New copulas model external shocks with different effects on system components.
problem Modeling external shocks with different impacts on system components.
method Introduced reflected maxmin (RMM) copulas to extend maxmin copulas.
result Symmetric RMM copulas relate to general RMM copulas similarly to semilinear copulas to Marshall copulas.
Paper introduces new copulas from shock models, improving on maxmin copulas.
problem Improving on maxmin copulas for better characteristics.
method Developed RMM copulas with dependent endogenous shocks and proved convergence of iteration procedures.
result RMM copulas exhibit better characteristics than maxmin copulas, including convergence properties.
Study finds cheapest possible payoff under ambiguity, linking to maxmin expected utility.
problem Finding cost-efficient payoffs in uncertain market conditions.
method Developed a new concept of robust cost-efficient payoff and linked it to maxmin expected utility.
result Solutions to maxmin robust expected utility are robust cost-efficient.
SharedRep-RLHF learns shared traits for diverse groups, improving fairness and performance.
problem Uniform-reward RLHF fails to capture diverse preferences, leading to unfairness.
method SharedRep-RLHF learns shared traits among various groups, improving fairness and performance.
result SharedRep-RLHF outperforms MaxMin-RLHF by up to 20% in win rate.
A new landmark sampling method improves TDA performance on biomedical data.
problem Improving landmark samplers for pseudometric spaces with varying density and multiplicities.
method Proposes 'lastfirst' procedure based on ranked distances, proving landmarks have desired properties.
result lastfirst outperforms maxmin on homology detection tasks and comparable on prediction tasks.
Model cash management under ambiguity using maxmin preferences and diffusion.
problem Optimizing cash reserves in the presence of ambiguity.
method Singular control model with maxmin preferences, verified using Dynkin games.
result Higher expected costs and narrower inaction region under increased ambiguity.
This paper explores non-exchangeability in copulas from shock models and computes asymmetry bounds.
problem Understanding the non-exchangeability of copulas from shock models.
method Analyzes and computes asymmetry bounds for various copulas families.
result Sharp bounds for asymmetry measures of Marshall, maxmin, and RMM copulas.
Study examines insurance demand under ambiguity aversion.
problem Demand for insurance indemnification under ambiguity aversion.
method Characterizes optimal indemnity functions using Maxmin-Expected Utility model.
result Optimal indemnity functions involve full insurance on low-probability events.
This paper analyzes a game between insurer and reinsurer under ambiguity and risk aversion, optimizing reinsurance and investment strategies.
problem Optimizing reinsurance and investment strategies in a game between insurer and reinsurer under ambiguity and risk aversion.
method Stackelberg game, α-maxmin mean-variance criterion, Heston's stochastic volatility, Hamilton-Jacobi-Bellman equations, Riccati differential equations. result Excess-of-loss reinsurance is optimal for the insurer, and the equilibrium strategies are determined by specific equations.
New technique prevents Q-learning collapse by maximizing diversity among ensembles.
problem Value function collapse in ensemble Q-learning.
method Maximizing representation diversity through regularization.
result Regularized approach significantly outperforms existing methods.
Clustering is an extensive research area in data science. The aim of clustering is to discover groups and to identify interesting patterns in datasets. Crisp (hard) clustering considers that each data point belongs to one and only one cluster. However, it is inadequate as some data points may belong to several clusters…
Dynamic pricing model considers ambiguity in endowment growth rate.
problem Dynamic asset pricing under ambiguous endowment growth rate.
method α-maxmin expected utility model for ambiguity, intra-personal equilibrium strategies, market equilibrium.
result Asset prices reflect ambiguity in endowment growth rate.
The paper analyzes insurance contracts under distributional uncertainty using Bregman-Wasserstein divergence.
problem Optimal insurance contracts under distributional ambiguity.
method Utilizes Bregman-Wasserstein ball to characterize ambiguity sets, employs robust optimization.
result Derives optimal indemnity functions in closed form and studies their properties.
Efficient local Lipschitz bounds improve neural network robustness.
problem Certifying robustness of neural networks is challenging and often leads to over-regularization.
method Proposes an efficient trainable local Lipschitz upper bound by considering activation functions and weight matrices.
result Consistently outperforms state-of-the-art methods in clean and certified accuracy on various datasets.
