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This article is composed of two parts; In the first part (Sec. 1), the ultra-large-scale electronic structure theory is reviewed for (i) its fundamental numerical algorithm and (ii) its role in nano-material science. The second part (Sec. 2) is devoted to the mathematical foundation of the large-scale electronic structure theory and their numerical aspects.

This article is composed of two parts; In the first part (Sec. 1), the ultra-large-scale electronic structure theory is reviewed for (i) its fundamental numerical algorithm and (ii) its role in nano-material science. The second part (Sec. 2) is devoted to the mathematical foundation of the large-scale electronic structure theory and their numerical aspects.

This article is composed of two parts; In the first part (Sec. 1), the ultra-large-scale electronic structure theory is reviewed for (i) its fundamental numerical algorithm and (ii) its role in nano-material science. The second part (Sec. 2) is devoted to the mathematical foundation of the large-scale electronic structure theory and their numerical aspects.

A heatbath algorithm is proposed for pure SU(N) lattice gauge theory based on the Manton action of the plaquette element for general gauge group N. Comparison is made to the Metropolis thermalization algorithm using both the Wilson and Manton actions. The heatbath algorithm is found to outperform the Metropolis algorithm in both execution speed and decorrelation rate. Results, mostly in D=3, for N=2 through 5 at several values for the inverse coupling are presented.

The objective of this paper is to build the neutrosophic version of the RSA crypto-algorithm, where we use the foundations of fusion neutrosophic number theory such as neutrosophic phi-Euler's function, neutrosophic congruencies, and neutrosophic inverses to build novel algorithms for cryptography depending of famous RSA algorithm.

A sequential conjugate gradient-restoration algorithm is developed in order to solve optimal control problems involving a functional subject to differential constraints, nondifferential constraints, and terminal constraints. The algorithm is composed of a sequence of cycles, each cycle consisting of two phases, a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves a single iteration and is designed to decrease the value of the functional while satisfying the constraints to first order. The restoration phase involves one or more iterations and is designed to restore the constraints to a predetermined accuracy, while the norm of the variations of the variations of the control and the parameter is minimized, subject to the linearized constraints. The sequential conjugate gradient-restoration algorithm is characterized by two main properties. First, at the end of each cycle, the trajectory satisfies the constraints to a given accuracy. Second, the conjugate gradient stepsize and the restoration stepsize can be chosen so that the restoration phase preserves the descent property of the conjugate gradient phase.

The dynamic and composite nature of propagation impairments that are incurred on Earth-space communications links at frequencies in and above 30/20 GHz Ka band, i.e., rain attenuation, cloud and/or clear air scintillation, etc., combined with the need to counter such degradations after the small link margins have been exceeded, necessitate the use of dynamic statistical identification and prediction processing of the fading signal in order to optimally estimate and predict the levels of each of the deleterious attenuation components. Such requirements are being met in NASA's Advanced Communications Technology Satellite (ACTS) Project by the implementation of optimal processing schemes derived through the use of the Rain Attenuation Prediction Model and nonlinear Markov filtering theory.

In this paper, we analyse an identification algorithm in the evidence theory framework. The identification algorithm is composed of four main steps: (1) sensor reports are transformed into initial Basic Probability Assignments, (2) the successive BPAs are combined through Dempster's rule, (3) the resulting BPAs are approximated to avoid algorithm explosion, and (4) in parallel to step (3) a decision is taken on the identification/classification of an object from a database based on the maximum of pignistic probability criterion. The identification algorithm is applied to a Direct Fleet Support scenario where ESM reports are fused to identify six targets among a possibility of 142 in the database. As a basis for the analysis, we observe the behaviour of (1) the pignistic probability of the singletons of the database, used as decision rule, (2) the distance between a BPA and a solution (ground truth), (3) the distance between an approximated BPA and a non-approximated one, and (4) the non-specificity of the BPA.

