Abstract: This paper describes how damage propagation can be modeled within the modules of aircraft gas turbine engines. To that end, response surfaces of all sensors are generated via a thermo-dynamical simulation model for the engine as a function of variations of flow and efficiency of the modules of interest. An exponential rate of change for flow and efficiency loss was imposed for each data set, starting at a randomly chosen initial deterioration set point. The rate of change of the flow and efficiency denotes an otherwise unspecified fault with increasingly worsening effect. The rates of change of the faults were constrained to an upper threshold but were otherwise chosen randomly. Damage propagation was allowed to continue until a failure criterion was reached. A health index was defined as the minimum of several superimposed operational margins at any given time instant and the failure criterion is reached when health index reaches zero. Output of the model was the time series (cycles) of sensed measurements typically available from aircraft gas turbine engines. The data generated were used as challenge data for the prognostics and health management (PHM) data competition at PHMpsila08.

Abstract: We consider the problem of minimizing the sum of a smooth function and a separable convex function This problem includes as special cases bound-constrained optimization and smooth optimization with l1-regularization We propose a (block) coordinate gradient descent method for solving this class of nonsmooth separable problems We establish global convergence and, under a local Lipschitzian error bound assumption, linear convergence for this method The local Lipschitzian error bound holds under assumptions analogous to those for constrained smooth optimization, eg, the convex function is polyhedral and the smooth function is (nonconvex) quadratic or is the composition of a strongly convex function with a linear mapping We report numerical experience with solving the l1-regularization of unconstrained optimization problems from More et al in ACM Trans Math Softw 7, 17–41, 1981 and from the CUTEr set (Gould and Orban in ACM Trans Math Softw 29, 373–394, 2003) Comparison with L-BFGS-B and MINOS, applied to a reformulation of the l1-regularized problem as a bound-constrained optimization problem, is also reported

Abstract: In free energy calculations based on thermodynamic integration, it is necessary to compute the derivatives of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivatives as the average of a mean force acting on the order parameters, which involves first derivatives with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivatives of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, especially for complicated order parameters. It is also straightforward to implement in a molecular dynamics code, as can be seen from the pseudocode given at the end. We further discuss how the approach based on time derivatives can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calculations. Using the backbone dihedral angles Phi and Psi in N-acetylalanyl-N'-methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivatives, a calculation that presents some difficulties in the vector case because of the statistical errors affecting the derivatives.

Abstract: The increasing wealth of biological data coming from a large variety of platforms and the continued development of new high-throughput methods for probing biological systems require increasingly more sophisticated computational approaches. Putting all these data in simple-to-use databases is a first step; but realizing the full potential of the data requires algorithms that automatically extract regularities from the data, which can then lead to biological insight. Many of the problems in computational biology are in the form of prediction: starting from prediction of a gene's structure, prediction of its function, interactions, and role in disease. Support vector machines (SVMs) and related kernel methods are extremely good at solving such problems [1]–[3]. SVMs are widely used in computational biology due to their high accuracy, their ability to deal with high-dimensional and large datasets, and their flexibility in modeling diverse sources of data [2], [4]–[6]. The simplest form of a prediction problem is binary classification: trying to discriminate between objects that belong to one of two categories—positive (+1) or negative (−1). SVMs use two key concepts to solve this problem: large margin separation and kernel functions. The idea of large margin separation can be motivated by classification of points in two dimensions (see Figure 1). A simple way to classify the points is to draw a straight line and call points lying on one side positive and on the other side negative. If the two sets are well separated, one would intuitively draw the separating line such that it is as far as possible away from the points in both sets (see Figures 2 and ​and3).3). This intuitive choice captures the idea of large margin separation, which is mathematically formulated in the section Classification with Large Margin. Open in a separate window Figure 1 A linear classifier separating two classes of points (squares and circles) in two dimensions. The decision boundary divides the space into two sets depending on the sign of f(x) = 〈w,x〉+b. The grayscale level represents the value of the discriminant function f(x): dark for low values and a light shade for high values.

