A new SNN model explains decision-making with learning and spiking neurons.
problem Lack of learning mechanism in existing models for decision-making.
method Proposes a Spiking Neural Network (SNN) model that incorporates a learning mechanism and uses multivariate Hawkes processes.
result Shows a coupling between DDM and Poisson counter models and derives a DDM from a Hawkes network of spiking neurons.
The Jacobian Conjecture is proven for all Jacobian maps.
problem Proving the Jacobian Conjecture for all Jacobian maps.
method Using the Weyl algebra and holonomic modules, the paper shows that the Jacobian module is 1-generated and has finite length.
result The Jacobian Conjecture is true for all Jacobian maps.
Study on pairwise counter-monotonicity, a type of negative dependence.
problem Understanding and quantifying extremal negative dependence structures.
method Established stochastic representation and invariance property; showed implications and connections.
result Pairwise counter-monotonicity implies negative association and joint mix dependence.
Extends micro-price concept to RFQ markets for fair pricing.
problem Valuing securities in illiquid RFQ markets.
method Bidimensional Markov-modulated Poisson processes for liquidity.
result Introduces Fair Transfer Price for fair securities valuation.
In [1] Zawadoski introduces a banking network model in which the asset and counter-party risks are treated separately and the banks hedge their assets risks by appropriate OTC contracts. In his model, each bank has only two counter-party neighbors, a bank fails due to the counter-party risk only if at least one of its …
This paper shows how to calculate risk measures for sums of two counter-monotonic risks.
problem Calculating risk measures for sums of two counter-monotonic risks.
method Using a fixed distortion function and expressing the risk measure of a sum as the sum of two related measures of the marginals.
result The risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals.
We give a counter example to a conjecture of E. Bueler stating the equality between the DeRham cohomology of complete Riemannian manifold and a weighted L2 cohomology where the weight is the heat kernel.
Over-the-counter markets are at the center of the postcrisis global reform of the financial system. We show how the size and structure of such markets can undergo rapid and extensive changes when participants engage in portfolio compression, a post-trade netting technology. Tightly-knit and concentrated trading structu…
Exploration is a fundamental aspect of Reinforcement Learning, typically implemented using stochastic action-selection. Exploration, however, can be more efficient if directed toward gaining new world knowledge. Visit-counters have been proven useful both in practice and in theory for directed exploration. However, a m…
Counterexample disproves Yashiro's theorem on surface knots.
problem Yashiro's theorem on pseudo-cycles of surface knots is not universally true.
method Provided a counterexample to Yashiro's theorem.
result Yashiro's theorem is disproven for pseudo-cycles of surface knots.
The paper studies risk-sharing allocations for risk-seeking agents using a common distortion risk measure.
problem Characterizing Pareto-optimal risk-sharing allocations for risk-seeking agents.
method Modeling preferences with a common distortion risk measure and analyzing three settings: risk-averse, risk-seeking, and inverse S-shaped distortion.
result Pareto-optimal allocations for risk-seeking agents are counter-monotonic, not comonotonic.
We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which tog…
Study risk sharing among agents with varying risk preferences.
problem Risk sharing among agents with heterogeneous risk measures.
method Derive explicit solutions for inf-convolution and counter-monotonic inf-convolution under varying risk seeking.
result Explicit solutions for inf-convolution and counter-monotonic inf-convolution can be represented by a generalization of distortion risk measures.
A new method for estimating adversarial strategies in nonlinear systems.
problem Inferring an intelligent adversarial agent's strategy in highly nonlinear systems.
method Formulated inverse cognition as a nonlinear Gaussian state-space model and developed an inverse UKF (IUKF) system.
result The estimation error of IUKF converges and closely follows the recursive Cramér-Rao lower bound.
Paper finds a counter-example invalidating a spectral asymptotic algorithm.
problem Invalidation of spectral asymptotic algorithm for elastic eigenvalues.
method Discussion of a counter-example for elastic eigenvalues.
result Most conclusions in Yu. Safarov and D. Vassiliev's book are fundamentally wrong.
