French Female Managers from North African origin: an integration "à la française" Dr Arnaud Lacheret

Arabian Gulf University

The integration process of migrants from a different culture is an important subject in developed countries, especially in France. Due to its colonial past, France has welcomed many workers from North Africa since the 60s. This first generation was composed of non-skilled workers who occupied jobs mostly in the industrial sector. This immigration was supposed to be temporary and the immigrants, mostly men, were not supposed to become French let alone be integrated in French society. However, after several years, most of these workers arranged the immigration of their spouses and founded households in France. This settlement was not really anticipated in France and from the early 80s onward, the integration of those new French citizens became a political priority.

In our research, we assumed that the integration of the second generation of French North African immigrants can be compared with one that was the subject of a previous study we conducted: a study of the integration of female managers in the Gulf. After various reforms by local Governments it had become easier for women to raise in the social scale in those countries (Lacheret, 2020;Lacheret and Farooq, 2021).

These women negotiated small steps to obtain spaces of freedom and eventually they could obtain the job they had chosen. Afterward, the father's conservative values became more flexible eventually becoming proud of his daughter and trying to promote this empowerment process himself. This way of progressively changing the conservative values of their own family is what we can call a "social non-movement" (Bayat, 2013): many actors adopt the same behaviour and change some values in their neighbourhood without concerted movement. This leads to a global change of the values of an entire society.

We wanted to compare this process of change conducted in the Gulf countries with the integration of young female managers of the second generation of North African immigration in France. These women were raised in relatively poor conditions, most of time with fathers employed as unskilled labour workers and with non-working mothers . Moreover, most of the interviewees in the study said that their families had difficulties speaking French and had conservative values, especially with regard to the place of women in the society. Despite these obstacles, the integration rates of the second generation are impressive. According to statistics, 11% of foreigners who arrived before 1974 in France had a university degree. In 2010, for 22% of the daughters of workers of Algerian origin, had a university degree and 31% of those who were of Tunisian and Moroccan origin. The number of university graduates in France today is 34%. In one generation, women have almost attained the average education level of the French population. Therefore, we wanted to ask them how they had managed to move upwards on the scale so quickly. We interviewed 23 women and conducted the same qualitative interview with the female managers from the Gulf, The Gulf study was inspired an existing study run of Muslim female managers of South Asian origin in Great Britain [START_REF] Tariq | Intersectionality at Work: South Asian Muslim Women's Experiences of Employment and Leadership in the United Kingdom[END_REF].

Our main findings, which will be published in a book in November 2021, are that the integration process is partly comparable to the one of the Gulf female managers. Both studies demonstrate a kind of a negotiation process with the family and especially with the reluctant fathers; and once the daughter's freedom of choice is obtained, the parents become less conservative and more integrated, too.

The main difference between both samples consists in the fact that the social origins are not the same: Gulf families are part of the upper middle class and educated while in France, the first generation of migrants is often uneducated and very poor. Therefore, in France, even if the families eventually become convinced of the need to study and to apply for qualified jobs, the families do not have the cultural capital [START_REF] Bourdieu | The forms of capital[END_REF][START_REF] Putnam | Bowling Alone: The Collapse and Revival of American Community[END_REF] to help their daughters once the latter have started following higher education.

A further finding sheds light on the fact that the families' conservative behaviours subsist in the French case, especially in private life. For example, we were told, during the interviews, of many attempts of forced or arranged marriage. However, the most important thing is that the women interviewed were blaming far more their backward qualified culture of origins for misfortunes than their religion. In that sense, the responses are similar to those of their Gulf counterparts as they explain that the main obstacle for their empowerment is the conservative traditions and not the religion.

In conclusion, our study states that integration processes have to be accompanied by the public authorities not by on over focusing on religion because religion does not appear as a significant obstacle to integration, but rather on cultural and social issues such as avoiding ghettos, promoting more social diversity at school and, last but not least, defining precisely what kind of values French society has in order to be able to promote them to the second and third generation of immigrants.


Frédéric Danjon
email: frederic.danjon@inrae.fr

Antoine Danquechin Dorval

Céline Meredieu

Tiphaine Archereau

Raphaël Ségura

Bernard Issenhuth

Chantal Giroux

Pascal Barla

Ambre Leferrec

Sébastien Cavaignac

Guillaume Silande

Cédric Sedillot-Gasmi

Resilience from perturbation of architectural scheme through planting varies largely in Pinus pinaster

Keywords: Root architecture, Pinus pinaster, planting, root deformation, 3D digitizing, coarse root architecture

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Three hundred 3 to 5-years-old P. pinaster saplings planted in 16 forest stands were uprooted with hand tool and digitized using a magnetic field Polhemus 3D digitizer (Danjon & Reubens 2008). They were compared to 30 direct seeded trees from one stand. The resulting database contained 67000 segments and 10250 axes. We set up and used an original architectural analysis to characterise deformations and thus root type modifications in order to examine the resulting root architecture and potential stability.

MATERIAL AND METHODS

Introduction:

Planting is a widespread propagation technique for woody plants. Container-growth and plantation is likely to heavily alter root architecture and thus modify anchorage.

The Landes forest is located South-West France and produces 20% of french wood, it is mainly composed of intensively managed even-aged stands of P. pinaster (Ait). Most reforestation is made by planting genetically improved varieties, from seeded nursery stock. Soils are entic to albic spodosols which are acidic, sandy, and lenses of cemented spodic horizon can occur. Root system architecture is a key component in mechanical stability of trees. In their first 15 years, pines are mainly anchored by a rigid vertical and deep taproot (Danquechin Dorval 2016). Older trees are anchored by a rigid cage mainly composed of regularly spaced strong shallow roots from which branch secondary sinkers (Danjon et al. 2005). The main framework of the central part of the root system is established at 4-years-old with a clear identification of root types (Saint Cast et al. 2020). In this study, we characterize the deformations of root systems of P. pinaster saplings grown in containers and planted in the field. Incidence on root system architecture is analysed.

RESULTS

Potential shallow roots:

The distribution of these roots along the first order root was not modified by container planting and the largest ones grew from the upper plug zone. Heavy deformations of laterals due to nursery growth in grilled and vertically grooved containers and by planting were located within 6 cm radial distance from the taproot (fig 8). When the 6 first cm of a lateral root was maintained in a non-horizontal position, 27% of these originally shallow roots grew as oblique roots and 17% as sinkers. Conversely, when horizontal at base, 89% of the lateral roots remained shallow (fig 9). The largest azimuth angle between shallow roots (LABS) is mainly determined by their number at 12 cm radial distance from the first order root (ρ = 0.7), which is lowered when shallow roots lose their plagiogravitropism (fig 10). Ten planted stand showed significantly larger clustering of azimuth of their shallow roots resulting in significantly larger angle between shallow roots (ρ = 0.84).

Stump-taproot axis:

The root system of planted trees was 1.8 cm deeper on average than seeded trees, few plugs showed on the soil surface or were crushed. Plug tortuosity averaged 14% in the planted trees and 5% in the seeded trees, below plug and soil zone tortuosity was weak. In the below-plug zone, vertical deviation of the first order root peaked at a 40° average vs. 20° in the seeded trees (fig 5). Overall, 17% of planted trees have a non vertical taproot vs. 1.5% for the seeded (fig 6). When the taproot was not vertical in the 4 cm long below-plug zone, 30% of the taproots did not recover their verticality. Conversely, only 7% lost it when the below plug zone was vertical (fig 7).

Conclusions:

The studied planted stands showed low mortality and a small number of badly planted seedlings. They displayed a very large variability in type and degree of deformations which could not be related to variables like the planting season or the type of soil preparation. About half the planted trees showed a good resilience as they were able to grow a root system which is likely to provide a good anchorage, other trees posses a non-vertical or weak taproot or show large LABS, except in planted stands b3, e3 and f3 where less than 20% of the root systems has no unacceptable defect We concluded that change in root tropism through nursery growth, planting and initial root regrowth is likely to weaken the anchorage of the trees both in juvenile or mature stage. Thus orientation of root ends at interface of the plug and the soil, just after plantation is a major issue for tree anchorage.

  Fig. 3: Variables of deformation of the shallow roots branching from stump, Two other variables are calculated: sum of radial distance (tortuosity %) and Depth (cm) variations from the base of the root and 6 cm radial distance the

Fig. 5 :

 5 Fig. 5: Vertical deviation of stump-taproot axis every centimetre. Black dotted line is for the seeded trees.

Fig 1 :(

 1 Fig 1: Spatio-temporal landmarks on the stump-taproot axis

Fig. 6 :Fig. 8 :Fig. 10 :

 6810 Fig. 6: Boxplot per stand of taproot vertical deviation. "*" when significantly different from the seeded control (C) stand

supported by Caisse des Dépots et Consignation, the Ministry of Agriculture, SERFOB and Aquitaine Regional Council, Diademe and Fortius projects


Mahmoud Amin

Noha Mohamed

The Evolution of Wi-Fi Technology in Human Motion Recognition: Concepts, Techniques and Future Works

Keywords: Human Motion Recognition, Wi-Fi, Sensors, Computer vision, Cybersecurity

Human motion recognition is an important topic in computer vision as well as security. It is used in scientific research, surveillance cameras industry and robotics technology as well. The human interaction with the objects creates a complex stance. Multiple artefacts such as clutter, occlusions, and backdrop diversity contribute to the complexity of this technology. Wi-Fi signals with the usage of their features could help solve some of these issues, with the help of other wearable sensors, such as: RGB-D camera, IR sensor (thermal camera), inertial sensor etc. This paper reviews various approaches for Wi-Fi human motion recognition systems, their analytical methodologies, challenges and proposed techniques along with the aspects to this paper: (a) applications; (b) single and multi-modality sensing; (c) Wi-Fi-based techniques; d) challenges and future works. More research related to Wi-Fi human related activity recognition can be encouraged and improved.

