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Masked Diffusion Language Models (MDLMs) have recently emerged as a strong class of generative models, paralleling state-of-the-art (SOTA) autoregressive (AR) performance across natural language modeling domains. While there have been advances in AR as well as both latent and discrete diffusion-based approaches for protein sequence design, masked diffusion language modeling with protein language models (pLMs) is unexplored. In this work, we introduce MeMDLM, an MDLM tailored for membrane protein design, harnessing the SOTA pLM ESM-2 to de novo generate realistic membrane proteins for downstream experimental applications. Our evaluations demonstrate that MeMDLM-generated proteins exceed AR-based methods by generating sequences with greater transmembrane (TM) character. We further apply our design framework to scaffold soluble and TM motifs in sequences, demonstrating that MeMDLM-reconstructed sequences achieve greater biological similarity to their original counterparts compared to SOTA inpainting methods. Finally, we show that MeMDLM captures physicochemical membrane protein properties with similar fidelity as SOTA pLMs, paving the way for experimental applications. In total, our pipeline motivates future exploration of MDLM-based pLMs for protein design.

Inorganic halide perovskites have become attractive for many optoelectronic applications due to their outstanding properties. While chemical synthesis techniques have been successful in producing high-quality perovskite crystals, scaling up to wafer-scale thin films remains challenging. Vapor deposition methods, particularly physical vapor deposition and chemical vapor deposition, have emerged as potential solutions for large-scale thin film fabrication. However, the control of phase purity during deposition remains problematic. Here, we investigate single-source (CsPbBr3) and dual-source (CsBr and PbBr2) vapor deposition techniques to achieve phase-pure CsPbBr3 thin films. Utilizing Knudsen Effusion Mass Spectrometry, we demonstrate that while the single-source CsPbBr3 evaporation is partially congruent, it leads to compositional changes in the evaporant over time. The dual-source evaporation, with a precise control of the PbBr2/CsBr flux ratio, can improve phase purity, particularly at elevated substrate temperatures at excess PbBr2 conditions. Our results give direct evidence that the growth is CsBr-limited. Overall, our findings provide critical insights into the vapor phase deposition processes, highlighting the importance of evaporation conditions in achieving the desired inorganic perovskite stoichiometry and morphology., Comment: 33 pages, 5 figures, 8 figures in Supporting Information

A Hamiltonian path (cycle) in a graph is a path (cycle, respectively) which passes through all of its vertices. The problems of deciding the existence of a Hamiltonian cycle (path) in an input graph are well known to be NP-complete, and restricted classes of graphs which allow for their polynomial-time solutions are intensively investigated. Until very recently the complexity was open even for graphs of independence number at most 3. So far unpublished result of Jedli\v{c}kov\'{a} and Kratochv\'{\i}l [arXiv:2309.09228] shows that for every integer $k$, Hamiltonian path and cycle are polynomial-time solvable in graphs of independence number bounded by $k$. As a companion structural result, we determine explicit obstacles for the existence of a Hamiltonian path for small values of $k$, namely for graphs of independence number 2, 3, and 4. Identifying these obstacles in an input graph yields alternative polynomial-time algorithms for Hamiltonian path and cycle with no large hidden multiplicative constants., Comment: arXiv admin note: text overlap with arXiv:2309.09228

We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called teaching dimension. A recent paper [7] conjectured that the worst case for this model, as a function of the size of the concept class, occurs when the consistency matrix contains the binary representations of numbers from zero and up. In this paper we prove their conjecture. The result can be seen as a generalization of a theorem resolving the edge isoperimetry problem for hypercubes [12], and our proof is based on a lemma of [10]., Comment: 14 pages, 1 figure

A Hamiltonian path (a Hamiltonian cycle) in a graph is a path (a cycle, respectively) that traverses all of its vertices. The problems of deciding their existence in an input graph are well-known to be NP-complete, in fact, they belong to the first problems shown to be computationally hard when the theory of NP-completeness was being developed. A lot of research has been devoted to the complexity of Hamiltonian path and Hamiltonian cycle problems for special graph classes, yet only a handful of positive results are known. The complexities of both of these problems have been open even for $4K_1$-free graphs, i.e., graphs of independence number at most $3$. We answer this question in the general setting of graphs of bounded independence number. We also consider a newly introduced problem called \emph{Hamiltonian-$\ell$-Linkage} which is related to the notions of a path cover and of a linkage in a graph. This problem asks if given $\ell$ pairs of vertices in an input graph can be connected by disjoint paths that altogether traverse all vertices of the graph. For $\ell=1$, Hamiltonian-1-Linkage asks for existence of a Hamiltonian path connecting a given pair of vertices. Our main result reads that for every pair of integers $k$ and $\ell$, the Hamiltonian-$\ell$-Linkage problem is polynomial time solvable for graphs of independence number not exceeding $k$.

Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line segment. Given a planar graph $G$, the segment number of $G$ is the minimum number of segments that can be achieved by any planar straight-line drawing of $G$. The line cover number of $G$ is the minimum number of lines that support all the edges of a planar straight-line drawing of $G$. Computing the segment number or the line cover number of a planar graph is $\exists\mathbb{R}$-complete and, thus, NP-hard. We study the problem of computing the segment number from the perspective of parameterized complexity. We show that this problem is fixed-parameter tractable with respect to each of the following parameters: the vertex cover number, the segment number, and the line cover number. We also consider colored versions of the segment and the line cover number., Comment: The conference version of this paper appeared in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023)

Monolayer (1L) transition metal dichalcogenides (TMDC) are of strong interest in nanophotonics due to their narrow-band intense excitonic transitions persisting up to room temperature. When brought into resonance with surface plasmon polariton (SPP) excitations of a conductive medium opportunities for studying and engineering strong light-matter coupling arise. Here, we consider a most simple geometry, namely a planar stack composed of a thin silver film, an Al2O3 spacer and a monolayer of WS2. We perform total internal reflection ellipsometry which combines spectroscopic ellipsometry with the Kretschmann-Raether-type surface plasmon resonance configuration. The combined amplitude and phase response of the reflected light at varied angle of incidence proves that despite the atomic thinness of 1L-WS2, the strong coupling (SC) regime between A excitons and SPPs propagating in the thin Ag film is reached. The phasor representation of rho corroborates SC as rho undergoes a topology change indicated by the occurrence of a double point at the cross over from the weak to the strong coupling regime. Our findings are validated by both analytical transfer matrix method calculations and numerical Maxwell simulations. The findings open up new perspectives for applications in plasmonic modulators and sensors benefitting from the tunability of the optical properties of 1L-TMDCs by electric fields, electrostatic doping, light and the chemical environment., Comment: 15 pages, 3 figures

We study the following problem: Given a set $S$ of $n$ points in the plane, how many edge-disjoint plane straight-line spanning paths of $S$ can one draw? A well known result is that when the $n$ points are in convex position, $\lfloor n/2\rfloor$ such paths always exist, but when the points of $S$ are in general position the only known construction gives rise to two edge-disjoint plane straight-line spanning paths. In this paper, we show that for any set $S$ of at least ten points, no three of which are collinear, one can draw at least three edge-disjoint plane straight-line spanning paths of~$S$. Our proof is based on a structural theorem on halving lines of point configurations and a strengthening of the theorem about two spanning paths, which we find interesting in its own right: if $S$ has at least six points, and we prescribe any two points on the boundary of its convex hull, then the set contains two edge-disjoint plane spanning paths starting at the prescribed points., Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023)

The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and complexity perspectives. Nonetheless, disconnected graphs were usually omitted from the considerations with the explanation that it is sufficient to understand coverings of the connected components of the target graph by components of the source one. However, different (but equivalent) versions of the definition of covers of connected graphs generalize to non-equivalent definitions for disconnected graphs. The aim of this paper is to summarize this issue and to compare three different approaches to covers of disconnected graphs: 1) locally bijective homomorphisms, 2) globally surjective locally bijective homomorphisms (which we call \emph{surjective covers}), and 3) locally bijective homomorphisms which cover every vertex the same number of times (which we call \emph{equitable covers}). The standpoint of our comparison is the complexity of deciding if an input graph covers a fixed target graph. We show that both surjective and equitable covers satisfy what certainly is a natural and welcome property: covering a disconnected graph is polynomial-time decidable if such it is for every connected component of the graph, and it is NP-complete if it is NP-complete for at least one of its components. We further argue that the third variant, equitable covers, is the most natural one, namely when considering covers of colored graphs. Moreover, the complexity of surjective and equitable covers differ from the fixed parameter complexity point of view. In line with the current trends in topological graph theory, as well as its applications in mathematical physics, we consider graphs in a very general sense[...], Comment: full version

