3,998 research outputs found
On systems of continuity equations with nonlinear diffusion and nonlocal drifts
This paper is devoted to existence and uniqueness results for classes of
nonlinear diffusion equations (or systems) which may be viewed as regular
perturbations of Wasserstein gradient flows. First, in the case. where the
drift is a gradient (in the physical space), we obtain existence by a
semi-implicit Jordan-Kinderlehrer-Otto scheme. Then, in the nonpotential case,
we derive existence from a regularization procedure and parabolic energy
estimates. We also address the uniqueness issue by a displacement convexity
argument
A Universal Model of Commuting Networks
We test a recently proposed model of commuting networks on 80 case studies
from different regions of the world (Europe and United-States) and with
geographic units of different sizes (municipality, county, region). The model
takes as input the number of commuters coming in and out of each geographic
unit and generates the matrix of commuting flows betwen the geographic units.
We show that the single parameter of the model, which rules the compromise
between the influence of the distance and job opportunities, follows a
universal law that depends only on the average surface of the geographic units.
We verified that the law derived from a part of the case studies yields
accurate results on other case studies. We also show that our model
significantly outperforms the two other approaches proposing a universal
commuting model (Balcan et al. (2009); Simini et al. (2012)), particularly when
the geographic units are small (e.g. municipalities).Comment: 11 pages, 5 figure
Formalized linear algebra over Elementary Divisor Rings in Coq
This paper presents a Coq formalization of linear algebra over elementary
divisor rings, that is, rings where every matrix is equivalent to a matrix in
Smith normal form. The main results are the formalization that these rings
support essential operations of linear algebra, the classification theorem of
finitely presented modules over such rings and the uniqueness of the Smith
normal form up to multiplication by units. We present formally verified
algorithms computing this normal form on a variety of coefficient structures
including Euclidean domains and constructive principal ideal domains. We also
study different ways to extend B\'ezout domains in order to be able to compute
the Smith normal form of matrices. The extensions we consider are: adequacy
(i.e. the existence of a gdco operation), Krull dimension and
well-founded strict divisibility
Private Multi-party Matrix Multiplication and Trust Computations
This paper deals with distributed matrix multiplication. Each player owns
only one row of both matrices and wishes to learn about one distinct row of the
product matrix, without revealing its input to the other players. We first
improve on a weighted average protocol, in order to securely compute a
dot-product with a quadratic volume of communications and linear number of
rounds. We also propose a protocol with five communication rounds, using a
Paillier-like underlying homomorphic public key cryptosystem, which is secure
in the semi-honest model or secure with high probability in the malicious
adversary model. Using ProVerif, a cryptographic protocol verification tool, we
are able to check the security of the protocol and provide a countermeasure for
each attack found by the tool. We also give a randomization method to avoid
collusion attacks. As an application, we show that this protocol enables a
distributed and secure evaluation of trust relationships in a network, for a
large class of trust evaluation schemes.Comment: Pierangela Samarati. SECRYPT 2016 : 13th International Conference on
Security and Cryptography, Lisbonne, Portugal, 26--28 Juillet 2016. 201
The frontotemporal organization of the arcuate fasciculus and its relationship with speech perception in young and older amateur singers and non-singers
The ability to perceive speech in noise (SPiN) declines with age. Although the etiology of SPiN decline is not well understood, accumulating evidence suggests a role for the dorsal speech stream. While age-related decline within the dorsal speech stream would negatively affect SPiN performance, experience-induced neuroplastic changes within the dorsal speech stream could positively affect SPiN performance. Here, we investigated the relationship between SPiN performance and the structure of the arcuate fasciculus (AF), which forms the white matter scaffolding of the dorsal speech stream, in aging singers and non-singers. Forty-three non-singers and 41 singers aged 20 to 87 years old completed a hearing evaluation and a magnetic resonance imaging session that included High Angular Resolution Diffusion Imaging. The groups were matched for sex, age, education, handedness, cognitive level, and musical instrument experience. A subgroup of participants completed syllable discrimination in the noise task. The AF was divided into 10 segments to explore potential local specializations for SPiN. The results show that, in carefully matched groups of singers and nonsingers (a) myelin and/or axonal membrane deterioration within the bilateral frontotemporal AF segments are associated with SPiN difficulties in aging singers and non-singers; (b) the structure of the AF is different in singers and non-singers; (c) these differences are not associated with a benefit on SPiN performance for singers. This study clarifies the etiology of SPiN difficulties by supporting the hypothesis for the role of aging of the dorsal speech stream
Statics and dynamics of magnetocapillary bonds
When ferromagnetic particles are suspended at an interface under magnetic
fields, dipole-dipole interactions compete with capillary attraction. This
combination of forces has recently given promising results towards controllable
self-assemblies, as well as low Reynolds swimming systems. The elementary unit
of these assemblies is a pair of particles. Although equilibrium properties of
this interaction are well described, dynamics remain unclear. In this letter,
the properties of magnetocapillary bonds are determined by probing them with
magnetic perturbations. Two deformation modes are evidenced and discussed.
These modes exhibit resonances whose frequencies can be detuned to generate
non-reciprocal motion. A model is proposed which can become the basis for
elaborate collective behaviours
Remote control of self-assembled microswimmers
Physics governing the locomotion of microorganisms and other microsystems is
dominated by viscous damping. An effective swimming strategy involves the
non-reciprocal and periodic deformations of the considered body. Here, we show
that a magnetocapillary-driven self-assembly, composed of three soft
ferromagnetic beads, is able to swim along a liquid-air interface when powered
by an external magnetic field. More importantly, we demonstrate that
trajectories can be fully controlled, opening ways to explore low Reynolds
number swimming. This magnetocapillary system spontaneously forms by
self-assembly, allowing miniaturization and other possible applications such as
cargo transport or solvent flows.Comment: 5 pages, 5 figures articl
Finite-rate sparse quantum codes aplenty
We introduce a methodology for generating random multi-qubit stabilizer codes
based on solving a constraint satisfaction problem (CSP) on random bipartite
graphs. This framework allows us to enforce stabilizer commutation, X/Z
balancing, finite rate, sparsity, and maximum-degree constraints simultaneously
in a CSP that we can then solve numerically. Using a state-of-the-art CSP
solver, we obtain convincing evidence for the existence of a satisfiability
threshold. Furthermore, the extent of the satisfiable phase increases with the
number of qubits. In that phase, finding sparse codes becomes an easy problem.
Moreover, we observe that the sparse codes found in the satisfiable phase
practically achieve the channel capacity for erasure noise. Our results show
that intermediate-size finite-rate sparse quantum codes are easy to find, while
also demonstrating a flexible methodology for generating good codes with custom
properties. We therefore establish a complete and customizable pipeline for
random quantum code discovery that can be geared towards near to mid-term
quantum processor layouts
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