Ali El Amine

Mauricio Iturralde

Hussein Al

Haj Hassan
email: hhajhassan@aust.edu.lb

Loutfi Nuaymi

Ali El-Amine

A Distributed Q-Learning Approach for Adaptive Sleep Modes in 5G Networks

Keywords: Energy consumption, 5G, sleep modes, Qlearning

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

With the explosive increase in the number of mobile subscribers and services, mobile networks will have to support a much higher capacity demand [START_REF]Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update[END_REF]. Nevertheless, the growing increase in traffic demand is proliferating the energy consumption of the Information and Communication Technology (ICT) sector. It is estimated that ICT consumes around 4.7% of the world's electrical energy, releasing into the atmosphere about 1.7% of the global CO 2 emissions [START_REF] Gelenbe | The impact of information technology on energy consumption and carbon emissions[END_REF].

On the other hand, the Fifth Generation of Cellular Mobile Communications (5G) is expected to provide ubiquitous internet access with 1000 times higher data rate compared to present cellular systems. As a result, the innovations in 5G systems are not limited to physical layers techniques, but also introduce new network architectures and application scenarios. In particular, a major trend in 5G networks is the deployment of a large number of small-scale BSs, also known as network densification. Trying to achieve this ambitious goal relying on the above paradigm and architecture is not sustainable since it will lead to an energy crunch with serious economic and environmental concerns.

Owing to the economic concerns of mobile operators as well as the environmental ones and in order to cater for the vision of 5G communication systems, a lot of studies have investigated distinct approaches to reduce the energy consumption in mobile networks. Since the energy consumption of a telecommunication network is dominated by the Radio Access Network (RAN) and in particular the BS consuming 75 -80% of the network's energy [START_REF] Debaillie | A flexible and future-proof power model for cellular base stations[END_REF], most of the work focus on reducing the power at this level to enhance the energy efficiency of cellular networks. Several techniques attack the aforementioned challenge on different layers: a) network planning and deployment, b) switching-off techniques, c) radio resource management optimization, d) component level enhancement, and e) the use of renewable energy resources [START_REF] Suarez | An overview and classification of research approaches in green wireless networks[END_REF]. Among the different layers, sleep mode techniques are considered to be among the most efficient approaches for energy savings.

In [START_REF] Debaillie | A flexible and future-proof power model for cellular base stations[END_REF], 5G BSs sleep model are proposed to reduce the energy consumption of a cellular network. The proposed model describes different levels of SM the BS can switch to, where each SM level is characterized by an activation/deactivation period and a power consumption. Implementing these different stages of SM in 4G networks is challenging due to backwards compatibility and reference signaling requirements. However, in 5G, the Cell Reference Signals (CRS) are removed [START_REF] Gpp | On requirements and design of ss burst set and ss block index indication[END_REF] making it possible for a BS to explore these different SM levels. In contrast to models that apply only one type of SM, in this work, we study the trade-off between energy savings and added service delay, i.e., the time the user has to wait in the buffer until the BS reactivates. We consider a cellular network with unbalanced traffic where each BS chooses its appropriate SM level in order to achieve a desirable balance between energy consumption and latency. We propose an adaptive sleep scheme algorithm based on RL that controls the states of the BSs, where each BS has access only to its local information in order to learn the best energy saving policy.

The rest of the paper is organized as follows. Section II presents an overview of the existing work. In Section III, we detail the system model along with the 5G sleep mode model. We give an overview of the distributed Q-learning algorithm in Section IV, whereas the proposed algorithm is presented in Section V. Finally, we present the simulation results in Section VI before concluding in Section VII.

II. RELATED WORK

The literature on Energy Efficiency (EE) cellular networks is huge [START_REF] Wu | Energy-efficient basestations sleep-mode techniques in green cellular networks: A survey[END_REF], [START_REF] Feng | Base station ON-OFF switching in 5G wireless networks: Approaches and challenges[END_REF], and the references therein. BS ON-OFF switching is considered among the best methods to save energy since it does not require changes to current network architecture, and it is easy to implement. This well known method initially proposed in IEEE 802.11b [START_REF]IEEE Std[END_REF] has attracted a lot of attention on the research community. For example, the authors in [START_REF] Peng | Stochastic analysis of optimal base station energy saving in cellular networks with sleep mode[END_REF] studied the energy savings problem by switching-off macro BSs under coverage constraints using stochastic geometry. Their results achieved an EE gain of around 1.6 compared to the case where all the BSs are active. In [START_REF] Feng | Boost: Base station ON-OFF switching strategy for energy efficient massive MIMO hetnets[END_REF], the authors opted to maximize the EE of a heterogeneous network using ON-OFF switching subject to traffic load constraints. In [START_REF] Guo | Delay-constrained energyoptimal base station sleeping control[END_REF], the authors proposed an optimization mechanism based on delay-constrained energyoptimal BS sleeping policies. In [START_REF] Che | Dynamic base station operation in large-scale green cellular networks[END_REF], dynamic programming is applied to find the optimal BS ON-OFF policy given the on-grid energy price in order to minimize the on-grid energy cost purchased by the operator while assuring the downlink transmission quality at the same time. However, the above mentioned work focused only on one level of SM, and do not take into account the activation/deactivation times required for the BS to switch between states ON and OFF.

In contrast to binary BS models (active and sleep), recent models have split the SMs state into several levels [START_REF] Liu | Small cell base station sleep strategies for energy efficiency[END_REF]- [START_REF] Ezzahra | Reinforcement learning approach for advanced sleep modes management in 5G networks[END_REF]. Considering that a BS can switch to different SM levels gives it more flexibility to adjust with the type and pattern of traffic to further enhance the system performance. In [START_REF] Liu | Small cell base station sleep strategies for energy efficiency[END_REF], the EE of a heterogeneous network is studied by switching small cells to different SM levels while preserving the Quality of Service (QoS). Using stochastic geometry, the authors determined the optimal operating probability for each SM level of each BS. However, the proposed solution is offline, and the SM levels discussed are not suitable for 5G networks. In [START_REF] Lähdekorpi | Energy efficiency of 5G mobile networks with base station sleep modes[END_REF]- [START_REF] Ezzahra | Reinforcement learning approach for advanced sleep modes management in 5G networks[END_REF], the authors proposed the concept of Advanced Sleep Mode (ASM) which corresponds to gradual deactivation of the BSs components in order to decrease the energy consumption of the BS. Even though the used sleep model do not violate the 5G requirements, [START_REF] Lähdekorpi | Energy efficiency of 5G mobile networks with base station sleep modes[END_REF], [START_REF] Salem | Advanced sleep modes and their impact on flow-level performance of 5G networks[END_REF] focused on the energy savings potential and not the best SM policy to be applied, while [START_REF] Ezzahra | Reinforcement learning approach for advanced sleep modes management in 5G networks[END_REF] is limited to only one BS.

Recently, artificial intelligence has received significant attention as a highly effective alternative to conventional methods [START_REF] Bengio | Representation learning: A review and new perspectives[END_REF]. In particular, machine learning has found wideranging applications in wireless networks [START_REF] Jiang | Machine learning paradigms for next-generation wireless networks[END_REF]. In [START_REF] Zhao | Transfer learning for QoS aware topology management in energy efficient 5G cognitive radio networks[END_REF], a cognitive engine with reinforcement learning is implemented at each BS to improve the system capacity and QoS. Furthermore, a BS switching operation algorithm is proposed to dynamically switch between sleep and active modes. In [START_REF] Miozzo | Distributed Q-Learning for energy harvesting heterogeneous networks[END_REF], the authors presented a distributed Q-learning-based algorithm that learns energy inflow and traffic demand patterns in a heterogeneous network. By interacting with the environment, each agent (i.e. BS) decides its optimal policy (ON or OFF) to improve the system performance. The authors in [START_REF] Li | Deep Q-Learning based dynamic resource allocation for self-powered ultra-dense networks[END_REF] proposed a method for optimizing ON-OFF policies for ultra dense networks. The mechanism is based on Deep Q-Learning (DQL) to solve the dynamic optimization problem. Using DQL, the authors looked for maximizing the EE while respecting the QoS of the network.

The above mentioned studies take advantage of machine learning in order to find the best ON-OFF policy to reduce the energy consumption of the BS. However, none of them respect the requirement of 5G on the SS bursts that need to be transmitted periodically (ranging from 5 to 160ms); hence, limiting the duration time a 5G BS can switch to SM. For example, [START_REF] Liu | Small cell base station sleep strategies for energy efficiency[END_REF] applies SMs that requires several seconds for the BS to wake up from. The work in [START_REF] Ezzahra | Reinforcement learning approach for advanced sleep modes management in 5G networks[END_REF] use Q-learning to apply 5G adapted SMs; however, the work is limited to only one BS.

In this paper, in contrast to most prior work we focus on 5G SM proposed in [START_REF] Debaillie | A flexible and future-proof power model for cellular base stations[END_REF]. We do not limit the work to only one type of SM, rather we consider a network where each BS can choose different SM states to switch to. We propose a distributed Q-learning approach that finds the best policy for each BS in order to reduce the energy savings while maintaining the QoS of the users under the 5G requirements.