With the capacity of today's computers; one can envisage the resolution of shape optimization problems in aerodynamics. Nevertheless, optimization methods require many evaluations of different aerodynamic configurations, and so are much more expensive than a single analysis. It is therefore mandatory to find methods that evaluate aerodynamic functions and their gradient at the lowest possible computational cost; as well as fast and robust optimization methods.

A nonlinear African vulture optimization algorithm combining Henon chaotic mapping theory and reverse learning competition strategy 作者： Baiyi Wang 1 Zipeng Zhang 1 Patrick Siarry 2 Xinhua Liu 1 Grzegorz Królczyk 3 Dezheng Hua 1 Frantisek Brumercik 4 Zhixiong Li 3 作者单位： 1. School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou, China 2. University Paris-Est Créteil Val de Marne, 61 Av. du General de Gaulle, Creteil 94010, France 3. Department of Manufacturing Engineering and Automation Products, Opole University of Technology, Opole 45-758, Poland 4. Department of Design and Machine Elements, Faculty of Mechanical Engineering, University of Zilina, Univerzitna 1, Zilina 010 26, Slovakia 通讯作者： Xinhua Liu Email:[email protected] 提交时间： 2024-03-28 18:49:16 摘要: As a new intelligent optimization algorithm, the African vultures optimization algorithm (AVOA) has been widely used in various fields today. However, when solving complex multimodal problems, the AVOA still has some shortcomings, such as low searching accuracy, deficiency on the search capability and tendency to fall into local optimum. In order to alleviate the main shortcomings of the AVOA, a nonlinear African vulture optimization algorithm combining Henon chaotic mapping theory and reverse learning competition strategy (HWEAVOA) is proposed. Firstly, the Henon chaotic mapping theory and elite population strategy are proposed to improve the randomness and diversity of the vulture’s initial population; Furthermore, the nonlinear adaptive incremental inertial weight factor is introduced in the location update phase to rationally balance the exploration and exploitation abilities, and avoid individual falling into a local optimum; The reverse learning competition strategy is designed to expand the discovery fields for the optimal solution and strengthen the ability to jump out of the local optimal solution. HWEAVOA and other advanced comparison algorithms are used to solve classical and CEC2022 test functions. Compared with other algorithms, the convergence curves of the HWEAVOA drop faster and the line bodies are smoother. These experimental results show the proposed HWEAVOA is ranked first in all test functions, which is superior to the comparison algorithms in convergence speed, optimization ability, and solution stability. Meanwhile, HWEAVOA has reached the general level in the algorithm complexity, and its overall performance is competitive in the swarm intelligence algorithms. African vultures optimization algorithm Henon chaotic mapping theory Nonlinear adaptive incremental inertial weight factor Reverse learning competition strategy 来自： Zhixiong Li 分类： 工程与技术科学 >> 工程通用技术 投稿状态： 已被期刊接收 引用： ChinaXiv:202403.00412 (或此版本 ChinaXiv:202403.00412V1 ) DOI:10.12074/202403.00412V1 CSTR:32003.36.ChinaXiv.202403.00412.V1 推荐引用方式： Baiyi Wang ,Zipeng Zhang,Patrick Siarry,Xinhua Liu,Grzegorz Królczyk,Dezheng Hua,Frantisek Brumercik,Zhixiong Li.(2024).A nonlinear African vulture optimization algorithm combining Henon chaotic mapping theory and reverse learning competition strategy.中国科学院科技论文预发布平台.[ChinaXiv:202403.00412] 版本历史 [V1] 2024-03-28 18:49:16 ChinaXiv:202403.00412V1 下载全文

The "Tate forms" for elliptically fibered Calabi-Yau manifolds are reconsidered in order to determine their general validity. We point out that there were some implicit assumptions made in the original derivation of these "Tate forms" from the Tate algorithm. By a careful analysis of the Tate algorithm itself, we deduce that the "Tate forms" (without any futher divisiblity assumptions) do not hold in some instances and have to be replaced by a new type of ansatz. Furthermore, we give examples in which the existence of a "Tate form" can be globally obstructed, i.e., the change of coordinates does not extend globally to sections of the entire base of the elliptic fibration. These results have implications both for model-building and for the exploration of the landscape of F-theory vacua.

