Sabrina Sayah

Jean-Yves Rotgé

Hélène Francisque

Marcela Gargiulo

Virginie Czernecki

Damian Justo

Khadija Lahlou-Laforet

Valérie Hahn

Massimo Pandolfo

Antoine Pelissolo

Philippe Fossati

Alexandra Durr
email: alexandra.durr@upmc.fr

Personality and Neuropsychological Profiles in Friedreich Ataxia

Keywords: Friedreich ataxia, Cerebellum, Neuropsychology, Personality, Emotional recognition, Social cognition

Friedreich ataxia, an autosomal recessive mitochondrial disease, is the most frequent inherited ataxia. Many studies have attempted to identify cognitive and affective changes associated with the disease, but conflicting results have been obtained, depending on the tests used and because many of the samples studied were very small. We investigated personality and neuropsychological characteristics in a cohort of 47 patients with genetically confirmed disease. The neuropsychological battery assessed multiple cognition domains: processing speed, attention, working memory, executive functions, verbal memory, vocabulary, visual reasoning, emotional recognition, and social cognition. Personality was assessed with the Temperament and Character Inventory, and depressive symptoms were assessed with the Beck Depression Inventory. We found deficits of sustained attention, processing speed, semantic capacities, and verbal fluency only partly attributable to motor deficit or depressed mood. Visual reasoning, memory, and learning were preserved. Emotional processes and social cognition were unimpaired. We also detected a change in automatic processes, such as reading. Personality traits were characterized by high persistence and low self-transcendence. The mild cognitive impairment observed may be a developmental rather than degenerative problem, due to early cerebellum dysfunction, with the impairment of cognitive and emotional processing. Disease manifestations at crucial times for personality development may also have an important impact on personality traits.

Introduction

Friedreich ataxia (FRDA) is an autosomal recessive disease and the most common inherited form of ataxia. Clinical presentation includes cerebellar and sensory ataxia, associated with pyramidal signs (extensor plantar response and spasticity), an absence of tendon reflexes in the legs, deep sensory loss, and foot deformity. Mean onset of symptoms is around puberty, even if late-onset cases exist [START_REF] Parkinson | Clinical features of Friedreich's ataxia: classical and atypical phenotypes[END_REF]. Cardiomyopathy is typically found and is the most common cause of death [START_REF] Pousset | A 22-year follow-up study of long-term cardiac outcome and predictors of survival in Friedreich ataxia[END_REF]. Other clinical features, reminiscent of those seen in other mitochondrial diseases, include optic atrophy, deafness, and diabetes. FRDA results from the abnormal expansion of a GAA (guanine, adenine, adenine) triplet repeat in a non-coding region of both alleles of the frataxin (FXN) gene, resulting in the production of only small amounts of frataxin, a small mitochondrial protein [START_REF] Campuzano | Friedreich's ataxia: autosomal recessive disease caused by an intronic GAA triplet repeat expansion[END_REF][START_REF] Campuzano | Frataxin is reduced in Friedreich ataxia patients and is associated with mitochondrial membranes[END_REF]. In less than 2% of cases, the GAA expansion in one allele is associated with a point mutation [START_REF] Cossée | Friedreich's ataxia: point mutations and clinical presentation of compound heterozygotes[END_REF] or an exonic deletion in the other allele [START_REF] Anheim | Exonic deletions of FXN and early-onset Friedreich ataxia[END_REF]. Age at onset depends partly on expansion size, and onset may occur late, at or beyond the age of about 40 years, in some individuals with short expansions (< 500 GAA repeats) [START_REF] Dürr | Clinical and genetic abnormalities in patients with Friedreich's ataxia[END_REF][START_REF] Lecocq | Delayed-onset Friedreich's ataxia revisited[END_REF]. Neuronal loss begins in the dorsal root ganglia, with T cell degeneration explaining the observed areflexia. Dentate nucleus lesions cause atrophy of the superior cerebellar peduncle, but the Purkinje cell axons are usually preserved [START_REF] Koeppen | Friedreich ataxia: neuropathology revised[END_REF]. Patients suffer a loss of coordination and gait disorders due to spinal cord degeneration, cerebellar atrophy, or both. FRDA therefore differs from other inherited cerebellar ataxias in which the lesions are found principally in the cerebellum, pons, and cortex.

In addition to its role in motor control, the cerebellum also contributes to non-motor functions. Schmahmann described a cerebellar cognitive affective syndrome (CCAS) consisting of cognitive and affective deficits due to cerebellar disease [START_REF] Schmahmann | The cerebellar cognitive affective syndrome[END_REF][START_REF] Manto | Schmahmann's syndrome-identification of the third cornerstone of clinical ataxiology[END_REF]. CCAS, or Schmahmann syndrome, is characterized by multimodal disturbances, including executive and visuospatial deficits, linguistic impairment, and personality changes [START_REF] Schmahmann | The neuropsychiatry of the cerebellum-insights from the clinic[END_REF]. The cerebellum has been shown to play a key role in social cognition, the cognitive processes required to understand, generate, and regulate social behavior [START_REF] Fiske | Social cognition: from brains to culture[END_REF]. Hoche et al. showed that patients with cerebellar disorders find it difficult to attribute emotions to faces [START_REF] Hoche | Cerebellar contribution to social cognition[END_REF]. The recognition of emotions is essential for appropriate social functioning and is a key element of social cognition. Van Overwalle et al. conducted a meta-analysis on social cognition and the cerebellum [START_REF] Van Overwalle | Social cognition and the cerebellum: a meta-analysis of over 350 fMRI studies[END_REF]. They found robust clusters of activation in the cerebellum that were recruited during these social-cognitive processes. A meta-analytic connectivity analysis suggested a key role for the cerebellum in social cognition [START_REF] Van Overwalle | Social cognition and the cerebellum: a meta-analytic connectivity analysis[END_REF]. Van Overwalle et al. showed that the pattern of activation differed between understanding actions (reading body language) and mentalizing (Bmind-reading^), two different aspects of social cognition. Thus, lesions in the cerebellum may cause difficulties with social cognition.

Subtle cognitive and psychiatric abnormalities have been described in FRDA patients [START_REF] Mantovan | Exploring mental status in Friedreich's ataxia: a combined neuropsychological, behavioral and neuroimaging study[END_REF][START_REF] Nieto | Cognition in Friedreich ataxia[END_REF][START_REF] Nieto | Cognition in late-onset Friedreich ataxia[END_REF][START_REF] Wollmann | Neuropsychological test performance of patients with Friedreich's ataxia[END_REF][START_REF] De Nóbrega | Differential impairment in semantic, phonemic, and action fluency performance in Friedreich's ataxia: possible evidence of prefrontal dysfunction[END_REF]. A first study of 13 patients showed a higher than normal frequency of personality traits such as increased irritability, poor control over impulses, poor self-presentation, and cognitive dysfunctions characterized by impaired learning processes and verbal fluency. It also showed that mean IQ was lower in FRDA patients than that in controls, this difference being observed for both verbal and performance IQ scores. GAA expansion size was not correlated with neuropsychological performance [START_REF] Mantovan | Exploring mental status in Friedreich's ataxia: a combined neuropsychological, behavioral and neuroimaging study[END_REF].

Other studies highlighted impairments in verbal fluency [START_REF] Nieto | Cognition in Friedreich ataxia[END_REF][START_REF] Nieto | Cognition in late-onset Friedreich ataxia[END_REF][START_REF] Wollmann | Neuropsychological test performance of patients with Friedreich's ataxia[END_REF], particularly for tasks requiring major executive processing [START_REF] De Nóbrega | Differential impairment in semantic, phonemic, and action fluency performance in Friedreich's ataxia: possible evidence of prefrontal dysfunction[END_REF]. Some authors have also reported an impairment of conceptual thinking in FRDA patients [START_REF] Nieto | Cognition in Friedreich ataxia[END_REF]. These findings suggest that these patients present prefrontal function deficits. Verbal fluency and working memory deficits have recently been confirmed in a cohort of 22 patients, together with an impairment of social cognition [START_REF] Dogan | Cognition in Friedreich's ataxia: a behavioral and multimodal imaging study[END_REF].

Long-term follow-up of FRDA patients at the French national reference center for rare diseases defined a recognizable clinical pattern, with increased irritability and poor control of impulses, with consequences for family and social life. We therefore investigated personality and neuropsychological characteristics in a large cohort of patients with genetically confirmed FRDA, through a battery of personality and neuropsychological tests.

Materials and Methods

Participants

Between 2012 and 2014, 50 patients with genetically confirmed FRDA were enrolled in the EFACTS (European Friedreich's Ataxia Consortium for Translational Studies, ongoing prospective and longitudinal study, NCT02069509) consortium study. Informed consent was obtained from all individual participants included in the study. Two patients refused to participate and one could not be evaluated due to marked impairment in oral and written communication.

Genetic and Clinical Assessments

We recorded the number of GAA repeats in each allele (the second allele is the longer allele). Age at onset was assessed retrospectively, according to information provided by patients and their families concerning the first symptoms. Disease duration, in years, was calculated as the interval between age at onset and age at examination. Clinical examinations included the determination of a functional disability score ranging from 1 (no functional handicap but signs at examination) to 7 (confined to bed), and SARA (Scale for the Assessment and Rating of Ataxia) score ranging from 0 to 40.