III. SYSTEM DESCRIPTION A. 5G Energy Savings Sleep Modes

In [START_REF] Debaillie | A flexible and future-proof power model for cellular base stations[END_REF], GreenTouch identified four distinct SM levels by grouping sub-components with similar transition latency when being activated or deactivated. The presented model enables to quantify the power consumption of the BS in each of the four SMs. These are:

• SM 1: It considers the shortest time unit of one OFDM symbol (i.e. 71µs) comprising both deactivation and reactivation times. In this mode only the power amplifier and some processing components are deactivated. to the whole radio frame of 1s. It is the standby mode where the BS is out of operation but retains wake-up functionality. Higher energy savings can be achieved when switching BSs to a deeper SM, since more components will be deactivated. However, this will be associated with longer transition latency which may impact the QoS of the system. In Table I, we present the SM levels characteristics.

Along with SM and users' dynamics, the BS has to wake up periodically to send signalling bursts. In contrast to Long Term Evolution (LTE) systems where each antenna must transmit every 0.2 ms a unique CRS for channel quality estimates and mobility measurements among other SS, no CRS is required for 5G [START_REF] Gpp | On requirements and design of ss burst set and ss block index indication[END_REF]. Instead, SS and Physical Broadcast CHannel (PBCH) are transmitted in SS/PBCH block periodically. It has been agreed in Third Generation Partnership Project (3GPP) [START_REF] Gpp | On requirements and design of ss burst set and ss block index indication[END_REF] that this periodicity can be set to any value among [5, 10, 20, 40, 80, 160 ms]. With these values, SM 4 cannot be used. Hence, we limit our work to the first three SM levels.

B. Network Description

We consider a large-scale wireless downlink cellular network composed of M BSs serving K users. We further Whenever a user requests a service from a BS in SM, it triggers the activation mode and the user is buffered until the BS wakes up. This has an impact on the latency added to the system. The deeper the SM is, the more time the user will have to wait until the BS reactivates. When the user is served and if the BS is in idle mode, it goes back to its SM level to save energy until the next users arrival.

We further consider BSs with different users arrival rates. Thus, we divide the BS into two sets. One corresponds to the BSs with high users arrival rate denoted by B Dense , and the other grouping the BSs with low users arrival rate denoted by B Light , such that |B| = |B Dense | + |B Light | = M . Note that the users are uniformly distributed within the cell of each BS.

C. Downlink Transmission Model

We measure the downlink transmission quality between the serving BS m and a user k based on the Signal-to-Interferenceplus-Noise Ratio (SINR) as follows:

SINR m (k) = P Tx m h m (k) σ 2 + m ∈S,m =m P m h m (k) (1)
where P Tx m is the transmitted power of BS m, h m (k) is the channel gain from BS m to user k, which accounts for the path loss and shadowing effect, and σ 2 is the additive white Gaussian noise power density.

We can express the peak rate offered to user k and served by BS m using Shannon-Hartley theorem as follows:

R m (k) = α × W × log 2 (1 + SINR m (k)) (2)
where W represents the bandwidth and α the fraction of bandwidth used for the data transmission.

IV. DISTRIBUTED Q-LEARNING

Distributed Q-learning is an online optimization technique that aims at controlling multi-agent systems, i.e., a system featuring M BSs which take decisions (select the appropriate SM level) in an uncoordinated fashion. Each BS has to learn independently a policy (SM 1, SM 2 or SM 3) through real-time interactions with the environment. Q-learning finds the optimal policy in the sense that it maximizes the expected value of the total reward (Q-value) over all successive episodes. The agents (i.e., BSs) have a partial view of the overall system, and their actions may differ since the users are unevenly distributed over the network. In particular, the decision of a BS to choose a SM level is affected by how many users it has to serve, and on how delay-tolerant these users are.

In Q-learning, each agent takes an action a t m from an action set A, then moves to a new state s t+1 m while receiving a reward r t m . This reward is then used to update the Q-value locally, Q(s t m , a t m ), indicating the level of convenience of selecting action a t m when in state s t m . The Q-value is updated following the update rule:

Q(s t m , a t m ) ← Q(s t m , a t m )+ α[r t m + γ max a∈A Q(s t+1 m , a t+1 m ) -Q(s t m , a t m )] ( 3
)
where α is the learning rate that represents the speed of convergence, and γ ∈ [0, 1] is the discount factor that determines the current value of the future state costs.

During the learning phase, each agent selects the corresponding action based on the -greedy policy, i.e., it selects with probability 1the action associated with the maximum Q-value, and with probability selects a random action:

a t m =    argmax a∈A Q(s t m , a t m ), if y > rand(A), otherwise m = 1, . . . , M.
(4) By implementing the -greedy policy, the BS would have explored all possible actions and avoided local minima. For more details on RL and Q-learning the reader is referred to, e.g., [START_REF] Sutton | Introduction to Reinforcement Learning[END_REF].

V. ADAPTIVE PARTIAL SCHEME ALGORITHM

In this section, we present the proposed Q-learning-based algorithm that controls the states of the BSs. Consider the state representation S of the BSs. Each BS can be active (serving users), in sleep mode (SM 1, SM 2 or SM 3) or idle (active but not serving any user).

S = {Active, Idle, SM 1, SM 2, SM 3}

We define the set of possible actions A the state to which the BS can switch to. In contrast to schemes that implement only one type of SM (i.e., SM 1, SM 2 or SM 3), in this work we emphasis the potential of traffic-aware scheduling where each group of BSs in a given network can switch to different SM levels. This will fully utilize the advantages of BSs in the different states for both energy savings and delay reduction. For instance, the group of BSs switching to SM 1 will serve rate sensitive users (i.e. VoIP), whereas the other group of BSs in SM 3 level will serve delay tolerant users (i.e. HTTP requests). We call such a schedule an adaptive partial scheme. The final policy is then to determine how many BSs chose to switch to SM 1, SM 2 and SM 3.

An episode starts when all the BSs are in idle mode, and it finishes when all the users are served. During each episode, a BS chooses an action, then stores a quality-value linking the states s ∈ S to the chosen action a m ∈ A following Eq. ( 3). The action consists of choosing the best sleep mode level having the highest Q-value.

Our goal is to find the best combination of SMs levels each group of BSs can switch to in order to maximizes the reward r t m . We define the reward as the weighted-sum of the energy gain G and the added delay D, both resulting from the sleep mode level chosen during an episode.

r = (1 -η)G -ηD (5)
where η ∈ [0, 1] is a parameter which controls the trade-off between energy gain and the delay performance. Note that for η = 0, the problem reduces to maximizing the energy gain without considering the added delay, whereas for η = 1 the problem becomes minimizing the delay. We note the delay measured in this work is the time a user has to wait in the buffer until the BS reactivates from its sleep mode state.

VI. NUMERICAL ANALYSIS

A. Simulation Parameters

We consider a network of 25 BSs with an inter-site distance of 500 m. We model the arrival of the users following a Log-normal distribution with mean λ a and variance ν. We consider that a user request to download a file with mean size 500 MBytes. The file size follows a Weibull distribution having a CDF of

F (x) = 1 -e -(x/λ) k
, where λ > 0 is the scale parameter, and k > 0 is the shape parameter. Table II summarizes the assumptions and parameters used in our simulation. In order to show the impact of SM levels on the energy consumption, we consider in this study a low load traffic with mean arrival rate λ a = 1 user/s/Km 2 . We run 500 independent simulations on Matlab in order to acquire the average energy gain and the average added delay on the performance of the network. From [START_REF]IMEC power model tool[END_REF], we found the power figures for the different states of the BS. These values are given in Table III.

B. Convergence Analysis

The Q-learning algorithm requires a training phase in which the agent explores the state-action couples to converge towards the optimal policy. Fig. 1 shows the convergence of the momentary Q-values (initialized to zero) corresponding to the best action over the different states summed over all the BSs with η = 0.7. Then, the best policy is stored in a look-up table that will be used during the exploitation process. We can observe that after few iterations, the algorithm converges for all BSs and over all the state-action pairs.

C. Numerical Results

In Fig. 2, we present the distribution of the states of the BSs for different values of η, where 25% of the sites ∈ B Dense . We observe that when energy saving is prioritized over delay (η = 0), all BSs choose SM 3 that saves energy the most, whereas staying idle policy is preferred when the users are delay sensitive (η = 1). The states combination is observed for other values of η. In these cases, we observe a gradual shift from SM 3 to the other states. The incentive behind this shift is in the non-uniformity distribution of the traffic resulting in having some BSs with no traffic (since the overall traffic is low), thus able to switch to a deeper sleep mode level than the others. Figures 3 and4 illustrate the average network energy savings and added delay for different values of η and for different percentage of BSs with higher users arrival rate. We observe that the performance of the system depends on the reward function and in particular η. An energy saving gain of around 90% is achieved but at a cost of increased delay (5ms). It is then important to carefully choose η in order to satisfy the requirements of the different 5G use cases. We also note that having an unbalanced traffic diversifies the best policy for each BS, and thus we observe better performance when having different arrival rates for each BS.