Abstract: We investigate the growth of the Nevanlinna characteristic of f(z+η) for a fixed η∈C in this paper. In particular, we obtain a precise asymptotic relation between T(r,f(z+η)) and T(r,f), which is only true for finite order meromorphic functions. We have also obtained the proximity function and pointwise estimates of f(z+η)/f(z) which is a discrete version of the classical logarithmic derivative estimates of f(z). We apply these results to give new growth estimates of meromorphic solutions to higher order linear difference equations. This also allows us to solve an old problem of Whittaker (Interpolatory Function Theory, Cambridge University Press, Cambridge, 1935) concerning a first order difference equation. We show by giving a number of examples that all of our results are best possible in certain senses. Finally, we give a direct proof of a result in Ablowitz, Halburd and Herbst (Nonlinearity 13:889–905, 2000) concerning integrable difference equations.

Abstract: This paper presents a theoretical analysis of the problem of domain adaptation with multiple sources. For each source domain, the distribution over the input points as well as a hypothesis with error at most ∊ are given. The problem consists of combining these hypotheses to derive a hypothesis with small error with respect to the target domain. We present several theoretical results relating to this problem. In particular, we prove that standard convex combinations of the source hypotheses may in fact perform very poorly and that, instead, combinations weighted by the source distributions benefit from favorable theoretical guarantees. Our main result shows that, remarkably, for any fixed target function, there exists a distribution weighted combining rule that has a loss of at most ∊ with respect to any target mixture of the source distributions. We further generalize the setting from a single target function to multiple consistent target functions and show the existence of a combining rule with error at most 3∊. Finally, we report empirical results for a multiple source adaptation problem with a real-world dataset.

Abstract: Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Q-value function Q*. Finally, unifying some previous approaches for solving Dec-POMDPs, we describe a family of algorithms for extracting policies from such Q-value functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem.

Abstract: We propose a quantitative function for community partition---i.e., modularity density or $D$ value. We demonstrate that this quantitative function is superior to the widely used modularity $Q$ and also prove its equivalence with the objective function of the kernel $k$ means. Both theoretical and numerical results show that optimizing the new criterion not only can resolve detailed modules that existing approaches cannot achieve, but also can correctly identify the number of communities.

Abstract: Suppose we are given a perfect n+ c-to-nbit compression function fand we want to construct a larger m+ s-to-sbit compression function Hinstead. What level of security, in particular collision resistance, can we expect from Hif it makes rcalls to f? We conjecture that typically collisions can be found in 2(nr+ cri¾? m)/(r+ 1)queries. This bound is also relevant for building a m+ s-to-sbit compression function based on a blockcipher with k-bit keys and n-bit blocks: simply set c= k, or c= 0 in case of fixed keys. We also exhibit a number of (conceptual) compression functions whose collision resistance is close to this bound. In particular, we consider the following four scenarios: 1 A 2n-to-nbit compression function making two calls to an n-to-nbit primitive, providing collision resistance up to 2n/3/nqueries. This beats a recent bound by Rogaway and Steinberger that 2n/4queries to the underlying random n-to-nbit function suffice to find collisions in any rate-1/2 compression function. In particular, this shows that Rogaway and Steinberger's recent bound of 2(nri¾? mi¾? s/2)/r)queries (for c= 0) crucially relies upon a uniformity assumption; a blanket generalization to arbitrary compression functions would be incorrect. 1 A 3n-to-2nbit compression function making a single call to a 3n-to-nbit primitive, providing collision resistance up to 2nqueries. 1 A 3n-to-2nbit compression function making two calls to a 2n-to-nbit primitive, providing collision resistance up to 2nqueries. 1 A single call compression function with parameters satisfying m≤ n+ c, n≤ s, c≤ m. This result provides a tradeoff between how many bits you can compress for what level of security given a single call to an n+ c-to-nbit random function.

Abstract: Suppose that a target function is monotonic and an available original estimate of this target function is not monotonic. Rearrangements, univariate and multivariate, transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function. Furthermore, suppose an original confidence interval, which covers the target function with probability at least 1-α, is defined by an upper and lower endpoint functions that are not monotonic. Then the rearranged confidence interval, defined by the rearranged upper and lower endpoint functions, is monotonic, shorter in length in common norms than the original interval, and covers the target function with probability at least 1-α. We illustrate the results with a growth chart example.

