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Results for "Jakub J. Borkala"

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Multiparty quantum random access codesMay 14 2019May 15 2019Random access code (RAC), a primitive for many information processing protocols, enables one party to encode nbit string into one bit of message such that another party can retrieve partial information of that string. We introduce the multiparty version ... More
Multiparty quantum random access codesMay 14 2019Random access code (RAC), a primitive for many information processing protocols, enables one party to encode nbit string into one bit of message such that another party can retrieve partial information of that string. We introduce the multiparty version ... More
A density version of Cobham's theoremOct 19 2017Nov 01 2017Cobham's theorem asserts that if a sequence is automatic with respect to two multiplicatively independent bases, then it is ultimately periodic. We prove a stronger density version of the result: if two sequences which are automatic with respect to two ... More
Connections Between Mutually Unbiased Bases and Quantum Random Access CodesSep 14 2017Mar 28 2018We present a new quantum communication complexity protocol, the promise--Quantum Random Access Code, which allows us to introduce a new measure of unbiasedness for bases of Hilbert spaces. The proposed measure possesses a clear operational meaning and ... More
Automatic sequences and generalised polynomialsMay 24 2017Dec 18 2017We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic. Using methods from ergodic theory, we are able to partially resolve this conjecture, proving ... More
Generalised polynomials and integer powersMay 08 2019We show that there does not exist a generalised polynomial which vanishes precisely on the set of powers of two. In fact, if $k \geq 2$ is and integer and $g \colon \mathbb{N} \to \mathbb{R}$ is a generalised polynomial such that $g(k^n) = 0$ for all ... More
Boundedly simple groups of automorphisms of treesMay 06 2009Jun 28 2012A group is boundedly simple if, for some constant N, every nontrivial conjugacy class generates the whole group in N steps. For a large class of trees, Tits proved simplicity of a canonical subgroup of the automorphism group, which is generated by pointwise ... More
Absolute connectedness and classical groupsFeb 08 2010Sep 07 2012We introduce and develop the model-theoretic notions of absolute connectedness and type-absolute connectedness for groups. We prove that groups of rational points of split semisimple linear groups (that is, Chevalley groups) over arbitrary infinite fields ... More
Multipass greedy coloring of simple uniform hypergraphsOct 22 2013Oct 22 2014Let $m^*(n)$ be the minimum number of edges in an $n$-uniform simple hypergraph that is not two colorable. We prove that $m^*(n)=\Omega(4^n/\ln^2(n))$. Our result generalizes to $r$-coloring of $b$-simple uniform hypergraphs. For fixed $r$ and $b$ we ... More
Second order differentiability of paths via a generalized 1/2-variationNov 21 2005Jul 16 2006We find an equivalent condition for a continuous vector-valued path to be Lebesgue equivalent to a twice differentiable function. For that purpose, we introduce the notion of a $VBG_{{1/2}}$ function, which plays an analogous role for the second order ... More
Learning Deep Architectures for Interaction Prediction in Structure-based Virtual ScreeningOct 23 2016Sep 19 2017We introduce a deep learning architecture for structure-based virtual screening that generates fixed-sized fingerprints of proteins and small molecules by applying learnable atom convolution and softmax operations to each compound separately. These fingerprints ... More
Effect of a skin-deep surface zone on formation of two-dimensional electron gas at a semiconductor surfaceJun 02 2016Two dimensional electron gases (2DEGs) at surfaces and interfaces of semiconductors are described straightforwardly with a 1D self-consistent Poisson-Schr\"{o}dinger scheme. However, their band energies have not been modeled correctly in this way. Using ... More