In Fig. 5 and Fig. 6, we compare our algorithm with a benchmark that uses only one type of sleep mode. We observe that the adaptive scheme outperforms all three benchmarks in terms of energy savings. Even though using SM 3 only

Average added delay (ms)

Adaptive scheme SM3 only SM2 only SM1 only Fig. 6: Added delay comparison between our proposed algorithm and the cases of using only one type of sleep mode.

has slightly better energy savings for some range of η, it adds more delay to the user as shown in Fig. 6. Thus, for applications when there is a hard restriction on delay, using SM 3 only may not be tolerated, rather an adaptive scheme is required. Similarly, in applications where both delay and energy consumption are considered, the adaptive scheme algorithm finds its best policy to combine the different sleep modes to achieve the necessary requirements.

In order to show the performance of our proposed algorithm, we compare the reward that evaluates both the energy savings and added delay. We notice that the adaptive algorithm combines the advantages of the different sleep mode levels in order to maximize the reward. For instance, the adaptive algorithm prefers SM 3 when the users are rate sensitive (small epsilon) and SM 1 when the users are delay sensitive. The combination

Reward (r)

Adaptive scheme SM3 only SM2 only SM1 only Fig. 7: Performance comparison between our proposed algorithm and the cases of using only one type of sleep mode. of these states gives a higher reward than if these states where solely chosen.

VII. CONCLUSIONS In this work, we investigated the problem of energy savings and delay associated with 5G networks. While it is critical to reduce the energy consumption of these networks, hard constraints are agreed on in the 5G requirements to periodically activate 5G cells for signaling synchronization. In this work, we proposed an adaptive partial sleep scheme algorithm based on reinforced learning that controls the state of the base stations in order to maintain a desirable trade-off between energy consumption and delay. We focused on 5G sleep modes that respect the 5G requirements. We showed that having a combination of different states of sleep modes in a network can achieve better performance than having one state only. Simulation results revealed an energy gain ranging between 90% and 50% for rate and delay tolerant users, respectively. This work opens the door for accessing the performance of dense networks, where a huge number of cells are deployed, without violating the 5G requirements. The effect of signaling bursts on the energy consumption is not studied in this work. This might affect the optimal policies that might be used for different signaling periodicities allowed in 5G networks. Another interesting topic is to study the optimal policies in the context of renewable energy and smart grid where the amount of energy harvested varies from one location to another, and the price of electricity varies from one retailer to another.

Fig. 1 :Fig. 2 :

 12 Fig. 1: Convergence of the Q-learning algorithm.

Fig. 4 :

 4 Fig. 4: Average network added delay of our proposed algorithm for different users distribution.

Fig. 5 :

 5 Fig.5: Energy savings comparison between our proposed algorithm and the cases of using only one type of sleep mode.

TABLE I :

 I BS Sleep Modes Characteristics[START_REF] Debaillie | A flexible and future-proof power model for cellular base stations[END_REF].

	Sleep	Deactivation	Minimum	Activation
	level	duration	sleep duration	duration
	SM 1	35.5 µs	71 µs	35.5 µs
	SM 2	0.5 ms	1 ms	0.5 ms
	SM 3	5 ms	10 ms	5 ms
	SM 4	0.5 s	1 s	0.5 s
	consider that each BS can switch to one of the following SM
	levels: SM 1, SM 2 or SM 3.

TABLE II :

 II Simulation Parameters.

	Parameter	value
	Antenna height	30 m
	BS Tx Power	45 dBm
	Bandwidth	20 MHz
	Thermal noise	-174 dBm/Hz
	Pathloss	128.1 +37.6 log 10 (d) dB
	Shadowing	Log-normal (6 dBm)
	User's arrival	Log-normal, λa = 1, υ= λa/10
	Service type	file with mean=4 Mbps
	Scale parameter	λ = 441.305
	Shape parameter	k = 0.8

TABLE III :

 III Power Consumption of a 2 × 2 MIMO BS.

	Active	Idle	SM 1	SM 2	SM 3
	250 W	109 W	52.3 W	14.3 W	9.51 W


Edgard Verdura

Dominique Herve ´

Eva Scharrer

Maria Del Mar Amador

Lucie Guyant-Mare

Anne Philippi

Astrid Corlobe

Bergamettii

Steven Gazal

Carol Prieto-Morin

Nathalie Beaufort

Benoit Le Bail

Irina Viakhireva

Martin Dichgans

Hugues Chabriat

Christof Haffnner

Elisabeth Tournier-Lasserve
email: tournier-lasserve@univ-paris-diderot.fr

Pr Elisabeth Tournier-Lasserve

Heterozygous HTRA1 mutations are associated with autosomal dominant cerebral small vessel disease

Keywords: small vessel diseaseE vascular dementiaE HTRA1, E CARASILE CADASIL

These authors contributed equally to this

Introduction

Cerebral small vessel disease (SVD) is a heterogeneous group of disorders affnecting small arteries, arterioles, veins, and/or capillaries of the brain (Pantoni, 2010E Wardlaw et al., 2013). Their two main clinical consequences are stroke and cognitive impairment.

Typical neuroimaging features include white mattier lesions associated with small infarctions, microbleeds, and macrobleeds. In most cases, SVD is sporadic, with age and hypertension representing the prevailing risk factors.

However, several early-onset monogenic forms of SVD have been reported in adult patients, the majority of them with a dominant inheritance pattiern. They include CADASIL (cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy), inherited cerebral amyloid angiopathies and angiopathies associated with mutations of COL4A1 and COL4A2 genes (Joutel et al., 1996E Gould et al., 2006E Revesz et al., 2009). CADASIL is caused by NOTCH3 mutations and is by far the most common hereditary SVD with more than 500 families reported and a 10-15% mutation rate in patients with SVD referred for NOTCH3 molecular screening, the second one being COL4A1/COL4A2 angiopathies (unpublished data) [START_REF] Chabriat | Cadasil [Review][END_REF]. By contrast, CARASIL (cerebral autosomal recessive arteriopathy with subcortical infarcts and leukoencephalopathy) is a very rare autosomal recessive SVD caused by biallelic mutations of the HTRA1 gene (high temperature requirement protease A1)E only 12 HTRA1 mutated CARASIL families have been reported worldwide so far [START_REF] Hara | Association of HTRA1 mutations and familial ischemic cerebral small-vessel disease[END_REF]E Nozaki et al., 2014). While the identification of mutated genes has provided invaluable tools for diagnosing monogenic SVD forms, molecular screening of those genes in routine diagnosis identifies the causative mutation in 520% of patients referred for a familial SVD, which strongly suggests that other genes may be involved.

Herein, we used genome-wide linkage analysis and whole exome sequencing to identify the gene involved in an autosomal dominant SVD family in which SVD genes previously known to lead to an autosomal dominant SVD were excluded. We then screened a panel of 201 unrelated patients with a familial SVD of unknown aetiology to estimate the frequency of mutations of this gene in familial SVD.

Materials and methods

Participants and study design

Two siblings and one of their first cousins (Family F1) were referred for stroke and/or cognitive impairment associated with diffnuse white mattier hyperintensities (genealogical tree shown in Fig. 1). Detailed clinical and neuroimaging features of these patients are presented in the 'Results' section.

A panel of 201 unrelated SVD probands referred for NOTCH3 molecular screening in the Genetics department of Lariboisie`re hospital were also included in this study on the basis of the following criteria: (i) having at least one first or second degree relative with a clinical history of stroke and/or vascular dementiaE and (ii) being screened negative for mutations in the 23 exons of NOTCH3 known to be involved in CADASIL.

Mean age of this cohort at referral for molecular screening was 57 years (standard deviation = 11.6). This panel was used to search for mutations in the candidate genes identified in Family F1 (see below and Supplementary material).

All patients and participating relatives provided writtien informed consent for participation in genetic studies, in accordance with ethical recommendations in France for genetic disorders. Informed consent forms were approved by local medical ethics comittiees or CPP Ile de France (N 007110588).

One hundred and ninety-two healthy controls of French origin were used as a control group for HTRA1 candidate variants analysis. Additional control data were obtained from the public Exome Variant Server (EVS) database (n = 4300 European Americans) and 1000 Genomes database (n = 379 Europeans).

Procedures

Whole-genome linkage analysis was performed in Family F1 with data obtained with Affnymetrix GeneChip Õ Human Mapping 250K arrays (Supplementary material). Parametric multipoint linkage analysis was performed with MERLIN assuming an autosomal dominant inheritance, a complete penetrance, a disease allele frequency of 0.0001 1, and no phenocopy. Intervals reaching the maximum theoretical LOD score achievable in this family were considered as possibly linked. Intervals with LOD scores lower than 2 and larger than 2 cM were considered as excluded for linkage.

Whole exome sequencing of the three patients of Family F1 was performed at IntegraGen platform. Variant annotation was done by an internal bioinformatics pipeline (IntegraGen). Only missense, nonsense, insertion/deletion variants or variants potentially affnecting splicing were kept for further analysis. Variants present in dbSNP132, as well as those reported with a minor allele frequency 40.1% in the 1000 Genomes Project, EVS or IntegraGen exome database (96 French exomes) were excluded. Candidate variants were further selected when (i) shared by all three affnected patients in a heterozygous stateE and (ii) located outside regions previously excluded by genome-wide linkage analysis. Frequency of likely deleterious variants was compared between cases and two control samples from online databases: European-American controls from Exome Variant Server (EVSE n = 4300) and European controls from 1000 Genomes project (n = 379). The frequency of HTRA1 variants in cases and controls was compared by a Fisher's exact test on a 2 2 contingency table. All the tests were two-sided, with a P-value of 0.05 considered significant and odds ratios (OR) and 95% confidence intervals (CI) were calculated. Analyses were performed using the statistical analysis package R.

