arXiv research

The paper identifies all link projections with isolate-region number one.

In this paper we study flows $\varphi:M\times\mathbb{R}\longrightarrow M$ having an isolated non-saddle set. We see that the complexity of the region of influence of an isolated non-saddle set $K$ depends on the way in which $K$ sits on the phase space at the cohomological level. We construct flows in surfaces having i…

The paper finds singular isoperimetric regions in high-dimensional spaces.

Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations in sparsely populated regions. We show that heavy-tailed stochastic processes (…

One-hot CNN (convolutional neural network) has been shown to be effective for text categorization (Johnson & Zhang, 2015). We view it as a special case of a general framework which jointly trains a linear model with a non-linear feature generator consisting of `text region embedding + pooling'. Under this framework, we…

Theorem proves topological censorship for universes with positive cosmological constant.

Develops a machine learning method for parameter estimation in branching processes models.

Automatic detection of anomalies in space- and time-varying measurements is an important tool in several fields, e.g., fraud detection, climate analysis, or healthcare monitoring. We present an algorithm for detecting anomalous regions in multivariate spatio-temporal time-series, which allows for spotting the interesti…

The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, wa…

The study extends $L^p$-spectrum analysis to warped products and Kleinian groups.

Study global geometry of dynamical systems with entire vector fields.

For one-hidden-layer ReLU networks, we prove that all differentiable local minima are global inside differentiable regions. We give the locations and losses of differentiable local minima, and show that these local minima can be isolated points or continuous hyperplanes, depending on an interplay between data, activati…

We present a method to desingularize a compact G_2 manifold with isolated conical singularities by cutting out a neighbourhood of each singular point and glueing in an asymptotically conical G_2 manifold. Controlling the error on the overlap glueing region enables us to use a result of Joyce to conclude that the result…

We show that discrete synaptic weights can be efficiently used for learning in large scale neural systems, and lead to unanticipated computational performance. We focus on the representative case of learning random patterns with binary synapses in single layer networks. The standard statistical analysis shows that this…

Study examines dependence of extreme electricity prices in Australian markets.

Study identifies high-density anomalies in normal data regions.

Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights naturally gives prominence to exponentially rare dense regions of solutions with a numb…

We study whether a neural network optimizes to the same, linearly connected minimum under different samples of SGD noise (e.g., random data order and augmentation). We find that standard vision models become stable to SGD noise in this way early in training. From then on, the outcome of optimization is determined to a …

Study of $G_2$-structures with isolated singularities and bounded torsion.

New stability and isolation results for Einstein manifolds.

Map quandle orders to actions, characterize isolated orders, and prove no isolated right orders.

This paper presents a new insight into improving the performance of Stochastic Neighbour Embedding (t-SNE) by using Isolation kernel instead of Gaussian kernel. Isolation kernel outperforms Gaussian kernel in two aspects. First, the use of Isolation kernel in t-SNE overcomes the drawback of misrepresenting some structu…

Defines Perelman's functionals on manifolds with non-isolated conical singularities.

iMondrian forest combines isolation forest and Mondrian forest for better anomaly detection.

We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities and establishing lower bound theorems when the singularities are also homological…

We explore the geometry of nonpositively curved spaces with isolated flats, and its consequences for groups that act properly discontinuously, cocompactly, and isometrically on such spaces. We prove that the geometric boundary of the space is an invariant of the group up to equivariant homeomorphism. We also prove that…

Federated learning (FL) is a distributed learning approach where a set of end-user devices participate in the learning process by acting on their isolated local data sets. Here, we process local data sets of users where worst-case optimization theory is used to reformulate the FL problem where the impact of local data …

The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.

Quantifies how geodesic planes isolate in hyperbolic 3-manifolds.

New bounds on trajectory safety in training models with Langevin Dynamics.

We define two types of local indices of a vector field at an isolated zero on the boundary, and prove Poincare-Hopf-type index theorems for certain vector fields on a compact smooth manifold which have only isolated zeros.

Study reveals GAGA phenomenon in Poisson cohomology for plane structures with isolated singularities.

Proves conditions for positive scalar curvature on certain manifolds with conical singularities.

Study dynamics and topology of flows near non-saddle sets or W-sets.

We study the Euler obstruction of essentially isolated determinantal singularities (EIDS). The EIDS were defined by W. Ebeling and S. Gusein-Zade, as a generalization of isolated singularity. We obtain some formulas to calculate the Euler obstruction for the determinantal varieties with singular set an ICIS.

The paper builds complex hyperbolic 2-manifolds with isolated singularities.

The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.

Robert Bryant (Theorie des varietes minimales et applications, 1988, 154: 321-347) proved that an isolated singularity of a conformal metric of positive constant curvature on a Riemann surface is a conical one. Using Complex Analysis, we find all of the local models for an isolated singularity of a flat metric whose ar…

Study on solutions near isolated singularities in 6D Yamabe equation.

Two new scoring methods improve anomaly detection in Isolation Forest.

We study solutions to conformally invariant equations with isolated singularties.

A generalized semitoric system F:=(J,H): M --> R^2 on a symplectic 4-manifold is an integrable system whose essential properties are that F is a proper map, its set of regular values is connected, J generates an S^1-action and is not necessarily proper. These systems can exhibit focus-focus singularities, which corresp…

Local data coverage governs memorization in diffusion models.

The purpose of this erratum is to correct the proof of Theorem A.0.1 in the appendix to our article ``Hadamard spaces with isolated flats'' math.GR/0411232, which was jointly authored by Mohamad Hindawi, Hruska and Kleiner. In that appendix, many of the results of math.GR/0411232 about CAT(0) spaces with isolated flats…

New isolated geometric triangulations found in once-punctured torus bundles.

Proposes methods to improve interpretability of Isolation Forest for anomaly detection.

Model predicts insolvency risks in banks due to liquidity and credit risks.

Score-based methods fail with isolated components and incorrect mixing proportions.