Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

ML-Based Analysis of Particle Distributions in High-Intensity Laser Experiments: Role of Binning Strategy

When entering the phase of big data processing and statistical inferences in experimental physics, the efficient use of machine learning methods may require optimal data preprocessing methods and, in particular, optimal balance between details and noise. In experimental studies of strong-field quantum electrodynamics with intense lasers, this balance concerns data binning for the observed distributions of particles and photons. Here we analyze the aspect of binning with respect to different machine learning methods (Support Vector Machine (SVM), Gradient Boosting Trees (GBT), Fully-Connected Neural Network (FCNN), Convolutional Neural Network (CNN)) using numerical simulations that mimic expected properties of upcoming experiments. We see that binning can crucially affect the performance of SVM and GBT, and, to a less extent, FCNN and CNN. This can be interpreted as the latter methods being able to effectively learn the optimal binning, discarding unnecessary information. Nevertheless, given limited training sets, the results indicate that the efficiency can be increased by optimizing the binning scale along with other hyperparameters. We present specific measurements of accuracy that can be useful for planning of experiments in the specified research area.     

Resonance phenomena of π-mode forming in multi-element gratings

An analysis of resonances of scattering from multi-element grating formed by a finite number of resonant elements is presented. It has been shown that gratings with three and more elements on its period can support the π-mode. The π-mode of a grating is characterized by the existence of the regions in the vicinity of the grating and along its period where the electromagnetic field has opposite phases. The existence and excitation of the π-mode in finite gratings with resonant cells formed by several scatterers having open cavities have been studied. The particular case of the grating with cells formed by three identical slotted cylinders has been considered in detail. An application of gratings which support the π-mode in electron-vacuum oscillators of millimeter waves for efficient deceleration of electrons and extracting energy from electron beam is discussed.     

Synthesis, structure, and X-band (9.5 GHz) EPR characterization of the new series of pH-sensitive spin probes: N,N-disubstituted 4-amino-2,2,5,5-tetramethyl-3-imidazoline 1-oxyls

[reaction: see text] An approach to the synthesis of new imidazoline nitroxides bearing an N',N'-disubstituted amidine group is reported. The approach is based on the alkylation of diamagnetic 4-R-amino-1,2,2,5,5-pentamethyl-3-imidazolines with bromoacetic acid ethyl ester; the products of alkylation are further oxidized to the corresponding nitroxides. The approach allows a variety of functional groups to be introduced into the nitroxide molecule structure. Alkylation with bromoacetic acid ethyl ester was found to proceed with high regioselectivity and afford the products of exo-alkylation. The regiochemical assignment is made on the basis of 13C NMR spectra and confirmed by X-ray diffraction study. All of the nitroxides synthesized here were shown to have pH-dependent EPR spectra with pKa ranging from 3.5 to 6.2. For nitroxides 13 bearing the carboxylic group remote to the nitroxide moiety, the changes in isotropic magnetic parameters of EPR spectra due to reversible deprotonation of the carboxylic group were found to be small. For these nitroxides, we demonstrate an alternative approach for pKa determination that is based on measuring the peak-to-peak line width of the EPR spectrum in the presence of the paramagnetic broadening agent potassium ferricyanide. The partition coefficients of nitroxides in octanol/H2O and octanol/phosphate buffer solution mixtures were measured to reveal a range of their lipophilicities.     

The behavior of benzene confined in a single wall carbon nanotube

We present the molecular dynamics study of benzene molecules confined into the single wall carbon nanotube. The local structure and orientational ordering of benzene molecules are investigated. It is found that the molecules mostly group in the middle distance from the axis of the tube to the wall. The molecules located in the vicinity of the wall demonstrate some deviation from planar shape. There is a tilted orientational ordering of the molecules which depends on the location of the molecule. It is shown that the diffusion coefficient of the benzene molecules is very small at the conditions we report here. © 2015 Wiley Periodicals, Inc.     

Comparison of engineering methods of loss prediction in thin ferromagnetic laminations

The loss predictive methods based on the static and dynamic components of power loss are compared with the methods where the total loss is subdivided into hysteresis, classical and excess components. It is explained why the simplest two-component methods can be preferable. An approach to the characterization of a given steel is outlined.     

Contractions with rank one defect operators and truncated CMV matrices

The main issue we address in the present paper are the new models for completely nonunitary contractions with rank one defect operators acting on some Hilbert space of dimension N?∞. These models complement nicely the well-known models of Livšic and Sz.-Nagy-Foias. We show that each such operator acting on some finite-dimensional (respectively, separable infinite-dimensional Hilbert space) is unitarily equivalent to some finite (respectively semi-infinite) truncated CMV matrix obtained from the “full” CMV matrix by deleting the first row and the first column, and acting in CN (respectively ?²(N)). This result can be viewed as a nonunitary version of the famous characterization of unitary operators with a simple spectrum due to Cantero, Moral and Velázquez, as well as an analog for contraction operators of the result from [Yu. Arlinski?, E. Tsekanovski?, Non-self-adjoint Jacobi matrices with a rank-one imaginary part, J. Funct. Anal. 241 (2006) 383-438] concerning dissipative non-self-adjoint operators with a rank one imaginary part. It is shown that another functional model for contractions with rank one defect operators takes the form of the compression f(ζ)→PK(ζf(ζ)) on the Hilbert space L²(T,dμ) with a probability measure μ onto the subspace K=L²(T,dμ)?C. The relationship between characteristic functions of sub-matrices of the truncated CMV matrix with rank one defect operators and the corresponding Schur iterates is established. We develop direct and inverse spectral analysis for finite and semi-infinite truncated CMV matrices. In particular, we study the problem of reconstruction of such matrices from their spectrum or the mixed spectral data involving Schur parameters. It is pointed out that if the mixed spectral data contains zero eigenvalue, then no solution, unique solution or infinitely many solutions may occur in the inverse problem for truncated CMV matrices. The uniqueness theorem for recovered truncated CMV matrix from the given mixed spectral data is established. In this part the paper is closely related to the results of Hochstadt and Gesztesy-Simon obtained for finite self-adjoint Jacobi matrices.