Recent publications

This article provides a study on the feasibility of applying gravitational potential interpolation for high-precision ballistic calculations.

The accurate simulation of additional interactions at the ATLAS experiment for the analysis of proton–proton collisions delivered by the Large Hadron Collider presents a significant challenge to the computing resources. During the LHC Run 2 (2015–2018), there were up to 70 inelastic interactions per bunch crossing, which need to be accounted for in Monte Carlo (MC) production. In this document, a new method to account for these additional interactions in the simulation chain is described. Instead of sampling the inelastic interactions and adding their energy deposits to a hard-scatter interaction one-by-one, the inelastic interactions are presampled, independent of the hard scatter, and stored as combined events. Consequently, for each hard-scatter interaction, only one such presampled event needs to be added as part of the simulation chain. For the Run 2 simulation chain, with an average of 35 interactions per bunch crossing, this new method provides a substantial reduction in MC production CPU needs of around 20%, while reproducing the properties of the reconstructed quantities relevant for physics analyses with good accuracy.

The ATLAS experiment at the Large Hadron Collider has a broad physics programme ranging from precision measurements to direct searches for new particles and new interactions, requiring ever larger and ever more accurate datasets of simulated Monte Carlo events. Detector simulation with Geant4 is accurate but requires significant CPU resources. Over the past decade, ATLAS has developed and utilized tools that replace the most CPU-intensive component of the simulation—the calorimeter shower simulation—with faster simulation methods. Here, AtlFast3, the next generation of high-accuracy fast simulation in ATLAS, is introduced. AtlFast3 combines parameterized approaches with machine-learning techniques and is deployed to meet current and future computing challenges, and simulation needs of the ATLAS experiment. With highly accurate performance and significantly improved modelling of substructure within jets, AtlFast3 can simulate large numbers of events for a wide range of physics processes.

Biologically plausible models of learning may provide a crucial insight for building autonomous intelligent agents capable of performing a wide range of tasks. In this work, we propose a hierarchical model of an agent operating in an unfamiliar environment driven by a reinforcement signal. We use temporal memory to learn sparse distributed representation of state–actions and the basal ganglia model to learn effective action policy on different levels of abstraction. The learned model of the environment is utilized to generate an intrinsic motivation signal, which drives the agent in the absence of the extrinsic signal, and through acting in imagination, which we call dreaming. We demonstrate that the proposed architecture enables an agent to effectively reach goals in grid environments.

This paper is devoted to the development of algorithms for finding unit distance graphs with chromatic number greater than 4, embedded in a two-dimensional sphere or plane. Such graphs provide a lower bound for the Hadwiger–Nelson problem on the chromatic number of the plane and its generalizations to the case of the sphere. A series of 5-chromatic unit distance graphs on 64513 vertices embedded into the plane is constructed. Unlike previously known examples, these graphs do not use the Moser spindle as the base element. The construction of 5-chromatic graphs embedded in a sphere at two values of the radius is given. Namely, the 5-chromatic unit distance graph on 372 vertices embedded into the circumsphere of an icosahedron with a unit edge length, and the 5-chromatic graph on 972 vertices embedded into the circumsphere of a great icosahedron are constructed.

We deal with an extremal problem concerning panchromatic colorings of hypergraphs. A vertex r-coloring of a hypergraph H is panchromatic if every edge meets every color. We prove that for every 2≤r<n100lnn3, every n-uniform hypergraph H with |E(H)|≤cr2nlnnr−1rrr−1n−1 has a panchromatic coloring with r colors, where c>0 is an absolute constant.

The deck of a graph G is the multiset of cards {G−v:v∈V(G)}. Myrvold (1992) showed that the degree sequence of a graph on n≥7 vertices can be reconstructed from any deck missing one card. We prove that the degree sequence of a graph with average degree d can be reconstructed from any deck missing O(n/d3) cards. In particular, in the case of graphs that can be embedded on a fixed surface (e.g. planar graphs), the degree sequence can be reconstructed even when a linear number of the cards are missing.

In this short note, we show that for any ϵ>0 and k<n0.5−ϵ the choice number of the Kneser Graph KGn,k is Θ(nlogn).

Quantitative estimates related to the classical Borsuk problem of splitting set in Euclidean space into subsets of smaller diameter are considered. For a given k there is a minimal diameter of subsets at which there exists a covering with k subsets of any planar set of unit diameter. In order to find an upper estimate of the minimal diameter we propose an algorithm for finding sub-optimal partitions. In the cases 10⩽k⩽17 some upper and lower estimates of the minimal diameter are improved. Another result is that any set M⊂R3 of a unit diameter can be partitioned into four subsets of a diameter not greater than 0.966.