Abstract: In a wide class of situations of uncertainty, the available information concerning the event space can be described as follows. There exists a true probability that is only known to belong to a certain set P of probabilities: moreover, the lower envelope f of P is a belief function, i.e., a nonadditive measure of a particular type, and characterizes P, i.e., P is the set of all probabilities that dominate f. The effect of conditioning on such situations is examined. The natural conditioning rule in this case is the Bayesian rule. An explicit expression for the Mobius transform phi /sup E/ of f/sup E/ in terms of phi , the transform of f, is found, and an earlier finding that the lower envelope f/sup E/ of P/sup E/ is itself a belief function is derived from it. However, f/sup E/ no longer characterizes P/sup E/ unless f satisfies further stringent conditions that are both necessary and sufficient. The difficulties resulting from this fact are discussed, and suggestions to cope with them are made. >

Abstract: We study what we call functional monitoring problems. We have k players each tracking their inputs, say player i tracking a multiset Ai(t) up until time t, and communicating with a central coordinator. The coordinator's task is to monitor a given function f computed over the union of the inputs ∪iAi(t), continuously at all times t. The goal is to minimize the number of bits communicated between the players and the coordinator. A simple example is when f is the sum, and the coordinator is required to alert when the sum of a distributed set of values exceeds a given threshold τ. Of interest is the approximate version where the coordinator outputs 1 if f ≥ τ and 0 if f ≤ (1 - e)τ. This defines the (k, f, τ, e) distributed, functional monitoring problem. Functional monitoring problems are fundamental in distributed systems, in particular sensor networks, where we must minimize communication; they also connect to problems in communication complexity, communication theory, and signal processing. Yet few formal bounds are known for functional monitoring. We give upper and lower bounds for the (k, f, τ, e) problem for some of the basic f's. In particular, we study frequency moments (F0, F1, F2). For F0 and F1, we obtain continuously monitoring algorithms with costs almost the same as their one-shot computation algorithms. However, for F2 the monitoring problem seems much harder. We give a carefully constructed multi-round algorithm that uses "sketch summaries" at multiple levels of detail and solves the (k, F2, τ, e) problem with communication O(k2/e+ (√k/e)3). Since frequency moment estimation is central to other problems, our results have immediate applications to histograms, wavelet computations, and others. Our algorithmic techniques are likely to be useful for other functional monitoring problems as well.

Abstract: We consider a generalization of stochastic bandit problems where the set of arms, Χ, is allowed to be a generic topological space. We constraint the mean-payoff function with a dissimilarity function over Χ in a way that is more general than Lipschitz. We construct an arm selection policy whose regret improves upon previous result for a large class of problems. In particular, our results imply that if Χ is the unit hypercube in a Euclidean space and the mean-payoff function has a finite number of global maxima around which the behavior of the function is locally Holder with a known exponent, then the expected regret is bounded up to a logarithmic factor by √n, i.e., the rate of the growth of the regret is independent of the dimension of the space. Moreover, we prove the minimax optimality of our algorithm for the class of mean-payoff functions we consider.

Abstract: Lambert W function, hyperpower function, special function, inequality. Abstract: In this note, we obtain inequalities for the Lambert W function W(x), defined by W(x)e W(x) = x for x e 1 . Also, we get upper and lower bounds for the hyperpower function h(x) = x x x. ..

Abstract: There is a whole range of emergent phenomena in non-equilibrium behaviors can be well described by a set of stochastic differential equations. Inspired by an insight gained during our study of robustness and stability in phage lambda genetic switch in modern biology, we found that there exists a classification of generic nonequilibrium processes: In the continuous description in terms of stochastic differential equations, there exists four dynamical elements: the potential function $\phi$, the friction matrix $ S$, the anti-symmetric matrix $ T $, and the noise. The generic feature of absence of detailed balance is then precisely represented by $T$. For dynamical near a fixed point, whether or not it is stable or not, the stochastic dynamics is linear. A rather complete analysis has been carried out (Kwon, Ao, Thouless, cond-mat/0506280; PNAS, {\bf 102} (2005) 13029), referred to as SDS I. One important and persistent question is the existence of a potential function with nonlinear force and with multiplicative noise, with both nice local dynamical and global steady state properties. Here we demonstrate that a dynamical structure built into stochastic differential equation allows us to construct such a global optimization potential function. First, we provide the construction. One of most important ingredient is the generalized Einstein relation. We then present an approximation scheme: The gradient expansion which turns every order into linear matrix equations. The consistent of such methodology with other known stochastic treatments will be discussed in next paper, SDS III; and the explicitly connection to statistical mechanics and thermodynamics will be discussed in a forthcoming paper, SDS IV.

