Approximation for sums and densities of state of vibrations coupled with symmetric top K-rotor

The energy of a symmetric top rotor depends on quantum numbers J and K. In unimolecular rate theory the energy of the K-rotor, i.e. the K-dependent part of the symmetric top rotor energy, may be considered under some conditions as “active”, i.e. mixed with vibrational energy and thus contributing to the sum and density of vibrational states of the molecule, subject to the restriction − J ⩽ K ⩽ + J. In these cases proper evaluation of the sum/density of vibrational plus active K-rotor states at specified energy and J involves a summation of sums/densities over all the allowed Ks, a computationally intensive exercise. This work proposes simple and accurate approximations that require only trivial machine time. For the prolate symmetric top, the K-dependence of vibrational + rotational sum/density of states is approximated by a truncated Gaussian, and for the oblate top by a hyperbolic cosine. In each case the necessary parameters are obtained by a fit to smoothed “exact” vibrational sums/densities at K = 0 and one, or at most two, other values of K. The approximations are tested on a selection of typical symmetric top molecules at several energies and values of J with satisfactory results. The use of symmetry numbers is briefly invoked.     

Computational competition of symmetric mixed FEM in linear elasticity

The Navier–Lamé equation for linear elasticity has evoked the design of various non-standard finite element methods (FEM) in order to overcome the locking phenomenon. Recent developments of Arnold and Winther in 2002 involve a stable mixed method which strongly fulfils the symmetry constraint. Subsequently, two H(div) non-conforming symmetric mixed methods arose. This paper comments on the implementation of all those mixed FEM and provides a numerical comparison of the different symmetric mixed schemes for linear elasticity. The computational survey also includes the low-order elements of weak symmetry (PEERS), the non-conforming Kouhia and Stenberg (KS) elements plus the conforming displacement P_k-FEM for k = 1, 2, 3, 4. Numerical experiments confirm the theoretical convergence rates for sufficiently smooth solutions and illustrate the superiority of the symmetric MFEM amongst the methods of second or third order.     

Scalable processing of continuous K-nearest neighbor queries with uncertain velocity

Continuous K-nearest neighbor (CKNN) query is an important type of spatio-temporal queries. Given a time interval [t_s, t_e] and a moving query object q, a CKNN query is to find the K-nearest neighbors (KNNs) of q at each time instant within [t_s, t_e]. In this paper, we focus on the issue of scalable processing of CKNN queries over moving objects with uncertain velocity. Due to the large amount of CKNN queries that need to be evaluated concurrently, efficiently processing such queries inevitably becomes more complicated. We propose an index structure, namely the CI-tree, to predetermine and organize the candidates for each query issued by the user from anywhere and anytime. When the CKNN queries are evaluated, their corresponding candidates can be rapidly retrieved by traversing the CI-tree so that the processing time is greatly reduced. A comprehensive set of experiments is performed to demonstrate the effectiveness and the efficiency of the CI-tree.     

Numerical algorithms for undamped gyroscopic systems

The solutions of a gyroscopic vibrating system oscillating about an equilibrium position, with no external applied forces and no damping forces, are completely determined by the quadratic eigenvalue problem (−λ²_iM + λ_iG + K)x_i = 0, for i = 1, …, 2n, where M, G, and K are real n × n matrices, and M is symmetric positive definite (denoted by M > 0), G is skew symmetric, and either K > 0 or − K > 0. Gyroscopic system in motion about a stable equilibrium position (with − K > 0) are well understood. Two Lanczos-type algorithms, the pseudo skew symmetric Lanczos algorithm and the J-Lanczos algorithm, are studied for computing some extreme eigenpairs for solving gyroscopic systems in motion about an unstable equilibrium position (with K > 0). Shift and invert strategies, error bounds, implementation issues, and numerical results for both algorithms are presented in details.     

Computing the Primary Decomposition of Zero-dimensional Ideals

Let K be an infinite perfect computable field and let I ⊆ K [ x ] be a zero-dimensional ideal represented by a Gröbner basis. We derive a new algorithm for computing the reduced primary decomposition of I using only standard linear algebra and univariate polynomial factorization techniques. In practice, the algorithm generally works in finite fields of large characteristic as well.     

Eigenvalues and eigenvectors of large order banded matrices

An algorithm is developed to calculate eigenvalues and eigenvectors of large order symmetric band matrices of the form [K]{ν}—λ[M]{v} = 0. This algorithm, needs storage of only one matrix in the half banded form in the core of the computer; as such the algorithm will be very useful for computers with small core memory. Two numerical examples are given to show the effectiveness of this algorithm.     