Expression constructs, conditions used for transfection, collection of conditioned media, protein electrophoresis, immunoblottiing and procedures used to measure the activity [START_REF] Beaufort | Cerebral small vessel disease-related protease Htra1 processes latent TGF-b binding protein 1 and facilitates TGF-b signaling[END_REF] of the various HTRA1 mutants are detailed in the Supplementary material.

Results

Clinical and neuroimaging features of Family F1 patients

The genealogical tree of Family F1 is shown in Fig. 1. Patient F1-9, the proband of this family, is a senior executive 69-year-old male with moderate hypercholesterolaemia but no other vascular risk factor. He had a history of sciatica related to a lumbar disk prolapse. Since age 66 he reported a progressive reduction of cognitive performances without significant impact on his daily activities and complained of gait disturbance since age 68.

At age 69 he experienced an acute episode of leftw-sided hemiparesis that completely resolved within 8 days. His neurological examination performed at the time of MRI examination showed a subtle leftw-sided ataxia. His blood pressure was 134/ 70 mmHg. Neuropsychological testing revealed mild alterations in processing speed, executive functions, and verbal episodic and visuospatial memory performances suggestive of subcortical cognitive impairment. Mini-Mental State Examination score was 29/30. Mood was found to be mildly depressed. The standard vascular work-up (EKG, echocardiography, cervical and transcranial ultrasound examination, blood cell count, sedimentation rate, creatinine level) and fundus examination were normal.

His 64-year-old brother (Patient F1-10) had no vascular risk factor. He had a history of arthritis of small and large joints. At age 55, he presented a major depressive episode. He subsequently had cognitive complaints and decided to retire early at age 58 years. At 62 years of age, he experienced recurrent attiacks of visual, sensory and aphasic migraine aura with or without headache.

His neurological examination was normal. His blood pressure was at 136/ 78 mmHg. Cognitive testing showed alterations of performances in tests evaluating attiention, executive functions and verbal episodic memory, and executive functions. Mini-Mental State Examination score was 25/30. The standard vascular work-up was normal at time of MRI examination, as well as the fundus examination. In addition, the following exams were in the normal range: 24-h blood pressure monitoring, anticardiolipid antibodies, antinuclear antibodies, anti-beta-2 GP1 antibodies, and homocysteine level.

Patient F1-8, a first cousin of Patients F1-9 and F1-10, is a 65-year-old female with a long history of well-controlled hypertension and hypercholesterolaemia. At age 60 years, she had some cognitive complaints and at 61 years, an acute episode of right hemiparesis that lasted 24 h. Her neurological examination showed mild bradykinesia, micrographia, pyramidal signs with diffnuse increased reflexes. Blood pressure was 140/90 mmHg. She had a cognitive slowing, but cognitive testing including Mini-Mental State Examination, Mattiis Dementia Rating Scale, Grober and Buschke Verbal Learning Test, verbal fluencies, Rey figure copy and oral naming were normal. The standard vascular work-up was normal at time of MRI examination. Complete ophthalmological examination, electrophysiological studies of the limbs and electronic microscopy skin biopsy were normal.

The father of Patients F1-9 and F1-10 had a history of dementia starting during the sixth decade of life. He died at 75 years while he was still able to walk with help. His father, died in his late seventies several days aftwer the sudden onset of a hemiplegia. Patient F1-7, sister of Patient F1-8, presents a cognitive impairment that started aftwer 60 years of age. Their mother died at age 70 years of unknown cause.

MRI showed in all three patients diffnuse white mattier hyperintensities affnecting supratentorial white mattier, external capsules and pons but sparing the temporal lobes (Fig. 2). Patients F1-9 and F1-8 had confluent and diffnuse white mattier hyperintensities in the centrum semi-ovale associated with hemispheric and pontine lacunes, while Patient F1-10 had early confluent, less diffnuse white mattier hyperintensities and no lacune. Patient F1-8 was the only one to show microbleeds on gradient-echo imagesE those numerous microbleeds were located in the deep grey nuclei and subcortical areas. All patients had multiple dilated perivascular spaces, clearly visible on T 2 images and leading to so-called e ´tat crible´in Patients F1-9 and F1-10.

Sequence analysis of the 23 exons encoding the 34 epidermal growth factor (EGF)-like repeats in the extracellular region of the NOTCH3 receptor was negative in all patients. Screening of genomic DNA of Patient F1-8 for APP mutations and duplication was also negative.

Identification of candidate variants in Family F1

Genome-wide linkage analysis conducted in Family F1 excluded 79% of the genome (LOD score 5 2), including all known SVD loci. We identified 28 regions reaching the theoretical maximal LOD score achievable in this family (LS = 0.903) over a minimum distance of 2 cM (Supplementary Fig. 1).

Subsequent whole exome sequencing of the three affnected family members was performed. Filtering strategy and data obtained are presented in Supplementary Table 1.

A total of 11 candidate variants, including six single nucleotide variants and five insertion/deletion (Indel) variants were identified. Six of 11 variants were located in regions excluded by linkage analysis and were therefore not considered. The five remaining variants were missense variants located in HTRA1 (NM_0020775.4), TTBK2 (NM_1730500.3), C15orf43 (NM_1520448.2), CPEB1 (NM_0300594.4) and ZNF785 genes (NM_1520458.6) (Supplementary Table 2). They were all absent from 1000 Genomes, EVS and IntegraGen databases, and confirmed by Sanger sequencing to cosegregate with the affnected phenotype in Family F1. The HTRA1 variant (c.497G 4 T, p.Arg166Leu) was predicted to be pathogenic by all three in silico prediction tools (PolyPhen-2, SIFT and MutationTaster)

(Table 1). The TTBK2 variant (c.1101 0A 4 T, p.Lys367Ile) was considered benign by PolyPhen-2, and the other three variants, located in C15orf43 (c.307A 4 C, p.Ser103Arg), CPEB1 (c.699G 4 C, p.Met233Ile), and ZNF785 (c.1011 1C 4 G, p.Ser337Arg) were considered benign by at least two prediction tools.

Heterozygous HTRA1 variants are associated with familial cerebral SVD

To test the relevance of the five candidate genes (HTRA1, TTBK2, C15orf43, CPEB1, ZNF785) in additional patients with SVD, multiplex Fluidigm PCR amplification of exonic regions of these genes followed by massive parallel sequencing was conducted in 191 unrelated patients with familial SVD and in Patient F1-9, used as a positive control. In addition, mutations of these five genes were searched for in whole exome sequencing data of 10 additional unrelated familial SVD probands. Eighteen exonic and/or splice site rare candidate variants were identified in 17 unrelated patients of the cohort. Fourteen of those heterozygous variants were located in HTRA1.

Each of the four remaining variants, located in the four remaining genes, was identified in only one patient. They were all excluded based on either their prevalence in control genomic databases, or their predicted benignity by at least two in silico prediction tools or their occurrence in a proband showing a deleterious HTRA1 variant (Supplementary Table 3).

Sanger sequencing was then used to confirm the presence of candidate HTRA1 variants in all mutated probands. In addition, Sanger sequencing of HTRA1 exon 1 and part of exons 2 and 4 was performed in all 201 probands as Fluidigm coverage of these exons was not complete. Thirteen heterozygous HTRA1 variants were confirmed in 14 distinct probands, including F1 proband (Table 1, Fig. 3 and Supplementary Fig. 2). Eleven of these variants, including R166L (the variant identified in Family F1), were considered to be most likely deleterious. Ten of them were missense variants that were (i) absent from all interrogated databases (1000 Genomes, EVS, and IntegraGen exome databases) and from a cohort of 96 French healthy control individualsE (ii) predicted to be pathogenic by at least two in silico prediction toolsE and (iii) affnecting highly conserved amino acids (Supplementary Fig. 3). The remaining one was a splice site variant (c.973-1 G 4 A) absent from all databases and predicted to lead to an abnormal splicing of exon 5. This abnormally spliced mRNA would skip 33 codons including codon 328, which encodes for a serine residue required for HTRA1 activity. The last two variants, p.Ala20Val (shared by two unrelated patients) and p.Glu51Gly, located in exon 1, were absent from databases and from our French control group but were predicted to be benign with all three prediction tools. They were not considered further. Altogether, 11 unique, and heterozygous HTRA1 variants, including Family F1 variant, were considered as deleterious (Fig. 3).

The genealogical trees of these 11 unrelated mutated carriers are shown in Fig. 1. Family history was consistent with an autosomal dominant pattiern of inheritance for at least eight of these families. Three additional affnected relatives were available for Sanger sequencing in Families F5 and F8E all three were shown to be mutation carriers.

