Ertuğrul took as the capital of his emirate. [11] The reason for the lack of information available about this stage of Osman's life, is due to the fact that the oldest known source about this time period, was written about a hundred years after Osman's death. Among these sources are: Destan-ı Tevarih-i Al-i Osman (the oral history of the Ottomans), written in the 14 th century by the Ottoman poet and court physician Tâceddîn İbrâhîm bin Hızîr better known as Ahmedî (1334-1413 CE), Behcetü't Tevârîh (the joy of histories) by Şükrullah (d. 1464 CE), and Tevarih-i Âl-i Osman (history of the Ottomans) by Derviş Ahmed Âşıkî known as Âşıkpaşazâde (1400 -1484 CE). ِ Additionally, these remaining sources are not the originals, but rather copies, or copies of the copies that were rewritten over the years, leading to a probable loss or altering in the information. [12] In fact, it is accepted that Ottoman, European, and Byzantine sources are not very reliable when considering the origins of Osman and his clan. On one hand, the oldest known records originally written by the Ottomans all date back to the period that followed the conquest of Constantinople (1453 CE). On the other hand, none of the Byzantine historians did refer in their writings to the origin of the Ottomans. As for European historians, these Turkic Muslim peoples were out of their interests. However, that changed after a century of this period, when the Ottomans began to pose a threat to Europe. [13] Ottoman historian Kemalpaşazâde mentioned that Osman was Ertuğrul's youngest son and that he was raised in the traditional nomadic Turkic ways: he learned wrestling, swordsmanship, horse riding, arrow shooting, and falconry, from an early age. He quickly mastered the previously mentioned skills outperforming all his brothers. He was also taught the principles of Islam, and was influenced by the teachings of Sufi Sheikhs, mostly his mentor Sheikh Edebali, and this was reflected in his personality and lifestyle. [11] In terms of proportions, the most popular and classic narration is that Osman is the grandson of Süleyman Şah who died drowning while crossing the Euphrates River on horseback. Turkish historian Yılmaz Öztuna considers that Osman's Grandfather, and Ertuğrul's father, is called Gündüz Alp, saying that it is more likely that Süleyman Şah is a name stuck in Anatolian popular memory, and it actually refers to Süleyman bin Qutulmish who founded the Seljuk Sultanate of Rûm. Öztuna adds that it is possible that Ottoman historians tried forming a connection between the Ottomans and the Seljuks, especially since the Ottomans appeared on the stage of history claiming to be the legitimate successors of the Seljuks.

Based on this, Osman's assumed lineage is as follows: Osman bin Ertuğrul bin Gündüz Alp bin Kaya Alp bin Gökalp bin Sarquk Alp bin Kayı Alp. [START_REF] Yılmaz | Mawsūʻat tārīkh al-Imbarāṭūrīyah al-ʻUthmānīyah al-siyāsī wa-al-ʻaskarī wa-al-ḥaḍārī [Encyclopedia of the political, military and cultural history of the Ottoman Empire[END_REF] Other researchers agree that the connection between Ertuğrul, Osman, and the Seljuks, may have been largely invented by court chroniclers a century later, and the true origins of the Ottomans thus remain obscure. [START_REF] Fleet | The rise of the Ottomans[END_REF] On the other hand, some Ottoman sources indicate further lineage to Osman and the Oghuz Turks, which is closer to myth than reality, saying that these people are descendants of Japheth son of Noah and that Osman's genealogical tree contains 52 ancestors or more and ends with the Prophet Noah himself. This lineage includes Gökalp and Oghuz Han (which is said to be the father of Gökalp), and all the Oghuz Turkic peoples, including the Seljuks. [13] In this claim, one can notice the features of some of what Yılmaz Öztuna pointed out in his hypothesis, that the Ottomans were always trying to connect or relate themselves to the Seljuks, and to appear as their heirs. Thus, Osman was rewarded with titles and land, which increased his power and was himself followed by many men. [START_REF] Iyās | Badā'iʻ al-zuhūr fī waqā'iʻ al-duhūr [Flowers in the Chronicles of the Ages[END_REF] Rise of the Osmanic (Ottoman) Beylik

Osman became Emir, or Bey, upon his father's death around 680 AH / 1281 CE. [8] According to some historians, Osman's accession to power wasn't peaceful as he had to fight his relatives before he got hold of his clan's leadership. One of Osman's major rivals was his uncle Dündar Bey, who might have plotted to kill his nephew or rebelled against him when the latter decided to attack a small Greek island. Dündar Bey saw that Osman's ambition as a threat that might put the whole clan in danger. However, Osman had to pull out his sword to kill his uncle for disobeying. [START_REF] Sakaoğlu | Bu mülkün kadın sultanları: Vâlide sultanlar, hâtunlar, hasekiler, kadınefendiler, sultanefendiler [The Queen Women of the Sultanate: Vâlide sultans, wives, hasekis, women's children, sultan's children[END_REF] The Philosopher and mystic Ḥājī Baktāš Walī tells of another story about Osman's accession to power, in the Vilayetname. According to Ḥājī, Gündüz Alp, Osman's younger uncle, was the one who became Bey after Ertuğrul's death. During that time, Osman and several other warriors started organizing raids on Byzantine lands adjacent to Söğüt, such as Yarhisar, Bilecik, İnegöl, and İznik. As a result, the Byzantine Tekfur (governor) of Bursa was provoked, and he sent envoys to the Seljuk Sultan Alâeddin Kayqubad III, complaining about these constant assaults. Thus, the Sultan ordered Gündüz Alp to bring forth his young nephew to stand before him, and so Osman was arrested and sent to Konya. According to this narration, Sultan Kayqubad admired Osman's courage and deeds, and didn't wish to punish him, instead, Osman was sent to Ḥājī Baktāš Walī to consider his matter. Osman was warmly received by the Sufi mystic, who then ordered his release saying: "I have been waiting for someone like him for years". After that, Ḥājī Baktāš Walī wrapped Osman's head with the same turban associated with Sufi sheikhs, and sent him back to Konya with a message to the sultan, asking that Osman to become the Kayı Emir. Thus, Osman became the clan's leader. [START_REF] Ibrāhīm | -Islām al-muwāzī fī Turkiyā: al-Biktāshīyah wajadal al-ta'sīs [Parallel Islam in Turkey: Bektashi Order and Janissary Supervision[END_REF] Importance of the Osmanic Beylik location

