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.
Estimates derivatives of max-stable fields for risk analysis.
Study extreme values of stable random fields on geometric spaces.
The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when the projection operator achieves a stable embedding of the data by satisfying th…
An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the risk due to events having …
We propose a new non-parametric framework for learning incrementally stable dynamical systems x' = f(x) from a set of sampled trajectories. We construct a rich family of smooth vector fields induced by certain classes of matrix-valued kernels, whose equilibria are placed exactly at a desired set of locations and whose …
A meticulous assessment of the risk of impacts associated with extreme wind events is of great necessity for populations, civil authorities as well as the insurance industry. Using the concept of spatial risk measure and related set of axioms introduced by Koch (2017, 2019), we quantify the risk of losses due to extrem…
HTFM improves mode coverage and tail-statistic recovery for heavy-tailed data.
This work extracts stochastic dynamical systems with -stable Lévy noise.
The gradient flow of the Yang-Mills action acts pointwise on closed loops of gauge fields. We construct a topologically nontrivial loop of SU(2) gauge fields on S4 that is locally stable under the flow. The stable loop is written explicitly as a path between two gauge fields equivalent under a topologically nontrivial …
Method proves connection stability of vector fields on noncompact manifolds.
The Poincare-Hopf theorem tells us that given a smooth, structurally stable vector field on a surface of genus g, the number of saddles is 2-2g less than the number of sinks and sources. We generalize this result by introducing a more complex combinatorial invariant. Using this tool, we demonstrate that many such struc…
Study on Yang-Mills fields on proving self-duality constraints.
Study the topology of stable vector fields and Lyapunov functions on R^n.
Paper proves no stable Yang-Mills fields on spheres.
We study the use of "sign -stable random projections" (where ) for building basic data processing tools in the context of large-scale machine learning applications (e.g., classification, regression, clustering, and near-neighbor search). After the processing by sign stable random projections, the inner pr…
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively …
Stable knots and links can exist in electromagnetic fields.
We investigate link homology theories for stable equivalence classes of link diagrams on orientable surfaces. We apply (1+1)-dimensional unoriented topological quantum field theories to Bar-Natan's geometric formalism to define new theories for stable equivalence classes.
New invariants derived from random matrices for words in free groups.
fcHMRF-LIS controls FDR in neuroimaging data, improving power and scalability.
Generators for the module of vector fields liftable over corank 1 stable complex analytic maps from an n-manifold to an (n+1)-manifold are found. This is applied to the classification of the singularities occuring in generic one-parameter families of maps between these spaces.
In this paper, we discuss two topics: first, we show how to convert 1+1-topological quantum field theories valued in symmetric bimonoidal categories into stable homotopical data, using a machinery by Elmendorf and Mandell. Then, we discuss, in this framework, two recent results (independent of each other) on refinement…
The problem of existence of solution for the Heath-Jarrow-Morton equation with linear volatility and purely jump random factor is studied. Sufficient conditions for existence and non-existence of the solution in the class of bounded fields are formulated. It is shown that if the first derivative of the Levy-Khinchin ex…
Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its propert…
This paper studies large-width asymptotics for ReLU neural networks with α-Stable initializations.
The study examines stable regions in weighted manifolds with boundary properties.
Semisimple 4D field theories can't distinguish smooth 4-manifolds.
An arbitrary homomorphism between groups is nonincreasing for stable commutator length, and there are infinitely many (injective) homomorphisms between free groups which strictly decrease the stable commutator length of some elements. However, we show in this paper that a random homomorphism between free groups is almo…
The paper tackles drift identification in Lévy α-stable stochastic systems, proposing a Fourier space approach.
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for process which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.
Research describes all possible gradient vector fields on a sphere with up to ten singular points.
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce stable graphical (SG) models, a class of multivariate st…
The paper studies deformations of singular minimal hypersurfaces in dimensions 7 and above.
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy tailed jumps, and the time-fractional version codes heavy tailed waiting times. Thi…
This paper describes the construction of a canonical compactification of the space of trajectories and of the unstable/stable sets of a generic gradient like vector field on a closed manifold as well as a canonical structure of a smooth manifold with corners of these spaces. As an application we discuss the geometric c…
Paper introduces S-SSE for stable sparse subspace embedding.
A spiking neural network model for probabilistic inference of binary Markov random fields.
The study examines spectral dynamics in deep neural networks, predicting how outliers evolve during training.
SIRUS creates interpretable rules from random forests for manufacturing.
New tree-structured Markov fields with Poisson marginals for counting variables.
Classifies very stable Higgs bundles for complex groups.
Study on spin random fields using chaos decomposition for cosmic microwave background modeling.
Partition functions arise in a variety of settings, including conditional random fields, logistic regression, and latent gaussian models. In this paper, we consider semistochastic quadratic bound (SQB) methods for maximum likelihood inference based on partition function optimization. Batch methods based on the quadrati…
Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, calle…
Study on Gaussian random fields' singularities on manifolds.
Electromagnetic fields can be knotted and stable, linked to quasipositive links.
Develops a new model for cross-currency derivatives pricing.