We provide an upper bound on the number of neurons required in a shallow neural network to approximate a continuous function on a compact set with a given accuracy. This method, inspired by a specific proof of the Stone-Weierstrass theorem, is constructive and more general than previous bounds of this character, as it applies to any continuous function on any compact set.

Longhorn is an open-source, cloud-native software-defined storage (SDS) engine that delivers distributed block storage management in Kubernetes environments. This paper explores performance optimization techniques for Longhorn's core component, the Longhorn engine, to overcome limitations in leveraging high-performance server hardware, such as solid-state NVMe disks and low-latency, high-bandwidth networking. By integrating ublk at the frontend, to expose the virtual block device to the operating system, restructuring the communication protocol, and employing DBS, our simplified, direct-to-disk storage scheme, the system achieves significant performance improvements with respect to the default I/O path. Our results contribute to enhancing Longhorn's applicability in both cloud and on-premises setups, as well as provide insights for the broader SDS community.

Self-supervised image denoising implies restoring the signal from a noisy image without access to the ground truth. State-of-the-art solutions for this task rely on predicting masked pixels with a fully-convolutional neural network. This most often requires multiple forward passes, information about the noise model, or intricate regularization functions. In this paper, we propose a Swin Transformer-based Image Autoencoder (SwinIA), the first fully-transformer architecture for self-supervised denoising. The flexibility of the attention mechanism helps to fulfill the blind-spot property that convolutional counterparts normally approximate. SwinIA can be trained end-to-end with a simple mean squared error loss without masking and does not require any prior knowledge about clean data or noise distribution. Simple to use, SwinIA establishes the state of the art on several common benchmarks.

We study the labelled growth rate of an $\omega$-categorical structure $\fa$, i.e., the number of orbits of $Aut(\fa)$ on $n$-tuples of distinct elements, and show that the model-theoretic property of monadic stability yields a gap in the spectrum of allowable labelled growth rates. As a further application, we obtain gap in the spectrum of allowable labelled growth rates in hereditary graph classes, with no a priori assumption of $\omega$-categoricity. We also establish a way to translate results about labelled growth rates of $\omega$-categorical structures into combinatorial statements about sets with weak finiteness properties in the absence of the axiom of choice, and derive several results from this translation.

In the present paper, we study the asymptotic properties of the semi-exponential Post-Widder operator. It is connected with $p(x) = x^2$. The main result is a pointwise complete asymptotic expansion valid for locally smooth functions of exponential growth. All coefficients are derived and explicitly given. As a special case we recover the complete asymptotic expansion for the classical Post-Widder operator.

The design of embedded systems, that are ubiquitously used in mobile devices and cars, is becoming continuously more complex such that efficient system-level design methods are becoming crucial. My research aims at developing systems that help the designer express the complex design problem in a declarative way and explore the design space to obtain divers sets of solutions with desirable properties. To that end, we employ knowledge representation and reasoning capabilities of ASP in combination with background theories. As a result, for the first time, we proposed a sophisticated methodology that allows for the direct integration of multi-objective optimization of non-linear objectives into ASP. This includes unique results of diverse sub-problems covered in several publications which I will present in this work.

Hardware Transactional Memory (HTM) allows lock-free programming as easy as with traditional coarse-grain locks or similar, while benefiting from the performance advantages of fine-grained locking. Many HTM implementations have been proposed, but they have not received widespread adoption because of their high hardware complexity, their need for additions to the Instruction Set Architecture (ISA), and often for modifications to the cache coherence protocol. We show that HTM can be implemented without adding new instructions -- merely by extending the semantics of two existing, Load-Linked and Store-Conditional. Also, our proposed design does not modify or extend standard coherence protocols. We further propose to drastically simplify the implementation of HTM -- confined to modifications in the L1 Data Cache only -- by restricting it to applications where the write set plus the read set of each transaction do not exceed a small number of cache lines. We also propose two alternative mechanisms to guarantee forward progress, both based on detecting retrial attempts. We simulated our proposed design in Gem5, and we used it to implement several popular concurrent data structures, showing that a maximum of eight (8) words (cache lines) suffice for the write plus read sets. We provide a detailed explanation of selected implementations, clarifying the intended usage of our HTM from a programmer's perspective. We evaluated our HTM under varying contention levels to explore its scalability limits. The results indicate that our HTM provides good performance in concurrent data structures when contention is spread across multiple nodes: in such cases, the percentage of aborts relative to successful commits is very low. In the atomic fetch-and-increment benchmark for multiple shared counters, the results show that, under low-congestion, our HTM improves performance relative to the TTS lock.