From a military point of view, the location of Osman's Beylik had a significant impact on his success as a conquering warrior. His capital Söğüt was located on a hill in a well-defended position, mediating the main road from Constantinople to Konya. The importance of this site emerged due to the political fragmentation of Anatolia that gave small states greater importance than they originally had. [18] Being an Emir to a beylik bordering Byzantine lands, Osman had the opportunity to direct all his efforts towards war and jihad following the footsteps of the Seljuks with intentions to conquer all Byzantine territories, and absorb them into the Islamic Caliphate. Encouraged by the weakness of the ancient Empire and its ongoing wars in Europe, Osman had the chance to expand towards western Anatolia crossing the Dardanelles to southeastern Europe. [18] Commenting on these actions, some historians argue that Osman's strategy of increasing his territories at the expense of the Byzantines was due to his intention to avoid conflicts with his more powerful Turkic neighbours. [8] Politically, Osman showed great skills forming and applying new administrative systems in his beylik. During his reign, the Ottomans made great strides towards transitioning from the nomadic tribe system to settling down in permanent settlements. This helped them consolidate their position and rapidly develop into a major power. Moreover, the beylik's location in northwestern Anatolia, next to Christendom, imposed a military policy on the Ottomans, which gave them better chances to grow and expand compared to the beyliaks of the interior. [18] Osman's beylik was also relatively far from both the Mongol invasions and the influence of the powerful Turkoman beyliks in southern and southwestern Anatolia. Add to that, its proximity to the Silk Road linking Byzantine lands in the west to areas controlled by the Mongols in the east, gave it prominent strategic and economic characteristics. Also, the Osmanic beylik was the only Islamic base facing the yet unconquered Byzantine regions, which made it a magnet to many Turkomen farmers, warriors, and Dervishes fleeing the Mongols, and aspiring to conquer new lands for economic and religious reasons. [START_REF] Collins | al-Uthmānīyūn fī Ūrūbbā [The Ottomans in Europe[END_REF] Osman's Dream

Osman had a close relationship with a local religious leader of dervishes named Sheikh Edebali, whose daughter he married. A story emerged among later Ottoman writers to explain the relationship between the two men. According to the writers, Osman had a dream while he was staying in the Sheikh's house. The story appeared in the late fifteenth-century chronicle of Aşıkpaşazade as follows:

"

He saw that a moon arose from the holy man's breast and came to sink in his own breast. A tree then sprouted from his navel and its shade compassed the world. Beneath this shade there were mountains, and streams flowed forth from the foot of each mountain. Some people drank from these running waters, others watered gardens, and yet another group caused fountains to flow. When Osman awoke he told the story to the holy man, who said 'Osman, my son, congratulations, for God has given the imperial office to you and your descendants and my daughter Malhun shall be your wife. [START_REF] Finkel | Osman's Dream: The Story of the Ottoman Empire[END_REF] "

The dream became an important foundational myth for the empire, imbuing the House of Osman with God-given authority over the earth and providing its fifteenth-century audience with an explanation for Ottoman success. [START_REF] Finkel | Osman's Dream: The Story of the Ottoman Empire[END_REF] The dream story may also have served as a form of compact: just as God promised to provide Osman and his descendants with sovereignty, it was also implicit that it was the duty of Osman to provide his subjects with prosperity. [START_REF] Kafadar | Between Two Worlds: The Construction of the Ottoman State[END_REF] Political relations at the beginning of Osman's reign

According to the Bektashi narration, whose accuracy cannot be confirmed since it was only mentioned in Bektashi sources, plus the fact that it did not enjoy much support from the majority of researchers; Ḥājī Baktāš Walī was one of the Wafā'īyyah tariqah dervishes, a murid of Bābā Eliyās al-Khorāsānī. [START_REF] Gül | Taḥawwulāt al-fikrīyah fī al-ʻālam al-Islāmī: aʻlām, wa-kutub wa-ḥarakāt wa-afkār, min al-qarn al-ʻāshir ilá althānī ʻashar al-Hijrī [Intellectual transformations in the Islamic world: people, books, movements and ideas, from the tenth to the[END_REF] Once Bābā Eliyās died, both Ḥājī Baktāš Walī and Sheikh Edebali became among his 60 successors, and grandmasters of the Ahyan Rûm brotherhood of warriors and farmers, who enjoyed great influence among the people. When Osman married Sheikh Edebali's daughter, he secured his control over the brotherhood, and soon became their new grandmaster. As a result of this marriage, all the Ahyan sheikhs became under Ottoman control. This has a major impact on the establishment and development of the Osmanic beylik after Osman's death during the reign of his son Orhan. [START_REF] Ibrāhīm | -Islām al-muwāzī fī Turkiyā: al-Biktāshīyah wajadal al-ta'sīs [Parallel Islam in Turkey: Bektashi Order and Janissary Supervision[END_REF] Some argue that Osman's marriage to sheikh Edebali's daughter was his first brilliant political undertake. [START_REF] Mantran | A Turkish or Mongolian Islam[END_REF] On the other hand, Turkish historian Professor Cemal Kafadar considers that the intermarriage between the Osmanic and Edebali's houses, explains the hostilities that later rose between the Ottomans and the Germiyanids, since the Germiyanid Turkoman house was rewarded lands and titles by the Seljuks because of their services in subjugating the Bābā'ī revolt in 1240 CE, and because Sheikh Edebali was considered by his followers a leader and successor to Bābā Ishāq, they all became the focus of attention of the Germiyanids. [26] Kafadar adds that early in Osman reign, the young Emir showed political ingenuity forming relations with his neighbours. Osman's alliances transcended tribal, ethnic, and religious lines. and he may have followed his instinct and the requirements of his political aspirations, not mistaking the future results of the family connections he created and secured for his son after him. Osman reconstituted the political culture of the Seljuk Sultanate of Rûm in line with the needs of his beylik. He was more creative than his Turkomen neighbours in combining Turkic, Islamic, and Byzantine traditions.

