High-energy physics experiments rely on reconstruction of the trajectories of particles produced at the interaction point. This is a challenging task, especially in the high track multiplicity environment generated by p-p collisions at the LHC energies. A typical event includes hundreds of signal examples (interesting decays) and a significant amount of noise (uninteresting examples). This work describes a modification of the Artificial Retina algorithm for fast track finding: numerical optimization methods were adopted for fast local track search. This approach allows for considerable reduction of the total computational time per event. Test results on simplified simulated model of LHCb VELO (VErtex LOcator) detector are presented. Also this approach is well-suited for implementation of paralleled computations as GPGPU which look very attractive in the context of upcoming detector upgrades.

High-energy physics experiments rely on reconstruction of the trajectories of particles produced at the interaction point. This is a challenging task, especially in the high track multiplicity environment generated by p-p collisions at the LHC energies. A typical event includes hundreds of signal examples (interesting decays) and a significant amount of noise (uninteresting examples). This work describes a modification of the Artificial Retina algorithm for fast track finding: numerical optimization methods were adopted for fast local track search. This approach allows for considerable reduction of the total computational time per event. Test results on simplified simulated model of LHCb VELO (VErtex LOcator) detector are presented. Also this approach is well-suited for implementation of paralleled computations as GPGPU which look very attractive in the context of upcoming detector upgrades.

We consider N-component synchronization models defined in terms of stochastic particle systems with special interaction. For general (nonsymmetric) Markov models we discuss phenomenon of the long time stochastic synchronization. We study behavior of the system in different limit situations related to appropriate changes of variables and scalings. For N = 2 limit distributions are found explicitly.

We investigate combinatorial properties of a higher invariant of magnetic lines. Assume that a 3-component link L is modeled by a magnetic eld B, which is represented by 3 closed magnetic lines. Main Theorem relates the integral invariant M(B) and a combinatorial invariant ~M (L), dened from the Conway polynomial. As a corollary of Main Theorem, asymptotic properties for combinatorial links are proposed. The combinatorial invariant ~M satises these asymptotic properties.

L´evy stochastic processes and related fine analytic properties of probability distributions such as infinite divisibility play an important role in construction of stochastic models of various distributed networks (e.g., local clock synchronization), of some physical systems (e.g., anomalous diffusions, quantum probability models), of finance etc. Nevertheless, little is known about limit probability laws resulted from the long time behavior of such stochastic systems. In this paper we will focus on the impact of interaction graph topologies on limit laws of multicomponent synchronization models.

We review recent advances in the analysis of the Wang–Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random walk in the energy space biased with the Wang–Landau probability. Properties of the TMES can explain some features of the Wang–Landau algorithm, for example, the flatness of the histogram. We show that the Wang–Landau probability with the true DOS generates a Markov process in the energy space and the inverse spectral gap of the TMES can estimate the mixing time of this Markov process. We argue that an efficient implementation of theWang–Landau algorithm consists of two simulation stages: the original Wang–Landau procedure for the first stage and a 1/t modification for the second stage. The mixing time determines the characteristic time for convergence to the true DOS in the second simulation stage. The parameter of the convergence of the estimated DOS to the true DOS is the difference of the largest TMES eigenvalue from unity. The characteristic time of the first stage is the tunneling time, i.e., the time needed for the system to visit all energy levels.

In this paper we construct a smooth arc without bifurcation points joining source- sink diffeomorphisms on the two-dimensional sphere.

We consider a family of nonlinear diffusion equations with nonlinear sources. Weassume that all nonlinearities are polynomials with respect to a dependent variable. Thetraveling wave reduction of this family of equations is an equation of the Lienard–type. Applyingrecently obtained criteria for integrability of Lienard–type equations we find some new integrablefamilies of traveling wave reductions of nonlinear diffusion equations as well as their generalanalytical solutions.

We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the mixing time of the Markov chain. We estimate numerically the dependence of the mixing time on the lattice size, and extract the mixing exponent.

The SHiP experiment is designed to search for very weakly interacting particles beyond the Standard Model which are produced in a 400 GeV/c proton beam dump at the CERN SPS. The critical challenge for this experiment is to keep the Standard Model background level negligible. In the beam dump, around 10^11 muons will be produced per second. The muon rate in the spectrometer has to be reduced by at least four orders of magnitude to avoid muoninduced backgrounds. It is demonstrated that new improved active muon shield may be used to magnetically deflect the muons out of the acceptance of the spectrometer.

In this work, we experimentally studied optical delay lines on silicon nitride platform for telecomm wavelength (1550 nm). We modeled the group delay time and fabricated spiral optical delay lines with different waveguide widths and radii as well as measured their transmission. For the half etched rib waveguides we achieved the losses in the range of 3 dB/cm

We discuss a class of optimization problems related to stochastic models of wireless sensor networks (WSNs). We consider a sensor network that consists of a single server node and m groups of identical client nodes. The goal is to minimize the cost functional which accumulates synchronization errors and energy consumption over a given time interval. The control function u(*t*) = (*u*1(*t*),...,um(*t*)) corresponds to the power of the server node transmitting synchronization signals to the groups of clients. We find the structure of extremal trajectories. We show that optimal solutions for such models can contain singular arcs.

