Fast Algorithm

The eddy current non-destructive evaluation (NDE) modelling using Stratton-Chu formulation-based fast algorithm is analysed. Stratton-Chu formulations, which have no low frequency breakdown issue, are selected for modelling electromagnetic NDE problems with low frequency and high conductivity approximations. As the main contribution of this article, the robustness and efficiency of the approximations, which result in big savings in both memory and CPU time, are validated and analysed using examples from practical EC testing. The boundary element method (BEM) is used to discretize the integral equations into a linear system of equations: the first order Rao-Wilton-Glisson (RWG) vector basis functions with the flat triangle meshes of the object and pulse basis functions are selected to expand the equivalent surface currents and the normal component of magnetic fields, respectively. Then the multilevel adaptive cross approximation (MLACA) algorithm is applied to accelerate the iterativ...

This article presents a new Fast Hash-based File Existence Checking (FHFEC) method for archiving systems. During the archiving process, there are many submissions which are actually unchanged files that do not need to be re-archived. In this system, instead of comparing the entire files, only digests of the files are compared. Strong cryptographic hash functions with a low probability of collision can be used as digests. We propose a fast algorithm to check if a certain hash, that is, a corresponding file, is already stored in the system. The algorithm is based on dividing the whole domain of hashes into equally sized regions, and on the existence of a pointer array, which has exactly one pointer for each region. Each pointer points to the location of the first stored hash from the corresponding region and has a null value if no hash from that region exists. The entire structure can be stored in random access memory or, alternatively, on a dedicated hard disk. A statistical performa...

In this paper, we develop a discrete wavelet Petrov–Galerkin method for integral equations of the second kind with weakly singular kernels suitable for solving boundary integral equations. A compression strategy for the design of a fast algorithm is suggested. Estimates for the rate of convergence and computational complexity of the method are provided.

An orthogonal drawing of a planar graph G is a drawing of G such that each vertex is drawn as a point, each edge is drawn as a sequence of alternate horizontal and vertical line segment, and any two edges do not cross except at their common end. An L-shaped drawing of a graph G is an orthogonal drawing of G where each edge has exactly one bend. Clearly the maximum degree of a graph G is at most 4 if G has an L-shaped drawing. It is known that every planar graph of maximum degree 3 does not have L-shaped drawing. In this paper we study Lshaped drawings of series-parallel graphs in variable embedding settings. We show that every series-parallel graph of maximum degree 3 and every maximal outerplane graph of maximum degree 4 admit L-shaped drawings.

An algorithm is presented, that provides a fast and robust reconstruction of neutrino induced upward-going muons and a discrimination of these events from downward-going atmospheric muon background in data collected by the ANTARES neutrino telescope. The algorithm consists of a hit merging and hit selection procedure followed by fitting steps for a track hypothesis and a point-like light source. It is particularly well-suited for real time applications such as online monitoring and fast triggering of optical follow-up observations for multi-messenger studies. The performance of the algorithm is evaluated with Monte Carlo simulations and various distributions are compared with that obtained in ANTARES data.

We present a fast algorithm for continuous collision detection between a moving avatar and its surrounding virtual environment. We model the avatar as an articulated body using line-skeletons with constant offsets and the virtual environment as a collection of polygonized objects. Given the position and orientation of the avatar at discrete time steps, we use an arbitrary in-between motion to interpolate the path for each link between discrete instances. We bound the swept-space of each link using a swept volume (SV) and compute a bounding volume hierarchy to cull away links that are not in close proximity to the objects in the virtual environment. We generate the SV's of the remaining links and use them to check for possible interferences and estimate the time of collision between the surface of the SV and the objects in the virtual environment. Furthermore, we use graphics hardware to perform collision queries on the dynamically generated swept surfaces. Our overall algorithm requires no precomputation and is applicable to general articulated bodies. We have implemented the algorithm on a 2.4 GHz Pentium IV PC with NVIDIA GeForce FX 5800 graphics card and applied it to an avatar with 16 links, moving in a virtual environment composed of hundreds of thousands of polygons. Our prototype system is able to detect all contacts between the moving avatar and the environment in 10 -30 milliseconds.