This paper presents inference rules for Resource Description Framework (RDF), RDF Schema (RDFS) and Web Ontology Language (OWL). Our formalization is based on Notation 3 Logic, which extended RDF by logical symbols and created Semantic Web logic for deductive RDF graph stores. We also propose OWL-P that is a lightweight formalism of OWL and supports soft inferences by omitting complex language constructs.

For graphs $G$ and $H$, we write $G \overset{\mathrm{rb}}{\longrightarrow} H $if any proper edge-coloring of$G$contains a rainbow copy of$H$, i.e., a copy where no color appears more than once. Kohayakawa, Konstadinidis and the last author proved that the threshold for $G(n,p) \overset{\mathrm{rb}}{\longrightarrow}H$is at most$n^{-1/m_2(H)}$. Previous results have matched the lower bound for this anti-Ramsey threshold for cycles and complete graphs with at least 5 vertices. Kohayakawa, Konstadinidis and the last author also presented an infinite family of graphs $H$ for which the anti-Ramsey threshold is asymptotically smaller than $n^{-1/m_2(H)}$. In this paper, we devise a framework that provides a richer and more complex family of such graphs that includes all the previously known examples.

Entity linking (EL) is the task of automatically identifying entity mentions in text and resolving them to a corresponding entity in a reference knowledge base like Wikipedia. Throughout the past decade, a plethora of EL systems and pipelines have become available, where performance of individual systems varies heavily across corpora, languages or domains. Linking performance varies even between different mentions in the same text corpus, where, for instance, some EL approaches are better able to deal with short surface forms while others may perform better when more context information is available. To this end, we argue that performance may be optimised by exploiting results from distinct EL systems on the same corpus, thereby leveraging their individual strengths on a per-mention basis. In this paper, we introduce a supervised approach which exploits the output of multiple ready-made EL systems by predicting the correct link on a per-mention basis. Experimental results obtained on existing ground truth datasets and exploiting three state-of-the-art EL systems show the effectiveness of our approach and its capacity to significantly outperform the individual EL systems as well as a set of baseline methods.

The semantic expert recommender extension for the Jira bug tracking system semantically searches for similar tickets in Jira and recommends experts and links to existing organizational (Wiki) knowledge for each ticket. This helps to avoid redundant work and supports the search and collaboration with experts in the project management and maintenance phase based on semantically enriched tickets in Jira.

This paper presents the design and evolution of the RELATE platform. It provides a high-performance environment for natural language processing activities, specially constructed for Romanian language. Initially developed for text processing, it has been recently updated to integrate audio processing tools. Technical details are provided with regard to core components. We further present different usage scenarios, derived from actual use in national and international research projects, thus demonstrating that RELATE is a mature, modern, state-of-the-art platform for processing Romanian language corpora. Finally, we present very recent developments including bimodal (text and audio) features available within the platform.

These pages covers my expository talks during the seminar "Sub-Riemannian geometry and Lie groups" organised by the author and Tudor Ratiu at the Mathematics Department, EPFL, 2001. However, this is the first part of three, in preparation, dedicated to this subject. It covers, with mild modifications, an elementary introduction to the field.

Let $X$ count the number of $r$-stars in the random binomial graph $\mathbb{G}(n,p)$. We determine, for fixed $r$ and $\varepsilon > 0$, the asymptotics of $\log \mathbb{P}(X \ge (1 + \varepsilon)\mathbb{E} X)$ assuming only $\mathbb{E} X \to \infty$ and $p \to 0$ thus giving a first class of irregular graphs for which the upper tail problem for subgraph counts (stated by Janson and Ruciński in 2004) is solved in the sparse setting.

Propositional Dynamic Logic, PDL, is a modal logic designed to formalize the reasoning about programs. By extending accessibility between states to states and state sets, concurrent propositional dynamic logic CPDL, is introduced to include concurrent programs due to Peleg and Goldblatt. We study a many-valued generalization of CPDL where the satisfiability and the reachability relation between states and state sets are graded over a finite Łukasiewicz chain. Finitely-valued dynamic logic has been shown to be useful in formalizing reasoning about program behaviors under uncertainty. We obtain completeness results for all finitely valued PDL.

An Enskog-Vlasov finite-difference Lattice Boltzmann (EV-FDLB) for liquid-vapor systems with variable temperature is introduced. The model involves both the simplified Enskog collision operator and the self-consistent force field which accounts for the long-range interaction between the fluid particles. Full-range Gauss-Hermite quadratures were used for the discretization of the momentum space. The numerical solutions of the Enskog-Vlasov equation obtained employing the EV-FDLB model and the Direct Simulation Monte Carlo (DSMC)-like particle method (PM) are compared. Reasonable agreement is found between the two approaches when simulating the liquid-vapor phase separation and the liquid slab evaporation.