1-INTRODUCTION

Human motion recognition has been recently been an important topic in many fields, including computer vision, computer networks, cyber security, surveillance-based industry and ubiquitous assistive living [START_REF] Abdelnasser | UbiBreathe: A Ubiquitous non-Invasive WiFi-based Breathing Estimator[END_REF]. HAR seeks to comprehend people's daily habits by observing them and their surroundings. Sensors in cellphones, wearables, and home settings capture this data. Computer vision uses a digital and video-based systems to collect daily human actions and identify them automatically [START_REF] Abdelnasser | WiGest: A Ubiquitous WiFi-based Gesture Recognition System[END_REF]. With the evolution of digital logic and computer systems, low-power, high-capacity, lowcost sensors, as well as wireless networking networks, have become increasingly common. This is the main reason individuals use technology and technologies for daily subsistence. The activity recognition mechanism can be used to track daily exercise [START_REF] Adib | See Through Walls with WiFi![END_REF].

Identifying static and dynamic tasks with postural shifts can also help monitor worker health and productivity. These systems can also help people maintain a healthy lifestyle by advising little changes in their behavior. Soldiers in strategic circumstances require precise information on their activities, health, and locations [START_REF] Ali | Keystroke Recognition Using WiFi Signals[END_REF]. This data can be quite useful in combat and practice settings. Smart houses use external sensing to track daily tasks. The use of cameras for surveillance and interactive reasons is appropriate. These systems use motion history photos and computer vision to distinguish action [START_REF] Ali | Recognizing Keystrokes Using WiFi Devices[END_REF].

Human activity recognition is important in human-to-human interactions. It is tough to extract since it contains information about a person's identity, personality, and mental state. The ability of humans to detect other people's actions is a major research topic in machine learning and artificial intelligence [START_REF] Arshad | Wi-Chase: A WiFi based Human Activity Recognition System for Sensorless Environments[END_REF]. As an outcome of the study, numerous applications such as video surveillance, HCI, and human behavior modelling demand a multiple action identification system. In order for a computer to identify human activities efficiently, the person's kinetic states must be determined. Human behaviors like "walking" and "running" come effortlessly and are easily recognized. Complex tasks. Complex tasks can be broken down into simpler ones that are easier to recognize [START_REF] Bagci | Using Channel State Information for Tamper Detection in the Internet of Things[END_REF].

Fig 1.: Examples for wearable sensors with human body for motion detection

Object detection in a scenario can help understand human activities and provide relevant information about the current occurrence. Problems including backdrop clutter, partial occlusion, length, perspective, sunlight, and look make it difficult to identify human activities in video or still photographs. Many applications, such as video surveillance, HCI, and human behavior modelling, require multiple activity recognition [START_REF] Banerjee | Violating Privacy Through Walls by Passive Monitoring of Radio Windows[END_REF]. We cover recent and current research advancements of human activity identification. We categorize human activity approaches and examine their benefits and drawbacks as well as categorizing human activity classification approaches into two broad categories based on whether they employ data from several modalities. This is followed by sub-categories that represent how they simulate human behavior and their interests.

Many researchers from various fields have sought to comprehend human mobility. The issue is unique to each discipline. With so many reasons for researchers, many methods have been introduced across fields. These contributions provide a better knowledge of human mobility. However, this article focuses on the computer vision part of human motion understanding, namely entire body movement [START_REF] Barbera | Signals from the Crowd: Uncovering Social Relationships Through Smartphone Probes[END_REF]. This article attempts to recall some of the most quoted and recent evaluations over the last two decades, while highlighting the subject's relevance and wide-ranging applications. The large range of challenging and promising applications for human motion analysis, recognition, and understanding has sparked significant research in computer vision. Following is a survey of multiple applications in several domains:

 Smart Surveillance: Due to the boring and hypnotizing nature of monitoring video scenes, and the increasing number of cameras covering vast areas, the human operator becomes more costly and unreliable (Such as:, a survey of CCTV (Closed Circuit Television) systems). So the demand for automated surveillance systems becomes urgent. Smart surveillance can be used to detect suspicious behavior and unusual events, understand and describe human behavior in dynamic situations (Such as:, monitoring activities over a large area using a distributed network of active video sensors), and control access to sensitive areas like military bases and government offices [START_REF] Chen | Rapid: A Multimodal and Device-free Approach Using Noise Estimation for Robust Person Identification[END_REF].

 Behavioral Biometrics: Recognition of individuals using behavioral signals (Such as: stride, length, facial features) does not require subject participation or involvement [START_REF] Cheng | How Can I Guard My AP?: Non-intrusive User Identification for Mobile Devices Using WiFi Signals[END_REF].

 Human-Computer Interaction: Examples of perception user interfaces include gesture-driven control, eye gaze monitoring, voice recognition, sign language processing and understanding, signaling in noisy environments such as factories and airports, and cognitive user interfaces which enables people to interact with computers without using a keyboard or mouse [START_REF] Chollet | Deep Learning with Python[END_REF].

 Virtual Reality: in which an allows the user to interact with a virtual computer systems environment, such military training or fireman and rescue team training. Games and entertainment sectors have various uses for virtual reality [START_REF] Chon | Sensing WiFi Packets in the Air: Practicality and Implications in Urban Mobility Monitoring[END_REF].

 Smart Environments: Extracting and keeping awareness of a broad range of activities and human behaviors, Such as:, monitoring conference room exchanges [START_REF] De Sanctis | WIBECAM: Device Free Human Activity Recognition Through WiFi Beacon-Enabled Camera[END_REF].

 Games Industry: Several games feature gesture-based interactive technology, which uses motion capture to allow non-intrusive body movement involvement. Like the popular Microsoft Kinect Xbox [START_REF] Di | A Trained-once Crowd Counting Method Using Differential WiFi Channel State Information[END_REF].

 Entertainment Industry: Motion-captured characters replace actors in science fiction films (digital avatars) [START_REF] Duan | WiDriver: Driver Activity Recognition System Based on WiFi CSI[END_REF].

 Sports Motion Analysis: such as soccer, where referee decisions and tactics are analyzed, as well as automatic highlight identification and video annotation and browsing [START_REF]USRP Software Defined Radio Device[END_REF].

 Robotics Learning to Copy Human Behavior: utilizing robots to set up or clean tables, or in dangerous scenarios or surroundings like vehicle crash tests, skating during an arctic blast, etc. [START_REF] Fang | BodyScan: Enabling Radio-based Sensing on Wearable Devices for Contactless Activity and Vital Sign Monitoring[END_REF].

 Smart Driver Support Systems: Such as: Monitoring Driver Consciousness, Sleep Identification, Airbag Network Management, Anticipating Driver Turn purpose ,etc. [START_REF] Fang | HeadScan: A Wearable System for Radio-based Sensing of Head and Mouth-Related Activities[END_REF].

In order to achieve human motion analysis and recognition, these applications demand varying levels of performance (Such as: human modelling, real-time processing, video resolution) and environmental control (Such as: regulated or uncontrolled) [START_REF] Feng | MAIS: Multiple Activity Identification System Using Channel State Information of WiFi Signals[END_REF]. These applications' requirements for body motion recognition and classification differ (Such as:, human modelling, real-time analysis, video resolution, controlled or uncontrolled environments, active or passive sensing, types and number of sensors, performance robustness and accuracy) [START_REF] Gao | LiveTag: Sensing Human-Object Interaction through Passive Chipless WiFi Tags[END_REF].

Background

A wireless signal rebounds off walls, objects, as well as other surfaces. The innovative idea is used to save hostages in a difficult and dynamic situation. Indoor location uses finegrained Wi-Fi signal information to find people based on path-loss characteristics [START_REF] Gao | CSI-based Device-free Wireless Localization and Activity Recognition Using Radio Image Features[END_REF]

Challenges

This study analyses motion detection algorithms and evaluates motion impact on Wi-Fi based applications. Overall, estimating the impact of motion behavior poses the following issues. This problem stems from two aspects: target proximity to non-target and device-free motion detection.

• Create a framework for estimating motion behavior.

Work already done on dealing with unusual motion behavior in experiments cannot be applied to a new context.

• Estimate the link between motion and Wi-Fi signal variations in a random interior environment.

As a result of this relationship, it is possible to determine the performance of data sets from various experimental situations. The recognition difficulties in the domain of sensor-based motion identification can indeed be examined. The difficulty of the activities varies depending on their quantity, kind, sensor selection, power usage, obtrusiveness, and information gathering procedures.

