Study bounds variance modulation function for K-spider distributions.
problem Bounding variance modulation function for K-spider distributions.
method Used folded moments and total probabilities of spider legs.
result Gave an interval for the variance modulation function.
New algorithm for contextual combinatorial bandits with probabilistic arm triggering.
problem Optimizing decisions in dynamic environments with probabilistic arm availability.
method C^2-UCB-T and VAC^2-UCB algorithms with TPM and VM conditions.
result Achieved improved regret bounds for contextual combinatorial bandits.
Variance-Calibrated Modulation (VCM) addresses the likelihood trap in LLMs by reshaping the probability distribution before truncation.
problem LLMs fall into the likelihood trap, leading to repetitive degeneration and vocabulary dullness.
method VCM reshapes the probability distribution before truncation through Contextual Searchlight and Adaptive Self-Debiasing.
result VCM mitigates the likelihood trap across open-ended generation, factual QA, and mathematical reasoning.
This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigen-value and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for financial markets with Markov-modulated volatilities. We consider multiple assets in the portfolio for …
Representations in the auditory cortex might be based on mechanisms similar to the visual ventral stream; modules for building invariance to transformations and multiple layers for compositionality and selectivity. In this paper we propose the use of such computational modules for extracting invariant and discriminativ…
Study variance-optimal hedging of forward curve derivatives under stochastic volatility.
problem Variance-optimal hedging of forward curve derivatives with stochastic volatility.
method Assumes HJM-Musiela dynamics modulated by stochastic covariance, uses Galtchouk-Kunita-Watanabe projection.
result Density of finite-maturity strategies, convergence of finite-rank projections, decomposition of hedging error.
Adversaries with multiple antennas can fool deep learning modulators more effectively.
problem Improving evasion attacks on deep learning-based modulation classifiers.
method Utilizing multiple antennas to enhance adversarial attacks on deep learning classifiers.
result Adversarial attacks with multiple antennas significantly improve classifier accuracy.
Enhanced X-ray polarimetry with deep learning for better exposure times.
problem Improving sensitivity of X-ray telescopic observations with imaging polarimeters.
method A weighted maximum likelihood combination of predictions from a deep ensemble of ResNet convolutional neural networks trained on Monte Carlo event simulations.
result Improves effective exposure times by ~45% for power-law source spectra.
A DRL framework optimizes portfolios using a LFSS module for feature extraction.
problem Optimizing dynamic portfolios in financial markets.
method Deep Reinforcement Learning with a Latent Feature State Space module.
result The proposed DRL framework outperforms benchmarks in portfolio optimization.
Develops a neural network for global minimum variance portfolio optimization.
problem Minimizing portfolio variance for large equity covariance matrices.
method Rotation-invariant neural network that learns lag-transformed returns and covariance regularization.
result End-to-end trained model outperforms competitors in realized volatility and Sharpe ratios.
In this paper, a neural network-aided bit-interleaved coded modulation (NN-BICM) receiver is designed to mitigate the nonlinear clipping distortion in the LDPC coded direct currentbiased optical orthogonal frequency division multiplexing (DCOOFDM) systems. Taking the cross-entropy as loss function, a feed forward netwo…
The paper proves the law of one price in a continuous-time setting without friction.
problem Identifying conditions under which the law of one price holds in a continuous-time setting without frictions.
method Formulating a new mechanism for LOP failure and proving a novel variant of the uniform boundedness principle.
result Establishes the equivalence of the economic concept of LOP with the probabilistic property of the existence of a local $\scr{E}$-martingale state price density.
Self-attention networks localize when eigenspectrum variance is small.
problem Self-attention mechanisms can lead to rank and entropy collapses, reducing model expressivity and trainability.
method Characterized attention localization using query-key eigenspectrum variance.
result Small eigenspectrum variance prevents both rank and entropy collapses, improving model performance.