We study two classes of over-the-counter markets specified by systems of ODE's, in the spirit of Duffie-Garleanu-Pedersen, Econometrica, 2005. We first compute the steady states for many of these ODE's. Then we obtain the prices at which investors trade with each other at these steady states. Finally, we study the stab…
We provide here a counter-example to the second inequality of Corollary (19.10) in the Clay Institute Monograph by J.Morgan and G.Tian entitled "Ricci Flow and the Poincare Conjecture". We had announced the existence of this counter-example in our paper "Five Gaps in Mathematics", Advanced Non-linear Studies, vol 15, N…
Experience replay is an important technique for addressing sample-inefficiency in deep reinforcement learning (RL), but faces difficulty in learning from binary and sparse rewards due to disproportionately few successful experiences in the replay buffer. Hindsight experience replay (HER) was recently proposed to tackle…
In this paper, we have studied the pricing of a continuously collateralized CDS. We have made use of the "survival measure" to derive the pricing formula in a straightforward way. As a result, we have found that there exists irremovable trace of the counter party as well as the investor in the price of CDS through thei…
Revises a theorem by Thurston, finding a counter-example and a weaker version.
problem The bounded image theorem in Haken manifolds.
method Providing a counter-example and a weaker version of the second statement of Thurston's theorem.
result A counter-example and a weaker version of the second statement of Thurston's theorem are presented.
Paper uses reinforcement learning to optimize bid-ask spreads in OTC markets.
problem Optimizing bid-ask spreads in over-the-counter markets with dynamic order sizes.
method Reinforcement learning to solve high-dimensional stochastic control problem.
result Optimal bid-ask spreads follow a Gaussian distribution under certain conditions.
Forward-Euler fails for simulating Wasserstein gradient flows with KL divergence.
problem Simulating Wasserstein gradient flows with forward-Euler discretization fails for KL divergence.
method Forward-Euler discretization for Wasserstein gradient flows with KL divergence.
result Forward-Euler discretization can be incorrect for Wasserstein gradient flows with KL divergence.
This work describes simple and efficient algorithms for interactively learning non-binary concepts in the learning from random counter-examples (LRC) model. Here, learning takes place from random counter-examples that the learner receives in response to their proper equivalence queries. In this context, the learning ti…
Researchers create a framework to value player actions in CSGO.
problem Lack of accessible data and analytical frameworks for esports players.
method Data model, graph distance measure, context-aware framework.
result Demonstrated framework's consistency and independence compared to existing methods.
The paper disproves a generalized toral rank conjecture with various counter-examples.
problem The conjecture that the sum of Betti numbers of a compact manifold with a torus action is bounded by 2r. method Provided counter-examples of smooth nilpotent fibre bundles of nilmanifolds with torus fibres of rank r. result There are sequences of torus fibrations with total space cohomology dimensions converging to 0 as rank r increases. Cincer cleans both new and past data by identifying and relabeling suspicious and counter-examples.
problem Sequential learning under label noise, especially in applications with human supervision.
method Cincer uses example-based explanations to identify and relabel suspicious and counter-examples, leveraging Fisher information matrix approximation.
result Cincer achieves better data and models by clarifying the model's suspicions, especially with FIM approximation.
Researchers found a counterexample disproving a 1962 conjecture.
problem Disproving the Homogeneity Conjecture for Lie groups.
method Constructing a specific counterexample on the Lie group Sp(2).
result The Riemannian quotient of the group is not homogeneous.
In this note, we will show one example of hamiltonian Lie algebra action which has no invariant star product.
Geometrically proves twisted Poincaré duality for orientable Poisson manifolds.
problem Establishing twisted Poincaré duality for Poisson manifolds.
method Geometrically reinterprets algebraic constructions of twisted Poisson modules and Poisson chain complexes.
result Explicit chain isomorphism between Poisson cochain and chain complexes with coefficients in Poisson modules.
Solves the invariant linearization problem for Lie groupoids.
problem Understanding invariant linearization for Lie groupoids.
method Introduced a counter-example and a sufficient criterion using compatible complete metrics and covers of proper group actions.
result Proved a sufficient criterion for invariant linearization of Lie groupoids.
