We recently showed that the S&P500 stock market index is well described by Tsallis non-extensive statistics and nonlinear Fokker-Planck time evolution. We argued that these results should be applicable to a broad range of markets and exchanges where anomalous diffusion and `heavy' tails of the distribution are present.…
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48 results for “non-extensive systems”
Excess Demand Financial Market Modelcond-mat.stat-mech
Recently we reported on an application of the Tsallis non-extensive statistics to the S&P500 stock index. There we argued that the statistics are applicable to a broad range of markets and exchanges where anamolous (super) diffusion and 'heavy' tails of the distribution are present, as they are in the S&P500. We have c…
This paper uses Tsallis relative entropy to optimize stock portfolios, showing better consistency in risk-return profiles.
problem Optimizing stock portfolios with consistent risk-return profiles.
method Constructing portfolios by binning risk values and allocating stocks based on risk values, comparing with four risk measures.
result Tsallis relative entropy yields more consistent risk-excess return profiles compared to other measures.
This research improves value-at-risk estimation during financial crises using non-extensive statistical methods.
problem Underestimation of value-at-risk during financial crises.
method Non-extensive value-at-risk model based on Tsallis entropy and q-Gaussian probability density function.
result The q-Gaussian model provides better value-at-risk estimation during financial crises.
Maximizing energy on flexible curves yields regular or convex polygons.
problem Finding the shape of a flexible curve that maximizes a given energy function.
method Analyzing the energy function and properties of flexible curves.
result Maximizers are regular or convex n-gons, with each edge of length 1.
On anomalous distributions in intra-day financial time series and Non-extensive Statistical Mechanicscond-mat.stat-mech
In this paper one studies the distribution of log-returns (tick-by-tick) in the Lisbon stock market and shows that it is well adjusted by the solution of the equation, {}, which corresponds to a generalization of the differential …
Euclidean and Riemannian Geometrical Approaches to Non-Extensive Thermo-Statistical Mechanicscond-mat.stat-mech
I introduce a new geometrical approach to thermo--statistical mechanics. Here I highlight the main physical ideas, and how do they translate into geometrical language. I contrast the present approach with previous thermo--statistical--geometrical formalisms, (pseudo-)Riemannian [Weinhold 1975; Ruppeiner 1979] as well a…
Financial Market Dynamicscond-mat.stat-mech
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S&P500…
This paper presents an empirical investigation of the intraday Brazilian stock market price fluctuations, considering q-Gaussian distributions that emerge from a non-extensive statistical mechanics. Our results show that, when returns are measured over intervals less than one hour, the empirical distributions are well …
The exponentially truncated q-distribution: A generalized distribution for real complex systemscond-mat.stat-mech
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus can not be used as a standard distribution. Normally professionals in the area …
Characteristic Function of the Tsallis -Gaussian and Its Applications in Measurement and Metrologystat.CO
Paper presents characteristic function of Tsallis q-Gaussian and its applications.
problem Modeling input quantities in measurement models using Tsallis q-Gaussians.
method Developed a characteristic function and proposed a numerical method for its inversion.
result Exact probability distribution of output quantities can be determined.
This work models financial market returns with asymmetric Tsallis distributions, improving fit over symmetric q-Gaussians.
problem Non-symmetric behavior of stock market returns over time scales.
method Linear combination of two independent normalized half q-Gaussians with different parameters.
result Asymmetric distributions provide better fits to stock market returns than symmetric q-Gaussians, especially over longer time scales.
For the first time ever, we analyze a unique public procurement database, which includes information about a number of bidders for a contract, a final price, an identification of a winner and an identification of a contracting authority for each of more than 40,000 public procurements in the Czech Republic between 2006…
We seek to utilize the nonextensive statistics to the microscopic modeling of the interacting many-investor dynamics that drive the price changes in a market. The statistics of price changes are known to be fit well by the Students-T and power-law distributions of the nonextensive statistics. We therefore derive models…
Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of non-extensive thermostatistics. We show that these functions are suitable to describe and un…
Tsallis Relative entropy from asymmetric distributions as a risk measure for financial portfoliosq-fin.ST
New method uses asymmetric Tsallis relative entropy for better risk assessment in financial portfolios.
problem Improving risk assessment for financial portfolios using asymmetric data.
method Generalized Tsallis relative entropy (ATRE) for asymmetric distributions of returns.
result ATRE shows better risk-return profiles, especially during market crashes.
