arXiv research

A method to describe Riemann surfaces using graph profiles is proposed.

Framework detects shape shifts in functional profiles using Fréchet mean and shape invariant model.

Study compares isoperimetric profiles on manifolds with integral Ricci curvature bounds.

We establish the existence, finiteness, and uniqueness up to scaling of various isoperimetric profiles of a group, in all dimensions. We also show that these profiles all coincide in dimensions 4 and higher; in particular, the nth Dehn function is equal to FV^{n+1} for n at least 3. Even for dimension 3, there is signi…

Let $M$ be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of $M$ is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatur…

New method for unbinned, profiled unfolding in particle physics.

The virtualization of compute and network resources enables an unseen flexibility for deploying network services. A wide spectrum of emerging technologies allows an ever-growing range of orchestration possibilities in cloud-based environments. But in this context it remains challenging to rhyme dynamic cloud configurat…

Study of integral flows on Riemannian manifolds with focus on blow-up profiles and concentration-compactness.

Matrix profile has been recently proposed as a promising technique to the problem of all-pairs-similarity search on time series. Efficient algorithms have been proposed for computing it, e.g., STAMP, STOMP and SCRIMP++. All these algorithms use the z-normalized Euclidean distance to measure the distance between subsequ…

Order submission and cancellation are two constituent actions of stock trading behaviors in order-driven markets. Order submission dynamics has been extensively studied for different markets, while order cancellation dynamics is less understood. There are two positions associated with a cancellation, that is, the price…

New method resolves causal heterogeneity by defining a resolution profile.

After introducing the sub-Riemannian geometry of the Heisenberg group Hn, n \geq 1, we recall some basics about hypersurfaces endowed with the H-perimeter measure and horizontal Green's formulas. Then, we describe a class of compact closed hypersurfaces of constant horizontal mean curvature called "Isoperimetric Profil…

We show that the Cheeger constant of compact surfaces is bounded by a function of the area. We apply this to isoperimetric profiles of bounded genus non-compact surfaces, to show that if their isoperimetric profile grows faster than $\sqrt t$, then it grows at least as fast as a linear function. This generalizes a resu…

Modeling curvature-sensitive cells in visual cortex using manifold geometry.

A method to produce personalized classification models to automatically review online dating profiles on Tinder is proposed, based on the user's historical preference. The method takes advantage of a FaceNet facial classification model to extract features which may be related to facial attractiveness. The embeddings fr…

Profile entropy measures learnability and compressibility of discrete distributions.

The paper explores inequalities for strongly-convex sets in weighted Riemannian manifolds.

A method for profiling systematic uncertainties in SBI using Factorizable Normalizing Flows.

In cheminformatics, compound-target binding profiles has been a main source of data for research. For data repositories that only provide positive profiles, a popular assumption is that unreported profiles are all negative. In this paper, we caution audience not to take this assumption for granted, and present empirica…

Method controls extrapolation in prediction profiles for statistical and machine learning models.

This article is about a natural distance function induced by smooth cobordisms between links. We show that the cobordism distance of torus links is determined by the profiles of their signature functions, up to a constant factor.

Enhanced estimates for ancient ovals and translators in 3D and 4D.

Background: While machine learning (ML) models are rapidly emerging as promising screening tools in critical care medicine, the identification of homogeneous subphenotypes within populations with heterogeneous conditions such as pediatric sepsis may facilitate attainment of high-predictive performance of these prognost…

We equip many non compact non simply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly non generic property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new result…

We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincaré profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by Benjamini--Schramm--Timár. In this paper we focus on properties of the Poincaré profiles of groups with …

Let X be a finite CW complex or compact Lipschitz neighborhood retract with universal cover Z; let M be a compact orientable manifold of dimension at least 2 and nonempty boundary. We establish the existence of an isoperimetric profile for functions from M to Z, in the metric and cellular senses, and show that they are…

Logarithmic separation profile in hyperbolic groups shows hierarchical structure.

Uniswap analyzes liquidity provider risk and impermanent loss.

K-Models clusters functional data with ordinal constraints for better interpretability.

There has been a rapid proliferation of machine learning/deep learning (ML) models and wide adoption of them in many application domains. This has made profiling and characterization of ML model performance an increasingly pressing task for both hardware designers and system providers, as they would like to offer the b…

Recently, researchers have started decomposing deep neural network models according to their semantics or functions. Recent work has shown the effectiveness of decomposed functional blocks for defending adversarial attacks, which add small input perturbation to the input image to fool the DNN models. This work proposes…

We provide an isoperimetric comparison theorem for small volumes in an $n$-dimensional Riemannian manifold $(M^n,g)$ with strong bounded geometry, as in Definition $2.3$, involving the scalar curvature function. Namely in strong bounded geometry, if the supremum of scalar curvature function $S_g<n(n-1)k_0$ for some $k_…

Estimates lower bounds for isoperimetric profiles and improves on previous estimates for specific manifolds.

In the context of sub-Riemannian Heisenberg groups Hn, n \geq 1, we shall study Isoperimetric Profiles, which are closed compact hypersurfaces having constant horizontal mean curvature, very similar to ellipsoids. Our main goal is to study the stability of Isoperimetric Profiles.

A novel criterion selects optimal distance metrics for cell profile analysis.

Paper describes profiles of multivariate normal distributions and novel estimators for mutual information.

Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination of these profiles. The non-negativity constraint is imposed while estimating arch…

Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form $(ρ(λX))_{λ\ge 0}$, where $ρ$ is a convex risk measure and $X$ a random variable, and we call such a curve a \emph{liqu…

Random layer-wise pruning profiles are as effective as metric-based ones for various datasets.

Study optimizes perimeter in convex domains with anisotropic constraints.

The vanishing of reduced $\ell^2$-cohomology for amenable groups can be traced to the work of Cheeger & Gromov. The subject matter here is reduced $\ell^p$-cohomology for $p \in ]1,\infty[$, particularly its vanishing. Results showing its triviality are obtained, for example: when $p \in ]1,2]$ and $G$ is amenable; whe…

Study lampshuffler groups' isoperimetric profiles, refining previous estimates.

The study analyzes how large language models form and express investor risk profiles.

Uniform Lipschitz continuity of isoperimetric profiles in evolving surfaces.

A new framework for adaptive behavior using reusable value profiles.

It is shown that, in dimensions $<8$, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.

The hypercube's perimeter is significantly larger than expected near half volume.

The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.