Personality Assessments

The Temperament and Character Inventory (TCI) was used to assess the personality dimensions of participants [START_REF] Cloninger | The Temperament and Character Inventory (TCI): a guide to its development and use[END_REF][START_REF] Pélissolo | Normative data and factor structure of the Temperament and Character Inventory (TCI) in the French version[END_REF]. This 226-item questionnaire deals with seven dimensions of personality traits: four temperament dimensions and three character dimensions. The temperament dimensions considered are novelty seeking (score range 0-40), harm avoidance (score range 0-36), reward dependence (score range 0-24), and persistence (score range 0-8). Novelty seeking targets the tendency of the patient to become excited when presented with novel stimuli. Harm avoidance is the inhibition or cessation of behavior in the face of adverse stimuli (such as pessimistic worry, passive dependent behavior). Reward dependence is a tendency to respond by sentimentality, social attachment, or dependence to signals associated with rewards. Persistence is the tendency to persevere in a particular pattern of behavior despite frustration or fatigue. The character dimensions investigated are self-directedness (score range 0-44), cooperativeness (score range 0-42), and self-transcendence (score range 0-33). Self-directedness is to the ability to control, regulate, and adapt behavior in accordance with personal goals and values. Cooperativeness is the degree of maturity and social tolerability. Self-transcendence relates to spiritual ideas.

Neuropsychological Assessments

Our neuropsychological battery comprised eight different tests in their French-validated versions:

1. A visual reasoning test was used to measure global cognitive efficiency. The test used was Raven's Progressive Matrices (PM38, SPM), which has been identified as the best instrument for measuring the Bg^factor strongly correlated with general mental ability. PM38 is a 60-item non-timed test, in which each item presents a pattern problem to resolve [START_REF] Raven | Raven's progressive matrices and vocabulary scales[END_REF]. 2. A vocabulary test was used to assess semantic capacities.

The test used was the Mill-Hill part B test [START_REF] Raven | Raven's progressive matrices and vocabulary scales[END_REF][START_REF] Deltour | Echelle de vocabulaire de Mill Hill de JC Raven[END_REF].

Participants were asked to select the synonym of the target word from a list of six words. They were presented with 44 target words of increasing difficulty during the test. This multiple choice test was considered to be the most appropriate as it requires a smaller contribution of executive function than part A. Vocabulary is known to increase with age and education level, whereas reasoning ability is considered to be independent of schooling.

Verbal learning and memory were assessed with the

Hopkins Verbal Learning Test (HVLT) [START_REF] Rieu | Adaptation française du «Hopkins verbal learning test[END_REF]. This test consists of a list of 12 words from three semantic categories (4 words per category). Participants undergo three learning trials each followed by free recall. After the third recall and an interval of 20-25 min, a last recall is performed, followed by a yes-/no-delayed recognition trial. 4. Attentional skills were assessed with the Paced Auditory Serial Addition Test [START_REF] Gronwall | The psychological effects of concussion[END_REF][START_REF] Naegele | Test d'attention auditive soutenue PASAT modifié[END_REF], which evaluates sustained attention, short-term memory, working memory, and inhibitory control. Single-digit numbers were presented to the participant at 4-s intervals. The participant had to give the sum of the last two digits before being presented with the next digit. This test had a total duration of 5 min. We evaluated effects on sustained attention, by separating the test into three equal parts and counting the incorrect responses for each part.

Focused attention was assessed with the Golden version

of the Stroop test, including word reading, color naming, and interference conditions (non-matching words and colors) [START_REF] Golden | Stroop color and word test[END_REF][START_REF] Stroop | Studies of interference in serial verbal reactions[END_REF]. The performance of the Stroop test also requires inhibitory control, and this test can therefore be considered to assess executive functions too. The number of correct responses in 45 s was recorded. 6. We assessed mental flexibility, by asking participants to give as many words as possible beginning with the letter P (P-fluency test) in a 2-min period. The total number of correct words was recorded.

The mini Social Cognitive and Emotional Assessment

(SEA) was used to evaluate social cognition and emotional recognition. Social cognition abilities, including theory of mind, in particular, were evaluated with the short version of the Faux-Pas-Recognition test [START_REF] Gregory | Theory of mind in patients with frontal variant frontotemporal dementia and Alzheimer's disease: theoretical and practical implications[END_REF][START_REF] Stone | Frontal lobe contributions to theory of mind[END_REF][START_REF] Funkiewiez | The SEA (Social cognition and Emotional Assessment): a clinical neuropsychological tool for early diagnosis of frontal variant of frontotemporal lobar degeneration[END_REF]. Ten stories were proposed and the participant was asked to explain, for each, whether or not it contained a faux-pas. 8. Emotional recognition was assessed on the basis of the identification of [START_REF] Ekman | Pictures of facial affect[END_REF] Ekman facial expressions: fear, anger, happiness, surprise, disgust, sadness, neutral [START_REF] Ekman | Pictures of facial affect[END_REF].

Finally, we checked that neuropsychological performances were not driven by possible depressive symptoms, by assessing the intensity of such symptoms with the Beck Depression Inventory (BDI-II), a 13-item self-administered questionnaire [START_REF] Beck | Inventaire de dépression de Beck[END_REF].

Data Analyses

For demographic characteristics and BDI, categories were compared in χ 2 tests and means were compared in t tests. The Kolmogorov-Smirnov test was used to evaluate the normality of dependent variables in the whole sample. Three variables did not follow a normal distribution: age at onset (d = 0.25, p < 0.01, Lilliefors p < 0.01), disability score (d = 0.29, p < 0.01, Lilliefors p < 0.01), and HVLT discrimination (d = 0.48, p < 0.01, Lilliefors p < 0.01). One-sample t tests were conducted to compare the mean value for the patient with the reference value. For the personality questionnaire, mean TCI scores for the French population (n = 602) were used as reference values. We limited the risk of false-positive results due to the performance of multiple independent statistical tests, by applying Bonferroni correction systematically, to adjust the p values (p = 0.05/7 = 0.007). For neuropsychological characteristics, individual scores were compared with French population norms for age and education level. The results were converted into standard scores (Z scores; i.e., number of standard deviations above or below the mean) as follows: {[individual score]-[population mean]/[standard deviation of the population]}. Standard scores took into account gender, age, and educational level. Z scores were then compared with the reference value of 0. Bonferroni correction was also applied to adjust the p values for multiple analyses (p = 0.05/13 = 0.003).

We performed stepwise multiple regression analyses, to explain the possible effects of clinical characteristics on personality and neuropsychological profile. Regression analyses were therefore conducted only when measured values significantly differed from reference values. The following clinical variables were entered into the model as independent variables: age, sex, level of education, age at onset, disease duration, disability score, SARA score, GAA repeats in the shorter allele only (as the smaller allele determines the amount of residual protein and, thus, severity), BDI score. Dependent variables were defined on the basis of the results of onesample t tests with Bonferroni correction. The best multiple regression model was selected by a stepwise approach. The alpha risk threshold was set at 0.05. Finally, we analyzed the correlation between neuropsychological assessment and personality scores.

Results

Participants

In total, 47 patients (29 women and 18 men) gave informed consent for participation in the study. The demographic and clinical characteristics of the participants are presented in Table 1 and Fig. 1 for age at onset distribution. Education level is the number of years spent in education; in France, the Baccalauréat, corresponding to 12 years of education, is the equivalent of the American high-school diploma. Disease manifestations first appeared at or before the age of 16 years in 62% of patients (29/47). Psychotropic medication was noted in one third of the patients, including six with SSRI, three with anxiolytics, three took both. One took lithium and another one neuroleptics in conjunction with SSRI. This is comparable to the psychotropic drug use in the French population (32% in the report of the French National Agency for Drug Security, ANSM).

Personality Assessments

FRDA patients had higher scores for persistence temperament (t = 5.38; p < 0.005), but lower scores for the selftranscendence character (t = -3.13, p < 0.005) than those of the French general population. No difference between FRDA patients and the general population was observed for other temperament and character dimensions (see p values in Table 2). Self-transcendence and persistence were not

Neuropsychological Assessments

FRDA patients performed less well than the French general population in the Mill-Hill B test: they had a significantly lower vocabulary level (t = -7.53, p < 0.001). Attention was found to be impaired: six of the patients failed the training trials for the Paced Auditory Serial Addition Test (PASAT) and therefore did not perform the full test. The other participants made more errors in the last third of the PASAT (t = -4.07; p < 0.001) than in the preceding PASAT trials. Stroop test scores were significantly lower in patients than those in the general population for color (t = -8.85; p < 0.001) and word reading (t = -9.53, p < 0.001), but there was no interference effect (t = 1.15, p = 0.26). We took the cerebellar dysarthria likely to interfere with Stroop test performances into account by assessing the correlation between the SARA dysarthria item and the scores for the three parts of the Stroop test. Dysarthria was negatively correlated with the scores for all three parts of the Stroop test: color (r = -0.34; p = 0.028), word reading (r = -0.41; p = 0.007), and interference (r = -0.32; p = 0.042).

All other neuropsychological functions, as assessed with Raven's test, and the HVLT, P-fluency, emotional recognition, and faux-pas tests, were similar in patients and in the general population. The results of the neuropsychological assessments are reported in Table 2.

