Comparing large graphs efficiently by margins of feature vectors

Measuring the structural similarity of graphs is a challenging and outstanding problem. Most of the classical approaches of the so-called exact graph matching methods are based on graph or subgraph isomorphic relations of the underlying graphs. In contrast to these methods in this paper we introduce a novel approach to measure the structural similarity of directed and undirected graphs that is mainly based on margins of feature vectors representing graphs. We introduce novel graph similarity and dissimilarity measures, provide some properties and analyze their algorithmic complexity. We find that the computational complexity of our measures is polynomial in the graph size and, hence, significantly better than classical methods from, e.g. exact graph matching which are NP-complete. Numerically, we provide some examples of our measure and compare the results with the well-known graph edit distance. (c) 2006 Elsevier Inc. All rights reserved.

Finite domination and Novikov rings. Iterative approach

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ? L R((x)) and C ? L R((x -1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619–632). Here R((x)) = R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.

Efficient advanced encryption standard implementation using lookup and normal basis

A new type of advanced encryption standard (AES) implementation using a normal basis is presented. The method is based on a lookup technique that makes use of inversion and shift registers, which leads to a smaller size of lookup for the S-box than its corresponding implementations. The reduction in the lookup size is based on grouping sets of inverses into conjugate sets which in turn leads to a reduction in the number of lookup values. The above technique is implemented in a regular AES architecture using register files, which requires less interconnect and area and is suitable for security applications. The results of the implementation are competitive in throughput and area compared with the corresponding solutions in a polynomial basis.

Double complexes and vanishing of Novikov cohomology

We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new and transparent proof that a finitely dominated cochain complex over a Laurent polynomial ring has trivial (positive and negative) Novikov cohomology.

Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In
particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Model categories for orthogonal calculus

We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and n-homogeneous functors, along with Quillen pairs relating them. We then classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an O(n)-action. This improves upon the classification theorem of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.

On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

A Wavelet Approach to the Selective Computation of Eigenvalues for Small Signal Stability Analysis

This paper proposes a method to assess the small signal stability of a power system network by selective determination of the modal eigenvalues. This uses an accelerating polynomial transform, designed using approximate eigenvalues
obtained from a wavelet approximation. Application to the IEEE 14 bus network model produced computational savings of 20%,over the QR algorithm.

Hexavalent Chromium Adsorption by a Novel Activated Carbon Prepared by Microwave Activation

Microwave heating reduces the preparation time and improves the adsorption quality of activated carbon. In this study, activated carbon was prepared by impregnation of palm kernel fiber with phosphoric acid followed by microwave activation. Three different types of activated carbon were prepared, having high surface areas of 872 m2 g-1, 1256 m2 g-1, and 952 m2 g-1 and pore volumes of 0.598 cc g-1, 1.010 cc g-1, and 0.778 cc g-1, respectively. The combined effects of the different process parameters, such as the initial adsorbate concentration, pH, and temperature, on adsorption efficiency were explored with the help of Box-Behnken design for response surface methodology (RSM). The adsorption rate could be expressed by a polynomial equation as the function of the independent variables. The hexavalent chromium adsorption rate was found to be 19.1 mg g-1 at the optimized conditions of the process parameters, i.e., initial concentration of 60 mg L-1, pH of 3, and operating temperature of 50 oC. Adsorption of Cr(VI) by the prepared activated carbon was spontaneous and followed second-order kinetics. The adsorption mechanism can be described by the Freundlich Isotherm model. The prepared activated carbon has demonstrated comparable performance to other available activated carbons for the adsorption of Cr(VI).

Comportamento flessionale di nodi esterni in calcestruzzo fibrorinforzato

SOMMARIO – Si presenta un macro modello di tipo reticolare in grado di riprodurre il comportamento in presenza di taglio e momento di nodi esterni trave-colonna di telai in calcestruzzo fibrorinforzato con fibre di acciaio
uncinato ed ordinario. Il caricamento del sistema è di tipo monotono come nel caso dell’analisi di pushover. Il modello considera la presenza di armature orizzontali e verticali della regione nodale e tiene in conto delle modalità
di rottura legate allo snervamento delle barre e allo schiacciamento delle regioni compresse in regime di sforzi pluriassiali. Il modello include le deformazioni flessionali della trave e della colonna in presenza di sforzo normale costante e restituisce la risposta del sistema colonna-nodo-trave (sub-assembralggio) tramite le curve carico-freccia all’estremità della semitrave. Per i singoli costituenti (trave, colonna e nodo) si è considerata la prima fessurazione, lo snervamento e lo schiacciamento delle regioni compresse e si sono fornite precise indicazioni sulla sequenza degli eventi che come è noto sono di fondamentale importanza per lo sviluppo di un progetto plastico che rispetti la gerarchia delle resistenze. Con l’uso del modello il controllo della gerarchia delle resistenze avviene a livello sezionale (lo snervamento delle barre deve avvenire prima dello schiacciamento delle regioni compresse) o di macro elemento (nella regione nodale lo snervamento delle staffe precede la crisi dei puntoni) e dell’intero elemento
sub-assemblaggio trave debole, colonna forte e nodo sovraresistente.
La risposta ottenuta con i modello proposto è in buon accordo con le risposte sperimentali disponibili in letteratura (almeno in termini di resistenza del sub-assemblaggio). Il modello è stato ulteriormente validato con analisi
numeriche agli elementi finiti condotte con il codice ATENA-2D. Le analisi numeriche sono state condotte utilizzando per il calcestruzzo fibroso adeguate leggi costitutive proposte dagli autori ed in grado di cogliere gli effetti
di softening e di resistenza residua a trazione legati alla presenza di fibre. Ulteriori sviluppi del modello saranno indirizzati a includere gli effetti di sfilamento delle barre d’armatura della trave e del conseguente degrado delle
tensioni d’aderenza per effetto di carichi monotonici e ciclici.

