Maximization of eigenvalues using topology optimization

Topology optimization is used to optimize the eigenvalues of plates. The results are intended especially for MicroElectroMechanical Systems (MEMS) but can be seen as more general. The problem is not formulated as a case of reinforcement of an existing structure, so there is a problem related to localized modes in low density areas. The topology optimization problem is formulated using the SIMP method. Special attention is paid to a numerical method for removing localized eigenmodes in low density areas. The method is applied to numerical examples of maximizing the first eigenfrequency. One example is a practical MEMS application; a probe used in an Atomic Force Microscope (AFM). For the AFM probe the optimization is complicated by a constraint on the stiffness and constraints on higher order eigenvalues. Received June 10, 1999     

Simultaneous cognitive origin of life and information

Shannon’s information quantity I(E) = log(1/P(E)) is defined under an assumption of the existence of a “cognitive subjective entity” capable of judging yes/no or occurred/not-occurred of an event E (which occurs with a probability P(E)). The final acceptor/user of information is a living individual, although first and/or intermediate sender(s) and/or acceptor(s) of information may be either living individual(s) or nonliving element(s) or man-made machine(s). Therefore we can conclude that information is a most essential character of living individuals, and that information and life must have emerged simultaneously as a “minimum cognitive system” (MCS). Since then, living individuals/lives must have evolved as “self-revising learning neural network machines” capable of “active evolution”. How MCS could have emerged was discussed.     

Dexterous workspace optimization of an asymmetric six-degree of freedom Stewart–Gough platform type manipulator

In this paper, an asymmetric Generalized Stewart–Gough Platform (GSP) type parallel manipulator is designed by considering the type synthesis approach. The asymmetric six-Degree Of Freedom (DOF) manipulator optimized in this paper is selected among the GSPs classified under the name of 6D. The dexterous workspace optimization of Asymmetric parallel Manipulator with tEn Different Linear Actuator Lengths (AMEDLAL) subject to kinematics and geometric constraints is performed by using the Particle Swarm Optimization (PSO). The condition number and Minimum Singular Value (MSV) of homogenized Jacobian matrix are employed to obtain the dexterous workspace of AMEDLAL. Finally, the six-DOF AMEDLAL is also compared with the optimized Traditional Stewart–Gough Platform Manipulator (TSPM) considering the volume of the dexterous workspace in order to demonstrate its kinematic performance. Comparisons show that the manipulator proposed in this study illustrates better kinematic performance than TSPM.     

The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states

We study remarkable sub-lattice effect algebras of Archimedean atomic lattice effect algebras E, namely their blocks M, centers C(E), compatibility centers B(E) and sets of all sharp elements S(E) of E. We show that in every such effect algebra E, every atomic block M and the set S(E) are bifull sub-lattice effect algebras of E. Consequently, if E is moreover sharply dominating then every atomic block M is again sharply dominating and the basic decompositions of elements (BDE of x) in E and in M coincide. Thus in the compatibility center B(E) of E, nonzero elements are dominated by central elements and their basic decompositions coincide with those in all atomic blocks and in E. Some further details which may be helpful under answers about the existence and properties of states are shown. Namely, we prove the existence of an (o)-continuous state on every sharply dominating Archimedean atomic lattice effect algebra E with B(E)\not = C(E).B(E)\not =C(E). Moreover, for compactly generated Archimedean lattice effect algebras the equivalence of (o)-continuity of states with their complete additivity is proved. Further, we prove “State smearing theorem” for these lattice effect algebras.     

Connecting Polygonizations via Stretches and Twangs

We show that the space of polygonizations of a fixed planar point set S of n points is connected by O(n ²) “moves” between simple polygons. Each move is composed of a sequence of atomic moves called “stretches” and “twangs,” which walk between weakly simple “polygonal wraps” of S. These moves show promise to serve as a basis for generating random polygons.     

Trace monoids with idempotent generators and measure-only quantum automata

In this paper, we analyze a model of 1-way quantum automaton where only measurements are allowed ( MON -1qfa). The automaton works on a compatibility alphabet (S, E)(\Sigma, E) of observables and its probabilistic behavior is a formal series on the free partially commutative monoid FI(S, E)\hbox{FI}(\Sigma, E) with idempotent generators. We prove some properties of this class of formal series and we apply the results to analyze the class LMO(S, E){\bf LMO}(\Sigma, E) of languages recognized by MON -1qfa’s with isolated cut point. In particular, we prove that LMO(S, E){\bf LMO}(\Sigma, E) is a boolean algebra of recognizable languages with finite variation, and that LMO(S, E){\bf LMO}(\Sigma, E) is properly contained in the recognizable languages, with the exception of the trivial case of complete commutativity.     