Multiple Regression Analyses

Regression analyses were conducted to assess the influence of clinical variables on the observed differences. The low Mill-Hill B Z scores obtained were related to sex, age at onset, education level, and BDI score (F = 4.68, R 2 = 0.48, p < 0.05). The beta-values, indicative of the direction and strength of the relationship between each independent variable and Mill-Hill B Z scores, were -0.54 for the proportion of women, 0.38 for age at onset, 0.23 for education level, and 0.18 for BDI score. Thus, a more extensive vocabulary was associated with a later age at onset, a higher education level, and also a higher level of depression. In order to inspect the correlation on possible outliers, the correlation with age at onset is shown in Fig. 2a.

Attention performances were related to age (Fig. 2b), sex, disability score, and disease duration (F = 3.14, R 2 = 0.42, p < 0.05). Attention in the third part of the test was poorer only in the younger patients (b = 0.28), with greater disability (b = -0.73).

In the Stroop test for color, performances were correlated with disability score, disease duration (Fig. 2c), and the number of GAA repeats in the smaller allele (F = 8.17, R 2 = 0.48, p < 0.05). The best performances were obtained for patients with lower levels of disability (b = -0.22), shorter disease duration (b = -0.41), and smaller numbers of GAA repeats in the smaller allele was (b = -0.31). For the Stroop word test, performances were correlated with disability score, disease duration (Fig. 2d), and the numbers of GAA repeats in both alleles (F = 7.55, R 2 = 0.56, p < 0.05). The best performances for the Stroop word test were obtained for the patients with the lowest disability scores (b = -0.19), the shortest disease duration (b = -0.43), and the smallest numbers of GAA repeats (b = -0.32).

Discussion

This study in a large cohort of FRDA patients assessed personality and neuropsychological profiles and included the first assessment of theory of mind and emotional processes. A comparison of the neuropsychological testing results for 47 FRDA patients with those for the general population revealed deficits in sustained attention, processing speed, semantic capacities, and verbal capacities. Visual reasoning, memory, and learning were preserved. Emotional processes and social cognition were also unimpaired. Deficits in sustained attention, assessed with the PASAT, were linked to disability score, indicating a direct link to disease severity. Previous studies have given conflicting results concerning volitional sustained attention: one study [START_REF] Nieto | Cognition in Friedreich ataxia[END_REF] suggested that sustained attention was preserved, whereas others have shown it to be impaired in FRDA patients, with this deficit not due to articulatory deficits [START_REF] Mantovan | Exploring mental status in Friedreich's ataxia: a combined neuropsychological, behavioral and neuroimaging study[END_REF][START_REF] Klopper | The test of everyday attention reveals significant sustained volitional attention and working memory deficits in Friedreich ataxia[END_REF]. Our study goes one step further, by separating the PASAT into three parts. Those patients able to perform the whole test succeeded in the first two parts of the PASAT, suggesting that these patients have an efficient working memory and a normal capacity to maintain a high level of cognitive effort. Nevertheless, we show here that sustained attention is impaired in FRDA patients, as their time-dependent attention skills were poor.

The Stroop test revealed that patients performed significantly less well than the general population in the color and word tests, whereas there was no difference for the interference test. The results of the three parts of the Stroop test were correlated with dysarthria, suggesting that this condition may account for these results. Our findings confirm that FRDA patients have slower information processing, linked to cerebellar dysarthria [START_REF] Wollmann | Neuropsychological test performance of patients with Friedreich's ataxia[END_REF]. Despite this link between dysarthria and the three parts of the Stroop test, patients were able to perform the interference test as well as the general population, whereas they performed poorly in the color and word tests. This very specific pattern in FRDA patients suggested that dysarthria cannot entirely explain the poor performances of these patients in the Stroop test. In the general population, individuals take longer to respond in the color test than in the word test, and their response times increase still further when faced with a color name printed in an incongruent color (e.g., the word Bblue^printed in red ink) due to a conflict between the naming of the color and word reading. Indeed, in the general population, reading mechanisms are more automatic than color naming. This conflict seems to be reduced in FRDA patients, allowing them to perform normally in the interference test, despite their dysarthria. Previous studies have demonstrated a link between the cerebellum and reading. Vlachos and colleagues reported such a link, particularly in individuals with reading disabilities [START_REF] Vlachos | Cerebellum and reading[END_REF]. Travis et al. reported an association between reading skills and cerebellar white matter pathways, and, more specifically, with the microstructure of the cerebellar peduncles [START_REF] Travis | Cerebellar white matter pathways are associated with reading skills in children and adolescents[END_REF]. Based on the results reported here and published findings, we suggest that the ability to activate automatisms, such as reading, is altered in patients with FRDA.

As expected, semantic capacities were linked to education level. However, comparison with the French general population revealed mild impairment in terms of vocabulary. FRDA patients have been shown to present a deficit in the acquisition of verbal information [START_REF] Nieto | Cognition in Friedreich ataxia[END_REF]. This deficit may reflect the effects of articulatory deficits on verbal communication, leading to poorer exchanges and vocabulary acquisition. Nevertheless, the lower verbal and IQ levels in FRDA patients suggest a more global deficit [START_REF] Mantovan | Exploring mental status in Friedreich's ataxia: a combined neuropsychological, behavioral and neuroimaging study[END_REF]. We found a positive link between Mill-Hill score and age at onset. Semantic capacities were lower in patients with earlier onset disease, but were unrelated to disease duration, consistent with a significant contribution of the cerebellum to the development of cognitive abilities.

We found a trend towards lower verbal fluency in FRDA patients. It might be possible to establish a link with information processing speed capacities by considering the time dependence of the test. However, dysarthria is not the only cause of the decrease in processing speed [START_REF] Mantovan | Exploring mental status in Friedreich's ataxia: a combined neuropsychological, behavioral and neuroimaging study[END_REF][START_REF] Nieto | Cognition in Friedreich ataxia[END_REF][START_REF] Wollmann | Neuropsychological test performance of patients with Friedreich's ataxia[END_REF][START_REF] Dogan | Cognition in Friedreich's ataxia: a behavioral and multimodal imaging study[END_REF][START_REF] De Nóbrega | Differential impairment in semantic, phonemic, and action fluency performance in Friedreich's ataxia: possible evidence of prefrontal dysfunction[END_REF][START_REF] Nachbauer | Friedreich ataxia: executive control is related to disease onset and GAA repeat length[END_REF]. The impairment of phonemic and action fluencies may, therefore, be better explained by the strong executive component of these tasks requiring shifting abilities, because semantic fluency was unimpaired [START_REF] De Nóbrega | Differential impairment in semantic, phonemic, and action fluency performance in Friedreich's ataxia: possible evidence of prefrontal dysfunction[END_REF][START_REF] White | Neuropsychologic and neuropsychiatric characteristics of patients with Friedreich's ataxia[END_REF].

The neuropsychological profile of the FRDA patients in this study was associated with a specific personality presentation characterized by enhanced persistence and reduced selftranscendence. A limitation of questionnaires is that selfreport may obscure impairments of socioemotional functioning due to lack of self-insight. The fact that the patients score lower on self-transcendence may hint towards this. Typically, socioemotional problems arise in the context of social interactions or daily life activities. Observational scores from, for example, family or friends may be a better way to capture problems in this domain. Nevertheless, our study is the first exploring both, social cognition and emotional recognition, and there was no impairment of theory of mind in FRDA. This allowed us to take into account the low scores of selfrated transcendence. The personality assessment revealed that patients were more likely to persevere in the face of fatigue or frustration than members of the general population. Selftranscendence is a personality trait relating to the experience of spiritual aspects of the self. It is seen as an identification of the self with a unified whole. FRDA-induced uncertainty about the future, disability, and shortened life expectancy may bring out feelings of otherness, making this identification with a unified whole more difficult. Previous studies have shown that self-transcendence is associated with self-wellbeing and adaptation [START_REF] Cloninger | Personality and the perception of health and happiness[END_REF][START_REF] Cloninger | A psychobiological model of temperament and character[END_REF]. Some authors have reported that high scores for the self-transcendence trait characterize individuals open to unusual and divergent feelings, thoughts, and behaviors [START_REF] Kaasinen | Mapping brain structure and personality in late adulthood[END_REF]. However, persistence and transcendence were not correlated with clinical characteristics and neuropsychological data. It should be borne in mind that disease manifestations often begin during adolescence. The diagnosis of a chronic disease at this crucial age may influence personality development [START_REF] Jokela | Personality change associated with chronic diseases: pooled analysis of four prospective cohort studies[END_REF]. However, contrary to our findings, chronic diseases have consistently been shown to be associated with high levels of harm avoidance and low self-directedness and cooperativeness [START_REF] Boz | Effect of serotonergic antidepressant therapy on temperament and character scales in patients with chronic tension-type headache[END_REF][START_REF] Conrad | Temperament and character personality profiles and personality disorders in chronic pain patients[END_REF][START_REF] Kahraman | Temperament and character profiles of male COPD patients[END_REF], suggesting that the personality changes observed here are more specific to FRDA. We can therefore assume that the observed changes are also linked to the FRDA-related lesions of cerebellar pathways. This idea is consistent with the cognitive and affective functions of the cerebellum [START_REF] Schmahmann | The cerebellar cognitive affective syndrome[END_REF][START_REF] Dolan | A cognitive affective role for the cerebellum[END_REF]. A close relationship between cerebellar volumes and personality traits in a healthy population has been reported, suggesting a role for the cerebellum in personality development [START_REF] Picerni | New evidence for the cerebellar involvement in personality traits[END_REF][START_REF] Laricchiuta | Linking novelty seeking and harm avoidance personality traits to cerebellar volumes[END_REF][START_REF] Petrosini | Cerebellum and personality traits[END_REF]. However, further studies are required to assess specifically the putative relationship between personality changes and cerebellar lesions in FRDA.

