New infinite-dimensional representations with bounded multiplicity found for Lie groups.
problem Finding representations with bounded multiplicity for Lie groups.
method Proving existence of infinite-dimensional irreducible representations with bounded multiplicity property.
result Infinite-dimensional irreducible representations with bounded multiplicity found for non-compact semisimple Lie groups.
Study shows strong multiplicity one property for 3D hyperbolic spaces.
problem Understanding the spectrum of length-holonomy in 3D hyperbolic spaces.
method Analyzing Selberg-Gangolli-Wakayama zeta functions.
result Established a strong multiplicity one type property for length-holonomy spectrum.
Generative model creates drug-like molecules with multiple properties.
problem Designing molecules with multiple desired properties.
method Conditional Variational Autoencoder (VAE) in latent space control.
result Can generate drug-like molecules with five target properties.
New method proves Jones Polynomial's connect sum property.
problem Jones Polynomial's behavior under connect sums.
method Trip matrix method for calculating Jones Polynomial.
result Jones Polynomial is multiplicative under connect sums.
Paper shows unique decomposition of 3-manifolds and multiplicative property of Reidemeister torsion.
problem Unique decomposition of compact 3-manifolds.
method Study of adjoint Reidemeister torsion on disk sum decompositions.
result Adjoint Reidemeister torsion has a multiplicative property on unique decompositions.
Generative model learns to create molecules with multiple properties using interpretable substructures.
problem Creating molecules with multiple chemical properties is challenging.
method Compose molecules from substructures identified as responsible for each property, using graph generative models.
result Significant improvements in accuracy, diversity, and novelty of generated compounds over state-of-the-art baselines.
We give a complete proof of a propagation theorem of multiplicity-free property from fibers to spaces of global sections for holomorphic vector bundles. The propagation theorem is formalised in three ways, aiming for producing various multiplicity-free theorems in representation theory for both finite and infinite dime…
XIMP improves molecular property prediction by integrating multiple graph representations.
problem Graph neural networks struggle in data-scarce regimes and fail to surpass traditional methods.
method Cross-graph inter-message passing with multiple graph abstractions.
result XIMP outperforms state-of-the-art baselines across diverse molecular property tasks.
Extended symmetric union with multiple tangle regions and Alexander polynomial properties.
problem Characterizing knots with multiple tangle regions.
method Generalizing the symmetric union construction to include multiple tangle regions and analyzing the Alexander polynomial.
result The Alexander polynomial of the constructed knot is the product of the Alexander polynomials of the tangles and the square of the partial knot's Alexander polynomial.
Improved guarantees and multiple-descent curve for data approximations.
problem Improving the effectiveness of small low-rank approximations of large datasets.
method Spectral properties of the data matrix to obtain improved approximation guarantees.
result Revealed a multiple-descent curve in approximation factor as a function of k.
Paper defines multiplicities for quaternion eigenvalues without complex matrix concepts.
problem Defining multiplicities for quaternion eigenvalues without traditional matrix concepts.
method Introduces two definitions for algebraic and geometric multiplicities equivalent to classical definitions.
result Definitions are equivalent to classical ones and prove all properties easily.
In this note, we combine the work of Ilmanen and of Colding-Ilmanen-Minicozzi to observe a uniqueness property for tangent flows at the first singular time of a smooth mean curvature flow of a closed surface in 3-dimensional Euclidean space. Specifically, if, at a fixed singular point, one tangent flow is a positive in…
We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the syste…
Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely depend on the number of transactions. We introduce the multiplicative stochastic mod…
New algorithm finds optimal sample complexity for pure exploration with multiple good answers.
problem Determining the optimal number of samples needed to explore multiple good answers in a bandit problem.
method Derive lower bound using game equilibrium, extend Track-and-Stop algorithm to multiple answers.
result New algorithm has asymptotic sample complexity matching the derived lower bound.
Study on geodesics in spacetime, proving properties of multiple maximizing paths.
problem Characterizing multiple maximizing geodesics in globally hyperbolic spacetimes.
method Analyzing topological properties of the locus of multiple maximizing geodesics.
result The set of multiple maximizing geodesics is locally contractible.