We prove that any polynomial-time $\alpha(n)$-approximation algorithm for the $n$-vertex metric asymmetric Traveling Salesperson Problem yields a polynomial-time $O(\alpha(C))$-approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where $C$ is the number of weakly connected components in the subgraph induced by the positive-demand arcs---a small number in many applications. In conjunction with known results, we obtain constant-factor approximations for $C\in O(\log n)$ and $O(\log C/\log\log C)$-approximations in general. Experiments show that our algorithm, together with several heuristic enhancements, outperforms many previous polynomial-time heuristics. Finally, since the solution quality achievable in polynomial time appears to mainly depend on $C$ and since $C=1$ in almost all benchmark instances, we propose the Ob benchmark set, simulating cities that are divided into several components by a river.

Across the sciences, a fundamental setting for representing and interpreting information about entities, the structure and organization of communities, and changes in these over time, is a stochastic network that is topologically rewiring and semantically evolving over time, or over a genealogy. While there is a rich literature in modeling invariant networks, until recently, little has been done toward modeling the dynamic processes underlying rewiring networks, and on recovering such networks when they are not observable. In this talk, I will present some recent developments in analyzing what we refer to as the dynamic tomography of evolving networks. I will first present a new class of statistical models known as dynamic exponential random graph models for evolving social networks, which offers both good statistical property and rich expressivity; then, I will present new sparse-coding algorithms for estimating the topological structures of latent evolving networks underlying nonstationary time-series or tree-series of nodal attributes, along with theoretical results on the asymptotic sparsistency of the proposed methods; finally, I will present a new Bayesian model for estimating and visualizing the trajectories of latent multi-functionality of nodal states in the evolving networks. I will show some promising empirical results on recovering and analyzing the latent evolving social networks in the US Senate and the Enron Corporation at a time resolution only limited by sample frequency. In all cases, our methods reveal interesting dynamic patterns in the networks. ©2011 Microsoft Corporation. All rights reserved.

Across the sciences, a fundamental setting for representing and interpreting information about entities, the structure and organization of communities, and changes in these over time, is a stochastic network that is topologically rewiring and semantically evolving over time, or over a genealogy. While there is a rich literature in modeling invariant networks, until recently, little has been done toward modeling the dynamic processes underlying rewiring networks, and on recovering such networks when they are not observable. In this talk, I will present some recent developments in analyzing what we refer to as the dynamic tomography of evolving networks. I will first present a new class of statistical models known as dynamic exponential random graph models for evolving social networks, which offers both good statistical property and rich expressivity; then, I will present new sparse-coding algorithms for estimating the topological structures of latent evolving networks underlying nonstationary time-series or tree-series of nodal attributes, along with theoretical results on the asymptotic sparsistency of the proposed methods; finally, I will present a new Bayesian model for estimating and visualizing the trajectories of latent multi-functionality of nodal states in the evolving networks. I will show some promising empirical results on recovering and analyzing the latent evolving social networks in the US Senate and the Enron Corporation at a time resolution only limited by sample frequency. In all cases, our methods reveal interesting dynamic patterns in the networks. ©2011 Microsoft Corporation. All rights reserved.