The main limitation of this study was the absence of a control group matched for age, sex, and number of years spent in education. However, this bias was minimized by comparing our results with mean values for a very large French general population for the TCI, and with standardized scores for neuropsychological measures. This strategy involved the use of multiple independent statistical tests, potentially increasing the risk of false-positive results. We therefore systematically applied Bonferroni correction, the most conservative method for controlling for the risk of type I error. However, it should be acknowledged that the lack of impairments was due to type II errors. As an example, the significant lower fluency did not survive correction but we felt that the difference was clinically important. In addition, our population had an older mean age at onset than reported (20.4 ± 13.7 versus 15.5 ± 10.4 in a 2year cohort study [START_REF] Reetz | Progression characteristics of the European Friedreich's Ataxia Consortium for Translational Studies (EFACTS): a 2 year cohort study[END_REF] that makes generalization of our results more hazardous. In fact, patients with onset after 25 years may have different phenotypic and brain structural features compared to classical FRDA [START_REF] Rezende | Structural signature of classical versus lateonset friedreich's ataxia by multimodality brain MRI[END_REF].

The cognitive impairment and the specific personality profile in FRDA patients demonstrated here provide additional evidence concerning the role of the cerebellum in cognitive and affective processing and personality development. Compared to other ataxias, such as SCA3, similar cognitive processes are impaired in FRDA, such as attention, processing speed, and executive functions [START_REF] Braga-Neto | Cerebellar cognitive affective syndrome in Machado Joseph disease: core clinical features[END_REF]. The neuropsychological dysfunctions in FRDA are clearly milder despite a higher motor disability. Imaging comparison between SCA3 and FRDA showed that volume of the cerebellum is not reduced in FRDA compared to that of SCA3 [START_REF] Stefanescu | Structural and functional MRI abnormalities of cerebellar cortex and nuclei in SCA3, SCA6 and Friedreich's ataxia[END_REF]. Therefore, attribution of FRDA-related cognitive deficits exclusively to CCAS is difficult, even though there were functional MRI abnormalities in the cerebellar cortex in both groups.

Conclusion

In conclusion, FRDA patients had a specific personality and neuropsychological profile. Our findings highlight the presence of very mild cognitive impairment in a large cohort of patients with a genetically confirmed diagnosis. The neuropsychological profile was characterized by a low vocabulary level, changes in automatisms, such as reading, and deficits in sustained attention, and processing speed. The FRDA-related personality traits, characterized by high persistence and low self-transcendence, may be linked to this particular neuropsychological profile.

Fig. 1

 1 Fig. 1 Age at onset distribution of patients with Friedreich's Ataxia (n = 50). The mean age at onset was 20.4 ± 13.7 years

Fig. 2

 2 Fig. 2 Correlation scatterplots of four neuropsychological tests (Mill-Hill B, PASAT, Stroop color, and Stroop word) in Friedreich's ataxia. A more extensive vocabulary was associated with a later age at onset (r 2 = 0.156) (a); attention in the third part of the PASAT was poorer in

Table 1

 1 Demographics and clinical characteristics of FRDA patients (n = 47)

	Mean SD	Range

Table 2

 2 Personality evaluation and neuropsychological test performances of FRDA patients

		n	Mean SD t	p
	Psychopathological evaluation
	BDI-II	33	9.8	8.3 -	-
	Personality evaluation (TCI)
	Novelty seeking (0-40)	42	18.3	5.8 2.10	0.04
	Harm avoidance (0-36)	42	18.6	7.5 2.14	0.04
	Reward dependence (0-24) 42	15.1	3.7 1.61	0.11
	Persistence (0-8)	42	5.4	1.7 5.38	< 0.005*
	Self-directedness (0-44)	42	32.8	5.2 1.00	0.32
	Cooperativeness (0-42)	42	32.8	5.2 1.39	0.17
	Self-transcendence (0-33)	42	10.8	5.9 -3.13 < 0.005*
	Neuropsychological test performance
	Z scores
	Mill-Hill B	47 -1.7	1.6 -7.53 < 0.001*
	Raven's	4 1 -0.3	1.3 -1.44 0.16
	HVLT total	47	0.3	1.0 1.84	0.07
	PASAT 1/3	40 -0.5	1.4 -2.32 0.03
	PASAT 2/3	40 -0.7	1.7 -2.64 0.01
	PASAT 3/3	40 -1.3	2.0 -4.07 < 0.001*
	P-fluency	46 -0.6	1.4 -2.88 0.006
	Emotional recognition	41 -0.1	1.0 -0.72 0.47
	Faux-pas	44	0.2	1.1 1.26	0.22
	Mini SEA	41	0.1	1.2 0.59	0.56
	T scores
	Stroop color	46	38.7	8.5 -8.85 < 0.001*
	Stroop word	46	36.8	8.9 -9.53 < 0.001*
	Stroop interference	46	40.1	9.9 1.15	0.26

SD standard deviation, FRDA Friedreich's ataxia, BDI Beck Depression Inventory, TCI Temperament and Character Inventory, HVLT Hopkins Verbal Learning Test, PASAT Paced Auditory Serial Addition Test, SEA Social Cognition and Emotional Assessment *Significant after Bonferroni correction

Acknowledgments This study is an ancillary substudy of EFACTS (European Friedreich Ataxia Consortium for Translational Studieswww.e-facts.eu, NCT02069509) coordinated by M. Pandolfo. We thank the participants for their patience, and Aurelie Guignebert, Martine Frischmann, and Mathieu Anheim for fruitful initial discussions.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Ethical Approval All procedures performed in studies involving human participants were carried out in accordance with the ethical standards of the institutional and/or national research committee and the 1964 Helsinki declaration and its later amendments or comparable ethical standards.


Farah Gabsi
email: farah.gabsi@univ-lorraine.fr

Frederic Hamelin
email: frederic.hamelin@univ-lorraine.fr

Remi Pannequin
email: remi.pannequin@univ-lorraine.fr

Mohamed Chaabane
email: mohamed.chaabane@sta-tn.com

Energy efficiency of a multizone office building: MPC-based control and Simscape modelling

Keywords: Energy-efficient buildings, Simscape TM models, Model Predictive Control, Multi-room building model

This paper deals with the problem of modelling and controlling a multi-zone office building to ensure its thermal comfort by an optimal and cost effective management of the energy consumption. A thermal behaviour analysis of the building is carried out using the Simscape TM library in MATLAB/Simulink R environment that leads to a multi-model representation. Based on this modelling, the Yalmip toolbox in the MATLAB programming environment or an iterative optimization algorithm can be used to solve the control optimisation problem. The design of a model predictive control associated with a wise choice of the cost function makes it possible to obtain in simulation substantial energy benefits.

INTRODUCTION

Over the last years, a large number of researchers have been interested in controlling strategies for energy saving of buildings [START_REF] Scherer | Efficient building energy management using distributed model predictive control[END_REF], [START_REF] Atam | Control-oriented thermal modeling of multizone buildings: Methods and issues: Intelligent control of a building system[END_REF]. Indeed, the construction sector, especially electrical energy, is the largest energy consumer. It represents approximately 40% of the total energy consumption between all sectors of the economy in France and in the US [START_REF] Agbi | Scalable and Robust Designs of Model -Based Control Strategies for Energy -Efficient Buildings[END_REF]. One of possible approaches to reduce energy consumption in buildings is to use advanced control tools to effectively monitor all the building actuators to ensure its hygrothermal comfort [START_REF] Goyal | Occupancy-based zone-climate control for energyefficient buildings: Complexity vs. performance[END_REF], [START_REF] Privara | Model predictive control of a building heating system: The first experience[END_REF]. In this paper, a thorough methodology of modelling/controlling a building part is proposed to ensure the thermal comfort of its inhabitants while minimizing energy consumption. It uses the Simscape TM toolboxes to model the thermal behaviour of the building [START_REF] Lapusan | Development of a multi-room building thermodynamic model using simscape library[END_REF], and an iterative algorithm (or Yalmip [START_REF] Lofberg | Yalmip: a toolbox for modeling and optimization in matlab[END_REF]) to solve the optimization problem related to the synthesis of a predictive control. The applied target is the "Eco-safe" platform (CRAN Nancy, France) that fits in a global context of smart home. The developed Simscape TM model is based on a physical description of the building. This approach allows the description of the system as a physical structure rather than by abstract mathematical equations. Furthermore, the differential equa-tions that describe the thermal behaviour of the system can be directly generated from the Simscape TM model. This modelling step in the form of a statespace representation is essential for the development of a predictive control model (MPC) [START_REF] Camacho | Model predictive control. Advanced textbooks in control and signal processing[END_REF]. This type of control is favoured because it has the advantage of taking into account the disturbance predictions that greatly influence the interior comfort of a building (outside temperature, sunshine, occupations of parts) while anticipating their effects [START_REF] Ma | Model predictive control for the operation of building cooling systems[END_REF], [START_REF] Oldewurtel | Use of model predictive control and weather forecasts for energy efficient building climate control[END_REF], [START_REF] Privara | Model predictive control of a building heating system: The first experience[END_REF]. Knowing that each control action is associated with a different state-space model of the system, the predictive control used is considered as a hybrid type [START_REF] Le | Optimal control of shading system using hybrid model predictive control[END_REF]. In view of the control objectives, the associated optimization criterion is defined to integrate the energy cost of each actuator in kW h, the resolution of the optimization problem is executed using the Yalmip tool of Matlab or an iterative algorithm for important prediction horizon. The first part of this work is focused on the thermal modelling of a set of building parts because few works have been interested in this issue. The validation of the model and the control will be conducted on the "Eco-safe" platform. Next a model predictive control is put in order to ensure the thermal comfort of the rooms of the platform with a minimum of energy consumption. Tests of simulation with various scenarios were developed to exhibit the energy benefits.