Computing Local Artin Maps,and Solvability of Norm Equations

Let L = K(α) be an Abelian extension of degree n of a number field K, given by the minimal polynomial of α over K. We describe an algorithm for computing the local Artin map associated with the extension L / K at a finite or infinite prime v of K. We apply this algorithm to decide if a nonzero a ∈ K is a norm from L, assuming that L / K is cyclic.     

Potassium ion sensing using a self-assembled calix[4]crown monolayer by surface plasmon resonance

The precise detection of K⁺ ion is crucial because K⁺ ion plays a leading role in membrane transport. Current K⁺ ion detection methods suffered low resolution and detection limit. Calix[4]crown-5 derivatives are well known as K⁺ ionophores. We described here a K⁺ ion-sensing system using a self-assembled monolayer of calix[4]crown-5 derivative (calix[4]crown) modified gold chip based on surface plasmon resonance (SPR). The calix[4]crown sensing layer was characterized by atomic-force microscopy (AFM), SPR, Fourier transform infrared reflection absorption spectroscopy (FTIR-RAS) and cyclic voltammetry (CV). It was found calix[4]crown was assembled as a monolayer on Au surface. The SPR angle was found to be modulated by various concentrations of K⁺ ion due to the interaction between the calix[4]crown and K⁺ ion. This calix[4]crown monolayer showed a more sensitive and selective binding toward potassium ion over other alkali and alkaline earth metal ions. From the simple SPR spectroscopic analysis, we were able to monitor K⁺ ion concentration with a wide range of 1.0 × 10⁻¹² to 1.0 × 10⁻² M in an aqueous solution with a pH 6–8. These experimental results showed a useful method for the design of simple and precise potassium ion biosensors.     

Analysis of symmetric or partially symmetric structures

This paper combines group-theoretic methods with substructuring techniques to treat the symmetric or partially symmetric structures subjected to arbitrary loads. First, for a given substructure module, whose symmetry group is G, it gives a method to find the generalized displacements associated with irreducible representations of G based on some concepts presented in this paper, and then points out that for these displacements the analysis problem for a substructure module can be divided into a series of uncoupled subproblems. For each subproblem the triangularization as well as condensation can be carried out individually. Finally a simplified calculation formula of condensed stiffness coefficients for the original displacements is established, in which only the coefficients relating to the displacements in the basic region are necessary to be calculated.A series of computer programs has been developed by the methods presented in this paper [1–4]. These programs enable us to reduce the CPU time and save the memory noticeably.     

Dielectric and piezoelectric properties of [0 0 1] and [0 1 1]-poled relaxor ferroelectric PZN–PT and PMN–PT single crystals

The properties of PZN–PT and PMN–PT single crystals of varying compositions and orientations have been investigated. Among the various compositions studied, [0 0 1]-optimally poled PZN-(6–7)%PT and PMN-30%PT exhibit superior dielectric and piezoelectric properties, with K^T ≈ 6800–8000, d₃₃ ≈ 2800 pC/N, d₃₁ ≈ −(1200–1800) pC/N for PZN-(6–7)%PT; and K^T = 7500–9000, d₃₃ = 2200–2500 pC/N and d₃₁ = −(1100–1400) pC/N for PMN-30%PT. These two compositions are also fairly resistant to over-poling. The [0 0 1]-poled electromechanical coupling factors (k₃₃, k₃₁ and k_t) are relatively insensitive to crystal composition. [0 1 1]-optimally poled PZN-7%PT single crystal also exhibits extremely high d₃₁ values of up to −4000 pC/N with k₃₁ ≈ 0.90–0.96. While [0 1 1]-poled PZN-7%PT single crystal becomes over-poled with much degraded properties when poled at and above 0.6 kV/mm, PZN-6%PT crystal shows no signs of over-poling even when poled to 2.0 kV/mm. The presence of a certain amount (i.e., 10–15%) of orthorhombic phase in a rhombohedral matrix has been found to be responsible for the superior transverse piezoelectric properties of [0 1 1]-optimally poled PZN-(6–7)%PT. The present work shows that flux-grown PZN–PT crystals exhibit superior and consistent properties and improved over-poling resistance to flux-grown PMN–PT crystals and that, for or a given crystal composition, flux-grown PMN–PT crystals exhibit superior over-poling resistance to their melt-grown counterparts.     