We report on the optical properties of CsPbBr3 polycrystalline thin film on a single grain level. A sample comprised of isolated nanocrystals (NCs) mimicking the properties of the polycrystalline thin film grains that can be individually probed by photoluminescence spectroscopy was prepared. These NCs were analyzed using correlative microscopy allowing the examination of structural, chemical, and optical properties from identical sites. Our results show that the stoichiometry of the CsPbBr3 NCs is uniform and independent of the NCs' morphology. The photoluminescence (PL) peak emission wavelength is slightly dependent on the dimensions of NCs, with the blue shift up to 9 nm for the smallest analyzed NCs. The magnitude of the blueshift is smaller than the emission linewidth, thus detectable only by high-resolution PL mapping. By comparing the emission wavelengths obtained from the experiment and a rigorous effective mass model we can fully attribute the observed variations to the size-dependent quantum confinement effect., Comment: 25 pages, 3 figures

This paper presents a self-contained system for the robust utilization of aerial robots in the autonomous exploration of cave environments to help human explorers, first responders, and speleologists. The proposed system is generally applicable to an arbitrary exploration task within an unknown and unstructured subterranean environment and interconnects crucial robotic subsystems to provide full autonomy of the robots. Such subsystems primarily include mapping, path and trajectory planning, localization, control, and decision making. Due to the diversity, complexity, and structural uncertainty of natural cave environments, the proposed system allows for the possible use of any arbitrary exploration strategy for a single robot, as well as for a cooperating team. A multi-robot cooperation strategy that maximizes the limited flight time of each aerial robot is proposed for exploration and search & rescue scenarios where the homing of all deployed robots back to an initial location is not required The entire system is validated in a comprehensive experimental analysis comprising of hours of flight time in a real-world cave environment, as well as by hundreds of hours within a state-of-the-art virtual testbed that was developed for the DARPA Subterranean Challenge robotic competition. Among others, experimental results include multiple real-world exploration flights traveling over 470 meters on a single battery in a demanding unknown cave environment.

In 1992 Bir\'{o}, Hujter and Tuza introduced, for every fixed connected graph $H$, the class of $H$-graphs, defined as the intersection graphs of connected subgraphs of some subdivision of $H$. Recently, quite a lot of research has been devoted to understanding the tractability border for various computational problems, such as recognition or isomorphism testing, in classes of $H$-graphs for different graphs $H$. In this work we undertake this research topic, focusing on the recognition problem. Chaplick, T\"{o}pfer, Voborn\'{\i}k, and Zeman showed, for every fixed tree $T$, a polynomial-time algorithm recognizing $T$-graphs. Tucker showed a polynomial time algorithm recognizing $K_3$-graphs (circular-arc graphs). On the other hand, Chaplick at al. showed that recognition of $H$-graphs is $NP$-hard if $H$ contains two different cycles sharing an edge. The main two results of this work narrow the gap between the $NP$-hard and $P$ cases of $H$-graphs recognition. First, we show that recognition of $H$-graphs is $NP$-hard when $H$ contains two different cycles. On the other hand, we show a polynomial-time algorithm recognizing $L$-graphs, where $L$ is a graph containing a cycle and an edge attached to it ($L$-graphs are called lollipop graphs). Our work leaves open the recognition problems of $M$-graphs for every unicyclic graph $M$ different from a cycle and a lollipop. Other results of this work, which shed some light on the cases that remain open, are as follows. Firstly, the recognition of $M$-graphs, where $M$ is a fixed unicyclic graph, admits a polynomial time algorithm if we restrict the input to graphs containing particular holes (hence recognition of $M$-graphs is probably most difficult for chordal graphs). Secondly, the recognition of medusa graphs, which are defined as the union of $M$-graphs, where $M$ runs over all unicyclic graphs, is $NP$-complete.

The Bardeen-Cooper-Schrieffer (BCS) condensation and Bose-Einstein condensation (BEC) are the two limiting ground states of paired Fermion systems, and the crossover between these two limits has been a source of excitement for both fields of high temperature superconductivity and cold atom superfluidity. For superconductors, ultra-low doping systems like graphene and LixZrNCl successfully approached the crossover starting from the BCS-side. These superconductors offer new opportunities to clarify the nature of charged-particles transport towards the BEC regime. Here we report the study of vortex dynamics within the crossover using their Hall effect as a probe in LixZrNCl. We observed a systematic enhancement of the Hall angle towards the BCS-BEC crossover, which was qualitatively reproduced by the phenomenological time-dependent Ginzburg-Landau (TDGL) theory. LixZrNCl exhibits a band structure free from various electronic instabilities, allowing us to achieve a comprehensive understanding of the vortex Hall effect and thereby propose a global picture of vortex dynamics within the crossover. These results demonstrate that gate-controlled superconductors are ideal platforms towards investigations of unexplored properties in BEC superconductors.

