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Boguslaw Zegarlinski

Publications and source records attributed to Boguslaw Zegarlinski.

18 recordsLinked to original sources

Label-Efficient Learning for Ground-Based Sky-Image Classification: A Benchmark of Transfer Learning, Active Learning, and Pseudo-Labeling on GCD

Accurate ground-based cloud classification is important for atmospheric monitoring, solar-energy forecasting, aviation weather assessment, and climate observation systems. However, reliable sky-image annotation is time-consuming, especially when cloud types are visually similar or mixed. We study the label efficiency of deep learning for ground-based cloud classification using the Ground-based Cloud Dataset (GCD). Rather than proposing a new architecture, we benchmark three practical strategies under limited annotation budgets: supervised transfer learning, uncertainty-based active learning, and high-confidence pseudo-labeling. An ImageNet-pretrained ResNet50 is used as a common frozen backbone, with experiments repeated over five random seeds for label budgets from $1\%$ to $100\%$ of the training labels. Supervised transfer learning is already highly label-efficient: test accuracy increases from $0.635 \pm 0.018$ with $1\%$ labels to $0.730 \pm 0.002$ with $40\%$ labels, approaching the full-label result of $0.735 \pm 0.003$. Active learning and pseudo-labeling are competitive with supervised sampling and provide small improvements for some metrics and budgets, but neither gives a large or consistent aggregate gain. Diagnostic analyses show that accepted pseudo-labels are reliable, with accuracy from $0.946$ to $0.977$, but biased toward easier high-confidence sky-type groups. In contrast, uncertainty sampling preferentially queries visually challenging groups, including Mixed and the confusable Stratocumulus and Cumulonimbus groups, but these targeted acquisitions yield only modest gains. Overall, transfer learning substantially reduces annotation requirements for GCD, while simple active and semi-supervised strategies provide limited additional benefit over a strong supervised baseline.

cs.LG↗

Poincaré inequalities on Carnot Groups and spectral gap of Schrödinger operators

In this work we give a sufficient condition under which the global Poincaré inequality on Carnot groups holds true for a large family of probability measures absolutely continuous with respect to the Lebesgue measure. The density of such probability measure is given in terms of homogeneous quasi-norm on the group. We provide examples to which our condition applies including the most known families of Carnot groups. This, in particular, allows to extend the results in the previous work [CFZ21]. A consequence of our result is that the associated Schrödinger operators have a spectral gap.

math.FA↗

On thermally driven fluid flows arising in astrophysics

We consider the Navier-Stokes-Fourier-Poisson system driven by an inhomogeneous temperature distribution on the boundary of an exterior fluid domain. We impose the finite mass constraint, positive far field condition for the temperature as well as the no--slip boundary conditions for the velocity. The existence of global--in--time weak solutions and the weak-strong principle are proved.

math.AP↗

KMS Dirichlet forms, coercivity and super-bounded Markovian semigroups on von Neumann algebras

We introduce a construction of Dirichlet forms on von Neumann algebras M associated to any eigenvalue of the Araki modular Hamiltonian of a faithful normal non tracial state, providing also conditions by which the associated Markovian semigroups are GNS symmetric. The structure of these Dirichlet forms is described in terms of spatial derivations. Coercivity bounds are proved and the spectral growth is derived. We introduce a regularizing property of positivity preserving semigroups (superboundedness) stronger than hypercontractivity, in terms of the symmetric embedding of M into its standard space L2(M) and the associated noncommutative Lp(M) spaces. We prove superboundedness for a special class of positivity preserving semigroups and that some of them are dominated by the Markovian semigroups associated to the Dirichlet forms introduced above, for type I factors M. These tools are applied to a general construction of the quantum Ornstein-Uhlembeck semigroups of the Canonical Commutation Relations CCR and some of their non-perturbative deformations.

math.OA↗

Dissipative dynamics for infinite lattice systems

We study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of explicit examples of such models. Using an idea of quasi-invariance of a state, we show how one can construct unitary representations of various groups. Moreover in models with locally conserved quantities associated to an infinite lattice we show that there is no spectral gap and the corresponding dissipative dynamics decay to equilibrium polynomially in time.

math-ph↗

$q$-Poincaré inequalities on Carnot Groups with filiform type Lie algebra

In this paper, we prove (global) $q$-Poincaré inequalities for probability measures on nilpotent Lie groups with filiform Lie algebra of any length. The probability measures under consideration have a density with respect to the Haar measure given as a function of a suitable homogeneous norm.

math.FA↗

Coercive Inequalities on Carnot Groups: Taming Singularities

In the setting of Carnot groups, we propose an approach of taming singularities to get coercive inequalities. To this end, we develop a technique to introduce natural singularities in the energy function $U$ in order to force one of the coercivity conditions. In particular, we explore explicit constructions of probability measures on Carnot groups which secure Poincaré and even Logarithmic Sobolev inequalities. As applications, we get analogues of the Dyson-Ornstein-Uhlenbeck model on the Heisenberg group and obtain results on the discreteness of the spectrum of related Markov generators.

math.FA↗

Spectral Gap Inequalities on Nilpotent Lie Groups in Infinite Dimensions

We develop a general framework for spectral gap inequalities for Gibbs measures on infinite dimensional spin spaces over nilpotent Lie groups in terms of weak U-bounds and weak single-site spectral gap inequalities. We then provide sufficient conditions on the local specification and give examples of measures constructed using the Kaplan norm and generalising a few results for the Carnot-Caratheodory distance on the Heisenberg group.

math.FA↗

Logarithmic Schrödinger Equations in Infinite Dimensions

We study the logarithmic Schrödinger equation with finite range potential on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we associate and construct a global Gibbs measure and show that it satisfies a logarithmic Sobolev inequality. We find estimates on the solutions in arbitrary dimension and prove the existence of weak solutions to the infinite-dimensional Cauchy problem.

math.AP↗

Higher Order Coercive Inequalities

We study the higher order q- Poincaré and other coercive inequalities for a class probability measures satisfying Adam's regularity condition.

math.FA↗

A non-linear kinetic model of self-propelled particles with multiple equilibria

We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single particle phase-space, of a collection of interacting particles confined to move on the one-dimensional torus. The corresponding stochastic differential equation for the position and velocity of the particles is a conditional McKean-Vlasov type of evolution (conditional in the sense that the process depends on its own law through its own conditional expectation). In this paper, we study existence and uniqueness of the solution of the PDE in consideration. Challenges arise from the fact that the PDE is neither elliptic (the linear part is only {\em hypoelliptic}) nor in gradient form. Moreover, for some specific choices of the interaction function and for the simplified case in which the density profile does not depend on the spatial variable, we show that the model exhibits multiple stationary states (corresponding to the particles forming a coordinated clockwise/anticlockwise rotational motion) and we study convergence to such states as well. Finally, we prove mean-field convergence of an appropriate $N$-particles system to the solution of our PDE: more precisely, we show that the empirical measures of such a particle system converge weakly, as $N \rightarrow \infty$, to the solution of the PDE.

math-ph↗