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The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the…

Machine Learning · Statistics 2015-05-12 Zhenwen Dai , James Hensman , Neil Lawrence

We consider the problem of algorithmically sampling from the Gibbs measure of a mixed $p$-spin spherical spin glass. We give a polynomial-time algorithm that samples from the Gibbs measure up to vanishing total variation error, for any…

Probability · Mathematics 2024-04-25 Brice Huang , Andrea Montanari , Huy Tuan Pham

Spielman and Teng introduced the smoothed analysis of algorithms to provide a framework in which one could explain the success in practice of algorithms and heuristics that could not be understood through the traditional worst-case and…

Optimization and Control · Mathematics 2007-05-23 Daniel A. Spielman , Shang-Hua Teng

This open problem, first posed by Erd{\omicron}s, was further explored by Terence Tao. Tao work shows that the series can converge conditionally, but only under a sufficiently strong form of the Hardy-Littlewood conjecture for k-primary…

General Mathematics · Mathematics 2025-05-13 Nikos Mantzakouras

We extend classical tools from rational homotopy theory to topological data analysis by introducing persistent Sullivan minimal models of persistent topological spaces. Our main result establishes that the interleaving distance between such…

Algebraic Topology · Mathematics 2025-04-08 Ling Zhou

This manuscript describes in detail the symplectic sum formulas in Gromov-Witten theory and related topological and analytic issues. In particular, we analyze and compare two analytic approaches to these formulas. The Ionel-Parker formula…

Symplectic Geometry · Mathematics 2014-12-30 Mohammad F. Tehrani , Aleksey Zinger

We give an alternative proof of the Schoen--Simon--Yau curvature estimates and associated Bernstein-type theorems (1975), and extend the original result by including the case of $6$-dimensional (stable minimal) immersions. The key step is…

Analysis of PDEs · Mathematics 2025-09-15 Costante Bellettini

In Part II of this two-part paper, we prove the convergence of the simplified information geometry approach (SIGA) proposed in Part I. For a general Bayesian inference problem, we first show that the iteration of the common second-order…

Information Theory · Computer Science 2024-11-27 Jiyuan Yang , Yan Chen , Mingrui Fan , Xiqi Gao , Xiang-Gen Xia , Dirk Slock

The Symplectic Pontryagin method was introduced in a previous paper. This work shows that this method is applicable under less restrictive assumptions. Existence of solutions to the Symplectic Pontryagin scheme are shown to exist without…

Numerical Analysis · Mathematics 2009-02-02 Mattias Sandberg

Parameter Efficient Fine-Tuning (PEFT) methods have gained popularity and democratized the usage of Large Language Models (LLMs). Recent studies have shown that a small subset of weights significantly impacts performance. Based on this…

Under the assumption of the uniform local Sobolev inequality, it is proved that Riemannian metrics with an absolute Ricci curvature bound and a small Riemannian curvature integral bound can be smoothed to having a sectional curvature bound.…

Differential Geometry · Mathematics 2011-04-12 Yunyan Yang

On August 20, 2025, GPT-5 was reported to have solved an open problem in convex optimization. Motivated by this episode, we conducted a controlled experiment in the Malliavin--Stein framework for central limit theorems. Our objective was to…

Probability · Mathematics 2025-09-04 Charles-Philippe Diez , Luis da Maia , Ivan Nourdin

The paper deals with a question of robustness of inferences, carried out on a continuous-time stationary process contaminated by a small trend, to this departure from stationarity. We show that a smoothed periodogram approach to parameter…

Statistics Theory · Mathematics 2016-01-27 M. S. Ginovyan , A. A. Sahakyan

In this paper, we report the development of the generalized proximal smoothing (GPS) algorithm for phase retrieval of noisy data. GPS is a optimization-based algorithm, in which we relax both the Fourier magnitudes and object constraints.…

Optimization and Control · Mathematics 2019-02-20 Minh Pham , Penghang Yin , Arjun Rana , Stanley Osher , Jiawei Miao

The leading correction to the smoothed connected energy density-density correlation function is obtained for the large energy difference, within the context of the Gaussian Random Matrix Theory. In order to achieve this result, the…

Condensed Matter · Physics 2015-06-25 Vladan Lucic

Let $m \in \mathbb{N}$ be large. We show that there exist infinitely many primes $q_{1}< \cdot\cdot\cdot < q_{m+1}$ such that \[ q_{m+1}-q_{1}=O(e^{7.63m}) \] and $q_{j}+2$ has at most \[ \frac{7.36m}{\log 2} + \frac{4\log m}{\log 2} + 21…

Number Theory · Mathematics 2025-07-17 Bin Chen

The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…

Differential Geometry · Mathematics 2021-08-31 Thomas Bendokat , Ralf Zimmermann

This paper reformulates and streamlines the core tools of robust stability and performance for LTI systems using now-standard methods in convex optimization. In particular, robustness analysis can be formulated directly as a primal convex…

Systems and Control · Computer Science 2015-03-27 Seungil You , Ather Gattami , John C. Doyle

In this article we introduce a new class of weighted sequence spaces of Sobolev type and prove several compact embedding theorems for them. It is our contention that the chosen class is general enough so as to allow applications in various…

Functional Analysis · Mathematics 2025-03-27 Pierre-A. Vuillermot

Mirror Descent is a popular algorithm, that extends Gradients Descent (GD) beyond the Euclidean geometry. One of its benefits is to enable strong convergence guarantees through smooth-like analyses, even for objectives with exploding or…

Optimization and Control · Mathematics 2024-04-19 Hadrien Hendrikx