Study shows solutions of differential inclusions are homotopy equivalent in W1,p-topology.
problem Homotopy properties of solutions in differential inclusions.
method Analyzes differential inclusion with specific assumptions on corank one distribution.
result Solutions are homotopy equivalent to loop spaces in W1,p-topology. Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensi…
When looking at Bott's original proof of his periodicity theorem for the stable homotopy groups of the orthogonal and unitary groups, one sees in the background a differential geometric periodicity phenomenon. We show that this geometric phenomenon extends to the standard inclusion of the orthogonal group into the unit…
Study shows 'Belt and Road' node cities boost digital finance in China.
problem Impact of 'Belt and Road' node cities on digital inclusive finance.
method Descriptive analysis, literature review, theoretical model, differential differential method.
result Establishment of 'Belt and Road' node cities promotes digital inclusive finance in China, with Internet development as a mediating variable.
Study on existence of metrics in conformal geometry with constraints on Schouten tensor.
problem Existence of metrics conformal to a given Riemannian metric with constraints on Schouten tensor.
method Use differential inclusions and viscosity solutions to prove existence and uniqueness of metrics.
result Existence and uniqueness results for fully nonlinear eigenvalue problems for the Schouten tensor.
Proposes a new approach to generate sparse models from deep networks.
problem Training small networks can get stuck in local optima; over-parameterized models are preferred.
method Differential inclusion paths to generate a family of models from simple to complex.
result Algorithm converges to a critical point of empirical risks from any initializations.
In this paper, we propose two discontinuous dynamical systems in continuous time with guaranteed prescribed finite-time local convergence to strict local minima of a given cost function. Our approach consists of exploiting a Lyapunov-based differential inequality for differential inclusions, which leads to finite-time …
In this paper the stability theorem of Borkar and Meyn is extended to include the case when the mean field is a differential inclusion. Two different sets of sufficient conditions are presented that guarantee the stability and convergence of stochastic recursive inclusions. Our work builds on the works of Benaim, Hofba…
Study normal curves in sub-Finsler Lie groups with specific norms, focusing on branching and face stability.
problem Analyzing normal curves in sub-Finsler Lie groups with different norms.
method Using tools from convex analysis, the Pontryagin Maximum Principle is revisited to express the normal equation as a differential inclusion involving the subdifferential of the dual norm.
result Normal curves in polyhedral norms have controls that locally take values in a single face of a sphere with respect to the norm.
In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics. Our goal here is to bring this idea to address a challenging problem in statistics, \emph{i.e.} finding …
The paper guarantees global stability for stochastic subgradient methods in nonsmooth nonconvex optimization.
problem Minimizing nonsmooth nonconvex functions with convergence guarantees.
method Developed a framework for stochastic subgradient methods with global stability guarantees.
result Iterates are uniformly bounded and asymptotically stabilize around the stable set of the differential inclusion.
Algorithm identifies correct hypothesis from alternatives in bandit problems.
problem Efficiently identifying the correct hypothesis from a finite set of alternatives in structured stochastic multi-armed bandits.
method Frank-Wolfe Self-Play (FWSP) reformulates the game as a saddle-point problem, using a differential-inclusion argument to prove convergence.
result Convergence of the game value for best-arm identification in linear bandits, with uniform global convergence to the optimal value.
Study of H-eigenvalues for complex tensors and their applications in differential geometry.
problem Characterizing H-eigenvalues of Hermitian tensors. method Introduced H-eigenvalues, derived inclusion sets, and established criteria for definiteness. result Determined inclusion sets and criteria for Hermitian and CPS tensors.
Establishes necessary conditions for cylindrical curves using curvature and torsion.
problem Geometrically identifying curves on cylindrical surfaces.
method Identifying a fundamental function ψ and reducing the problem to a compatibility condition between an eighth-degree polynomial and a differential equation for ψ.
result Proves that for curves with constant curvature κ0 = 1/ρ, the torsion τ admits an explicit, exact solution.
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the use of options whose prices were fixed by the Black-Scholes formula.
Boosting as gradient descent algorithms is one popular method in machine learning. In this paper a novel Boosting-type algorithm is proposed based on restricted gradient descent with structural sparsity control whose underlying dynamics are governed by differential inclusions. In particular, we present an iterative reg…
New method enhances graph neural networks using contractions and hourglass persistence.
problem Limitations of traditional persistent homology in graph neural networks.
method Hourglass Persistence, Contraction Homology, contractions as a topological operation.
result Hourglass Persistence boosts expressivity, learnability, and stability in graph representation learning.