In this paper, we study structural and adsorption properties of graphene irradiated with 46 MeV Ar ions and 240 keV H ions on SiO2/Si and copper substrates by micro-Raman spectroscopy. Graphene irradiated with H ions demonstrated evidence of both high and low defect density regions on a sub-micron scale. TRIM calculations showed that substrate was the dominant defect source with a contribution from about 55% for H ions in graphene on SiO2/Si to 90% for Ar in graphene on SiO2/Si. Charge carrier density analysis showed p-type adsorption doping saturating at (0.48 ± 0.08) × 10¹³ cm⁻² or (0.45 ± 0.09) × 10¹³ cm⁻² with a defect density of 1.5 × 10¹¹ cm⁻² or 1.2 × 10¹¹ cm⁻² for graphene on SiO2/Si or copper, respectively; this was analyzed in the framework of physisorption and dissociative chemisorption. This study is useful towards the development of functionalization methods, molecular sensor design, and any graphene application requiring modification of this material by controlled defect introduction.

In this paper, we prove new complexity bounds for zeroth-order methods in non-convex optimization with inexact observations of the objective function values. We use the Gaussian smoothing approach of Nesterov and Spokoiny(Found Comput Math 17(2): 527–566, 2015. https://doi.org/10.1007/s10208-015-9296-2) and extend their results, obtained for optimization methods for smooth zeroth-order non-convex problems, to the setting of minimization of functions with Hölder-continuous gradient with noisy zeroth-order oracle, obtaining noise upper-bounds as well. We consider finite-difference gradient approximation based on normally distributed random Gaussian vectors and prove that gradient descent scheme based on this approximation converges to the stationary point of the smoothed function. We also consider convergence to the stationary point of the original (not smoothed) function and obtain bounds on the number of steps of the algorithm for making the norm of its gradient small. Additionally we provide bounds for the level of noise in the zeroth-order oracle for which it is still possible to guarantee that the above bounds hold. We also consider separately the case of \(\nu = 1\) and show that in this case the dependence of the obtained bounds on the dimension can be improved.

We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the objective is given as an expectation of a function given as a solution to a random optimization problem. We employ the structure of the problem and obtain a convex–concave stochastic saddle-point reformulation of this problem. In the setting when the distribution of random probability measures is discrete, we propose a stochastic optimization algorithm and estimate its complexity. The second result, based on kernel methods, extends the previous one to the arbitrary distribution of random probability measures. Moreover, this new algorithm has a total complexity better than the Stochastic Approximation approach combined with the Sinkhorn algorithm in many cases. We also illustrate our developments by a series of numerical experiments.

Let A,B⊆Rd both span Rd such that 〈a,b〉∈{0,1} holds for all a∈A, b∈B. We show that |A|⋅|B|≤(d+1)2d. This allows us to settle a conjecture by Bohn, Faenza, Fiorini, Fisikopoulos, Macchia, and Pashkovich (2015) concerning 2-level polytopes. Such polytopes have the property that for every facet-defining hyperplane H there is a parallel hyperplane H′ such that H∪H′ contain all vertices. The authors conjectured that for every d-dimensional 2-level polytope P the product of the number of vertices of P and the number of facets of P is at most d2d+1, which we show to be true.

We consider β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-smooth (satisfies the generalized Hölder condition with parameter β>2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta > 2$$\end{document}) stochastic convex optimization problem with zero-order one-point oracle. The best known result was (Akhavan et al. in Exploiting higher order smoothness in derivative-free optimization and continuous bandits, 2020): Ef(x¯N)-f(x∗)=On2γNβ-1β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\mathbb {E}}\left[ f(\overline{x}_N) - f(x^*)\right] = {\mathcal {O}} \left( \dfrac{n^{2}}{\gamma N^{\frac{\beta -1}{\beta }}} \right) \end{aligned}$$\end{document}in γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}-strongly convex case, where n is the dimension. In this paper we improve this bound: Ef(x¯N)-f(x∗)=On2-1βγNβ-1β.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\mathbb {E}} \left[ f(\overline{x}_N) - f(x^*)\right] = {\mathcal {O}} \left( \dfrac{n^{2-{\frac{1}{\beta }}}}{\gamma N^{\frac{\beta -1}{\beta }}} \right) . \end{aligned}$$\end{document}

