arXiv research

Given a smooth closed oriented manifold $M$ of dimension $n$ embedded in $\mathbb{R}^{n+2}$ we study properties of the `solid angle' function $Φ\colon\mathbb{R}^{n+2}\setminus M\to S^1$. It turns out that a non-critical level set of $Φ$ is an explicit Seifert hypersurface for $M$.

New study shows min-max algorithms can converge to non-stationary points.

A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as C^1 surfaces in Euclidean spaces. As in Euclidean spaces, intrinsic regular surfaces can be locally defined in different ways: e.g. as non critical level …

We study/construct (proper and non-proper) Morse functions on complete Riemannian manifolds, the level hypersurfaces of which have positive mean curvatures at all non-critical points. We show, for instance, that if a complete Rieannin manifold admits no such (not necessarily proper) function, then it contains a (possib…

In [3], the authors showed the existence and the uniqueness of a sl(m+1,\R)-equivariant quantization in the non-critical situations. The curved generalization of the sl(m+1,\R)-equivariant quantization is the natural and projectively equivariant quantization. In [1] and [7], the existence of such a quantization was pro…

Shorter time windows and carefully selected features outperform longer periods and extra features in mortgage default prediction.

Eigenfunction gradients on curved spaces imply rigid structure.

In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the GJMS operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal…

One computes the cohomology of the projective embedding of sl(m+1,R) acting on the differential operators on densities on R^m of various weights. This cohomology is non vanishing only for some special critical values of the weights. This allows us first to explain some strange feature pointed out by Gargoubi in his cla…

In this paper, we analyse the question of existence of a natural and projectively equivariant symbol calculus, using the theory of projective Cartan connections. We establish a close relationship between the existence of such a natural symbol calculus and the existence of an \sl(m+1,\R)-equivariant calculus over \R^{m}…

Text analytics based on supervised machine learning classifiers has shown great promise in a multitude of domains, but has yet to be applied to Seismology. We test various standard models (Naive Bayes, k-Nearest Neighbors, Support Vector Machines, and Random Forests) on a seismological corpus of 100 articles related to…

Survey on pruning CNN models to reduce size for edge devices.

Epanechnikov Mean Shift is a simple yet empirically very effective algorithm for clustering. It localizes the centroids of data clusters via estimating modes of the probability distribution that generates the data points, using the `optimal' Epanechnikov kernel density estimator. However, since the procedure involves n…

Recent work in signal propagation theory has shown that dropout limits the depth to which information can propagate through a neural network. In this paper, we investigate the effect of initialisation on training speed and generalisation for ReLU networks within this depth limit. We ask the following research question:…

Nowadays, advanced intrusion detection systems (IDSs) rely on a combination of anomaly detection and signature-based methods. An IDS gathers observations, analyzes behavioral patterns, and reports suspicious events for further investigation. A notorious issue anomaly detection systems (ADSs) and IDSs face is the possib…

The paper analyzes how SGD visits different regions of a non-convex problem's state space.

We consider the space of differential operators $\mathcal{D}_{λμ}$ acting between $λ$- and $μ$-densities defined on $S^{1|2}$ endowed with its standard contact structure. This contact structure allows one to define a filtration on $\mathcal{D}_{λμ}$ which is finer than the classical one, obtained by writting a differen…

Study shows Julia sets and gasket limit sets are quasiconformally different.

Study shows non-symmetric convex sets have full boundary limits.

The paper analyzes set-to-set matching with neural networks, focusing on theoretical generalization.

Generative model learns to autoencode and generate sets of images.

Study on cold and freezing sets in digital images.

Paper solves whether zero sets are mapping degree sets.

Matching two different sets of items, called heterogeneous set-to-set matching problem, has recently received attention as a promising problem. The difficulties are to extract features to match a correct pair of different sets and also preserve two types of exchangeability required for set-to-set matching: the pair of …

New set-valued star-shaped risk measures introduced for better risk assessment.

We introduce the concept of hereditarily non uniformly perfect sets, compact sets for which no compact subset is uniformly perfect, and compare them with the following: Hausdorff dimension zero sets, logarithmic capacity zero sets, Lebesgue 2-dimensional measure zero sets, and porous sets. In particular, we give an exa…

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

The study explores mapping degree sets and their properties for manifolds.

Current approaches for predicting sets from feature vectors ignore the unordered nature of sets and suffer from discontinuity issues as a result. We propose a general model for predicting sets that properly respects the structure of sets and avoids this problem. With a single feature vector as input, we show that our m…

This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.

Consider a general machine learning setting where the output is a set of labels or sequences. This output set is unordered and its size varies with the input. Whereas multi-label classification methods seem a natural first resort, they are not readily applicable to set-valued outputs because of the growth rate of the o…

Deep Sets approximates functions on sets with high-dimensional latent space.

Study online learning with set-valued feedback, showing differences between deterministic and randomized approaches.

A stability-based method selects the most desirable conformal prediction set.

The paper links set cuspidality to function regularity and flatness.

This work establishes properties on diffeological structures for set-valued maps and measures.

Causal Set Theory's Hauptvermutung is resolved in two ways, one of which is true.

This letter introduces an abstract learning problem called the "set embedding": The objective is to map sets into probability distributions so as to lose less information. We relate set union and intersection operations with corresponding interpolations of probability distributions. We also demonstrate a preliminary so…

Find limiting sets for digital cones and suspensions.

Analytic sets with unique infinite tangent cone are algebraic.

Study freezing sets for digital images in a 2D grid.

Fuzzy prediction sets generalize binary predictions to include elements at varying confidence levels.

Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed to learn a permutation-invariant representation of that set, avoid…

Develops deep neural network techniques for sets as input and output.

Proves a theorem for Assouad dimension with applications to distance sets and radial projections.

The paper explores connections between perimeter, area, and visual angle of convex sets.

The paper defines cyclic sets from ribbon string links and connects them to quantum invariants.

New tools for constructing fixed point sets in digital topology.