Multi$^{\mathbf{3}}$Net: Segmenting Flooded Buildings via Fusion of Multiresolution, Multisensor, and Multitemporal Satellite ImageryDec 05 2018We propose a novel approach for rapid segmentation of flooded buildings by fusing multiresolution, multisensor, and multitemporal satellite imagery in a convolutional neural network. Our model significantly expedites the generation of satellite imagery-based ... More
On base point free theorem and Mori dream spaces for log canonical threefolds over the algebraic closure of a finite fieldMar 20 2016The authors and D. Martinelli proved the base point free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field. In this paper, we drop the bigness condition when the characteristic ... More
Intermediate spectral statistics in the many--body localization transitionJul 18 2018Mar 04 2019Spectral statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between transitions in random ... More
Level statistics across the many--body localization transitionAug 08 2018Mar 04 2019Level statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between transitions in random ... More
A simpler proof of the negative association property for absolute values of measures tied to generalized Orlicz ballsSep 23 2009Negative association for a family of random variables $(X_i)$ means that for any coordinate--wise increasing functions $f,g$ we have $$\E f(X_{i_1},...,X_{i_k}) g(X_{j_1},...,X_{j_l}) \leq \E f(X_{i_1},...,X_{i_k}) \E g(X_{j_1},...,X_{j_l})$$ for any ... More
On the total neighbour sum distinguishing index of graphs with bounded maximum average degreeMar 05 2018A proper total $k$-colouring of a graph $G=(V,E)$ is an assignment $c : V \cup E\to \{1,2,\ldots,k\}$ of colours to the edges and the vertices of $G$ such that no two adjacent edges or vertices and no edge and its end-vertices are associated with the ... More
Algebraic approach to promise constraint satisfactionNov 02 2018Apr 05 2019The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years. A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about the approximability ... More
Hölder continuity of velocity gradients for shear-thinning fluids under perfect slip boundary conditionsOct 02 2016This paper is concerned with non-stationary flows of sheart-hinning fluids in a bounded two-dimensional C^{2;1} domain. Assuming perfect slip boundary conditions, we provide a proof of the existence of a solution with the H\"older continuous velocity ... More
Spectral estimation for diffusions with random sampling timesMar 02 2015Dec 17 2015The nonparametric estimation of the volatility and the drift coefficient of a scalar diffusion is studied when the process is observed at random time points. The constructed estimator generalizes the spectral method by Gobet, Hoffmann and Rei{\ss} [Ann. ... More
The Bolzano mean-value theorem and partial differential equationsNov 05 2016We study the existence of solutions to abstract equations of the form $0 = Au + F(u)$, $u\in K\subset E$, where A is an abstract differential operator acting in a Banach space $E$, $K$ is a closed convex set of constraints being invariant with respect ... More
Algebraic approach to promise constraint satisfactionNov 02 2018The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years. A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about the approximability ... More
Streaming k-mismatch with error correcting and applicationsJul 19 2016Nov 11 2016We present a new streaming algorithm for the $k$-Mismatch problem, one of the most basic problems in pattern matching. Given a pattern and a text, the task is to find all substrings of the text that are at the Hamming distance at most $k$ from the pattern. ... More
Estimation error for occupation time functionals of stationary Markov processesOct 17 2016The approximation of integral functionals with respect to a stationary Markov process by a Riemann-sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to get a better understanding ... More
Continuous time portfolio choice under monotone preferences with quadratic penalty - stochastic interest rate caseApr 22 2014This is a follow up of our previous paper - Trybu{\l}a and Zawisza \cite{TryZaw}, where we considered a modification of a monotone mean-variance functional in continuous time in stochastic factor model. In this article we address the problem of optimizing ... More