The mechanisms of void growth and coalescence are key contributors to the ductile failure of crystalline materials. At the grain scale, single crystal plastic anisotropy induces large strain localization leading to complex shape evolutions. In this study, an Arbitrary Lagrangian-Eulerian (ALE) framework for 2D crystal plasticity combined with dynamic remeshing is used to study the 2D shape evolution of cylindrical voids in single crystals. The large deformation and shape evolution of the voids under two types of loading are considered: (i) radial and (ii) uni-axial loadings. In both cases, the voids undergo complex shape evolutions induced by the interactions between slip bands, lattice rotations and large strain phenomena. In case (i), the onset of the deformation revealed the formation of a complex fractal network of slip bands around the voids. Then, large deformations unearth an unexpected evolution of the slip bands network associated with significant lattice rotations, leading to a final hexagonal shape for the void. In case (ii), we obtain shear bands with very large accumulated plastic strain (> 200%) compared to the macroscopic engineering strains (< 15%). A high dependence between crystalline orientations, slip band localization and therefore shape evolution was observed, concluding in a high dependency between crystalline orientation and void shape elongation, which is of prime importance regarding coalescence of the voids, thus to the formation of macro-cracks.

Relationships between the energy and the finance markets are increasingly important. Understanding these relationships is vital for policymakers and other stakeholders as the world faces challenges such as satisfying humanity's increasing need for energy and the effects of climate change. In this paper, we investigate the causal effect of electricity market liberalization on the electricity price in the US. By performing this analysis, we aim to provide new insights into the ongoing debate about the benefits of electricity market liberalization. We introduce Causal Machine Learning as a new approach for interventions in the energy-finance field. The development of machine learning in recent years opened the door for a new branch of machine learning models for causality impact, with the ability to extract complex patterns and relationships from the data. We discuss the advantages of causal ML methods and compare the performance of ML-based models to shed light on the applicability of causal ML frameworks to energy policy intervention cases. We find that the DeepProbCP framework outperforms the other frameworks examined. In addition, we find that liberalization of, and individual players' entry to, the electricity market resulted in a 7% decrease in price in the short term.

Compression experiments are widely used to study the mechanical properties of materials at micro- and nanoscale. However, the conventional engineering stress measurement method used in these experiments neglects to account for the alterations in the material's shape during loading. This can lead to inaccurate stress values and potentially misleading conclusions about the material's mechanical behavior especially in the case of localized deformation. To address this issue, we present a method for calculating true stress in cases of localized plastic deformation commonly encountered in experimental settings: (i) a single band and (ii) two bands oriented in arbitrary directions with respect to the vertical axis of the pillar (either in the same or opposite directions). Our simple analytic formulas can be applied to homogeneous and isotropic materials and crystals, requiring only standard data (displacement-force curve, aspect ratio, shear band angle and elastic strain limit) obtained from experimental results and eliminating the need for finite element computations. Our approach provides a more precise interpretation of experimental results and can serve as a valuable and simple tool in material design and characterization.

In this paper, we provide a Hilbert-style axiomatisation for the crisp bi-Gödel modal logic $\KbiG$. We prove its completeness w.r.t.\ crisp Kripke models where formulas at each state are evaluated over the standard bi-Gödel algebra on $[0,1]$. We also consider a paraconsistent expansion of $\KbiG$ with a De Morgan negation $\neg$ which we dub $\KGsquare$. We devise a Hilbert-style calculus for this logic and, as a~con\-se\-quence of a~conservative translation from $\KbiG$ to $\KGsquare$, prove its completeness w.r.t.\ crisp Kripke models with two valuations over $[0,1]$ connected via $\neg$. For these two logics, we establish that their decidability and validity are $\mathsf{PSPACE}$-complete. We also study the semantical properties of $\KbiG$ and $\KGsquare$. In particular, we show that Glivenko theorem holds only in finitely branching frames. We also explore the classes of formulas that define the same classes of frames both in $\mathbf{K}$ (the classical modal logic) and the crisp Gödel modal logic $\KG^c$. We show that, among others, all Sahlqvist formulas and all formulas $\phi\rightarrow\chi$ where $\phi$ and $\chi$ are monotone, define the same classes of frames in $\mathbf{K}$ and $\KG^c$.