arXiv research

New method estimates discrete distributions while protecting privacy.

Let $E_{n}$ be an holomorphic bundle of rank two on an algebraic curve $X$ (the degree of $E_{n}$ is $n$ apart from an additive constant). Note by $Met(E_{n})$ the space of hermitian metrics $h$ on $E_{n}$. Also, consider $Met(W_{n})$, the space of metrics on $H^{0}(X,E_{n})$. Although $Met(W_{n})$ is finite dimensiona…

We study the geometry of fanning curves in the Grassmann manifold of n-dimensional subspaces of $\mathbb{R}^{kn}$; we construct a complete system of invariants which solve the congruence problem. The geometry of the invariants themselves and their relation with classical invariants is also studied.

On base of three-dimensional flat metrics obtained with the help of solutions of the KdV-equation were constructed the examples of six-dimensional metrics, which are determined by the help of solutions of Krichever-Novikov and KdV. Their properties are discussed.

The nullity of a minimal submanifold $M\subset S^{n}$ is the dimension of the nullspace of the second variation of the area functional. That space contains as a subspace the effect of the group of rigid motions $SO(n+1)$ of the ambient space, modulo those motions which preserve $M$, whose dimension is the Killing nulli…

Holomorphic families of knots in conformal 3-manifolds

We propose a new algorithm for adversarial multi-armed bandits with unrestricted delays. The algorithm is based on a novel hybrid regularizer applied in the Follow the Regularized Leader (FTRL) framework. It achieves $\mathcal{O}(\sqrt{kn}+\sqrt{D\log(k)})$ regret guarantee, where $k$ is the number of arms, $n$ is the …

The aim of this research is the study of Gray curvature identities, introduced by Alfred Gray in \cite{kn:Gra76} for the class of almost hermitian manifolds. As known till now, there is no equivalent for the class of almost contact manifolds. For this purpose we use the Boohby-Wang fibration and the warped manifolds co…

DMTG groups tasks for multi-task learning in one shot.

Let M be a connected d-dimensional complex projective manifold, and let A be a holomorphic positive Hermitian line bundle on M, with normalized curvature. Let G be a compact and connected Lie group of dimension d(G), and let T be a compact torus T of dimension d(T). Suppose that both G and T act on M in a holomorphic a…

The main result of this article states that the (K;N)-cone over some metric measure space satisfies the reduced Riemannian curvature-dimension condition RCD^*(KN;N+1) if and only if the underlying space satisfies RCD^*(N-1;N). The proof uses a characterization of reduced Riemannian curvature-dimension bounds by Bochner…

Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In this paper, we study the family of GGMs with small feedback vertex sets (FVSs), whe…

In this paper we investigate what kind of manifolds arise as the total spaces of iterated $S^1$-bundles. A real Bott tower studied in \cite{CMO}, \cite{KM} and \cite{KN} is an example of an iterated $S^1$-bundle. We show that the total space of an iterated $S^1$-bundle is homeomorphic to an infra-nilmanifold. A real Bo…

A {\em good drawing\/} of $K_n$ is a drawing of the complete graph with $n$ vertices in the sphere such that: no two edges with a common end cross; no two edges cross more than once; and no three edges all cross at the same point. Gioan's Theorem asserts that any two good drawings of $K_n$ that have the same rotations …

The elliptic Hall algebra governs torus link homology.

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a distance-ba…

Generalizes complex manifolds to manifolds with corners and generalized corners.

This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion problem to situations in which the matrix rank can be quite high or even full r…

This paper shows that pairwise PageRank orders emerge from two-hop walks. The main tool used here refers to a specially designed sign-mirror function and a parameter curve, whose low-order derivative information implies pairwise PageRank orders with high probability. We study the pairwise correct rate by placing the Go…

We study the problem of partitioning a small sample of $n$ individuals from a mixture of $k$ product distributions over a Boolean cube $\{0, 1\}^K$ according to their distributions. Each distribution is described by a vector of allele frequencies in $\R^K$. Given two distributions, we use $γ$ to denote the average $\el…

Warped products over one-dimensional base spaces satisfy curvature-dimension condition under specific conditions.

We propose a framework for Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to interact with a domain expert, asking whether two given instances belong to the same cluster or not. We study the query and computational complexity of clustering in this framework. We consider a setting where…

Kuroda and Nagai \cite{KN} state that the factor process in the Risk Sensitive control Asset Management (RSCAM) is stable under the Föllmer-Schweizer minimal martingale measure . Fleming and Sheu \cite{FS} and more recently Föllmer and Schweizer \cite{FoS} have observed that the role of the minimal martingale measure i…

The tangent bundle $T^kM$ of order $k$, of a smooth Banach manifold $M$ consists of all equivalent classes of curves that agree up to their accelerations of order $k$. In the previous work of the author he proved that $T^kM$, $1\leq k\leq \infty$, admits a vector bundle structure on $M$ if and only if $M$ is endowed w…

A long standing open problem in the theory of neural networks is the development of quantitative methods to estimate and compare the capabilities of different architectures. Here we define the capacity of an architecture by the binary logarithm of the number of functions it can compute, as the synaptic weights are vari…

Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we address on-line learning with matrix parameters. It is often easy to obtain onlin…

Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to subspace clustering, often takes on a sparse representation or a low-rank represent…

The definition of balanced metrics was originally given by Donaldson in the case of a compact polarized Kähler manifold in 2001, who also established the existence of such metrics on any compact projective Kähler manifold with constant scalar curvature. Currently, the only noncompact manifolds on which balanced metrics…

We consider the problem of multi-objective maximization of monotone submodular functions subject to cardinality constraint, often formulated as $\max_{|A|=k}\min_{i\in\{1,\dots,m\}}f_i(A)$. While it is widely known that greedy methods work well for a single objective, the problem becomes much harder with multiple objec…

We prove the following: Let $2p + 1$ be no less than 5 and $p$ be a natural number. Let $K$ and $J$ be closed, oriented, $(2p+1)$-dimensional connected, $(p-1)$-connected, simple submanifolds of the standard $(2p+3)$-sphere. Then $K$ is equivalent to $J$ if and only if a Seifert matrix associated with a simple Seifert …

New algorithms use offline data to improve online decision-making with latent states.

We study the robust one-bit compressed sensing problem whose goal is to design an algorithm that faithfully recovers any sparse target vector $θ_0\in\mathbb{R}^d$ \textit{uniformly} via $m$ quantized noisy measurements. Specifically, we consider a new framework for this problem where the sparsity is implicitly enforced…

Exact cluster recovery with same-cluster queries for arbitrary ellipsoidal clusters.

A new algorithm FastGM speeds up generating Gumbel-Max variables.

Algorithms learn and test variable partitions in various groups and error metrics.

The paper studies braid groups and splitting problems in projective plane configurations.

Proactive DP optimizes privacy and utility in DP-SGD with a fixed privacy budget.

New method tightens federated probe-logit distillation rates under varying bandwidths.