Characterizes chains in 3D CR and para-CR structures.
problem Determining when a 3D path geometry comes from CR or para-CR chains.
method Provides necessary and sufficient conditions for a 3D path geometry to arise from chains of CR or para-CR 3-manifolds, and verifies computationally.
result Characterization of chains in 3D CR and para-CR structures.
Study canonical curves and Kropina metrics in Lagrangian contact geometry.
problem Characterize canonical curves and their relationship to Lagrangian contact structures.
method Construct Fefferman-type spaces, analyze chains and null-chains, use Kropina metrics, apply Fermat principle.
result Chains and null-chains in integrable Lagrangian contact structures are geodesics of Kropina metrics.
We show that a model of chain complex of the free loop space of a C∞-manifold, which is proposed in arxiv:1404.0153, admits an action of a certain dg operad. This is a chain level structure under the Chas-Sullivan BV structure on loop space homology. Our dg operad is a variant of the cacti operad, and we introd…
Study on CR structures on 3D Lie groups, focusing on equivalence and closed chains.
problem Characterizing CR structures on 3D Lie groups and their chains.
method Analyzing left-invariant CR structures on 3D Lie groups and their equivalence.
result All chains on G are closed if and only if G is CR equivalent to specific spherical CR structures.
The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented C∞-manifold. For this purpose, we define a (nonsymmetric) cyclic dg operad which consists of "de Rham chains" of free loops with marked points…
We compute the chains associated to the left-invariant CR structures on the three-sphere. These structures are characterized by a single real modulus a. For the standard structure a=1, the chains are well-known and are closed curves. We show that for almost all other values of the modulus a either two or three ty…
The chains studied in this paper generalize Chern-Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be equivalently encoded as Cartan geometries (of d…
Lie contact structures generalize the classical Lie sphere geometry of oriented hyperspheres in the standard sphere. They can be equivalently described as parabolic geometries corresponding to the contact grading of orthogonal real Lie algebra. It follows the underlying geometric structure can be interpreted in several…
Contact projective structures have been profoundly studied by D.J.F. Fox. He associated to a contact projective structure a canonical projective structure on the same manifold. We interpret Fox' construction in terms of the equivalent parabolic (Cartan) geometries, showing that it is an analog of Fefferman's constructi…
Subcartesian spaces follow Leibniz' rule, simplifying differential calculus.
problem Simplifying differential calculus in subcartesian spaces.
method Showed derivations satisfy the chain rule and have maximal integral curves.
result Subcartesian spaces follow Leibniz' rule, simplifying differential calculus.
Deep neural network improves amino acid side chain prediction accuracy.
problem Predicting amino acid side chain conformation for protein modeling and design.
method Deep neural network architecture without physics-based assumptions.
result Improved accuracy by more than 25% for aromatic residues.
Study on identifying AMP chain graph models under known and unknown component decompositions.
problem Identifying AMP chain graph models with known and unknown chain component decompositions.
method Analyzes conditions for identifiability of AMP models and proposes algorithms for structure recovery.
result Conditions for DAG identifiability in AMP models extend equal variance criteria for Bayes nets.
New insights into Markov chain geometry via positive transition measures.
problem Lack of statistical meaning in the space of transition probabilities.
method Constructing an extension of the space of transition probabilities using Amari's theory of positive measures.
result Introduction of a new dually flat structure for the space of positive transition measures.
A new approach uses circuit topology to study complex polymer interactions.
problem Understanding structural phase transitions in entangled polymer systems.
method Braided circuit topology framework for multiple-chain systems.
result Circuit topological motif fractions are effective order parameters for structural transitions.
NAS for financial time series forecasts using chain-structured architectures.
problem Optimizing neural architectures for financial time series forecasting.
method Comparison of three NAS strategies (Bayesian optimization, hyperband, reinforcement learning) on chain-structured search spaces for simple and complex architectures.
result Bayesian optimization and hyperband outperform other strategies, and RNN and 1D CNN perform best among architectures.
We prove (without using Federer's structure theorem) that a finite-mass flat chain over any coefficient group is rectifiable if and only if almost all of its 0-dimensional slices are rectifiable. This implies that every flat chain of finite mass and finite size is rectifiable. It also leads to a simple necessary and su…
A new metric based on hitting probabilities for directed graphs and Markov chains.
problem Lack of metrics specifically adapted to asymmetric structure of directed graphs and Markov chains.
method Metric based on hitting probabilities, insensitive to shortest and average walk distances.
result New structural theory of directed graphs and utility for various applications.