Additionally, the Emir also cooperated with the Byzantine Tekfurs of the neighbouring cities and villages. He forged an agreement, so his clan, whenever they move between grazing areas in the summer, leave their belongings in the Byzantine fortress of Bilecik, and upon their return, they give its governer a token of appreciation, in the form of cheese and butter made from sheep milk and preserved in animal skins, or a good carpet made from wool. This agreement reflects the coexistence between herders, farmers and urban dwellers, during Osman's reign. [26] Osman's friendship with Köse Mihal, governor of Chirmenkia (modern Harmanköy), was the culmination of this coexistence between Muslims and Byzantines. As for his relations with other peoples, such as the Mongols, most of whom moved to the borders of western Anatolia, and the Germiyanid Turkomen, it was hostile. That is because the Turks, in general, despised the Mongols, and the Germiyanids were probably of non-Oghuz origin. [26] Osman allied with the Ahyan Rûm brotherhood, they formed organized groups, members in each of which worked in a single trade. The brotherhood took the responsibility to preserve justice, prevent injustice, stop oppression, follow sharia law, dictate good morals, and carry out military duties if the need arises, to defend their rights and the rights of Muslims. [27][28] The Emir also allied with newly arrived Turkomen clans to Anatolia. In general, the nomads have always had a strong militarized spirit compared to people installed in the cities. Thus, the clans were more active and effective than their city-dwelling kin. Soon enough, they become the beating heart of the Seljuk border provinces in total, and the Osmanic beylik in particular. Osman also enticed many Turkomen from the region of Paphlagonia to join his forces. [18] These Turkomen were fine warriors, eager for jihad and conquest, each of them followed a tariqah (an order of Sufism) and was supervised by a sheikh who taught them the meaning of jihad alongside many Islamic principles. However, another section of these Turkomen did not have close ties to Islam for various reasons, thus Osman entrusted them to several sheikhs and dervishes to be given proper Islamic education and be satiated with the values that glorify conquests aiming to spread the word of Islam. In fact, these sheikhs and dervishes were very enthusiastic about promoting the Turuq of the Khorasani Walis, and Osman's request gave them this chance. [START_REF] Öztuna | Mawsūʻat tārīkh al-Imbarāṭūrīyah al-ʻUthmānīyah al-siyāsī wa-al-ʻaskarī wa-al-ḥaḍārī [Encyclopedia of the political, military and cultural history of the Ottoman Empire[END_REF] As for the ruling hierarchy, Osman was firstly subordinate to the Chobanid Emir in Kastamonu, followed by the Seljuk Sultan through the Germiyanid Bey in Kütahya, who was in turn subordinate to the Mongol Ilkhan in Tabriz. During this period, the Seljuk Sultans had lost their power over their local Emirs, and the Mongol Ilkhan practised his authority in Anatolia through his appointed Generals, where he requested that every local governer, including Osman, sends him soldiers whenever he requests so. [30] As for the hierarchy of name delivering in khuṭbah, Imams used to pray for the guidance of the: Abbasid caliph in Egypt first, the Mongol Ilkhan in Tabriz, Seljuk Sultan in Konya, and finally the local Bey or Emir. [30] Expansion of the Osmanic Beylik Nevertheless, he chose to clash with the Byzantines and he was defeated and forced to withdraw with casualties, including his nephew Koca Saruhan bey, son of Savcı Bey. [11][32] Based on this, around 685 AH / 1286 CE, Osman went forward to Kulacahisar at the head of a military force of three hundred fighters, it was a fortress located two leagues away from İnegöl, within the scope of mount Uludağ. The Emir attacked the fort at night and managed to conquer it, extending his beylik northwards toward Lake İznik's proximity. The Ottoman victory at Kulacahisar triggered the fort's governor, who refused to be a subordinate subject to a Muslim ruler, especially a border Emir, so he allied himself with Karacahisar's governor, and both men agreed to fight the Muslims aiming at retaking all Byzantine lands that were lost recently. Thus, the Ottomans and the Byzantines met again in battle, somewhere between Bilecik and İnegöl, where fierce fighting took place in which Osman's brother Savcı Bey and the Byzantine commander Pilatos were killed. The Battle ended with an Ottoman victory. Then, the Ottomans entered Karacahisar where they, reportedly for the first time, converted the town's church into a mosque. Osman appointed a Qadi (magistrate) and a Subaşı (chief of police) for the newly conquered city.