The "Eco-safe" platform consists of 6 rooms and a corridor (Figure 1). The rooms are equipped with sensors and actuators to model their thermal behaviour and control their comfort. Regarding the area, the platform is characterized by two main activity rooms: "a room of research and development" (R&D, 1 ) of 51m 2 and a piece of applications 5 of 34m 2 . Four other rooms, 17m 2 each, allow to store tools and various materials (parts 2 + 4 ) or to have an estimate of the rooms temperature located in the upper and lower floors ( 3 + 6 ), because with the same neutral behaviour. The platform consists of heterogeneous equipment architecture such as the sensors needed for the modelling of its thermal response, the equipment contributing to the thermal comfort of the rooms and a weather station that integrates several sensors. To ensure the thermal comfort of this platform by implementing a predictive control based on the minimization of energy consumption, it is necessary to determine a model for the thermal behaviour of the platform. The following paragraph provides an answer to this objective through the definition of a simulator.

THERMAL MODELLING OF THE PLATFORM

The simplified physical model we aim to establish has the role to predict the thermal behaviour of the whole platform. The latter is decomposed piece by piece taking into account their orientation in order to further simulate the influence of the solar radiation. Each room consists of different elements (walls, ceiling, floor, windows), some of which benefit from some solar energy inputs. The temperature of the R&D room, ( 1 ) and applications ( 5) is also influenced by a main source of energy which is a reversible heat pump to produce the heat and cold. In addition, air flow is provided between these same rooms through two controlled mechanical ventilation (CMV). Overall, the energy balance for each of the rooms can be translated by the following equation:

C int dT int dt = f ext (T ext , T int ) + n ∑ i=1 f i (T int , T int,i )
+θ occupancy + θ energy (1) with:

• C int : heat capacity (J/K) of the considered room; • T int , T ext and T int,i : temperature (K) of the considered room, of outside and of the adjacent rooms; • θ energy and θ occupancy : energy contributions (W ) and heat generated by the inhabitants of the room; • f ext (T ext , T int ) and f i (T int , T int,i ): functions reflecting the thermal behaviour of interfaces between the room and the outside or adjacent rooms.

In order to establish the complete thermal model of the "Eco-safe" platform, we use a physical approach based on the Simscape TM tool [START_REF] Lapusan | Development of a multi-room building thermodynamic model using simscape library[END_REF] in the environment Simulink R . The global model of the platform is the result of the integration of all room models. Each room includes walls and windows that are interacting with the external environment and neighbouring rooms by each mode of heat transfer. While this issue is the subject of the section that follows, the energy sources influencing the room thermodynamics are modelled in the last paragraph.

Thermal modelling of a room

The room model is developed using the thermal elements library of Simscape TM . If a correspondence is established between the flow of heat and electric power as well as between the temperature and the potential difference, it is conventional to establish thermoelectric analogies [START_REF] Achterbosch | The development of a convenient thermal dynamic building model[END_REF]. This analogy will be used in the transcript of the Simscape TM model of the platform to a state-space model.

Models of a wall and a set of windows

Wall The thermal equilibrium is established taking into account the convective exchange between the wall and the air that surrounds it on each side. Inside the wall, the heat is transferred through conduction phenomenon. The wall model developed on Simscape TM model is presented in Figure 2a, in which it is assumed that the wall is the interface between the inside of a room and the outside air. By electrical analogy, the wall can also be described by a 2R1C model (2 resistors and 1 capacitor) and schematically represented in Figure 2b, which presents the following notations: Set of windows To model the thermal behaviour of all windows in a room, we assumed that it was identical to consider a single window of equivalent surface. Knowing that the windows in the rooms are all double glazed, their modelling requires to take into account not only the surface/superficial resistance of inside and outside exchange (transfer by convection/ convective transfer) but also transfers by conduction within the two glass panes and the air space between them (see Figure 3a). By analogy, a 4R3C model is used to determine the associated state-space representation (see Figure 3b). with:

• X 1 (p), X 2 (p)
• X 1 (p), X 2 (p), X 3 (p) and X 4 (p): temperature (K) of the room and in the middle of the inner glass, of the air space and of the outer glass; • (R 12 , R 82 ) and (R 22 , R 32 ,. . ., R 62 , R 72 ): thermal resistances (K/W ) of convection and conduction; • C 22 , C 32 , C 42 : heat thermal capacities (J/K) of the glass and of the air space/blade; The state-space representations of a wall and of a set of windows are then obtained by the application of Millman's theorem.

Models of a room and "Eco-safe" platform

Room A room being made up of several walls, a slab, a ceiling (whose thermal behaviour is similar to that of a wall in our case) and possible windows, the one-room model is obtained by the integration of the models of each of these elements within a unique state-space representation. Considering the R&D room ( 1 ) of the platform "Eco-safe" represented in Figure 4, the state-space model thus obtained is of order 11 (5 adjacent walls (order 1) + 1 ceiling (order 1) + 1 ground (order 1) + 1 set of windows (order 3) + heat capacity of the room (order 1)).

"Eco-safe" platform The platform is modelled by a set of rooms delimited by the walls that are in thermal contact with the outside environment and neighbouring rooms. Applying the same technique of modelling than for room 1 , we get a state-space representation of order 72 to simulate the thermal behaviour of the platform. In this model, the temperature values of the upper and lower floors are considered to be identical to those of the reference rooms ( 3 + 6 ).

Modelling of energy sources

The most important elements that produce the heat or cold inside the building are the reversible heat pump, the ventilation system and sun radiation. These different equipments/contributions of energy are modelled in this paragraph to be integrated in the simulator. The model also takes into account the effect of the people inside the platform and that of different electrical appliances that generate heat.

CMV

The CMV is used to circulate the air between rooms 1 and 5 (see Figure 1). It is assumed that the air taken in the 'source' room is replaced by the outside air through the openings at the level of the windows.

On the other hand, air received by the 'destination' room replaces a part of its air that is equally displaced through the openings at the level of the windows. If we take the example that the air flows from room 5 to room 1 , the energy flows generated by the CMV are at the level of the 'source' room:

φ CMV 1 (t) = ρc 1 D CMV 3600 (T ext (t) -T 5 (t)) (2)
and at the level of the 'destination' room:

φ CMV 2 (t) = ρc 1 D CMV 3600 (T 5 (t) -T 1 (t)) (3)

Reversible heat pump (HP)

A heat pump is a thermodynamic device that allows capturing heat from outdoor air and transmitting it inside the building. Being reversible, the HP air -water of the platform is capable of providing air conditioning in the summer. It starts running in heating mode in the order of 312K and 290K into cooling mode. Essentially, and without taking into account the transitional aspects, the equation translating this energy flow is in the heating mode:

φ HP1 (t) = ρc 1 D HP 3600 (312 -T i (t)) (4)
and in air conditioning mode:

φ HP2 (t) = ρc 1 D HP 3600 (290 -T i (t)) (5)
with D HP = 5000 m 3 /h the air flow of the HP and T i the room temperature (K) in which the HP is used.

Modelling of the occupation

Each individual has a sensible heat (by his/her body at 37 • C) and a latent heat (by his/her production of steam in breathing and perspiration). Different values are given in the literature (ASHRAE, 2013). A person generates about 100W . By multiplying this value by the number of people in a room, we get the energy released by them.

Inputs of energy by solar radiation

The sun provides heat that greatly influences the temperature within the platform rooms. The estimated brought solar energy requires to instantly follow the positioning of the sun and to take into account the radiation so that diffuse direct. In order to understand the calculations to quantify the global radiation, it is important to define not only the various solar components, but also the different angles used for calculations [START_REF] Antonic | Modelling daily topographic solar radiation without site-specific hourly radiation data[END_REF]. The energy related to the direct radiation is such that:

S = 1230 exp(- 1 3.8 sin(h + 1.6) ) cos(β) ( 6
)
where h is the height of the sun and β is the angle between the normal to the windows and the solar rays. They depend on the the latitude, the hour angle, the solar declination and the solar azimuth. As for the energy associated to the diffused radiation energy, it is calculated by the relationship :

D = 125(sin(h) 0.4 )((1 + cos(i))/2) +alb(((1 + cos(i))/2)(1080(sin(h) 1.22 ) (7)
-125(sin(h) 0.4 ))) sin(h) + 125(sin(h) 0.4 )(1sin(h))

where alb = 0.2 is the albedo and i = 90 corresponds to the inclination of the windows according to the horizontal.