The formation of alternating amorphous-crystalline structures on the surface of Ge2Sb2Te5 thin film upon the single-pass direct writing by a femtosecond laser beam was demonstrated. We obtained high quality periodic surface structures in non-ablative mode and determined the optimal laser fluence, pulse number and scanning speed for their scaling. The produced structures were stripes up to 1-mm long and consisted of up to 50 parallel amorphous-crystalline lines oriented perpendicular to the light polarization. These two-phase binary stripes had a period equal to the recording beam wavelength and exhibited diffraction grating behavior due to remarkable optical contrast. Diffraction spectra were investigated experimentally and also simulated using scalar and vector theory of diffraction.

We propose a direct arbitrary Lagrangian-Eulerian (ALE) variant of the previously developed discrete velocity method to solve the kinetic equation with the Bhatnagar–Gross–Krook (BGK) model collision integral. The effectiveness and robustness of the new scheme are demonstrated by computing the axisymmetric plume expansion into a low pressure gas due to evaporation from the solid surface caused by a nanosecond laser pulse. The numerical studies show that the new numerical scheme provides a very significant reduction of the required computing time as compared to the discrete velocity method on a fixed mesh. Cross-comparisons with the direct simulation Monte Carlo (DSMC) approach further confirm the accuracy of the new scheme and model kinetic equations as applied to plume expansion studies. Finally, the good parallel scalability of the new ALE scheme as implemented into the in-house code Nesvetay is demonstrated. The use of two very different approaches to numerical prediction of the transient flow pattern allows us to obtain a reliable numerical solution, which can be regarded as a new transient benchmark test.

A multigraph drawn in the plane is called non-homotopic if no pair of its edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. Edges are allowed to intersect each other and themselves. It is easy to see that a non-homotopic multigraph on n>1 vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and m>4n edges is larger than cm2n for some constant c>0, and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and m tends to infinity.

We introduce an inexact oracle model for variational inequalities with monotone operators, propose a numerical method that solves such variational inequalities, and analyze its convergence rate. As a particular case, we consider variational inequalities with Hölder-continuous operator and show that our algorithm is universal. This means that, without knowing the Hölder exponent and Hölder constant, the algorithm has the least possible in the worst-case sense complexity for this class of variational inequalities. We also consider the case of variational inequalities with a strongly monotone operator and generalize the algorithm for variational inequalities with inexact oracle and our universal method for this class of problems. Finally, we show how our method can be applied to convex–concave saddle point problems with Hölder-continuous partial subgradients.

The interference of electromagnetic signals from lightning discharges in the frequency range below 100 Hz is the source of a global electromagnetic phenomenon in the Earth's atmosphere known as the Schumann resonance (SR). Changes in the parameters of SR signals caused by geophysical disturbances make it possible to study the state and dynamics of the lower ionosphere. When calculating the SR parameters, there are problems associated with the impact of electromagnetic interference of natural and anthropogenic origin. The main natural sources of interference are signals associated with the radiation of nearby lightning discharges, as well as the influence of the Alfvén ionospheric resonator. The paper presents a new method for calculating the SR parameters, which makes it possible to find the spectra distorted by interference, mention above, and exclude them from further processing. The developed technique significantly increased the temporal resolution of the obtained data on the frequency and amplitude of the SR. Due to this, it became possible to study the influence of fast heliogeophysical disturbances (such as solar X‐ray flares) on the lower ionosphere and, as a consequence, on the parameters of the SR. An analysis of the experimental data made it possible to establish a linear dependence of the SR frequency on the logarithm of the X‐ray flux in the range up to 0.2 nm during a class X solar flare.

Effect of in situ formed silver nanoparticles doping on electrorheological response of highly porous chitosan particles in suspensions of polydimethylsiloxane (silicone oil) is considered. Silver nanoparticles are directly reduced by chitosan from solution. Highly porous chitosan particles with different silver content are fabricated by spraying from solution followed by freeze-drying. A high and stable electrorheological response of suspensions in wide range of electric field strength is observed at a very low filler content of 1 wt%. The nature of the electrorheological effect is considered from the standpoint of dielectric spectroscopy. The activation energies of polarization processes are determined from the temperature dependences of the dielectric loss modulus. The study shows the opportunity to control the properties of stimuli-responsive materials by changing the structure and physicochemical properties of the functional filler. This approach opens up new possibilities for creating materials with high performance and predetermined properties.

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