New formulations capture aversion to ambiguity about volatility.
problem Capturing aversion to ambiguity about unknown and time-varying volatility.
method Introduces novel preference formulations and compares them with existing models.
result Illustrates the impact of ambiguity aversion in static and dynamic models.
Automates bias control in reinforcement learning algorithms.
problem Overestimation bias in reinforcement learning algorithms.
method Data-driven approach for automatic selection of bias control hyperparameters.
result Significant reduction in the number of interactions while maintaining performance.
We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random return unde…
A novel Q-learning variant reduces underestimation bias in deep actor-critic methods for reinforcement learning.
problem Underestimation bias in deep actor-critic methods for reinforcement learning.
method Introduces a parameter-free Q-learning variant that combines maximum and minimum operators to bound value estimates.
result Improves state-of-the-art performance on OpenAI Gym tasks.
A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions.
New method produces reflections with nonseparating fixed points.
problem Constructing hyperbolic manifolds with reflective symmetries.
method Standard method for constructing closed hyperbolic manifolds.
result Fixed point sets of reflections are nonseparating.
Survey explores interactions between four conformal dynamics branches.
problem Understanding complex dynamics through different mathematical concepts.
method Examples and general results with technical tools.
result Dynamical relations between Schwarz reflection parameter spaces and anti-rational maps/ reflection groups.
One reflection suffices for orthogonal weights, reducing GPU usage.
problem Efficiently computing orthogonal weight matrices without high GPU utilization.
method Use an auxiliary neural network to compute one reflection instead of many.
result One reflection is sufficient for orthogonal weights, improving GPU utilization.
Minimal surfaces in 3-sphere created by reflections from polygons, with new examples based on pentagons.
problem Constructing minimal surfaces in 3-sphere using reflections.
method Minimal n-gon solves free boundary problem; curvature lines combinatorics investigated. result New examples of minimal reflection surfaces based on pentagons.
Study thin hyperbolic reflection groups and their properties.
problem Characterize and enumerate thin hyperbolic reflection groups.
method Analyze Zariski dense subgroups of hyperbolic isometries, apply Vinberg algorithm.
result All thin hyperbolic reflection groups are enumerable.
Minimal surfaces reflect across spheres, proving annulus uniqueness.
problem Uniqueness of free boundary minimal annuli in balls.
method Reflection principle applied to minimal surfaces meeting spheres at 90 degrees.
result Every embedded free boundary minimal annulus in a ball is the critical catenoid.
The paper classifies a specific type of hyperbolic lattices using geometric properties.
problem Classifying (1,2)-reflective anisotropic hyperbolic lattices of rank 4. method Using geometric properties of the fundamental polyhedron of a cocompact reflection group in three-dimensional Lobachevsky space.
result A classification of (1,2)-reflective anisotropic hyperbolic lattices of rank 4. Hausdorff reflection keeps space shape intact.
problem Preserving shape type in spaces.
method Hausdorff reflection method.
result Hausdorff reflection preserves shape type.
Study extends reflective submanifold theory to compact homogeneous spaces.
problem Characterize reflective submanifolds in compact isotropy irreducible spaces.
method Extend previous results to infinite-dimensional Hilbert spaces.
result Inverse image of reflective submanifolds is also reflective.
New reflection groups derived from torus knots with finite meridians.
problem Understanding reflection groups derived from torus knot groups with finite meridians.
method Using the theory of J-groups and Coxeter groups, study quotients of torus knot groups.
result Classification of toric reflection groups and their properties.
We introduce a representation theory for risk operations on locally compact groups in a partition of unity on a topological manifold for Markowitz-Tversky-Kahneman (MTK) reference points. We identify (1) risk torsion induced by the flip rate for risk averse and risk seeking behaviour, and (2) a structure constant or co…
Constructs a Hodge filtration for vector fields of complex reflection groups.
problem Understanding vector fields with logarithmic poles in complex reflection groups.
method Explicit construction using a flat connection on primitive vector fields.
result Yields a Hodge filtration for the module of vector fields.