Maintenance of a Piercing Set for Intervals with Applications

   Abstract. We show how to maintain efficiently a minimum piercing set for a set S of intervals on the line, under insertions and deletions to/from S. A linear-size dynamic data structure is presented, which enables us to compute a new minimum piercing set following an insertion or deletion in time O(c( S) log |S|), where c (S) is the size of the new minimum piercing set. We also show how to maintain a piercing set for S of size at most (1+ɛ)c (S), for 0 < ɛ ≤ 1 , in

Optimal trajectory generation algorithm for serial and parallel manipulators

In this paper, an Optimal Trajectory Generation Algorithm (OTGA) is developed for generating minimum-time smooth motion trajectories for serial and parallel manipulators. OTGA is divided into two phases. The first phase encompasses derivation of minimum-time optimal trajectory using cubic spline due to its less vibration and overshoot characteristics. Although cubic splines are widely used in robotics, velocity and acceleration ripples in the first & last knots can worsen manipulator trajectory. The second phase includes changing cubic spline interpolation in the first and last knots of optimized trajectory with 7th order polynomial for having zero jerk at the beginning and end points of trajectory. Performing this modification eliminate undesired worsening in the trajectory and provide smoother start and stop of joint motions. Particle Swarm Optimization (PSO) is chosen as optimization algorithm because of its easy implementation and successful optimization performance. OTGA has been tested in simulation for PUMA robot and results are compared with algorithms proposed by earlier authors. In addition, a discrete-time PID control scheme for PUMA robot is designed for comparing energy consumption of OTGA with algorithms developed by previous authors. Comparison results illustrated that OTGA is the better trajectory generation algorithm than the others.     

Sequential approximate optimization using dual subproblems based on incomplete series expansions

In this paper, dual formulations for nonlinear multipoint approximations with diagonal approximate Hessian matrices are proposed; these approximations for example derive from the incomplete series expansion (ISE) proposed previously. A salient feature of the ISE is that it may be used to formulate strictly convex and separable (recast) primal approximate subproblems for use in sequential approximate optimization (SAO). In turn, this allows for the formulation of highly efficient dual formulations, and different combinations of direct, reciprocal, and exponential intervening variables for the objective and the constraint functions may be used. Two frequently encountered problems in structural optimization, namely the weight minimization problem with sizing design variables and the minimum compliance topology optimization problem, are degenerate cases of the formulations we present. Computational experiments confirm the efficiency of our proposed methodology; to this end, comparative results for the method of moving asymptotes (MMA) are presented. Based on the paper entitled “Duality in Convex Nonlinear Multipoint Approximations with Diagonal Approximate Hessian Matrices Deriving from Incomplete Series Expansions,” presented at the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, VA, USA, September 2006, paper no. AIAA-2006-7090.     

Correlation between the gradients of the quadratic functional and its clipped prototype

Applicability of clipping of quadratic functional E = −0.5x ⁺ Tx + Bx in the minimization problem is considered (here x is the configurational vector and B ∈ R ^N is real valued vector). The probability that the gradient of this functional and the gradient of clipped functional ɛ = −0.5x ⁺ τx + bx are collinear is shown to be very high (the matrix τ is obtained by clipping of original matrix T: τ_ij = sgnT _ij ). It allows the conclusion that minimization of functional ɛ implies minimization of functional E. We can therefore replace the laborious process of minimizing functional E by the minimization of its clipped prototype ɛ. Use of the clipped functional allows sixteen-times reduction of the computation time and computer memory usage.     

A 199-line Matlab code for Pareto-optimal tracing in topology optimization

The paper ‘A 99-line topology optimization code written in Matlab’ by Sigmund (Struct Multidisc Optim 21(2):120–127, 2001) demonstrated that SIMP-based topology optimization can be easily implemented in less than hundred lines of Matlab code. The published method and code has been used even since by numerous researchers to advance the field of topology optimization. Inspired by the above paper, we demonstrate here that, by exploiting the notion of topological-sensitivity (an alternate to SIMP), one can generate Pareto-optimal topologies in about twice the number of lines of Matlab code. In other words, optimal topologies for various volume fractions can be generated in a highly efficient manner, by directly tracing the Pareto-optimal curve.     