Dimensionality reduction methods have found vast application as visualization tools in diverse areas of science. Although many different methods exist, their performance is often insufficient for providing quick insight into many contemporary datasets, and the unsupervised mode of use prevents the users from utilizing the methods for dataset exploration and fine-tuning the details for improved visualization quality. We present BlosSOM, a high-performance semi-supervised dimensionality reduction software for interactive user-steerable visualization of high-dimensional datasets with millions of individual data points. BlosSOM builds on a GPU-accelerated implementation of the EmbedSOM algorithm, complemented by several landmark-based algorithms for interfacing the unsupervised model learning algorithms with the user supervision. We show the application of BlosSOM on realistic datasets, where it helps to produce high-quality visualizations that incorporate user-specified layout and focus on certain features. We believe the semi-supervised dimensionality reduction will improve the data visualization possibilities for science areas such as single-cell cytometry, and provide a fast and efficient base methodology for new directions in dataset exploration and annotation., Comment: For software see https://github.com/molnsona/blossom

We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for {\em graphs with semi-edges}. The notion of graph covering is a discretization of coverings between surfaces or topological spaces, a notion well known and deeply studied in classical topology. Graph covers have found applications in discrete mathematics for constructing highly symmetric graphs, and in computer science in the theory of local computations. In 1991, Abello et al. asked for a classification of the computational complexity of deciding if an input graph covers a fixed target graph, in the ordinary setting (of graphs with only edges). Although many general results are known, the full classification is still open. In spite of that, we propose to study the more general case of covering graphs composed of normal edges (including multiedges and loops) and so-called semi-edges. Semi-edges are becoming increasingly popular in modern topological graph theory, as well as in mathematical physics. They also naturally occur in the local computation setting, since they are lifted to matchings in the covering graph. We show that the presence of semi-edges makes the covering problem considerably harder; e.g., it is no longer sufficient to specify the vertex mapping induced by the covering, but one necessarily has to deal with the edge mapping as well. We show some solvable cases, and completely characterize the complexity of the already very nontrivial problem of covering one- and two-vertex (multi)graphs with semi-edges. Our NP-hardness results are proven for simple input graphs, and in the case of regular two-vertex target graphs, even for bipartite ones. This provides a strengthening of previously known results for covering graphs without semi-edges, and may contribute to better understanding of this notion and its complexity.

The class of exact transferable utility coalitional games, introduced in 1972 by Schmeidler, has been studied both in the context of game theory and in the context of imprecise probabilities. We characterize the cone of exact games by describing the minimal set of linear inequalities defining this cone; these facet-defining inequalities for the exact cone appear to correspond to certain set systems (= systems of coalitions). We noticed that non-empty proper coalitions having non-zero coefficients in these facet-defining inequalities form set systems with particular properties. More specifically, we introduce the concept of a semi-balanced system of coalitions, which generalizes the classic concept of a balanced coalitional system in cooperative game theory. The semi-balanced coalitional systems provide valid inequalities for the exact cone and minimal semi-balanced systems (in the sense of inclusion of set systems) characterize this cone. We also introduce basic classification of minimal semi-balanced systems, their pictorial representatives and a substantial concept of an indecomposable (minimal) semi-balanced system of coalitions. The main result of the paper is that indecomposable semi-balanced systems are in one-to-one correspondence with facet-defining inequalities for the exact cone. The secondary relevant result is the rebuttal of a former conjecture claiming that a coalitional game is exact iff it is totally balanced and its anti-dual is also totally balanced. We additionally characterize those inequalities which are facet-defining both for the exact cone and the cone of totally balanced games., Comment: 39 pages, to be submitted (probably) to Mathematical Methods of Operation Research