Conquest of Karacahisar

Historians differed in determining the date of this conquest, yet none made it prior to 685 AH / 1286 CE, or exceeding 691 AH / 1291 CE. Osman made his new city a staging base of his military campaigns against the Byzantines, and ordered that his name be delivered at the Friday khuṭbah, which was the first manifestation of his sovereignty and authority. [8][31] Osman's latest victory was his greatest up to that date. Seljuk Sultan Alâeddin Kayqubad III expressed his deep appreciation for Osman's accomplishments in the name of the Seljuks and Islam, giving him the title of Ḥaḍrat ʻUthmān ghāzī marzubān 'Âli Jâh ʻUthmān Shāh (the honourable conqueror and border guardian Osman Shāh). [START_REF]Dawlah al-ʻUthmānīyah: Dawlah Islāmīyah Muftara ʻalayhā[END_REF] The Sultan also bestowed upon Osman the governance of all the land he did conquered as well as the towns of Eskişehir and İnönü. Moreover, The Seljuk Sultan issued a decree exempting Osman from all types of taxes. Osman also recived several gifts from the Sultan reflecting the new high stature to the Seljuk court. These gifts included: a golden war banner, a Mehter (war drum), a Tuğ (a pole with circularly arranged horse tail hairs), a tassel, a gilded sword, a loose saddle, and one hundred thousand dirhams.

[30] [START_REF] Akgündüz | Dawlah al-ʻUthmānīyah almajhūlah: 303 sū'al wa-jawāb tuwaḍiḥ ḥaqā'iq ghā'ibah ʻan al-dawlah al-ʻUthmānīyah[END_REF] The decree also included the recognition of Osman's right to be mentioned in the Friday khuṭbah in all areas subject to him, and was permitted to mint coins in his name. [35] Thus, Osman became a Sultan, but lacking only the title. [36] It is narrated that when drums were beaten announcing Sultan's Kayqubad's arrival, Osman stood up in glorification, and remained so till the music halted. Since that day, Ottoman soldiers enacted standing in glorification for their Sultan whenever drums were beaten. [37][38]

Conquest of Bilecik, Yarhisar, and İnegöl

Soon after the conquest of Karacahisar, Osman marched with his soldiers north towards Sakarya River. Upon his arrival there, he raided and looted the forts of Göynük and Yenice Taraklı. Many argue that during this time, Osman received a message from his Byzantine friend Köse Mihal, warning him of a secret conspiracy that is being prepared to by tekfurs of Bilecik and Yarhisar. The two were aiming at killing Osman after inviting him to attend their children's wedding. Osman was disappointed in being betrayed by Bilecik's tekfur. That is because he considered the relationship with Bilecik to be built on trust and good faith, especially that his clan was used to leave their belongings in this fortress whenever they moved between grazing areas, as previously mentioned. Osman devised a plan to escape the trap and take over the fortress. He sent forty of his soldiers carrying some of the clan's belongings to be kept in Bilecik, while most of its inhabitants were outside attending the wedding. Once his men entered the fort, they quickly overpowered small garrison, and it fell to the Ottomans. Then, Osman went the feast followed by some Byzantine knights who were easily ambushed by his men later. A short battle took place in which Osman was victorious, and most of the Byzantines were killed. After that, Osman rode towards Yarhisar and took it by surprise; A large part of the fort's garrison was killed, while the rest were taken prisoners. The tekfur's daughter Holophira, was also captured in this action, she soon became Osman's daughter in law, having married his son Orhan sometime later, and her name was changed to Nilüfer Hatun.

[39] [START_REF] Peirce | The Imperial Harem: Women and Sovereignty in the Ottoman Empire[END_REF] Afterwards, Osman and several of his men took over all towns and villages surrounding İnegöl, before laying siege on the fort itself and taking it with ease. Osman ordered the execution of İnegöl's tekfur since he was known for persecuting his Muslim neighbours, then placed a new garrison for the town, and distributed the loot among his men. [39] Fall of the Seljuk Sultanate of Rûm, and the Osmanic Beylik's independence

Osman aspired, after his multiple victories, to expand on two axes, aiming to isolate the Byzantine cities he was looking to conquer. First, he blocked the road leading to İznik from the eastern side. Then, he advanced from the west towards Lopadion and Evrenos.

After that Osman turned around Mount Uludağ from both north and south, avoiding the fortified city of Bursa, connecting with his Muslim neighbours in the southeast. During that time, the Byzantine Empire was preoccupied with ongoing clashes with its powerful enemies in Anatolia, such as the Germiyanids and the coastal beyliks, not to mention suppressing unrest and discord in Constantinople and the Balkans. The Empire was unable to face Osman's threats, thus, he felt free to expand at the Byzantines expense exploiting the current situation.

[31] [START_REF] Köprülü | Qiyām al-Dawlah al-ʻUthmānīyah [Rise of the Ottoman Empire[END_REF] At the same time, the Seljuk Sultanate of Rûm was seeing its final days. The Sultanate grip was slowly weakened over its Turkoman Beyliks. Sultan Alâeddin Kayqubad III became deeply unpopular after he purged the Seljuk administration of his predecessor's men with extreme violence. This prompted the Mongol Ilkhan Mahmud Ghazan to call upon Kayqubad to appear before him, and once the latter did in 1302, he was executed and replaced with his predecessor Ghiyāth ad-Dīn Mas'ūd bin Kaykāwūs in order to keep the peace in Anatolia. [42] According to another account, Mongol and Tatar hordes raided Asia Minor in 699 AH / 1300 CE, and killed Sultan Kayqubad in his capital Konya. It was also said that Kaykāwūs himself killed his rival, coveting his own return on the throne. Another story suggests that Kayqubad escaped and sought refuge in the Byzantine court where he remained until his death. [36] In all cases, Kaykāwūs's rule was short-lived, lasting between 4 and 6 years at most, and when he died in 1308 CE, the Seljuk Sultanate of Rûm was no more to be mentioned in the historical records, [42] giving the way for the Turkoman beyliks to emerg as independent states.

