We describe financial systems as condensates, similar to Bose-Einstein condensates, and calculate statistical distributions following from the model. The calculated distributions of investments into speculated financial assets are found equivalent to a Pareto distribution, and the calculated distributions of the price …
Dataset of Bose-Einstein condensates images aids ML in many-body physics.
problem Understanding solitons in Bose-Einstein condensates.
method Machine learning (ML) framework with convolutional neural networks and physics-informed classifiers.
result Automatic labeling of solitonic excitations in experimental images.
The Yukawa term in statistical mechanics quantifies information generation.
problem Understanding information generation in statistical mechanics.
method Defining a statistical product and Yukawa term to quantify information generation.
result The Yukawa term diverges in the quantum case, indicating Bose-Einstein condensation.
The study analyzes social and economic systems using bosonic and fermionic statistics.
problem Analyzing hierarchical social and economic systems.
method Intermediate Gentile statistics and derivation of thermodynamic laws.
result Introduces concepts like temperature and pressure for economic systems.
A theory of exceptional extreme events, characterized by their abnormal sizes compared with the rest of the distribution, is presented. Such outliers, called "dragon-kings", have been reported in the distribution of financial drawdowns, city-size distributions (e.g., Paris in France and London in the UK), in material f…
We introduce an irreversible discrete multiplicative process that undergoes Bose-Einstein condensation as a generic model of competition. New players with different abilities successively join the game and compete for limited resources. A player's future gain is proportional to its ability and its current gain. The the…
We examine on the static and dynamical properties of quantum knots in a Bose-Einstein condensate. In particular, we consider the Gross-Pitaevskii model and revise a technique to construct ab initio the condensate wave-function of a generic torus knot. After analysing its excitation energy, we study its dynamics relatin…
Researchers create topologically protected knots in a realizable system.
problem Creating topologically protected vortex knots in experimentally realizable systems.
method Investigated non-Abelian vortices in tetrahedral order in spin-2 Bose--Einstein condensates and bent-core nematic liquid crystals.
result Discovered the first topologically protected knots in an experimentally realizable system.
The origin of economic crises is a key problem for economics. We present a model of long-run competitive markets to show that the multiplicity of behaviors in an economic system, over a long time scale, emerge as statistical regularities (perfectly competitive markets obey Bose-Einstein statistics and purely monopolist…
Topologically protected vortex knots and links are proposed and proven.
problem Decaying of tangled vortex structures through local reconnections and strand crossings.
method Proposed and proven topologically protected vortex structures using non-Abelian topological vortices.
result Existence of topologically protected Q8-colored links and classification using the Q-invariant. We applied Dirac distribution, Bose-Einstein distribution, and occasionally Boltzmann-Gibbs distribution in order to determine which is optimal for income distribution on a large pool of countries. The best fit to the data was observed in the case of Fermi-Dirac distribution, for which the coefficient of determination …
Study local topological constraints on Berry curvature in spin-orbit coupled Bose-Einstein condensates.
problem Understanding local topological obstructions to flattening Berry curvature in spin-orbit-coupled Bose-Einstein condensates.
method Adapting Pigazzini-Toda lower bound to Kaluza-Klein setting, analyzing harmonic part of torsion 3-form, and using exact pointwise curvature analysis.
result Obstruction kernel vanishes, preventing complete gauging-away of Berry phases even at zero net topological charge.
The study describes society as a probabilistic system with entropy and diversity, finding new statistical approaches.
problem Understanding entropy and diversity in social systems.
method Modeling society as a probabilistic system, analyzing entropy and inequality, applying thermodynamic principles.
result New statistical approaches (Fermi-Dirac and Bose-Einstein) for employment and income distribution.
Income and wealth distribution affect stability of a society to a large extent and high inequality affects it negatively. Moreover, in the case of developed countries, recently has been proven that inequality is closely related to all negative phenomena affecting society. So far, Econophysics papers tried to analyse in…
Study lightlike submanifolds in indefinite statistical manifolds, finding conditions and curvature expressions.
problem Characterize lightlike submanifolds in indefinite statistical manifolds.
method Analyze conditions for lightlike submanifolds to be lightlike statistical submanifolds, derive statistical sectional curvature, and investigate induced statistical Ricci tensor symmetry.
result Conditions for lightlike submanifolds to be lightlike statistical submanifolds and expressions for statistical sectional curvature and induced Ricci tensor symmetry.
