Study on MMV in jump-diffusion models resolves MV's non-monotonicity issues.
problem Non-monotonicity and free cash flow stream problems in MV preferences.
method Explicit solution for MMV preferences in jump-diffusion models, proving non-negative potential measures.
result MMV resolves MV's non-monotonicity and free cash flow stream issues.
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. New method recovers block-sparse signals with common sparsity patterns.
problem Recovering block-sparse signals with common sparsity patterns in MMV.
method Pattern-coupled hierarchical Gaussian prior model with EM framework.
result Proposed method automatically captures block sparse structure.
Study finds equivalence between MMV and MV preferences with conic constraints.
problem Monotone mean-variance portfolio selection under conic constraints.
method Closed-form solutions for optimal strategies under MMV and MV preferences.
result Optimal strategies coincide with and without the conic constraint.
Investigates time-inconsistent portfolio selection under MMV preferences.
problem Time-inconsistent optimal strategies for MMV preferences.
method Nash equilibrium controls for MMV and MV preferences, solving FBSDE and HJB equations.
result MMV optimal strategies lead to higher investment amounts than MV strategies, narrowing over time.
The paper characterizes optimal dynamic portfolios for a modified mean-variance utility.
problem Optimal dynamic portfolio choice for a modified mean-variance utility.
method Complete characterization under minimal assumptions, no restrictions on asset return moments.
result Maximal MMV utility is linked to the monotone Sharpe ratio, with global squared MSR as the nominal yield.
Model for EEG source localization with spatio-temporal structure.
problem Solving MMV problems with spatio-temporal sparsity patterns.
method Generalized spike and slab prior with Expectation Propagation.
result Demonstrated viability of the proposed model and inference scheme.
We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorithms do not consider such temporal correlations and thus their performance degrades significantly with the correlations. I…
This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a self-dictionary multiple measurement vector (SD-MMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SD-MMV formalism is special in that…
The paper solves MMV and MV problems with random coefficients and finds shared optimal strategies.
problem Optimal trading strategies with random market coefficients.
method Backward stochastic differential equations (BSDEs) to find optimal strategies.
result MMV and MV problems share the same optimal portfolio and value under random coefficients.
Study optimal investment-reinsurance strategy for insurers under random coefficients and jumps.
problem Optimal investment-reinsurance strategy for insurers with random coefficients and jumps.
method Solves backward stochastic differential equations with jumps under a convex cone constraint.
result Optimal strategy and value remain the same even with random coefficients and jumps.
A tuning-free method recovers jointly sparse signals in MMV using implicit regularization.
problem Recovering jointly sparse signals in MMV with minimal tuning or prior knowledge.
method Reparameterizes MMV estimation matrix into decoupled factors and applies gradient descent to a least-squares objective.
result Gradient descent dynamics exhibit a momentum-like effect, converging towards an idealized row-sparse solution.
Iterative reweighted algorithms, as a class of algorithms for sparse signal recovery, have been found to have better performance than their non-reweighted counterparts. However, for solving the problem of multiple measurement vectors (MMVs), all the existing reweighted algorithms do not account for temporal correlation…
Introduces SMMV preferences to avoid inconsistency in portfolio selection.
problem Monotone mean-variance preferences fail to differentiate strictly dominant payoffs.
method Introduces strictly monotone mean-variance preferences and applies them to portfolio selection problems.
result SMMV preferences provide a more rational basis for assessing prospects and coincide with MV preferences under certain conditions.
This paper tackles permutation recovery in unlabeled sensing from multiple measurement vectors.
problem Permutation recovery in unlabeled sensing from multiple measurement vectors.
method The paper studies the case of multiple noisy measurement vectors (MMVs) resulting from a common permutation and proposes computational schemes for permutation recovery.
result A large stable rank of the signal significantly reduces the required signal-to-noise ratio (SNR) for permutation recovery, and the problem can be solved efficiently using ADMM.