Metric derived numbers and continuous metric differentiability via homeomorphismsAug 15 2006We define the notions of unilateral metric derivatives and ``metric derived numbers'' in analogy with Dini derivatives (also referred to as ``derived numbers'') and establish their basic properties. We also prove that the set of points where a path with ... More
Multivariate integration in C^\infty([0,1]^d) is not strongly tractableMar 04 2008It has long been known that the multivariate integration problem for the unit ball in $C^r([0,1]^d)$ is intractable for fixed finite $r$. H. Wo\'zniakowski has recently conjectured that this is true even if $r=\infty$. This paper establishes a partial ... More
Irreducible 4-critical triangle-free toroidal graphsJan 31 2018The theory of Dvorak, Kral, and Thomas (2015) shows that a 4-critical triangle-free graph embedded in the torus has only a bounded number of faces of length greater than 4 and that the size of these faces is also bounded. We study the natural reduction ... More
Leaking Information Through Cache LRU StatesMay 20 2019The widely deployed Least-Recently Used (LRU) cache replacement policy and its variants are an essential component of modern processors. However, we show for the first time in detail that the LRU states of caches can be used to leak information. The LRU ... More
The square negative correlation property for generalized Orlicz ballsMar 04 2008Antilla, Ball and Perissinaki proved that the squares of coordinate functions in $\ell_p^n$ are negatively correlated. This paper extends their results to balls in generalized Orlicz norms on R^n. From this, the concentration of the Euclidean norm and ... More
On the infimum convolution inequalityJan 25 2008In the paper we study the infimum convolution inequalites. Such an inequality was first introduced by B. Maurey to give the optimal concentration of measure behaviour for the product exponential measure. We show how IC-inequalities are tied to concentration ... More
The negative association property for the absolute values of random variables equidistributed on a generalized Orlicz ballMar 04 2008Random variables equidistributed on convex bodies have received quite a lot of attention in the last few years. In this paper we prove the negative association property (which generalizes the subindependence of coordinate slabs) for generalized Orlicz ... More
Current Correlations in a Quantum Dot Ring: A Role of Quantum InterferenceApr 30 2019We present studies of electron transport and circular currents, those induced by the bias voltage and the magnetic flux threaded a ring of three quantum dots coupled with two electrodes. Quantum interference of electron waves passing through the states ... More
Un anneau de deformation universel en conducteur superieur (A universal deformation ring in higher conductor)Oct 14 2009Let k denote a perfect field of characteristic 5. We show that the versal deformation ring of an element of order 5 and Hasse conductor 2 as automorphism of a ring of formal power series k[[t]] computed by Bertin and Mezard, is in fact universal. This ... More
A concept of biopharmaceutical nanosatelliteFeb 12 2018The article is a short overview of a proposal of a CubeSat type nanosatellite designed to conduct biopharmaceutical tests on the low earth orbit. Motivations behind the emerging demand for such solution nowadays and in the close future are emphasized. ... More
Many-body localization for randomly interacting bosonsJul 27 2017We study many-body localization in a one dimensional optical lattice filled with bosons. The interaction between bosons is assumed to be random, which can be realized for atoms close to a microchip exposed to a spatially fluctuating magnetic field. Close ... More
Gaussian process regression as a predictive model for Quality-of-Service in Web service systemsJul 30 2012May 08 2013In this paper, we present the Gaussian process regression as the predictive model for Quality-of-Service (QoS) attributes in Web service systems. The goal is to predict performance of the execution system expressed as QoS attributes given existing execution ... More
On generalized choice and coloring numbersJan 21 2018Feb 26 2019A well-known result of Alon shows that the coloring number of a graph is bounded by a function of its choosability. We explore this relationship in a more general setting with relaxed assumptions on color classes, encoded by a graph parameter.
