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.
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.
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.
We give some general results on proper-biharmonic submanifolds of a complex space form and, in particular, of the complex projective space. These results are mainly concerned with submanifolds with constant mean curvature or parallel mean curvature vector field. We find the relation between the bitension field of the i…
Let S be a compact oriented surface. A homology cobordism of S is a cobordism C between two copies of S, such that both the "top" inclusion and the "bottom" inclusion of S in C induce isomorphisms in homology. Homology cobordisms of S form a monoid, into which the mapping class group of S embeds by the mapping cylinder…
GRUs predict flu at state and city levels with lower error.
problem Influenza prediction at multiple spatial resolutions.
method Gated Recurrent Unit (GRU) neural network, real-time search data.
result GRU outperforms state-of-the-art methods for flu prediction.
The paper extends knot theory to annular and toroidal pseudo knots.
problem Defining and classifying pseudo knots in annular and toroidal settings.
method Introducing pseudo knots as equivalence classes under moves, lifting to torus, and exploring inclusion relations.
result New invariants for classifying pseudo knots and links in solid and thickened torus.
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…
Determines regular homotopy classes for link immersions of simple singularities.
problem Classifying immersions of link singularities.
method Computing complete invariants of immersions and comparing with Dynkin diagrams.
result Inclusion map of link into 5-sphere is regularly homotopic to immersion associated with Dynkin diagram.
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.
In this paper we consider an interval portfolio selection problem with uncertain returns and introduce an inclusive concept of satisfaction index for interval inequality relation. Based on the satisfaction index, we propose an approach to reduce the interval programming problem with uncertain objective and constraints …
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.
Let M be an open Riemann surface. It was proved by Alarcón and Forstnerič (arXiv:1408.5315) that every conformal minimal immersion M→R3 is isotopic to the real part of a holomorphic null curve M→C3. In this paper, we prove the following much stronger result in this direction: for any $n\geq …
PAC learning simplified as bipartite matching.
problem Efficiently solving PAC learning problems.
method Transductive learning and one-inclusion graphs.
result PAC learning can be reduced to bipartite matching.
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. 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.
Basic binary relations such as equality and inequality are fundamental to relational data structures. Neural networks should learn such relations and generalise to new unseen data. We show in this study, however, that this generalisation fails with standard feed-forward networks on binary vectors. Even when trained wit…
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.
We give an example of two JSJ decompositions of a group that are not related by conjugation, conjugation of edge-inclusions, and slide moves. This answers the question of Rips and Sela stated in "Cyclic splittings of finitely presented groups and the canonical JSJ decomposition," Ann. of Math. 146 (1997), 53-109. On th…
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.
Proves Congruence Subgroup Property for two types of groups.
problem Proving Congruence Subgroup Property for specific groups.
method Elementary proof of Johnson filtration and geometric subsurface inclusions.
result Proves Congruence Subgroup Property for nilpotent quotients and subsurface subgroups.
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.
Spatial information is not always necessary for spatio-temporal models.
problem The necessity of including spatial information in spatio-temporal models.
method Comparison of spatial agnostic neural networks with state-of-the-art models on ten datasets.
result Spatial information is not always needed in most spatio-temporal models.
Paper connects cohomologies on almost complex manifolds.
problem Relating J-invariant cohomology to Dolbeault cohomology. method Relating cohomologies through necessary and sufficient conditions.
result Conditions for isomorphism between cohomologies found.
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…
TransINT embeds KGs by preserving implication rules, outperforming existing methods.
problem Embedding KGs while preserving relation implications for better access and analysis.
method Isomorphic intersections of linear subspaces with shared parameters for missing facts.
result Significant performance improvement in link prediction and triple classification.
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…
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.
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 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.