Integrated, highly sensitive and reversible sensor devices for toxic and hazardous gases in environmental pollution monitoring can be realized with graphene-based materials. Here we show that, single layer graphene grown on SiC can be utilized to implement sensor devices being extremely sensitive towards NO2 showing an n-type response. A second type of sensor with an added NiO layer on top of the single layer graphene changed its response to p-type but did not reduce its sensitivity. We show that the conduction switch from n-type to p-type was not a consequence of an alteration of the graphene layer but is found to be an effect of the NiO layer. We find that the NiO leads to lowering of the Fermi level to a point that a crossing of the Dirac Point in the graphene switched the conduction type. These sensors were tested in the 100 ppb NO2 regime, showing good response and a detection limit extrapolated to be below 1 ppb. This new NiO/graphene/SiC configuration can be an attractive p-type sub-ppb sensor platform for NO2 and related gases.

This paper is an ELITR system submission for the non-native speech translation task at IWSLT 2020. We describe systems for offline ASR, real-time ASR, and our cascaded approach to offline SLT and real-time SLT. We select our primary candidates from a pool of pre-existing systems, develop a new end-to-end general ASR system, and a hybrid ASR trained on non-native speech. The provided small validation set prevents us from carrying out a complex validation, but we submit all the unselected candidates for contrastive evaluation on the test set., Comment: IWSLT 2020

Interval graphs, intersection graphs of segments on a real line (intervals), play a key role in the study of algorithms and special structural properties. Unit interval graphs, their proper subclass, where each interval has a unit length, has also been extensively studied. We study mixed unit interval graphs---a generalization of unit interval graphs where each interval has still a unit length, but intervals of more than one type (open, closed, semi-closed) are allowed. This small modification captures a much richer class of graphs. In particular, mixed unit interval graphs are not claw-free, compared to unit interval graphs. Heggernes, Meister, and Papadopoulos defined a representation of unit interval graphs called the bubble model which turned out to be useful in algorithm design. We extend this model to the class of mixed unit interval graphs and demonstrate the advantages of this generalized model by providing a subexponential-time algorithm for solving the MaxCut problem on mixed unit interval graphs. In addition, we derive a polynomial-time algorithm for certain subclasses of mixed unit interval graphs. We point out a substantial mistake in the proof of the polynomiality of the MaxCut problem on unit interval graphs by Boyaci, Ekim, and Shalom (2017). Hence, the time complexity of this problem on unit interval graphs remains open. We further provide a better algorithmic upper-bound on the clique-width of mixed unit interval graphs. Clique-width is one of the most general structural graph parameters, where a large group of natural problems is still solvable in the tractable time when an efficient representation is given. Unfortunately, the exact computation of the clique-width representation is \NP-hard. Therefore, good upper-bounds on clique-width are highly appreciated, in particular, when such a bound is algorithmic., Comment: Accepted to Mathematical Foundations of Computer Science (MFCS 2020), 25 pages, 4 figures

We present a test corpus of audio recordings and transcriptions of presentations of students' enterprises together with their slides and web-pages. The corpus is intended for evaluation of automatic speech recognition (ASR) systems, especially in conditions where the prior availability of in-domain vocabulary and named entities is benefitable. The corpus consists of 39 presentations in English, each up to 90 seconds long. The speakers are high school students from European countries with English as their second language. We benchmark three baseline ASR systems on the corpus and show their imperfection., Comment: SLSP 2019

Mechanical stability of Ag and Cu printed and evaporated metallization lines on polymer substrates is investigated by means of monotonic tensile and cyclic bending tests. It is shown that lines which demonstrate good performance during monotonic tests fail at lower strains during a cyclic bending tests. Evaporated lines with the grain size of several hundreds of nanometers have good ductility and consequently good stability during monotonic loading but at the same time they fail at low strains during cyclic bending. Printed lines with nanocrystalline microstructure, in contrast, demonstrate more intensive cracking during monotonic loading but higher failure strains during cyclic bending. Apart from the grain size effect, the effect of film thickness on the saturation crack density after cyclic bending is also demonstrated. Thinner films have higher crack density in accordance with the shear lag model.