The frequency of deleterious variants was compared between our cases and control samples from two online databases: European American controls from EVS (n = 4300) and European controls from 1000 Genomes project (n = 379). All nine exons of HTRA1 have been sequenced by the 1000 Genomes consortium whereas only eight exons (exons 2 to 9) have been sequenced in EVS. Ten likely deleterious variants located in exons 2-9 have been identified in the 4300 European American controls from EVS (one splice site change, two nonsense, and seven missense variants), as compared to seven exons 2-9 variants in our panel of 201 patients with SVD (P = 4.2 10 6 ; ; ; E OR = 15.4E 95% CI 4.9-45.5). There is no deleterious variant in any of the HTRA1 exons 1-9 in the 379 European controls from 1000 Genome project as compared to a total number of 10 variants in our panel of patients with SVD (P = 2.1 10 5 ).

Functional characterization of HTRA1 mutations

HTRA1 encodes a conserved serine protease consisting of several domains (Fig. 3) [START_REF] Clausen | The HTRA family of proteases: implications for protein composition and cell fate[END_REF]. Most of the previously identified homozygous HTRA1 mutations have been demonstrated to strongly reduce proteolytic activity (Nozaki, 2014). We therefore assessed the catalytic capacity of a subset of our heterozygous variants in vitro using conditioned supernatants of transiently transfected HEK 293T cells and two diffnerent substrates [bovine serum albumin for A173P and D450H, which were present at somewhat reduced levels, possibly due to increased autodegradation (Fig. 4A). In the BSA assay HTRA1 mutants R166L, A173P, S284R, P285Q and F286V showed a loss of activity comparable to the S328A mutant (Fig. 4B). In contrast, the reduction observed for S284G and D450H was only partial. These results were fully confirmed using casein as substrate in a Fluorescent Resonance Energy Transfer (FRET) assay yielding a fluorescence increase upon casein degradation (Fig. 4C). While D450H and S284G displayed residual activity, all other mutants showed a behaviour similar to the loss-of-function controls.

Main clinical features of the unrelated probands with heterozygous HTRA1 mutations

Main clinical and MRI features of the 11 unrelated probands with HTRA1 heterozygous mutations are summarized in Table 2, Figs 2, 5 and Supplementary Fig. 4. Genealogical trees are shown in Fig. 1. The clinical picture is characterized by the association of subcortical ischaemic events and cognitive decline starting in most patients in the sixth decade. None of these patients had early-onset alopecia or early-onset spondylosis. Three of them F3 and F6 index) suffnered from a lumbar disk prolapse but late in life. Typical neuroimaging findings include confluent or early confluent white mattier hyperintensities on MRI T 2 -weighted and FLAIR images, with frequent involvement of the external and internal capsules, sometimes associated with multiple lacunar infarcts and microbleeds (Figs 2, 5 and Supplementary Fig. 4). Anterior temporal regions and U fibres were spared. Dilated perivascular spaces with a typical 'status cribrosum' characterized by an innumerable number of dilated Virchow-Robin spaces and resulting in a cribriform change in basal ganglia were observed in most patients. Altogether, the clinical and MRI features of these HTRA1 heterozygous patients are similar to the ones of sporadic SVD cases. excluded) strongly suggest that (i) the causative mutation in Family F1 is a heterozygous mutation located in HTRA1; ; ; E and (ii) roughly 5% of familial SVD of unknown aetiology are associated with heterozygous HTRA1 mutations.

Clinical features of this autosomal dominant SVD diffner from those of CARASIL by a later age at onset of stroke and cognitive decline (20-30 years in age at onset) and the absence of the typical CARASIL extra-neurological symptoms (Maeda et al., 1976E Nozaki et al., 2014). Indeed, none of our patients presented with early-onset alopecia or early-onset spondylosis. Three of them were reported to have osteoporosis and lumbago, but those manifestations occurred late in life. The phenotype of this condition is very close to those observed in sporadic SVD cases. Indeed, the occurence of lacunar ischaemic events between 55 and 72 years in half of the cases and the progressive gait disturbance and subcortical cognitive impairment from the age of 60 are comparable with the phenotype of age and hypertension related SVD. The MRI pattiern is also very similar except for the presence of a status cribrosum, which seems to be more frequent in this condition, and for the location of microbleeds which involves preferentially the deep and juxtacortical hemispheric areas.

Several observations strongly support the pathogenic role of the heterozygous HTRA1 mutations in the 11 probands reported herein. First, all these mutations are absent from the 1000 Genomes (n = 379 Europeans) and EVS databases as well as from our panel of French controls. Second, there is a highly significant diffnerence between the frequency of deleterious HTRA1 variants in our panel of familial SVD probands and that in control databases, including the EVS database (n = 4300 European-AmericansE P = 4.2 10 6 ; ; ; E OR = 15.4E 95% CI 4.9-45.5) and 1000 Genomes database (n = 379 EuropeansE P = 2.1 10 5 ). Third, all 11 mutations are predicted to be deleterious by at least two in silico prediction tools. Fourth, a complete loss of activity was observed for five of the seven variants tested. An additional variant located in a consensus splice site (c.973-1G 4 A), is predicted to lead to an in-frame deletion of exon 5, which includes the codon 328 encoding a serine required for enzyme activityE this variant is also most likely a lossof-function mutant. The residual activity of the variants S284G and D450H might be the result of a pathomechanism diffnerent from intrinsic proteolytic activity alteration such as protein destabilization or mislocalization. In any case, both our genetic data and the results of in silico prediction tools analyses strongly argue for their pathogenic potential. Additional work on large series of patients is required to elucidate how these mutants might alter HTRA1 function.

The most surprising finding of this study is the deleterious role of heterozygous mutations in HTRA1, a gene previously reported to be involved in a very rare autosomal recessive SVD [START_REF] Hara | Association of HTRA1 mutations and familial ischemic cerebral small-vessel disease[END_REF]. Indeed, CARASIL was initially reported in siblings from a consanguineous family with unaffnected parents.

So far 12 mutated CARASIL families have been reported, including 10 consanguineous families (Nozaki et al., 2014). The largest series includes six families from JapanE all of these were consanguineous families and parents of affnected cases were reported as being unaffnected [START_REF] Hara | Association of HTRA1 mutations and familial ischemic cerebral small-vessel disease[END_REF]. Half of these families harboured homozygous stop codons. Unaffnected parents were further mentioned in two other consanguineous families from Japan and Turkey [START_REF] Nishimoto | A novel mutation in the HTRA1 gene causes CARASIL without alopecia[END_REF]E Bayrakli et al., 2012). Interestingly, however, in three additional families, cerebral MRI performed in either one or both parents was reported to show a leukoencephalopathy, raising the question of the causality of the heterozygous variants carried by these parentsE in the last family, both parents were said to be deceased in their fiftwies with emotional liability, but MRI was not available (Mendioroz et al., 2010E Wang et al., 2012E Chen et al., 2013E Bianchi et al., 2014). None of our families is consanguineous and 8 of 11 of them show a pattiern of inheritance consistent with autosomal dominant inheritance. Altogether, these data strongly suggest that in some cases HTRA1 mutations behave as autosomal recessive mutations, with heterozygous carriers being clinically unaffnected, as observed in Japanese CARASIL patients.

In other cases, HTRA1 mutations behave as dominant mutations, with heterozygous carriers being clinically affnected E based on our data, their frequency is predicted to be much higher than recessive type mutations. One of our current hypotheses to reconcile those data is that some of the missense mutations reported herein might be dominant negative mutations, the mutated allele being a loss of function mutant which interferes with the normal function of the remaining wild-type allele, leading to a further decrease in enzyme activity. In contrast, mutations leading to premature stop codons would lead to the decay of the mutated mRNA, the absence of synthesis of the protein encoded by the mutated allele and therefore to a haploinsufficiency which by itself would not be sufficient to cause SVD. This has been reported in several other diseases, such as hypertension caused by KLHL3 mutations or myopathies associated with COL6A1 mutations [START_REF] Boyden | Mutations in Kelch-like 3 and cullin 3 cause hypertension and electrolyte abnormalities[END_REF]E Zou et al., 2014). Interestingly, in most of these diseases that exist both as dominant and recessive disorders, the causative gene encodes proteins acting as dimers or multimers. HTRA1 encodes a serine protease whose functional unit is a trimer stabilized by residues of the protease domain [START_REF] Clausen | The HTRA family of proteases: implications for protein composition and cell fate[END_REF]. Another non-mutually exclusive hypothesis would be that some of these missense mutations are semi-dominant mutations. Comparative measurement of the residual HTRA1 endogenous activity of fibroblasts from missense and stop codons heterozygous carriers would be needed to investigate further this question but this test is not currently available.

Our last hypothesis would be that in some CARASIL families the affnected status of the heterozygous parents would have been overlooked due to the much later age at onset in heterozygous carriers as compared to offnsprings with biallelic mutationsE indeed, there is roughly 20-30 years diffnerence in age at onset between heterozygous and biallelic mutated patients.

The identification of the causative gene in these families now allows molecular genetic screening for this condition. Knowing that the clinical and MRI features of the patients reported herein were similar to those observed in sporadic SVD cases except for the familial nature of the disease, molecular screening of HTRA1 would be indicated in all cases with a familial SVD, in the absence of clinical or MRI findings suggestive of another condition. However, the familial nature of the disease may be overlooked due to the late onset of clinical symptoms. Therefore, molecular screening should be considered in sporadic cases when the extent of microvascular lesions on MRI contrasts with the paucity of vascular risk factors.