We present a fast algorithm for continuous collision detection between a moving avatar and its surrounding virtual environment. We model the avatar as an articulated body using line-skeletons with constant offsets and the virtual environment as a collection of polygonized objects. Given the position and orientation of the avatar at discrete time steps, we use an arbitrary in-between motion to interpolate the path for each link between discrete instances. We bound the swept-space of each link using a swept volume (SV) and compute a bounding volume hierarchy to cull away links that are not in close proximity to the objects in the virtual environment. We generate the SV's of the remaining links and use them to check for possible interferences and estimate the time of collision between the surface of the SV and the objects in the virtual environment. Furthermore, we use graphics hardware to perform collision queries on the dynamically generated swept surfaces. Our overall algorithm requires no precomputation and is applicable to general articulated bodies. We have implemented the algorithm on a 2.4 GHz Pentium IV PC with NVIDIA GeForce FX 5800 graphics card and applied it to an avatar with 16 links, moving in a virtual environment composed of hundreds of thousands of polygons. Our prototype system is able to detect all contacts between the moving avatar and the environment in 10 -30 milliseconds.

The late Professor Stephen Benton, co-inventor of the world's first holographic video system, sometimes quipped that we were "only 3 Nobel Prizes away" from a practical product. This presentation describes the baby steps, technical breakthroughs, and most recent (perhaps even prize-worthy) developments in this exciting new medium. Topics covered include: Why is it so difficult? (Or, how to handle a terabyte per second.) What technologies enabled the invention of holographic video, and how far have they progressed in the 20 years since? What technological advances will be part of holographic video 20 years hence? How might visual entertainment and communication adapt to a (holographic) volume paradigm? (Or, how we will learn to "box" a shot -rather than "frame" it?) Light-modulation technologies, computational architectures, holographic algorithms, photonic processing, and spatial scene representations -all of these cutting-edge technologies play important roles. Included will be a glimpse of the new full-parallax, full-color holographic display prototype, developed by Zebra Imaging during the past 5 years with support from DARPA.

In this study, a new Hamiltonian loop construction algorithm is proposed for planar 3-regular diagrams of specific structures. Based on the original element theory and the perfect matching algorithm I proposed earlier, the algorithm establishes a deterministic Hamiltonian loop construction method by analyzing the local structural characteristics and global topological relationships of the graph. Theoretical analysis shows that for a specific structural plane 3-regular graph with a vertex number of 6k or 4i (k,i ≥ 1), the proposed algorithm can construct a Hamiltonian loop in linear time. The correctness of the algorithm is verified by rigorous mathematical proof, and its time complexity is significantly better than that of the Hamiltonian loop algorithm on the general graph. In addition, this study also reveals the intrinsic relationship between the Hamiltonian circuit, perfect matching, and graph coloring properties of this type of graph, which provides a new theoretical perspective for the study of the structural characteristics of specific graph classes. At the application level, the algorithm can be effectively applied to practical problems such as integrated circuit wiring optimization and network topology design. Experimental results show that compared with existing methods, the proposed algorithm has significant advantages in efficiency and scalability.

In this paper we study the problem of reconstructing orthogonal polyhedra from a putative vertex set, i.e., we are given a set of points and want to find an orthogonal polyhedron for which this is the set of vertices. We are especially interested in testing whether such a polyhedron is unique. Since this is not the case in general, we focus on orthogonally convex polyhedra, and give an O(n log n) algorithm to find the answer. We then consider the case where the given set of points may be rotated beforehand. For 2D, we prove uniqueness and provide an O(n log n) algorithm to obtain the answer, which can then be used for an O(n 2 log n) algorithm in 3D.

This paper presents an extension over a novel, three dimensional high frequency method for the calculation of the scattered electromagnetic (EM) field from a Perfect Electric Conductor (PEC) plate, which is based on the Physical Optics (PO) approximation and the Stationary Phase Method (SPM). This extension defines a new analytical method which is proved to be very efficient in computer execution time and enhances the accuracy of its predecessor around the area of the main scattering lobe. This new analytical method accomplishes high accuracy through the use of higher order approximation terms, which imply the use of Fresnel functions (SPM-F method). By using higher order Fresnel approximation terms, no impact on the time efficiency of the SPM method appears to

Sequencing technologies used to generate long strands of DNA are susceptible to laboratory errors that may result in several DNA nucleotides being deleted from the genome. Detecting such deletions in the protein coding regions is of utmost importance. Missing even a single nucleotide may lead to frame shifts with all the following codons (and consequently the encoded amino acids) being identified incorrectly. In addition to the deletion of nucleotides during sequencing, frame shifts can occur because of a variety of other reasons including mutations. In this paper, we present a fast computational technique to identify frame shifts in protein coding regions in DNA sequences. Our technique is based on Fourier spectral characteristics of coding regions in DNA sequences. We provide two applications of our technique -detecting deletions in DNA sequences in coding regions and also detecting frame shifts in viral DNA.