As illustrated in the figure 2 below, ambulation activities are grouped as static, dynamic, either with postural changes. It is easier to identify static actions (sleeping, sitting, etc.) than monitoring compliance (running, training, etc.). Due to significant overlap in feature space, extremely comparable poses (sleeping, standing, etc.) cause tremendous complexity in separation. Additionally, dynamic activities (going upstairs and downwards) are difficult to distinguish due to comparable movement patterns. b-Chosen Sensors Numbers: In addition to the usual Wi-Fi and Bluetooth sensors on a mobile are sensors for temperature and relative humidity as well as light conditions and proximity. However, an identification system with a limited number of sensors makes the procedure quicker and easier in real-life applications. The quantity of wearable sensors is crucial for convenience. Users cannot carry several sensors. The balance between sensor count and efficiency should be handled with attention [START_REF] Gu | MoSense: An RF-based Motion Detection System via Offthe-Shelf WiFi Devices[END_REF].

c-Wearable Sensors Location: Typically, people carry their cellphones in the coat pocket, trouser wallet, or hand. Because trackers detect motion along an axis and the accelerometer identifies direction, the posture of the device must be evaluated when gathering information, as data might vary depending on the sensor placement on a person's body, even within the same activity. However, owing to the placement of phones and wireless sensors, incorrect detection of a certain activity might impair recognition rate. Further issue is that some users may forget the device at home, making it hard to follow their behavior. In this situation, a wearable sensor may be a viable alternative, however several consumers may find it uncomfortable to keep it every day while doing tasks [START_REF] Guo | HuAc: Human Activity Recognition Using Crowdsourced WiFi Signals and Skeleton Data[END_REF].

The paper is organized as following: Section

WIFI SIGNALS AND MOTION TYPES 2.1 Wi-Fi Signals

Path loss, middle-scale shadowing, with narrow multi-path fading could all be used to mimic wireless transmission in a complicated environment. Earlier investigations focused on receiving signal strength (RSS), easily obtained in wireless environments. It's only that RSS is prone to multi-path effects.

Then, instead of RSS, some works use channel state information (CSI). It proposes super-resolution methods that reliably compute multi-path component AoAs with a median precision of 40cm. A 65cm precision Chronos could calculate sub-nanosecond moment using cheap Wi-Fi devices. Table 1 shows Wi-Fi signal properties exploited in various Wi-Fi applications.

Table 1: Most used Wi-Fi Signals Approaches with their properties

Approach Properties AoA

A well-known approach for analyzing multiple activities in a project, particularly the time necessary to accomplish each activity.

RSS Average, Range, and Signal Variance ToF

The time delay between the signal ransmission and its arrival to the sensor after becoming returned by an element.

CSI

Motion Patterns Types

TECHNIQUES AND PERFORMANCE

Techniques 3.1.1 Signal processing of Wi-Fi sensing

Signal processing for Wi-Fi sensing includes noise reduction, signal transformation, and signal extraction [START_REF] Han | WiFall: Device-free Fall Detection by Wireless Networks[END_REF].

Noise Reduction

Raw CSI data contains noise and outliers that might degrade Wi-Fi sensing capability [START_REF] He | WiG: WiFi-based Gesture Recognition System[END_REF]. As seen in figure 4 above, unprocessed CSI stages vary regularly between and, but pre-processed CSI stages vary almost linearly throughout a broader range. Additionally, time-dependent CSI phase variations are rectified. As seen in the figure above, the raw CSI stages of the first and second frequency channels vary identically, but their shapes after preprocessing are indeed different [START_REF] Husted | Mobile Location Tracking in Metro Areas: Malnets and Others[END_REF].

Outliers Removal

Moving Average and Median Filters are both straightforward and commonly used techniques for filtering out high frequency noise [START_REF] Jamil | Classifying Smartphone Screen ON/OFF State Based on WiFi Probe Patterns[END_REF]. Every data point is changed by the median of the datasets immediately adjacent to it. Typically, a sliding window and multiplication factors are employed to generate various weights, for examples:

 Weighted Moving Average (WMA)  Exponentially Weighted Moving Average (EWMA).

 Low Pass Filters (LPF)

They can also be used to eliminate high frequency noise when signal transform techniques such as the Discrete Fourier Transform are used (FFT). Wavelet Filters are identical to LPFs; the primary distinction is that they employ the Discrete Wavelet Transform (DWT) rather than the Fourier Transform (FFT) [START_REF] Jayarajah | Fusing WiFi and Video Sensing for Accurate Group Detection in Indoor Spaces[END_REF].

Where:

σi represents Standard Deviation

The Hampel Filter calculates the mean score and standard deviation of such a region of closely spaced data points [START_REF] Jiang | Rejecting the Attack: Source Authentication for Wi-Fi Management Frames Using CSI Information[END_REF].

If it exceeds a certain threshold, the existing point is considered an outlier and is substituted with the median. Occasionally, outliers are eliminated instead of being substituted by medians.

The Local Outlier Factor (LOF) is a frequently used technique for detecting anomalies [START_REF] Mourad | Improving Wireless Sensor Networks Life Time Using Neural Network[END_REF]. It quantifies a data point's local density in relation to its neighbors. The local density is determined by the Wi-Fi tethering distance between two points. Outliers are number of observations with a considerably lower density distribution than their neighbors. Signal Nulling is a specialized approach for removing outliers from Wi-Fi sensing. Wi-Fi devices may employ both hardware, such as antenna arrays, and software, such as transmit beam shaping and noise cancellation algorithms [START_REF] Chitra | 3D Throughwall Imaging with Unmanned Aerial Vehicles Using WiFi[END_REF].

Signal Transformation

Time-frequency analysis of CSI readings uses signal transform techniques. In this perspective, the signal convert output shows CSI change pattern frequency instead of carrier frequency [START_REF] Kim | Modeling Users' Mobility Among WiFi Access Points[END_REF].

Signal Extraction

Signal extraction is used to extract goal frequencies from CSI data. Unidentified or repetitive signals may need thresholding, filtration, or signal encoding [START_REF] Kumar | Bringing Cross-layer MIMO to Today's Wireless LANs[END_REF]. To acquire additional information, various signal sources are combined and data is interpolated. These approaches are shown in the table below.

Probability Model:

dataset and training methodology. The probability model may modify if the training set or training technique changes [START_REF] Tawfik | Filtering and analysis of multiparameter radar measurements in rain using wavelets[END_REF].

Fingerprint-based:

The fingerprint-based solution incorporates two phases: gathering RSS from each place inside a building and matching it with the fingerprint database. These works can achieve meter-level precision without a site survey [START_REF] Li | AR-Alarm: An Adaptive and Robust Intrusion Detection System Leveraging CSI from Commodity Wi-Fi[END_REF]. High implementation costs and lack of adaptability to changing environments limit its usefulness. We illustrate three flaws in fingerprinting approaches [START_REF] Li | IndoTrack: Device-free Indoor Human Tracking with Commodity Wi-Fi[END_REF].

Expensive: Building a fingerprint database requires a lot of labor and hardware. The more location data collected, the more accurate indoor location becomes. A fingerprint database must be updated in real-time when the indoor environment changes. This constraint increases system burden in practice [START_REF] Liu | Practical User Authentication Leveraging Channel State Information (CSI)[END_REF].

Best Location Choice: Various works choose some places of interior maps to save money and preserve high accuracy. That is, only a few places may depict indoor maps coarsely [START_REF] Liu | Authenticating Users Through Fine-Grained Channel Information[END_REF].

The difficulty is to select several areas to accurately portray indoor maps.

Crowdsourcing Model

Crowdsourcing-based systems collect data from a large number of mobile devices located across an indoor space, saving time and money. However, as illustrated below, actual crowdsourcing applications face some problems [START_REF] Liu | A Research on CSI-based Human Motion Detection in Complex Scenarios[END_REF].

Device Diversity: Device diversity is a problem in wireless environments. Wi-Fi transmissions are sensitive to both indoor and outdoor environments, as well as device kinds. The impact of device diversity on data collection is often overlooked [START_REF] Liu | Tracking Vital Signs During Sleep Leveraging Off-the-shelf WiFi[END_REF].

Destabilization of Data Source: Smart phones used in crowdsourcing are unknown and cannot ensure data authenticity [START_REF] Ashraf | MANET's Energy Consumption using proposed Ant-Colony Optimization and Integer Linear Programming Algorithms[END_REF].

Time Synchronization: Due to the nature of Wi-Fi transmissions, crowdsourcing requires time synchronization of the devices collecting data. Nevertheless, numerous mobile devices do not have synchronization capabilities [START_REF] Liu | Contactless Respiration Monitoring Via Off-the-Shelf WiFi Devices[END_REF].

Performance: Existing works aim for higher performance at affordable cost. The effectiveness of existing approaches is shown below.

Accuracy: Because RSS is easily accessed by commodity Wi-Fi infrastructure, existing works still use RSS information to identify motion. These devices use Wi-Fi signals and human movement to attain excellent accuracy.

a. WiSee uses doppler shifts in radio waves to detect human activity with 97 percent accuracy and E-eyes with 92 percent. b. Smokey uses CSI to recognize smoking activities in NLOS and through-wall situations. c. The system uses foreground detection to retrieve useful information from numerous noisy sub-carriers, even when posture changes.