The demise of the Seljuk Sultanate of Rûm gave Osman autonomy over his dominion, he soon dubbed himself Padişah Āl-ıʿOsmān (sovereign of the house of Osman). [31] After that, Osman set his sights towards conquering the last of the Byzantine cities, towns, and fortresses in Anatolia. According to one account, after Sultan Alâeddin Kayqubad III was killed by the Mongols, vizirs and notable leaders met and decided that Emirs should take his place, and they found Osman perfect fitting the candidacy. Thus, the leaders offered the Emir the position, and Osman accepted becoming a Sultan since that date. It is likely that Kayqubad's and Kaykāwūs's deaths led the to Sultanate of Rûm falling into chaos, and promoted many of its regular soldiers to join the armies of local Emirs, including Osman. This gave the latter a great momentum and important military experiences enriching his army for the upcoming conquests. [START_REF]Fadhlakat aqwāl al-akhyār fī ʻilm al-tārīkh wa-al-akhbār [A historiographical compendium of what was told by the good folk[END_REF]

Battle of Bapheus

Soon after Osman secured his independence and established control over all fortresses he conquered, he sent messages to all remaining Byzantine tekfurs in Anatolia asking them to choose between accepting Islam, Ottoman sovereignty and paying Jizyah, or war. Some of theses tekfurs ended up accepting Islam, including Osman's old friend Köse Mihal, who became the Turkic leader's companion, and would play a considerable part in the upcoming expansions of the Osmanic beylik. His descendants became known in Ottoman history as Mihaloğulları (children of Michael, plural of Mihaloğlu). [44][45] Other governors acknowledged Osman's sovereignty, while the rest kept their loyalty to the Byzantine Emperor. Thus, Osman started harassing their fortresses such as Bursa and Nicaea which was besieged in 1301 CE. [START_REF] Kazhdan | The Oxford Dictionary of Byzantium[END_REF] The Ottoman raids also threatened the port city of Nicomedia with famine, as the Ottomans roamed the countryside prohibiting peasants from harvesting wheat. This provoked Bursa's tekfur among others to unite their efforts in order to eliminate this new emerging Islamic power. [START_REF] Abū Ghunaymah | Jawānib Muḍī'ah fī tārīkh al-ʻUthmānīyīn al-Atrāk [Luminous aspects of the history of the Ottoman Turks[END_REF] In the spring of 1302 CE, Emperor Michael IX launched a campaign which reached south to Magnesia. The Ottomans, awed by his large army, avoided an open battle. The Emperor sought to confront The Ottomans, but he was dissuaded by his generals. Encouraged by that, The Ottomans resumed their raids, virtually isolating the Emperor at Magnesia. Soon, the imperial army started dissolving without engaging in a single battle, that is because the local troops left to defend their homes which were continuously raided by the Ottomans, and the Alan mercenaries left as well, aiming to rejoin with their families in Thrace. The Byzantine emperor was forced to withdraw by the sea, followed by a wave of refugees. [48][49][50] To counter the threat to Nicomedia, Michael's father, Andronikos II, sent a Byzantine force of some 2,000 men (half of whom were recently hired Alan mercenaries), under the megas hetaireiarches, Giorgios Mouzalon, to cross the Bosporus and relieve the city. [48][49] The Byzantine response was a warning for the Islamic border villages and towns. However, when the locals noticed Osman's leadership and military strength, as well as his devotion to Islam, they rallied to support and stand with him in order to consolidate a new Islamic state that would unite them and form an impenetrable wall against the Byzantines. Bapheus was the first major victory for the nascent Osmanic Beylik, and of major significance for its future expansion: the Byzantines effectively lost control of the countryside of Bithynia, withdrawing to their forts, which became isolated and fell one by one eventually. The Byzantine defeat also sparked a mass exodus of the Christian population from the area into the European parts of the empire, further altering region's demographic balance. [53] Coupled with the defeat at Magnesia, the Ottomans were able to reach the coasts of the Aegean Sea, threatening Byzantium with a final loss for their territory in Asia Minor. [50] According to Turkish historian Halil İnalcık, the allowed the Ottomans to achieve the characteristics and qualities of a true state. [START_REF] İnalcık | Osman Ghazi's Siege of Nicaea and the Battle of Bapheus[END_REF]