We introduce a conceptually novel structured prediction model, GPstruct, which is kernelized, non-parametric and Bayesian, by design. We motivate the model with respect to existing approaches, among others, conditional random fields (CRFs), maximum margin Markov networks (M3N), and structured support vector machines (S…
Approach for assessing supply chain cyber risks using expert judgment and forecasting.
problem Supply chain managers face challenges in assessing cyber risks affecting business factors.
method Structured expert judgment and forecasting models to assess various attack techniques and impacts.
result Facilitates implementation of risk management activities and decision-making processes.
Enhanced coloring invariant distinguishes folded molecular chain topologies.
problem Apparent indistinguishability of folded chain topologies using current coloring invariants.
method Introduced Boltzmann weights to improve the resolving power of quandle colorings.
result Improved resolution in distinguishing folded chain topologies.
Chains in CR geometry are geodesics of a Kropina metric.
problem Understanding chains in CR geometry.
method Generalization of Fermat principle and Kropina metric construction.
result Chains determine CR structure up to conjugacy.
Simpler method derived for path geometries on surfaces, characterizing projective path geometries.
problem Characterizing projective path geometries on surfaces.
method Solving the equivalence problem of sub-Riemannian geometry of signature (1,1) on a contact 3-manifold.
result Characterization of projective path geometries in terms of their chains.
Polynomial invariants classify molecular chains based on their contact arrangements.
problem No established invariants for molecular chains with both hard and soft contacts.
method Developed polynomial invariants for circuit topology of molecular chains.
result Polynomial invariants efficiently classify chains with various contact types.
Model interest rates and energy futures with regime-switching dynamics.
problem Modeling interest rates and energy futures with regime-switching dynamics.
method HJM model with Markov-chain modulated forward rates, proving affine structure for term structure.
result Explicit solutions for forward curves in many cases.
We construct a space of string diagrams, which are a type of fatgraph with some additional data, and show that there are string topology operations on the chains of the free loop space of a closed Riemannian manifold which are parameterized by the chains on the space of string diagrams. These operations are shown to re…
Study reveals supply chain correlations in firm growth rates.
problem Understanding correlations in firm growth rates and their supply chain relationships.
method Investigated correlation structure of firm growth rates and used Gaussian Markov Models to reconstruct supply chain networks.
result Supply chain-linked firms exhibit stronger correlation in growth rates than non-linked firms.
Paper tackles order-dependence in structure learning of multivariate regression chain graphs.
problem Order-dependence in structure learning of multivariate regression chain graphs.
method Proposes modifications to the PC-like algorithm to remove order-dependence.
result Improved performance in high-dimensional settings with modifications to the PC-like algorithm.
We analyze a functor from cyclic operads to chain complexes first considered by Getzler and Kapranov and also Markl. This functor is a generalization of the graph homology considered by Kontsevich, which was defined for the three operads Comm, Assoc, and Lie. More specifically we show that these chain complexes have a …
New training method for neural nets using multilevel entropic regularization.
problem Training efficiency and generalization bounds for neural nets.
method Multilevel relative entropy, chaining mutual information, Gibbs posterior distribution.
result Proves the Gibbs posterior achieves the unique minimum of the empirical risk minimization problem.
Inspired by bordered Floer homology, we describe a type A structure on a Khovanov homology for a tangle, which complements the type D structure in a previous paper. The type A structure is a differential module over a certain algebra. This can be paired with the type D structure to recover the Khovanov chain complex. T…
Efficient variance reduction for Markov chains using martingale representations.
problem Reducing variance in estimating additive functionals of Markov chains.
method A novel discrete time martingale representation approach for variance reduction.
result The proposed method achieves a lower cost-to-variance product than the naive approach.
Multi-output inference tasks, such as multi-label classification, have become increasingly important in recent years. A popular method for multi-label classification is classifier chains, in which the predictions of individual classifiers are cascaded along a chain, thus taking into account inter-label dependencies and…
Efficiently learns sparse low-dimensional Markov chain representations.
problem Learning low-dimensional representations for large-scale Markov chains with sparse structures.
method Formulates as constrained nonnegative matrix factorization and uses gradient descent.
result Proves the effectiveness of the proposed method through convergence analysis.