2) Cost: Earlier, experts believed that the more APs deployed, the better the accuracy. APs are typically used in early works to achieve precision. Horus has an average inaccuracy of 0.6m by 4-6 APs. In recent years, single APs like Chronos, with a median inaccuracy of 65cm, have achieved the same degree of precision as multi-Aps [START_REF] Lv | Robust WLAN-based Indoor Intrusion Detection Using PHY Layer Information[END_REF].

3) Robustness: In a dynamic indoor environment, resiliency is a significant measure of system quality. Several works offer methods with great LOS precision but poor NLOS accuracy [START_REF] Lyu | BikeLoc: A Real-time High-Precision Bicycle Localization System Using Synthetic Aperture Radar[END_REF].

These days researches can supply different methods. Smokey [START_REF] Ma | When Can We Detect Human Respiration with Commodity WiFi Devices?[END_REF] can detect smoking in LOS, NLOS, and through walls.

MOTION INFLUENCE

Advantage

Previous works were made to avoid motion because it affects the changing of Wi-Fi signals. We studied mobility detection strategies and their influence in recent years. Three points are summarized below.

1) Enrich Multi-Path Data:

The interior setting, multi-path effect is common. Indoors, there are usually 6-8 paths.

Understanding people circulation patterns can assist discover energy hotspots and corridors that can help commercial site selection. Human mobility can reset an indoor environment's floor plan, and multi-paths respond. Li-Fi detects LOS by skewed CSI distribution. PhaseU also completes real-time LOS identification indoors. Others use multi-paths to achieve internal localization or human motion detection. [START_REF] Ma | SignFi: Sign Language Recognition Using WiFi[END_REF]. A moving target is focused on by using MIMO disturbance nulling to reduce static object reflections. We can consider people in a closed space if they don't move [START_REF] Maheshwari | Walking Parameters Estimation through Channel State Information Preliminary Results[END_REF]. Indoor fingerprinting is not feasible since the signature varies with the environment. Authors often seek to suggest an ubiquitous plan for dealing with dynamic tests [START_REF] Lyu | BikeLoc: A Real-time High-Precision Bicycle Localization System Using Synthetic Aperture Radar[END_REF].

Table 3: Common proposed approaches along with highest accuracy results

Proposed Methods Approach Accuracy ArrayTrack [START_REF] Ma | When Can We Detect Human Respiration with Commodity WiFi Devices?[END_REF] AoA 35cm SAIL [START_REF] Ma | SignFi: Sign Language Recognition Using WiFi[END_REF] ToF 2.2m SpotFi [START_REF] Maheshwari | Walking Parameters Estimation through Channel State Information Preliminary Results[END_REF] AoA 39cm CUPID [START_REF] Melgarejo | Leveraging Directional Antenna Capabilities for Fine-grained Gesture Recognition[END_REF] Human Mobility 4.2m and 1.5-4 APs: 3.6m Chronos [START_REF] Mohammadmoradi | Room Occupancy Estimation Through WiFi, UWB, and Light Sensors Mounted on Doorways[END_REF] ToF 63cm & NLOS: 96cm

Disadvantage

1) Infected Wi-Fi signal datasets: In general, Wi-Fi signal data packages allow RSS and CSI acquired by receivers indoors. Motion has a greater impact on Wi-Fi signals compared static. We gather dataset, measurements, and other background data. Without particular approaches, it is hard to identify targets' data from collected data sets. Researchers offer a few approaches to resolve other noisy data [START_REF] Elfakhrany | IRIS recognition using conventional approach[END_REF].

2) Difficult Pre-processing: Due to the complexity of motion characteristics, the preprocess phase becomes more difficult. Static behaviors modify Wi-Fi signals slightly, but motion behaviors produce considerable changes. Meanwhile, gathering data from the receiver is difficult to identify outlier from motion behavior [START_REF] Palipana | Channel State Information Based Human Presence Detection Using Non-linear Techniques[END_REF].

3) Hardware Consumption Increment: Motion lowers the stability of mobile device data sets and the effectiveness of Wi-Fi based technologies. It acquires more APs [START_REF] Ali | Recognizing Keystrokes Using WiFi Devices[END_REF][START_REF] Arshad | Wi-Chase: A WiFi based Human Activity Recognition System for Sensorless Environments[END_REF] as well as other detectors for great accuracy. Currently, some studies integrate Signal strength with sensor information to obtain the same purpose as Wi-Fi signals alone.

5-DISCUSSION

In this part, we compare prior classification techniques for several of the baseline methods. Using a waist-mounted accelerator, they devised a method for collecting data from 6 participants on 12 everyday tasks. This paper presented a way to maximize signal processing within the wearable unit's PCB [START_REF] Palipana | FallDeFi: Ubiquitous Fall Detection Using Commodity Wi-Fi Devices[END_REF]. Their concept uses embedded cognition and actual categorization systems. Their total accuracy was 90.8 percent, while postural orientation identification was 94.1 percent and potential fall detection was 95.6 percent.

In contrast, the study [START_REF] Paul | MobileRF: A Robust Device-free Tracking System Based on a Hybrid Neural Network HMM Classifier[END_REF] In recent years, deep learning and generic classification algorithms have been used to recognize sensor-based activity. Semi-supervised ML based motion detection approach for a little quantity of labelled training data to solve the problem of incorrect labelling. [START_REF] Prasertsung | How Does Coffee Shop Get Crowded?: Using WiFi Footprints to Deliver Insights into the Success of Promotion[END_REF] utilized an unsupervised machine learning approach based on KMeans clustering to detect human activity. However, these approaches perform poorly when the datasets contain both static and dynamic activity. While [START_REF] Ramadan | Energy aware routing algorithm in manet using linear programming[END_REF] began fresh research on estimating a user's path using sensor data. This could enhance context-aware services, and location-aware services, they claim. In order to enhance mobile detection and recognition with erroneous time stamps, [START_REF] Kun Qian | Enabling Contactless Detection of Moving Humans with Dynamic Speeds Using CSI[END_REF] Using machine learning algorithms, fine-grained Wi-Fi signal information accurately represents micro-mobility behavior, perceives the environment, and anticipates unknown behavior. Several research groups focus on device-free motion detection Wi-Fi signals.

 Human Detection: Researchers are focusing on noninvasive human detection. Noninvasive means no attachment required, and passive participant in detection. Non-invasive applications can increase people's freedom (convenience) and lower hardware costs. For now, it poses severe obstacles such as reliance on environment and good quality data.

 Identifying Motions: The wireless channel between both the application and the AP is supposed to change. The finegrained multi-path topology may vary as the surroundings or device shifts. RSS cannot capture small variations in the wireless channel since it collects an average indicator of all multi-path variables. So, in the complexity environment, we use CSI or AoA to identify between motions.

 Tracking User Activity: Monitoring user behavior uses Wi-Fi signals to monitor human behavior and forecast unknown behavior. Wi-Fi connections can track shoppers at the entryway. We use fine-grained Wi-Fi signal information to follow and evaluate human behavior.

CONCLUSION

Activity identification is the next wave of context-aware customized applications in several developing computer domains. However, being a new area of study, sensor-based activity identification has little survey works. Most researchers struggle to locate benchmark datasets, which hampers their work. This study reviews the state-of-the-art human motion detection utilizing Wi-Fi and sensors. These dataset's features, activity classifications, sensor types, and devices are described in detail. We've also compiled a list of all possible sensing and application technologies for creating new datasets. Several noise filtering approaches, filter selection, segmentation methods, and window length selection parameters have been detailed. Previous activity recognition approaches have also been summarized and analyzed.

There are also several suggestions for further study into more realistic and widespread circumstances. An overview of motion detection techniques is presented in this paper, as motion has a significant impact on Wi-Fi transmissions. To begin, we'll go over some basic knowledge about Wireless signals and activity types. Following that, we will discuss various methods of detecting mobility, including probability model-based, fingerprint-based, and crowdsourcing-based methods. Furthermore, we demonstrate how to explore the effects of motion in applications that take place in an indoor environment. Finally, in the future, we will release additional applications that will be dependent on Wi-Fi signals.

Fig. 2 . 1 -

 21 Fig. 2. The classification different common activities techniques for human. In most situations, the correlation between completed tasks is inconsistent during the duration of the activity, making identification even more difficult. For example, whereas sitting and standing are closely linked, they are quite distinct from walking. Transitional activities may be classified into four categories [25]: 1-Static to Static Postural Transitions. 2-Static to Dynamic Postural Transitions 3-Dynamic to Static Postural Transitions. 4-Dynamic to Dynamic Postural Transitions.

Figure 3

 3 Figure 3 below divides motion patterns into three types. First, target motions have a massive effect on Wi-Fi signals in

Fig. 3 .