Simulation results

The simulator is implemented by integrating the set of energy sources described in the previous paragraph to the Simscape TM model of the "Eco-safe" platform. The associated state-space representation is determined by adding these different energy sources on the equivalent electrical schemas/diagrams in terms of the correspondence between a heat flow and an electric current. The use of the CMV or HP has the effect of changing the state-space model of the system. Considering different scenarios of following control, it is possible to define 6 state-space models of the platform:

• Scenario 0: no action on the system,

• Scenario 1: CMV switched room 5 to 1 ,

• Scenario 2: CMV switched room 1 to 5 ,

• Scenario 3: HP operated in the room 1 ,

• Scenario 4: HP operated in the room 5 ,

• Scenario 5: 2 HP operated in rooms 1 and 5 .

For simulation, continuous time models are finally discretized with a 5-mn sampling period. They become:

x(k + 1) = A sim i x(k) + B sim i d(k) y(k) = C sim x(k) (8)
with:

• i ∈ {0, ..., 5}: the type of implemented control on the system identically to the number of scenario; • A sim i and B sim i : state and input matrices associated with the number of scenario; C sim : output matrix; • x(k) ∈ R 72 : state vector grouping all temperatures of walls, windows and rooms of the platform.

• d(k) = T ext,k Occ k Sol west k Sol east k T HP,k T ; • y(k) = T 1 ,k T 2 ,k T corridor,k T 4 ,k T 5 ,k T ;
• T ext,k : outside temperature (K);

• Occ k : energy brought by occupants of room 1 ;

• Sol west k and Sol east k : energy provided by solar radiation for rooms 1 , 2 , 3 and 4 , 5 , 6 resp.; • T HP,k : temperature of the air forced through the HP, T HP,k =290K (cold mode) or 312K (hot mode). Parameters R i j and C i j of the simulator were calculated from the nature and characteristics of the different materials used in the wall dividers, walls and windows of the platform. They have been adjusted from the temperature curves actually observed on the system. According to figures 7a and 7b, it appears that the profiles of actual and estimated temperature values are found to be very similar. The simulated curves were generated according to the different scenarios of control represented in Figure 6b and from the entries T ext,k (Figure 5), Sol west k and Sol east k (Figure 6a), which are the data issued from the meteorology station over the period 14/09/2016 -20/09/2016. Figure 8b represents the temperature estimated by the simulator within rooms 1 and 5 in scenario 0. In addition to the previous inputs, the energy released from occupancy Occ k (figure 8a) is also considered. The latter represents approximatively the energy generated by 24 people in room 1 assuming their presence all the open days from 8h to 12h and from 14h to 18h.

The following paragraph aims to implement a control law on the platform, which is capable of ensuring thermal comfort in the occupied rooms while minimizing energy consumption. A predictive control is used on the basis of the simulator of the platform.

PREDICTIVE CONTROL

The principle of the predictive control [START_REF] Camacho | Model predictive control. Advanced textbooks in control and signal processing[END_REF] is to optimize a cost function allowing to describe the aim of control over a finite time horizon. To calculate the sequence of controls that minimizes this cost function, we offer the platform "Eco-safe" a multi-model linear representation to predict its behaviour. At each moment, an optimal control sequence is calculated to minimize the cost function on a prediction horizon. Only the first element is applied to the system. As part of our application, this procedure is repeated every 5 minutes.

Cost function and constraints

Since the objective is to ensure the thermal comfort with a minimum of energy consumption, the cost function must reflect these performances in a mathematical formulation. In the light of the European thermal regulation ISO7730 and ASHRAE 55 standard, which define the thermal comfort as a temperature interval defined by a lower limit and an upper limit and according to the nature of the models of the platform, the cost function is chosen such that:

J 1 = min i 1 ...,i N N ∑ j=1 || y i j (k + j) -y re f || 2 Q + cost(k + j) (9)
where:

• y min ≤ y i j (k+ j) ≤ y max ;

y re f = y min +y max 2 •    x (k + 1) = A com i j x (k) + B com i j d(k) y i j (k) = C com x (k) cost(k) = α i j • d(k) = T ext,k Occ k Sol west k Sol east k T HP,k
T includes all the estimations of the disturbances.

T ext,k , Sol west k and Sol east k are issued from meteorological forecasts in the short term ( Sol west k and Sol east k require a basic calculation according to the orientation of the windows and predicted solar radiation). Occ k is a prediction based on a planning of the energy generated by the people in the room 1 . T HP,k depends on the value of i j (see below). • i j ∈ 0, ..., 8 represents the used control scenario (cf. part 3.3) and α i j the associated energy cost:

i j = 0: Scenario 0, α 0 = 0W h and T HP,k = 0,

-i j = 1: Scenario 1, α 1 = 30W h and T HP,k = 0, -i j = 2: Scenario 2, α 2 = 30W h and T HP,k = 0, -i j =3: Scenario 3, α 3 =1000W h and T HP,k =290K,
i j =4: Scenario 4, α 4 =1000W h and T HP,k =290K, -i j =5: Scenario 5, α 5 =2000W h and T HP,k =290K, -i j =6: Scenario 3, α 6 =1000W h and T HP,k =312K, -i j =7: Scenario 4, α 7 =1000W h and T HP,k =312K, -i j =8: Scenario 5, α 8 =2000W h and T HP,k =312K.

• Matrices A com i , B com i and C com are such that they define a reduced-order model of the simulator for 0 ≤ i ≤ 5, whereas we have A com i = A com i-3 and B com i = B com i-3 for 6 ≤ i ≤ 8 considering that the energy consumption of HP in warm mode is exactly the same as in cool mode. Indeed, the order of the simulation system, being important (72), the calculations that would require the development of an optimal control would become very complicated and time consuming. Without immersing into the theoretical details of this model reduction, matrices A com i , B com i and C com are obtained through the determination of balanced state-space realizations. Furthermore, in order not to overly complicate the synthesis of the control law that normally requires the development of state observers to switch from one model to another, we have imposed on the systems of reduced order to be all of the order 5 (the number of temperature sensors). This allows, for a simple basic change, C com = I 5 and initial state condition x (0) = y(0).

Optimization problem

To minimize criterion J 1 , the Yalmip software (in the Matlab environment) can be used [START_REF] Lofberg | Yalmip: a toolbox for modeling and optimization in matlab[END_REF]. It turns out however that the design load increases with the horizon of prediction N. Also, due to the combinatorial explosion in computation time, for a number of control scenarios equal to 9 (i j ∈ 0, ..., 8 ), the value of N may not exceed 6. For larger values of N, using the Yalmip software no longer makes it possible to obtain a digital solution to the optimization problem. Yet, it can be very interesting to consider a more important prediction horizon. Indeed, a scenario of optimal control on a low prediction horizon may become inappropriate on a larger horizon. This happens especially when the heating and/or cooling capabilities of the building are modest or y min and y max are time-dependent. It is important to specify that temporal changes in y min and y max are beneficial in a context of minimization of the energy cost because the constraints in temperature of the parts of a building are not the same in the absence or in the presence of people. Figures 9 and 10 illustrate this phenomenon in the simple case of a number of control scenarios equal to 4 and when y min and y max are time-dependent. Figure 9 shows in red the control scenario predicted from k + 1 until k + 4 (in agreement with the cost function J 1 plotted vertically to the right of the figure) for y min and y max constant. It is characterized by the sequence of controls i 1 = 2, i 2 = 3, i 3 = 2 and i 4 = 3. In the case of y min and y max become time-dependent (figure 10), it should be noted that the sequence of optimal controls becomes i 1 = 1, i 2 = 2, i 3 = 1 and i 4 = 1 (always in agreement with J 1 plotted to the right of the figure). Therefore, in this example, if the prediction horizon N is chosen equal to 1, 2 or 3, the optimal control scenario to be applied at time k is associated to i 1 = 2 whereas it is associated to i 1 = 1 for N = 4 and greater. In order to consider a prediction horizon up some hours, we will subsequently use an iterative approach. Its goal is to approach the best scenario of optimal control on a given prediction horizon while controlling the design load. The idea is to subdivide at iteration j interval I j defined by:

I j = [max (y min , min i j ŷi j (k + j)| ŷ(k + j -1)), min (y max , max i j ŷi j (k + j)| ŷ(k + j -1))] (10)
in an ordered set of n small-intervals I j,l with the same width: In this expression, ŷ(k)=y(k) and ŷi j (k + j)| ŷ(k+ j-1) represents n predictions of y at k + j from the model associated with control scenario i j and from n particular predictions of y made the iteration before ( j-1).

I j = l I j,l (11)
At each of the intervals I j,l is joined a set of predictions ŷi α (k + j). In order to remove the control scenarios associated to a more important energy cost than others, it keeps only a unique prediction ŷ(k + j) per interval I j,l . It corresponds to the smallest value of ŷi α (k + j). Figure 11 represents the principle of the proposed iterative approach on the same example as before with n = 4, N = 5, i j ∈ 0, ..., 3 = I and |I| = 4: number of members of I. At every moment of prediction, the n best predictions ŷ(k + j) (in the sense of cost function J 1 ) are represented in red on the diagram. It can be observed that the scenario of optimal control i 1 = 1, i 2 = 2, i 3 = 1 and i 4 = 1 is the same as one obtained by considering all the control scenarios in a comprehensive way. On the other hand, the computational load is greatly reduced with the iterative algorithm. Indeed, if the number of calculations to predict ŷ(k + j) is of |I|(nNn + 1) for this algorithm when dim (y) = 1, it becomes maximum of (|I| N+1 -|I|)/(|I| -1) by exhaustive research.