In summary, we show herein that nearly 5% of familial SVDs referred for molecular screening are associated with deleterious heterozygous mutations of HTRA1. Therefore, these mutations would be so far the second cause of autosomal dominant SVD aftwer CADASIL. This autosomal dominant SVD is characterized by a much later age of onset than in CARASIL and the absence of typical extraneurological CARASIL features. Further assessment of pathogenic molecular effnects of those heterozygous variants and delineation of the complete mutation spectrum will now be needed to develop efficient genetic diagnosis.

Figure 1

 1 Figure 1 Genealogical trees of the 11 mutated probands. Square = maleE circle = femaleE diagonal black line = deceased individual Eblack filled symbol = clinically and MRI proven affnected individualE empty symbol = clinically healthy relative Eblack dot = affnected individual based on family history and/or clinicalcharts E question mark = unknown status E syringe symbol = blood sampled individuall Easterisk: individualshowing an HTRA1 deleterious variant.

Figure 2

 2 Figure 2 MRI data obtained in Patients F1-9, F1-10 and F1-8. Leftw column: T 2 -weighted images. Centralcolumns: FLAIR images. Right column:T 1 -weighted image (top), 3D time of flight image (middle) and gradient-echo image (bottiom). Extensive white mattier hyperintensities in Patients F1-9 and F1-8 and less diffnuse white mattier hyperintensities in Patient F1-10 are detected on FLAIR images. Multiple dilated perivascular spaces corresponding to so-called e ´tat crible ´were observed in Patients F1-9 and F1-10 on T 2 -weighted images. Lacunes are found in Patients F1-9 and F1-8. Microbleeds were detected on gradient-echo images only in Patient F1-8 (juxtacortical areas and deep grey nuclei).

a

  PolyPhen-2 (HumVar) / SIFT / Mutation Taster: predicted pathogenicity using these three programs. b Absence: absence from the 1000 Genomes database (version 2014) or Exome Variant Server (ESP6500v2). c NA: not analysed because splice variants cannot be analysed with those prediction tools. d NA: not analysed because exon 1 was not covered in EVS exome database.

Figure 3

 3 Figure 3 Schematic representation of HTRA1 gene/protein and location of mutations. (A) cDNA structure of human HTRA1 transcript NM_0020775.4. Positions are annotated from the first coding nucleotide. Positions of heterozygous SVD mutations identified in this study are indicated above the figure. Numbers represent the first coding nucleotide of each exon, and the last coding nucleotide (nt 1443). (B) Domain organization of human HTRA1 protein (protein NP_0020766.1). Above, positions of HTRA1 protein changes identified in patients with SVD in this study. Below, mutations that have been previously reported in CARASIL patients. SP = signalpeptide E PDZ = PDZ-like domain. Numbers above the figure represent the first and last coding amino acids for each one of the protein domains, and the last coding amino acid (aa 480).

(Figure 4

 4 Figure 4 Most heterozygous HTRA1 mutants are proteolytically inactive. (A) Mutants are effniciently expressed and secreted. Upon transient transfection in HEK293T cells, anti-myc immunoblottiing was performed on conditioned supernatants. Full-length HTRA1 migrates at 55 kDa, lower molecular weight bands represent degradation products. (B) Proteolytic activity of conditioned supernatants was analysed towards denatured BSA and evaluated by SDS-PAGE and Coomassie Blue staining. (C) Proteolytic activity of conditioned supernatants was analysed towards fluorescently labeled casein over 10 h by measuring FRET. vec = vector E WT = wild-type.

Figure 5

 5 Figure 5 Status cribrosum and white mattier hyperintensity characteristics in HTRA1 mutated probands. Status cribrosum is well visible on T 2 -weighted images in Patients F133-7, F8-11, F6-5, and F1-9. white mattier hyperintensitiess on FLAIR images were extensive in all cases aftwer 60 years of age. Some of the younger patients had more limited white mattier hyperintensities, such as Patient F133-7.

Table 1

 1 Rare heterozygous HTRA1 variants identified in the familial SVD probands

	Family cDNA change	Predicted protein	Protein domain	Intron/ Exon	PolyPhen-2 a (HumVar)	SIFT a	Mutation Taster a	1000 Genomes	EVS frequency	Sanger sequen-
			change							frequency		cing
												results
	F1	c.497 G 4 T	p.Arg166Leu None	Exon 2	Probably	Deleterious Disease	Absence b	Absence Confirmed
							damaging		causing
	F2	c.517 G 4 C	p.Ala173Pro None	Exon 2	Possibly	Deleterious Disease	Absence	Absence Confirmed
							damaging		causing
	F3	c.852 C 4 A	p.Ser284Arg Serine	Exon 4	Probably	Deleterious Disease	Absence	Absence Confirmed
					protease		damaging		causing
	F4	c.854 C 4 A	p.Pro285Gln Serine	Exon 4	Probably	Deleterious Disease	Absence	Absence Confirmed
					protease		damaging		causing
	F5	c.856 T 4 G	p.Phe286Val Serine	Exon 4	Possibly	Tolerated	Disease	Absence	Absence Confirmed
	F6	c.973-1 G 4 A	p.(Tyr325_	protease Serine	damaging Intron 4 NA c	NA c	causing NA c	Absence	Absence Confirmed
			Leu335del)		protease
	F7	c.1341 8 G 4 C	p.Asp450His PDZ	Exon 9	Possibly	Deleterious Disease	Absence	Absence Confirmed
							damaging		causing
	F8	c.850 A 4 G	p.Ser284Gly Serine	Exon 4	Probably	Deleterious Disease	Absence	Absence Confirmed
	F39	c.59 C 4 T	p.Ala20Val	-	protease	Exon 1	damaging Benign	Tolerated	causing Polymorphism Absence	NA d	Confirmed
	F78	c.59 C 4 T	p.Ala20Val	-		Exon 1	Benign	Tolerated	Polymorphism Absence	NA d	Confirmed
	F133	c.367 G 4 T	p.Ala123Ser Kazal-type	Exon 1	Possibly	Tolerated	Disease	Absence	NA d	Confirmed
	F134	c.397 C 4 G	p.Arg133Gly Kazal-type	Exon 1	damaging Possibly	Tolerated	causing Disease	Absence	NA d	Confirmed
	F167	c.152 A 4 G	p.Glu51Gly	IGFBP-like	Exon 1	damaging Benign	Tolerated	causing Polymorphism Absence	NA d	Confirmed
	F186	c.361 A 4 C	p.Ser121Arg Kazal-type	Exon 1	Probably	Deleterious Disease	Absence	NA d	Confirmed
							damaging		causing

Candidate variants predicted to be damaging by at least two pathogenicity prediction so ftwwares,or affnecting splicing sites.

Acknowledgements

We thank all families for their participation in this study. We are also indebted to F.

Marchelli for excellent figures editing.

Funding

The research was funded by INSERM, Programme Hospitalier de Recherche Clinique AOM060037 (grant to E.T.L.), Leducq Foundation 2007 grant 'Identification of novel targets for hemorrhagic stroke' (grant to E.T.L.), the Leducq transatlantic network 'Pathogenesis of Small Vessel Disease of the Brain' (grant to M.D.), the Vascular Dementia Research Foundation and the Deutsche Forschungsgemeinschaftw (DFG).

Discussion

We report herein a family including three affnected individuals with a cerebral SVD of previously unknown aetiology, which segregates as an autosomal dominant disorder. Linkage analysis in combination with whole exome sequencing performed in this family (F1) as well as high throughput sequencing in a panel of 201 unrelated familial SVD cases (in whom NOTCH3 mutations were previously Affnected relatives, based on family history and/or clinicalcharts (see Fig. 1).

b Symptoms which led to MRI are possibly not related to the disease. c The presence of 'status cribrosum' was evaluated when T 2 sequence or/and T 1 sequence with thin-slice were available.

Supplementary material

Supplementary material is available at Brain online.


Johannes Greil

Emmerich Bertagnolli

Bassem Salem

Thierry Baron

Pascal Gentile

Alois Lugstein
email: alois.lugstein@tuwien.ac.at

Fabrication and characterization of a germanium nanowire light emitting diode

In this letter we demonstrate the feasibility of a germanium nanowire light emitting diode as a reasonable approach for downscaling of CMOS compatible light sources. We show room-temperature direct bandgap electroluminescence from axial p-n junction nanowire devices. The electron population in the Γ valley, necessary for direct bandgap emission, is achieved by high injection current densities. Carrier temperature is consistently found to be higher than the lattice temperature, indicating inhibited carrier cooling in small diameter wires. Strong polarization of the emission parallel to the nanowire axis is observed and attributed to dielectric contrast phenomena.