 3 Fig.3.: The intersection between Motion Pattern along with Target/non-target Motion along with Smart Phones. It is the main obstacle for current Wi-Fi-based applications. Finally, wireless device latency effects motion pattern. a-Target Motion: Target motion depicts an object's activity in an indoor setting. The target's motion and direction are crucial factors in assessing the influence of motion on Wi-Fi transmissions. A moving target can alter the range between the object and the transmitter, enhancing the multi-path impact. Wi-Fi signal effects caused by object movements can anticipate target traces and behavior [29]. b-Non-target Motion: Non-target objects are persons who do not engage in the experiment but effect Wi-Fi transmissions. Non-target activities modify Wi-Fi signals faster than static targets. In this case, distinguishing non-target activities with static objects is critical for Wi-Fi based applications. DeMan uses chest motion signal model to identify object activity from non-target activity [30]. c-Wireless Device Jitter: In mobile situations, it is difficult to maintain constant state. The target's arm movement causes a slight shift in Wi-Fi signals. If it simply uses Wi-Fi signals, it's hard to tell the difference. As example, word recognition algorithms establish a relationship model among keywords and Wi-Fi signal variations represented by keyboards by imposing environmental constraints [31].

3. 1 . 1 . 2 Fig. 4 :

 1124 Fig. 4: Raw CSI observations might not represent the mechanism CSI processes; as it vary with both time and sub-channels

2 )

 2 Lowering Device Cost: Wi-Fi offered a moving target to replicate the antenna array (Fig. It can lower device costs and improve applications including indoor localization, people tracking, and access management.

Fig. 5 . 3 )

 53 Fig.5.: The detection of moving objects through Single Antenna and Antenna Array

Table 2

 2

	below summarizes signal conversion
	techniques.

Table 2 :

 2 Approaches for Wi-Fi Sensing Signal Transformation

	Technique	Equation
	Fast Fourier
	Discrete Wavelet
	Short Time Fourier
	Discrete Hilbert

With an LPF, FFT can eliminate high frequency sounds. It can also acquire target signals with Band Pass Filters (BPF). Examples of this include when a person is stationary or moving nearby. The Short-Time Fourier Transform (STFT) splits the input into equal-length segments and computes the FFT coefficients independently for each segment, as shown in The acquired data is used to train a probability model. Nevertheless, probability model-based methods are not universal. Horus displays model invalidation whenever the environment changes. We illustrate two flaws in probabilitybased techniques [48].

the table above

[START_REF] Kim | Device-free Activity Recognition Using CSI Big Data Analysis: A Survey[END_REF]

. By displaying data from both time and Time-dependent environment: The same device gathers frequency, STFT may detect changes in dominating frequencies over time. As seen in the Table above, DHT adds a /2 phase shift to the lower frequency range of FFT. It transforms a time series of legitimate data into a complicated helical sequence. DHT can analyze the immediate information from a certain environment at various times. Also, the probability pattern of every training differs somewhat, causing a huge inaccuracy to applications reliant on Wi-Fi signals

[START_REF] Li | WiFinger: Talk to Your Smart Devices with Fingergrained Gesture[END_REF]

. characteristics of a CSI measurement series. STFT does not Instability: The probability theory depends on the training ensure good frequency and temporal resolution

[START_REF] Amal | High Connectivity with Minimum BER in Wireless Sensor Networks[END_REF]

.

  proposes 1D Haar-like filtering approaches, which are not only novel feature extraction techniques but also need less computing. Their technique improved recognition accuracy by 93.91 percent while lowering computation costs by 21.22 percent.

	To make features more robust, [70] used both (1-Kernel
	Component Analysis & 2-Linear Discriminant Analysis)
	following extraction. Finally, they utilized a DBN to train the
	features. They found 89.61 percent accuracy, beating out
	multi-class SVM (82.02 percent) and Artificial Neural
	Networks (65.31 percent ).

  in their research used EM+Sparse and EM+Dense techniques for the HASC and UCI HAR datasets.

	Hardware-friendly SVM Classifier technique employs fixed-
	point arithmetic for the classification of actions rather than the
	conventional. In their research [75] introduced the Mod
	method using Random Forest classifiers to classifying
	mobility and distribution and transportation. A weighted
	mixture of multiple classifiers is utilized in earlier work [76]
	to recognize activity data from body sensors.
	6. FUTURE WORKS
	Future study should analyze resource use, including memory,
	CPU, sensor count, and most significantly, battery usage. The
	most prevalent trade-off between identification accuracy,
	precision, and resource use should be investigated further. A
	collection of classifiers could be used to correctly identify
	comparable behaviors like sitting and standing, walking
	upstairs and downstairs. Most current efforts have failed to
	differentiate comparable actions precisely using one
	classifier. Future plans should also include working with
	incorrectly classified manual training data, including walking
	activity being mislabeled as running owing to human error.
	Video data fusion with sensor data is an important topic to
	investigate.
	Using a deep recurrent neural network, Inoue et al. [74]
	presented a technique with high throughput using raw
	accelerator data. other simplistic techniques. The Multi-Class


A Manceau
email: alain.manceau@ujf-grenoble.fr

S Skanthakumar

L Soderholm

PDF analysis of ferrihydrite: Critical assessment of the underconstrained akdalaite model

Keywords: structure, ferrihydrite, pair distribution function, PDF, HEXS

In an effort to shed light on the intricate structure of ferrihydrite, its pair distribution function (PDF) derived from high-energy X-ray scattering (HEXS) data was refined with the single-phase akdalaite model, possessing 20% of the Fe atoms in tetrahedral coordination, and a modified akdalaite model in which Fe has only octahedral coordination. The second model is analogous to the predominant f-phase (ABAC stacking sequence) of classical multi-phase ferrihydrite. The contribution from the disordered d-phase component (randomly stacked ABA and ACA doublelayer fragments) of the classical model was recovered in the modified akdalaite description by increasing the atomic motion of the ABAC motif above the double-layer distance 4.2 Å to simulate aperiodic stacking faults. Results show that the original and modified akdalaite representations provide near-identical fits to the ferrihydrite PDF. In the original single-phase and periodic model, the plurality of the Fe-O and Fe-Fe distances resulting from phase mixtures and defects are reconciled artificially by taking a large unit-cell with three independent Fe sites, two Fe coordinations, and underconstrained atomic positions. Correlation matrices reveal that many fitted parameters are linearly correlated, thus explaining the crystallographic and chemical inconsistencies of the as-refined akdalaite model which have been identified in the literature. Structurally more constrained, the modified akdalaite model does not suffer from bias and provides a more robust description of the PDF data. However, because structural defects and inhomogeneities are not physically present but introduced artificially in PDF modeling, the crystallographic description of ferrihydrite by real-space modeling of HEXS data has an idealized character. To facilitate further understanding of the ferrihydrite structure, the PDF data are provided as supplementary material for interlaboratory testing, and as a resource as more sophisticated tools may be brought to bear on this complex problem.

INTRODUCTION

Ferrihydrite (Fh), of average composition FeOOH•0.2-0.4H 2 O [START_REF] Rancourt | Constraints on structural models of ferrihydrite as a nanocrystalline material[END_REF][START_REF] Hiemstra | A surface structural model for ferrihydrite I: Sites related to primary charge, molar mass, and mass density[END_REF], is the most common iron oxyhydroxide in soils, oxidized sediments and mine wastes, the main iron-rich core of the ferritin protein present in all kingdoms of life, and a likely constituent in extraterrestrial materials [START_REF] Cowley | The structure of ferritin cores determined by electron nanodiffraction[END_REF][START_REF] Fortin | Formation and occurrence of biogenic iron-rich minerals[END_REF][START_REF] Farrand | Discovery of jarosite within the Mawrth Vallis region of Mars: Implications for the geologic history of the region[END_REF][START_REF] Theil | Ferritins for chemistry and for life[END_REF]. It is also a key reactive nanoparticle that regulates nutrient availability, the mobility of metal(loid)s contaminants such as arsenic, and an efficient catalyst of the degradation of organic polluants and H 2 O 2 decomposition [START_REF] Jambor | Occurrence and constitution of natural and synthetic ferrihydrite, a widespread iron oxyhydroxide[END_REF][START_REF] Cornell | The Iron Oxides: Structure, Properties, Reactions, Occurrence and Uses[END_REF][START_REF] Ma | New insight on kinetics of catalytic decomposition of hydrogen peroxide on ferrihydrite: Based on the preparation procedures of ferrihydrite[END_REF]. Although ferrihydrite is critical to numerous geochemical and biological processes, and a material of choice in technological and industrial applications, its atomic structure has remained a point of speculation. Five structural models have been proposed over the years [START_REF] Harrison | Ferric oxyhydroxide core of ferritin[END_REF][START_REF] Towe | Mineralogical constitution of colloidal "hydrous ferric oxides[END_REF][START_REF] Eggleton | New data and a revised structural model for ferrihydrite[END_REF][START_REF] Drits | Structural model for ferrihydrite[END_REF][START_REF] Michel | The structure of ferrihydrite, a nanocrystalline material[END_REF]; the first three have been invalidated [START_REF] Drits | Structural model for ferrihydrite[END_REF], and the two most recent only partly accepted, because neither of them satisfactorily describe all X-ray, electron and neutron diffraction, and spectroscopic data. The two competing structural descriptions are expressed as the 'Drits model', which is multi-phase, and the 'Michel model', which is single-phase and isostructural to akdalaite ( VI Al 8 IV Al 2 O 14 (OH) 2 ; Fig. 1) [START_REF] Drits | Structural model for ferrihydrite[END_REF][START_REF] Michel | The structure of ferrihydrite, a nanocrystalline material[END_REF].

