Fields Medal

The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics. The prize includes a monetary award which, since 2006, has been 15,000. Fi

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Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These top

The ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) for contributions of lasting and major technical importance to computer science.

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus

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P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Zeta function.

The goal of this course is the study of the physical and conceptual consequences of Maxwell equations.

Algebraic number theory is the study of the properties of solutions of polynomial equations with integral coefficients; Starting with concrete problems, we then introduce more general notions like algebraic number fields, algebraic integers, units, ideal class groups...

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On the advantages of P2P ML on mobile devices

Rachid Guerraoui, Alexandre David Olivier Maurer

Many fields make use nowadays of machine learning (ML) enhanced applications for cost optimization, scheduling or forecasting, in- cluding the energy sector. However, these very ML algorithms consume a significant amount of energy, sometimes going against the whole purpose of their employment. To this day, solutions for an energy-efficient execution of these algorithms have not been addressed adequately. In this paper, we demonstrate the advantage of executing ML algorithms on mobile devices (ARM) over a stan- dard server machine (RISC), from the perspective of energy. To do so, we first propose a novel methodology to quantify the amount of energy consumed by an ML algorithm. Then, we compare the energy consumption of existing algorithms running on mobile de- vices and server machines. To motivate running ML algorithms on mobile devices, we also propose a new peer-to-peer personalized ML algorithm (P3) that shows better convergence properties than related works, and provably converging to a ball centered at a criti- cal point of a non-convex cost function, under mild assumptions. Most importantly, we show that running the P3 algorithm on mo- bile devices is extremely energy-efficient, consuming 2700x, 200x and 20x less energy than centralized learning algorithms for 10, 100, and 300 peers respectively. Finally, unlike centralized learning algorithms, the proposed P2P algorithm can generate personalized models, and does not have issues of single-point-of-failure nor data privacy. Thus, we give evidence on the supremacy of our proposed P3 algorithm over the other state-of-the-art centralized ML ones.

ACM2022

Autoradiographic mapping of [mono[125I]iodo-Tyr10, MetO17]vasoactive intestinal peptide binding sites in the rat brain

Pierre Magistretti, Jean-Luc Martin

The distribution of vasoactive intestinal peptide binding sites in the rat brain was examined by in vitro autoradiography on slide-mounted sections. A fully characterized monoiodinated form of vasoactive intestinal peptide (M-[125I]VIP) previously shown to maintain in the central nervous system the full biological activity of native vasoactive intestinal peptide was used for this study. In initial kinetic and pharmacological experiments the binding of M-[125I]vasoactive intestinal peptide to slide-mounted sections was shown to be time-dependent, saturable and reversible. Association of M-[125I]VIP specific binding was maximal within 90-120 minutes. Specific binding, corresponding to approximately 50% of total binding was saturable, of high affinity (Kd of 76.6 pM) and low capacity (fmol/mg prot range). Dissociation of M-[125I]VIP was maximal at 10 minutes. Unlabeled vasoactive intestinal peptide and the two structurally related peptides "peptide-histidine-isoleucine" (PHI) and secretin competed in a concentration-dependent manner for sites labeled by M-[125I]vasoactive intestinal peptide with the following rank order of potencies: vasoactive intestinal peptide greater than PHI greater than secretin. Vasoactive intestinal peptide receptors, as revealed by quantitative autoradiography, are present at various levels of the neuraxis. High densities were observed in olfactory bulb, cerebral cortex (highest in layers I, II, IV and VI), dentate gyrus, subiculum, various thalamic and hypothalamic nuclei, superior colliculus, locus coeruleus, area postrema, subependymal layer and pineal gland. Intermediate densities were found in the amygdala, nucleus accumbens, caudate-putamen, septum, bed nucleus of the stria terminalis, CA1 to CA4 fields of the hippocampus and central gray. No specific binding of M-[125I]vasoactive intestinal peptide was observed in white matter tracts such as corpus callosum, anterior commissure, medial forebrain bundle and fornix. The mapping of M-[125I]vasoactive intestinal peptide binding sites as revealed by autoradiography on slide-mounted sections indicates an association, although not exclusive, of vasoactive intestinal peptide receptors with brain regions involved in the processing of specific sensory inputs.

1987

The ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) for contributions of lasting and major technical importance to computer science.

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus

The goal of this course is the study of the physical and conceptual consequences of Maxwell equations.