arXiv research

We introduce the notion of a conjugation-free geometric presentation for a fundamental group of a line arrangement's complement, and we show that the fundamental groups of the following family of arrangements have a conjugation-free geometric presentation: A real arrangement L, whose graph of multiple points is a union…

New algorithms detect and react to multiple change points in online learning.

Topology of space line arrangements depends on line count and multiple points.

The paper finds multiple points in maps from sphere to Euclidean space.

Invariant counts maximum stable umbilic splits.

The paper proves no multiple equichordal points exist in convex bodies.

While Multiple Instance (MI) data are point patterns -- sets or multi-sets of unordered points -- appropriate statistical point pattern models have not been used in MI learning. This article proposes a framework for model-based MI learning using point process theory. Likelihood functions for point pattern data derived …

Study restricts line arrangements with odd points using topological arguments.

Study finds multiple solutions for Gross-Pitaevskii equations on curved spaces.

Adaptive multiple kernel learning predicts railway points failures.

Motivated by our attempt to recast Cartan's work on Lie pseudogroups in a more global and modern language, we are brought back to the question of understanding the linearization of multiplicative forms on groupoids and the corresponding integrability problem. From this point of view, the novelty of this paper is that w…

The study finds the minimum number of critical points for functionals on Frechet spaces and Finsler manifolds.

Proposes a method to estimate and infer networks from multiple high-dimensional point processes.

Study shows unique tangent cones for area-minimizing currents at boundary points.

We present the group fused Lasso for detection of multiple change-points shared by a set of co-occurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional total variation, leading to piecewise-constant approximations. Fast algorithms are …

For successful deployment of deep neural networks on highly--resource-constrained devices (hearing aids, earbuds, wearables), we must simplify the types of operations and the memory/power resources used during inference. Completely avoiding inference-time floating-point operations is one of the simplest ways to design …

We propose a probabilistic formulation that enables sequential detection of multiple change points in a network setting. We present a class of sequential detection rules for certain functionals of change points (minimum among a subset), and prove their asymptotic optimality properties in terms of expected detection del…

Geometric pruning rules improve change point detection in multiple time series.

The paper strengthens a theorem on crossings under linear perturbations with Hausdorff measure estimates.

New MIP approach for efficient change-point detection.

The paper discusses conditions for gluing multiple Alexandrov spaces into an Alexandrov space.

A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such marginals when the underlying graph is a tree. But it has gained its popularity as …

Let $M$ be a compact Riemannian manifold endowed with an isometric action of a compact Lie group. The method of the Witten deformation is used to compute the virtual representation-valued equivariant index of a transversally elliptic, first order differential operator on $M$. The multiplicities of irreducible represent…

Paper speeds up matrix multiplication on Intel PIII using SIMD.

We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The combination coefficients are als…

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional …

In this note, we combine the work of Ilmanen and of Colding-Ilmanen-Minicozzi to observe a uniqueness property for tangent flows at the first singular time of a smooth mean curvature flow of a closed surface in 3-dimensional Euclidean space. Specifically, if, at a fixed singular point, one tangent flow is a positive in…

Proves new fixed point formulae for complex manifolds with boundary.

Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately multiplicative into a genuinely multiplicative connection. The proof of this fa…

New families of translation surfaces with multiple oblivious points discovered.

We construct a 2-dimensional twisted nonabelian multiplicative integral. This is done in the context of a Lie crossed module (an object composed of two Lie groups interacting), and a pointed manifold. The integrand is a connection-curvature pair, that consists of a Lie algebra valued 1-form and a Lie algebra valued 2-f…

A new algorithm tackles bilevel optimization with multiple inner minima.

New method learns cell trajectories from multiple snapshots.

Noninjective monodromy found in polynomial critical point tracking.

The paper extends intensity models for limit order books using marked point processes.

Novel optimization method detects change points in Gaussian data.

Bound critical points for minimal Radó functions.

The paper tackles efficient change point detection with limited samples.

We show that any 2-valued C^{1, α} (α\in (0, 1)) function u = {u_{1}, u_{2}} on an open ball B in {\mathbb R}^{n} with values u_{1}, u_{2} \in {\mathbb R}^{k} whose graph, viewed as a varifold with multiplicity 2 at points where u_{1} = u_{2} and with multiplicity 1 at points where u_{1}, u_{2} are distinct, is station…

We give multiplicity results for the problem of prescribing the scalar curvature on Cauchy- Riemann spheres under Beta-flatness condition. To give a lower bound for the number of solutions, we use Bahri methods based on the theory of critical points at infinity and a Poincare-Hopf type formula.

This paper tackles fair clustering with multiple types and provides scalable coreset solutions.

System detects multiple patients' behaviors in real-time using mmWave radar and CNN.

BatchBALD selects multiple informative points for deep Bayesian active learning, improving data efficiency.

We consider a continuous map $f :M\to N$ between two manifolds and try to estimate its multiplicity from below, i.e. find a $q$-tuple of pairwise distinct points $x_1,..., x_q\in M$ such that $f(x_1) = f(x_2) = ... = f(x_q)$. We show that there are certain characteristic classes of vector bundle $f^*TN-TM$ that guarant…

Method constructs prediction intervals for time-varying individual treatment effects.

We show that Tolman's example (of a six dimensional Hamiltonian $T^2$-space with isolated fixed points and no compatible Kähler structure) can be constructed from the flag variety $U(3)/U(1)^3$ by $U(2)$-equivariant symplectic surgery. This implies that Tolman's space has a ``transversal multiplicity-free'' action of $…

Study higher genus polylogarithms under Riemann surface degenerations.

This thesis is about the study of Lie groupoids endowed with a compatible (multiplicative) differential 1-form. The motivation and scope of the present work is to study the geometry of PDEs using the formalism of Lie groupoids and multiplicative forms; as such, ideas from the two theories have to be introduced and expl…