The Drits multi-phasic model was derived from powder X-ray diffraction data. It is composed dominantly of the "f-phase" (FeO 0.85 OH) mixed with lesser amounts of the "d-phase" (FeOOH) and nanocrystalline hematite (-Fe 2 O 3 ). The f-phase consists of oxygen and hydroxyl sheets stacked in an ABAC packing sequence along the c direction, and Fe atoms which occupy at random 50% of the octahedral sites in each anionic layer (Fig. 1a). The d-phase is a disordered feroxyhite (-FeOOH) and consists of ABA and ACA double-layer fragments randomly stacked. The three components of the Drits model have been observed using high-resolution transmission electron microscopy (HRTEM), including single-crystal electron nanodiffraction [START_REF] Cowley | The structure of ferritin cores determined by electron nanodiffraction[END_REF][START_REF] Janney | Structure of synthetic 2-line ferrihydrite by electron nanodiffraction[END_REF]Janney et al., , 2001)). The feroxyhite-type local structure of the d-phase was described in terms of a "double chain structure" by [START_REF] Janney | Structure of synthetic 2-line ferrihydrite by electron nanodiffraction[END_REF], but in reality this structural component is the same as the d-phase [START_REF] Manceau | Evaluation of the structural model for ferrihydrite derived from real-space modelling of high-energy X-ray diffraction data[END_REF]. The alternative akdalaite model for ferrihydrite was derived from the pair distribution function (PDF) analysis of high-energy X-ray and neutron scattering data [START_REF] Michel | The structure of ferrihydrite, a nanocrystalline material[END_REF]. It has the same ABAC stacking sequence as the f-phase, but differs from it by 20% Fe occupancy of the tetrahedral sites and 80% Fe occupancy of the octahedral sites and fewer OH groups (Fig. 1b).

The Drits model accounts for all available chemical, structural and spectroscopic data except the PDF, which does not fit well. In addition, it predicts that ferrihydrite containing ordered feroxyhite fragments would have seven diffraction lines (7Fh), not six (6Fh) as commonly observed for natural and synthetic crystalline ferrihydrite [START_REF] Jambor | Occurrence and constitution of natural and synthetic ferrihydrite, a widespread iron oxyhydroxide[END_REF][START_REF] Cornell | The Iron Oxides: Structure, Properties, Reactions, Occurrence and Uses[END_REF]. This prediction has been verified recently with the successful synthesis of a well-crystallized seven-line ferrihydrite (Fig. 2) [START_REF] Berquo | High crystallinity Siferrihydrite: An insight into its Néel temperature and size dependence of magnetic properties[END_REF]. In contrast to the Drits model, the akdalaite model reproduces the PDF for both highly defective two-line ferrihydrite (2Fh) and crystalline six-line ferrihydrite (6Fh), but is inconsistent with other experimental observations [START_REF] Manceau | Incorporation of Al in ferrihydrite: Implications for the structure of ferrihydrite[END_REF]. Two important shortcomings of the akdalaite structure are the failure to reproduce the X-ray diffraction (XRD) pattern of 6Fh and 7Fh (Fig. 2) [START_REF] Rancourt | Constraints on structural models of ferrihydrite as a nanocrystalline material[END_REF]Manceau, 2012), and the lack of evidence for tetrahedral Fe, as reported in the most diagnostic spectroscopic study to date [START_REF] Paktunc | Incorporation of Ge in ferrihydrite: Implications for the structure of ferrihydrite[END_REF]. Because the akdalaite model entirely relies on the interpretation of the ferrihydrite PDF, results warrant further examination.

In PDF analyses, a structural model is assumed and its unit cell dimensions and atomic coordinates regressed against the experimental data under the symmetry constraints of a space group [START_REF] Billinge | Beyond crystallography: the study of disorder, nanocrystallinity and crystallographically challenged materials with pair distribution functions[END_REF][START_REF] Neder | Structure of nanoparticles from powder diffraction data using the pair distribution function[END_REF][START_REF] Farrow | PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals[END_REF][START_REF] Proffen | Advances in total scattering analysis[END_REF]. As powerful as this method is, its applicability for the resolution of the average structure of defective and multi-component nanomaterials is intrinsically limited by the presumption of a unit cell repeated in three dimensions. If defects are ordered, they can be described with proper models using a supercell. In the case of aperiodic stacking fault with low probability, modeling still is possible, although in an approximate way, by introducing anisotropic atomic displacements (i.e., U parameter) in the stacking direction [START_REF] Petkov | Structure of V 2 O 5 .nH 2 O xerogel solved by the atomic pair distribution function technique[END_REF][START_REF] Masadeh | Quantitative size-dependent structure and strain determination of CdSe nanoparticles using atomic pair distribution function analysis[END_REF]. Here, these two approaches are deceptive because ferrihydrite is a mixture of nanoparticles with different structures, shape, domain size, point defects, and stacking disorder, and also has randomness. Clearly, its structure is too complex to be captured realistically by PDF with a simple physical description, as is the case also for nanostructured and defect phyllomanganates (Manceau et al., 2013). This difficulty raises questions about the reason why the periodic akdalaite structure provides a good fit to PDF. We show that the large range of interatomic distances and bond angles, typical of Fh, is reconciled in the akdalaite fit with an apparently unfaulted average structure by employing a large unit-cell with three independent Fe sites and under-constrained atomic positions. The demonstration is carried out through comparison of the best-fit calculations obtained, (1) with the original akdalaite model, in which two Fe are octahedral and one tetrahedral (Fig. 1b), and (2) a modified akdalaite model in which Fe is fully octahedral with 50% occupancy (Fig. 1c).

EXPERIMENTAL METHOD AND DATA REDUCTION

The PDF of the 6Fh sample used to derive the Drits model (Fig. 1a) was measured at the Advanced Photon Source (APS) on beamline 11-ID-B with an X-ray energy of 90.480 keV (= 0.13702 Å). For consistency quality of the results, the total X-ray scattering data used to calculate the PDF was acquired on the same instrument as the one used to derive the akdalaite model [START_REF] Michel | The structure of ferrihydrite, a nanocrystalline material[END_REF]. The total scattering structure function, S(q), was obtained as described previously [START_REF] Soderholm | Determination of actinide speciation in solution using high-energy X-ray scattering[END_REF][START_REF] Skanthakumar | Studying actinide correlations in solution using highenergy x-ray scattering[END_REF], and the PDF was calculated by integration of the reduced structure function F(q) [START_REF] Egami | Underneath the Bragg Peaks: Structural Analysis of Complex Materials[END_REF][START_REF] Billinge | Beyond crystallography: the study of disorder, nanocrystallinity and crystallographically challenged materials with pair distribution functions[END_REF]) over the 0.5 ≤ q ≤ 21 Å -1 interval. The PDF data are provided as Supplementary material for interlaboratory testing and as a resource for further analysis with more sophisticated tools.

RESULTS

Simulation of the ferrihydrite PDF with tetrahedral and octahedral Fe

The PDFs for the six-line ferrihydrites of Michel (fhyd6) and Drits (6Fh) are essentially identical (Fig. 3a,b). The positions and relative intensities of the PDF peaks are in close proximity out to r max = 20 Å, indicating that the two nanomaterials have about the same domain size. The first peak at r = 1.99 Å is from the Fe-(O,OH,H 2 O) pairs, and the next two at r ~ 3.0 Å and 3.4-3.5 Å dominantly from the Fe-Fe distances across shared-edges and shared-corners (Fig. 1a).

Lattice constants and atomic positions were refined in the same space group (P6 3 mc) using the same least-squares PDF-profile fitting program (PDFgui 1.0) [START_REF] Farrow | PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals[END_REF] as [START_REF] Michel | The structure of ferrihydrite, a nanocrystalline material[END_REF]. The structure of the model and its parametrization in PDFgui are shown in Supplementary Figure 1. A main criticism of the 2007 refinement (fhyd6) has been its failure to satisfy the bond valence sums of cations and anions, in violation of Pauling's 2 nd rule (Table 1) [START_REF] Manceau | Evaluation of the structural model for ferrihydrite derived from real-space modelling of high-energy X-ray diffraction data[END_REF]. This inconsistency was corrected in 2010 with a new refinement (ferrifh) [START_REF] Michel | Ordered ferrimagnetic form of ferrihydrite reveals links among structure, composition, and magnetism[END_REF], but at the expense of introducing strong distortions in violation of Pauling's distortion rule (Table 2) (Manceau, 2011). Twenty parameters were allowed to vary in the fhyd6 refinement and nineteen in the ferrifh refinement. Adjusting the 6Fh PDF with twenty or nineteen parameters, similar to the fit strategy adopted for the fhyd6 and ferrifh refinements, produced near-identical agreement factors (R w = 28.5 % vs. 27.0 %; Supplementary Tables 1 and2), and the same fit quality as the akdalaite model (R w = 26.7 %; Fig. 3a,b). The new atomic coordinates and unit cell parameters coincide with those reported previously. Electrical charges are also unbalanced and the Fe polyhedra strongly distorted in the new simulation (Tables 1,2). The polyhedral representations of the two refined structures show that some Fe octahedra are anomalously elongated and the tetrahedral Fe atom excessively off-centered and unrealistically close to one tetrahedral face (Fig. 1b), consistent with previous observations for fhyd6 [START_REF] Manceau | Evaluation of the structural model for ferrihydrite derived from real-space modelling of high-energy X-ray diffraction data[END_REF].