Byzantine-Mongol convergence attempt

After the victory in Bapheus, Osman divided the conquered lands among his kin and army leaders establishing Islamic hegemony and ending the Byzantine era in his new areas. He gave Eskişehir to his brother Gündüz bey, Karacahisar to his son Orhan, Yarhisar to Hasan Alp, and İnegöl to Turgut Alp. [11] By that time, Emperor Andronikos II felt the pressure of the Ottoman expansion. The Emperor watched in fear how the demographic changes were rapidly taking place in Anatolia, and he decided to stop it. Yet, being recently defeated, Andronikos II couldn't face the Ottomans in an open battle. To add insult to injury for the Byzantine, conflicts were taking place in the Balkans. Thus, Andronikos II had no choice but to try making an alliance with the Mongols in Persia, who were controlling central and eastern Anatolia. To achive that, the Emperor sent a letter to Ilkhan Mahmud Ghazan offering him a family rapprochement through marriage and establishing an alliance between both Empires. [31][55] At that time, The Mongols were passing through a period of high tension with the Mamluks in Egypt and Syria, this did overwhelm the relations with the Byzantines, especially that Ghazan was preparing for another campaign to Damascus and Palestine after his first invasion in 699 AH / 1299 CE, in which many civilians were massacred and where the Mamluk army suffered a massive defeat at the Battle of Wadi al-Khaznadar near Ḥimṣ. The Mamluks themselves were preparing for the upcoming war with the Mongols aiming to wash away the shame of their previous defeat. As a result, On 2 Ramaḍān 702 AH / 20 April 1303 CE, the Mongols and Mamluks engaged in a fierce battle on the outskirts of Damascus, known as the Battle of Shaqhab or Battle of Marj al-Saffar, in which the Mamluks won a decisive victory. [START_REF] Al-Maqrīzī | Kitāb al-Sulūk li-Ma'rifat Duwal al-Mulūk [The book of ways on how to learn about kings states[END_REF] This devastating defeat had a heavy toll on Ghazan and seems to have contributed to deteriorating his health further more, until he died in Qazvin on Sunday 11 Shawwāl 703 AH / 17 May 1304 CE. [START_REF] Al-Nuwayrī | Nihāyat al-arab fī funūn al-adab [The Ultimate Ambition in the Arts of Erudition[END_REF] This eliminated any hope of a Byzantine-Mongol alliance, and allowed the Ottomans to continue on with their conquests. , and was promised a four months payment for him and his men. [58][59] The Catalans soon crossed to Asia Minor and fought against the Karasids and Germiyanids winning a fast victory. Afterward, they resolved to attack the maritime provinces of the Ottomans and moved to the town of Philadelphia which was besieged by Osman, who suffered a defeat at the hands of the Catalans and was forced to lift his siege and retreat. This victory proved that Byzantium had been able to gather sufficient military forces and material capabilities, it would have been able to eliminate the emerging Ottoman power, but it had neither. It was not long before the Catalans abandoned fighting the Muslims and turned their attention towards the Byzantines themselves. The reason for that was that the local population of Magnesia beheaded the Catalan garrison and stolen its treasure, which infuriated Roger de Flor and made him march towards that city intending on revenge. The Byzantines were horrified by the mercenaries attacks, and became preoccupied in defending themselves. [59] Roger de Flor was soon killed by order of the emperor's son Michael IX, who saw the indiscipline of the Catalan mercenaries as a growing danger, [START_REF] Goodenough | Chronicle of Muntaner[END_REF] as did the people of Constantinople, who rose up against the Catalans and killed many of them. Once the news reached the main Catalan force in Gallipoli, they went on a killing spree of their own, killing all the local Byzantines. [START_REF] Rubió Y Lluch | Diplomatari de l'Orient català (1301-1409): col•leció de documents per a la història de l'expedició catalana a Orient i dels ducats d'Atenes i Neopàtria [Diplomat of the Catalan East (1301-1409[END_REF] Soon after this the Byzantines and the Catalans were at war with each other, giving way to Osman to move on with his conquests.

Conquest of Yenişehir and Its surroundings

After securing his northern borders by reaching the Black and Marmara seas, Osman turned his attention towards the southern borders of his beylik. Thus, he attacked the Byzantine towns, villages, and fortresses surrounding the city of Yenişehir preparing to conquer it. Osman sent a large campaign to the fortress of Yāvandhisar and annexed it. Then, he attacked Yenişehir, took it with ease, and made it his temporary capital after fortifying and strengthening its defenses. [START_REF] Dūrī | Dawāfiʻ al-Tawajjuhāt al-ʻUthmānīyah naḥw Ūrūbbā al-sharqīyah 1299-1358[END_REF] Soon after that Osman started sending more campaigns against the remaining Byzantine cities conquering several fortresses including Lefke, Akhisar, Koçhisar, Yenicehisar, Marmaracık, and Köprühisar. In fact, conquering the aforementioned forts aimed at imposing a security belt around Yenişehir, thus Osman surrounded it with a series of front forts to ward off any invasions. [55]

Conquest of Bursa

With Yenişehir in hands, Osman focused his efforts on isolated large cities starting with Bursa, unaware that this will be his last campaign. [START_REF] Runciman | The Fall of Constantinople 1453[END_REF] He gave the orders to start building two forts overseeing and surrounding the city, then, when the construction was completed, Osman provided the forts with large garrisons. This allowed his men to tighten the blockade and prevent any provisions reaching Bursa. [64] The Ottoman siege lasted between six and nine years, this was due to the fact that the Ottomans had no Siege engines and they had never captured a large fortified city before. [65] During the long siege, Osman and some of his military commanders conquered the smaller Byzantine fortresses on the vicinity of the beylik, in which Several tekfurs acknowledged Osman's sovereignty, and became among his subjects, some of them accepting Islam in the process. Soon after that, Osman started suffering from Gout, and couldn't accompany his men in any more campaigns or witness the siege of Bursa, so he entrusted his son Orhan to complete this major task, while he retired in his capital. Orhan's continued the siege without any fighting, but he continued isolating Bursa from its surrounding forts, conquering Mudanya to cut off the city's connection to the sea. He also captured the city of Praenetos on the southern coast of İzmit, changing its name to Karamürsel, after the Muslim leader who took it "Karamürsel Bey". The last fort to fall was Beyce, which was considered Bursa's key as it overlooked it, and it was renamed Orhaneli.