Research finds investors may lose from more diverse workplaces.
problem Investors' returns may be lower in more diverse companies.
method Examined D&I scores by Refinitiv in US and European markets.
result Investors may suffer lower returns for investing in more diverse companies.
Extends machine learning models for analytic boundary conditions in differential equations.
problem Inclusion of data in differential equations using symbolic algorithms.
method Combines computer algebra with Gaussian processes and extends to analytic boundary conditions using Gröbner and Janet bases of Weyl algebras.
result Describes divergence-free flow in domains bounded by analytic functions.
Confirming a conjecture, we show fundamental groups of certain abelian differentials are framed mapping class groups.
problem Confirming a 1997 conjecture about fundamental groups of abelian differentials.
method Algebraic-geometric approach using Shimada's techniques for computing fundamental groups via morphisms of varieties.
result Orbifold fundamental groups of these strata are described as framed mapping class groups.
Dagma-DCE improves causal discovery with interpretable measures and open-source code.
problem Arbitrary proxy measures of causal strength in non-parametric causal discovery.
method Uses weighted adjacency matrices based on an interpretable measure of causal strength.
result Achieves state-of-the-art performance in simulated datasets.
Paper analyzes inclusive KL inference using Wasserstein gradient flows.
problem Analyzing inclusive KL inference with mathematical tools.
method Gradient flows derived from PDE analysis.
result Unified view of existing sampling algorithms as inclusive-KL inference.
This paper describes how, in the case of algebraic surfaces, the well-known theorem of Donaldson-Uhlenbeck-Yau can be proved in a framework of generalized 'multiplier ideal sheaves', following the ideas of Siu. The key concept is that the destabilizing sheaf satisfies a differential inclusion relation. This relation is…
New solutions for soft materials' nonlinear behavior in growing spheroidal inclusions.
problem Understanding soft materials' behavior under microstructure effects.
method Presented an accurate semi-inverse solution for isotropically growing spheroidal inclusions.
result Existence of a non-spherical asymptotic shape and associated asymptotic pressure (isomorphic pressure).
Study shows financial literacy, social capital, and financial tech positively impact financial inclusion of Indonesian students.
problem Financial literacy, social capital, and financial technology's impact on financial inclusion of Indonesian students.
method Quantitative research using questionnaires distributed to 100 students from 7 private colleges in Tangerang, Indonesia.
result Financial literacy, social capital, and financial technology have a positive and significant influence on financial inclusion.
Extends unique continuation theorem to manifolds with boundary, proving zero set codimension.
problem Proving unique continuation for exterior differential forms on manifolds with boundary.
method Extends Aronszajn-Krzywicki-Szarski theorem to manifolds with boundary, assuming suitable boundary conditions.
result Hausdorff dimension of zero sets of harmonic forms and eigenfields has codimension at least 2.
The paper studies cohomology on incomplete manifolds and stratified spaces.
problem Analyzing cohomology groups on incomplete Riemannian manifolds and stratified spaces.
method Proves injective/surjective maps between Lp and L2 cohomology groups under certain conditions. result Injective/surjective maps between Lp and L2 cohomology groups are established. Invariant reduction preserves Poisson structures in PDEs.
problem Preserving Poisson structures in invariant solutions of PDEs.
method Invariant reduction applied to PDEs through Hamiltonian operators and Poisson bivectors.
result Inherited Poisson brackets match original systems up to sign.
Inspired by the recent work of Chen-Stiénon-Xu on Atiyah classes associated to inclusions of Lie algebroids, we give a very simple criterium (in terms of those classes) for relative Poincaré-Birkhoff-Witt type results to hold. The tools we use (e.g. the first infinitesimal neighbourhood Lie algebroid) are straightforwa…
Study new bounds on TC of spaces with subgroup inclusions.
problem Lower bounds on TC of spaces with subgroup inclusions.
method Generalizes TC results from aspherical spaces to spaces with subgroup inclusions.
result Establishes new lower bounds on sequential TCs of aspherical spaces.
Paper presents a novel time series clustering algorithm for financial inclusion.
problem Difficulty in understanding consumer financial behavior without restrictive credit scoring.
method Developed a novel time series clustering algorithm.
result Allows institutions to offer unique financial products based on customer needs.