Simulation tests

Aiming to illustrate the above approach and knowing that the main rooms of the platform are 15b) and Occ k (figure 15a). By these different simulations, the effect of the term ∑ N j=1 || y i j (k + j)y re f || 2 Q can be clearly seen on the optimal order scenario. The more Q is important, the more actuators with high power energy are solicited (HP in our case) in on-off (hot-cold) control in order to maintain the temperature of the rooms 1 and 5 close to y re f = y min +y max 2 = 20.5 • C. This type of scenario is highly energy-consuming (see Figure 13c compared to Figure 12c). Similarly, a low prediction horizon N makes the control more pre-emptive, resulting in a slight increase in the cost of energy in kW h. N equal to 30 samples (equivalent to 150 minutes) seems to be the best adapted in view of the ability of cooling/warming of the two HP.

CONCLUSION

In this paper, a whole simulator of the thermal behaviour of a building platform has been established. In a relatively high order (72), this simulator integrates the behaviours of the set of the partitions wall dividers/walls/windows of the platform rooms and all energy sources (solar radiation, temperature, rooms' occupancy, ventilation (CMV), heat pumps). Based on a multi model representation of the building and on an energy cost function in kW h, a predictive control has been successfully implemented to ensure the thermal comfort of the platform rooms with a minimum of energy consumption.

Figure 1 :

 1 Figure 1: The "Eco-safe" deck plans.

  , T ext (p): temperature (K) of the room, in the middle of the wall and of outside; • (R 11 , R 41 ) and (R 21 , R 31 ): thermal resistances (K/W ) of convection and conduction; • C 11 , C 21 : heat thermal capacities (J/K) of the room and of the exterior wall.

Figure 2 :

 2 Figure 2: Model of a wall (a) by Simscape TM (b) by electrical analogy.

Figure 4 :

 4 Figure 4: Model Simscape TM exhibit R&D ( 1 ).

Figure 3 :

 3 Figure 3: Model of a set of windows (a) by Simscape TM (b) par electrical analogy.

Figure 5 :

 5 Figure 5: Outside temperature (14/09 -20/09/2016).

Figure 6 :

 6 Figure 6: (a) Solar energy (W ) Sol west k (green) and Sol east k (blue), (b) Control scenarios: HP in cold mode on 16/09 and hot mode on 19/09 in room 1 (inversely for room 5 ).

Figure 7 :

 7 Figure 7: Actual (in red line) and estimated (in blue line) temperature values of (a) room 1 , (b) room 5 .

Figure 8 :

 8 Figure 8: (a) Occ k , (b) estimated temperature in rooms 1 (T 1 ,k in green) and 5 (T 5 ,k in blue).

Figure 9 :

 9 Figure 9: Control scenario predicted from k + 1 until k + 4 for y min and y max constant.

Figure 10 :

 10 Figure 10: Control scenario predicted from k + 1 until k + 4 for time-dependent y min and y max .

Figure 11 :

 11 Figure 11: Control scenario predicted for time-dependent y min and y max using an iterative approach.

Figure 12 :

 12 Figure 12: (a) Control scenarios, (b) temperature of rooms T 1 ,k (blue) and T 5 ,k (green), (c) kW h energy cost for Q = 0 and N = 30.

Figure 13 :

 13 Figure 13: (a) Control scenarios, (b) Temperature of rooms T 1 ,k (blue) and T 5 ,k (green), (c) kW h energy cost for Q = diag([10 4 0 0 0 10 4 ]) and N = 3.

  1 and 5 rooms, the vectors y min and y max are chosen such that y min = 18 16 16 16 18 and y max = 23 25 25 25 23 . Figures 12 -13 represent the evolution of temperatures T 1 ,k and T 5 ,k as well as the different scenarios of the control with their associated energy cost in kW h over the period 17/05 -23/05/2016 for different values of N and Q. The inputs of the simulator are T ext,k (Figure 14), Sol west k and Sol east k (figure

Figure 14 :

 14 Figure 14: Outside temperature (17/05 -23/05/2016).

Figure 15 :

 15 Figure 15: (a) Occ k , (b) Solar energy (W ) Sol west k (green) and Sol east k (blue).

ACKNOWLEDGEMENTS

This work was supported by the 7th Framework Programme FP7-NMP-608981 "Energy IN TIME" and has financial support from the Contrat de Plan Etat-Région (CPER) 2015-2020, project "Matériaux, Energie, Procédés".


Farouk Mezghani
email: farouk.mezghani@inria.fr

Nathalie Mitton
email: nathalie.mitton@inria.fr

Benchmarking smartphone performances for cooperative disaster alert diffusion

When a disaster strikes, communication infrastructure such as cellular network may get destroyed, which makes rescue operations more challenging. Short range-based opportunistic communications using daily mobile devices such as smartphones present a promising solution to support infrastructure failure. In a previous work, we have proposed COPE, a cooperative opportunistic alert diffusion solution useful for trapped survivors during disasters to ease and speed up their rescue and assistance. It targets to maintain mobile devices alive as long as possible for a maximum network coverage until reaching proximate rescuers. COPE leverage mobile devices that come with multiple network technologies and aims to perform a systematic network interface selection. We have implemented a proof-of-concept of COPE for android smartphones using two network technologies: Bluetooth and Wi-Fi. This work presents a benchmark analysis of performances of smartphones based on COPE. Testing experiments have been carried out to measure the performance of smartphones in terms of energy consumption, clock synchronization and transmission range. We believe that such experimental results can support technological choices for rescue operations but also for many other applications relying on smartphone performances.

Introduction

Opportunistic communications have attracted considerable attention as a possible alternative to support infrastructure failure during disaster scenarios [START_REF] Nishiyama | Relay-by-smartphone: realizing multihop deviceto-device communications[END_REF][START_REF] Trifunovic | A decade of research in opportunistic networks: challenges, relevance, and future directions[END_REF]. Indeed, mobile devices used daily by everyone such as smartphones can be useful to offer direct communications helpful to ease rescue operations during disasters such as to report location position of trapped survivors after earthquake.

Several research works have proposed solutions for disaster recovery leveraging mobile devices. However, these latter have left behind two important features: (i) multi-network assortment and (ii) various energy levels. These works have considered mobile devices that come with only one network technology while nowadays, mobile devices such as smartphones are equipped with multiple network technologies (e.g. Wi-Fi, Bluetooth and cellular) and users have no idea which is the best. Moreover, they do not consider mobile devices that come with various initial energy levels which obviously has an impact on the disaster recovery solution.

Unlike existing works, in a previous work, we have proposed a cooperative opportunistic alert diffusion solution named COPE useful for survivors during disasters to report their location, thus, to speed up their rescue operation [START_REF] Mezghani | Alternative opportunistic alert diffusion to support infrastructure failure during disasters[END_REF]. COPE leverages multiple network technologies and considers mobile devices that come with various initial energy levels. It aims to maintain a maximum network coverage by keeping mobile devices alive for as long as possible. We have implemented a proof-of-concept of COPE for android smartphones considering Bluetooth and Wi-Fi technologies [START_REF] Mezghani | An android application for opportunistic alert diffusion in disaster scenario[END_REF]. An overview of COPE solution is presented in the next section.

The contribution of this paper lies in a benchmark analysis of performances of smartphones considering COPE. We have conducted testing experiments and we provide results showing the performance of smartphones in terms of energy consumption, clock synchronization and transmission range. These results can also serve to support technological choices for rescue operations but also for many other applications relying on smartphone performances.

2 Background : The COPE mechanism Fig. 1 illustrates a multi-technology communication view of COPE considering mobile devices equipped each with three network technologies (n 1 , n 2 and n 3 ) corresponding for instance to those available nowadays in smartphones (Bluetooth, Wi-Fi, Cellular). This work classifies the available network technologies according to their energy consumption (E) and transmission range (TR) as follows:

TR n3 > TR n2 > TR n1 and EC n3 > EC n2 > EC n1 .
e.g. Bluetooth provides the shortest transmission range, thus consuming the lowest energy amount. This work relies on the assumption that network technologies can be sorted from the lowest to the higher energy-consuming and that there is a direct correlation between energy consumption and network performances (especially in terms of range). One of the goals of this paper is to validate or invalidate this assumption.

Nodes exchange periodic beacon messages to form cliques based on the less power network technology n 1 (i.e. cliques C i , i=1..5). Inside each clique, a cooperative communication is performed based on the n 2 network technology. Indeed, inside each clique, nodes alternately diffuse the alert message and discover neighbors using the network technology n 2 . Time is divided into equal time-slots τ and each node determines its wake-up schedule based on the clique information (IDs and energy levels of nodes belonging to the same clique). The wake-up order is determined based on the node ID in comparison to those of nodes belonging to the same clique (i.e. node with the lowest ID occupies the first period during the time-slot). During its wake-up, each node activates its network interface n 2 for neighboring discovery and alert diffusion, otherwise, it switches to the power save mode.