SUMMARY – A softened strut-and-tie macro model able to reproduce the flexural behavior of external beam-tocolumn joints with the presence of horizontal and vertical steel bars, including softening of compressed struts and yielding of main and secondary steel bars, is presented, to be used for the pushover analysis. The model proposed is able to calculate also the flexural response of fibrous reinforced concrete (FRC) beam-to-column sub-assemblages in term of a multilinear load-deflection curves. The model is able to take into account of the tensile behavior of main bars embedded in the surrounding concrete and of the softening of the compressed strut, the arrangement and percentage of the steel bars, the percentage and the geometry of steel fibers. First cracking, yielding of main steel and crushing of concrete were identified to determine the corresponding loads and displacement and to plot the simplified monotonic load-deflection curves of the sub-assemblages subjected in the column to constant vertical
load and at the tip of the beam to monotonically increasing lateral force. Through these load-delfection curves the component (beam, joint and column) that first collapse can be recognized and the capacity design can be verified.
The experimental results available in the literature are compared with the results obtained through the proposed model. Further, a validation of the proposed model is numerically made by using a non linear finite element program (ATENA-2D) able to analyze the flexural behavior of sub-assemblages.

A multi-output two-stage locally regularized model construction method using the extreme learning machine

This paper investigates the construction of linear-in-the-parameters (LITP) models for multi-output regression problems. Most existing stepwise forward algorithms choose the regressor terms one by one, each time maximizing the model error reduction ratio. The drawback is that such procedures cannot guarantee a sparse model, especially under highly noisy learning conditions. The main objective of this paper is to improve the sparsity and generalization capability of a model for multi-output regression problems, while reducing the computational complexity. This is achieved by proposing a novel multi-output two-stage locally regularized model construction (MTLRMC) method using the extreme learning machine (ELM). In this new algorithm, the nonlinear parameters in each term, such as the width of the Gaussian function and the power of a polynomial term, are firstly determined by the ELM. An initial multi-output LITP model is then generated according to the termination criteria in the first stage. The significance of each selected regressor is checked and the insignificant ones are replaced at the second stage. The proposed method can produce an optimized compact model by using the regularized parameters. Further, to reduce the computational complexity, a proper regression context is used to allow fast implementation of the proposed method. Simulation results confirm the effectiveness of the proposed technique. © 2013 Elsevier B.V.

The Influence of Structural Modeshape Variability on Limit Cycle Oscillation Behaviour

Modal analysis is a popular approach used in structural dynamic and aeroelastic problems due to its efficiency. The response of a structure is compo
sed of the sum of orthogonal eigenvectors or modeshapes and corresponding modal frequencies. This paper investigates the importance of modeshapes on the aeroelastic response of the Goland wing subject to structural uncertainties. The wing undergoes limit cycle oscillations (LCO) as a result of the inclusion of polynomial stiffness nonlinearities. The LCO computations are performed using a Harmonic Balance approach for speed, the modal properties of the system are extracted from MSC NASTRAN. Variability in both the wing’s structure and the store centre of gravity location is investigated in two cases:- supercritical and subcritical type LCOs. Results show that the LCO behaviour is only sensitive to change in modeshapes when the nature of the modes are changing significantly.

Analysis of Transonic Limit Cycle Oscillations under Uncertainty

For the computation of limit cycle oscillations (LCO) at transonic speeds, CFD is required to capture the nonlinear flow features present. The Harmonic Balance method provides an effective means for the computation of LCOs and this paper exploits its efficiency to investigate the impact of variability (both structural a nd aerodynamic) on the aeroelastic behaviour of a 2 dof aerofoil. A Harmonic Balance inviscid CFD solver is coupled with the structural equations and is validated against time marching analyses. Polynomial chaos expansions are employed for the stochastic investiga tion as a faster alternative to Monte Carlo analysis. Adaptive sampling is employed when discontinuities are present. Uncertainties in aerodynamic parameters are looked at first followed by the inclusion of structural variability. Results show the nonlinear effect of Mach number and it’s interaction with the structural parameters on supercritical LCOs. The bifurcation boundaries are well captured by the polynomial chaos.

Vector bundles on the projective line and finite domination of chain complexes

We present an algebro-geometric approach to a theorem on finite domination of chain complexes over a Laurent polynomial ring. The approach uses extension of chain complexes to sheaves on the projective line, which is governed by a K-theoretical obstruction.

Investigation of Limit Cycle Oscillations Using Aeroelastic-Harmonic Balance Method

This work investigates limit cycle oscillations in the transonic regime. A novel approach to predict Limit Cycle Oscillations using high fidelity analysis is exploited to accelerate calculations. The method used is an Aeroeasltic Harmonic Balance approach, which has been proven to be efficient and able to predict periodic phenomena. The behaviour of limit cycle oscillations is analysed using uncertainty quantification tools based on polynomial chaos expansions. To improve the efficiency of the sampling process for the polynomial-chaos expansions an adaptive sampling procedure is used. These methods are exercised using two problems: a pitch/plunge aerofoil and a delta-wing. Results indicate that Mach n. variability is determinant to the amplitude of the LCO for the 2D test case, whereas for the wing case analysed here, variability in the Mach n. has an almost negligible influence in amplitude variation and the LCO frequency variability has an almost linear relation with Mach number. Further test cases are required to understand the generality of these results.