xiv, 81 pages : 24 cm

We study the minimization problem of a non-convex sparsity promoting penalty function, the transformed $l_1$ (TL1), and its application in compressed sensing (CS). The TL1 penalty interpolates $l_0$ and $l_1$ norms through a nonnegative parameter $a \in (0,+\infty)$, similar to $l_p$ with $p \in (0,1]$. TL1 is known in the statistics literature to enjoy three desired properties: unbiasedness, sparsity and Lipschitz continuity. We first consider the constrained minimization problem and prove the uniqueness of global minimizer and its equivalence to $l_0$ norm minimization if the sensing matrix $A$ satisfies a restricted isometry property (RIP) and if $a > a^*$, where $a^*$ depends only on $A$. The solution is stable under noisy measurement. For general sensing matrix $A$, we show that the support set of a local minimizer corresponds to linearly independent columns of $A$, and recall sufficient conditions for a critical point to be a local minimum. Next, we present difference of convex algorithms for TL1 (DCATL1) in computing TL1-regularized constrained and unconstrained problems in CS. For the unconstrained problem, we prove convergence of DCALT1 to a stationary point satisfying the first order optimality condition. Finally in numerical experiments, we identify the optimal value $a=1$, and compare DCATL1 with other CS algorithms on three classes of sensing matrices: Gaussian random matrices, over-sampled discrete cosine transform matrices (ODCT), and uniformly distributed M-sphere matrices. We find that for all three classes of sensing matrices, the performance of DCATL1 algorithm (initiated with $L_1$ minimization) always ranks near the top (if not the top), and is the most robust choice insensitive to RIP (incoherence) of the underlying CS problems.

We use graded Specht modules to calculate the graded decomposition numbers for the Iwahori-Hecke algebra of the symmetric group over a field of characteristic zero at a root of unity. The algorithm arrived at is the Lascoux-Leclerc-Thibon algorithm in disguise. Thus we interpret the algorithm in terms of graded representation theory.

A recursive multisensor association algorithm has been developed based on fuzzy logic. It simultaneously determines fuzzy grades of membership and fuzzy cluster centers. It is capable of associating data from various sensor types and performing without operator intervention. It associates data from the same target for multiple sensor types. The algorithm also provides an estimate of the number of targets present, reduced noise estimates of the quantities being measured, and a measure of confidence to assign to the data association. The fuzzy logic formalism used offers the opportunity to incorporate additional information or heuristic rules easily. A comparison of the algorithm to a more conventional Bayesian association algorithm is provided. Also, procedures for defuzzification, i.e., mapping fuzzy results to hard results are discussed as well as the method of determining target validity. Various simulated real time data sets are analyzed and provide a basis for comparison of the fuzzy and Bayesian association algorithms.

A recursive multisensor association algorithm has been developed based on fuzzy logic. It simultaneously determines fuzzy grades of membership and fuzzy cluster centers. It is capable of associating data from various sensor types and performing without operator intervention. It associates data from the same target for multiple sensor types. The algorithm also provides an estimate of the number of targets present, reduced noise estimates of the quantities being measured, and a measure of confidence to assign to the data association. The fuzzy logic formalism used offers the opportunity to incorporate additional information or heuristic rules easily. A comparison of the algorithm to a more conventional Bayesian association algorithm is provided. Also, procedures for defuzzification, i.e., mapping fuzzy results to hard results are discussed as well as the method of determining target validity. Various simulated real time data sets are analyzed and provide a basis for comparison of the fuzzy and Bayesian association algorithms.

A recursive multisensor association algorithm has been developed based on fuzzy logic. It simultaneously determines fuzzy grades of membership and fuzzy cluster centers. It is capable of associating data from various sensor types and performing without operator intervention. It associates data from the same target for multiple sensor types. The algorithm also provides an estimate of the number of targets present, reduced noise estimates of the quantities being measured, and a measure of confidence to assign to the data association. The fuzzy logic formalism used offers the opportunity to incorporate additional information or heuristic rules easily. A comparison of the algorithm to a more conventional Bayesian association algorithm is provided. Also, procedures for defuzzification, i.e., mapping fuzzy results to hard results are discussed as well as the method of determining target validity. Various simulated real time data sets are analyzed and provide a basis for comparison of the fuzzy and Bayesian association algorithms.

