arXiv research

VES-Gamma adapts EI using information-theoretic principles.

The paper analyzes the score field of diffusion models using Burgers dynamics.

F.: Good morning Hermann, I would like to talk with you about infinitesimals. G.: Tell me Pierre. F.: I'm fed up of all these slanders about my attitude to be non rigorous, so I've started to study nonstandard analysis (NSA) and synthetic differential geometry (SDG). G.: Yes, I've read something ... F.: Ok, no problem …

This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface $M$ which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by $Ω(M)$. Firstly, we've obtained the topological classificat…

Study on mean curvature flow in a cone, proving existence and homogenization.

In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent the loca…

Unified framework connects EI and information-theoretic acquisition functions.

This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from readers, I've decided to make a presentable half-finished version available here.…

A new method improves estimation of COVID-19 vaccine effectiveness.

A graph (digraph) $G=(V,E)$ with a set $T\subseteq V$ of terminals is called inner Eulerian if each nonterminal node $v$ has even degree (resp. the numbers of edges entering and leaving $v$ are equal). Cherkassky and Lovász showed that the maximum number of pairwise edge-disjoint $T$-paths in an inner Eulerian graph $G…

Lecture notes on CAT(0) cube complexes for beginners.

This study compares Bitcoin and Litecoin using cryptocurrency metrics and trading strategies.

Study uses neural processes to predict and classify crack patterns in moving disks.

New metrics with constant Q-curvature created by gluing.

We consider the following singularly perturbed Neumann problem \begin{eqnarray*} \ve^2 Δu -u +u^p = 0 \, \quad u>0 \quad {\mbox {in}} \quad Ω, \quad {\partial u \over \partial ν}=0 \quad {\mbox {on}} \quad \partial Ω, \end{eqnarray*} where $p>2$ and $Ω$ is a smooth and bounded domain in $\R^2$. We construct a new class…

We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on proba-bilistic graphical models. These include two mechanisms for adding noise to the Bayesia…

We derive a new, exact and transparent expansion for option smiles, which lends itself both to analytical approximation and, perhaps more importantly, to congenial numerical treatments. We show that the skew and the curvature of the smile can be computed as exotic options, for which the Hedged Monte Carlo method is par…

Nontrivial boundary Dehn twist found on K3#K3 manifold.

Invariants for 3D manifolds with boundaries using crossed modules.

SAIL improves graph node representation learning by distilling knowledge between graphs.

Auto-detection system identifies safety issues in baby products from reviews.

In distributed ML applications, shared parameters are usually replicated among computing nodes to minimize network overhead. Therefore, proper consistency model must be carefully chosen to ensure algorithm's correctness and provide high throughput. Existing consistency models used in general-purpose databases and moder…

iEFM trains CNF models from unnormalized densities efficiently.

ICYM2I corrects missingness bias in multimodal learning.

Surveying strategies for making machine learning models robust against adversarial attacks.

Paper adapts GMs for heterogeneous inference scenarios.

We created financial benchmarks for distribution shifts in crude oil prices and volatility.

Researchers describe and compare decompositions of Poincaré duality pairs.

This paper generalizes Michell Truss to higher dimensions using geometric measure theory.

The paper proposes and discusses semiorthogonal decompositions for moduli spaces of vector bundles.

New complexity notion connects finite decomposition and asymptotic property C.

The paper classifies decompositions of 3-sphere and lens spaces with handlebodies.

Conservation of heat in manifolds with boundary under mixed conditions.

This paper generalizes octahedral decomposition to links in thickened surfaces.

A new tensor decomposition method that minimizes KL divergence.

Researchers compute Goeritz groups for all (1,1)-link decompositions.

Systematizes blockchain decentralization taxonomy and metrics.

Study of Quillen metric on Riemann surfaces with cusps and compactification.

Study concordance of decompositions from defining sequences in 3-sphere.

Study shows OAT decomposition generates unexplained profit and loss, while SU decompositions depend on risk factor order.

Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the `empty disks' circumscribing the regions of the decomposition. The main result of this paper is a characterization of when a given topological decom…

New tensor network decompositions improve CNN performance.

A new algorithm speeds up CP decomposition for large tensors.

Paper characterizes optimization landscape of Tucker decomposition.

A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced in arXiv:1005.0073v2. There are two natural operations acting on double pants decompositions: flips and handle twists. It is shown in arXiv:1005.0073v2 that the groupoid generated by flips and h…

Smooth 4-manifolds have simple horizontal decompositions.

Let $\mathcal{J}^1$ be the real form of a complex simple Jordan algebra such that the automorphism group is $\mathrm{F}_{4(-20)}$. By using some orbit types of $\mathrm{F}_{4(-20)}$ on $\mathcal{J}^1$, for $\mathrm{F}_{4(-20)}$, explicitly, we give the Iwasawa decomposition, the Oshima--Sekiguchi's $K_ε-$Iwasawa decomp…

We study the topological types of pants decompositions of a surface by associating to any pants decomposition $P,$ in a natural way its pants decomposition graph, $Γ(P).$ This perspective provides a convenient way to analyze the maximum distance in the pants complex of any pants decomposition to a pants decomposition c…