The chemical modification of electrodes with organic materials is a common approach to tune the electronic and electrostatic landscape between interlayers in optoelectronic devices, thus facilitating charge injection at the electrode/semiconductor interfaces and improving their performance. The use of photochromic molecules for the surface modification allows dynamic control of the electronic and electrostatic properties of the electrode and thereby enables additional functionalities in such devices. Here, we show that the electronic properties of a transparent indium tin oxide (ITO) electrode are reversibly and dynamically modified by depositing organic photochromic switches (diarylethenes) in the form of self-assembled monolayers (SAMs). By combining a range of surface characterization and density functional theory calculations, we present a detailed picture of the SAM binding onto ITO, the packing density of molecules, their orientation, as well as the work function modification of the ITO surface due to the SAM deposition. Upon illumination with ultraviolet and green light, we observe a reversible shift of the frontier occupied levels by 0.7 eV, and concomitantly a reversible work function change of ca. 60 meV. Our results prove the viability of dynamic switching of the electronic properties of the electrode with external light stimuli, which could be used to fabricate ITO-based photo-switchable optoelectronic devices.

Application of transition metal dichalcogenides (TMDC) in photonic, optoelectronic or valleytronic devices requires the growth of continuous monolayers, heterostructures and alloys of different materials in a single process. We present a facile pulsed thermal deposition method which provides precise control over layer thickness and stoichiometry of two-dimensional systems. The versatility of the method is demonstrated on ternary monolayers of Mo$_{1-x}$W$_{x}$S$_{2}$ and on heterostructures combining metallic TaS$_{2}$ and semiconducting MoS$_{2}$ layers. The fabricated ternary monolayers cover the entire composition range of $x$ = 0...1 without phase separation. Band gap engineering and control over the spin-orbit coupling strength is demonstrated by absorption and photoluminescence spectroscopy. Vertical heterostructures are grown without intermixing. The formation of clean and atomically abrupt interfaces is evidenced by high-resolution transmission electron microscopy. Since both the metal components as well as the chalcogenides are thermally evaporated complex alloys and heterostructures can thus be prepared.

We initiate the study of the vertex-ply of straight-line drawings, as a relaxation of the recently introduced ply number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-ply of a drawing is determined by the vertex covered by the maximum number of disks. The main motivation for considering this relaxation is to relate the concept of ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-ply number 1 can be seen as a weak proximity drawing, which we call empty-ply drawing. We show non-trivial relationships between the ply number and the vertex-ply number. Then, we focus on empty-ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the ply and the vertex-ply of planar drawings., Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017)

Inferring model parameters from experimental data is a grand challenge in many sciences, including cosmology. This often relies critically on high fidelity numerical simulations, which are prohibitively computationally expensive. The application of deep learning techniques to generative modeling is renewing interest in using high dimensional density estimators as computationally inexpensive emulators of fully-fledged simulations. These generative models have the potential to make a dramatic shift in the field of scientific simulations, but for that shift to happen we need to study the performance of such generators in the precision regime needed for science applications. To this end, in this work we apply Generative Adversarial Networks to the problem of generating weak lensing convergence maps. We show that our generator network produces maps that are described by, with high statistical confidence, the same summary statistics as the fully simulated maps., Comment: 11 pages, 8 figures

We propose an Eulerian thermodynamically compatible model for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space. The model is based on the additive splitting of the velocity gradient into the crystal lattice part and the plastic part. The approach extends a Gibbs-potential-based formulation developed by Rajagopal and Srinivasa for obtaining the response functions for elasto-visco-plastic crystals. The framework makes constitutive assumptions for two scalar functions: the Gibbs potential and the rate of dissipation. The constitutive equations relating the stress to kinematical quantities is then determined using the condition that the rate of dissipation is maximal providing that the relevant constraints are met. The proposed model is applied to three-dimensional micropillar compression, and its features, both on the level of modelling and computer simulations, are discussed and compared to relevant studies.

Recently introduced composition operator for credal sets is an analogy of such operators in probability, possibility, evidence and valuation-based systems theories. It was designed to construct multidimensional models (in the framework of credal sets) from a system of low- dimensional credal sets. In this paper we study its potential from the computational point of view utilizing methods of polyhedral geometry.