In the process of astronomical observations collected vast amounts of data. BSA (Big Scanning Antenna) LPI used in the study of impulse phenomena, daily logs 87.5 GB of data (32 TB per year). These data have important implications for both short-and long-term monitoring of various classes of radio sources (including radio transients of different nature), monitoring the Earth's ionosphere, the interplanetary and the interstellar plasma, the search and monitoring of different classes of radio sources. In the framework of the studies discovered 83096 individual pulse events (in the interval of the study highlighted July 2012 - October 2013), which may correspond to pulsars, twinkling springs, and a rapid radio transients. Detected impulse events are supposed to be used to filter subsequent observations. The study suggests approach, using the creation of the multilayered artificial neural network, which processes the input raw data and after processing, by the hidden layer, the output layer produces a class of impulsive phenomena.

We consider a quasi-one-dimensional model of a two-component Fermi gas at zero temperature on one, two and three-leg attractive-U Hubbard ladders. We construct the grand canonical phase diagram of a two-component spin-polarized gas. We find that the structure of the phase diagram of the attractive-U Hubbard model for two and three leg ladders significantly differs q from the structure of the phase diagram of a single chain. We argue that the single chain model is a special case, and that multichain ladders display qualitative features of the 1D-to-3D crossover, observed in experiments with trapped ultracold gases.

Cryo-filters are essential while studying electronic properties of nanoscale structures at very low temperatures. In this report we present the simple measuring methodology and experimental impedance characteristics of customized lumped filters cooled down to 4.2K in the 10 Hz-500 MHz frequency range. In particular, we tested the home-made permalloy-core RL filters, the MurataTMChip Ferrite Bead filter, and the ToshibaTMAmobeadsTMcores. We use the high-frequency generalization of four-terminal sensing method to account for the wiring retardation effects, which are important when working with ultralow temperature systems.

The problem of constructing and classifying stationary equilibria of point vortices in the plane is studied. An ordinary differential equation that enables one to find positions of point vortices with circulations $Γ_1$, $Γ_2$, and $Γ_3$ in stationary equilibrium is obtained. A necessary condition of an equilibrium existing is derived. The case of point vortex systems consisting of $*n* + 2$ point vortices with $*n$* vortices of circulation $Γ_1$ and two vortices of circulations $Γ_2 = *a*Γ_1$ and $Γ_3 = *b*Γ_1$, where $*a$* and $*b$ *are integers, is considered in detail. The properties of polynomial solutions of the corresponding ordinary differential equation are investigated. A set of positive–dimensional equilibrium configurations is found. A continuous free parameter is presented in the coefficients of corresponding polynomial solutions. These free parameters affect the positions of the roots and hence the vortex positions. Stationary equilibrium that could be derived from each other by rotation, extension, parallel translation is considered as equivalent. All found configurations seem to be new.

The canonical technique for Monte Carlo simulations in statistical physics is importance sampling via a suitably constructed Markov chain. While such approaches are quite successful, they are not particularly well suited for parallelization as the chain dynamics is sequential, and if replicated chains are used to increase statistics each of them relaxes into equilibrium with an intrinsic time constant that cannot be reduced by parallel work. Population annealing is a sequential Monte Carlo method that simulates an ensemble of system replica under a cooling protocol. The population element makes it naturally well suited for massively parallel simulations, and bias can be systematically reduced by increasing the population size. We present an implementation of population annealing on graphics processing units and discuss its behavior for different systems undergoing continuous and first-order phase transitions.

The one-dimensional discrete Tent map is a well-known example of a map whose fixed points are all unstable on the segment [0,1]. This map leads to the positivity of the Lyapunov exponent for the corresponding recurrent sequence. Therefore in a situation of general position, this sequence must demonstrate the properties of deterministic chaos. However if the first term of the recurrence sequence is taken as a decimal fraction with a fixed number "k" of digits after the decimal point and all calculations are carried out accurately, then the situation turns out to be completely different. In this case, first, the Tent map does not lead to an increase in significant digits in the terms of the sequence, and secondly, demonstrates the existence of a finite number of eventually periodic orbits, which are attractors for all other decimal numbers with the number of significant digits not exceeding "k".

The density functional theory (DFT) is a research tool of the highest importance for electronic structure calculations. It is often the only affordable method for ab initio calculations of complex materials. The pseudopotential approach allows reducing the total number of electrons in the model that speeds up calculations. However, there is a lack of pseudopotentials for heavy elements suitable for condensed matter DFT models. In this work, we present a pseudopotential for uranium developed in the Goedecker–Teter–Hutter form. Its accuracy is illustrated using several molecular and solid-state calculations.

By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is actually determined by the structure of the universal R-matrix. We call functional relations between such universal integrability objects, and so, being independent of the representation in the quantum space, the universal functional relations. We present a short review of the universal functional relations for the quantum integrable systems associated with the quantum groups of loop Lie algebras.

This short note is a review of the intriguing connection between the quantum Gaudin model and the classical KP hierarchy recently established in [A.Alexandrov, S.Leurent, Z.Tsuboi, A.Zabrodin, The master T-operator for the Gaudin model and KP hierarchy, Nuclear Physics B 883 (2014) 173-223]. We construct the generating function of integrals of motion for the quantum Gaudin model with twisted boundary conditions (the master T-operator) and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. This implies that zeros of eigenvalues of the master T-operator in the spectral parameter have the same dynamics as the Calogero-Moser system of particles.