[64] [START_REF] Farīd | Tārīkh al-Dawlah al-ʻAlīyah al-ʻUthmānīyah [History of the Exalted Ottoman State[END_REF] Orhan tightened the blockade around Bursa till its garrison fell into despair. Soon, the Byzantine emperor realized that the fall of the city into Muslim hands was inevitable, thus, he made a difficult decision ordering his governor to evacuate the city. Orhan entered Bursa on 2 Jumādā al-ʾŪlā 726 AH / 6 April 1326 CE, its people were not subjected to any harm after they recognized Ottoman sovereignty and pledged to pay Jizyah. [START_REF] Efendi | Tâcü't-Tevârih [The Crown of Histories[END_REF] Saroz, the garrison's leader, surrendered to Orhan and pledged allegiance to his father Osman. He also converted to Islam and was given the title of "Bey" out of respect to his courage and patience during the long siege. [68] According to some sources, Osman passed away just before the fall of the city, [65] while others suggest that he lived long enough to hear about the victory on his death-bed. [START_REF] Rogers | The Oxford Encyclopaedia of Medieval Warfare and Military Technology[END_REF][70] [START_REF] Pitcher | An Historical Geography of the Ottoman Empire: From Earliest Times to the End of the Sixteenth Century[END_REF] Osman's Death

According to the sources that say Osman lived to hear of the fall of Bursa, Orhan rushed back to Söğüt to inform his father of his great victory. Once he reached it, he was immediately summoned to Osman, who was on his death-bed. Soon after Osman heard the news, he passed away from natural causes. However, Osman managed to name Orhan to be his successor, although the latter was not Osman's first-born. Yet the dead Emir believed that Orhan better fits to rule compared with his elder half-brother Alâeddin, who was more passive and pious than Orhan. [68] As for the exact cause of Osman's death, it is well-known that he suffered from gout for several years, which seemingly caused his eventual death. This is confirmed by what Aşıkpaşazade mentioned in Tevarih-i Âl-i Osman when he talked about the late period of Osman's life, saying: "Osman had a bad foot from which he experienced severe pain". It is noted that Aşıkpaşazade used a similar expression when he talked about the death of Sultan Mehmed the Conqueror: "The cause of his death was the issue in his feet". It is now known that gout is a genetic disease in the Ottoman dynasty, and many sultans suffered from it. [72] The exact date of Osman's death is debatable. [11][72] It is also certain that Osman's death was three or four months after the death of his father-inlaw, Sheikh Edebali, and two months after the death of his wife, Malhun Hatun, because it is known that Osman buried the two in Bilecik.

Once Osman died, Orhan ordered the transfer of his body to Bursa, his new capital. Thus, Osman's body was laid there to rest. [START_REF] Sarhank | Tārīkh al-Dawlah al-ʻUthmānīyah [History of the Ottoman Empire[END_REF] His grave is located today in the neighbourhood of Tophane. The reason behind the transferring Osman's body was due to a will Osman did tell his son about during the early years of besieging Bursa: "My Son, when I die, bury me under that silver dome in Bursa". However, Osman's current tomb dates back to the time of Sultan ʻAbdü'l-ʻAzīz (1861 -1876 CE), because the first tomb was completely destroyed in a severe earthquake that struck the region in 1855 CE, it was rebuilt by the aforementioned Sultan. Sultan Abdü'l-Ḥamīd II (1876 -1909 CE) also constructed a shrine in Söğüt where Osman was buried for a while before he was moved to Bursa. [72] Osman's Will

According to some sources, Osman left a written will to his son Orhan instructing him to move on with conquests and jihad against the Byzantines, that he abides by the teachings of Islam, accompany the ʿUlamāʾ, amend his parish, and dedicates himself to spread the word of Islam: [74][75] In the name of God, the Most Gracious, the Most Merciful My Son: Never be concerned with something that God, Lord of the Worlds, has not commanded, and if you encounter a dilemma in your ruling, follow the advice of religious scholars. Son: Honor those who follow you and accept your rule, bestow possessions upon your soldiers, allow not Satan to deceive you with your soldiers and your kingdom, and never stray far from the people of the sharīʿah. My son: know that our goal is to gain God's grace, and that through jihad that the light of our religion shall pervade and shine to all horizons. My son: We are not among those who start wars seeking the lust of ruling a land or controlling its people, for we live by Islam, and by Islam, we die. And this, my son, is what I know you are capable of doing. Know, my son, that spreading the word of Islam, guiding people to it, and protecting the Muslims families and possessions, is the task I entrust to you, and that God Almighty will ask you about it [on Judgment day].

My son: I pass on next to our Almighty Lord, proud and certain that you will be fair and just with your people, striving in the path of God, to spread the religion of Islam. My son: protect the scholars of the Ummah, maintain their care, venerate them, and listen to their advice, for they only command benevolence. My son: Do not do something that does not satisfy God Almighty, and if you faced any difficulties then ask the ʿUlamāʾ, for they will guide you to the right path. And know, my son, that our only path in this world is that of God, our only intention is to spread God's religion, that we are neither fortune nor worldly possessions seekers. My will to my children and companions: persist in transcending Islam, hold high its honourable banner, carry the tawḥīd to the furthest of lands.

[May] whoever of my lineage deviates from the path of truth and justice be deprived of our Prophet's intercession. My son: all in this world shall be subjected to death, and my life has come to its end by the command of God, I surrender and entrust this state to you, and bid you farewell, seek justice in all your affairs.

