arXiv research

A smooth curve $γ: [0,1] \to \Ss^2$ is locally convex if its geodesic curvature is positive at every point. J. A. Little showed that the space of all locally convex curves $γ$ with $γ(0) = γ(1) = e_1$ and $γ'(0) = γ'(1) = e_2$ has three connected components $L_{-1,c}$, $L_{+1}$, $L_{-1,n}$. The space $\cL_{-1,c}$ is kn…

New invariants from divisibility of Lee classes for slice-torus.

Defines spherical type surfaces via support function and classifies them.

The state space (SS) representation of Gaussian processes (GP) has recently gained a lot of interest. The main reason is that it allows to compute GPs based inferences in O(n), where $n$ is the number of observations. This implementation makes GPs suitable for Big Data. For this reason, it is important to provide a SS …

SS-GEN simulates rare events in heavy and light-tailed data.

In this note we revisit the notion of conformal barycenter of a measure on $\SS^n$ as defined by Douady and Earle in Acta Math. Vol 157, 1986. The aim is to extend rational maps from the Riemann sphere $\Cbar\isom\SS^2$ to the (hyperbolic) three ball $\BB^3$ and thus to $\SS^3$ by reflection. The construction which was…

Introduces Star-Shaped DDPMs for non-Gaussian distributions.

This paper introduces SS-MAMP to address convergence issues in AMP algorithms.

We prove that any $n$--dimensional complete gradient Ricci soliton with pinched Weyl curvature is a finite quotient of $\RR^{n}$, $\RR \times \SS^{n-1}$ or $\SS^{n}$. In particular, we do not need to assume the metric to be locally conformally flat.

We solve spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in Schwarzschild spacetimes and analyze their asymptotic behavior near the coordinate singularity r = 2M. Furthermore, we join SS-CMC hypersurfaces in the Kruskal extension to obtain complete ones and discuss the smooth properties.

We first summarize the characterization of smooth spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in the Schwarzschild spacetime and Kruskal extension. Then use the characterization to prove special SS-CMC foliation property, and verify part of the conjecture by Malec and Ó Murchadha in t…

New method for estimating mean in SS inference with selection bias and decaying overlap.

A CBR system investigates the TS-SS metric for document similarity.

Bayesian method improves SS settings by leveraging unlabeled data.

Conjectures on universal structures in algebraic geometry enumerative invariants.

Enhances pairs trading with neural networks and Kalman Filters.

The set of osculating circles of a given curve in $\SS^3$ forms a curve in the set of oriented circles in $\SS^3$. We show that its "${\frac12}$-dimensional measure" with respect to the pseudo-Riemannian structure of the set of circles is proportional to the conformal arc-length of the original curve, which is a confor…

FLAME improves privacy in federated learning without trusted parties.

Paper proposes an efficient bandit-based algorithm for hyperparameter optimization.

We consider contracting and expanding curvature flows in $\Ss$. When the flow hypersurfaces are strictly convex we establish a relation between the contracting hypersurfaces and the expanding hypersurfaces which is given by the Gauß map. The contracting hypersurfaces shrink to a point $x_0$ while the expanding hypersur…

Develops robust and efficient SS estimators for treatment effects.

A fast, approximate method for variable selection in GLMs tackles correlated data.

We construct a compactification $M^{μss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $γ\colon M^{ss} \to M^{μss}$, where $M^{ss}$ is the moduli space of S-equiva…

SS-SARSA tackles recovering bandits by treating rounds as states.

KalmanNet uses neural networks to improve state estimation in systems with unknown dynamics.

The paper constructs many ancient solutions to the Yamabe flow on spheres.

We study a class of 3-dimensional paracontact metric manifolds and we revise some of the results obtain in \cite{SS}.

We propose a new random pruning method (called "submodular sparsification (SS)") to reduce the cost of submodular maximization. The pruning is applied via a "submodularity graph" over the $n$ ground elements, where each directed edge is associated with a pairwise dependency defined by the submodular function. In each s…

A new framework using kernel packets overcomes limitations of state space models for multi-dimensional data.

New classification of Kähler-Ricci solitons linked to isoparametric functions and contact geometry.

We derive a relationship between the eigenvalues of the Weyl-Schouten tensor of a conformal representative of the conformal infinity of a hyperbolic Poincaré manifold and the principal curvatures on the level sets of its uniquely associated defining function with calculations based on [9] [10]. This relationship genera…

Develops state-space deep Gaussian processes for irregular signals.

We prove that any flat family $(\mathcal{ F}_u)_{u\in U}$ of rank 2 torsion-free sheaves on a Gauduchon surface defines a continuous map on the semi-stable locus $U^{\mathrm {ss}}:=\{u\in U \ |\ \mathcal{ F}_u\hbox{ is slope semi-stable}\}$ with values in the Donaldson-Uhlenbeck compactification of the corresponding in…

Let $Γ$ be a finite d-valent graph and G an n-dimensional torus. An ``action'' of G on $Γ$ is defined by a map, $α$, which assigns to each oriented edge e of $Γ$ a one-dimensional representation of G (or, alternatively, a weight, $α_e$, in the weight lattice of G). For the assignment, $e \to α_e$, to be a schematic des…

Regression problems that have closed-form solutions are well understood and can be easily implemented when the dataset is small enough to be all loaded into the RAM. Challenges arise when data is too big to be stored in RAM to compute the closed form solutions. Many techniques were proposed to overcome or alleviate the…

Let $M$ be either the 2-sphere $\SS^2 \subset\RR^3$ or the hyperbolic plane $\HH^2 \subset \RR^3$. If $Δ(abc)$ is a geodesic triangle on $M$ with corners at $a,b,c\in M$, we denote by $α, β, γ\in M$ the midpoints of their sides. If $Ω$ denotes the oriented area of this triangle on $M$, it satisfies the relations: $$ \s…

There has been an increasing interest in semi-supervised learning in the recent years because of the great number of datasets with a large number of unlabeled data but only a few labeled samples. Semi-supervised learning algorithms can work with both types of data, combining them to obtain better performance for both c…

Paper tackles causal inference with partially labeled data, introducing robust methods.

Convolutional neural networks (CNNs) attained a good performance in hyperspectral sensing image (HSI) classification, but CNNs consider spectra as orderless vectors. Therefore, considering the spectra as sequences, recurrent neural networks (RNNs) have been applied in HSI classification, for RNNs is skilled at dealing …

Spike-and-Slab Deep Learning (SS-DL) is a fully Bayesian alternative to Dropout for improving generalizability of deep ReLU networks. This new type of regularization enables provable recovery of smooth input-output maps with unknown levels of smoothness. Indeed, we show that the posterior distribution concentrates at t…

This paper is devoted to pricing American options using Monte Carlo and the Malliavin calculus. Unlike the majority of articles related to this topic, in this work we will not use localization fonctions to reduce the variance. Our method is based on expressing the conditional expectation E[f(St)/Ss] using the Malliavin…

DRSS method identifies unnecessary samples and features in DR covariate shift.

Develops a new tensor PCA method for analyzing multiple network data.

Third-order PDEs describe spherical and pseudospherical surfaces.

We consider the problem of learning a sparse rule model, a prediction model in the form of a sparse linear combination of rules, where a rule is an indicator function defined over a hyper-rectangle in the input space. Since the number of all possible such rules is extremely large, it has been computationally intractabl…

Existence of translating solutions shown for curve diffusion flow.

The paper classifies equations describing spherical or pseudospherical surfaces.

Deep Partition Aggregation defends against poisoning attacks with provable certificates.