Parameter correlations, which are not reported in [START_REF] Michel | The structure of ferrihydrite, a nanocrystalline material[END_REF], show that many fitted parameters are linearly correlated ( = 1) when twenty variables are refined simultaneously (Supplementary Table 1). Fixing the VI Fe1 site occupancy to 1.0 suppresses almost all correlations, except the VI Fe2 and IV Fe3 occupancies, which remain severely anti-correlated ( = -0.87; Supplementary Table 2). This result casts doubt on the accuracy of the precision reported in the previous refinements. High correlations between atomic coordinates mean that some atoms can be moved in one direction and others in another with no significant change in quality of the fit to the PDF. For example, constraining the model to satisfy Pauling's bond valence sum introduces, or reinforces, other structural irregularities, such as the violation of Pauling's distortion rule (Tables 1,2). One reason for model bias is the impossibility to define upper and lower bounds for the adjusted values in PDFgui, causing some parameters to take unrealistic values and to be correlated if the refinement is under-constrained (Supplementary Tables 1 and2). The akdalaite model has more adjustable parameters than independent data points in the PDF. The PDF fitting software seeks structural solutions in a deep flat-bottomed valley with countless "local" minima, and so will always find the best "local" solution that it can, which is highly dependent on the initial parametrization. Actually, modelers are cautioned against the risk of overfitting PDF data in the PDFFIT User Guide: ''The problem of determining the structure of a nanoparticle remains difficult.

PDFgui is not intended to necessarily provide the solution; it is rather a helpful tool in the process of determining new details and exploring the space of possible solution candidates, yielding success in some instances'' [START_REF] Farrow | PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals[END_REF].

Simulation of the ferrihydrite PDF with octahedral Fe

The co-existence in the Drits model of the f-phase, d-phase, and nanohematite with different space groups ( P31c , P3m1, and R3c , respectively) makes the PDF parametrization difficult. In addition, the multi-component model has four Fe positions and four O positions; clearly the data lack sensitivity to quantify the full distribution of all generated atomic pairs. As a first approximation, the problem can be simplified by omitting contributions from the minor d-phase and nanohematite. Also, the d-phase is too disordered to produce a signal at intermediate to long distances (r > ~5 Å). Another source of complication is that the PDF sees the short-to long-range structure of the f-phase, which deviates from the Bragg-average structure derived from diffraction. The f-phase was refined with only one crystallographic parameter, the z position of Fe. Its asymmetric unit contains one Fe in the 4f position (1/3, 2/3, z) and two O atoms at the special positions of undeformed ABAC close packing. Therefore, the eight octahedra from the 2x2x1 supercell represented in Figure 1c are all equivalent in the Drits model, and have only two Fe-O distances. Clearly, this model is now over-constrained and its symmetry needs to be lowered to fit the PDF. In comparison, the asymmetric unit of the akdalaite structure has three Fe (two VI Fe and one IV Fe) and four O atoms, resulting in eight Fe-O distances and 10 independent crystallographic positions refined in the PDF analysis (Supplementary material).

A f-phase model suitable for PDF refinement can be derived from the akdalaite structure with the following changes and constraints: (1) the IV Fe position is unoccupied; (2) one of the three VI Fe atoms in the AB and AC layers are moved to the adjacent BA and CA layers to satisfy the 50% occupancy of each anion layer in the f-phase; (3) the distribution of Fe across the anion layers is such that there are no face-sharing arrangements between Fe octahedra along the B and C planes of the structure (Fig. 1c, Supplementary Fig. 2). The modified akdalaite model also has 10 independent crystallographic positions (3 VI Fe + 4 O positions), but a narrower distribution of the Fe-O and Fe-Fe distances because Fe has only one coordination ( VI Fe) vs. two in the original akdalaite model ( VI Fe + IV Fe).

Correlated atomic motion was accounted for differently in the fits of the original and modified akdalaite models to the 6Fh PDF. The motion of the two contributing atoms in an atomic pair is uncorrelated at large distance, but correlated when their distance separation is small [START_REF] Jeong | Lattice dynamics and correlated atomic motion from the atomic pair distribution function[END_REF]. This effect sharpens the first peaks in the observed PDF. The radial dependence of this effect on the PDF peak width ( ij ) usually is described with a delta/r or delta/r 2 function, as was the case for the original akdalaite model. The analytical expression implemented in PDFgui is:

' 2 2 12 2 1 ij ij broad ij ij ij Qr rr      
where ' is the peak width without correlation, calculated from the U values of the (an)isotropic displacement parameter (Supplementary material), and Q broad is the experimental broadening. However, a continuous delta function may not be the most appropriate term to account for the loss of structural coherence caused by stacking faults, especially if they occur at some specific distance separations, as the randomness of the ABA and ACA double-layer fragments from the d-phase would suggest. This inference is supported by the comparison of the PDFs from phyllomanganates (Fig. 4) (Manceau et al., 2013). The KBi8 and AcidBir layer manganates have the same structural formula and short-range layer structure, but a different density of stacking faults along the layer stack. The most c-disordered material (AcidBir) shows a discontinuity in peak intensity at distances greater than the interslab separation of 7.2 Å. A more extreme case is -MnO 2 , in which the MnO 2 layers are randomly stacked. The loss of structural coherence in the c direction beyond 7.2 Å is manifested in the PDF as a sharp decrease in peak intensity beyond this distance (Fig. 4b). This type of disorder cannot be modeled with a delta function (Manceau et al., 2013).

Simulations of the 6Fh PDF with a delta function to test a similar effect in ferrihydrite resulted in a significant amplitude mismatch between experiment and theory beyond r = 4.5 Å. Here, the loss of structural coherence occurs on a length scale corresponding to the separation between two next-nearest O/OH sheets, i.e., to the thickness of a double-layer fragment. This effect on the PDF can be accounted for empirically by defining a low-r to high-r PDF peak ratio with a cutoff value of 4.5 Å. The value of the peak ratio, which depends on the density of stacking faults, was optimized in the refinement with the fit parameter sratio replacing the delta function. The fit to the modified akdalaite model with nineteen parameters returned an R w value of 32.7 %, which is about 20% higher than the best-fit value obtained with the original akdalaite model (Fig. 3, Supplementary Table 3). Does it mean that the modified model is less reasonable? We contend instead that it provides a more realistic description of the data based on the following considerations.

First, comparing the two theoretical PDFs (Fig. 3c), we see that they are nearly identical, meaning that the two models indistinctly capture the short-and longer-range correlations of the ferrihydrite PDF. The small difference of amplitude at 4.7 Å is related to how stacking faults are captured empirically in the two refinements.

Second, a two-site occupation model ( VI Fe + IV Fe) is expected to yield a better fit than a onesite model ( VI Fe). However, the difference between the two fits is marginal, and therefore insignificant given that structural defects and variability are not physically present but introduced artificially in the two models.

Third, correlations between parameters are all lower than 0.8 in the modified akdalaite model (Supplementary Table 3). Although somewhat arbitrary, this value corresponds to the hard-coded PDFgui threshold below which the refinement parameters are considered independent. Therefore, although the quality of the PDF fit improves when Fe is octahedral and tetrahedral, parameters are correlated (Supplementary Tables 1 and2) indicating that the robustness of the modified akdalaite model in fact is improved relative to the original two-site model. Although the optimized one-site model is statistically more robust, the structure remains strongly distorted; the real sample is more complicated and cannot be assumed to be single-phase. This distortion is evaluated in Table 2 with the eccentricity parameter, which measures the distance between the centroid of the Fe polyhedron and the central Fe atom, and the volume eccentricity, which describes the volume distortion of the polyhedron [START_REF] Balic-Zunic | Determination of the centroid or 'the best centre' of a coordination polyhedra[END_REF][START_REF] Balic-Zunic | Use of the three-dimensional parameters in the analysis of crystal structures under compression[END_REF]. The larger the eccentricity, the more a polyhedron deviates from the ideal.

Fourth, and most compelling, a comparison of the first PDF peaks for 6Fh and the crystalline phyllomanganate KBi8, used as a reference for octahedral Mn coordinated to 6O at 1.91 Å [START_REF] Gaillot | Structure of synthetic K-rich birnessites obtained by high-temperature decomposition of KMnO4. I. Two-layer polytype from a 800°C experiment[END_REF], shows that Fe is fully octahedral in ferrihydrite, similar to Mn in KBi8 (Fig. 5). The two metal-oxygen peaks are symmetrical, and the Fe-O peak broader than the Mn-O peak because the Fe atoms are bonded to three types of ligands, O, OH and H 2 O, in various polyhedral associations. If 20% of the Fe atoms were tetrahedrally coordinated, as in the original akdalaite model, the distribution of the Fe-(O,OH,H 2 O) distances would be asymmetric and the PDF peak broadened to lower r-values relative to the KBi8 peak.

To date, there is a consensus that the main structural component of six-line ferrihydrite has a hexagonal ABAC layer stacking sequence. A main difference between the Drits and Michel models is the site occupation of Fe, which is fully octahedral in the first model, and octahedral and tetrahedral in the second model. We showed that introducing three Fe sites and two Fe coordinations, as in the Michel model, slightly improves the match to PDF data, but decreases confidence in the results.