Influence diagrams are a decision-theoretic extension of probabilistic graphical models. In this paper we show how they can be used to solve the Goddard problem. We present results of numerical experiments with this problem and compare the solutions provided by influence diagrams with the optimal solution., Comment: 10 pages, 2 figures

In this paper, electrothermal field phenomena in electronic components are considered. This coupling is tackled by multiphysical field simulations using the Finite Integration Technique (FIT). In particular, the design of bonding wires with respect to thermal degradation is investigated. Instead of resolving the wires by the computational grid, lumped element representations are introduced as point-to-point connections in the spatially distributed model. Fabrication tolerances lead to uncertainties of the wires' parameters and influence the operation and reliability of the final product. Based on geometric measurements, the resulting variability of the wire temperatures is determined using the stochastic electrothermal field-circuit model., Comment: submitted to DATE, available at http://ieeexplore.ieee.org/document/7459510/

A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular covers where this homomorphism is prescribed by the action of a semiregular subgroup of $\textrm{Aut}(G)$. We study computational aspects of regular covers that have not been addressed before. The decision problem RegularCover asks for given graphs $G$ and $H$ whether $G$ regularly covers $H$. When $|H|=1$, this problem becomes Cayley graph recognition for which the complexity is still unresolved. Another special case arises for $|G| = |H|$ when it becomes the graph isomorphism problem. Our main result is an involved FPT algorithm solving RegularCover for planar inputs $G$ in time $O^*(2^{e(H)/2})$ where $e(H)$ denotes the number of edges of $H$. The algorithm is based on dynamic programming and employs theoretical results proved in a related structural paper. Further, when $G$ is 3-connected, $H$ is 2-connected or the ratio $|G|/|H|$ is an odd integer, we can solve the problem RegularCover in polynomial time. In comparison, B\'ilka et al. (2011) proved that testing general graph covers is NP-complete for planar inputs $G$ when $H$ is a small fixed graph such as $K_4$ or $K_5$., Comment: The journal version of the second part of arXiv:1402.3774. arXiv admin note: substantial text overlap with arXiv:1402.3774

We introduce and study the $\textit{OrthoSEFE}-k$ problem: Given $k$ planar graphs each with maximum degree 4 and the same vertex set, do they admit an OrthoSEFE, that is, is there an assignment of the vertices to grid points and of the edges to paths on the grid such that the same edges in distinct graphs are assigned the same path and such that the assignment induces a planar orthogonal drawing of each of the $k$ graphs? We show that the problem is NP-complete for $k \geq 3$ even if the shared graph is a Hamiltonian cycle and has sunflower intersection and for $k \geq 2$ even if the shared graph consists of a cycle and of isolated vertices. Whereas the problem is polynomial-time solvable for $k=2$ when the union graph has maximum degree five and the shared graph is biconnected. Further, when the shared graph is biconnected and has sunflower intersection, we show that every positive instance has an OrthoSEFE with at most three bends per edge., Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016)

The cop number of a graph $G$ is the smallest $k$ such that $k$ cops win the game of cops and robber on $G$. We investigate the maximum cop number of geometric intersection graphs, which are graphs whose vertices are represented by geometric shapes and edges by their intersections. We establish the following dichotomy for previously studied classes of intersection graphs: The intersection graphs of arc-connected sets in the plane (called string graphs) have cop number at most 15, and more generally, the intersection graphs of arc-connected subsets of a surface have cop number at most $10g+15$ in case of orientable surface of genus $g$, and at most $10g'+15$ in case of non-orientable surface of Euler genus $g'$. For more restricted classes of intersection graphs, we obtain better bounds: the maximum cop number of interval filament graphs is two, and the maximum cop number of outer-string graphs is between 3 and 4. The intersection graphs of disconnected 2-dimensional sets or of 3-dimensional sets have unbounded cop number even in very restricted settings. For instance, we show that the cop number is unbounded on intersection graphs of two-element subsets of a line, as well as on intersection graphs of 3-dimensional unit balls, of 3-dimensional unit cubes or of 3-dimensional axis-aligned unit segments.

Seidel's switching is a graph operation which makes a given vertex adjacent to precisely those vertices to which it was non-adjacent before, while keeping the rest of the graph unchanged. Two graphs are called switching-equivalent if one can be made isomorphic to the other one by a sequence of switches. Jel\'inkov\'a et al. [DMTCS 13, no. 2, 2011] presented a proof that it is NP-complete to decide if the input graph can be switched to contain at most a given number of edges. There turns out to be a flaw in their proof. We present a correct proof. Furthermore, we prove that the problem remains NP-complete even when restricted to graphs whose density is bounded from above by an arbitrary fixed constant. This partially answers a question of Matou\v{s}ek and Wagner [Discrete Comput. Geom. 52, no. 1, 2014]., Comment: 19 pages, 7 figures. An extended abstract submitted to COCOON 2016