A gap in a paper of Rubinstein-Scharlemann is explored: new examples are found of closed orientable 3-manifolds with possibly multiple genus 2 Heegaard splittings. Properties common to all the examples in the original paper are not universally shared by the new examples: some of the new examples have Hempel distance 3,…
We prove several results on Almgren's multiple valued functions and their links to integral currents. In particular, we give a simple proof of the fact that a Lipschitz multiple valued map naturally defines an integer rectifiable current; we derive explicit formulae for the boundary, the mass and the first variations a…
Most content-based image retrieval systems consider either one single query, or multiple queries that include the same object or represent the same semantic information. In this paper we consider the content-based image retrieval problem for multiple query images corresponding to different image semantics. We propose a…
In this paper, we introduce several mixed Lp geominimal surface areas for multiple convex bodies for all p=−n. Our definitions are motivated from an equivalent formula for the mixed p-affine surface area. Some properties, such as the affine invariance, for these mixed Lp geominimal surface areas are prove…
We prove a strong multiplicity one theorem for the length spectrum of compact even dimensional hyperbolic spaces i.e. if all but finitely many closed geodesics for two compact even dimensional hyperbolic spaces have the same length, then all closed geodesics have the same length.
Affine structures on Lie groupoids are studied, showing rich algebraic properties.
problem Understanding affine structures on Lie groupoids.
method Analyzing affine k-vector fields, k-forms, and (p,q)-tensors, and showing their algebraic properties. result The space of affine structures forms a 2-vector space over multiplicative structures, and affine multivector fields have a Lie 2-algebra structure.
This paper tackles robust control of LQR systems with multiplicative noise using policy gradient methods.
problem Robustness in reinforcement learning control of complex systems with multiplicative noise.
method Policy gradient algorithms with gradient domination property for non-convex cost functions.
result Global convergence of policy gradient algorithms to the globally optimum control policy.
Solves optimal control for trading multiple mean-reverting assets.
problem How to construct a portfolio from mean-reverting assets.
method Optimal control problem for power utility agent.
result Nearly explicit solution with properties of optimal solution.
In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the Lévy Libor market model, it allows in a natural way for…
Quantum reservoir computing needs coherence influx for effective information processing.
problem Understanding and optimizing quantum reservoir computing.
method Theoretical and numerical analysis of quantum systems, focusing on coherence influx and spectral radius of Pauli transfer matrix.
result Coherence influx is essential for realizing nonstationary echo state property in quantum reservoir computing.
This paper studies MMV problem and its performance, proving a decoupling property for MMV algorithms.
problem Joint estimation of multiple signal realizations with common sparse support.
method Proved a decoupling property for ℓ2,1-LS algorithm, decomposing it into coupled and decoupled phases. result Performance of ℓ2,1-LS and MMV algorithms are affected by signal correlations and dictionary mismatch. Invariant counts maximum stable umbilic splits.
problem Counting stable umbilic splits on surfaces.
method Introducing an invariant to count maximum stable umbilic splits.
result Established properties of the multiplicity invariant.
Develops a method for solving optimal stopping problems with multiple exercise rights.
problem Optimal stopping with multiple exercise rights under model uncertainty.
method Pathwise duality approach based on robust martingale dual representation.
result Establishes upper and lower bounds that converge to the true solution.
For functions of a single complex variable, points of multiplicity greater than k are characterized by the vanishing of the first k derivatives. There are various quantitative generalizations of this statement, showing that for functions that are in some sense close to having multiplicity greater than k, the firs…
This paper analyzes optimal consumption strategies for loss-averse investors with multiplicative habit formation.
problem Optimal consumption strategies for loss-averse investors with multiplicative habit formation.
method The study uses a concave envelope of the S-shaped utility function and a nonlinear free boundary problem to analyze the HJB equation.
result The paper provides optimal consumption and investment policies in feedback form.
Investigates the fundamental components of attention mechanisms.
problem Understanding the building blocks of attention in deep learning.
method Classified and studied three key mechanisms: additive, multiplicative output, and synaptic attention.
result Additive activation attention is central in proofs of lower bounds.