The Ship Applied Fire Engineering (SAFE) computer program evaluates the probability of limiting the spread of fire from one compartment to another throughout a vessel. The results from SAFE are expressed in terms of the frequency of expected loss of each compartment. To evaluate these frequencies, it is necessary to determine the cumulative probability of loss of each compartment in the ship as a target from all possible fire paths from all possible rooms of origin. The existing algorithm in SAFE for calculating the loss of target compartments, referred to as the Cumulative L-Curve Algorithm," errs on the conservative side since it permits the contribution of a particular compartment to be counted more than once toward the total probability of loss for a target compartment. The approach selected to develop a mathematically valid cumulative L-Curve algorithm utilizes the mathematical tools of reliability theory, specifically for interconnected systems. The implication of this research is that with the new algorithm, SAFE will be able to more accurately calculate the fire safety levels of all compartments. Performance-based fire protection results must accurately indicate whether compartments are under- or over-protected relative to desired objectives. The improved algorithm will help achieve this goal.

The Ship Applied Fire Engineering (SAFE) computer program evaluates the probability of limiting the spread of fire from one compartment to another throughout a vessel. The results from SAFE are expressed in terms of the frequency of expected loss of each compartment. To evaluate these frequencies, it is necessary to determine the cumulative probability of loss of each compartment in the ship as a target from all possible fire paths from all possible rooms of origin. The existing algorithm in SAFE for calculating the loss of target compartments, referred to as the Cumulative L-Curve Algorithm," errs on the conservative side since it permits the contribution of a particular compartment to be counted more than once toward the total probability of loss for a target compartment. The approach selected to develop a mathematically valid cumulative L-Curve algorithm utilizes the mathematical tools of reliability theory, specifically for interconnected systems. The implication of this research is that with the new algorithm, SAFE will be able to more accurately calculate the fire safety levels of all compartments. Performance-based fire protection results must accurately indicate whether compartments are under- or over-protected relative to desired objectives. The improved algorithm will help achieve this goal.

We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation -- the locality of the dark matter equations and the scale invariance of the problem -- as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm, including the applications described here.

We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation -- the locality of the dark matter equations and the scale invariance of the problem -- as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm, including the applications described here.

It is now well known that the moduli space of a vector bundle for heterotic string compactifications to four dimensions is parameterized by a set of sections of a weighted projective space bundle of a particular kind, known as Looijenga's weighted projective space bundle. We show that the requisite weighted projective spaces and the Weierstrass equations describing the spectral covers for gauge groups E_N (N=4,...,8) and SU(n+1) (n=1,2,3) can be obtained systematically by a series of blowing-up procedures according to Tate's algorithm, thereby the sections of correct line bundles claimed to arise by Looijenga's theorem can be automatically obtained. They are nothing but the four-dimensional analogue of the set of independent polynomials in the six-dimensional F-theory parameterizing the complex structure, which is further confirmed in the constructions of D_4, A_5, D_6, E_3 and SU(2) x SU(2) bundles. We also explain why we can obtain them in this way by using the structure theorem of the Mordell-Weil lattice, which is also useful for understanding the relation between the singularity and the occurrence of chiral matter in F-theory.

We present an algorithm for Monte Carlo simulations which is able to overcome the suppression of transitions between the phases in compact U(1) lattice gauge theory in 4 dimensions.

We develop an efficient algorithm for evaluating divergent perturbation expansions of field theories in the bare coupling constant g_B for which we possess a finite number L of expansion coefficients plus two more informations: The knowledge of the large-order behavior proportional to (- alpha)^kk!k^beta g_B^k, with a known growth parameter alpha, and the knowledge of the approach to scaling being of the type c+c'/g_B^ omega, with constants c,c' and a critical exponent of approach omega . The latter information leads to an increase in the speed of convergence and a high accuracy of the results. The algorithm is applied to the six- and seven-loop expansions for the critical exponents of O(N)-symmetric phi^4-theories, and the result for the critical exponent alpha is compared with the recent satellite experiment.

For SU(2) lattice gauge theory with the fundamental-adjoint action an efficient heat-bath algorithm is not known so that one had to rely on Metropolis simulations supplemented by overrelaxation. Implementing a novel biased Metropolis-heat-bath algorithm for this model, we find improvement factors in the range 1.45 to 2.06 over conventionally optimized Metropolis simulations. If one optimizes further with respect to additional overrelaxation sweeps, the improvement factors are found in the range 1.3 to 1.8.