New Fixed-Parameter Algorithms for the Minimum Quartet Inconsistency Problem

Let S be a set of n taxa. Given a parameter k and a set of quartet topologies Q over S such that there is exactly one topology for every subset of four taxa, the parameterized Minimum Quartet Inconsistency (MQI) problem is to decide whether we can find an evolutionary tree inducing a set of quartet topologies that differs from the given set in at most k quartet topologies. The best fixed-parameter algorithm devised so far for the parameterized MQI problem runs in time O(4 ^k n+n ⁴). In this paper, first we present an O(3.0446 ^k n+n ⁴) fixed-parameter algorithm and an O(2.0162 ^k n ³+n ⁵) fixed-parameter algorithm for the parameterized MQI problem. Finally, we give an O ^*((1+ε) ^k ) fixed-parameter algorithm, where ε>0 is an arbitrarily small constant.     

Algorithmic aspects of Suslin's proof of Serre's conjecture

LetF be a unimodularr×s matrix with entries beingn-variate polynomials over an infinite fieldK. Denote by deg(F) the maximum of the degrees of the entries ofF and letd=1+deg(F). We describe an algorithm which computes a unimodulars×s matrixM with deg(M)=(rd) ^O(n) such thatFM=[I _r ,O], where [I _r ,O] denotes ther×s matrix obtained by adding to ther×r unit matrixI _r s–r zero columns.We present the algorithm as an arithmetic network with inputs fromK, and we count field operations and comparisons as unit cost.The sequential complexity of our algorithm amounts to field operations and comparisons inK whereas its parallel complexity isO(n ⁴ r ⁴log²(srd)).The complexity bounds and the degree bound for deg(M) mentioned above are optimal in order. Our algorithm is inspired by Suslin's proof of Serre's Conjecture.     

Measures on MV-algebras

 We study sequentially continuous measures on semisimple M V-algebras. Let A be a semisimple M V-algebra and let I be the interval [0,1] carrying the usual Łukasiewicz M V-algebra structure and the natural sequential convergence. Each separating set H of M V-algebra homomorphisms of A into I induces on A an initial sequential convergence. Semisimple M V-algebras carrying an initial sequential convergence induced by a separating set of M V-algebra homomorphisms into I are called I-sequential and, together with sequentially continuous M V-algebra homomorphisms, they form a category SM(I). We describe its epireflective subcategory ASM(I) consisting of absolutely sequentially closed objects and we prove that the epireflection sends A into its distinguished σ-completion σ _H (A). The epireflection is the maximal object in SM(I) which contains A as a dense subobject and over which all sequentially continuous measures can be continuously extended. We discuss some properties of σ _H (A) depending on the choice of H. We show that the coproducts in the category of D-posets [9] of suitable families of I-sequential M V-algebras yield a natural model of probability spaces having a quantum nature. The motivation comes from probability: H plays the role of elementary events, the embedding of A into σ _H (A) generalizes the embedding of a field of events A into the generated σ-field σ(A), and it can be viewed as a fuzzyfication of the corresponding results for Boolean algebras in [8, 11, 14]. Sequentially continuous homomorphisms are dual to generalized measurable maps between the underlying sets of suitable bold algebras [13] and, unlike in the Loomis–Sikorski Theorem, objects in ASM(I) correspond to the generated tribes (no quotient is needed, no information about the elementary events is lost). Finally, D-poset coproducts lift fuzzy events, random functions and probability measures to events, random functions and probability measures of a quantum nature. Supported by VEGA Grant 2/7193/01     

