We consider the problem of estimating the partition function $Z(β)=\sum_x \exp(β(H(x))$ of a Gibbs distribution with the Hamiltonian $H:Ω\rightarrow\{0\}\cup[1,n]$. As shown in [Harris & Kolmogorov 2024], the log-ratio $q=\ln (Z(β_{\max})/Z(β_{\...
This note examines financial distributions to competing teams at the end of the most famous multiple stage professional (male) bicyclist race, TOUR DE FRANCE. A rank-size law (RSL) is calculated for the team financial gains. The RSL is found to be hy...
The asymptotic efficiency of the spatial sign covariance matrix (SSCM) relative to affine equivariant estimates of scatter is studied in detail. In particular, the SSCM is shown to be asymptoticaly inadmissible, i.e. the asymptotic variance-covarianc...
First discovered by L. R. Taylor (1961, Nature), Taylor's Power Law (TPL) correlates the mean (M) population abundances and the corresponding variances (V) across a set of insect populations using a power function (V=aM^b). TPL has demonstrated its '...
Data from e+e- annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV were used to study moments of event shape distributions. The data were compared with Monte Carlo models and with predicti...
We present an Artificial Neural Network (ANN) model of photospheric lithium depletion in cool stars (3000 < Teff / K < 6500), producing estimates and probability distributions of age from Li I 6708A equivalent width (LiEW) and effective temperature d...
Jul 10, 2017 · In "cross"-entropy, as the name suggests, we focus on the number of bits required to explain the difference in two different probability distributions. The best case scenario is that both …
Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic distributions...
Consider the case of many sensors, each returning very different types of data (e.g., a camera returning images, a thermometer returning probability distributions, a newspaper returning articles, a traffic counter returning numbers). Additionally we...
We propose to develop a wide-field and ultra-high-precision photometric survey mission, temporarily named "Earth 2.0 (ET)". This mission is designed to measure, for the first time, the occurrence rate and the orbital distributions of Earth-sized plan...
The equation of state of the linear sigma model in the mean field approximation is used as input in a relativistic hydrodynamical numerical routine. Longitudinal and transverse energy distributions are calculated and compared with those obtained fr...
We explore the house price distributions for the English cities of London, Manchester, Bristol, Newcastle, Birmingham and Leeds. We find Pareto (power law) behaviour in their upper tails, which is clearly distinct from lognormal and gamma distributio...
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the present work is...
We study two M 51-type systems Arp 68 and Arp 58, which strongly differ by their stellar masses, gas content and environment. Long-slit spectral observations obtained at the 6-m telescope BTA were used to trace the distributions of a line-of-sight (L...
We compare the elongation rate and Xmax distributions for three air-fluorescence experiments: Stereo Fly's Eye, HiRes/MIA, and HiRes. A shift of 13 gm/cm^3 of the stereo Fly's Eye data, well within the quoted systematic errors, brings the elongatio...
We consider the CEO problem for non-regular source distributions (such as uniform or truncated Gaussian). A group of agents observe independently corrupted versions of data and transmit coded versions over rate-limited links to a CEO. The CEO then es...
Determining whether two sets of images belong to the same or different distributions or domains is a crucial task in modern medical image analysis and deep learning; for example, to evaluate the output quality of image generative models. Currently, m...
Motivated by Kleinberg's (2000) and subsequent work, we consider the performance of greedy routing on a directed ring of $n$ nodes augmented with long-range contacts. In this model, each node $u$ is given an additional $D_u$ edges, a degree chosen fr...
As many other machine learning driven medical image analysis tasks, skin image analysis suffers from a chronic lack of labeled data and skewed class distributions, which poses problems for the training of robust and well-generalizing models. The abil...