Proof of a Conjectured Three-Valued Family of Weil Sums of Binomials

We consider Weil sums of binomials of the form $W_{F,d}(a)=\sum_{x \in F} \psi(x^d-a x)$, where $F$ is a finite field, $\psi\colon F\to {\mathbb C}$ is the canonical additive character, $\gcd(d,|F^\times|)=1$, and $a \in F^\times$. If we fix $F$ and $d$ and examine the values of $W_{F,d}(a)$ as $a$ runs through $F^\times$, we always obtain at least three distinct values unless $d$ is degenerate (a power of the characteristic of $F$ modulo $|F^\times|$). Choices of $F$ and $d$ for which we obtain only three values are quite rare and desirable in a wide variety of applications. We show that if $F$ is a field of order $3^n$ with $n$ odd, and $d=3^r+2$ with $4 r \equiv 1 \pmod{n}$, then $W_{F,d}(a)$ assumes only the three values $0$ and $\pm 3^{(n+1)/2}$. This proves the 2001 conjecture of Dobbertin, Helleseth, Kumar, and Martinsen. The proof employs diverse methods involving trilinear forms, counting points on curves via multiplicative character sums, divisibility properties of Gauss sums, and graph theory.Comment: 19 page

Integral Constraints On cosmological Perturbations and their Energy

We show the relation between Traschen's integral equations and the energy, and ``position of the centre of mass'', of the matter perturbations in a Robertson-Walker spacetime. When the perturbations are ``localised'' we get a set of integral constraints that includes hers. We illustrate them on a simple example.Comment: 19 pages, Tex file, submitted to Classical and Quantum Gravit

Système de télé-alarme médical : application à la détection des chutes de la personne âgée

In a context of a growing elderly population in industrialised countries, elderly-care is becoming a majorproblem. As traditional solutions (e.g. retirement homes) are no longer able to satisfy the increasing need,it would be desirable to give the healthiest part of this population a solution for their home care in a secureenvironment.Thus, the concept of smart-home for health, coming from home automation, has emerged in the last twodecades. The general principle of this field is to propose a set of solutions for monitoring compliance, earlydetection of neurodegenerative diseases, social interation assistance or fall and emergency situations detection.Within this framework and to avoid the use of wearable sensors, we proposed a fall detection method basedon optical correlation using video data. Our approach consists of two parts, one for identifying the person onthe picture, the other for head tracking. The detection step is addressed by means of vertical and horizontalcelerityPréparée dans l'équipe VISION ISEN Brest Système de télé-alarme médical : application à la détection des chutes de la personne âgée Thèse soutenue le 16 décembre 2014Dans un contexte de vieillissement de la population des pays industrialisés se pose le problème de la priseen charge des personnes âgées dépendantes. La réponse proposée par les EPHAD ne pouvant constituer uneréponse suffisante et acceptable pour les personnes faiblement dépendantes, la question de leur maintien àdomicile dans un environnement sécurisé se pose.Ainsi, le concept d’habitat intelligent pour la santé, issu de la domotique, a émergé dans les deux dernièresdécennies. Le principe général de ce domaine est de proposer un ensemble de solutions permettant la surveillancede l’observance, la détection précoce de maladies neurodégénératives, le maintien du lien social oula détection de chutes et de situations d’urgences.Dans cette idée et afin de s’affranchir de capteurs portés par l’habitant, nous avons proposé une méthodede détection des chutes basée sur la corrélation optique à partir de données issues de caméras vidéo. Notreapproche se décompose en deux parties, l’une permettant l’identification de la personne présente sur l’image,l’autre le suivi de sa tête. L’étape de détection de la chute est réalisée à partir des données de vitesse verticaleet horizontale

Outcome of minimally invasive management of salivary calculi in 4,691 patients

Objective: To evaluate the application of minimally invasive techniques in the management of salivary stones. Background: The incidence of salivary calculi is 60 cases/million/year, with most stones situated in the mid or proximal duct. The current treatment of these stones is adenectomy. This paper reports the results of minimally invasive methods of stone removal that avoid gland excision. Methods: Observational study of 5,528 consecutive patients treated by lithotripsy, endoscopy, basket retrieval, and/or surgery in five centers from 1990 to 2004 inclusive. A total of 567cases were excluded, leaving 4,691 patients (parotid n=1,165, submandibular n=3,526) for analysis. Results: Salivary calculi were eliminated in 3,775/4,691 (80.5%) of cases and partly cleared in 782/4,691 (16.7%). Salivary glands were removed in 134/4,691 (2.9%) of patients with symptoms in whom treatment failed. Conclusions: Minimally invasive techniques move treatment of salivary calculi to an outpatient or a day case setting. They are reliable ways of both retrieving stones and eliminating symptoms, and mean that the gland rarely has to be removed

Conservation Laws and Cosmological Perturbations in Curved Universes

When working in synchronous gauges, pseudo-tensor conservation laws are often used to set the initial conditions for cosmological scalar perturbations, when those are generated by topological defects which suddenly appear in an up to then perfectly homogeneous and isotropic universe. However those conservation laws are restricted to spatially flat (K=0) Friedmann-Lema\^\i tre spacetimes. In this paper, we first show that in fact they implement a matching condition between the pre- and post- transition eras and, in doing so, we are able to generalize them and set the initial conditions for all $K$. Finally, in the long wavelength limit, we encode them into a vector conservation law having a well-defined geometrical meaning.Comment: 15 pages, no figure, to appear in Phys. Rev.

The landscape of tiered regulation of breast cancer cell metabolism

Altered metabolism is a hallmark of cancer, but little is still known about its regulation. In this study, we measure transcriptomic, proteomic, phospho-proteomic and fluxomics data in a breast cancer cell-line (MCF7) across three different growth conditions. Integrating these multiomics data within a genome scale human metabolic model in combination with machine learning, we systematically chart the different layers of metabolic regulation in breast cancer cells, predicting which enzymes and pathways are regulated at which level. We distinguish between two types of reactions, directly and indirectly regulated. Directly-regulated reactions include those whose flux is regulated by transcriptomic alterations (~890) or via proteomic or phospho-proteomics alterations (~140) in the enzymes catalyzing them. We term the reactions that currently lack evidence for direct regulation as (putative) indirectly regulated (~930). Many metabolic pathways are predicted to be regulated at different levels, and those may change at different media conditions. Remarkably, we find that the flux of predicted indirectly regulated reactions is strongly coupled to the flux of the predicted directly regulated ones, uncovering a tiered hierarchical organization of breast cancer cell metabolism. Furthermore, the predicted indirectly regulated reactions are predominantly reversible. Taken together, this architecture may facilitate rapid and efficient metabolic reprogramming in response to the varying environmental conditions incurred by the tumor cells. The approach presented lays a conceptual and computational basis for mapping metabolic regulation in additional cancers