We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson actions, the double group of a Poisson-Lie group and the reduction of Poisson manifold…
New Poisson structures on algebras linked to derivatives.
problem Understanding Poisson structures on trivial extension algebras.
method Introducing a correspondence between Poisson structures and derivatives, and formulating results in terms of Lie algebroids.
result One-to-one correspondence between Poisson structures and data involving derivatives.
New Lie groups found for Poisson diffeomorphisms.
problem Finding Lie group structures on Poisson diffeomorphism groups.
method Using Poisson groupoids, develop Lie group structures.
result Poisson diffeomorphism groups of various Poisson manifolds are regular Lie groups.
Optimal risk sharing found for heterogeneous risk attitudes using distortion risk measures.
problem Risk sharing in economies with diverse risk attitudes.
method Modeling preferences with distortion risk measures, using comonotonic and counter-monotonic principles.
result Optimal risk sharing strategies identified based on risk attitudes, reducing the n-agent problem to a two-agent formulation. We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space X is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the …
We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices…
The paper establishes a Poisson Poincaré-Dulac theorem for Poisson-flat connections.
problem Analyzing Poisson-flat connections with logarithmic poles.
method Defining an Euler-Poisson principal part and residue theory, establishing a Poisson Poincaré-Dulac theorem.
result Any logarithmic Poisson-flat connection is holomorphically gauge equivalent to a pure Euler-Poisson normal form.
The first cohomology of Poisson algebras is described and conditions for its vanishing are established.
problem Understanding the first cohomology of Poisson algebras.
method Description and mapping of first cohomology to intrinsic cohomologies of Poisson submanifolds, formulation of vanishing conditions.
result Necessary and sufficient conditions for the vanishing of the first cohomology of infinitesimal Poisson algebras are derived.
The paper normalizes Poisson saturation of coregular submanifolds.
problem Normalizing the Poisson saturation of coregular submanifolds.
method Normal form construction and Poisson geometry analysis.
result Local Poisson saturation of coregular submanifolds is an embedded Poisson submanifold with a normal form.
Develops reduction method for strong Dirac maps.
problem Generalizing Poisson momentum maps.
method General procedure for reduction along strong Dirac maps.
result Recover and introduce new Poisson, quasi-Poisson, and Dirac reduced structures.
We reformulate the Poisson structure discovered by Fock and Rosly on moduli spaces of flat connections over marked surfaces in the framework of Poisson structures defined by Lie algebra actions and quasitriangular r-matrices, and we show that it is an example of a mixed product Poisson structure associated to pairs o…
A new Poisson bracket defined on Poisson structures with applications to fixed points and cohomology.
problem Defining a Poisson bracket on the space of Poisson structures.
method Constructing a Poisson bracket on P(M) depending on a volume form, and defining invariant of Poisson structures. result Invariant of Poisson structures detects unimodularity and related Poisson bracket for symplectic structures.
Abstract: Homotopy Poisson algebra models for reduced spaces derived from Poisson structures.
problem Homotopy Poisson algebra models for reduced spaces.
method Cattaneo-Zambon compatibility and regularity conditions, equivariant map, homotopy Poisson algebra.
result Derivation of homotopy Poisson algebra generalizing classical BFV algebra.
Study Poisson algebras for Hamiltonian systems linearization.
problem Linearize dynamics along Poisson submanifolds.
method Use contravariant derivative to characterize Poisson algebras.
result Infinitesimal Poisson algebras provide a framework for Hamiltonization.
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
Gaussian surrogates improve Poisson imaging performance at low doses.
problem Improving Poisson imaging performance at low doses.
method Analysis of Poisson and Gaussian surrogate reconstruction objectives under Poisson noise.
result Gaussian surrogates can achieve MSE comparable to Poisson MAP at low doses.
Cohomology of 'book' Lie algebra Poisson structure computed.
problem Computing the cohomology of a specific Lie algebra structure.
method Direct computation of cohomology for the given Lie algebra structure.
result Explicit formula for Poisson cohomology of the 'book' Lie algebra.
TRASHFIRE improves model robustness by analyzing training rates and costs.
problem Understanding and predicting model robustness under adversarial conditions.
method Survival models, worst-case examples, cost-aware analysis.
result Deeper models offer marginal robustness gains due to inference time, not inherent robustness.