相关论文: $BP$: Close encounters of the $E_\infty$ kind
We establish a general method to produce cofibrant approximations in the model category $U_S(C,D)$ of $S$-valued $C$-indexed diagrams with $D$-weak equivalences and $D$-fibrations. We also present explicit examples of such approximations.…
An elementary notion of homotopy can be introduced between arrows in a cartesian closed category $E$. The input is a finite-product-preserving endofunctor $\Pi_0$ with a natural transformation $p$ from the identity which is surjective on…
Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…
We build model structures on the category of equivariant simplicial operads with a fixed set of colors, with weak equivalences determined by families of subgroups. In particular, by specifying to the family of graph subgroups (or, more…
A coupled map is suggested to investigate various spatial or temporal designs in biology: Several cells (or tissues) in an organ are considered as connected to each other in terms of some molecular diffusions or electrical potential…
We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…
In this article we consider the homotopy theory of stratified spaces through a simplicial point of view. We first consider a model category of filtered simplicial sets over some fixed poset $P$, and show that it is a simplicial…
We develop the theory of reflective subfibrations on an $\infty$-topos $\mathcal{E}$. A reflective subfibration $L_\bullet$ on $\mathcal{E}$ is a pullback-compatible assignment of a reflective subcategory $\mathcal{D}_X\subseteq…
The many-body theory of interacting electrons poses an intrinsically difficult problem that requires simplifying assumptions. For the determination of electronic screening properties of the Coulomb interaction, the Random Phase…
The space of E-infinity structures on an simplicial operad C is the limit of a tower of fibrations, so its homotopy is the abutment of a Bousfield-Kan fringed spectral sequence. The spectral sequence begins (under mild restrictions) with…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
We study some model-theoretic notions in NIP by means of spectral topology. In the o-minimal setting we relate the o-minimal spectrum with other topological spaces such as the real spectrum and the space of infinitesimal types of Peterzil…
Belief propagation (BP) is a popular method for performing probabilistic inference on graphical models. In this work, we enhance BP and propose self-guided belief propagation (SBP) that incorporates the pairwise potentials only gradually.…
We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given genus that start with a suitably tilted Brownian continuum…
In this paper we develop homotopy theoretical methods for studying diagrams. In particular we explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept we introduce is that of a model…
We study the entanglement entropy and entanglement spectrum of the paradigmatic Bose-Hubbard model, describing strongly correlated bosons on a lattice. The use of a controlled approximation - the slave-boson approach - allows us to study…
Let p be a singular point of a variety. Consider a resolution where the preimage of p is a simple normal crossing divisor E. The combinatorial structure of E is described by a cell complex D(E), called the dual graph or dual complex of E.…
A new theory, named the Circuit-Probability theory, is proposed to unveil the secret of electrical nerve stimulation, essentially explain the nonlinear and resonant phenomena observed when neural and non-neural tissues are electrically…
Both simplicial sets and simplicial spaces are used pervasively in homotopy theory as presentations of spaces, where in both cases we extract the "underlying space" by taking geometric realization. We have a good handle on the category of…
We study the ground state of a gapped quantum many-body system whose entanglement entropy $S_A$ can be expressed as $S_A = a|\partial A| - \gamma$, where $a, \gamma$ are some constants and $|\partial A|$ is an area of the subsystem $A$. By…