Euclidean gcd Algorithm - Given a, b _ Z, not both 0, �nd (a, b)Euclidean gcd Algorithm - Given a, b _ Z, not both 0, �nd (a, b)

A digital computer-based state variable controller was designed and applied to the 70-m antenna axis servos. The general equations and structure of the algorithm and provisions for alternate position error feedback modes to accommodate intertarget slew, encoder referenced tracking, and precision tracking modes are descibed. Development of the discrete time domain control model and computation of estimator and control gain parameters based on closed loop pole placement criteria are discussed. The new algorithm was successfully implemented and tested in the 70-m antenna at Deep Space Network station 63 in Spain.

Density gradient theory (DGT) allows fast and accurate determination of surface tension and density profile through a phase interface. Several algorithms have been developed to apply this theory in practical calculations. While the conventional algorithm requires a reference substance of the system, a modified "stabilized density gradient theory" (SDGT) algorithm is introduced in our work to solve DGT equations for multiphase pure and mixed systems. This algorithm makes it possible to calculate interfacial properties accurately at any domain size larger than the interface thickness without choosing a reference substance or assuming the functional form of the density profile. As part of DGT inputs, the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was employed for the first time with the SDGT algorithm. PC-SAFT has excellent performance in predicting liquid phase properties as well as phase behaviors. The SDGT algorithm with the PC-SAFT EoS was tested and compared with experimental data for several systems. Numerical stability analyses were also included in each calculation to verify the reliability of this approach for future applications.

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however, does not produce the parameter covariance matrix as an automatic byproduct upon convergence. In turn, researchers are limited in when they can employ RC-IRT, as the covariance matrix is needed for many statistical inference procedures. The present research remedies this problem by estimating the RC-IRT model parameters by the Metropolis-Hastings Robbins-Monro (MH-RM, Cai, 2010) algorithm. An attractive feature of MH-RM is that the structure of the algorithm makes estimation of the covariance matrix convenient. Additionally, MH-RM is ideally suited for multidimensional IRT, whereas EM is limited by the "curse of dimensionality." Based on the current research, when RC-IRT or similar semi-nonparametric IRT models are eventually generalized to include multiple latent dimensions, MH-RM would appear to be the logical choice for estimation. Complete Data Log-Likelihood and Derivatives for the Ramsay Curve is appended.

The data augmentation (DA) algorithm is a simple and powerful tool in statistical computing. In this note basic information theory is used to prove a nontrivial convergence theorem for the DA algorithm.

Applying Genetic Algorithm for the Lattice Gauge Theory is formed to be an effective method to minimize the action of gauge field on a lattice. In 4 dimensions, the critical point and the Wilson loop behaviour of SU(2) lattice gauge theory as well as the phase transition of U(1) theory have been studied. The proper coding methodi has been developed in order to avoid the increase of necessary memory and the overload of calculation for Genetic Algorithm. How hichhikers toward equlibrium appear against kidnappers is clarified.

Algorithms and data structures are among the primary constituents of computer software and thus are among basic objects of study in Computer Science. This project is concerned with the structure and automated design of algorithms and data structures. Our scientific hypothesis is the there exist general algorithm, data structure, and design concepts that underlie and explain most of the detailed structure of conventional software systems. By abstracting and formalizing these concepts and showing how to mechanize their application, we can prepare the way for the coming generation of automated software design environments. Our approach involves identifying classes of algorithms that solve a broad range of useful problems. In particular we have emphasized formalizing abstract algorithms that make minimal assumptions about the structure of a problem. Once a class of algorithms has been identified we represent its essence as a theory, called an algorithm theory.

