Tensors in modelling multi-particle interactions

In this work we present recent results on application of low-rank tensor decompositions to modelling of aggregation kinetics taking into account multi-particle collisions (for three and more particles). Such kinetics can be described by system of nonlinear differential equations with right-hand side requiring $N^D$ operations for its straight-forward evaluation, where $N$ is number of particles size classes and $D$ is number of particles colliding simultaneously. Such a complexity can be significantly reduced by application low rank tensor decompositions (either Tensor Train or Canonical Polyadic) to acceleration of evaluation of sums and convolutions from right-hand side. Basing on this drastic reduction of complexity for evaluation of right-hand side we further utilize standard second order Runge-Kutta time integration scheme and demonstrate that our approach allows to obtain numerical solutions of studied equations with very high accuracy in modest times. We also show preliminary results on parallel scalability of novel approach and conclude that it can be efficiently utilized with use of supercomputers.Comment: LaTEX, 8 pages, 3 figures, submitted to proceedings of LSSC'19 conference, Sozopol, Bulgari

Search for Axionlike and Scalar Particles with the NA64 Experiment

We carried out a model-independent search for light scalar (s) and pseudoscalar axionlike (a) particles that couple to two photons by using the high-energy CERN SPS H4 electron beam. The new particles, if they exist, could be produced through the Primakoff effect in interactions of hard bremsstrahlung photons generated by 100 GeV electrons in the NA64 active dump with virtual photons provided by the nuclei of the dump. The a(s) would penetrate the downstream HCAL module, serving as shielding, and would be observed either through their $a(s)\to\gamma \gamma$ decay in the rest of the HCAL detector or as events with large missing energy if the a(s) decays downstream of the HCAL. This method allows for the probing the a(s) parameter space, including those from generic axion models, inaccessible to previous experiments. No evidence of such processes has been found from the analysis of the data corresponding to $2.84\times10^{11}$ electrons on target allowing to set new limits on the $a(s)\gamma\gamma$-coupling strength for a(s) masses below 55 MeV.Comment: This publication is dedicated to the memory of our colleague Danila Tlisov. 7 pages, 5 figures, revised version accepted for publication in Phys. Rev. Let

Electro-Magnetic Nucleon Form Factors and their Spectral Functions in Soliton Models

It is demonstrated that in simple soliton models essential features of the electro-magnetic nucleon form factors observed over three orders of magnitude in momentum transfer $t$ are naturally reproduced. The analysis shows that three basic ingredients are required: an extended object, partial coupling to vector mesons, and relativistic recoil corrections. We use for the extended object the standard skyrmion, one vector meson propagator for both isospin channels, and the relativistic boost to the Breit frame. Continuation to timelike $t$ leads to quite stable results for the spectral functions in the regime from the 2- or 3-pion threshold to about two rho masses. Especially the onset of the continuous part of the spectral functions at threshold can be reliably determined and there are strong analogies to the results imposed on dispersion theoretic approaches by the unitarity constraint.Comment: 24 pages, (RevTeX), 5 PS-figures; Data points in fig.2 and corresponding references added. Final version, to be published in Z.Physik

Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

Improved exclusion limit for light dark matter from e+e- annihilation in NA64

The current most stringent constraints for the existence of sub-GeV dark matter coupling to Standard Model via a massive vector boson A′ were set by the NA64 experiment for the mass region mA′≲250 MeV, by analyzing data from the interaction of 2.84×1011 100-GeV electrons with an active thick target and searching for missing-energy events. In this work, by including A′ production via secondary positron annihilation with atomic electrons, we extend these limits in the 200-300 MeV region by almost an order of magnitude, touching for the first time the dark matter relic density constrained parameter combinations. Our new results demonstrate the power of the resonant annihilation process in missing energy dark-matter searches, paving the road to future dedicated e+ beam efforts

Search for Axionlike and Scalar Particles with the NA64 Experiment

We carried out a model-independent search for light scalar (s) and pseudoscalar axionlike (a) particles that couple to two photons by using the high-energy CERN SPS H4 electron beam. The new particles, if they exist, could be produced through the Primakoff effect in interactions of hard bremsstrahlung photons generated by 100 GeV electrons in the NA64 active dump with virtual photons provided by the nuclei of the dump. The a(s) would penetrate the downstream HCAL module, serving as a shield, and would be observed either through their a(s)→γγ decay in the rest of the HCAL detector, or as events with a large missing energy if the a(s) decays downstream of the HCAL. This method allows for the probing of the a(s) parameter space, including those from generic axion models, inaccessible to previous experiments. No evidence of such processes has been found from the analysis of the data corresponding to 2.84×10^{11} electrons on target, allowing us to set new limits on the a(s)γγ-coupling strength for a(s) masses below 55 MeV