Embedding K-ary Complete Trees into Hypercubes

In this paper, dilated embedding and precise embedding of K-ary complete trees into hypercubes are studied. For dilated embedding, a nearly optimal algorithm is proposed which embeds a K-ary complete tree of height h, T_K(h), into an (h − 1)[log K] + [log (K + 2)]-dimensional hypercube with dilation Max{2, φ(K), φ(K + 2)}. φ(x) = min{λ: Σ^λ_i=0Cⁱ_d ≥ x and d = [log x]}. It is clear that [([log x] + 1)/2] ≤ φ(x) ≤ [log x], for x ≥ 3.) For precise embedding, we show a (K − 1)h + 1-dimensional hypercube is large enough to contain T_K(h) as its subgraph, K ≥ 3.     

A novel approach to stance detection in social media tweets by fusing ranked lists and sentiments

Stance detection is a relatively new concept in data mining that aims to assign a stance label (favor, against, or none) to a social media post towards a specific pre-determined target. These targets may not be referred to in the post, and may not be the target of opinion in the post. In this paper, we propose a novel enhanced method for identifying the writer’s stance of a given tweet. This comprises a three-phase process for stance detection: (a) tweets preprocessing; here we clean and normalize tweets (e.g., remove stop-words) to generate words and stems lists, (b) features generation; in this step, we create and fuse two dictionaries for generating features vector, and lastly (c) classification; all the instances of the features are classified based on the list of targets. Our innovative feature selection proposes fusion of two ranked lists (top-$k$) of term frequency-inverse document frequency (tf-idf) scores and the sentiment information. We evaluate our method using six different classifiers: $K$ nearest neighbor (K-NN), discernibility-based K-NN, weighted K-NN, class-based K-NN, exemplar-based K-NN, and Support Vector Machines. Furthermore, we investigate the use of Principal Component Analysis and study its effect on performance. The model is evaluated on the benchmark dataset (SemEval-2016 task 6), and the results significance is determined using t-test. We achieve our best performance of macro $F$-score (averaged across all topics) of 76.45% using the weighted K-NN classifier. This tops the current state-of-the-art score of 74.44% on the same dataset.     

Functions that have read-once branching programs of quadratic size are not necessarily testable

A property of binary strings is constructed that has a representation by a collection of read-once branching programs of quadratic size but which is not ε-testable for some fixed ε>0. This shows that Newman's result [Proc. 41st FOCS, 2000, pp. 251-258] cannot be generalized to functions representable by read-once branching programs of polynomial size.     

A study of nonlinear dispersive equations with solitary-wave solutions having compact support

With the use of Adomian decomposition method, the prototypical, genuinely nonlinear K(m,n) equation, u_t+(u^m)_x+(uⁿ)_xxx=0, which exhibits compactons — solitons with finite wavelength — is solved exactly. Two numerical illustrations, K(2,2) and K(3,3), are investigated to illustrate the pertinent features of the proposed scheme. The technique is presented in a general way so that it can be used in nonlinear dispersive equations.     

(Weak) Dual hyper <Emphasis Type="Italic">K</Emphasis>-ideals

In this note by considering the notion of (weak) dual hyper K-ideal, we obtain some related results. After that we determine the relationships between (weak) dual hyper K-ideals and (weak) hyper K-ideals. Finally, we give a characterization of hyper K-algebras of order 3 or 4 based on the (weak) dual hyper K-ideals.     

On using forward error correction for loss recovery in optical burst switched networks

An important issue in optical burst switched (OBS) networks is the loss of bursts at intermediate nodes due to contention. Such contention losses, usually do not mean a situation of congestion. In this paper, we propose for the first time, a loss recovery mechanism using Forward Error Correction (FEC) to recover bursts that are lost due to contention. Using FEC, for every K bursts, N − K redundant bursts are also sent to the destination. This redundancy can be used to recover from losses in the K data bursts. Our mechanism can also be used to recover from losses due to network component (link/node) failures. We demonstrate the effectiveness of our mechanism by comparing with no protection and 1 + 1 protection using simulation studies.     

A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear Programs

We give an approximation algorithm for fractional packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm (with high probability) computes feasible primal and dual solutions whose costs are within a factor of 1+ε of opt (the optimal cost) in time O((r+c)log(n)/ε ²+n).