Main text

The ongoing scaling of CMOS technology and thus conceivable limitations of common metallization schemes, demands for silicon-compatible light sources, transmitters and detectors for on-chip communication and triggered enormous research activities in group IV semiconductor photonics. 1,2 Thereby novel light generation schemes like Raman lasers 3 , photonic crystals 4 , quantum dots 5 , and erbium doping 6 have already been demonstrated. From the material side germanium (Ge) is highlighted amongst the group IV materials due to its quasidirect nature with the conduction band minimum at the Γ-point only 140meV higher in energy than the minimum at the L-point. Beneficially, the direct bandgap energy of Ge translates to an emission wavelength in the telecommunication band of 1550nm. Moreover, it has already been demonstrated that the emission properties of Ge may be tailored by utilizing quantum confinement 7 , strain engineering 8,9 , n-type doping 10 , alloying with Sn 11 , tuning of the temperature 12 or combinations thereof.

Planar Ge LEDs [12][13][14][15][16] as well as optically 10 and electrically 17 pumped Ge lasers have recently been demonstrated in devices with dimensions on the micron scale. Following the route of downscaling, nanowire (NW) based devices are a next logical step. However, so far only III-V materials have been employed in axial p-n junction LED devices [18][19][20][21] . Here we present room temperature electroluminescence (EL) from Ge NW axial p-n diodes with a junction area of less than 0.01µm 2 . A bottom-up approach is pursued, with the potential for versatile integration of NW functional building blocks in various device architectures.

Ge NWs were synthesized in a low pressure chemical vapor deposition chamber with GeH4 (50sccm of 10% GeH4 in H2 ) as a precursor gas at a growth temperature of T=673K and a total chamber pressure of 12.8mbar. The vapor-liquid-solid growth mechanism 22 was employed to achieve axial p-n junction NWs with Au colloids as growth catalyzing particles. The p-and n-type segments are defined by introducing B2H6 (B2H6/GeH4 ratio = 2x10 -2 ) and PH3 (PH3/GeH4 ratio = 3x10 -2 ) into the growth chamber, respectively resulting in electrically active doping densities of about 10 19 at.cm -3 determined by four probe measurements.

Uncatalytic deposition on the NW sidewalls during the growth at this rather high temperature leads to strongly tapered NWs enabling efficient outcoupling of light. 23 However, the unintentional deposition of n-type material on the sidewalls of the foremost grown p-type section of the NW, potentially bypasses the p-n junction electrically 24 (see Figure 1a). Remarkably, as will be shown later, selective etching of this unintentional ntype layer greatly improves the electrical diode properties, whereas the optical emission properties are not altered significantly. To fabricate devices as shown in the SEM image in Figure 1a, the p-n junction NWs were removed from the growth substrate and deposited via mechanical transfer on a highly doped substrate covered by silicon oxide. Electrical contacts to individual NWs were established by electron beam lithography, Ni/Au sputter deposition and lift-off techniques. In agreement with literature we observed ohmic contacts to both highly doped p-and n-type Ge segments. NW diodes were electrically characterized and the I/Vs fitted according to the diode equation:

    sh s B s s R IR V q T nk IR V q I I                    1 exp (eq. 1)
with I s the diode saturation current, q the elementary charge, R s the series resistance, k B the Boltzmann constant, n the ideality factor, T the temperature, and R sh the resistance of the parasitic shunt (see Figure 1a). Electrical characterization of the as-grown NWs reveals the expected high reverse current due to shunting of the p-n junction by the unintentional deposited n-type layer (Figure 1b). A 30s dip in deionized water at room temperature is employed to remove the n-type Ge layer. The NW diameter in the n-type region is thereby reduced from ~57nm to ~33nm on average. After etching, diode characteristics are greatly improved and current rejection ratios as high as 10 5 are obtained. The shunt resistance that is estimated around 211kΩ for the as-grown NWs completely disappears, while the series resistance of around 27kΩ is not affected and the diode ideality factor improves from n=2.5 to n=1.4.

To gain further insight into the internal electric field distribution along the axial p-n NW junction, scanning photocurrent spectroscopy was employed (Figure 2). 26 Therefore the short-circuit current of the Ge NW device was recorded while a focused laser beam was scanned along the NW.

For NWs under certain constraints discussed by Allen et al. 27 the photocurrent I ph is expected to be proportional to the local electric field. Assuming further that the absorption strength along the tapered NWs is constant, the effective electrostatic potential profile Φ eff along the NW can be determined according to

  dx x I ph eff ) (  (eq. 2)
Independent of the excitation power Pexc, the position of the p-n junction is clearly determined in the electrostatic potential profile, while the potential in the vicinity of the (left) p-type contact is completely flat. Close to the (right) n-type contact there are indications of a Schottky barrier induced field, though negligible compared to the p-n junction related field. To elucidate the electro-optical properties of the axial p-n junction Ge NW device, the forward bias was varied between 0.4V to 0.8V and representative EL spectra were collected as a function of the injection current through the NW. Figure 3a shows exemplarily the near-infrared spectra down to an energy of 0.78eV, limited by the InGaAs detector sensitivity. The current density in the tapered NWs was calculated by normalizing the device current to the cross-sectional area in the small-diameter n-type region that provides the bottle neck for electrical current. Due to the limitations in detector range we can only observe the direct bandgap transition, expected at ~0.8eV at room temperature [START_REF]Handbook Series on Semiconductor Parameters[END_REF] . The spectra are fitted according to the Maxwell-Boltzmann distribution [START_REF] Chen | [END_REF] for spontaneous direct bandgap recombination:

            C B d g d g EL T k E h E h I , , exp   (eq. 3)
with h Planck's constant, ν the optical frequency, E g,d the direct bandgap of Ge and TC the carrier temperature. Furthermore, the polarization properties of the emission are plotted in Figure 3b. Strong polarization of the EL is observed along the NW axis with a degree of polarization of about ρ>73%. A high degree of polarization along the NW axis is frequently reported for cubic semiconductors 30,31 and can be understood in terms of the dielectric contrast of the NW and its surroundings. 32 For an electric field polarized parallel to the Ge NW, the field E i inside the NW equals the field E e outside (E i = E e ). For perpendicular polarization, though, the field inside is highly attenuated:

e i E E 0 0 2     
(eq. 4)

with the dielectric constant for Ge of ε=16.2 and the dielectric constant of air ε 0 =1. A theoretical polarization ratio of ρ=97% is expected, even higher than what is experimentally observed. Additionally, leaky-mode resonances confining light within subwavelength nanostructures exhibit a steep diameter dependency of the TM/TE polarization ratio. 33 Due to the tapering of the p-n NW devices, however, a complex mode profile may be expected and thus the degree of polarization is not predictable in a straight forward way.

The EL emission properties were investigated of as grown NWs as well as after the removal of the parasitic n-doped shell. Figure 4 shows parameters extracted from fits to the spectra according to eq. 3 before and after the etching procedure. The lattice temperature is estimated employing two independent approaches. First, temperature is extracted by employing Varshnis's law and the bandgap energy E g,d :

     T T E E d g 2 0 ,
(eq. 5)

with E 0 =0.89eV the bandgap at T=0K, α=5.82*10 -4 eV/K 2 , β=296K. [START_REF]Handbook Series on Semiconductor Parameters[END_REF] Second, Raman characterization of the NW junction region is employed and we estimate the lattice temperature via the Raman shift of the main optical phonon peak 34,35 according to the

linearization     k T
with ∆T the temperature and ∆Ω the Raman peak shift. The linear factor k=62.3K/rel.cm -1 was determined from a temperature dependent study. 34 The temperature of the charge carrier was extracted by fitting the high-energy wing of the electroluminescence spectra. 36 The lattice temperature estimated from Raman characterization appeared to be slightly lower than the lattice temperature estimated from the temperature dependency of the bandgap energy. We can speculate that locally within the recombination region the temperature is higher than derived from Raman characterization at the junction position. In these hot-spots recombination probability is higher and thus the emission from localized regions with increased temperature could dominate the emission. Considering the lattice temperature from both approaches, Joule heating is slightly increasing the temperature of the lattice with increasing current density.

However in this temperature regime we can exclude thermal radiation as a source of emission in the considered range. The peak wavelength and total radiated amount of a thermal emitter vary with temperature according to Wien's displacement law. Emission with a maximum at about 1.5m corresponds thus to a temperature of about 1200K, far above the temperature we determined for our light emitting device and even above the melting temperature of Ge.

Overall for all devices we observe a significantly higher carrier temperature of ≈550K as compared to the lattice temperature of ≈350K at high injection current, indicating nonequilibrium hot-carrier recombination. Similar to the observed behavior, carrier temperature has been frequently reported to be higher than the actual junction temperature in common planar LED structures. 36 Proposed mechanisms are Auger recombination, intervalence band absorption 37 or high-energy carrier injection in the active region under large forward bias 38 . Particularly for NWs, a recent work of Tedeschi et al. 39 has addressed the role of inhibited phonon emission in confined nanostructures for hot-carrier luminescence. Therein, a general trend of increasing carrier temperature with decreasing NW diameter was found under quasi-equilibrium conditions provided by continuous wave excitation. The proposed mechanism relates to effective phonon scattering at the NW surface, preventing the carriers from reaching thermal equilibrium with the lattice via phonon emission. Qualitatively this trend is reproduced in Figure 4b, since the etched NWs tend to exhibit a higher carrier temperature than the as-grown NWs with larger diameter.

