Concept

Arithmétique

Publications associées (81)

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Computation Over Gaussian Networks With Orthogonal Components

Michael Christoph Gastpar, Chien-Yi Wang

Function computation over Gaussian networks with orthogonal components is studied for arbitrarily correlated discrete memoryless sources. Two classes of functions are considered: 1) the arithmetic sum function and 2) the type function. The arithmetic sum f ...

Institute of Electrical and Electronics Engineers2014

Generalized Bombieri-Lagarias' Theorem And Generalized Li'S Criterion With Its Arithmetic Interpretation

We show that Li's criterion equivalent to the Riemann hypothesis, i.e., the statement that the sums k(n) = Sigma(rho)(1-(1-1/rho)(n)) over zeros of the Riemann xi-function and the derivatives lambda(n) equivalent to 1/(n-1)! d(n)/dz(n)(z(n-1) ln (xi(z)))ve ...

Springer Verlag2014

On the Generation of Precise Fixed-Point Expressions

Viktor Kuncak, Eva Darulova, Indranil Saha

Several problems in the implementations of control systems, signal-processing systems, and scientific computing systems reduce to compiling a polynomial expression over the reals into an imperative program using fixed-point arithmetic. Fixed-point arithmet ...

2013

Synthesis of Fixed-Point Programs

Viktor Kuncak, Eva Darulova, Indranil Saha

2013

On Sound Compilation of Reals

Viktor Kuncak, Eva Darulova

Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and sp ...

2013

Efficient Arithmetic Logic Gates Using Double-Gate Silicon Nanowire FETs, invited paper

Giovanni De Micheli, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù

Silicon NanoWire (SiNW) based Field Effect Tran- sistors (FETs) are promising candidates to extend Moore’s law in the coming years. Recently, Double-Gate (DG) SiNWFETs have been demonstrated to allow on-line configurability of n -type and p -type device po ...

2013

L-2-Betti numbers of locally compact groups

Henrik Densing Petersen

The present paper is a summary and overview of results obtained in the author's thesis, "L-2-Betti Numbers of Locally Compact Groups", wherein the definition of L-2-Betti numbers for countable groups is extended to locally compact unimodular groups. In man ...

Elsevier2013

Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

This article presents the design and a first pilot evaluation of the computer-based training program Calcularis for children with developmental dyscalculia (DD) or difficulties in learning mathematics. The program has been designed according to insights on ...

Frontiers Media SA2013

A lattice in more than two Kac–Moody groups is arithmetic

Nicolas Monod

Let Gamma be an irreducible lattice in a product of n infinite irreducible complete Kac–Moody groups of simply laced type over finite fields. We show that if n>2, then each Kac–Moody groups is in fact a simple algebraic group over a local field and Gamma i ...

2012

Toward one Symbol Network Coding Vectors

Pascal Frossard, Nikolaos Thomos

In this paper, we propose a novel design for network coding vectors that limits the overhead information. Network coding vectors contain information regarding the operations the packets have undergone in the network nodes. They are used at the decoder side ...

Institute of Electrical and Electronics Engineers2012