Influence diagrams are decision theoretic extensions of Bayesian networks. They are applied to diverse decision problems. In this paper we apply influence diagrams to the optimization of a vehicle speed profile. We present results of computational experiments in which an influence diagram was used to optimize the speed profile of a Formula 1 race car at the Silverstone F1 circuit. The computed lap time and speed profiles correspond well to those achieved by test pilots. An extended version of our model that considers a more complex optimization function and diverse traffic constraints is currently being tested onboard a testing car by a major car manufacturer. This paper opens doors for new applications of influence diagrams., Comment: Presented at the Twelfth Annual Bayesian Modeling Applications Workshop, Amtsterdam, The Netherlands, 16th July 2015

We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance constrained graph labeling problem as a specific uniform variant of the Channel Assignment problem and show that this problem is fixed parameter tractable when parameterized by the neighborhood diversity together with the largest weight. Consequently, every $L(p_1, p_2, \dots, p_k)$-labeling problem is FPT when parameterized by the neighborhood diversity, the maximum $p_i$ and $k.$ Our results yield also FPT algorithms for all $L(p_1, p_2, \dots, p_k)$-labeling problems when parameterized by the size of a minimum vertex cover, answering an open question of Fiala et al.: Parameterized complexity of coloring problems: Treewidth versus vertex cover. The same consequence applies on Channel Assignment when the maximum weight is additionally included among the parameters. Finally, we show that the uniform variant of the Channel Assignment problem becomes NP-complete when generalized to graphs of bounded clique width., Comment: 14 pages, 4 figers

A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular coverings in which this homomorphism is prescribed by an action of a semiregular subgroup $\Gamma$ of $\textrm{Aut}(G)$; so $H \cong G / \Gamma$. In this paper, we study the behaviour of regular graph covering with respect to 1-cuts and 2-cuts in $G$. We describe reductions which produce a series of graphs $G = G_0,\dots,G_r$ such that $G_{i+1}$ is created from $G_i$ by replacing certain inclusion minimal subgraphs with colored edges. The process ends with a primitive graph $G_r$ which is either 3-connected, or a cycle, or $K_2$. This reduction can be viewed as a non-trivial modification of reductions of Mac Lane (1937), Trachtenbrot (1958), Tutte (1966), Hopcroft and Tarjan (1973), Cuningham and Edmonds (1980), Walsh (1982), and others. A novel feature of our approach is that in each step all essential information about symmetries of $G$ are preserved. A regular covering projection $G_0\to H_0$ induces regular covering projections $G_i \to H_i$ where $H_i$ is the $i$-th quotient reduction of $H_0$. This property allows to construct all possible quotients $H_0$ of $G_0$ from the possible quotients $H_r$ of $G_r$. By applying this method to planar graphs, we give a proof of Negami's Theorem (1988). Our structural results are also used in subsequent papers for regular covering testing when $G$ is a planar graph and for an inductive characterization of the automorphism groups of planar graphs (see Babai (1973) as well)., Comment: The journal version of the first part of arXiv:1402.3774

Weak gravitational lensing is a powerful cosmological probe, with non--Gaussian features potentially containing the majority of the information. We examine constraints on the parameter triplet $(\Omega_m,w,\sigma_8)$ from non-Gaussian features of the weak lensing convergence field, including a set of moments (up to $4^{\rm th}$ order) and Minkowski functionals, using publicly available data from the 154deg$^2$ CFHTLenS survey. We utilize a suite of ray--tracing N-body simulations spanning 91 points in $(\Omega_m,w,\sigma_8)$ parameter space, replicating the galaxy sky positions, redshifts and shape noise in the CFHTLenS catalogs. We then build an emulator that interpolates the simulated descriptors as a function of $(\Omega_m,w,\sigma_8)$, and use it to compute the likelihood function and parameter constraints. We employ a principal component analysis to reduce dimensionality and to help stabilize the constraints with respect to the number of bins used to construct each statistic. Using the full set of statistics, we find $\Sigma_8\equiv\sigma_8(\Omega_m/0.27)^{0.55}=0.75\pm0.04$ (68% C.L.), in agreement with previous values. We find that constraints on the $(\Omega_m,\sigma_8)$ doublet from the Minkowski functionals suffer a strong bias. However, high-order moments break the $(\Omega_m,\sigma_8)$ degeneracy and provide a tight constraint on these parameters with no apparent bias. The main contribution comes from quartic moments of derivatives., Comment: 17 pages, 10 figures, 4 tables