We identify and study two common failure modes for early training in deep ReLU nets. For each we give a rigorous proof of when it occurs and how to avoid it, for fully connected and residual architectures. The first failure mode, exploding/vanishing mean activation length, can be avoided by initializing weights from a …
Classical (Itô diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential Lévy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \cite{Tank} for an overvi…
Proposes C2RM to mine cross-cryptocurrency relationships for better Bitcoin price prediction.
problem Limited consideration of historical relationships and interactions between cryptocurrencies for Bitcoin price prediction.
method C2RM module using Dynamic Time Warping for lead-lag relationship extraction and aggregation.
result Improves existing price prediction methods by significant performance improvement.
Classifies modules of surface-knots in terms of their properties.
problem Characterizing modules of surface-knots in terms of their properties.
method Using homology and covering spaces, the reduced first module is characterized.
result The reduced first module for every genus g is characterized in terms of properties of a finitely generated module.
Proves finiteness and holonomicity of skein modules for 3-manifolds.
problem Finiteness and holonomicity of skein modules for 3-manifolds.
method Defining skein transfer bimodules and using q-analogues of D-module theory.
result Internal skein modules are holonomic modules over the internal skein algebra of the boundary.
Defines super projective modules and explores their properties.
problem Exploring the geometric-algebraic link in super geometry.
method Defined and explored super projective modules over supersmooth functions.
result Module of vector fields over a supersphere is a super projective module.
We introduce higher skein modules of links generalizing the Conway skein module. We show that these modules are closely connected to the HOMFLY polynomial.
A new method to derive presentations of skein modules is developed. For the case of homotopy skein modules it will be shown how the topology of a 3-manifold is reflected in the structure of the module. The freeness problem for q-homotopy skein modules is solved, and a natural skein module related to linking numbers is …
Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current formulations of such networks only the parameters of the neural modules and/or the or…
Paper compares skein modules to Kauffman bracket modules.
problem Comparing skein modules to Kauffman bracket modules.
method Using skein relations and Reshetikhin-Turaev model.
result Resolved the problem of comparing skein modules to Kauffman bracket modules.
Skein modules are the main objects of an algebraic topology based on knots (or position). In the same spirit as Leibniz we would call our approach "algebra situs." When looking at the panorama of skein modules we see, past the rolling hills of homologies and homotopies, distant mountains - the Kauffman bracket skein mo…
Generalized Steinberg module presentation for Gaussian and Eisenstein integers.
problem Presenting Steinberg modules for specific number rings.
method Generalization of Bykovskii's presentation to Gaussian and Eisenstein integers.
result Generalization does not yield a presentation for all Euclidean number rings.
New Convolutional Unit improves Batch Whitening performance.
problem Improving the efficiency and effectiveness of Batch Whitening.
method Proposes a new Convolutional Unit that aligns with Batch Whitening theory and empirically analyzes the original Convolutional Unit.
result Significantly improved performance on multiple image classification datasets.
Enhanced Alexander module detects linking numbers in links.
problem Detecting linking numbers in links using Alexander modules.
method Defining and singling out meridians and longitudes in reduced Alexander modules.
result The enhanced Alexander module determines all linking numbers.
We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. A 2-crossed module bundle 2-gerbe over a manifold is defined in terms of a so called 2-crossed module bundle gerbe, which is a crossed module bundle gerbe equipped with an extra sructure. It is shown that s…
Combinatorial approach to compute satellite knot invariants using graph theory.
problem Computing knot invariants for satellite knots using bordered Heegaard Floer homology.
method Construct weighted A∞-modules using decorated planar graphs and prove their isomorphism. result Combinatorial proof of A∞ structure relations for the constructed modules. New sl(2) action defined on a mathematical module.
problem No specific problem stated; focuses on mathematical construction.
method Construction of sl(2)-action on equivariant skein lasagna module.
result Infinitesimal sl(2)-symmetries constructed.
Neuroscientific theory suggests that dopaminergic neurons broadcast global reward prediction errors to large areas of the brain influencing the synaptic plasticity of the neurons in those regions. We build on this theory to propose a multi-agent learning framework with spiking neurons in the generalized linear model (G…
Introduces admissible skein modules for non-semisimple categories.
problem No specific problem stated; generalization of Kauffman skein algebra.
method Introduces admissible skein modules associated to ideals in pivotal categories.
result These modules generalize Kauffman skein algebra and relate to quantum invariants.