In this work, we study Lie groupoids equipped with multiplicative foliations and the corresponding infinitesimal data. We determine the infinitesimal counterpart of a multiplicative foliation in terms of its core and sides together with a partial connection satisfying special properties, giving rise to the concept of I…
Unified framework models multiple financial and insurance term structures.
problem Modeling multiple term structures in various markets.
method Extended Heath-Jarrow-Morton (HJM) approach under real-world probability.
result Characterization of local martingale deflators and existence of affine realizations.
Improved SVMs learn from few samples with composition and multiple scales.
problem Learning with small sample sizes.
method Transformation-invariant SVMs with composition and locality at multiple scales.
result Kernels based on maximum similarity are positive definite and yield superior accuracy.
We study the generalization properties of stochastic gradient methods for learning with convex loss functions and linearly parameterized functions. We show that, in the absence of penalizations or constraints, the stability and approximation properties of the algorithm can be controlled by tuning either the step-size o…
The paper shows how the generalization curve can have multiple peaks, influenced by data and learning algorithm biases.
problem Understanding the generalization behavior of linear regression models under varying parameterizations.
method Analyzes generalization loss in linear regression models with varying parameterizations, both under- and over-parameterized.
result The generalization curve can have an arbitrary number of peaks, and their locations can be controlled.
Bayesian model ranks treatments in multi-response experiments.
problem Identifying the best treatment among competing ideal properties.
method Bayesian approach with Markov Chain Monte Carlo algorithm.
result Reliable inference of treatment ranks in practice.
Study local expansions of continuous-time processes using Ito signature properties.
problem Analyzing local expansions of continuous-time processes and their moments.
method Using the Ito signature, a basis of iterated integrals, to conduct expansions of the process' characteristic function.
result Explicit coefficients and stochastic representations for asymptotics as time shrinks or diverges.
New sampling-based approach for filtering problems using multiplicative Gaussian functions.
problem Approximate inference in filtering problems.
method Approximates distribution with a weighted sum of continuous functions using sampling for multiplications.
result Preliminary experiments show potential of the new method compared to particle filters.
Single-timescale analysis improves convergence in multi-sequence stochastic approximation.
problem Finite-time convergence of nonlinear stochastic approximation with multiple coupled sequences.
method Smoothness property of fixed points and analysis of fine-grained single-timescale SA.
result Improved iteration complexity for achieving ε-accuracy in multi-sequence single-timescale SA.
Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to noise of multiplicative nature. The special properties of multiplicative…
The article constructs a forward utility for markets with multiple default risks.
problem Characterizing forward performance processes in a market with multiple default risks.
method Using Jacod-Pham decomposition and recursive BSDEs, the article constructs a forward utility and proves its existence and uniqueness.
result The article identifies the risk-sensitive long-run growth rate of the optimal wealth process in a stochastic factor model with ergodic dynamics.
We analyze a notion of multiple valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and generalizes Almgren's Q-valued functions. We study some relevant properties o…
Introduces VB-structures for geometric objects on manifolds.
problem Properties of higher tangent lifts of geometric structures.
method Introduces weighted structures for various geometric objects on a manifold with a homogeneity structure.
result Proves interesting properties of various weighted structures.
The article discusses extensions of Harish-Chandra's admissibility theorem.
problem Restrictions of irreducible representations to non-compact subgroups.
method Representation-theoretic developments for new spectral analysis.
result Powerful methods for spectral analysis of standard locally symmetric spaces.
The paper tests properties of multiple distributions with limited samples.
problem Testing properties of multiple distributions with few samples.
method Designing testers for uniformity, identity, and closeness testing under specific conditions.
result Sample optimal testers for uniformity, identity, and closeness testing are provided.
Weakly Einstein Kähler surfaces are characterized and classified.
problem Characterizing and classifying weakly Einstein Kähler surfaces.
method Several conditions and constructions to characterize and classify weakly Einstein Kähler surfaces.
result Classification of weakly Einstein Kähler surfaces with specific properties and construction of new examples.