Study on statistical properties of Kenmotsu statistical manifolds and inequalities.
problem Investigate statistical curvature properties and inequalities in Kenmotsu statistical manifolds.
method Optimization techniques on submanifolds to prove inequalities.
result Proved a Chen-Ricci inequality for statistical submanifolds in Kenmotsu statistical manifolds.
Study anti-invariant submersions from holomorphic statistical manifolds.
problem Understanding submersions in statistical manifolds.
method Introduced and analyzed anti-invariant holomorphic statistical submersions.
result Supported results with examples.
Study on solitons in Kenmotsu statistical manifolds and submanifolds.
problem Investigating solitons in Kenmotsu statistical manifolds and their submanifolds.
method Examined statistical solitons and Yamabe solitons, studied curvature properties, and analyzed submanifolds with concircular and concurrent vector fields.
result Discussed the behavior of almost quasi-Yamabe solitons on submanifolds of Kenmotsu statistical manifolds.
Unified approach to private statistics from empirical to population data.
problem Divided focus on empirical vs population statistics in private statistics.
method Unified methods for both types of statistics.
result Methods for empirical statistics can be applied to population statistics.
The paper explores conditions for statistical manifolds to be immersed and dual to each other.
problem Conditions for statistical manifold structures to be dual and immersions into statistical manifolds.
method Obtained necessary and sufficient conditions for dual structures and immersion properties.
result Conditions for realizing and realizing in a dually flat statistical manifold of codimension two.
Study on statistical manifolds with product structures and their properties.
problem Investigating statistical manifolds with almost product structures.
method Proving properties of para-Kähler-like statistical manifolds and deriving properties of statistical submersions compatible with almost product structures.
result The statistical structure of a para-Kähler-like statistical manifold of constant curvature is a Hessian structure.
The paper introduces a statistical version of contact CR-product for Sasakian statistical manifolds.
problem Characterizing geometric properties of contact CR-submanifolds in Sasakian statistical manifolds.
method Characterization of integrability of invariant and anti-invariant distributions, development of results on specific types of contact CR submanifolds, introduction of statistical contact CR-product.
result Introduction of a statistical version of contact CR-product for Sasakian statistical manifolds.
Lightlike hypersurfaces in statistical manifolds have unique geometric properties.
problem Characterizing lightlike hypersurfaces in statistical manifolds.
method Analyzing geometric properties and induced structures of lightlike hypersurfaces.
result Lightlike hypersurfaces are not statistical manifolds but have a canonical screen distribution.
Optimization method yields geometric inequalities for submanifolds in statistical warped product manifolds.
problem Optimizing geometric inequalities for submanifolds in statistical warped product manifolds.
method Optimization techniques applied to statistical submanifolds in statistical warped product manifolds.
result Optimal Casorati inequalities and Chen-Ricci inequality derived for statistical submanifolds.
Enhances power of covariance matrix tests for high-dimensional data.
problem Testing large covariance matrices in high-dimensional data.
method Proposes a new Fisher's combined probability test for quadratic form and maximum form statistics.
result Boosts power against more general alternatives.
The Bonnet theorem is proven for statistical manifolds.
problem Locally embeddable statistical manifolds in flat spaces.
method Using statistical embedding and the Gauss--Codazzi--Ricci equations.
result Statistical manifolds with specific tensor properties are locally embeddable to flat statistical manifolds.
This paper simplifies computing higher-order U-statistics efficiently.
problem The inefficiency of computing higher-order U-statistics in practice. method Decomposition, connection to Einstein summation, and treewidth-based complexity estimate.
result A new, more efficient algorithm to compute U-statistics. Researchers use physics methods to predict gaps between computational and statistical problems.
problem Understanding gaps between information-theoretically possible but computationally unsolvable problems.
method Heuristics based on statistical physics.
result Predictions of computational-to-statistical gaps in statistical problems.
This work uses statistical mechanics to explain AI learning.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine learning.
Author presents the second variational formula for statistical biharmonic maps.
problem Developing a formula for statistical biharmonic maps.
method Introduced the second variational formula for the statistical bi-energy functional.
result The second variational formula can be represented using Hessian curvature in Hessian manifolds.