Studies modules over a category of Jacobi diagrams in handlebodies.
problem Understanding modules over a specific category of Jacobi diagrams.
method Generalizes adjunctions and studies subquotient modules.
result Generalizes adjunctions between modules and Casimir Lie algebra modules.
This paper generalizes L2 cohomology theory for complex manifolds.
problem Developing a L2 cohomology theory for Hodge modules on infinite covering spaces.
method Formulating a conjectural generalization of L2-Mixed Hodge structures using Saito's Mixed Hodge Modules.
result Partial results in the conjectural generalization of L2-Mixed Hodge structures.
Let {T1,…,Tn} be a set of n commuting bounded linear operators on a Hilbert space H. Then the n-tuple (T1,…,Tn) turns H into a module over C[z1,…,zn] in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \raro \clh, \quad \quad …
Study Kauffman bracket skein modules of Seifert fibered spaces.
problem Understanding the structure of Kauffman bracket skein modules.
method Investigate spanning sets and module structure.
result Kauffman bracket skein modules are finitely generated.
Formula for interleaving distance of rectangle persistence modules.
problem Calculating distances between rectangle persistence modules.
method Formulas based on rectangle geometry, extended to decomposable modules.
result Closed formulas for interleaving and bottleneck distances.
Introduces Floer lasagna modules using link Floer homology.
problem No specific problem stated; focuses on new mathematical concept.
method Inspired by skein lasagna module, uses link Floer homology.
result Computes Floer lasagna modules for specific 4-manifolds.
Coordination recognition and subtle pattern prediction of future trajectories play a significant role when modeling interactive behaviors of multiple agents. Due to the essential property of uncertainty in the future evolution, deterministic predictors are not sufficiently safe and robust. In order to tackle the task o…
We show that the Kauffman bracket skein module of a cylinder over the torus embeds as a subalgebra of the noncommutative torus. Using this we derive nice formulas for the Jones-Wenzl idempotents and analyze the structure of the Kauffman bracket skein module of the unknot as a module over the Kauffman bracket skein modu…
New knot theory module shows torsion-ness in number theory.
problem Torsion-ness of Selmer modules in Galois representations.
method Introducing adjoint homological Selmer module for SL2-representations of knot groups. result Finitely generated torsion-ness of the new Selmer module.
Study quandle modules over geometric quandles and their relation to Lie-Yamaguti representations.
problem Understanding quandle modules and their connection to Lie-Yamaguti representations.
method Examine quandle modules over quandle spaces, focusing on geometric structures.
result Modules over quandle spaces are linked to representations of Lie-Yamaguti algebras.
The multivariate Alexander module of a link L has several subsets that admit quandle operations defined using the module operations. One of them, the fundamental multivariate Alexander quandle, determines the link module sequence of L.
A complex vector space V is a prehomogeneous G-module if G acts rationally on V with a Zariski-open orbit. The module is called etale if dimV=dimG. We study etale modules for reductive algebraic groups G with one-dimensional center. For such G, even though every etale module is a regular prehomogeneou…
A commuting n-tuple (T1,…,Tn) of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module H over C[z1,…,zn] in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h…
Study on skein module dimensions at irreducible representations.
problem Dimension of skein module at irreducible representations.
method Localization of skein module at maximal ideal corresponding to irreducible representation.
result Localization forms a one-dimensional free module over the unreduced coordinate ring.
This document contains tables with the classification of prehomogeneous modules for reductive algebraic groups with up to two simple factors due to Sato, Kimura and many others, as well as corresponding tables of the étale modules appearing in this list, determined by the author. It is intended as a convenient referenc…
The paper studies deformations of cohesive modules on complex manifolds.
problem Deformation theory of cohesive modules on compact complex manifolds.
method Development of Kuranishi maps and obstructions for deformations of cohesive modules.
result Generalization of deformation theory for holomorphic vector bundles and coherent sheaves.