A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proves Hadamard states for Dirac fields on manifolds with timelike boundaries.
In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\MIT$ bag boundary condition. Then we give some applications of these constructions for each Green function.…
Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for …
In this paper, we prove the Hijazi inequality on compact Riemannian spin manifolds under two boundary conditions: the condition associated with a chirality operator and the Riemannian version of the $\MIT$ bag condition. We then show that the limiting-case is characterized as being a half-sphere for the first condition…
We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the $\MIT$ bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.
In the thesis at hand we give a comprehensive discussion of basic problems for generalized Maxwell equations with mixed boundary conditions using the calculus of alternating differential forms on Riemannian manifolds of arbitrary dimension. We prove compactness results, Hodge decompositions and Poincare type estimates.…
We show that the eigenvalues of the intrinsic Dirac operator on the boundary of a Euclidean domain can be obtained as the limits of eigenvalues of Euclidean Dirac operators, either in the domain with a MIT-bag type boundary condition or in the whole space, with a suitably chosen zero order mass term.
We consider the Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial-boundary value problem coupled to MIT-boundary conditions. This is achieved by transforming the problem locally into a symmetric positive hyperbolic system, proving existence and uniquene…
The paper proves a positive mass theorem for non-compact static domains in hyperbolic space.
Study proves positivity of quasi-local masses in general relativity using spinors.
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge et al. (2012), it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of d…
Study of Dirac-like operators on spin manifolds with large mass parameters.
Deep neural networks (DNNs) provide state-of-the-art results for a multitude of applications, but the approaches using DNNs for multimodal audiovisual applications do not consider predictive uncertainty associated with individual modalities. Bayesian deep learning methods provide principled confidence and quantify pred…
Random forests is a common non-parametric regression technique which performs well for mixed-type data and irrelevant covariates, while being robust to monotonic variable transformations. Existing random forest implementations target regression or classification. We introduce the RFCDE package for fitting random forest…
HiPart offers an efficient, interactive tool for hierarchical clustering.
Novel graph-based method detects R-peaks in noisy ECG signals without preprocessing.
Computational analysis on physiological signals would provide immense impact for enabling automated clinical analytics. However, the class imbalance issue where negative or minority class instances are rare in number impairs the robustness of the practical solution. The key idea of our approach is intelligent augmentat…
This paper is a commentary and a reading guide to three papers by Herbert Busemann, Über die Geometrien, in denen die "Kreise mit unendlichem Radius" die kürzesten Linien sind." (On the geometries where circles of infinite radius are the shortest lines) (1932), "Paschsches Axiom und Zweidimensionalität," (Pasch's Axiom…
This paper introduces libconform v0.1.0, a Python library for the conformal prediction framework, licensed under the MIT-license. libconform is not yet stable. This paper describes the main algorithms implemented and documents the API of libconform. Also some details about the implementation and changes in future versi…
The study of embedded minimal surfaces in $\RR^3$ is a classical problem, dating to the mid 1700's, and many people have made key contributions. We will survey a few recent advances, focusing on joint work with Tobias H. Colding of MIT and Courant, and taking the opportunity to focus on results that have not been highl…
metric-learn is an open source Python package implementing supervised and weakly-supervised distance metric learning algorithms. As part of scikit-learn-contrib, it provides a unified interface compatible with scikit-learn which allows to easily perform cross-validation, model selection, and pipelining with other machi…
Researchers prove a Penrose inequality for spacetime with specific conditions.
Electrocardiogram (ECG) can be reliably used as a measure to monitor the functionality of the cardiovascular system. Recently, there has been a great attention towards accurate categorization of heartbeats. While there are many commonalities between different ECG conditions, the focus of most studies has been classifyi…
Sparse DNNs face scalability issues; MIT/IEEE/Amazon challenge analyzes best solutions.
Homotopy proof for pseudomanifolds via branched covers.
We present the OpenAI Remote Rendering Backend (ORRB), a system that allows fast and customizable rendering of robotics environments. It is based on the Unity3d game engine and interfaces with the MuJoCo physics simulation library. ORRB was designed with visual domain randomization in mind. It is optimized for cloud de…
This paper explores four different visualization techniques for long short-term memory (LSTM) networks applied to continuous-valued time series. On the datasets analysed, we find that the best visualization technique is to learn an input deletion mask that optimally reduces the true class score. With a specific focus o…
Classifies local boundary conditions for Dirac-type operators on manifolds.
Proof of local well-posedness for a specific boundary condition in general relativity.
Under two boundary conditions, the generalized Atiyah-Patodi-Singer boundary condition and the modified generalized -Atiyah-Patodi-Singer boundary condition, we get the lower bounds for the eigenvalues of the fundamental Dirac operator on compact spin manifolds with nonempty boundary.
The transfer learning toolkit wraps the codes of 17 transfer learning models and provides integrated interfaces, allowing users to use those models by calling a simple function. It is easy for primary researchers to use this toolkit and to choose proper models for real-world applications. The toolkit is written in Pyth…
Develops a method to interpret deep learning models by identifying key features.
New boundary conditions solve Cauchy problem for Dirac operators on spacetimes.
We introduce new boundary conditions for differential forms on symplectic manifolds with boundary. These boundary conditions, dependent on the symplectic structure, allows us to write down elliptic boundary value problems for both second-order and fourth-order symplectic Laplacians and establish Hodge theories for the …
The paper studies Ricci flow on manifolds with boundary, proving existence, uniqueness, and boundary conditions preservation.
We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local. We show the equivalence of various characterisations of elliptic boundary conditions and demonst…
We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for long time existence of the flow with boundary conditions with assumptions on the curvature of a the Lorentz boundary manifold.
Novel boundary conditions for Ricci flow to deform compact manifolds.
Proves well-posedness for Einstein equations with specific boundary conditions.
PINN-FEM combines PINNs and FEM for accurate Dirichlet boundary condition enforcement.
Paper constructs solutions to Bogomolny equations with specific boundary and asymptotic conditions.
Study constant mean curvature surfaces with integrable boundary conditions.
Lower bounds for eigenvalues on manifolds with boundary conditions.
The Nahm pole boundary condition for certain gauge theory equations in four and five dimensions is defined by requiring that a solution should have a specified singularity along the boundary. In the present paper, we show that this boundary condition is elliptic and has regularity properties analogous to more standard …
Paper discusses gluing formula for zeta-determinants with Robin boundary condition.
Study well-poses Dirac operator problem with APS boundary conditions.
This paper presents a new open source Python framework for causal discovery from observational data and domain background knowledge, aimed at causal graph and causal mechanism modeling. The 'cdt' package implements the end-to-end approach, recovering the direct dependencies (the skeleton of the causal graph) and the ca…
BEKAN uses RBFs and evolutionary methods to solve PDEs with boundary conditions.