In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is we…
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.
A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in $\bbR^n$, or $\bbS^n$, $n\in \bbN$, which are distributed according to the configurational microcanonical measure , or rather some regularization thereof, where H is the configu…
The paper proves new applications of knot invariants and smooth group actions on 3-spheres.
problem Proving the Milnor conjecture and understanding smooth group actions on Brieskorn spheres.
method Developing equivariant Seiberg-Witten-Floer cohomology and applying it to knot invariants and smooth group actions.
result New proofs of the Milnor conjecture and insights into smooth group actions on Brieskorn spheres.
Study analyzes stock market dynamics using Tsallis statistics and GHE, revealing pre-bubble and post-bubble market characteristics.
problem Understanding stock market dynamics and predicting market bubbles.
method Non-linear analysis using time-dependent Tsallis statistics and Generalized Hurst Exponents.
result Temporal trends of q-triplet values differ before and after market bubbles, indicating significant market dynamics changes.
Overview of integrable systems with symmetries, focusing on toric and semitoric systems.
problem Classifying and understanding integrable systems with symmetries.
method Using decorated polygons and controlled bifurcations in one-parameter families of systems.
result Construction of explicit semitoric systems with prescribed invariants.
New method to derive integrable systems from existing Lax systems.
problem Deriving new integrable systems from existing ones.
method Systematic method of deriving new integrable systems from a given one.
result Examples of new integrable systems derived, including the dispersionless Hirota equation, the general heavenly equation, and the web equations.
Learning to control linear systems is statistically hard, especially for underactuated systems.
problem Statistical difficulty of learning to control linear systems, especially underactuated ones.
method Utilized minimax lower bounds and structural assumptions to prove learning complexity can be exponential.
result Learning complexity can be at most exponential with the controllability index of the system.
Discrete-time systems can be characterized by simple flat coordinates and their shifts.
problem Characterizing flatness of discrete-time systems.
method Developed a map from flat coordinates and their shifts to system state and input, fulfilling system equations identically.
result Derived necessary conditions for a system to be flat, without requiring differential geometry methods.
The paper explores when linear system identification is hard or easy, especially for under-actuated systems.
problem Statistical hardness of learning linear systems, especially under-actuated or under-excited systems.
method Using tools from minimax theory and recent statistical tools for finite sample analysis of system identification.
result The controllability index of linear systems affects the sample complexity of identification, making some systems hard to learn.
This paper improves system identification by reducing sample complexity for high-dimensional linear dynamical systems.
problem High sample complexity for learning partially observed linear dynamical systems in high dimensions.
method Introduces an -regularized estimation method that reduces sample complexity from linear to logarithmic with system dimension.
result Markov parameters can be learned with logarithmic number of samples relative to system dimension, improving sample complexity.
In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.
problem Existence of Riemannian invariants for integrable systems of hydrodynamic type.
method Finding coordinates where the generator and all symmetries are diagonal.
result In integrable hydrodynamic systems, there exist coordinates where the generator and all symmetries are diagonal.
Nonholonomic Controlled Hamiltonian System: Symmetric Reduction and Hamilton-Jacobi Equationsmath.SG
This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.
problem Analyzing nonholonomic constraints in Hamiltonian systems.
method Deriving distributional RCH systems, geometric constraint conditions, and Hamilton-Jacobi theorems.
result Derives precise geometric constraint conditions and Hamilton-Jacobi theorems for nonholonomic systems.
New method models unknown systems with hidden parameters using neural networks.
problem Modeling unknown dynamical systems with hidden parameters.
method Training a deep neural network (DNN) model using trajectory data of the unknown system.
result DNN model accurately predicts unknown dynamical systems with new initial conditions.