25

 25

Figure 1 .

 1 Figure 1. Ge p-n junction NW device. (a) SEM images of the Ge p-n NW, together with a sketch of the pand n-type regions of the device and a sketch of the equivalent circuits before and after etching of the parasitic n-doped Ge layer. (b) I/V characteristics before (black) and after (red) the etching procedure. Open circles are measured data points, solid lines are fits to the data according to eq. 1. The parasitic shunt disappears after the n-Ge layer removal, while the series resistance stays roughly the same. The diode ideality factor improves from 2.5 to 1.4.

Figure 2 .

 2 Figure 2. Scanning photocurrent spectroscopy. The uppermost panel shows an overlay of an optical image with the excitation laser spot and an SEM image of the etched NW. Independent of the excitation power, the photocurrent scales with the internal electric field and is highest at the p-n junction, linescans along the NW axis provide the exact position of the junction. The electrostatic potential profile reveals negligible Schottky barriers at the metal-semiconductor contacts. The lowermost panel shows the thereof calculated profile of the effective electrostatic potential.

Figure 3 .

 3 Figure 3. Room temperature EL of the Ge NW p-n diode biased in forward direction. (a) EL spectra for increasing current density, (b) Polarization dependence of the emission. A high degree of polarization >73% was found. Solid lines in both panels are fits to the Maxwell-Boltzmann distribution.

Figure 4 .

 4 Figure 4. Bandgap energy, temperature, and EL intensity as a function of current density. Direct bandgap energy, carrier temperature and integrated intensity are extracted from fits to the EL spectra. Black spheres correspond to as-grown NWs, red spheres to the NWs after the etching procedure. Lines represent linear fits. (a) The direct bandgap energy decreases due to Joule heating of the lattice. (b) Carrier and lattice temperature are increasing. Lattice temperature is derived in two independent ways, from Raman

Figure 4c shows the

  Figure 4c shows the integrated EL intensity as a function of current density. The linear

Figure 1 :

 1 Figure 1:

Figure 2 :

 2 Figure 2:

Figure 3 :

 3 Figure 3:

Figure 4 :

 4 Figure 4:

Acknowledgements

The authors gratefully acknowledge financial support by the Austrian Science Fund (FWF): project No.: P28175-N27. The authors further thank the Center for Micro-and Nanostructures for providing the cleanroom facilities.


Emmanuelle Anceaume

Antonella Del Pozzo

Romaric Ludinard

Maria Potop-Butucaru

POSTER: Blockchain Abstract Data Type

Keywords: Distributed computing models; Blockchain, Abstract Data Type, Consistency Criteria

This paper is the first to specify blockchains as a composition of abstract data types all together with a hierarchy of consistency criteria that formally characterizes the histories admissible for distributed programs that use them. The paper presents as well some results on implementability of the presented abstractions and a mapping of representative existing blockchains from both academia and industry in our framework.

CCS Concepts • Theory of computation →

Introduction

The paper proposes a new data type to formally model blockchains and their behaviors. We aim at providing consistency criteria to capture the correct behavior of current blockchain proposals in a unified framework encompassing both forkable and non-forkable blockchains. To this end, the key point is to define consistency criteria allowing mutable operations to create forks and restricting the values read, i.e. modeling the data structure as an append-only tree. This way we can easily define semantics equivalent to eventually consistent append-only queue for non-forkable blockchains but as well as weaker semantics for forkable ones. For nonforkable blockchain we introduce the Strong Prefix consistency criterion that guarantees that for any two reads, the value returned by one is a prefix of the value returned by the other one. A similar proposal has been presented in [START_REF] Girault | Monotonic Prefix Consistency in Distributed Systems[END_REF]. For forkable blockchains, we introduce the Eventual Prefix consistency criterion, which guarantees that eventually, for any two reads, the value returned by one read is a prefix of the value returned by the other one.

Another peculiarity of blockchains lies in the notion of validity of blocks, i.e. the blockchain must contain only blocks that satisfy a given predicate. To abstract away implementationspecific validation mechanisms, we propose to encapsulate the validation process in an oracle model separated from the process of updating the data structure. The oracle has two roles: first generating valid blocks, to be potentially appended to the append-only tree data structure, and second managing the append of the new valid blocks. This second role allows forks in the append-only tree data structure: from an unbounded number of forks (weak oracle) to none of them (strong oracle). The blockchain is then abstracted by an oracle-based construction in which the update and consistency of the tree data structure depend on the validation and synchronization power of the oracle. Related Work. In [START_REF] Garay | The Bitcoin Backbone Protocol: Analysis and Applications[END_REF] the authors extract Bitcoin backbone and define invariants that this protocol has to satisfy in order to verify with high probability an eventual consistent prefix. This line of work has been continued by [START_REF] Pass | FruitChains: A Fair Blockchain[END_REF]. However, to the best of our knowledge, no other previous attempt proposed a consistency unified framework and hierarchy capturing both Consensus-based and proof-of-work based blockchains. In [START_REF] Abraham | The Blockchain Consensus Layer and BFT[END_REF], the authors present a study about the relationship of BFT consensus and blockchains. In order to abstract out the proof-of-work mechanism the authors propose a specific oracle, in the same spirit of our oracle abstraction, but more specific than ours, since it makes a direct reference to proof-of-work properties. In parallel and independently of our work, [START_REF] Fernández Anta | Formalizing and Implementing Distributed Ledger Objects[END_REF] proposes a formalization of distributed ledgers modeled as an ordered list of records. The authors propose in their formalization three consistency criteria: eventual consistency, sequential consistency and linearizability. Interestingly, they show that a distributed ledger that provides eventual consistency can be used to solve the consensus problem. These findings confirm our results about the necessity of Consensus to solve Strong Prefix. On the other hand, the proposed formalization does not propose weaker consistency semantics more suitable for proof-of-work blockchains as BitCoin. The work achieved in [START_REF] Fernández Anta | Formalizing and Implementing Distributed Ledger Objects[END_REF] is complementary to the one presented in [START_REF] Anceaume | Bitcoin a Distributed Shared Register[END_REF], where the authors study the consistency of blockchain by modeling it as a register. Finally, [START_REF] Girault | Monotonic Prefix Consistency in Distributed Systems[END_REF] presents an implementation of the Monotonic Prefix Consistency (MPC) criterion and showed that no criterion stronger than MPC can be implemented in a partition-prone message-passing system.

Contribution

The main contribution of the paper is a formal unified framework providing blockchain consistency criteria that can be combined with oracle models in a proper hierachy of abstract data types [START_REF] Perrin | Causal Consistency: Beyond Memory[END_REF] independent of the underlying communication and failure model. The following implementability results are shown:

• The strongest oracle, guaranteeing no fork, has Consensus number ∞ in the Consensus hierarchy of concurrent objects [START_REF] Herlihy | Wait-free synchronization[END_REF]. It must be noted that we considered Consensus defined in [START_REF] Cachin | Secure and Efficient Asynchronous Broadcast Protocols[END_REF][START_REF] Crain | Leader/Randomization/Signature)-free Byzantine Consensus for Consortium Blockchains[END_REF][START_REF] Gilad | Algorand: Scaling byzantine agreements for cryptocurrencies[END_REF], in which the Validity property states that a valid block can be decided even if sent by a faulty process. • The weakest oracle, which validates a potentially unbounded number of blocks to be appended to a given block, has Consensus number 1. • The impossibility to guarantee Strong Prefix in a messagepassing system if forks are allowed. This means that Strong Prefix needs the strongest oracle to be implemented, which is at least as strong as Consensus. • A necessary condition for Eventual Prefix in a messagepassing system, called Update Agreement stating that each update sent by a correct process must be eventually received by every correct process. Thus, it is impossible to implement Eventual Prefix if even only one message sent by a correct process is dropped.

The proposed framework along with the above-mentioned results helps in classifying existing blockchains in terms of their consistency and implementability. We used the framework to classify several blockchain proposals. We showed that Bitcoin [START_REF] Nakamoto | Bitcoin: A Peer-to-Peer Electronic Cash System[END_REF] and Ethereum [START_REF] Wood | Ethereum: A secure decentralised generalised transaction ledger[END_REF] have a validation mechanism that maps to our weakest oracle and then they only implement Eventual prefix, while other proposals map to our strongest oracle, falling in the class of those that guarantee Strong Prefix (e.g. Hyperledger Fabric [START_REF] Androulaki | Hyperledger Fabric: A Distributed Operating System for Permissioned Blockchains[END_REF], PeerCensus [START_REF] Decker | Bitcoin Meets Strong Consistency[END_REF], ByzCoin [START_REF] Kokoris-Kogias | Enhancing Bitcoin Security and Performance with Strong Consistency via Collective Signing[END_REF]).

Conclusion and Future Work

We believe that the presented results are of practical interests since our oracle construction not only reflects the design of many current implementations but will help designers in choosing the oracle they want to implement with a clear semantics and inherent trade-offs in mind. Future work will

focus on several open issues, such as the solvability of Eventual Prefix in message-passing, the synchronization power of other oracle models, and fairness properties for oracles.

PPoPP ' 19 ,

 19 February 16-20, 2019, Washington, DC, USA E. Anceaume et al.