Classification of nasopharyngeal cell lines (C666-1, CNE2, NP69) via Raman spectroscopy and decision tree

Researchers have demonstrated that Raman spectroscopy can be used for characterization of tumor cells with excellent spatial resolution. However, performance evaluation of different algorithms in classifying multiclass of Raman spectra has not been reported yet. In this work, we present Raman spectra of nasopharyngeal carcinoma and nasopharyngeal normal cell lines. Combined with student’s t-test and several multivariate approaches, including decision tree, support vector classification, and linear discriminant analysis, our work shows that the relative content of two histological abnormality sensitive bands at 1449 and 1658 cm⁻¹ in tumor cells is significantly different from that of normal cells (p = 0.0132), and can be a biomarker to classify these cells. This difference is confirmed by importance analyses in the decision tree model. Furthermore, performances of statistical methods are compared with one another to explore the ability in classification. Results show that the decision tree can be more capable for classification between tumorous and normal cell lines with sensitivity and specificity of 99.0% and 96.9%, respectively. Findings of this work further support our previous work and indicate that the decision tree performs more robustly in cell classification. Our work will prove helpful to the early diagnosis of nasopharyngeal carcinoma, and will indicate the decision tree to be the primary algorithm in tumor-cell classification.     

The Quest for Polysulfides in Lithium–Sulfur Battery Electrolytes: An Operando Confocal Raman Spectroscopy Study

Confocal Raman spectra of a lithium–sulfur battery electrolyte are recorded operando in a depth‐of‐discharge resolved manner for an electrochemical cell with a realistic electrolyte/sulfur loading ratio. The evolution of various possible polysulfides is unambiguously identified by combining Raman spectroscopy data with DFT simulations.     

Differentiating bulk nanobubbles from nanodroplets and nanoparticles

History has shown that it is not as easy as one might think to differentiate between bulk nanobubbles and nanodroplets or nanoparticles. It is generally easy to detect colloids (i.e. something that looks different, e.g. scatters light differently than its surrounding solvent), but less easy to determine the nature of these colloids. This has led to misinterpretations in the literature, where nanodroplets or nanoparticles have mistakenly been assumed to be nanobubbles. In this paper, we review a multitude of experimental methods and approaches to prove the existence of bulk nanobubbles. We conclude that combinations of optical detection with physical perturbations such as pressure or ultrasound, or phase-sensitive holographic methods are the most promising and convenient approaches.     

Calculating approximation guarantees for partial set cover of pairs

As a part of a heuristic for the fast detection of new word combinations in text streams, we consider the NP-hard Partial Set Cover of Pairs problem. There we wish to cover a maximum number of pairs of elements by a prescribed number of sets from a given set family. While the approximation ratio of the greedy algorithm for the classic Partial Set Cover problem is completely understood, the same question for covering of pairs is intrinsically more complicated, since the pairs insert some graph-theoretic structure. The best approximation guarantee for the first greedy step can be rephrased as a problem in extremal combinatorics: Assume that we may place a fixed number of subsets of fixed and equal size in a set, how many different pairs of elements can we cover? In this paper we introduce a method to calculate optimal approximation guarantees, and we demonstrate its use on the smallest set families.     

The rigid movable inclusion in elastostatics and elastodynamics

The problem of a single rigid movable inclusion is solved both for elastostatics and elastodynamic, using the null field approach. It is also shown how the solution can be obtained as the limit of the solution for an elastic inclusion. Numerical results for scattering by a superspheroidal inclusion are given.     

Stability and exponential convergence for the Boltzmann equation

We prove existence, uniqueness and stability for solutions of the nonlinear Boltzmann equation in a periodic box in the case when the initial data are sufficiently close to a spatially homogeneous function. The results are given for a range of spaces, including L ¹, and extend previous results in L for the non-homogeneous equation, as well as the more developed L ^p -theory for the spatially homogeneous Boltzmann equation.We also give new L -estimates for the spatially homogeneous equation in the case of Maxwellian interactions.     

A note on nonassociated plastic flow rules

The analytical properties of the constitutive equations in plasticity with a nonassociated flow rule are investigated. Under the assumption of small deformations the directional stiffness (and compliance) rule is considered and the relevant spectral properties of the tangent stiffness tensor are assessed. It is shown that the directional stiffness may be larger than the elastic. It may also be negative in the case of a formally perfectly plastic material and so the nonassociative flow rule represents (spurious) softening in terms of an associated flow rule. The issue of uniqueness at finite strains is briefly addressed, whereby use is made of the tangent stiffness tensor relating the velocity gradient to the first Piola-Kirchhoff stress rate. The relevant spectral properties, which generalise those from the small deformation case, are found explicit. A sufficient condition for uniqueness is given in terms of a critical (upper bound) value of the hardening modulus.     

Lp-estimates for the nonlinear spatially homogeneous Boltzmann equation

This paper studies L^p-estimates for solutions of the nonlinear, spatially homogeneous Boltzmann equation. The molecular forces considered include inverse k^th-power forces with k > 5 and angular cut-off.The main conclusions are the following. Let f be the unique solution of the Boltzmann equation with f(v,t)(1 + ¦v²¦)^(s ₁ ^{+ /p)/2} L¹, when the initial value f ₀ satisfies f ₀(v) 0, f ₀(v) (1 + ¦v¦²)^(s ₁ ^{+ /p)/2} L¹, for some s₁ 2 + /p, and f ₀(v) (1 + ¦v¦²)^s/2 L^p. If s 2/p and 1 < p < , then f(v, t)(1 + ¦v¦²)^{(s s} ₁)^/2 L^p, t > 0. If s >2 and 3/(1+ ) < p < , thenf(v,t) (1 + ¦v¦²)^(s(s ₁ ^{+ 3/p))/2} L^p, t > 0. If s >2 + 2C₀/C₁ and 3/(l + ) < p < , then f(v,t)(1 + ¦v¦²)^s/2 L^p, t > 0. Here 1/p + 1/p = 1, x y = min (x, y), and C₀, C₁, 0 < 1, are positive constants related to the molecular forces under consideration; = (k – 5)/ (k – 1) for k^th-power forces.Some weaker conclusions follow when 1 < p 3/ (1 + ).In the proofs some previously known L-estimates are extended. The results for L^p, 1 < p < , are based on these L-estimates coupled with nonlinear interpolation.     

Measure-valued solutions of scalar conservation laws with boundary conditions

We define a solution concept for measure-valued solutions to scalar conservation laws with initial conditions and boundary conditions and prove a uniqueness theorem for such solutions. This result may be used to prove convergence, towards the unique solution, for approximate solutions which are uniformly bounded in L , weakly consistent with certain entropy inequalities and strongly consistent with the initial condition, i.e. without using derivative estimates. As an example convergence of a finite element method is demonstrated.