Related papers: Strong density of definable types and closed order…

We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space $\left(X,\tau\right)$ is definably homeomorphic to an affine definable space…

We study sets and groups definable in tame expansions of o-minimal structures. Let $\mathcal {\widetilde M}= \langle \mathcal M, P\rangle$ be an expansion of an o-minimal $\mathcal L$-structure $\cal M$ by a dense set $P$, such that three…

Force fields are usually formulated directly in nuclear configuration space, whereas density functional theory is naturally formulated in terms of external potentials, densities, and variational duality. We show that exact force fields are…

In this paper we give a conjectural refinement of the Davenport-Heilbronn theorem on the density of cubic field discriminants. We explain how this refinement is plausible theoretically and agrees very well with computational data.

Differentiable rendering is an essential operation in modern vision, allowing inverse graphics approaches to 3D understanding to be utilized in modern machine learning frameworks. Explicit shape representations (voxels, point clouds, or…

We introduce the notion of differential largeness for fields equipped with several commuting derivations (as an analogue to largeness of fields). We lay out the foundations of this new class of "tame" differential fields. We state several…

The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of…

Two-dimensional covalent organic frameworks (2D COFs) are an interesting class of 2D materials since their reticular synthesis allows the tailored design of structures and functionalities. For many of their applications the mechanical…

Let K be a subfield of the real field, D be a discrete subset of K and f : D^n -> K be a function such that f(D^n) is somewhere dense. Then (K,f) defines the set of integers. We present several applications of this result. We show that K…

Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize…

Density functional theory (DFT) is an essential building block for modern theoretical physics, chemistry, and engineering, especially those concerning electronic properties. Through decades of development, various program packages for…

Neural networks that map 3D coordinates to signed distance function (SDF) or occupancy values have enabled high-fidelity implicit representations of object shape. This paper develops a new shape model that allows synthesizing novel distance…

Deep implicit functions (DIFs), as a kind of 3D shape representation, are becoming more and more popular in the 3D vision community due to their compactness and strong representation power. However, unlike polygon mesh-based templates, it…

In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type,…

We give an elementary proof of a version of the implicit function theorem over Henselian valued fields $K$. It yields a density property for such fields (introduced in a joint paper with J. Koll{\'a}r), which is indispensable for ensuring…

Dipolar Dark Matter (DDM) is an alternative model motivated by the challenges faced by the standard cold dark matter model to describe the right phenomenology at galactic scales. A promising realisation of DDM was recently proposed in the…

Let $T$ be a complete, model-complete, geometric dp-minimal $\mathcal{L}$-theory of topological fields of characteristic $0$ and let $T(\partial)$ be the theory of expansions of models of $T$ by a derivation $\partial$. We assume that…

Let K be an expansion of either an ordered field or a valued field. Given a definable set X $\subseteq$ K^m let C(X) be the ring of continuous definable functions from X to K. Under very mild assumptions on the geometry of X and…

We introduce the notions of triviality and order-triviality for global invariant types in an arbitrary first-order theory and show that they are well behaved in the NIP context. We show that these two notions agree for invariant global…

A formulation of the density functional theory is constructed on the foundations of entropic inference. The theory is introduced as an application of maximum entropy for inhomogeneous fluids in thermal equilibrium. It is shown that entropic…