Article
Chemistry, Multidisciplinary
Der-Wen Chang, Chih-Wei Lu, Yu-Jhang Tu, Shih-Hao Cheng
Summary: This study verifies the settlement and soil reaction mechanisms of a surface raft foundation under different soil conditions using three-dimensional finite-element analyses. The results indicate that soil reactions are strongly influenced by soil stiffness and foundation dimensions, and different soil types also have different effects on soil reactions.
APPLIED SCIENCES-BASEL
(2022)
Article
Mathematics
Victor A. Boichenko, Alexey A. Belov, Olga G. Andrianova
Summary: An axiomatic development of control systems theory can systematize important concepts. The current research article investigates and compares two axiomatic approaches for analyzing discrete linear time-invariant systems affected by external random disturbances. The main goal of the paper is to explore and compare the anisotropy-based theory with the spectral entropy approach. The spectral entropy approach is shown to be mathematically rigorous and it proves that anisotropy-based controllers can guarantee the desired disturbance attenuation level for a wider set of input random signals.
Article
History & Philosophy Of Science
Michael Nielsen
Summary: The author demonstrates the equivalence between de Finetti's coherence theorem and the Hahn-Banach theorem, discussing the implications of this result. The coherence theorem implies the existence of a fair countable lottery and sets that are not Lebesgue measurable, offering a subjective interpretation in line with de Finetti's views. The study suggests that de Finetti's theory of subjective probability is inherently nonconstructive, prompting questions about the coherence theorem's ability to support a legitimate theory of rational belief.
Article
Physics, Multidisciplinary
Karl Svozil
Summary: This passage discusses extending Kolmogorov's axioms of probability theory to conditional probabilities among distinct contexts, which generalizes approaches to quantum probabilities.
Article
Statistics & Probability
Steven R. Howard, Aaditya Ramdas, Jon McAuliffe, Jasjeet Sekhon
Summary: The study develops confidence sequences with confidence intervals that are uniformly valid over an unbounded time horizon, and analyzes the widths of these intervals under nonparametric conditions. Connections are drawn between different concentration methods and the confidence sequences are extended to nonparametric settings, applied to covariance matrix estimation and estimation of sample average treatment effect.
ANNALS OF STATISTICS
(2021)
Article
History & Philosophy Of Science
Marco Zaffalon, Enrique Miranda
Summary: Recent work has formally linked the axiomatisation of incomplete preferences with the theory of desirability in the context of imprecise probability, showing that they are essentially the same theory. The equivalence has been established under the constraint of a finite set of possible prizes. This paper relaxes this constraint, creating one of the most general theories of rationality and decision making, and discusses the role of conglomerability as a rationality requirement.
Article
History & Philosophy Of Science
Toby Meadows
Summary: Consistency, interpretability, and probability are vital tools for mathematicians when comparing foundational theories. This paper focuses on theories that establish foundations for mathematics, particularly in set theory. It introduces a new framework called pointwise interpretability to address counterintuitive results and explores the application of this framework in the generic multiverse.
Review
Mathematics
Hykel Hosni, Jurgen Landes
Summary: This paper illustrates the usefulness of logical methods and techniques in the foundations and applications of reasoning under uncertainty, which are currently undervalued. The field encompasses logic, artificial intelligence, statistics, and decision theory. Instead of attempting a comprehensive survey, the paper focuses on a few notable examples. While the majority of attention is given to probabilistic frameworks for quantifying uncertainty, the paper also touches upon generalizations of probability measures that have gained significant interest in recent decades.
Article
Mathematics, Applied
Boyan Dimitrov
Summary: This article discusses the concept of axioms, presenting examples and emphasizing how axioms generate separate areas of study and application. Throughout, the importance of set theory for new areas of development is highlighted, as well as the impact of recent axioms such as uncertainty and probability on related fields.
Article
Mathematics, Applied
Marcin Kaminski
Summary: This paper presents the theoretical formulation and computational implementation of the Stochastic perturbation-based Finite Element Method (SFEM) for uncertainty analysis in solid mechanics with symmetric non-Gaussian input parameters. The method is based on general order Taylor expansions of all uncertain input parameters and state functions, with a focus on even orders only. The implementation of SFEM for the displacement version of FEM has been completed using statistically optimized nodal polynomial response bases, and the results have been validated using probabilistic semi-analytical approach and Monte-Carlo simulation.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2022)
Article
Physics, Multidisciplinary
Marcela Carena, Henry Lamm, Ying-Ying Li, Wanqiang Liu
Summary: This paper discusses the possibility of using improved Hamiltonians in quantum simulations of lattice gauge theories and designs corresponding quantum circuits. The effectiveness of this approach is demonstrated through explicit examples in Z(2) gauge theory.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
O. B. Ericok, J. K. Mason
Summary: Statistical thermodynamics is valuable for understanding equilibrium thermodynamic states, but there are unresolved questions about its foundations. This paper aims to develop statistical thermodynamics for finite non-equilibrium systems and proposes solutions to several paradoxes and thought experiments.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Engineering, Electrical & Electronic
Magda Amiridi, Nikos Kargas, Nicholas D. Sidiropoulos
Summary: This paper proposes a novel approach based on tensor factorization for non-parametric density estimation in high-dimensional multivariate data analysis. By using a tensor model of the characteristic function, the density can be accurately estimated and the curse of dimensionality can be overcome.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Computer Science, Theory & Methods
A. A. Vasil'eva
Summary: This paper provides order estimates for the nth Kolmogorov widths of the intersection of homothetic copies of the unit balls vB-alpha(pa)N in l(q)(N), where n <= N/2. This result for n = N/2 was obtained by Galeev in 1981.
JOURNAL OF COMPLEXITY
(2022)
Article
Mathematics, Applied
Emmanuil H. Georgoulis
Summary: This work focuses on developing a family of Galerkin finite element methods for the classical Kolmogorov equation, with the key attribute of admitting decay properties at the (semi)discrete level for general families of triangulations. The method construction combines ideas from the general theory of hypocoercivity developed by Villani and a judicious choice of numerical flux functions, allowing for robust error analysis for final times tending to infinity. The extension to three spatial dimensions is also briefly discussed.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2021)