Related papers: On VC-density in VC-minimal theories

We study compressible fluid flow in narrow two-dimensional channels using a novel molecular dynamics simulation method. In the simulation area, an upstream source is maintained at constant density and temperature while a downstream…

We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on $\R$. The formula is given in terms of the $R$-transform of the first measure, and…

The paper deals with a complex polynomial $H$ in two variables having - a generic highest homogeneous part (without multiple zero lines), - nonconstant lower terms. In particular, under these conditions the polynomial $H$ has at least two…

While the optimal sample complexity of binary classification in terms of the VC dimension is well-established, determining the optimal sample complexity of multiclass classification has remained open. The appropriate complexity parameter…

This paper presents a continuous, information-theoretic extension of the Free Energy Principle through the concept of Markov blanket density, i.e., a scalar field that quantifies the degree of conditional independence between internal and…

The dynamical equations describing the evolution of a physical system generally have a freedom in the choice of units, where different choices correspond to different physical systems that are described by the same equations. Since there…

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…

Using molecular simulation, we study the nucleation of liquid droplets from binary mixtures and determine the free energy of nucleation along entropic pathways. To this aim, we develop the $\mu_1 \mu_2 VT-S$ method, based on the…

We present a microscopic calculation of the energy dissipation in the core of a vortex moving in a two-dimensional or layered superconductor in the moderately clean regime. In this regime, the quasiclassical Bardeen--Stephen result remains…

The discontinuity of the vorticity is written as a function of the vector T grad s, (where T is the temperature and s the specific entropy). The expression is obtained thanks to potential equations and independently of the mass conservation…

We conduct a numerical study of relativistic viscous fluid dynamics in the Density Frame for one-dimensional fluid flows. The Density Frame is a formulation of relativistic viscous hydrodynamics that is first-order in time, requires no…

The existence of the limit of a sample scattering intensity, as the scattering vector approaches zero, requires and is ensured by the property that the mean value of the scattering density fluctuation over volume $V$ asymptotically behaves,…

In many areas of research it is interesting how lattices can be filled with particles that have no nearest neighbors, or they are in limited quantities. Examples may be found in statistical physics, chemistry, materials science, discrete…

We propose a thermodynamical definition of the vacuum energy density $\rho_{\rm vac}$, defined as $\langle 0| T_{\mu\nu} |0\rangle = - \rho_{\rm vac} \, g_{\mu\nu}$, in quantum field theory in flat Minkowski space in $D$ spacetime…

This dissertation is about the study of three important issues in the theory of relativistic fluid dynamics: the stability of dissipative fluid dynamics, the shear viscosity, and fluid dynamics with triangle anomaly.(1)The second order…

First steps towards developing a new perturbation theory for molecular liquids are taken. By choosing a new form of splitting the site-site potential functions between molecules, we will get a set of atomic fluids as the reference system…

Strongly correlated amorphous solids are a class of glass-formers whose inter-particle potential admits an approximate inverse power-law form in a relevant range of inter-particle distances. We study the steady-state plastic flow of such…

We prove that constant minimum degree already forces cycles with almost linearly many chords. Specifically, every graph $G$ with $\delta(G)\ge C$ contains a cycle of length $\ell\ge 4$ with $\Omega(\ell/\log^{C}\ell)$ chords for some…

We discuss the recently published numerical computations of the vortex free energy. They dramatically demonstrate that the excitation probability for a sufficiently thick vortex approaches unity at large beta, i.e. that thick vortices…

We show that first approximations to the bulk viscosity $\eta_v$ are expressible in terms of factors that depend on the sound speed $v_s$, the enthalpy, and the interaction (elastic and inelastic) cross section. The explicit dependence of…