If a node i discovers other proximate nodes j from the n 2 network perspective (nodes i and j are neighbors with n 2 technology), together, they form a zone that includes their respective cliques (the zone is a clique at an upper level). For instance, as shown in Fig. 1-Layer n 2 communication, nodes s 10 and s 13 discover each other based on the n 2 network interface. Then, they exchange information Inside each zone, a cooperative diffusion can be performed from the n 3 communication perspective based on an alternative alert diffusion. Each node computes its wake-up schedule from the n 3 communication perspective by referring to its energy level and ID and those of nodes inside the same zone.

The network topology is dynamic due to leaving and joining nodes. This latter can be detected through the periodic messages exchanged between nodes belonging to the same clique/zone. When the topology changes, nodes exchange their 1-hop neighbors and update their cliques information and re-computes their wake-up schedules.

Smartphone performance

We have conducted different experiments featuring six smartphones Wiko Tommy 2 and exploiting two network technologies Bluetooth and Wi-Fi. The main specifications of used smartphones are shown in Table 1. Testing scenarios target to measure and evaluate the performances of the smartphones using COPE application and considering the energy consumption, clock synchronization and transmission range metrics.

Energy consumption

COPE should be energy efficient in order to maintain mobile devices alive as long as possible since rescue operations might take long time. Testing scenarios have been conducted to measure the energy consumption considering three network topologies; (i) one node operates individually, (ii) two nodes cooperate based on COPE, and (iii) three nodes cooperate based on COPE. Measurements have been carried out by only running COPE application (i.e. no other applications running in parallel) and the smartphone screen is turned off. Fig. 2 illustrates the energy consumption over five minutes from the WiFi and Bluetooth perspective considering the three network topologies. Results show that when a node operates individually, it consumes more energy than in the other topologies where nodes are cooperating. Moreover, as we increase the number of nodes within the group, the energy consumption is reduced since nodes will be in a sleep mode for a longer period from the WiFi perspective. Therefore, cooperative scheme can help to reduce the energy consumption and thus to keep mobile devices alive for a longer time.

We would like to emphasize that these experiments validate that Bluetooth consumes less energy than WiFi in the context of applications requiring an exchange of small data (e.g. short text message). In the context of COPE that only needs to send short SOS messages, this confirms our assumptions.

Clock drift

COPE assumes that mobile nodes are already synchronized since smartphones get the local time from the network providers with millisecond accuracy before disasters occur. In the following, we study the clock drift of the smartphones to check weather an additional synchronization is required during the post-disaster period. We have carried out a first simple experiment to check weather smartphones belonging to different network operators are synchronized. Results have shown that smartphones are a few milliseconds apart. Next, we have conducted an experiment to test the clock drift featuring the six smartphones. We initially synchronized all the mobile phones through Internet via a NTP (Network Time Protocol) time server. Afterwards, we prevent the automatic synchronization and we measure the clock drift referring to the NTP time server. Fig. 3 shows the clock drift of the different smartphones during a period of 24 hours. Results show that mobile phones desynchronize by up to 0.3 s during 1 day which is not significant drift and does not impact the COPE scheme. Therefore, since the time-slot τ is at second level, COPE does not require an additional synchronization. We would like to emphasize that we have repeated the experiment considering various scenarios: smartphone display ON/OFF, smartphone in charge/not in charge and by running applications in parallel. We have obtained similar clock drift results. Smartphones synchronize their clock time with the cellular infrastructure. When disconnected from the cellular network, clock drift is not significant while difficult to predict. Indeed, results show that smartphones present different desynchronization behaviors even though we use the same mobile device model (i.e. Wiko Tommry 2).

Transmission range

We have carried out experiments to test the transmission ranges of Bluetooth and WiFi-Direct. Testing the quality of the link and the transmission speed are not in the scope of this work. Indeed, we consider the necessity of exchanging short text messages that can be useful for alerting or asking for assistance. Thus, in our testing scenarios, we simply try to exchange some short messages of few bytes between smartphones and we keep increasing the distance between mobile nodes until the link interruption. We have carried out various testing scenarios considering: windy and humid weathers; calm and dry weathers; outdoor line of sight (see yellow lines on Fig. 4); indoor with obstacles (1 to 2 walls); between two buildings with a distance of about 80 m (see red line on Fig. 4). Energy BLE) offers more important transmission ranges compared to what is expected even in theory. Moreover, experiments validate the assumptions considered in COPE solution that WiFi offers a higher transmission range than Bluetooth.

Related works

Some research works have studied the performance of smartphones mainly in terms of energy consumption. Work in [START_REF] Kalic | Energy consumption in android phones when using wireless communication technologies[END_REF] have evaluated the energy consumption of wireless technologies (Bluetooth, WiFi, and 3G) that can be useful to reduce energy consumption for collaborative downloading. Authors in [START_REF] Carroll | An analysis of power consumption in a smartphone[END_REF] evaluated the energy consumption based of smartphones based on its different components (e.g. CPU, displays). For data communication, most of these studies target to evaluate the performances of smartphones based on simple data exchange without referring to a specific application. In this work, we provide an evaluation of smartphone based on energy consumption and transmission range useful as reference for applications based on a short data communication. Additionally, we give an evaluation of clock synchronization between a group of smartphones.

Conclusion

This work investigates the smartphones behavior for opportunistic alert diffusion during disaster scenarios. It gives a benchmark analysis of performances of smartphones and provides additional experimental results of performances of COPE. Experiments have been conducted and results show that COPE can reduce energy consumption comparing to the individual alert diffusion. Moreover, testing experiments have been conducted showing results of clock synchronization and transmission range of Bluetooth and Wi-Fi that can facilitate deep study of advances for rescue operations and also for many other applications relying on smartphone performances. Adding another form of network technology (e.g. on the fly cellular network) to the proof-of-concept implementation and evaluating it in terms of energy consumption is a subject of our ongoing work.

Fig. 1 .

 1 Fig. 1. Multi-technology communication overview (i.e. nodes IDs and energy levels) about their corresponding cliques C 4 and C 5 and then form a zone Z 2 that includes their corresponding cliques C 4 and C 5 . Afterwards, they diffuse the zone information (nodes belonging to the zone and their energy levels) to their cliques through the active interface n 1 .Inside each zone, a cooperative diffusion can be performed from the n 3 communication perspective based on an alternative alert diffusion. Each node computes its wake-up schedule from the n 3 communication perspective by referring to its energy level and ID and those of nodes inside the same zone.The network topology is dynamic due to leaving and joining nodes. This latter can be detected through the periodic messages exchanged between nodes belonging to the same clique/zone. When the topology changes, nodes exchange their 1-hop neighbors and update their cliques information and re-computes their wake-up schedules.

Fig. 3 .

 3 Fig. 2. Energy consumption

Fig. 4 .

 4 Fig. 4. Transmission range testing area

Table 1 .

 1 Smartphones main specifications

	Smartphone model	Wiko Tommy 2
	OS	Android 7.1 (Nougat)
	Battery	Li-Po 2500 mAh 9.5 Wh
	Bluetooth	4.1, A2DP, LE
	WiFi	Wi-Fi Direct


Farouk Mezghani

Nathalie Mitton

Open problem: Energy

published or not. The documents may come

Optimization in transportation, telecommunications, social and supply chain networks

Open problem:

Energy-and time-efficient dynamic drone path planning for post-disaster network servicing Farouk Mezghani, Nathalie Mitton Inria, France {farouk.mezghani, nathalie.mitton}@inria.fr

Abstract. When a disaster strikes, the telecommunications infrastructure gets damaged making rescue operations more challenging. Connecting first responders through flying base stations (i.e. drone mounted LTE (Long-Term Evolution) femtocell base station) presents a promising alternative to support infrastructure failure during disasters [START_REF] Namuduri | When Disaster Strikes, Flying Cell Towers Could Aid Search and Rescue[END_REF].

The drone can travel the area and communicate with ground mobile devices, such as smartphones, and serves as flying data link to share information between survivors and rescuers.

Problem statement. We would like to submit the following open problem to the community. Given the position of the ground mobile devices to serve, the problem presented here is about the dynamic drone path planning. As the drone autonomy is very limited and due to the high cost of drone mounted base station, the goal of this problem is to determine the best energy-efficient and minimum-time path to travel the area as fast as possible while still remaining in range of each survivor long enough to assure full servicing. The problem can be formulated as a Close Enough Traveling Salesman Problem (CETSP) but where the following constraints apply:

-drone coverage depends on the drone altitude and speed; the drone presents a highly flexible 3-D mobility and the higher the altitude, the larger the coverage but the higher the energy consumption, -ground nodes locations; may be dynamic since ground nodes may cooperate [START_REF] Mezghani | Alternative opportunistic alert diffusion to support infrastructure failure during disasters[END_REF] and run an activity scheduling to periodically shut their radio off to save energy. In addition, locations are error prone, -pitstop duration has a mandatory minimum duration and should be proportional to the number of nodes to serve at this position.

Goal. Determine the full drone trajectory at once (altitude, speed, pitstops positions and duration) to ensure a minimun energy consumption to serve all mobile devices in a minimum time. Related work. Several solutions [START_REF] Gulczynski | The close enough traveling salesman problem: A discussion of several heuristics[END_REF] have been proposed to 2-D CETSP. However, these approaches decompose the problem into smaller sub-problems and operate in many phases (e.g. find a feasible pitstop, compute a near optimal TSP tour and economize the found tour) leading to non-optimal solutions. Also, they assume constant speed and altitude. Keywords: drone data link, path planning, energy efficiency