Let N⊂M be a finite Jones' index inclusion of II1 factors, and denote by UN⊂UM their unitary groups. In this paper we study the homogeneous space UM/UN, which is a (infinite dimensional) differentiable manifold, diffeomorphic to the orbit O(p)={upu∗:u∈UM} of the Jones …
Regulating crypto and DeFi for inclusive economic advancement.
problem Innovative financial systems pose challenges to traditional regulatory frameworks.
method Formulating regulatory structures that balance innovation and consumer protection.
result Regulatory frameworks are essential for leveraging crypto and DeFi for inclusive economic growth.
Construct intrinsic Langevin dynamics for rigid inclusions on curved surfaces.
problem Stochastic dynamics of rigid inclusions on curved surfaces.
method Cartan's method of moving frames, Hamiltonian equations, intrinsic Langevin equations, Fokker-Planck equation.
result Extracted overdamped equations for accurate simulations of diffusion processes.
Minding's most celebrated result is his namesake theorem of 1839 which established that all surfaces having the same constant curvature must be locally isometric. Today, Minding's theorem is a staple in differential geometry textbooks. But, to the best of our knowledge, all published proofs of it, inclusive of Minding'…
Novel algorithm reduces feature inclusion in online decision-making.
problem Optimizing decision-making for personalized user experiences with fairness.
method Online Batched Sequential Inclusion (OBSI) algorithm for sequential feature inclusion.
result OBSI outperforms other algorithms in terms of regret, relevance of features, and compute.
In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H01(Ω)↪Lp(Ω) on bounded convex domain in R2. We estimate the best constant by computing the corresponding extremal function using a verified numerical com…
We develop theory and computational methods to investigate particle inclusions embedded within curved lipid bilayer membranes. We consider the case of spherical lipid vesicles where inclusion particles are coupled through (i) intramembrane hydrodynamics, (ii) traction stresses with the external and trapped solvent flui…
In this work we will develop a new approach to solve the non repayment problem in microfinance due to the problem of asymmetric information. This approach is based on modeling and simulation of ordinary differential systems where time remains a primordial component, they thus enable microfinance institutions to manage …
Two accelerated extragradient methods converge at O(1/k) rate for co-hypomonotone inclusions.
problem Solving co-hypomonotone inclusions with sum of Lipschitz and multivalued operators.
method Developed two Nesterov's accelerated extragradient methods for co-hypomonotone inclusions.
result Achieve O(1/k) last-iterate convergence rates on the residual norm. Neural random fields (NRFs), referring to a class of generative models that use neural networks to implement potential functions in random fields (a.k.a. energy-based models), are not new but receive less attention with slow progress. Different from various directed graphical models such as generative adversarial netwo…
The paper explores how the unit inclusion affects topological quantum field theories in non-semisimple categories.
problem Understanding the effects of unit inclusion in non-semisimple braided tensor categories on topological quantum field theories.
method Analyzes the dualizability of the unit inclusion morphism in Morita 4-category of braided tensor categories and applies the Cobordism Hypothesis.
result Shows that the unit inclusion in non-semisimple modular categories leads to non-compact relative 3D topological quantum field theories.
TransBoost improves financial inclusion by evaluating individual financial risk.
problem Evaluating individual financial risk for new users and companies with limited data.
method Combines tree-based models and kernel methods, with parallel tree structure and efficient weights updating.
result Outperforms other transfer learning algorithms in prediction accuracy and robustness.
The great success of deep neural networks is built upon their over-parameterization, which smooths the optimization landscape without degrading the generalization ability. Despite the benefits of over-parameterization, a huge amount of parameters makes deep networks cumbersome in daily life applications. Though techniq…
We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by `controlled' Markov noise. In particular, both the faster and slower recursions have non-additive controlled Markov noise components in addition to martingale difference noise. We analyze the asymptotic…
Proof of injection from double shuffle to Kashiwara-Vergne Lie algebra.
problem Injecting double shuffle Lie algebra into Kashiwara-Vergne Lie algebra.
method Inclusion of brunnian braids group on different genus 0 surfaces, using lower central series of brunnian Lie algebras, and explicit links between maps.
result Injection of double shuffle Lie algebra into symmetric Kashiwara-Vergne Lie algebra.
New invariant identifies complex line arrangements with same combinatorics but different embeddings.
problem Identify Zariski pairs with same combinatorics but different line arrangements.
method Study inclusion map of boundary manifold to exterior, analyze homology classes, compute invariant using Sage.
result New invariant distinguishes line arrangements with same combinatorics but different embeddings.
Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the chordal structure of a probabilistic model from data. The algorithm is a greedy hill-climbing search algorithm that uses t…