Tests for common breaks in multivariate system equations.
problem Testing for common breaks in different parameters across or within equations.
method Quasi-likelihood ratio test with normal errors, considering rate of convergence for partitions.
result Good finite sample properties demonstrated through simulations.
Optimal rank-breaking estimator improves accuracy and complexity in rank aggregation.
problem Inconsistent estimates from naive rank-breaking approaches.
method Optimal rank-breaking estimator that treats pairwise comparisons unequally based on data topology.
result Achieves consistency and best error bound, characterizing accuracy-complexity tradeoff.
New model accurately predicts chemical bond breaking.
problem Challenges in describing bond breaking in quantum chemistry.
method Pretrained deep neural network wavefunction model Orbformer.
result Consistently converges to chemical accuracy (1 kcal/mol).
Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A com…
SymPE breaks symmetries in equivariant networks, improving performance across various tasks.
problem Equivariant networks cannot break symmetries, leading to poor performance in tasks with symmetrical inputs.
method Novel equivariant conditional distributions and randomized canonicalization.
result SymPE significantly improves performance of group-equivariant and graph neural networks.
We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient co…
Geometric mechanism mimics physics' symmetry breaking.
problem Understanding spontaneous symmetry breaking in geometry.
method Analogous to physics, studying symmetry breaking in differential geometry.
result Symmetry breaking can be used to solve geometric problems.
Researchers create BPS monopoles with any desired symmetry breaking.
problem Creating monopoles with specific symmetry breaking patterns.
method Using a new class of Nahm data to construct finite energy BPS monopoles.
result Arbitrary symmetry breaking monopoles can be constructed.
New formulae derived for conformal symmetry breaking operators.
problem Understanding conformal symmetry breaking operators.
method Bernstein-Sato identities for distribution kernels.
result New formulae for conformal symmetry breaking differential operators.
The paper classifies and proves properties of symmetry breaking operators for specific groups.
problem Classifying and understanding symmetry breaking operators for de Sitter and Lorentz groups.
method Constructing and classifying differential symmetry breaking operators, proving localness, and showing sporadic nature.
result All symmetry breaking operators are differential and sporadic, not obtainable by residue formulas.
Directly proves CRP from stick-breaking process without measure theory.
problem Indirect proof of CRP from stick-breaking process is complex.
method Direct proof using stick-breaking process to CRP, avoiding measure theory.
result Direct proof connects stick-breaking process to CRP.
We give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of G=O(n+1,1) and G'=O(n,1). We construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explic…
Investigates spontaneous symmetry breaking in non-equilibrium systems.
problem Spontaneous symmetry breaking of ergodicity in non-equilibrium systems.
method Mathematical and effective field theory approaches to investigate symmetry breaking.
result Symmetry breaking phenomena observed in stochastic processes.
SB-VAE uses Stick-Breaking processes for Bayesian nonparametric latent representations.
problem Learning latent representations with stochastic dimensionality.
method Stochastic Gradient Variational Bayes applied to Stick-Breaking processes.
result SB-VAE learns highly discriminative latent representations that outperform Gaussian VAE.
MultiDendrograms is a Java-written application that computes agglomerative hierarchical clusterings of data. Starting from a distances (or weights) matrix, MultiDendrograms is able to calculate its dendrograms using the most common agglomerative hierarchical clustering methods. The application implements a variable-gro…
Proves and tests methods for learning time-series with breaks.
problem Learning time-series with structural breaks.
method Complete proofs and experimental validation of a regularized loss function.
result Experimental results support the validity of the techniques.
The paper analyzes XVA reduction strategies in financial crises using Mandatory Breaks, Restructuring, and Resets.
problem Challenges in client XVA management during crises when continuous collateralization is not feasible.
method Compares multiple trade strategies including Mandatory Breaks, Restructuring, and Resets.
result Resets can be twice as effective as Mandatory Breaks/Restructuring if there is no credit recovery. When recovery is at least 1/3, Mandatory Breaks/Restructuring can be more effective.
The paper identifies short-term and long-term time scales in stock markets with and without structural breaks.
problem Understanding the nature of stock markets at short-term and long-term time scales.
method Applied Zivot and Andrews structural trend break model to identify structural breaks. Used empirical mode decomposition and Hurst exponent to analyze time scales.
result Identified short-term and long-term time scales in stock markets, with short-term scales within few days to 3 months and long-term scales greater than 5 months.