Search for pseudoscalar bosons decaying into e+e- pairs in the NA64 experiment at the CERN SPS

We report the results of a search for a light pseudoscalar particle a that couples to electrons and decays to e+e- performed using the high-energy CERN SPS H4 electron beam. If such light pseudoscalar exists, it could explain the ATOMKI anomaly (an excess of e+e- pairs in the nuclear transitions of Be8 and He4 nuclei at the invariant mass ≃17 MeV observed by the experiment at the 5 MV Van de Graaff accelerator at ATOMKI, Hungary). We used the NA64 data collected in the "visible mode"configuration with a total statistics corresponding to 8.4×1010 electrons on target (EOT) in 2017 and 2018. In order to increase sensitivity to small coupling parameter ϵ we also used the data collected in 2016-2018 in the "invisible mode"configuration of NA64 with a total statistics corresponding to 2.84×1011 EOT. The background and efficiency estimates for these two configurations were retained from our previous analyses searching for light vector bosons and axionlike particles (ALP) (the latter were assumed to couple predominantly to γ). In this work we recalculate the signal yields, which are different due to different cross section and lifetime of a pseudoscalar particle a, and perform a new statistical analysis. As a result, the region of the two dimensional parameter space ma-ϵ in the mass range from 1 to 17.1 MeV is excluded. At the mass of the central value of the ATOMKI anomaly (the first result obtained on the beryllium nucleus, 16.7 MeV) the values of ϵ in the range 2.1×10-4<ϵ<3.2×10-4 are excluded

PCA Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes

Multidimensional data distributions can have complex topologies and variable local dimensions. To approximate complex data, we propose a new type of low-dimensional ``principal object'': a principal cubic complex. This complex is a generalization of linear and non-linear principal manifolds and includes them as a particular case. To construct such an object, we combine a method of topological grammars with the minimization of an elastic energy defined for its embedment into multidimensional data space. The whole complex is presented as a system of nodes and springs and as a product of one-dimensional continua (represented by graphs), and the grammars describe how these continua transform during the process of optimal complex construction. The simplest case of a topological grammar (``add a node'', ``bisect an edge'') is equivalent to the construction of ``principal trees'', an object useful in many practical applications. We demonstrate how it can be applied to the analysis of bacterial genomes and for visualization of cDNA microarray data using the ``metro map'' representation. The preprint is supplemented by animation: ``How the topological grammar constructs branching principal components (AnimatedBranchingPCA.gif)''.Comment: 19 pages, 8 figure

On the definition and examples of cones and finsler spacetimes

The authors warmly acknowledge Professor Daniel Azagra (Universidad Complutense, Madrid) his advise on approximation of convex functions as well as Profs. Kostelecky (Indiana University), Fuster (University of Technology, Eindhoven), Stavrinos (University of Athens), Pfeifer (University of Tartu), Perlick (University of Bremen) and Makhmali (Institute of Mathematics, Warsaw) their comments on a preliminary version of the article. The careful revision by the referee is also acknowledged. This work is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Region de Murcia, Spain, by Fundacion Seneca, Science and Technology Agency of the Region de Murcia. MAJ was partially supported by MINECO/FEDER project reference MTM2015-65430-P and Fundacion Seneca project reference 19901/GERM/15, Spain and MS by Spanish MINECO/ERDF project reference MTM2016-78807-C2-1-P.A systematic study of (smooth, strong) cone structures C and Lorentz–Finsler metrics L is carried out. As a link between both notions, cone triples (Ω,T,F), where Ω (resp. T) is a 1-form (resp. vector field) with Ω(T)≡1 and F, a Finsler metric on ker(Ω), are introduced. Explicit descriptions of all the Finsler spacetimes are given, paying special attention to stationary and static ones, as well as to issues related to differentiability. In particular, cone structures C are bijectively associated with classes of anisotropically conformal metrics L, and the notion of cone geodesic is introduced consistently with both structures. As a non-relativistic application, the time-dependent Zermelo navigation problem is posed rigorously, and its general solution is provided.MINECO/FEDER project, Spain MTM2015-65430-PFundacion Seneca 19901/GERM/15Spanish MINECO/ERDF project MTM2016-78807-C2-1-