arXiv research

A cone projection maps complex plane arcs to conic sections with fixed focus and directrix.

The cone projection $f_R(z) = z/(1 + |z|/R)$ maps lines to conic arcs with specific properties.

We derive a closed formula for the Heegaard Floer correction terms of lens spaces in terms of the classical Dedekind sum and its generalization, the Dedekind-Rademacher sum. Our proof relies on a reciprocity formula for the correction terms established by Ozsvath and Szabo. A consequence of our result is that the Casso…

Defines spectral selectors on lens spaces for contactomorphisms.

For two solutions of the WDVV equations that are related by two types of symmetries of the equations given by Dubrovin, we show that the associated principal hierarchies of integrable systems are related by certain reciprocal transformation, and the tau functions of the hierarchies are either identical or related by a …

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

Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This …

Estimates growth of reciprocal classes in Hecke groups.

The paper models social networks with varying levels of reciprocity.

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

Formulates Hilbert reciprocity law on 3-manifolds.

Minimal spectral radii found for specific matrix types.

Study on geodesics and dihedral groups in lattices.

Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This le…

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

Reciprocal learning unifies various machine learning algorithms.

Study geodesics entering a fixed cusp neighborhood multiple times.

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

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 reformulate Lehmer's question from 1933 and a question due to Schinzel and Zassenhaus from 1965 in terms of a comparison of the Mahler measures and the houses, respectively, of monic integer reciprocal and skew-reciprocal polynomials of the same degree. This entails that understanding the difference between orientat…

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…

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 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.

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.

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

This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for asymmetric networks, every admissible method must be contained between reciprocal …

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.

New diffusion models improve counterfactual image generation with semantic control.

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

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

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

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.

A reciprocal recommendation problem is one where the goal of learning is not just to predict a user's preference towards a passive item (e.g., a book), but to recommend the targeted user on one side another user from the other side such that a mutual interest between the two exists. The problem thus is sharply differen…

We propose a novel class of network models for temporal dyadic interaction data. Our goal is to capture a number of important features often observed in social interactions: sparsity, degree heterogeneity, community structure and reciprocity. We propose a family of models based on self-exciting Hawkes point processes i…

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…

We show some fundamental results concerning $3$-dimensional foliated dynamical systems (FDS$^3$ for short) introduced by Deninger. Firstly, we give a decomposition theorem for an FDS$^3$, which yields a classification of FDS$^3$'s. Secondly, for each type of the classification, we construct concrete examples of FDS$^3$…

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.

The paper constructs a nontrivial diffeomorphism in 4-manifold topology.

We present a spectral rigidity result for the Dirac operator on lens spaces. More specifically, we show that each homogeneous lens space and each three dimensional lens space $L(q;p)$ with $q$ prime is completely characterized by its Dirac spectrum in the class of all lens spaces.

Study spectral analysis on lens spaces, proving isospectral lens spaces with prime order fundamental groups.