We introduce the concept of spontaneous symmetry breaking to arbitrage modeling. In the model, the arbitrage strategy is considered as being in the symmetry breaking phase and the phase transition between arbitrage mode and no-arbitrage mode is triggered by a control parameter. We estimate the control parameter for mom…
Formula proves symmetry breaking operators for differential forms.
problem Symmetry breaking operators between differential forms on spheres and their hyperplanes.
method Explicit residue formula for meromorphic continuation of operators.
result Simple construction of symmetry breaking operators and determination of zeros.
Paper detects and estimates breaks in high-dimensional functional time series.
problem Detecting and estimating structural breaks in heterogeneous mean functions of high-dimensional functional time series.
method Proposes a new test statistic combining functional CUSUM and power enhancement components, with a clustering algorithm for group structure estimation.
result The proposed techniques have satisfactory performance in finite samples, detecting and estimating breaks effectively.
Bayesian ARMA model with directional shifts captures structural breaks in compositional time series.
problem Structural breaks in compositional time series due to external shocks or policy changes.
method Developed a Bayesian Dirichlet ARMA model augmented with a directional-shift intervention mechanism.
result The model captures structural breaks through interpretable parameters and produces coherent probabilistic forecasts.
Noether's framework reveals symmetry-breaking in neural networks.
problem Understanding the role of symmetry breaking in neural networks.
method Developed a theoretical framework using Lagrangian mechanics.
result Identified 'kinetic symmetry breaking' and its effect on learning dynamics.
Paper proposes a method to efficiently estimate structural breaks in cointegrating regressions.
problem Estimating structural breaks in cointegrating regressions is challenging due to inconsistency of group lasso.
method Adaptive group lasso procedure using a first step group lasso estimation of diverging breakpoint candidates to produce weights for a second estimation.
result The adaptive group lasso estimator delivers consistent parameter changes and oracle properties.
Part I. We prove a one-to-one correspondence between differential symmetry breaking operators for equivariant vector bundles over two homogeneous spaces and certain homomorphisms for representations of two Lie algebras, in connection with branching problems of the restriction of representations. We develop a new method…
New method breaks symmetry in neural networks, improving sample efficiency.
problem Symmetry in neural networks limits their ability to learn unique features.
method Introduces 'relaxed equivariance' to overcome symmetry limitations.
result Equivariant multilayer perceptrons (E-MLPs) can now break symmetry at the sample level.
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has …
Classifies patterns of symmetry breaking and vacuum degeneracy in scalar and gauge fields.
problem Understanding patterns of symmetry breaking and vacuum degeneracy in complex field systems.
method Uses mathematical classification of singular foliations to encode and classify patterns of spontaneous symmetry breaking and vacuum degeneracy.
result Mathematical classification provides a qualitative understanding of possible patterns of vacuum degeneracy.
We provide some insights in the study of branching problems of reductive groups, and a method of investigations into symmetry breaking operators. First, we give geometric criteria for finiteness property of linearly independent continuous (respectively, differential) operators that intertwine two induced representation…
Study on spontaneous symmetry breaking in financial markets using quantum mechanics.
problem Analyzing spontaneous symmetry breaking in financial markets.
method Using Hamiltonian form of Black-Scholes and Merton-Garman equations, analyzing symmetry breaking and interpreting Nambu-Goldstone bosons.
result Interpretation of Nambu-Goldstone bosons in financial markets.
The seriousness of the current crisis urgently demands new economic thinking that breaks the austerity vs. deficit spending circle in economic policy. The core tenet of the paper is that the most important problems that natural and social science are facing today are inverse problems, and that a new approach that goes …
Study on wave-breaking phenomena in solutions of the Camassa-Holm equation.
problem Wave-breaking phenomena in solutions of the Camassa-Holm equation.
method Investigation of pseudospherical surfaces and singularities of the metric.
result The metric blows up if and only if the solution breaks in finite time.
New method learns decentralized policies in Dec-POMDPs using stick-breaking priors.
problem Learning optimal decentralized policies in large Dec-POMDPs with fixed-size controllers.
method Dec-SBPR framework using stick-breaking priors and variational Bayesian learning.
result Dec-SBPR outperforms other methods on large benchmark problems.
