Networks of polynomial pieces with application to the analysis of point clouds and images

We consider Hölder smoothness classes of surfaces for which we construct piecewise polynomial approximation networks, which are graphs with polynomial pieces as nodes and edges between polynomial pieces that are in ‘good continuation’ of each other. Little known to the community, a similar construction was used by Kolmogorov and Tikhomirov in their proof of their celebrated entropy results for Hölder classes.We show how to use such networks in the context of detecting geometric objects buried in noise to approximate the scan statistic, yielding an optimization problem akin to the Traveling Salesman. In the same context, we describe an alternative approach based on computing the longest path in the network after appropriate thresholding.For the special case of curves, we also formalize the notion of ‘good continuation’ between beamlets in any dimension, obtaining more economical piecewise linear approximation networks for curves.We include some numerical experiments illustrating the use of the beamlet network in characterizing the filamentarity content of 3D data sets, and show that even a rudimentary notion of good continuity may bring substantial improvement.     

Peculiar thermodynamic properties of LJ<Subscript> N</Subscript> (N = 39–55) clusters

The solid-liquid phase transitions of Lennard-Jones clusters LJ_N (N=39–55) were simulated by a microcanonical molecular dynamics method using Lennard-Jones potential, and their thermodynamic quantities were calculated. The caloric curves of clusters (except N=42) have S-bend. To understand this behaviour, configurational and total entropies were evaluated, and dents on the entropy curves were taken as a sign of negative heat capacity. The heat capacities were evaluated for N=39–55 clusters using configurational entropy data. The potential energy distributions have bimodal behaviour for all clusters in the given range at the melting temperature. The distinct melting behaviour of LJ₄₂ was explained by the topology of the potential energy surface by examining the isomer distributions at phase transitions for LJ₃₉-LJ₅₅. The isomer distributions were found to be a useful way to interpret this behaviour and melting dynamics in general. Melting temperature, latent heat and entropy change upon melting values were reported and are consistent with literature values and values calculated from bulk thermodynamic properties. The dependence of these quantities on the size of the clusters was examined and it is found that latent heat is the key quantity to determine the magic numbers.     

A new perspective to stress–strength models

The stress–strength models have been widely used for reliability design of systems. In these models the reliability is defined as the probability that the strength is larger than the stress. The analysis is then based on the binary reliability theory since there are two possible states for the system. In this paper, we study the stress–strength reliability in a different framework assigning more than two states to the system depending on the difference between strength and stress values. In other words, the stress–strength reliability is studied under multi-state system modeling. System state probabilities are evaluated and estimated under various assumptions on the system. The multicomponent form is also studied and some results are provided for large systems.     

The examination of molecular structure properties of 4,4′-oxydiphthalonitrile compound: combined spectral and computational analysis approaches

The synthesis process, X-ray diffraction analysis of its single crystal form and the structural properties of the 4,4′-oxydiphthalonitrile compound by Fourier transform infrared, nuclear magnetic resonance and ultraviolet-visible spectral methods were reported in this study. Density functional theory studies of the compound were carried out by designed modeling with the Becke three-parameter hybrid functional combined with Lee-Yang-Parr correlation functional and 6-311G(d,p) basis set. Some molecular structure parameters obtained theoretically were compared with those obtained from the crystallographic analysis. Vibrational modes and wavenumbers with the aid of the potential energy distribution analysis, carbon and proton chemical shift values with diversified approaches and absorption wavelengths using Time-Dependent Density Functional and Conductor-Like Polarizable Continuum Model in different solvent media were examined theoretically. The compatibility of spectral and theoretical results was evaluated by examining the correlation coefficients. In addition, the frontier molecular orbitals energies, global reactivity parameters, molecular electrostatic potential map, the potential for non-linear optical material and some thermodynamic parameters at different temperature values of the 4,4'-oxydiphthalonitrile compound were investigated at the same theoretical level.     

On system reliability in stress–strength setup

In this paper we study stress–strength reliability for a general coherent system. The exact expression as well as bounds and approximations for system reliability are presented. We also illustrate the estimation procedure for exponential stress–strength distributions.     

Joint distribution of run statistics in partially exchangeable processes

Let {X_i}_i≥1 be an infinite sequence of recurrent partially exchangeable random variables with two possible outcomes as either “1” (success) or “0” (failure). In this paper we obtain the joint distribution of success and failure run statistics in {X_i}_i≥1. The results can be used to obtain the joint distribution of runs in ordinary Markov chains, exchangeable and independent sequences.     

Finite size percolation in regular trees

In the context of percolation in a regular tree, we study the size of the largest cluster and the length of the longest run starting within the first d generations. As d tends to infinity, we prove almost sure and weak convergence results.     

On the mean and extreme distances between failures in Markovian binary sequences

This paper is concerned with the mean, minimum and maximum distances between two successive failures in a binary sequence consisting of Markov dependent elements. These random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes. Exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented.     

Flavonol Glycosides and Iridoids from Asperula lilaciflora

A new flavonol glycoside, quercetin 3‐O‐[6′′′‐O‐3,5‐dihydroxycinnamoyl‐β‐glucopyranosyl‐(1→2)]‐β‐galactopyranoside (named lilacifloroside; 1 ) and a new iridoid 2 (named asperulogenin), were isolated from the aerial parts of Asperula lilaciflora in addition to eight known secondary metabolites, i.e., quercetin, kaempferol, quercetin 3‐O‐β‐glucopyranosyl‐(1→2)‐β‐galactopyranoside, quercetin 3‐O‐β‐glucopyranosyl‐(1→2)‐arabinopyranoside, asperuloside, deacetylasperulosidic acid, asperulosidic acid methyl ester, and chlorogenic acid. The structures were elucidated on the basis of extensive 1D‐ and 2D‐NMR experiments as well as MS data. Compound 1 contains the rare 3,5‐dihydroxycinnamoyl moiety in its structure. This work constitutes the first phytochemical study of the title plant.     

On the lifetime of a random binary sequence

Consider a system with m elements which is used to fulfill tasks. Each task is sent to one element which fulfills a task and the outcome is either fulfillment of the task (“1”) or the failure of the element (“0”). Initially, m tasks are sent to the system. At the second step, a complex of length m₁ is formed and sent to the system, where m₁ is the number of tasks fulfilled at the first step, and so on. The process continues until all elements fail and the corresponding waiting time defines the lifetime of the binary sequence which consists of “1” or “0”. We obtain a recursive equation for the expected value of this waiting time random variable.