We present a retrospective analysis of Czech anti-covid governmental measures’ effectiveness for an unusually long three years of observation. Numerous Czech government restrictive measures illustrate this analysis applied to three years of COVID-19 data from the first three COVID-19 cases detected on 1st March 2020 till March 2023. It illustrates the course from the dramatic combat of unknown illness to resignation to country-wide measures and placing COVID-19 into a category of common nuisances. Our analysis uses the derived adaptive recursive Bayesian stochastic multidimensional Covid model-based prediction of nine essential publicly available COVID-19 data series. The COVID-19 model enables us to differentiate between effective measures and solely nuisance or antagonistic provisions and their correct or wrong timing. Our COVID model allows us to predict vital covid statistics such as the number of hospitalized, deaths, or symptomatic individuals, which can serve for daily control of anti-covid measures and the necessary precautions and formulate recommendations to control future pandemics.

In this work we make progress in understanding the relationship between learning models when given access to entangled measurements, separable measurements and statistical measurements in the quantum statistical query ($\mathsf{QSQ}$) model. To this end, we show the following results. $\textbf{Entanglement versus separable measurements.}$ The goal here is to learn an unknown $f$ from the concept class $\mathcal{C} \subseteq \{f:\{0,1\}^n\rightarrow [k]\}$ given copies of $\frac{1}{\sqrt{2^n}}\sum_x \ket{x,f(x)}$. We show that, if $T$ copies suffice to learn $f$ using entangled measurements, then $O(nT^2)$ copies suffice to learn $f$ using just separable measurements. Additionally, we exhibit a concept class $\mathcal{C}$ for which, in order to learn some \emph{property} of $f$, the sample complexity of learning using entangled measurements is exponentially smaller than separable measurements. $\textbf{Entangled versus statistical measurements}$ The goal here is to learn a function $f \in \mathcal{C}$ given access to separable measurements and statistical measurements. We exhibit a concept class $\mathcal{C}$ based on degree-$2$ functions that gives an exponential separation between $\mathsf{QSQ}$ learning and quantum learning with entangled measurements (even in the presence of noise). This proves the "quantum analogue" of the seminal result of (Blum, 2003) that separates classical $\mathsf{SQ}$ learning from classical $\mathsf{PAC}$ learning with classification~noise. $\textbf{$\mathsf{QSQ}$ lower bounds for learning states.}$ The main technical contribution is to introduce a quantum statistical query dimension ($\mathsf{QSDA}$), which we use to give lower bounds on the $\mathsf{QSQ}$ complexity of learning. Using this, we prove exponential $\mathsf{QSQ}$ lower bounds for testing purity of quantum states, learning CCHL states, coset states of Abelian groups, degree-$2$ functions, planted bi-clique states and learning output states of Clifford circuits of depth polylog($n$). $\textbf{Further applications.}$ Using our $\mathsf{QSQ}$ lower bounds give an $\textit{unconditional}$ separation between weak and strong error mitigation and prove lower bounds for learning distributions in the $\mathsf{QSQ}$ model. Prior works by (Quek et al., 2022), (Hinsche et al., 2022), and (Neitner et al., 23) proved the analogous results $\textit{assuming}$ diagonal measurements and our work removes this assumption.

This paper introduces a novel multidimensional statistical model for realistic modeling, enlargement, editing, and compression of the recent state-of-the-art bidirectional texture function (BTF) textural representation. The presented multispectral compound Markov random field model (CMRF) efficiently fuses a non-parametric random field model with several parametric random fields models. The primary purpose of our modeling texture approach is to reproduce, compress, and enlarge a given measured natural or artificial texture image so that ideally both natural and synthetic texture will be visually indiscernible for any observation or illumination directions. However, the model can be easily applied for BFT material texture editing as well. The CMRF model consists of several parametric sub-models each having different characteristics along with an underlying switching structure model which controls transitions between these sub models. The proposed model uses the non-parametric random field for distributing local texture models in the form of analytically solvable wide-sense BTF Markov representation for single regions among the fields of a mosaic approximated by the random field structure model. The non-parametric control field of BTF -CMRF is reiteratively generated to guarantee identical region-size histograms for all material sub-classes present in the target example texture. The local texture regions (not necessarily continuous) are represented by analytical BTF models modeled by the adaptive 3D causal auto-regressive (3DCAR) random field model which can be analytically estimated as well as synthesized. The visual quality of the resulting complex synthetic textures generally surpasses the outputs of the previously published simpler non-compound BTF -MRF models. The model allows reaching huge compression ratio incomparable with any standard image compression method.

Visual texture modeling based on multidimensional mathematical models is the prerequisite for both robust material recognition as well as for image restoration, compression or numerous physically correct virtual reality applications. A novel multispectral visual texture modeling method based on a descriptive, unusually complex, three-dimensional, spatial Gaussian mixture model is presented. Texture synthesis benefits from easy computation of arbitrary conditional distributions from the model. The model is inherently multispectral thus it does not suffer with the spectral quality compromises of the spectrally factorized alternative approaches. The model is especially well suited for multispectral textile textures and it can also describe the most advanced textural representation in the form of a bidirectional texture function (BTF).

This paper describes a novel compound Markov random field model capable of realistic modelling of multispectral bidirectional texture function, which is currently the most advanced representation of visual properties of surface materials. The proposed compound Markov random field model combines a non-parametric control random field with analytically solvable wide sense Markov representation for single regions and thus allows to avoid demanding Markov Chain Monte Carlo methods for both parameters estimation and the compound random field synthesis.

An algorithm for fast automatic acquisition of virtual models of planar-faced textured objects from registered range and colour images is introduced. The algorithm consists of four main steps-range image segmentation, texture analysis, virtual model geometry inference and texture synthesis. An efficient and robust range image segmentation is based on the combination of range profile modelling and line-based region growing. The texture is modelled using a multi-resolution Markov random field based model.