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.
3-manifold groups are uniquely identifiable via their profinite completions.
problem Identifying uniquely 3-manifold groups among finitely generated groups.
method Proving that the inclusion of profinite completions is not an isomorphism for proper subgroups.
result All finitely generated 3-manifold groups are Grothendieck rigid.
The paper explores rigidity and proximality in dynamical systems, proving new results about C∗-algebras.
problem Understanding rigidity and proximality in dynamical systems and their algebraic counterparts.
method Analyzing crossed products of dynamical systems and their C∗-algebras, focusing on uniform rigidity and proximality. result Uniformly rigid systems are almost reflecting, and certain crossed products are reflecting.
We show a rigidity theorem for the Seiberg-Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type inequality. As an application, we prove the existence of non-smoothable topological families of 4-manifolds whose fiber, base space, and tota…
Proves nearby Lagrangian cocores are homotopically rigid in certain dimensions.
problem Homotopy rigidity of nearby Lagrangian cocores in Weinstein sectors.
method Spectral wrapped Donaldson-Fukaya category with orthogonal group coefficients.
result Inclusion followed by retract and quotient is null-homotopic.
Sharp Veronese rigidity theorem for submanifolds of unit ball.
problem Veronese rigidity of submanifolds under harmonic structure.
method Intrinsic harmonic structure assumptions, Bochner-Gauss mechanism, shape operators.
result Sharp lower bound on maximal normal curvature for specific submanifolds.
The study shows how to embed cusp-decomposable manifolds quasi-isometrically.
problem Embedding cusp-decomposable manifolds quasi-isometrically.
method Using properties of the electric space of the universal cover, we show quasi-isometric embeddings.
result Isomorphisms between fundamental groups of higher graph manifolds preserve the decomposition into pieces.
Study character varieties of a Coxeter group in hyperbolic and Anti-de Sitter spaces.
problem Characterize the geometric transitions of a Coxeter group's holonomy representations.
method Analysis of rigidity properties and character varieties in hyperbolic and Anti-de Sitter spaces.
result Description of singularity at the collapse of a right-angled cuboctahedron.
This paper proves a theorem about Dehn surgery using a new theorem about PSL(2, C) character varieties. Confirming a conjecture of Boyer and Zhang, this paper shows that a small hyperbolic knot in a homotopy sphere having a non-trivial cyclic slope r has an incompressible surface with non-integer boundary slope strictl…
The Helfrich functional, denoted by H^{c_0}, is a mathematical expression proposed by Helfrich (1973) for the natural free energy carried by an elastic phospholipid bilayer. Helfrich theorises that idealised elastic phospholipid bilayers minimise H^{c_0} among all possible configurations. The functional integrates a sp…
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.
Let N be at least 4. We prove that every injective homomorphism from the Torelli subgroup into Out(FN) differs from the inclusion by a conjugation in Out(FN). This applies more generally to the following subgroups: every finite-index subgroup of Out(FN) (recovering a theorem of Farb and Handel); every subgro…
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.
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.
Researchers solve a question about embedding knots into Legendrian structures.
problem Whether every fixed knot type and Legendrian representative have surjective homomorphisms.
method Study of Legendrian embeddings and smooth embeddings in (S3,ξstd) from a homotopical viewpoint. result Positive answer for infinitely many knot types in three main families, showing rigidity at higher homotopy levels.
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.
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. Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: Parameter and prediction uncertainty become easily available, fac…
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…
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…
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.
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.
This work extends set-valued risk measures to discrete time, using difference inclusions and equations.
problem Defining set-valued dynamic risk measures in discrete time.
method Investigates discrete time setting with difference inclusions and difference equations.
result Provides insights for continuous time representations of set-valued dynamic risk measures.
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.
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…
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.
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.
Paper generalizes extragradient methods for solving equations and inclusions with improved convergence rates.
problem Solving equations and inclusions using extragradient methods.
method Unified and generalized extragradient methods for a broader class of algorithms, analyzing sublinear convergence rates.
result Unified and improved convergence results for various extragradient variants.
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…
In 2018, at the World Economic Forum in Davos it was presented a new countries' economic performance metric named the Inclusive Development Index (IDI) composed of 12 indicators. The new metric implies that countries might need to realize structural reforms for improving both economic expansion and social inclusion per…
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…
Graph machine learning and Super-App data improve credit risk prediction for financial inclusion.
problem Improving credit risk prediction for financial inclusion.
method Two graph-based experiments using centrality, behavior, and transactionality features.
result Graph features enhance credit risk models, leading to more inclusive financial systems.
This paper advances extragradient methods for solving inclusions under co-hypomonotonicity.
problem Solving inclusions with non-Lipschitz mappings.
method Unified and generalized extragradient methods under co-hypomonotonicity.
result Achieved O(1/k) convergence rates for residual norms. Identifying the flavour of neutral B mesons production is one of the most important components needed in the study of time-dependent CP violation. The harsh environment of the Large Hadron Collider makes it particularly hard to succeed in this task. We present an inclusive flavour-tagging algorithm as an upgrade of…
Survey on extragradient methods for solving nonlinear equations and inclusions.
problem Approximating solutions of nonlinear equations and inclusions.
method Unified convergence analysis of extragradient and its variants.
result Sublinear convergence rates for different classes of algorithms.
Study maximal antipodal sets in exceptional symmetric spaces.
problem Classify maximal antipodal sets in exceptional symmetric spaces.
method Combining existing literature and new results, classify maximal antipodal sets.
result Complete classification of maximal antipodal sets in all exceptional compact symmetric spaces.
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.
New algorithm minimizes inclusive KL for VI, improving accuracy.
problem Improving variational inference accuracy with KL(p||q).
method Markovian score climbing (MSC) using stochastic gradients.
result MSC converges to local optimum of inclusive KL without bias.
Some of the well known Fefferman like constructions of parabolic geometries end up with a new structure on the same manifold. In this paper, we classify all such cases with the help of the classical Onishchik's lists \cite{onish1} and we treat in detail the only new series of inclusions providing the spinorial structur…
We introduce a novel algorithm for the detection of possible sample corruption such as mislabeled samples in a training dataset given a small clean validation set. We use a set of inclusion variables which determine whether or not any element of the noisy training set should be included in the training of a network. We…
Given a surface of infinite topological type, there are several Teichmüller spaces associated with it, depending on the basepoint and on the point of view that one uses to compare different complex structures. This paper is about the comparison between the quasiconformal Teichmüller space and the length-spectrum Teichm…