A new financial system with ethics risk modeled using fractional calculus.
problem Modeling financial systems with ethical considerations and market confidence.
method Introduced a five-dimensional conformable derivative financial system and a discretization scheme.
result Numerical solutions of the conformable derivative system were tested for hyperchaos.
MLSys aims to bridge ML and systems research.
problem Designing ML systems for real-world deployment is challenging.
method Foster a new conference and research community.
result MLSys conference focuses on intersection of systems and ML.
Paper analyzes CCT sensitivity in constrained power systems, offering insights into system stability and parameter changes.
problem Identifying preventive control measures to avoid large generation losses during disturbances.
method Derived first-order CCT sensitivity for generic constrained power systems using trajectory sensitivity computation.
result Sensitivity of CCT to system parameters, providing insights into feasibility and stability.
Estimates input from output of nonlinear systems using ANN.
problem Estimating unknown compositional input from system output.
method Artificial Neural Networks (ANNs) for nonlinear system inversion.
result ANNs can compete with optimal bounds for linear systems and demonstrate promising results for nonlinear systems.
Study absolute equivalence for Pfaffian systems, applying to control systems.
problem Absolute equivalence of Pfaffian systems with specific independence conditions.
method Structural results for Pfaffian systems of corank 3, applied to control systems.
result Dynamic feedback linearization of control systems with 2 inputs.
Solves selecting the best optimizing system problems.
problem Selecting the best system among contenders with unknown performance.
method Adaptive algorithms integrating stochastic gradient descent and sequential elimination.
result Exponential rates of convergence to zero for false selection probability.
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and nonholonomic const…
Two new methods improve efficiency of conformal predictive systems.
problem Efficiency of conformal predictive systems in regression problems.
method Split conformal predictive systems and cross-conformal predictive systems.
result Cross-conformal predictive systems are more efficient but not guaranteed valid.
Superintegrable systems on curved manifolds found to have Hessian structures.
problem Characterizing superintegrable systems on curved manifolds.
method Identifying and computing Hessian coordinates for superintegrable systems.
result Examples of superintegrable systems in 2D and 3D have natural Hessian coordinates.
Measures of Systemic Riskq-fin.RM
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The current paper proposes a…
The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.
problem Finding general solutions for Lie systems.
method Develops mixed superposition rules for Lie systems with imprimitive Lie algebras and semidirect sums.
result Extends coalgebra method to Lie systems of partial differential equations.
Researchers solve boundary and scattering rigidity problems for magnetic systems.
problem Recovering magnetic systems from boundary or scattering data.
method Reduced to magnetic systems and applied results from [DPSU07].
result Recovering -system up to a gauge.
Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.
problem Reduction of controlled Lagrangian systems with symmetry and momentum map.
method Using Legendre transformation and Euler-Lagrange vector field, the paper extends symmetric reduction theory.
result Established regular reduction theory for RCL systems with symmetry and momentum map.
This paper proposes a system-agnostic policy for dynamic scheduling.
problem Dynamic scheduling in changing systems is challenging due to system-specific optimal policies.
method Descriptive policy that learns a system-agnostic scheduling principle.
result System-agnostic meta-learning enables adaptation to unseen system characteristics.
The paper studies connections in superintegrable systems, revealing geometric insights.
problem Understanding non- and semi-degenerate superintegrable systems.
method Analyzes two torsion-free connections associated with superintegrable systems.
result Semi-degenerate secondary structure tensor is the Ricci curvature of a natural torsion-free connection.
Learn dynamics of a system using auxiliary data from similar systems.
problem Learning dynamics of a linear system with limited data.
method Weighted least squares approach, incorporating auxiliary data.
result Auxiliary data can help reduce intrinsic error due to noise.
The inability to see and quantify systemic financial risk comes at an immense social cost. Systemic risk in the financial system arises to a large extent as a consequence of the interconnectedness of its institutions, which are linked through networks of different types of financial contracts, such as credit, derivativ…
New adaptive conformal predictive systems developed.
problem Severe restrictions on adapting predictive distributions to test objects.
method Calibrating existing predictive systems to ensure full adaptability and validity.
result Developed fully adaptive split-conformal and cross-conformal predictive systems.