A hyperbolic lattice is called \textit{1.2-reflective} if the subgroup of its automorphism group generated by all 1- and 2-reflections is of finite index. The main result of this article is a complete classification of 1.2-reflective maximal anisotropic lattices of rank 4.
A hyperbolic reflection group is a discrete group generated by reflections in the faces of an n-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis on the results that were obtained in the last ten years and on the open problems.
This paper compares self-reflection and budget tuning for LLMs, revealing domain-specific performance gains.
problem Improving inference-time performance of LLMs without retraining, balancing quality, cost, and latency.
method Systematic comparison of self-reflection and budget tuning across mathematical reasoning and translation tasks, evaluating various LLMs and model families.
result Substantial domain-dependent variation in self-reflection effectiveness, with up to 220% performance gains in mathematical reasoning.
This paper describes caustics of wave fronts reflected by a surface.
problem Understanding the geometry of caustics formed by wave fronts reflected by a surface.
method Purely geometric description of caustics, clarifying their dependence on surface characteristics.
result Clarifies the geometry and topology of caustics formed by wave fronts after reflection from a mirror surface.
Picard modular groups are shown to be generated by complex reflections.
problem Understanding the structure of Picard modular groups using reflections.
method Using presentations from previous works to show generation by reflections.
result Picard modular groups mPU(2,1,Od) are generated by complex reflections. The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.
problem Large deviation principles for stochastic volatility models with reflection.
method Sample path and small-noise large deviation principles for the log-price process.
result Asymptotic behavior of binary barrier options and call prices in the small-noise regime.
Differential equations are derived for a continuous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is o…
After establishing the uniqueness of the continuation of local Cauchy data for harmonic maps between two Riemannian manifolds M and N, we prove (i) a reflection principle for a smooth minimal submanifold Y of a Riemannian manifold M that contains a reflective submanifold of M as a hypersurface and (ii) the reflection p…
The paper finds many infinite-dimensional weakly reflective PF submanifolds in Hilbert spaces.
problem Minimal submanifolds in Hilbert spaces with reflective properties.
method Introduced weakly reflective PF submanifolds into Hilbert spaces and showed their existence.
result Existence of infinite-dimensional weakly reflective PF submanifolds in Hilbert spaces.
EMIX minimizes surprise in multi-agent reinforcement learning.
problem Surprise and approximation bias in multi-agent reinforcement learning.
method Energy-based MIXer (EMIX) for minimizing surprise across multiple agents.
result EMIX demonstrates consistent stable performance in challenging StarCraft II scenarios.
Proves a theorem for mechanical systems with reflections.
problem Action functionals on paths with reflections.
method Proves a Morse index theorem for action functionals on paths that can reflect.
result Action functionals on paths with reflections have a well-defined Morse index.
This paper studies parabolic quasi-Coxeter elements in complex reflection groups and their combinatorial properties.
problem Characterizing and studying parabolic quasi-Coxeter elements in complex reflection groups.
method Defining and characterizing parabolic quasi-Coxeter elements, studying collections of reduced reflection factorizations and relative generating sets.
result Computing cardinalities of collections of reduced reflection factorizations and relative generating sets for large families of parabolic quasi-Coxeter elements.
Automatic detection of reflective thinking in math problem solving using body movement data.
problem Detecting reflective thinking in children's mathematical problem solving.
method WeDraw-1 Movement Dataset, Long Short-Term Memory neural networks, end-to-end detection.
result Average F1 scores of 0.73 for automatic detection and 0.79 for end-to-end detection of reflective thinking.
Study reflection symmetry and APS boundary conditions on a warped cylinder.
problem Analyzing reflection symmetry and APS boundary conditions for twisted Dirac operators on a finite warped cylinder.
method Examined reflection symmetry and APS boundary conditions for twisted Dirac operators on a finite warped cylinder, considering both fixed and varying holonomy.
result Reflection symmetry lifts to a unitary symmetry under specific conditions, and the spectral flow admits an RO(O(2))-valued decomposition for fixed holonomy.
New method trains reflected Schrödinger bridges without complex derivatives.
problem Training reflected Schrödinger bridges efficiently in high dimensions.
method Partially simulation-free framework with new sampling method.
result Generative performance maintained or slightly improved with reflected dynamics.
We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of s-representations.