Neuromorphic MoS2 memtransistors fabricated by localised helium ion beam irradiationNov 23 2018Two-dimensional layered semiconductors have recently emerged as attractive building blocks for next-generation low-power non-volatile memories. However, challenges remain in the controllable sub-micron fabrication of bipolar resistively switching circuit ... More
Planar segment processes with reference mark distributions, modeling and estimationJan 07 2017Aug 28 2017The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide with the corresponding ... More
Asymptotically optimal neighbor sum distinguishing total colorings of graphsJul 27 2015Aug 05 2016Given a proper total $k$-coloring $c:V(G)\cup E(G)\to\{1,2,\ldots,k\}$ of a graph $G$, we define the value of a vertex $v$ to be $c(v) + \sum_{uv \in E(G)} c(uv)$. The smallest integer $k$ such that $G$ has a proper total $k$-coloring whose values form ... More
Self-Assembly of Spiral Patterns in Confined System with Competing InteractionsApr 26 2019Colloidal particles in polymer solutions and functionalized nanoparticles often exhibit short-range attraction coupled with long-range repulsion (SALR) leading to the spontaneous formation of symmetric patterns. Chiral nanostructures formed by thin film ... More
Arcwise connectedness of the set of ergodic measures of hereditary shiftsOct 03 2016Oct 07 2016We show that the set of ergodic invariant measures of a shift space with a safe symbol (this includes all hereditary shifts) is arcwise connected when endowed with the $d$-bar metric. As a consequence the set of ergodic measures of such a shift is also ... More
Liftability of the Frobenius morphism and images of toric varietiesAug 12 2017We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo $p^2$ - we expect that such varieties, after a finite \'etale cover, admit a Zariski-locally trivial fibration ... More
Non-Conforming Mesh Refinement for High-Order Finite ElementsMay 10 2019We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral ... More
Exactly solvable model of gene expression in proliferating bacterial cell population with stochastic protein bursts and protein partitioningApr 17 2019Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not concentration, the decay ... More
Model theoretic connected components of finitely generated nilpotent groupsDec 14 2011Sep 04 2012We prove that for a finitely generated infinite nilpotent group G with a first order structure (G,*,...), the connected component G*0 of a sufficiently saturated extension G* of G exists and equals $\bigcap_{n\in\N} {g^n : g\in G^*}$. We construct a first ... More
Energy level dynamics across the many-body localization transitionApr 10 2019The level dynamics across the many body localization transition is examined for XXZ-spin model with a random magnetic field. We compare different scenaria of parameter dependent motion in the system and consider measures such as level velocities, curvatures ... More
Querying Best Paths in Graph DatabasesOct 12 2017Querying graph databases has recently received much attention. We propose a new approach to this problem, which balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our approach is the ability ... More
Simultaneous $p$-orderings and minimising volumes in number fieldsJun 08 2015Nov 23 2016In the paper "On the interpolation of integer-valued polynomials" (Journal of Number Theory 133 (2013), pp. 4224--4232.) V. Volkov and F. Petrov consider the problem of existence of the so-called $n$-universal sets (related to simultaneous $p$-orderings ... More
A morphological study of galaxies in ZwCl0024+1652, a galaxy cluster at redshift z $\sim$ 0.4Feb 14 2019The well-known cluster of galaxies ZwCl0024+1652 at z $\sim$ 0.4, lacks an in-depth morphological classification of its central region. While previous studies provide a visual classification of a patched area, we used the public code called galaxy Support ... More
Band Selection from Hyperspectral Images Using Attention-based Convolutional Neural NetworksOct 24 2018This paper introduces new attention-based convolutional neural networks for selecting bands from hyperspectral images. The proposed approach re-uses convolutional activations at different depths, identifying the most informative regions of the spectrum ... More
Decorrelation of a class of Gibbs particle processes and asymptotic properties of U -statisticsMar 15 2019We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of a non-negative pair potential and an activity parameter. For small activity parameters, we prove a central limit theorem for certain ... More