Abstract: This paper considers the approximation of sufficiently smooth multivariable functions with a multilayer perceptron (MLP). For a given approximation order, explicit formulas for the necessary number of hidden units and its distributions to the hidden layers of the MLP are derived. These formulas depend only on the number of input variables and on the desired approximation order. The concept of approximation order encompasses Kolmogorov-Gabor polynomials or discrete Volterra series, which are widely used in static and dynamic models of nonlinear systems. The results are obtained by considering structural properties of the Taylor polynomials of the function in question and of the MLP function.

Abstract: The increase in complexity of computational neuron models makes the hand tuning of model parameters more difficult than ever. Fortunately, the parallel increase in computer power allows scientists to automate this tuning. Optimization algorithms need two essential components. The first one is a function that measures the difference between the output of the model with a given set of parameter and the data. This error function or fitness function makes the ranking of different parameter sets possible. The second component is a search algorithm that explores the parameter space to find the best parameter set in a minimal amount of time. In this review we distinguish three types of error functions: feature-based ones, point-by-point comparison of voltage traces and multi-objective functions. We then detail several popular search algorithms, including brute-force methods, simulated annealing, genetic algorithms, evolution strategies, differential evolution and particle-swarm optimization. Last, we shortly describe Neurofitter, a free software package that combines a phase–plane trajectory density fitness function with several search algorithms.

Abstract: This article presents a general formulation and general numerical scheme for a class of fractional optimal control problems (FOCPs). The fractional derivative is described in the Caputo sense. The performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of fractional differential equations. The calculus of variations, the Lagrange multiplier, and the formula for fractional integration by parts are used to obtain Euler-Lagrange equations for the FOCP. The formulation presented, and the resulting equations, are very similar to those that appear in classical optimal control theory. Thus, the present formulation essentially extends classical control theory to fractional dynamic systems. The formulation is used to derive the control equations for a quadratic linear fractional control problem. An iterative numerical scheme for finding the approximate numerical solution of the resulting equations is presented. For a li...

Abstract: Rank-width was defined by Oum and Seymour [2006] to investigate clique-width. They constructed an algorithm that either outputs a rank-decomposition of width at most f(k) for some function f or confirms that rank-width is larger than k in time O(vVv9log vVv) for an input graph G = (V,E) and a fixed k. We develop three separate algorithms of this kind with faster running time. We construct an O(vVv4)-time algorithm with f(k) = 3k + 1 by constructing a subroutine for the previous algorithm; we avoid generic algorithms minimizing submodular functions used by Oum and Seymour. Another one is an O(vVv3)-time algorithm with f(k) = 24k, achieved by giving a reduction from graphs to binary matroids; then we use an approximation algorithm for matroid branch-width by Hlinený [2005]. Finally we construct an O(vVv3)-time algorithm with f(k) = 3k − 1 by combining the ideas of the two previously cited papers.

Abstract: A generalized Prandtl–Ishlinskii model is proposed for characterizing the rate-dependent hysteresis behavior of smart actuators. A rate-dependent play operator is formulated and integrated to the Prandtl–Ishlinskii model together with a dynamic density function to predict hysteresis properties as a function of the rate of change of the input. Relaxation functions are further proposed to relax the congruency in the output of the Prandtl–Ishlinskii model. The fundamental properties of the proposed rate-dependent operator are systematically provided, which conform with important effects of the time rate of input on the hysteresis output established from the reported experimental data. Additional laboratory experiments were performed to characterize the rate-dependent hysteresis behavior of a PZT actuator under excitation in the 1–500 Hz frequency range. The measured data were used to demonstrate the validity of the proposed generalized model. The comparisons suggest that the proposed rate-dependent operator and density functions allow for prediction of the rate-dependent hysteresis under dynamically varying inputs. From the simulation results attained under varied dynamic inputs, it is shown that the proposed model can predict both major and minor hysteresis loops, and that the hysteresis increases significantly with increasing frequency.