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the Kaczmarz algorithm was shown to converge exponentially and independent of number of …
A trend in compressed sensing (CS) is to exploit structure for improved reconstruction performance. In the basic CS model, exploiting the clustering structure among nonzero elements in the solution vector has drawn much attention, and many algorithms have been proposed. However, few algorithms explicitly consider corre…
Paper presents a new sparse signal recovery algorithm using GGAMP in SBL.
problem Sparse signal recovery problem.
method Integrates GGAMP into EM-based SBL for robustness and lower complexity.
result GGAMP-SBL algorithm is more robust and lower complexity than standard methods.
GRRT recovers sparse signals without prior sparsity or noise variance knowledge.
problem Recovering sparse signals without prior sparsity or noise variance knowledge.
method Generalized residual ratio thresholding (GRRT) for SOMP and BOMP.
result Finite sample and finite SNR guarantees for exact support recovery.
CRDA improves gene selection in microarray studies by reducing feature space.
problem Gene selection in high-dimensional microarray datasets.
method CRDA combines ℓq,1 norm minimization and hard thresholding for feature elimination. result CRDA outperforms competitors in misclassification and feature selection accuracy.
We survey the status of some decision problems for 3-manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (Word Problem, Conjugacy Problem, Isomorphism Problem), and also the Homeomorphism Problem for 3-manifolds and the Membership Problem for 3-manifold gr…
Optimal transport reformulates multiple quantile hedging problem.
problem Multiple quantile hedging problem in incomplete markets.
method Reformulated as Monge optimal transport problem, introduced Kantorovitch version, proved no duality gap.
result Multiple quantile hedging problem can be seen as semi-discrete optimal transport problem.
Solves four problems related to circle families in the plane.
problem Four basic problems of circle families in the plane.
method Solves all four basic problems of circle families in the plane.
result All four basic problems are solved.
The paper solves optimal control problems for various convex sets using convex trigonometry.
problem Optimal control problems with 2D convex compact sets.
method Using convex trigonometry to derive extremals for various problems.
result Geodesics in multiple sub-Finsler problems are derived.
Solves four problems related to sphere families in 3D space.
problem Four basic problems of sphere families in Euclidean 3-space.
method Solves all four basic problems of sphere families in Euclidean 3-space.
result All four basic problems are solved.
Explains eigenvalue and generalized eigenvalue problems with examples.
problem Eigenvalue and generalized eigenvalue problems.
method Introduction and examples from machine learning.
result Solutions to eigenvalue and generalized eigenvalue problems.
This paper solves the Christoffel problem in hyperbolic space and its equivalent on spheres.
problem Prescribing curvatures for convex hypersurfaces in hyperbolic space.
method Proving a full rank theorem to establish the existence of solutions.
result Existence of solutions to the Christoffel problem and its equivalent Nirenberg-Kazdan-Warner problem on spheres.
MathChat uses LLM agents to solve challenging math problems through conversational problem-solving.
problem Solving math problems expressed in natural language.
method MathChat is a conversational framework combining an LLM agent and a user proxy agent for collaborative problem-solving.
result MathChat improves tool-using prompting methods by 6% on difficult math problems.
Study proves only origin-centered spheres solve certain curvature problems.
problem Proving uniqueness of solutions to curvature problems.
method Using the Heintze-Karcher inequality, the study proves the uniqueness of smooth, strictly convex solutions to a class of Minkowski type problems.
result Only origin-centered spheres solve isotropic and Lp-Gaussian-Minkowski problems. New algorithm solves non-convex min-max problems in signal processing.
problem Non-convex min-max problems in signal processing and communication.
method Hybrid Block Successive Approximation (HiBSA) algorithm alternating gradient descent and ascent steps.
result HiBSA converges to first-order stationary solutions with global rates.
This article reviews ranking problems and their solutions.
problem Ranking problems in statistical learning.
method Systematic review of ranking problems and optimization techniques.
result Unified notation for optimization problems and identification of strengths and limitations of algorithms.