Legacy

Osman is considered the founder of the Ottoman dynasty, He started an imperial line that will expand to include thirty-five sultans, who ruled one of the largest and mightiest Empires in history. The Ottoman empire will last till 1918 CE, where it collapsed alongside the other Central Powers, after their defeat in the First World War. Osman is often referred to as the 1st in the line of Ottoman Sultans, although he himself never carried this title in his life, and was instead called "Bey" or "Emir". One endowment written in Persian and dating back to 1324 CE, indicates that Osman was given the titles Muḥiuddin (Reviver of the faith) and Fakhruddin (Pride of the faith). [30] Osman's descendants are distributed today in several American, European and Arab countries after the royal Ottoman family was expelled from Turkey in 1924 CE shortly after the declaration of the Republic, by Mustafa Kemal Atatürk. [76] Eventually, several family members returned to Turkey, after the Turkish government allowed the females to return in 1951 CE. [76] However, male descendants had to wait until 1973 CE to be able to enter Turkey again. [START_REF] Opfell | Royalty who wait: the 21 heads of formerly regnant houses of Europe[END_REF] Other members remained in the countries where their ancestors had sought refuge, such as England, France, the United States, Egypt, Saudi Arabia, among others. Osman's descendants are known today as the Osmanoğlu (son of Osman) family.

Osman's best-known relic is his Sword, which was used during the coronation ceremony of the Ottoman Sultans, [START_REF] Hasluck | XLVI. The Girding of the Sultan[END_REF] since Sultan Murad II. [START_REF] Topbaş | al-ʻUthmānīyūn: rijāluhum al-ʻiẓām wa mu'assasātihim al-shāmikhah [The Ottomans: their great men and their majestic institutions[END_REF] It is said that this sword passed to Osman from his mentor and father-inlaw Sheikh Edebali, who gritted him with the "sword of Islam". [START_REF] Bagley | The Last Great Muslim Empires[END_REF] Additional information

Introduction

  Osman I. or Osman Bay (full form: Abū al-mulūk al-Sulṭān al-ghāzī Fakhr al-Dīn QaraʻUthmān Khān al-awwal bin Ertuğrul bin Sulaymān Shāh al-qayawi al-Turkumānī), was the leader of the Kayı Turkic clan and one of the border governors for the Sultanate of Rûm, and the founder of the Ottoman dynasty that ruled over the Balkans, Anatolia, the Levant, and North Africa for 600 years until it expired with the establishment of the Turkish Republic in 1922.

Figure 1 |of 16 |

 116 Figure 1 | Ertuğrul's türbe in Söğüt. Maderibeyza/GFDL Cc-bysa-3.0-migrated cc-by-sa-2.5,2.0,1.0

Figure 3 |Figure 4 |of 16 |

 3416 Figure 3 | Index of Behcetü't Tevârîh, one of the Ottoman sources that talks about Osman's origins. Şükrullah/PD-Ottoman

Figure 5 |of 16 |

 516 Figure 5 | Osman as the Kayı Emir, or Bey. Seyid Lockman/PD-Art (PD-old-100)

Figure 6 |

 6 Figure 6 | Area of the Ottoman Beylik during the reign of Osman I. DragonTiger23/cc-by-sa-3.0 GFDL Figure 7 | A map of independent Turkic beyliks in Anatolia during the 14th century, showing the neighbouring Ottoman and Germiyanid beyliks. Morningstar1814 (English Version)/CC-BY-SA-4.0

Figure 8 |of 16 |

 816 Figure 8 | Ilkhan Mahmud Ghazan (on horseback), higher ruler of Anatolia during the early years of Osman's reign. All Turkoman Beys or Emirs were subordinate to him despite the inherent hostility between Turks and Mongols. Rashīd al-Dīn al-Hamadānī/PD-Art (PD-old-100)

Figure 9 |Figure 10 |of 16 |

 91016 Figure 9 | Illustration of Osman rallying his warriors into battle. Unknown author/PD-Art (PD-old-100)

Figure 11 |of 16 |

 1116 Figure 11 | The declining Sultanate of Rûm, vassal of the Mongols, and the emerging beyliks, c. 1300. Khateeb88/CC-BY-SA-3.0

  [35] Several Byzantine deserters joined Osman as well, some of which were liberated prisoners of war who chose to align with him, reportedly due to his good treatment during their custody. Many Islamic warrior brotherhoods also joined the Ottomans. For example, the Gazi Rûm's (Raiders of the Romans), they were stationed on the borders of the Byzantine Empire and repelled its attacks on Muslim lands since the Abbasid era, gaining great experiences and knowledge in Byzantine strategies and tactics. Another example is the Ḥajjian Rûm's (pilgrims of [the land of] the Romans), a brotherhood of Muslim clergy concerned with teaching local villagers and recent converts the basics and different aspects of Islam, and had a side objective of assisting the Mujahideen in combat.[51][52]

Figure 12 |Figure 13 |

 1213 Figure 12 | Osman, an independent Emir, on his Takht. Arif Paşa/PD-old-100

Figure 14 |Figure 15 |

 1415 Figure 14 | Mongol soldiers, in Jāmiʿ al-tawārīkh by Rashīd al-Dīn al-Hamadānī. Rashīd al-Dīn al-Hamadānī/PD-Art (PD-old-100)

Figure 16 |

 16 Figure 16 | Roger de Flor being received by the Byzantine emperor Andronikos II Palaiologos. José Moreno Carbonero/PDold-70-1923

Figure 17 |Figure 18 |

 1718 Figure 17 | Gate of Bursa's Byzantine castle, which witnessed the long Ottoman siege. Citrat/CC-BY-SA-3.0-migrated GFDL

Acknowledgements

Special thanks to Michel Bakni, for his guidance, notes and help during writing this article and after it was finished.

Funding

None

Competing interests

The author declares no relevant conflicts of interest.