In this paper, we propose a new strategy for online placement algorithm on 2D partially reconfigurable devices, termed the Quad-Corner(QC). The main differences between our algorithm and related art are quad-corner spreading capability and dynamical searching sequences. Moreover, existing algorithms do not evaluate their algorithms with real hardware tasks; we do experimentations with real hardware tasks on a real FPGA. Our proposal achieves better placement quality and fast online placement compared to existing approaches. Experiments with real workloads (e.g. MDCT, matrix multiplication, hamming code, sorting, FIR, ADPCM, etc) on Virtex-4 show that the QC not only has 78 % less penalty and 93 % less wasted area than the existing algorithms on average but also has lower runtime overhead.

We develop a fast algorithm to calculate the entanglement of formation of a mixed state, which is defined as the minimum average entanglement of the pure states that form the mixed state. The algorithm combines conjugate gradient and steepest descent algorithms and outperforms both. Using this new algorithm, we obtain the statistics of the entanglement of formation on ensembles of random density matrices of higher dimensions than possible before. The correlation between the entanglement of formation and other quantities that are easier to compute, such as participation ratio and negativity are presented. Our results suggest a higher percentage of zero-entanglement states among zero-negativity states than previously reported.

En este trabajo se han propuesto y estudiado nuevas máscaras multifocales que permiten modular, en tiempo real, la intensidad relativa entre picos. Experimentalmente, utilizando un cristal líquido en fase nemática como modulador de fase, se han conseguido reproducido los resultados teóricos.

The discrete Hartley transform is generalized into four classes in the same way as the generalized discrete Fourier transform. Fast algorithms for the resulting transforms are de rived. The generalized transforms are expected to be useful in applications such as digital filter banks, fast computation of discrete Hartley transform for any composite number of data points, fast computations of convolution, and signal represen tation. The fast computation of skew-circular convolution by the generalized transforms is 4iscussed in detail.

Accuracy, speed and numerical stability are among the major factors restricting the use of Zernike moments (ZMs) in numerous commercial applications where they are a tool of significant utility. Often these factors are conflicting in nature. The direct formulation of ZMs is prone to numerical integration error while in the recent past many fast algorithms are developed for its computation. On the other hand, the relationship between geometric moments (GMs) and ZMs reduces numerical integration error but it is observed to be computation intensive. We propose fast algorithms for both the formulations. In the proposed method, the order of time complexity for GMs-to-ZMs formulation is reduced and further enhancement in speed is achieved by using quasi-symmetry property of GMs. The existing q-recursive method for direct formulation is further modified by incorporating the recursive steps for the computation of trigonometric functions. We also observe that q-recursive method provides numerical stability caused by finite precision arithmetic at high orders of moment which is hitherto not reported in the literature. Experimental results on images of different sizes support our claim.

Let S be a set of n > 2 points in the plane whose convex hull has perimeter t. Given a number P ≥ t, we study the following problem: Of all curves of perimeter P that enclose S, which is the curve that encloses the maximum area? In this paper, we give a complete characterization of this curve. We show that there are cases where this curve cannot be computed exactly and provide an O(n logn)-time algorithm to obtain an approximation of this curve, with arbitrary precision, having the same combinatorial structure.

We consider guarding classes of simple polygons using mobile guards (polygon edges and diagonals) under the constraint that no two guards may see each other. In contrast to most other art gallery problems, existence is the primary question: does a specific type of polygon admit some guard set? Types include simple polygons and the subclasses of orthogonal, monotone, and starshaped polygons. Additionally, guards may either exclude or include the endpoints (so-called open and closed guards). We provide a nearly complete set of answers to existence questions of open and closed edge, diagonal, and mobile guards in simple, orthogonal, monotone, and starshaped polygons, with some surprising results. For instance, every monotone or starshaped polygon can be guarded using hidden open mobile (edge or diagonal) guards, but not necessarily with hidden open edge or hidden open diagonal guards.

In this correspondence, an index permutation-based fast twodimensional discrete cosine transform (2-D DCT) algorithm is presented. It is shown that the N 2 N N 2 N N 2 N 2-D DCT, where N = 2 m N = 2 m N = 2 m , can be computed using only N N N 1-D DCT's and some post additions.

The central problem in the implementation of a Reed-Solomon code is finding the roots of the error locator polynomial. In 1967, Berlekamp et al. found an algorithm for finding the roots of an affine polynomial in GF(2 m ) that can be used to solve this problem. In this paper, it is shown that this Berlekamp-Rumsey-Solomon algorithm, together with the Chien-search method, makes possible a fast decoding algorithm in the standard-basis representation that is naturally suitable in a software implementation. Finally, simulation results for this fast algorithm are given.

