Tsallis
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Related Articles from SNS
A Perturbed q-Tsallis Self-Concordant Barrier for Spectrally Robust Semidefinite Programming
Announce Type: cross Abstract: We introduce and analyse a perturbed $q$-Tsallis barrier for semidefinite programming (SDP), defined as a spectral perturbation of the classical log-det barrier on the cone of positive definite matrices. The barrier introduces eigenvalue-adaptive stiffening through a Tsallis-type matrix-power term controlled by parameters $q>1$ and $\eta\geq0$. Our main theoretical contribution is a sharp characterisation of the differential self-concordance regime of the...
A q-Tsallis Safe Approximation for Chance-Constrained Programs
Announce Type: new Abstract: Classical chance-constrained programs are solved by safe approximations based on the empirical CVaR, which uses a uniform measure over scenarios and systematically underweights tail events under heavy-tailed distributions. We introduce \emph{q-CCP}, a non-extensive safe approximation grounded in the Riemannian geometry of the Tsallis statistical manifold: the rank-based q-CVaR escort weights are the $g^{(q)}$-geodesic projection onto the tail simplex face, and...
Group Entropies and Mirror Duality: A Class of Flexible Mirror Descent Updates for Machine Learning
arXiv:2603.08651v2 Announce Type: replace Abstract: We introduce a comprehensive theoretical and algorithmic framework that bridges formal group theory and group entropies with modern machine learning, paving the way for an infinite, flexible family of Mirror Descent (MD) optimization algorithms. Our approach exploits the rich structure of group entropies, which are generalized entropic functionals governed by group composition laws, encompassing and significantly extending all trace-form...
Beyond Gaussian Statistics in Polymer Melts: Statistical Masking of Persistent Local Constraints
arXiv:2605.25989v2 Announce Type: replace-cross Abstract: Short polymer chains exhibit clear deviations from Gaussian end-to-end distance statistics, yet the molecular mechanism by which Gaussian behavior is recovered in long chains remains unestablished. Atomistic molecular dynamics simulations of polyethylene melts reveal that conformational heterogeneity persists at the Kuhn scale across all chain lengths, consisting of a mosaic of slow-relaxing, extended aligned chain segments (ACS) and...