New statistics are introduced that maintain the Fisher metric structure closely, akin to sufficient statistics.
problem Maintaining the Fisher metric structure in statistical models.
method Characterizing statistics that maintain the Fisher metric structure bi-Lipschitz equivalently.
result Characterized statistics that preserve the Fisher metric structure closely.
Study CR-statistical submanifolds in holomorphic statistical spaces.
problem Characterize CR-statistical submanifolds and their properties.
method Optimization technique to relate Ricci curvature and mean curvature.
result Established relationship between Ricci curvature and mean curvature.
Proves Gerber statistic is always non-negative.
problem Verifying the positive semi-definiteness of Gerber statistic.
method Analytical proof of both forms of Gerber statistic.
result Gerber statistic is positive semi-definite.
The study examines almost cosymplectic statistical manifolds and their properties.
problem Characterizing and understanding almost cosymplectic statistical manifolds.
method Analyzing basic properties, proving a characterization theorem, studying curvature, and constructing examples.
result Characterization theorem and corollary for almost cosymplectic statistical manifolds with Kaehler leaves.
New statistical manifolds derived from identity map biharmonicity.
problem Deriving new statistical manifolds from identity map biharmonicity.
method Statistical biharmonicity of identity maps, semi-equiaffine condition, constant curvature.
result Determined statistical structures of new class of manifolds.
Paper develops risk statistics for portfolios considering regulator-based risk.
problem Traditional risk statistics fail to describe regulator-based risk.
method Develop dual representation for regulator-based risk statistics.
result Derived dual representation for regulator-based risk statistics.
Active inference framework improves U-statistic estimation efficiency.
problem Costly acquisition of labels for U-statistics. method Active inference framework with optimal sampling rule.
result Substantial gains in estimation efficiency over baseline methods.
Sharp inequalities and solitons studied in statistical submersions.
problem Understanding geometric properties of statistical submersions.
method Proving sharp inequalities and establishing geometrical properties of statistical submersions.
result Characterization of fibers as Ricci-Bourguignon solitons with conformal vector field.
A new method uses bandits to select summary statistics for Bayesian inference.
problem Dynamic selection of summary statistics for likelihood-free inference.
method Treats summary statistic selection as a multi-armed bandit problem.
result Improves efficiency and scalability of approximate Bayesian computation.
Survey of statistical queries and their applications.
problem Understanding statistical queries and their applications.
method Exploration of statistical queries model, definitions, and connections to learnability.
result Connections to learnability and applications in optimization, evolvability, and differential privacy.
Introduces generalized almost statistical convergence and its properties.
problem Developing a new convergence concept for sequences.
method Introducing generalized almost statistical convergence and proving its properties.
result Existence of a GAS convergent sequence that is neither statistical nor almost convergent.
Paper discusses the Fisher metric and differentiability in statistical models.
problem Understanding the relationship between Fisher metric and differentiability in statistical models.
method Comparison of different concepts and models in Information Geometry, mathematical statistics, and measure theory.
result Discussion of various models and their differentiability properties.
Study on lightlike geometry in indefinite Sasakian statistical manifolds.
problem Exploring lightlike hypersurfaces and their properties in indefinite Sasakian statistical manifolds.
method Introducing indefinite Sasakian statistical manifolds and analyzing lightlike hypersurfaces with respect to dual connections.
result An invariant lightlike submanifold of an indefinite Sasakian statistical manifold is itself an indefinite Sasakian statistical manifold.
A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and…
Machine learning used in German official statistics.
problem Identifying areas and tasks where machine learning is applied in official statistics.
method Surveys conducted at statistical institutions and divisions of Destatis.
result Machine learning methods are used in various statistical areas and tasks.
The paper derives Chen inequalities for statistical submanifolds in cosymplectic manifolds.
problem Deriving Chen inequalities for statistical submanifolds in cosymplectic manifolds.
method Analyzing statistical cosymplectic manifolds and Legendrian submanifolds to derive Chen inequalities.
result Chen inequalities for statistical submanifolds in cosymplectic manifolds and Legendrian submanifolds are derived.
Unified framework for Bayesian and Frequentist statistics.
problem Embedding Bayesian statistics within a broader decision-making framework.
method Game theory and statistical analysis.
result Statistical games unify Bayesian and Frequentist statistics.
New risk statistics for loss-based regulation.
problem Regulatory focus on losses over gains.
method Developed new risk statistics using scenario analysis.
result New risk statistics extend existing measures.