Algorithms and data structures are among the primary constituents of computer software and thus are among basic objects of study in Computer Science. This project is concerned with the structure and automated design of algorithms and data structures. Our scientific hypothesis is the there exist general algorithm, data structure, and design concepts that underlie and explain most of the detailed structure of conventional software systems. By abstracting and formalizing these concepts and showing how to mechanize their application, we can prepare the way for the coming generation of automated software design environments. Our approach involves identifying classes of algorithms that solve a broad range of useful problems. In particular we have emphasized formalizing abstract algorithms that make minimal assumptions about the structure of a problem. Once a class of algorithms has been identified we represent its essence as a theory, called an algorithm theory.

Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT .

Jacobi Symbol - used to compute Legendre Symbol ef�ciently(quadratic character)

This report proposes Pattern Theory as a basis for an engineering theory of algorithms design. Pattern Theory (PT) begins with a general statement of the problem and then makes deliberate specializations. The problem of finding a pattern in a function is the essence of algorithm design. The key to PT is its measure of pattern-ness: Decomposed Function Cardinality (SFC). Low DFC indicates pattern-ness. The principal result is a demonstration of the generality with which DFC measures pattern-ness. This generality is supported theoretically by relating DFC to time complexity, program length and circuit complexity. A test is developed, based on DFC, for whether or not a function will decompose. This test is used in Ada Function Decomposition (AFD) programs. AFD produces a decomposition (i.e. an algorithm in combinational form) and DFC. The generality of DFC is also supported experimentally. The Pattern Theory approach to machine learning and data compression demonstrated greater generality than other approaches. The DFC's of over 800 nonrandom functions (numeric, symbolic, string based, graph based, images and files) were measured. Roughly 98% of the nonrandom functions had low DFC versus less than 1% for random functions. AFD found the classical algorithms for several functions.

An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm allows the use of the same piece of computer code to evaluate any particular diagram in any specific order of the perturbation theory or to calculate similar terms in other areas of the many-body theory, like e.g. terms in the coupled-cluster equations. The use of the algorithm is illustrated by calculating the second and third order correlation corrections to the removal energies of electrons from the ground state of sodium, copper and gallium and by calculating the hyperfine structure constants of sodium in the linearized single-double coupled cluster approximation.

Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in the conventional approach, it is extremely difficult to compute the excited states. Here we present a different algorithm: the Monte Carlo Hamiltonian method, designed to overcome the difficulties of the conventional approach. As a new example, application to the Klein-Gordon field theory is shown.

This is the first experiment of a research project. Each experiment will have a mixed design in which Theory of Machine will be manipulated as between-subjects variable and task difficulty (Experiment 1) or experienced errs (Experiment 2) as within-subject variable. In both experiments half of the participants will be assigned to the Theory of Machine condition and the other half to the control condition. In the control condition, the algorithm is presented as a black box, as only instructions on how to use AI will be giving. In the Theory of Machine condition, the participants will gain understanding of the algorithm as in Theory of Machine. This will be done by giving instructions on how to use the AI as well as explaining how AI and human decision making differ. Experiment 1. We test whether the impact of Theory of Machine on the degree of ‘Weight on Advice’ (WOA) is moderated by task difficulty (high/ low). Each participant conducts a task with ten faces of which age it is easy and ten faces which are hard to judge, so in total two trials with ten faces each. Difficulty of judging the age of the faces will be determined by the standard deviation of perceived age. A low sd signals an easy to judge face, while a high sd in perceived age suggests it is hard to judge the persons age.