A Parallel Memetic Algorithm to Solve the Vehicle Routing Problem with Time WindowsFeb 27 2014This paper presents a parallel memetic algorithm for solving the vehicle routing problem with time windows (VRPTW). The VRPTW is a well-known NP-hard discrete optimization problem with two objectives. The main objective is to minimize the number of vehicles ... More
Quantitative Benchmarks and New Directions for Noise Power Estimation Methods in ISM Radio EnvironmentNov 15 2017Noise power estimation is a key issue in modern wireless communication systems. It allows resource allocation by detecting white spectral spaces effectively, and gives control over the communication process by adjusting transmission power. Thus far, the ... More
Semidefinite Programming in Timetabling and Mutual-Exclusion SchedulingApr 06 2019In scheduling and timetabling applications, the mutual-exclusion constraint stipulates that certain pairs of tasks that cannot be executed at the same time. This corresponds to the vertex colouring problem in graph theory, for which there are well-known ... More
Using Circular Polarisation to Test the Composition and Dynamics of Astrophysical Particle AcceleratorsJan 16 2019We investigate the production of circularly polarised X and gamma-ray signals in cosmic accelerators such as supernova remnants and AGN jets. Proton-proton and proton-photon collisions within these sites produce a charge asymmetry in the distribution ... More
A Higgsploding Theory of Dark MatterMar 14 2018We show that the Higgsplosion mechanism makes a prediction for the mass and coupling of a WIMP-like minimal scalar dark matter model. In particular the currently favoured minimal value for the Higgsplosion scale, $E_\mathrm{H}\sim 25$ TeV, implies a dark ... More
Estimation of geodesic tortuosity and constrictivity in stationary random closed setsApr 06 2018Dec 05 2018We investigate the problem of estimating geodesic tortuosity and constrictivity as two structural characteristics of stationary random closed sets. They are of central importance for the analysis of effective transport properties in porous or composite ... More
Scaling up Deep Learning for PDE-based ModelsOct 22 2018In numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, the uses have been restricted by the fact the training data are obtained using ... More
Delay controls chimera relay synchronization in multiplex networksJul 30 2018Aug 06 2018We study remote (or relay) synchronization in multilayer networks between parts of one layer and their counterparts in a second layer, where these two layers are not directly connected. A simple realization of such a system is a triplex network where ... More
Many-body localization in presence of cavity mediated long-range interactionsFeb 01 2019May 12 2019We show that a one-dimensional Hubbard model with all-to-all coupling may exhibit many-body localization in the presence of local disorder. We numerically identify the parameter space where many-body localization occurs using exact diagonalization and ... More
Hitting half-spaces or spheres by the Ornstein-Uhlenbeck type diffusionsSep 01 2011Nov 03 2011The purpose of the paper is to provide a general method for computing hitting distributions of some regular subsets D for Ornstein-Uhlenbeck type operators of the form 1/2\Delta + F\cdot\nabla, with F bounded and orthogonal to the boundary of D. As an ... More
Self-testing of unsharp measurementsMar 29 2019We consider unsharp quantum measurements as a recourse in scenarios where one faces the trade-off between information gain and disturbance. We analyse in detail the case of two-outcome qubit measurements and show that generalized measurements allow for ... More
Multi-task hypernetworksFeb 27 2019Hypernetworks mechanism allows to generate and train neural networks (target networks) with use of other neural network (hypernetwork). In this paper, we extend this idea and show that hypernetworks are able to generate target networks, which can be customized ... More
Round Compression for Parallel Matching AlgorithmsJul 11 2017Feb 01 2018For over a decade now we have been witnessing the success of {\em massive parallel computation} (MPC) frameworks, such as MapReduce, Hadoop, Dryad, or Spark. One of the reasons for their success is the fact that these frameworks are able to accurately ... More
Effect of data reduction on sequence-to-sequence neural TTSNov 15 2018Nov 23 2018Recent speech synthesis systems based on sampling from autoregressive neural networks models can generate speech almost undistinguishable from human recordings. However, these models require large amounts of data. This paper shows that the lack of data ... More
Automatic sequences, generalised polynomials, and nilmanifoldsOct 12 2016We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are periodic away from a finite set. Using methods from ergodic theory, we are able to partially resolve this conjecture, ... More
