arXiv research

Paper proposes a new Autoencoder for robustly encoding white matter streamlines.

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and …

Tractograms are mathematical representations of the main paths of axons within the white matter of the brain, from diffusion MRI data. Such representations are in the form of polylines, called streamlines, and one streamline approximates the common path of tens of thousands of axons. The analysis of tractograms is a ta…

We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is hindered by lack of sparseness in the underlying least squares system. Because of th…

The study identifies unique fluid flow patterns.

In this paper, we show the existence of real-analytic stationary Navier-Stokes flows with isotropic streamlines in all latitudes in some simply-connected flow region on a rotating round sphere. We also exclude the possibility of having a Poiseuille's flow profile to be one of these stationary Navier-Stokes flows with i…

Diffusion magnetic resonance imaging (dMRI) and tractography provide means to study the anatomical structures within the white matter of the brain. When studying tractography data across subjects, it is usually necessary to align, i.e. to register, tractographies together. This registration step is most often performed…

Diffusion magnetic resonance imaging (dMRI) data allow to reconstruct the 3D pathways of axons within the white matter of the brain as a tractography. The analysis of tractographies has drawn attention from the machine learning and pattern recognition communities providing novel challenges such as finding an appropriat…

Bianchi proves Mumford conjecture using branched covers.

In this note we give an overview of some applications of the Calabi-Yau theorem to the construction of singular positive (1,1) currents on compact complex manifolds. We show how recent developments allow us to give streamlined proofs of existing results, as well as new ones.

In this paper we give a proof of Lichnerowicz Conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids the {\it Nice Embeddings} into eigen spaces of the Laplacian. Even if one wants to use these embeddings this paper gives a more streamlined proof.

Proofs for spectral and geometric properties of hyperbolic surfaces.

Study on measurable pseudo-Anosov maps on surfaces.

We aim to develop off-policy DRL algorithms that not only exceed state-of-the-art performance but are also simple and minimalistic. For standard continuous control benchmarks, Soft Actor-Critic (SAC), which employs entropy maximization, currently provides state-of-the-art performance. We first demonstrate that the entr…

This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations without heavy use of inessential constants. They bridge classical asymptotic nota…

ParaMonte::Python streamlines Bayesian data analysis with fast Monte Carlo and MCMC routines.

A canonical hyperkaehler metric on the total space $T^*M$ of a cotangent bundle to a complex manifold $M$ has been constructed recently by the author (see alg-geom/9710026). This paper presents the results of alg-geom/9710026 in a streamlined and simplified form. The only new result is an explicit formula obtained for …

The simulator is an R package that streamlines the process of performing simulations by creating a common infrastructure that can be easily used and reused across projects. Methodological statisticians routinely write simulations to compare their methods to preexisting ones. While developing ideas, there is a temptatio…

Locally connected boundaries of Coxeter groups are studied.

We generalize optimal inequalities of C. Loewner and M. Gromov, by proving lower bounds for the total volume in terms of the homotopy systole and the stable systole. Our main tool is the construction of an area-decreasing map to the Jacobi torus, streamlining and generalizing the construction of the first author in col…

In this note we study the localization of Futaki-Morita integrals at isolated degenerate zeros by giving a streamlined exposition in the spirit of Bott and implement the localization procedure for a holomorphic vector field on $CP^n$ with a maximally degenerate zero, giving an essentially unique formula for the Futaki-…

Paper uses 3-circle theorem to study Willmore surfaces and prove decay estimates.

New family of measurable pseudo-Anosov maps on spheres.

Higher gauge theory via differential nonabelian cohomology

Optimizes deep learning models for ocean dynamics using Fourier neural operators.

Improves sampling, rounding, and integration of logconcave functions.

A new mathematical framework simplifies securitization structuring.

A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along a flow defined by the vector field which intuitively represents the desired move…

Paper solves Serrin problem for ring-shaped domains, showing velocity has finitely many maxima.

We provide an online convex optimization algorithm with regret that interpolates between the regret of an algorithm using an optimal preconditioning matrix and one using a diagonal preconditioning matrix. Our regret bound is never worse than that obtained by diagonal preconditioning, and in certain setting even surpass…

This paper classifies all planar p-elasticae and their properties.

Proposes an efficient algorithm for mHealth that makes real-time physical activity suggestions.

This work simplifies choosing reinforcement-learning algorithms.

In the 1980s Alano Ancona developed a profound potential theory on Gromov hyperbolic manifolds of bounded geometry. Since then, such hyperbolic spaces have become basic in geometry, topology and group theory. In this paper we make Ancona's original work, addressed to a rather advanced audience, approachable for a wider…

An instanton $(E, D)$ on a (pseudo-)hyperkähler manifold $M$ is a vector bundle $E$ associated to a principal $G$-bundle with a connection $D$ whose curvature is pointwise invariant under the quaternionic structures of $T_x M, \ x\in M$, and thus satisfies the Yang-Mills equations. Revisiting a construction of solution…

This paper is devoted to a deep analysis of the process known as Cheeger deformation, applied to manifolds with isometric group actions. Here, we provide new curvature estimates near singular orbits and present several applications. As the main result, we answer a question raised by a seminal result of Searle--Wilhelm …

We generalize the classical Bochner formula for the heat flow on M to martingales on the path space PM, and develop a formalism to compute evolution equations for martingales on path space. We see that our Bochner formula on PM is related to two sided bounds on Ricci curvature in much the same manner that the classical…

A tutorial on non-asymptotic system identification methods.

The paper studies the curvature behavior near the boundary of certain domains.

Paper outlines a new mathematical language for experiments.

Note improves confidence bounds for random variables.

Simplified approach to pseudo-Anosov flows on 3-manifolds.

We simplify and extend a 6D conformal gravity theory to 8D, linking it to Q-curvature.

Simpler, faster algorithm for uniformity testing in the shuffle model.

A family of hypersurfaces evolves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution equation in extrinsic geometry, and has been extensively studied ever since the pioneering work of Brakke and Huisken. In the last 15 years, Whi…

Many machine learning models have important structural tuning parameters that cannot be directly estimated from the data. The common tactic for setting these parameters is to use resampling methods, such as cross--validation or the bootstrap, to evaluate a candidate set of values and choose the best based on some pre--…

Automated extraction of concepts from patient clinical records is an essential facilitator of clinical research. For this reason, the 2010 i2b2/VA Natural Language Processing Challenges for Clinical Records introduced a concept extraction task aimed at identifying and classifying concepts into predefined categories (i.…

Develops a new method for minimal Lagrangian surfaces in complex quadrics.