Abstract: A fast and simple algorithm for designing time-optimal waveforms is presented. The algorithm accepts a given arbitrary multidimensional k-space trajectory as the input and outputs the time-optimal gradient waveform that traverses k-space along that path in minimum time. The algorithm is noniterative, and its run time is independent of the complexity of the curve, i.e., the number of switches between slew-rate limited acceleration, slew-rate limited deceleration, and gradient amplitude limited regions. The key in the method is that the gradient amplitude is designed as a function of arc length along the k-space trajectory, rather than as a function of time. Several trajectory design examples are presented.

Abstract: The Dendritic Cell Algorithm is an immune-inspired algorithm originally based on the function of natural dendritic cells. The original instantiation of the algorithm is a highly stochastic algorithm. While the performance of the algorithm is good when applied to large real-time datasets, it is difficult to analyse due to the number of random-based elements. In this paper a deterministic version of the algorithm is proposed, implemented and tested using a port scan dataset to provide a controllable system. This version consists of a controllable amount of parameters, which are experimented with in this paper. In addition the effects are examined of the use of time windows and variation on the number of cells, both which are shown to influence the algorithm. Finally a novel metric for the assessment of the algorithms output is introduced and proves to be a more sensitive metric than the metric used with the original Dendritic Cell Algorithm.

Abstract: The modeling and solving the optimization problem is one of the most important daily problem.By notation the nature of data in practice which are imprecise, fully fuzzy linear programming problem (FFLP) is a power full tool to modeling the practical optimization problem. In This paper after introducing FFLP, a new method to solve it is proposed. a linear ranking function for defuzzifying the FFLP is used , Equivalency between two problems is proved by some theorems.

Abstract: Coherent operations with individual trapped ${\text{Yb}}^{+}$ ions are demonstrated that are robust against variations in experimental parameters and intrinsically indeterministic system parameters. In particular, pulses developed using optimal control theory are demonstrated with trapped ions. Their performance as a function of error parameters is systematically investigated and compared to composite pulses. Such pulses are basic building blocks for single and multiqubit quantum gates.

Abstract: The mass attenuation coefficients, total interaction cross-sections, effective atomic numbers, effective electron densities and photon mean free paths of the Cu/Zn alloy were determined on the basis of the mixture rule at 356, 511, 662, 835 and 1275 keV gamma-ray energies. The gamma-rays were detected by using an ordinary NaI(Tl) scintillation detection system with a resolution of 10.2% at 662 keV.It was observed that the mixture rule is a suitable method for determination of these parameters. The effective atomic numbers and effective electron densities tend to be almost constant as a function of energy. There is good agreement between experiment and theory, calculated by WinXCom.

Abstract: A numerical algorithm for calculating the generalized Mittag-Leffler $\mathrm{E}_{\alpha,\beta}(z)$ function for arbitrary complex argument $z$ and real parameters $\alpha>0$ and $\beta\in\mathbb{R}$ is presented. The algorithm uses the Taylor series, the exponentially improved asymptotic series, and integral representations to obtain optimal stability and accuracy of the algorithm. Special care is applied to the limits of validity of the different schemes to avoid instabilities in the algorithm.

Abstract: Discovering additive structure is an important step towards understanding a complex multi-dimensional function because it allows the function to be expressed as the sum of lower-dimensional components. When variables interact, however, their effects are not additive and must be modeled and interpreted simultaneously. We present a new approach for the problem of interaction detection. Our method is based on comparing the performance of unrestricted and restricted prediction models, where restricted models are prevented from modeling an interaction in question. We show that an additive model-based regression ensemble, Additive Groves, can be restricted appropriately for use with this framework, and thus has the right properties for accurately detecting variable interactions.