In this work we discuss the development of fast algorithms for the inelastic Boltzmann equation describing the coUisional motion of a granular gas. In such systems the collisions between particles occur in an inelastic way and are characterized by a coefficient of restitution which in the general case depends on the relative velocity of the collision. In the quasi-elastic approximation the granular operator is replaced by the sum of an elastic Boltzmann operator and a nonlinear friction term. Fast numerical methods based on a suitable spectral representation of the approximated model are then presented.

Some of the fastest practical algorithms for IP route lookup are based on space-efficient encodings of multi-bit tries . Unfortunately, the time required by these algorithms grows in proportion to the address length, making them less attractive for IPv6. This paper describes and evaluates a new data structure called a shape-shifting trie, in which the data structure nodes correspond to arbitrarily shaped subtrees of the underlying binary trie for a given set of address prefixes. The ability to adapt the node shape to the trie reduces the number of nodes that must be accessed to perform a lookup, especially for tries with large sparse regions. We give a fast algorithm for optimally dividing a trie into nodes so as to minimize the maximum lookup depth. We show that seven data structure accesses are sufficient for route tables with more than 150,000 IPv6 prefixes. This makes it possible to achieve wire-speed processing for OC192 link using a single QDRII SRAM chip.

We present fast new algorithms for evaluating trees with respect to least squares and minimum evolution (ME), the most commonly used criteria for inferring phylogenetic trees from distance data. The new algorithms include an optimal O(N 2 ) time algorithm for calculating the edge (branch or internode) lengths on a tree according to ordinary or unweighted least squares (OLS); an O(N 3 ) time algorithm for edge lengths under weighted least squares (WLS) including the Fitch-Margoliash method; and an optimal O(N 4 ) time algorithm for generalized least-squares (GLS) edge lengths (where N is the number of taxa in the tree). The ME criterion is based on the sum of edge lengths. Consequently, the edge lengths algorithms presented here lead directly to O(N 2 ), O(N 3 ), and O(N 4 ) time algorithms for ME under OLS, WLS, and GLS, respectively. All of these algorithms are as fast as or faster than any of those previously published, and the algorithms for OLS and GLS are the fastest possible (with respect to order of computational complexity). A major advantage of our new methods is that they are as well adapted to multifurcating trees as they are to binary trees. An optimal algorithm for determining path lengths from a tree with given edge lengths is also developed. This leads to an optimal O(N 2 ) algorithm for OLS sums of squares evaluation and corresponding O(N 3 ) and O(N 4 ) time algorithms for WLS and GLS sums of squares, respectively. The GLS algorithm is time-optimal if the covariance matrix is already inverted. The speed of each algorithm is assessed analytically-the speed increases we calculate are confirmed by the dramatic speed increases resulting from their implementation in PAUP* 4.0. The new algorithms enable far more extensive tree searches and statistical evaluations (e.g., bootstrap, parametric bootstrap, or jackknife) in the same amount of time. Hopefully, the fast algorithms for WLS and GLS will encourage the use of these criteria for evaluating trees and their edge lengths (e.g., for approximate divergence time estimates), since they should be more statistically efficient than OLS.

This paper describes the purpose and recent summary of our research work which is a part of research project “Computational anatomy for computer-aided diagnosis and therapy: Frontiers of medical image sciences” that was funded by Grant-in-Aid for Scientific Research on Innovative Areas, MEXT, Japan. The main purpose of our research in this project focus on model construction of computational anatomy and model applications for analyzing and recognizing the anatomical structures of human torso region using high-resolution torso Xray CT images. A CT image database was constructed and a number of CT images were collected and will be used for training and testing of our model constructing approach. We believe our anatomical modes can reduce the complexity and increase the robustness of process flow for anatomical structure recognition and organ segmentation problems in CT images. Furthermore, such models also should be useful for computeraided diagnosis (CAD) systems by providing a quant...

This paper studies the application of preconditioned conjugate gradient methods in high resolution color image reconstruction problems. The high resolution color images are reconstructed from multiple undersampled, shifted, degraded color frames with subpixel displacements. The resulting degradation matrices are spatially variant. To capture the changes of re ectivity across color channels, the weighted H 1 regularization functional is used in the Tikhonov regularization. The Neumann boundary condition is also employed to reduce the boundary artifacts. The preconditioners are derived by taking the cosine transform approximation of the degradation matrices. We will show that the spectra of the preconditioned normal systems are clustered around 1 when the errors in the subpixel displacements are su ciently small. Numerical examples are given to illustrate the fast convergence of the preconditioned conjugate gradient method.