Symmetry in inverse problems leads to multiple solutions, but breaking symmetry helps deep learning.
problem Symmetry in physical systems causes multiple solutions in inverse problems, hindering deep learning.
method Careful symmetry breaking on training data helps solve inverse problems and improve deep learning performance.
result Symmetry breaking on training data significantly improves deep learning performance in inverse problems.
New theory shows how membranes can break symmetry.
problem Understanding symmetry breaking in membranes with boundaries.
method Applied bifurcation theory and reduced membrane equation.
result Existence of symmetry breaking bifurcation in membrane solutions.
Study of fastest paths in anisotropic media via Finsler geometry.
problem Optimal paths in media with varying speeds and interfaces.
method Finsler geodesics refracted at interfaces, satisfying specific conditions.
result Establishes generalized Snell's and reflection laws.
Machine learning predicts dam-break flood wave behavior accurately.
problem Predicting long-term wave behavior in dam-break floods.
method Solved Saint-Venant equations using Lax-Wendroff scheme, trained RC-ESN with flow depth data.
result RC-ESN model predicts 286 time-steps ahead with RMSE < 0.01, outperforming LSTM.
Paper defines the payback period for nonconventional cash flows using axioms.
problem Defining the payback period for nonconventional cash flows is challenging.
method Used axiomatic approach to define the payback period.
result The last break-even point of the project balance is the only definition consistent with axioms.
The main aim of this work is to incorporate selected findings from behavioural finance into a Heterogeneous Agent Model using the Brock and Hommes (1998) framework. Behavioural patterns are injected into an asset pricing framework through the so-called `Break Point Date', which allows us to examine their direct impact.…
New symmetry operators for differential forms on spheres.
problem Classifying symmetry breaking operators for differential forms.
method Illustrating a scheme for classification based on Program A-C.
result Generalization of scalar and local operator cases to differential forms.
This paper analyzes how kinetic terms in stock market equations can affect symmetry breaking.
problem Spontaneous symmetry breaking in quantum finance and its impact on stock market dynamics.
method Analyzes the role of kinetic terms in the context of the martingale condition in stock market equations.
result Kinetic terms can shift the effective location of the vacuum state, affecting symmetry breaking patterns.
Study symmetry breaking in quantum mechanics to understand many-body physics.
problem Understanding many-body physics from quantum mechanics.
method Analyzing potentials with unstable critical points and local minima.
result Emergence of many-body physics from spontaneous symmetry breaking.
The paper classifies and constructs differential symmetry breaking operators from a line bundle to a vector bundle over real projective spaces.
problem Classifying and constructing differential symmetry breaking operators.
method Utilizing factorization identities and branching laws of generalized Verma modules.
result Differential symmetry breaking operators from a line bundle to a vector bundle over real projective spaces are classified and constructed.
This paper examines how investors mislearn factor risk premia under structural breaks in a misspecified Bayesian framework.
problem Investors' mislearning of factor risk premia under structural breaks in asset pricing models.
method Proposes a minimal Bayesian framework to study how investors learn under a misspecified model that underestimates structural breaks.
result Elevated mislearning is associated with stronger long-horizon returns and Sharpe ratios, consistent with an equilibrium premium for acute model uncertainty.
Metric evaluates symmetry-breaking in datasets, revealing severe biases.
problem Symmetry-breaking in datasets can hinder the performance of symmetry-aware methods.
method Developed a metric to quantify symmetry-breaking using a two-sample classifier test.
result Symmetry-breaking can prevent optimal performance of invariant methods, even when labels are invariant.
SSA with a general recursive formula improves forecasting accuracy with structural breaks.
problem Forecasting time series with structural breaks.
method Singular Spectrum Analysis (SSA) with a general non-linear recurrence formula.
result SSA with the general recursive formula outperforms basic SSA and SSA bootstrap forecasting.
The paper finds formulas for Willmore surfaces and discusses symmetry breaking.
problem Understanding symmetry and symmetry breaking in Willmore surfaces.
method Proved explicit formulas and demonstrated symmetry breaking examples.
result Symmetric boundary conditions do not guarantee symmetric surfaces.
Compact framework for neural network representation and gradient calculation.
problem Non-standardized representation and component-based gradient calculation methods in neural networks.
method Standard notation and direct gradient calculation over the inner product space of parameters.
result General framework applied to Multilayer Perceptrons and Deep Autoencoders.