arXiv research

The paper introduces admissible hierarchical clustering methods for asymmetric networks.

A new hierarchical clustering method selects representative points from sub-minimum-spanning-trees.

New knot invariants derived using quantum cluster algebras.

Classifies reciprocal elements in Hecke groups, generalizing Sarnak's work.

The paper develops methods for clustering directed dissimilarity networks.

This paper introduces belief propagation for Gaussian reciprocal processes and links it to stability theory.

Estimates growth of reciprocal classes in Hecke groups.

Paper models reciprocal processes using probabilistic graphical models.

The paper models social networks with varying levels of reciprocity.

The study calculates the growth rate of reciprocal hyperbolic elements in Hecke groups.

New combinatorial method connects knot invariants to reflection groups.

Reformulates Lehmer and Schinzel-Zassenhaus questions on polynomial measures.

Formulates Hilbert reciprocity law on 3-manifolds.

Minimal spectral radii found for specific matrix types.

Study on geodesics and dihedral groups in lattices.

The paper models reciprocity in interbank markets using a statistical null model.

Reciprocal learning unifies various machine learning algorithms.

New method reconstructs interbank networks enforcing reciprocity to improve stability and risk prediction.

Study geodesics entering a fixed cusp neighborhood multiple times.

Growth rates of geodesics on modular orbifolds are studied.

The paper proves generalization bounds and stopping rules for self-selected data in reciprocal learning.

The abstract discusses conjectures about Chern-Simons invariants of 3-manifolds.

Given a knot and an SL(n,C) representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL(3,Z) representation that is not conjugate to its dual for …

Reciprocity laws for line bundles on circle fibrations over complex manifolds.

We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series, and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of the known rationality and reciprocity results for the growth series…

Study on 3D foliated dynamical systems with Hilbert reciprocity law.

We prove a reciprocity formula between Gauss sums that is used in the computation of certain quantum invariants of 3-manifolds. Our proof uses the discriminant construction applied to the tensor product of lattices.

This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a connectivity parameter, induced by the given dissimilarity structures. Our constructi…

This paper gives a new definition of the Contou-Carrere symbol in terms of an exponential of a Chen iterated integral and proves the corresponding reciprocity law.

Efficient algorithm uncovers mutual interests in reciprocal recommendation.

We prove that under certain linear reciprocal transformation, an evolutionary PDE of hydrodynamic type that admits a bihamiltonian structure is transformed to a system of the same type which is still bihamiltonian.

Novel network models capture social interaction features like reciprocity and community.

The study examines the growth of reciprocal classes in Hecke groups, proving an asymptotic formula.

We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in …

Paper tackles division difficulty, proposing new methods to improve accuracy.

FlexCMH learns effective hashing codes from weakly-paired data.

New model accounts for scale variation and noise in pairwise comparisons.

New model for clustering dependent community Hawkes processes in temporal networks.

Empirical study shows carriers ignore past shippers' behavior, focusing only on current actions.

Study how past eon's matter affects present eon in Penrose's cyclic cosmology.

This article investigates local properties of the further generalized Weierstrass relations for a spin manifold $S$ immersed in a higher dimensional spin manifold $M$ from viewpoint of study of submanifold quantum mechanics. We show that kernel of a certain Dirac operator defined over $S$, which we call submanifold Dir…

Schrödinger and Onsager's ideas linked in nonequilibrium thermodynamics.

Motivated by applications of large-scale graph clustering, we study random-walk-based LOCAL algorithms whose running times depend only on the size of the output cluster, rather than the entire graph. All previously known such algorithms guarantee an output conductance of $\tilde{O}(\sqrt{φ(A)})$ when the target set $A$…

Legendre transformations link related integrable hierarchies.

We rigorously define the Liouville action functional for finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that the classical action - the critical point of the Liouville action functional, considered as a funct…

Local classification of quasilinear systems with linearizable characteristic webs.

This paper argues that the fundamental principle of contemporary financial economics is balanced reciprocity, not the principle of utility maximisation that is important in economics more generally. The argument is developed by analysing the mathematical Fundamental Theory of Asset Pricing with reference to the emergen…

Bayesian rLASSO improves model selection and prediction.