GNNs improve supply chain analytics with real-world benchmarks.
problem Limited research on applying GNNs to supply chain management.
method Conceptual discussions, detailed formulations, examples, mathematical definitions, and task guidelines.
result GNN-based models outperform other methods by 10-40% in various supply chain tasks.
The Fefferman metric connects CR manifolds to conformal geodesics in 3D.
problem Understanding the Fefferman metric on CR manifolds.
method Explicit description of the Fefferman metric and variational characterization of conformal geodesics.
result Conformal geodesics have lifts to chains and null chains, and are characterized by total torsion.
James McClure recently showed that the domain for the intersection pairing of PL chains on a PL manifold M is a subcomplex of C∗(M)⊗C∗(M) that is quasi-isomorphic to C∗(M)⊗C∗(M) and, more generally, that the intersection pairing endows C∗(M) with the structure of a partially-defined commutati…
The paper constructs Morse complexes for orbifolds and shows their homologies are orbifold invariants.
problem Understanding the homology of orbifolds.
method Constructing invariant and coinvariant Morse chain complexes for orbifolds.
result The homology of coinvariant Morse complexes computes the singular homology of the underlying space.
Paper presents a new flat triangular form for systems.
problem Creating a structurally flat triangular form for systems.
method Developed a new triangular form based on the extended chained form with conditions for static feedback equivalence.
result Provided conditions for affine input systems to be static feedback equivalent to the new triangular form.
Constructs L∞ structure on symplectic cohomology.
problem None explicitly stated; focuses on construction.
method Constructs L∞ structure on symplectic cohomology. result Symplectic cohomology gains an L∞ structure. This paper compares HMC and RNN expressivity using SRT.
problem Comparing expressivity of HMC and RNN models.
method Embed HMC and RNN in a GUM, use SRT to compare structured covariance series.
result Conditions for realizing covariance series by GUM, HMC, or RNN.
The paper examines how cheaper and faster chains affect Uniswap v3 liquidity and profitability.
problem Impact of cheaper and faster chains on Uniswap v3 liquidity and profitability.
method Comparative analysis of Uniswap v3 activity on different chains with varying gas prices and block times.
result Liquidity providers are more capital efficient and receive higher fee returns on cheaper and faster chains.
Knot theory applied to proteins, distinguishing folded linear chains.
problem Classifying proteins as unknots when intra-chain interactions are ignored.
method Developing knot theory for folded linear molecular chains, considering self-bonding, and using Gauss codes and quandles.
result Extended knot theory to distinguish topologies of proteins with intra-chain bonds.
New Markov chains defined on simplicial complexes for understanding their topology.
problem Understanding the topology of simplicial complexes and hypergraphs.
method Defining new Markov chains on simplicial complexes and studying their properties.
result The generator of the new Markov chain is the upper Laplacian, and the Markov chain is positive recurrent.
We study body-and-hinge and panel-and-hinge chains in R^d, with two marked points: one on the first body, the other on the last. For a general chain, the squared distance between the marked points gives a Morse-Bott function on a torus configuration space. Maximal configurations, when the distance between the two marke…
Unified framework for complex financial networks using lattice theory.
problem Complex financial networks with multiple currencies and dependencies.
method Recast classical financial clearing model into lattice liability networks.
result Lattice-valued clearing sections form a complete lattice, enabling tractable analysis.
Study examines how COVID-19 intensified demand variability in U.S. supply chains.
problem The amplification of demand variability (Bullwhip Effect) in supply chains during the pandemic.
method Extensive industry-level data analysis using traditional and advanced empirical techniques.
result COVID-19 significantly amplified the Bullwhip Effect across different U.S. industries.
The paper calculates the asymptotics of quantum invariants for Whitehead chains.
problem Quantum invariants of Whitehead chains with colored clasps.
method Asymptotic analysis of colored Jones polynomials, considering limiting ratios of sequences.
result The exponential growth rate of invariants matches the hyperbolic volume of link complements.
We attempt to set a mathematical foundation of immunology and amino acid chains. To measure the similarities of these chains, a kernel on strings is defined using only the sequence of the chains and a good amino acid substitution matrix (e.g. BLOSUM62). The kernel is used in learning machines to predict binding affinit…