Multi-functional Building

Diplomová práce je vypracovaná ve formě projektové dokumentace polyfunkčního domu. Objekt má jeden podzemní a čtyři nadzemní podlaží. Navržená budova má plochou střechu a dosahuje výšku 16,650 m nad podlahou 1.NP. Budova má nosnou systém ze betonového monolitického skeletu. Stropní deska je řešená jako deska lokálně podepřená sloupy. Budova se skládá ze dvou částí. V prvním části jsou obchodní prostory v 1.NP a ve podsklepené podlaží je prostor pro Fitness. Druhá část slouží pro bydlení skládající se ze 12 obytných jednotekMaster thesis is composed from project documentation of Multi-functional building. The object has one basement floor and four floor. The building has flat roof and come up to height 16,65m. The structural system is designed from reinforced concrete skeleton. The building has two main parts. The first is commercial space, which is located on first floor and basement. The second part is used for living. The building has 12 apartments.

On the proof of some theorem on locally nilpotent subgroups in division rings

In Hai-Thin (2009), there is a theorem, stating that every locally nilpotent subnormal subgroup in a division ring $D$ is central (see Hai-Thin (2009, Th. 2.2)). Unfortunately, there is some mistake in the proof of this theorem. In this note we give the another proof of this theorem.Comment: 3 page

Diffeomorphic Information Neural Estimation

Mutual Information (MI) and Conditional Mutual Information (CMI) are multi-purpose tools from information theory that are able to naturally measure the statistical dependencies between random variables, thus they are usually of central interest in several statistical and machine learning tasks, such as conditional independence testing and representation learning. However, estimating CMI, or even MI, is infamously challenging due the intractable formulation. In this study, we introduce DINE (Diffeomorphic Information Neural Estimator)-a novel approach for estimating CMI of continuous random variables, inspired by the invariance of CMI over diffeomorphic maps. We show that the variables of interest can be replaced with appropriate surrogates that follow simpler distributions, allowing the CMI to be efficiently evaluated via analytical solutions. Additionally, we demonstrate the quality of the proposed estimator in comparison with state-of-the-arts in three important tasks, including estimating MI, CMI, as well as its application in conditional independence testing. The empirical evaluations show that DINE consistently outperforms competitors in all tasks and is able to adapt very well to complex and high-dimensional relationships.Comment: Accepted at the Thirty-Seventh AAAI Conference on Artificial Intelligence (AAAI 2023

Domain Generalisation via Risk Distribution Matching

We propose a novel approach for domain generalisation (DG) leveraging risk distributions to characterise domains, thereby achieving domain invariance. In our findings, risk distributions effectively highlight differences between training domains and reveal their inherent complexities. In testing, we may observe similar, or potentially intensifying in magnitude, divergences between risk distributions. Hence, we propose a compelling proposition: Minimising the divergences between risk distributions across training domains leads to robust invariance for DG. The key rationale behind this concept is that a model, trained on domain-invariant or stable features, may consistently produce similar risk distributions across various domains. Building upon this idea, we propose Risk Distribution Matching (RDM). Using the maximum mean discrepancy (MMD) distance, RDM aims to minimise the variance of risk distributions across training domains. However, when the number of domains increases, the direct optimisation of variance leads to linear growth in MMD computations, resulting in inefficiency. Instead, we propose an approximation that requires only one MMD computation, by aligning just two distributions: that of the worst-case domain and the aggregated distribution from all domains. Notably, this method empirically outperforms optimising distributional variance while being computationally more efficient. Unlike conventional DG matching algorithms, RDM stands out for its enhanced efficacy by concentrating on scalar risk distributions, sidestepping the pitfalls of high-dimensional challenges seen in feature or gradient matching. Our extensive experiments on standard benchmark datasets demonstrate that RDM shows superior generalisation capability over state-of-the-art DG methods.Comment: Accepted at 2024 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV 2024