Decomposition, Reformulation, and Diving in University Course TimetablingMar 05 2009Mar 20 2009In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft ... More
Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions: A unified frameworkJul 23 2018Sep 29 2018Charge transport through molecular junctions is often described either as a purely coherent or a purely classical phenomenon, and described using the Landauer-B\"uttiker formalism or Marcus theory, respectively. Using a generalised quantum master equation, ... More
Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous mediaMay 11 2018In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equations, employing the equivalent pore pressure. In practice a monolithic ... More
CHiVE: Varying Prosody in Speech Synthesis with a Linguistically Driven Dynamic Hierarchical Conditional Variational NetworkMay 17 2019The prosodic aspects of speech signals produced by current text-to-speech systems are typically averaged over training material, and as such lack the variety and liveliness found in natural speech. To avoid monotony and averaged prosody contours, it is ... More
Linear iterative schemes for doubly degenerate parabolic equationsJan 02 2018Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation. Here the backward ... More
Alquist: The Alexa Prize SocialbotApr 18 2018This paper describes a new open domain dialogue system Alquist developed as part of the Alexa Prize competition for the Amazon Echo line of products. The Alquist dialogue system is designed to conduct a coherent and engaging conversation on popular topics. ... More
Deep Learning for Multiple-Image Super-ResolutionMar 01 2019Super-resolution reconstruction (SRR) is a process aimed at enhancing spatial resolution of images, either from a single observation, based on the learned relation between low and high resolution, or from multiple images presenting the same scene. SRR ... More
Pseudo-Cartesian coordinates in a model of Causal Dynamical TriangulationsDec 27 2018Causal Dynamical Triangulations is a non-perturbative quantum gravity model, defined with a lattice cut-off. The model can be viewed as defined with a proper time but with no reference to any three-dimensional spatial background geometry. It has four ... More
Contracting a Planar Graph EfficientlyJun 30 2017We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in $O(1)$ time. Moreover, it can report all the arising ... More
On a Clique-Based Integer Programming Formulation of Vertex Colouring with Applications in Course TimetablingOct 18 2007Jul 07 2009Vertex colouring is a well-known problem in combinatorial optimisation, whose alternative integer programming formulations have recently attracted considerable attention. This paper briefly surveys seven known formulations of vertex colouring and introduces ... More
Space-time fractional diffusion in cell movement models with delayFeb 23 2018Oct 29 2018The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and the aim here ... More
Precision Diboson Observables for the LHCOct 28 2015Mar 03 2016Motivated by the restoration of $SU(2)\times U(1)$ at high energy, we suggest that certain ratios of diboson differential cross sections can be used as high-precision observables at the LHC. We rewrite leading-order diboson partonic cross sections in ... More
Effect of the nanowire diameter on the linearity of the response of GaN-based heterostructured nanowire photodetectorsApr 29 2019Nanowire photodetectors are investigated because of their compatibility with flexible electronics, or for the implementation of on-chip optical interconnects. Such devices are characterized by ultrahigh photocurrent gain, but their photoresponse scales ... More
Asymptotically optimal bound on the adjacent vertex distinguishing edge choice numberMay 03 2017An adjacent vertex distinguishing edge colouring of a graph $G$ without isolated edges is its proper edge colouring such that no pair of adjacent vertices meets the same set of colours in $G$. We show that such colouring can be chosen from any set of ... More
Factors of generalised polynomials and automatic sequencesFeb 07 2018The aim of this short note is to generalise the result of Rampersad--Shallit saying that an automatic sequence and a Sturmian sequence cannot have arbitrarily long common factors. We show that the same result holds if a Sturmian sequence is replaced by ... More
Sparse generalised polynomialsNov 30 2016We investigate generalised polynomials (i.e. polynomial-like expressions involving the use of the floor function) which take the value $0$ on all integers except for a set of density $0$. Our main result is that the set of integers where a sparse generalised ... More