CONCLUDING REMARKS

The PDF method was originally a tool for studying amorphous bulk materials like glasses, liquids, and solutions [START_REF] Waseda | The structure of non-crystalline materials[END_REF][START_REF] Magini | X-ray diffraction of ions in aqueous solutions: hydration and complex formation[END_REF][START_REF] Fischer | Neutron and x-ray diffraction studies of liquids and glasses[END_REF], and short-range ordered inorganic materials [START_REF] Billinge | Mercury binding sites in thiol-functionalized mesostructured silica[END_REF], to less than ~10 Å. Using this technique to determine the average structure of defective nanocrystals from full-pattern fitting of PDF decreases the sensitivity to details of the local structure, as reported recently for disordered phyllomanganates (Manceau et al., 2013). Similar issues were encountered in the analysis of biogenic MnO x produced by freshwater Acremonium sp. fungi. Incorrect a priori model assumption led to conclude that this material has a todorokite-type three-dimensional tunnel structure [START_REF] Petkov | Atomic-scale structure of biogenic materials by total X-ray diffraction: A study of bacterial and fungal MnO x[END_REF], when in reality the structure is two-dimensional [START_REF] Grangeon | Structure of nanocrystalline phyllomanganates produced by freshwater fungi[END_REF]. Therefore, PDF is of great value in determining the local atomic structure of materials, but can be biased for the average structure analysis of defective and multi-component materials because structural imperfections and heterogeneities are difficult to implement analytically. If caution is not exercised, multiple solutions may occur not only within a given model, but also among different models. For these types of materials, physically based models are easier to fit to HEXS data in reciprocal-space using Bragg analyses and the Debye equation [START_REF] Fernandez-Martinez | The structure of schwertmannite, a nanocrystalline iron oxyhydroxysulfate[END_REF]Manceau et al., 2013). and in perspective to show the polyhedral associations. Adapted from Manceau et al. (2011). (b and c) Akdalaite model [START_REF] Michel | The structure of ferrihydrite, a nanocrystalline material[END_REF], and modified akdalaite model which is structurally analogue to the 2x2x1 supercell of the f-phase [START_REF] Manceau | Incorporation of Al in ferrihydrite: Implications for the structure of ferrihydrite[END_REF][START_REF] Paktunc | Incorporation of Ge in ferrihydrite: Implications for the structure of ferrihydrite[END_REF]. The akdalaite model is composed of O,OH sheets closely-packed with ABACA stacking, and Fe atoms in both octahedral (80% of Fe sites) and tetrahedral (20% of Fe sites) coordination. The fphase has the same anionic packing, but a different proportion and distribution of O and OH, and 100% of the Fe atoms are octahedral occupying 50% of the octahedral sites in each anion layer [START_REF] Drits | Structural model for ferrihydrite[END_REF]. Distribution of Fe across the anion layers is such that there are no face-sharing arrangements between Fe octahedra along the B and C planes of the structure and that hydroxyls are confined to the A and oxygen to the B and C layers. (b) Structure refined from the 6Fh PDF with nineteen parameters (Supplementary Table S3).

Figure 2

Experimental XRD patterns for six-line [START_REF] Manceau | Evaluation of the structural model for ferrihydrite derived from real-space modelling of high-energy X-ray diffraction data[END_REF] and seven-line [START_REF] Berquo | High crystallinity Siferrihydrite: An insight into its Néel temperature and size dependence of magnetic properties[END_REF] ferrihydrite, and calculated XRD pattern for the fhyd6 variant of the akdalaite model [START_REF] Michel | The structure of ferrihydrite, a nanocrystalline material[END_REF].

Figure 3 (a) Experimental PDF for six-line ferrihydrite (fhyd6) and refined fit of the akdalaite model reproduced from Figure 2a of [START_REF] Michel | The structure of ferrihydrite, a nanocrystalline material[END_REF]. (b) Experimental PDF for 6Fh and refined fit of the akdalaite model. (c) Comparison of the best-fit PDFs obtained with the akdalaite model (Fig. 1b) and the modified akdalaite model (Fig. 1c).

Figure 4

Overlay plots of the experimental PDFs for three phyllomanganates having different layer stacking order [START_REF] Zhu | Structural study of biotic and abiotic poorly-crystalline manganese oxides using atomic pair distribution function analysis[END_REF]Manceau et al., 2013). K-birnessite (KBi8) is c-ordered with few stacking faults; -MnO 2 has turbostratic disorder, and AcidBir has intermediate stacking disorder. KBi8 and AcidBir have nearly the same structural formula, hence a similar short-range layer structure. The severe decrease of the peaks amplitude beyond 7.2 Å is caused by stacking faults which make unequal the layer-to-layer pair distances. Similar effect is observed in ferrihydrite beyond 4.5 Å.

Figure 5

Near-neighbor PDF peaks for six-line ferrihydrite (6Fh) and K-birnessite (KBi8) [START_REF] Gaillot | Structure of synthetic K-rich birnessites obtained by high-temperature decomposition of KMnO4. I. Two-layer polytype from a 800°C experiment[END_REF]Manceau et al., 2013). The difference of average Fe-O (~1.99 Å) and Mn-O (~1.91 Å) distances between the two materials was offset by shifting the KBi8 PDF by +0.085 Å. When aligned, the two peaks appear symmetrical, which argues against the presence of tetrahedral Fe in 6Fh. @1 is the scale factor and @2 is the resolution dampening (Q damp ). Q broad was fixed to 0.069 Å -1 . Full results are listed in Table S2. S3.

FIGURE CAPTIONS Figure 1 .

 CAPTIONS1 FIGURE CAPTIONS Figure 1. (a) Structural representation of the ferrihydrite f-phase in projection along the [ 1 10] axis

  13

  Figure 1

Figure

  Figure S2. Structure of the modified akdalaite model and its parametrization in PDFgui Polyhedral representation of the modified akdalaite unit cell. Independent atoms in the asymmetric unit are labeled. The oxgen atoms and hydroxyls are positioned as in the f-phase (Fig. 1). Screen shot of the PDFgui interface window showing the parametrization of the modified akdalaite model.

Table 1 .

 1 Calculated bond valence sums for three models of the ferrihydrite PDF. The values in bold are unrealistic. From Michel et al. (2007) with VI Fe and IV Fe and 20 parameters adjusted. b From Michel et al. (2010) with VI Fe and IV Fe and 19 parameters adjusted. c This study, with VI Fe and IV Fe and 20 parameters adjusted (Supplementary Table1). d This study with VI Fe and IV Fe and 19 parameters adjusted (Supplementary Table2). e This study with VI Fe only and 19 parameters adjusted.

	Atom Type	Akdalaite model -fhyd6 a	Akdalaite model -ferrifh b	Akdalaite model -this study c	Akdalaite model -this study d	Modified akdalaite model -this study e
	O1	OH	1.87	0.94	2.11	2.29	0.76
	O2	O	2.32	1.89	2.45	2.46	1.69
	O3	O	1.74	1.91	1.77	1.76	1.75-1.82
	O4	O	1.88	2.28	1.80	1.78	1.18-1.24
	Fe1	Fe 3+	2.82	2.97	2.86	2.95	2.39
	Fe2	Fe 3+	3.92	2.97	3.90	3.67	3.79
	Fe3	Fe 3+	2.70	2.74	2.81	2.88	2.79

a

Table 2 .

 2 Evaluation of the distortion of the Fe polyhedra in the different akdalaite models and akaganeite (-FeOOH). Values in bold indicate strong distortion. Distance of the central atom to the centroid. b volume eccentricity calculated as 1 -[(r s -)/r s ] 3 with r s the average distance from the centroid to the ligands. c This study, 20 parameters adjusted (SupplementaryTable 1). d This study, 19 parameters adjusted (Supplementary Table 2).

			Å a	Volume eccentricity b
	Akdalaite model -	VI Fe1	0.103	0.144
	fhyd6 -Michel et al.	VI Fe2	0.082	0.123
	(2007)	IV Fe3	0.155	0.221
	Akdalaite model -	VI Fe1	0.096	0.136
	ferrifh -Michel et al.	VI Fe2	0.285	0.363
	(2010)	IV Fe3	0.090	0.136
	Akdalaite model -this study c	VI Fe1 VI Fe2 IV Fe3	0.127 0.141 0.120	0.175 0.205 0.177
	Akdalaite model -this study d	VI Fe1 VI Fe2 IV Fe3	0.143 0.111 0.275	0.195 0.162 0.364
	Modified akdalaite model -this study	VI Fe1 VI Fe2 VI Fe3	0.179 0.080 0.227	0.234 0.120 0.297
	Akaganeite -(Post et	VI Fe1	0.112	0.159
	al., 2003)	VI Fe2	0.113	0.158
	a

ACKNOWLEDGEMENTS

The work at Argonne National Laboratory was supported by the U.S. Department of Energy, OBES, under contract number DE-AC02-06CH11357.

Table S1. Results from the akdalaite fit to the 6Fh PDF with 20 adjusted parameters.

19 Table S2. Results from the akdalaite fit to the 6Fh PDF with 19 adjusted parameters 21 Table S3. Results from the modified akdalaite fit to the 6Fh PDF with 19 adjusted parameters