This article is from Sensors (Basel, Switzerland) , volume 11 . Abstract For wireless sensor networks (WSNs), many factors, such as mutual interference of wireless links, battlefield applications and nodes exposed to the environment without good physical protection, result in the sensor nodes being more vulnerable to be attacked and compromised. In order to address this network security problem, a novel trust evaluation algorithm defined as NBBTE (Node Behavioral Strategies Banding Belief Theory of the Trust Evaluation Algorithm) is proposed, which integrates the approach of nodes behavioral strategies and modified evidence theory. According to the behaviors of sensor nodes, a variety of trust factors and coefficients related to the network application are established to obtain direct and indirect trust values through calculating weighted average of trust factors. Meanwhile, the fuzzy set method is applied to form the basic input vector of evidence. On this basis, the evidence difference is calculated between the indirect and direct trust values, which link the revised D-S evidence combination rule to finally synthesize integrated trust value of nodes. The simulation results show that NBBTE can effectively identify malicious nodes and reflects the characteristic of trust value that ‘hard to acquire and easy to lose’. Furthermore, it is obvious that the proposed scheme has an outstanding advantage in terms of illustrating the real contribution of different nodes to trust evaluation.

This proposal concerns development, analysis, implementation, and applications of efficient and accurate numerical methods for interface problems, especially with moving interface and free boundary problems, and problems defined on irregular and infinite domains. Specifically, we will develop numerical methods for various applications.

This proposal concerns development, analysis, implementation, and applications of efficient and accurate numerical methods for interface problems, especially with moving interface and free boundary problems, and problems defined on irregular and infinite domains. Specifically, we will develop numerical methods for various applications.

We propose a new algorithm for classical statistical simulations in scalar and gauge theories undergoing a one dimensional expansion, which allows simulations to study boxes of larger transverse extent and to continue for longer times, without losing lattice resolution in the expanding direction.

Algorithms and data structures are among the primary constituents of computer software and thus are among basic objects of study in Computer Science. This project is concerned with the structure and automated design of algorithms and data structures. Our scientific hypothesis is that there exist general algorithm, data structure,and design concepts that underlie and explain most of the detailed structure of conventional software systems. By abstracting and formalizing these concepts and showing how to mechanize their application, we can prepare the way for the coming generation of automated software design environments. Our approach involves identifying classes of algorithms that solve a broad range of useful problems. In particular we have emphasized formalizing abstract algorithms that make minimal assumptions about the structure of a problem. Once a class of algorithms has been identified we represent its essence as a theory, called and algorithm theory. (kr)

One challenge of simultaneous tracking and identification of targets is the fusion of continuous and discrete information. Recently a few fusionists including Mahler 1 and Mori 2 are using a set theory approach for a unified data fusion theory which is a correlation free paradigm 3 This paper uses the set theory approach as a basis for a method of fusing kinematic-continuous data and identification-discrete feature information. The set of features are high range resolution radar range-bin locations and amplitudes which are collected over a small aperture and a scrambled method is used to order a feature set. Once features are ordered, a recursive belief filter operates in feature space to combine track and identification measurements. The intersection of track and identification methods results in a simultaneous tracking and identification algorithm which accumulates evidence for belief in targets and rules out non-plausible targets.

The pace of progress in the fields of Evolutionary Computation and Machine Learning is currently limited -- in the former field, by the improbability of making advantageous extensions to evolutionary algorithms when their capacity for adaptation is poorly understood, and in the latter by the difficulty of finding effective semi-principled reductions of hard real-world problems to relatively simple optimization problems. In this paper we explain why a theory which can accurately explain the simple genetic algorithm's remarkable capacity for adaptation has the potential to address both these limitations. We describe what we believe to be the impediments -- historic and analytic -- to the discovery of such a theory and highlight the negative role that the building block hypothesis (BBH) has played. We argue based on experimental results that a fundamental limitation which is widely believed to constrain the SGA's adaptive ability (and is strongly implied by the BBH) is in fact illusionary and does not exist. The SGA therefore turns out to be more powerful than it is currently thought to be. We give conditions under which it becomes feasible to numerically approximate and study the multivariate marginals of the search distribution of an infinite population SGA over multiple generations even when its genomes are long, and explain why this analysis is relevant to the riddle of the SGA's remarkable adaptive abilities.

An overrelaxed variant of simulated annealing is applied to the problem of maximally abelian gauge fixing. The superiority of this algorithm over the commonly used relaxation procedure is demonstrated. Biases on non gauge invariant quantities due to gauge fixing ambiguities are discussed.