Point-defect engineering of MoN/TaN superlattice films: A first-principles and experimental studyMay 10 2019Superlattice architecture represents an effective strategy to improve performance of hard protective coatings. Our model system, MoN/TaN, combines materials well-known for their high ductility as well as a strong driving force for vacancies. In this work, ... More
Meta-Learning by the Baldwin EffectJun 06 2018Jun 22 2018The scope of the Baldwin effect was recently called into question by two papers that closely examined the seminal work of Hinton and Nowlan. To this date there has been no demonstration of its necessity in empirically challenging tasks. Here we show that ... More
Sets of recurrence as bases for the positive integersApr 09 2015We study sets of the form $A = \big\{ n \in \mathbb N \big| \lVert p(n) \rVert_{\mathbb R / \mathbb Z} \leq \varepsilon(n) \big\}$ for various real valued polynomials $p$ and decay rates $\varepsilon$. In particular, we ask when such sets are bases of ... More
Gowers norms for the Thue-Morse and Rudin-Shapiro sequencesNov 30 2016We estimate Gowers uniformity norms for some classical automatic sequences, such as the Thue-Morse and Rudin-Shapiro sequences. The methods can also be extended to other automatic sequences. As an application, we asymptotically count arithmetic progressions ... More
Algorithmic classification of noncorrelated binary pattern sequencesMay 08 2019We show that, following terminology of Zheng, Peng and Kamae, it is possible to classify all noncorrelated binary pattern sequences of any given degree. As an application, we verify computationally that there are exactly $2272$ noncorrelated binary pattern ... More
Symmetries and conservation laws for a generalization of Kawahara equationOct 05 2018Nov 28 2018We provide a complete classification of generalized and formal symmetries and local conservation laws for an evolution equation which generalizes the Kawahara equation having important applications in the study of plasma waves and capillary-gravity water ... More
Biophysical inference of epistasis and the effects of mutations on protein stability and functionFeb 23 2018Mar 30 2018Understanding the relationship between protein sequence, function, and stability is a fundamental problem in biology. While high-throughput methods have produced large numbers of sequence-function pairs, functional assays do not distinguish whether mutations ... More
On the homotopy transfer of $A_\infty$ structuresApr 06 2017Nov 30 2017The present article is devoted to the study of transfers for $A_\infty$ structures, their maps and homotopies, as developed in \cite{Markl06}. In particular, we supply the proofs of claims formulated therein and provide their extension by comparing them ... More
The 1-2-3 Conjecture almost holds for regular graphsSep 27 2018The well-known 1-2-3 Conjecture asserts that the edges of every graph without isolated edges can be weighted with $1$, $2$ and $3$ so that adjacent vertices receive distinct weighted degrees. This is open in general, while it is known to be possible from ... More
Stochastic, Distributed and Federated Optimization for Machine LearningJul 04 2017We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear convergence for strongly ... More
A note on asymptotically optimal neighbour sum distinguishing colouringsMar 01 2017The least $k$ admitting a proper edge colouring $c:E\to\{1,2,\ldots,k\}$ of a graph $G=(V,E)$ without isolated edges such that $\sum_{e\ni u}c(e)\neq \sum_{e\ni v}c(e)$ for every $uv\in E$ is denoted by $\chi'_{\Sigma}(G)$. It has been conjectured that ... More
Summary of Parallel Session: "Relativistic and Particle Astrophysics"Jan 21 2017The parallel session on "Relativistic and Particle Astrophysics" was held on 14th December 2015. Here a short summary of each presentation of this parallel session is given.
Big Bang as a critical pointApr 01 2014This essay addresses the issue of gravitational phase transitions in the early universe. We suggest that a second order phase transition observed in the Causal Dynamical Triangulations approach to quantum gravity may have a cosmological relevance. The ... More
Cluster size distribution in the autocatalytic growth modelNov 26 2013We generalize the model of transition-metal nanocluster growth in aqueous solution, proposed recently [Phys. Rev. E \textbf{87}, 022132 (2013)]. In order to model time evolution of the system, kinetic equations describing time dependence of the rate of ... More
Charge asymmetry in top quark pair production in the di-lepton channel at the ATLAS experimentNov 30 2012The charge asymmetry in top quark pair production in the di-lepton $t\bar t$ channel using the ATLAS experiment at Large Hadron Collider is presented. The asymmetry is studied in the distribution of absolute rapidity difference between top and anti-top. ... More