The paper solves a generalized Christoffel-Minkowski problem using a curvature flow.
problem Solving the (p,q)-Christoffel-Minkowski problem.
method Investigating the problem via an expanding curvature flow.
result Existence and uniqueness of smooth solutions to the (p,q)-Christoffel-Minkowski problem.
Paper solves Gromov-Wasserstein for point clouds efficiently.
problem Quantifying similarity between two formations or shapes.
method Reformulates QAP as low-rank concave quadratic optimization problem.
result Global solution for large-scale problems with thousands of points.
The paper explains how microlocal analysis solves geometric inverse problems.
problem Recovering geometric information from boundary measurements.
method Microlocal analysis applied to three inverse problems.
result Microlocal techniques solve specific inverse problems in Riemannian geometry.
Proves NP and co-NP status for knot core recognition in solid torus.
problem Determining if a knot is the core of a solid torus.
method Alternate proof and corollary of Hopf link recognition problem.
result Proves NP and co-NP status for solid torus core recognition problem.
Study on Cauchy problem solutions and inverse problems for PDEs.
problem Analyzing the domain of solutions for a specific type of PDE.
method Examined a second-order quasi-linear PDE with parabolic degeneration, studied inverse problems, and provided conditions for solutions.
result The domain of the solution contains gaps under certain conditions.
A new method solves complex control problems with random coefficients.
problem Solving LQ McKean-Vlasov control problems with random coefficients.
method Decomposes the problem into two decoupled stochastic optimal control problems.
result The sum of optimal controls of auxiliary problems equals the original problem's optimal control.
Paper solves inverse problem in continuous Markov fields using Bethe approximation and loopy belief propagation.
problem Solving the inverse problem in Markov random fields with non-parametric pair-wise energy function.
method Loopy belief propagation and orthonormal function expansion to approximate the partition function and solve functional optimization.
result Analytic solution to inverse problem in continuous Markov fields.
Replica analysis reveals dual structure in portfolio optimization.
problem Optimizing investment risk and return under constraints.
method Replica analysis in statistical mechanics.
result Optimal portfolios exhibit primal-dual structure.
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some necessary definitions and motivations, problems and some discussions of them. For ea…
We present updates to the problems on Hirzebruch's 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric problems about (almost) complex structures, both algebraic and non-algebraic, about co…
27 problems identified in automating movie/TV subtitle translation.
problem Challenges in translating movie/TV subtitles.
method Categorized problems into three categories and evaluated translation quality.
result Frontier NLP systems struggle with subtitles and require post-processing.
Solves Brezis' first open problem on ball solutions.
problem Existence of solutions to Brezis-Nirenberg problem on a 3D ball.
method Building on sign-changing solutions to the Yamabe problem.
result Infinitely many sign-changing, nonradial solutions found.
New method solves generalized Minkowski problem for torsional rigidity.
problem Generalized Minkowski problem for torsional rigidity.
method Flow method
result Existence of solutions for general measures.
Classical knot recognition problem solved in NP with exponential time algorithm.
problem Determining if a virtual knot is classical.
method Proved NP membership and provided an exponential time algorithm.
result Classical knot recognition problem is in NP.
Paper solves four problems of pseudo-circle envelopes in Minkowski plane.
problem Four problems of pseudo-circle envelopes in Minkowski plane.
method Solutions to four basic problems.
result Solved four problems of pseudo-circle envelopes in Minkowski plane.
Describes state variables in sequential decision problems, linking them to Markovian and non-Markovian models.
problem Sequential decision problems, especially in active learning and POMDPs, where decisions affect what is observed and learned.
method Canonical framework and novel two-agent perspective of POMDPs, defining state variables to claim Markovian or non-Markovian models.
result Properly modeled sequential decision problems are Markovian, while real decision problems are often non-Markovian.
Solves double coset problem for braid group H_n.
problem Double coset problem in braid group B_n modulo H_n.
method Uses Garside's decomposition of braids in B_n.
result Demonstrates stable equivalence of Link Problem to solvable algebraic problem.