Related papers: On VC-density in VC-minimal theories
We improve a recent result by giving the optimal conclusion possible both to the frequent universality criterion and the frequent hypercyclicity criterion using the notion of A-densities, where A refers to some weighted densities sharper…
In this paper, we study in detail a perfect fluid cosmological model with time-varying "constants" using dimensional analysis and the symmetry method. We examine the case of variable "constants" in detail without considering the perfect…
This paper sets a proposal of a new method and two new algorithms for Correspondence Analysis when we have Symbolic Multi--Valued Variables (SymCA). In our method, there are two multi--valued variables $X$ and $Y$, that is to say, the…
We consider the problem of determining which classes of functions can be tested more efficiently than they can be learned, in the distribution-free sample-based model that corresponds to the standard PAC learning setting. Our main result…
We consider two extensions of free probability that have been studied in the research literature, and are based on the notions of c-freeness and respectively of infinitesimal freeness for noncommutative random variables. In a 2012 paper,…
We use capacity theory to analyze Coppersmith's method for finding small solutions of linear two variable polynomial congruences. We show that the method will succeed in a positive proportion of cases and fail in a different positive…
In the framework of density functional theory, scaling and the virial theorem are essential tools for deriving exact properties of density functionals. Preexisting mathematical difficulties in deriving the virial theorem via scaling for…
Understanding the physics of blood is challenging due to its nature as a suspension of soft particles and the fact that typical problems involve different scales. This is valid also for numerical investigations. In fact, many computational…
A simple model accounting for the ejection of heavy particles from the vortical structures of a turbulent flow is introduced. This model involves a space and time discretization of the dynamics and depends on only two parameters: the…
Quasi-two-dimensional fluids can be generated by confining a fluid between two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous structure perpendicular to the walls due to the loss of translational symmetry.…
We introduce a new form of density functional theory for the {\em ab initio} description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of…
Density-dependent potentials are frequently used in materials simulations due to their approximate description of many-body effects at minimal computational cost. However, in order to apply such models to multi-component systems, an…
A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of…
Using state-of-the-art rare-event sampling simulations, we precisely characterize the nucleation of liquid droplets from a supersaturated Lennard-Jones gas and uncover a key physical feature: critical clusters nucleate with a density that…
During the last few years, a number of works in computer simulation have focused on the clustering and percolation properties of simple fluids based in an energetic connectivity criterion proposed long ago by T.L. Hill [J. Chem. Phys. 23,…
We consider the analogue of Rayleigh's conjecture for the clamped plate in Euclidean space weighted by a log-convex density. We show that the lowest eigenvalue of the bi-Laplace operator with drift in a given domain is bounded below by a…
It can be fruitful to view two-component physical systems of attractive monomers, A and B, ``chemically'' in terms of a reaction A + B <-> C, where C = AB is an associated pair or complex. We show how to construct free energies in the…
Although density functional theory provides reliable predictions for the static properties of simple fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence…
Unlike crystalline solids or ideal gases, transport properties remain difficult to describe from a microscopic point of view in liquids, whose dynamics result from complex energetic and entropic contributions at the atomic scale. Two…
We provide upper and lower bounds on the lowest free energy of a classical system at given one-particle density $\rho(x)$. We study both the canonical and grand-canonical cases, assuming the particles interact with a pair potential which…