Labeling Schemes for Tree Representation

This paper deals with compact label-based representations for trees. Consider an n-node undirected connected graph G with a predefined numbering on the ports of each node. The all-ports tree labeling ℒ _all gives each node v of G a label containing the port numbers of all the tree edges incident to v. The upward tree labeling ℒ _up labels each node v by the number of the port leading from v to its parent in the tree. Our measure of interest is the worst case and total length of the labels used by the scheme, denoted M _up (T) and S _up (T) for ℒ _up and M _all (T) and S _all (T) for ℒ _all . The problem studied in this paper is the following: Given a graph G and a predefined port labeling for it, with the ports of each node v numbered by 0,…,deg (v)−1, select a rooted spanning tree for G minimizing (one of) these measures. We show that the problem is polynomial for M _up (T), S _up (T) and S _all (T) but NP-hard for M _all (T) (even for 3-regular planar graphs). We show that for every graph G and port labeling there exists a spanning tree T for which S _up (T)=O(nlog log n). We give a tight bound of O(n) in the cases of complete graphs with arbitrary labeling and arbitrary graphs with symmetric port labeling. We conclude by discussing some applications for our tree representation schemes. A preliminary version of this paper has appeared in the proceedings of the 7th International Workshop on Distributed Computing (IWDC), Kharagpur, India, December 27–30, 2005, as part of Cohen, R. et al.: Labeling schemes for tree representation. In: Proceedings of 7th International Workshop on Distributed Computing (IWDC), Lecture Notes of Computer Science, vol. 3741, pp. 13–24 (2005). R. Cohen supported by the Pacific Theaters Foundation. P. Fraigniaud and D. Ilcinkas supported by the project “PairAPair” of the ACI Masses de Données, the project “Fragile” of the ACI Sécurité et Informatique, and by the project “Grand Large” of INRIA. A. Korman supported in part by an Aly Kaufman fellowship. D. Peleg supported in part by a grant from the Israel Science Foundation.     

Dependence of performance indices of a call center on the distribution of calls’ sojourn time in the orbit

The operation of a call center is described in the form of a retrial queuing system. The dependence of its performance indices on the Markovian and two-phase Erlang distributions of calls’ sojourn time in the orbit is considered. An analytical model of an M / M / c / / / E ₂ retrial queuing system is developed. An asymptotic analysis of some characteristics of M / M / c / 0 / 2/ / M and M / M / c / 0 / 2 / / E ₂ systems is performed. An application is developed for solving M / M / c / 0 / N / / N / / E ₂ and M / M / c / 0 / N / / M systems using sparse matrices. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 170–183, March–April 2009.     

Incomplete series expansion for function approximation

We present an incomplete series expansion (ISE) as a basis for function approximation. The ISE is expressed in terms of an approximate Hessian matrix, which may contain second, third, and even higher order “main” or diagonal terms, but which excludes “interaction” or off-diagonal terms. From the ISE, a family of approximation functions may be derived. The approximation functions may be based on an arbitrary number of previously sampled points, and any of the function and gradient values at suitable previously sampled points may be enforced when deriving the approximation functions. When function values only are enforced, the storage requirements are minimal. However, irrespective of the conditions enforced, the approximate Hessian matrix is a sparse diagonal matrix. In addition, the resultant approximations are separable. Hence, the proposed approximation functions are very well-suited for use in gradient-based sequential approximate optimization requiring computationally expensive simulations; a typical example is structural design problems with many design variables and constraints. We derived a wide selection of approximations from the family of ISE approximating functions; these include approximations based on the substitution of reciprocal and exponential intervening variables. A comparison with popular approximating functions previously proposed illustrates the accuracy and flexibility of the new family of approximation functions. In fact, a number of popular approximating functions previously proposed for structural optimization applications derive from our ISE. Based on the similarly named paper presented at the Sixth World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, May 2005     

Congruences and ideals in pseudoeffect algebras

This paper is devoted to congruences and ideals in pseudoeffect algebras. Let I be a normal ideal in a pseudoeffect algebra E. We show that: (1) the relation ~ _I induced by I is a congruence if and only if for every a∈E, I∩ [0,a] is upper directed; (2) the relation ~ _I induced by I is a strong congruence if and only if I is a normal weak Riesz ideal in a pseudoeffect algebra E. Moreover, we introduce a stronger concept of congruence—namely Riesz strong congruence—and we prove that, if I is a normal weak Riesz ideal in a pseudoeffect algebra E, then ~ _I is a Riesz strong congruence and, conversely, if ~ is a Riesz strong congruence, then I = [0]_~ is a normal weak Riesz ideal, and ~ _I = ~. This work was supported by the National Natural Science Foundation of China (Grant No. 10271069).