Partitions and representations 1 A2. Ferrers diagrams of partitions 2 A3. Addition on partitions 6 A4. Multiplication on partitions 6 A5. Dominance partial ordering 7 Chapter B. Generating Functions of Partitions Il BI. Basic generating functions of partitions B2. Classical partitions and the Gauss formula B3. Partitions into distinct parts and the Euler formula 19 B4. Partitions and the Gauss q-binomial coefficients B5. Partitions into distinct parts and finite q-differences Chapter C . Durfee Rectangles and Classical Partition Identities Cl. q-Series identities of Cauchy and Kummer: Unification C2. q-Binomial convolutions and the Jacobi triple product C3. The finite form of Euler's pentagon number theorem Chapter D. The Carlitz Inversions and Rogers-Ramanujan Identities DI. Combinatorial inversions and series transformations D2. Finite q-differences and further transformation D3. Rogers-Ramanujan identities and their finite forms Chapter E. Basic Hypergeometric Series El. Introduction and notation E2. The q-Gauss summation formula E3. Transformations of Heine and Jackson E4. The q-Pfaff-Saalschiitz summation theorem E5 . The terminating q-Dougall-Dixon formula E6. The Sears balanced transformations E7. Watson's q-Whipple transformation vii viii CHU Wenchang and DI CLAUDIO Leontina Chapter F. Bilateral Basic Hypergeornetric Series Fl. Definition and notation F2. Rarnanuj an's bilateral -series identity F3. Bailey's bilateral identity F4. Bilateral q-analogue of Dixon's theorern F5. Partial fraction decornposition rnethod Chapter G. The Lagrange Four Square Theorern G 1. Representations by two square surns G2. Representations by four square surns G3. Representations by six square surns G4. Representations by eight square surns G5. Jacobi's identity and q-difference equations Chapter H. Congruence Properties of Partition Function Hl. Proof of p(5n + 4) = O (rnod 5) H2. Generating function for p(5n + 4) H3. Proof of p(7n + 5) O (rnod 7) H4. Generating function for p(7n + 6) H5. Proof of p(l1n + 6) O (rnod 11

Extending the classical Legendre's result, we describe all solutions of the inequality |α -a/b| < c/b 2 in terms of convergents of continued fraction expansion of α. Namely, we show that a/b = (rpm+1 ± spm)/(rqm+1 ± sqm) for some nonnegative integers m, r, s such that rs < 2c. As an application of this result, we describe a modification of Verheul and van Tilborg variant of Wiener's attack on RSA cryptosystem with small secret exponent.

The Cascade Correlation [l] is a very flexible, efficient and fast algorithm for supervised learning. It incrementally builds the network by adding hidden units one at a time, until the desired input/output mapping is achieved. It connects all the previously installed units to the new unit being added. Consequently, each new unit in effect adds a new layer and the fan-in of the hidden and output units keeps on increasing as more units get added. The resulting structure could be hard to implement in VLSI, because the connections are irregular and the fan-in is unbounded. Moreover, the depth or the propagation delay through the resulting network is directly proportional to the number of units and can be excessive. We have modified the algorithm to generate networks with restricted fan-in and small depth (propagation delay) by controlling the connectivity. Our results reveal that there is a tradeoff between connectivity and other performance attributes like depth, total number of independent parameters, learning time, etc. When the number of inputs or outputs is small relative to the size of the training set, a higher connectivity usually leads to faster learning, and fewer independent parameters, but it also results in unbounded fan-in and depth. Strictly layered architectures with restricted connectivity, on the other hand, need more epochs to learn and use more parameters, but generate more regular structures, with smaller, limited fan-in and significantly smaller depth (propagation delay), and may be better suited for VLSI implementations. When the number of inputs or outputs is not very small compared to the size of the training set, however, a strictly layered topology is seen to yield an overall better performance.

The Cascade Correlation [l] is a very flexible, efficient and fast algorithm for supervised learning. It incrementally builds the network by adding hidden units one at a time, until the desired input/output mapping is achieved. It connects all the previously installed units to the new unit being added. Consequently, each new unit in effect adds a new layer and the fan-in of the hidden and output units keeps on increasing as more units get added. The resulting structure could be hard to implement in VLSI, because the connections are irregular and the fan-in is unbounded. Moreover, the depth or the propagation delay through the resulting network is directly proportional to the number of units and can be excessive. We have modified the algorithm to generate networks with restricted fan-in and small depth (propagation delay) by controlling the connectivity. Our results reveal that there is a tradeoff between connectivity and other performance attributes like depth, total number of independent parameters, learning time, etc. When the number of inputs or outputs is small relative to the size of the training set, a higher connectivity usually leads to faster learning, and fewer independent parameters, but it also results in unbounded fan-in and depth. Strictly layered architectures with restricted connectivity, on the other hand, need more epochs to learn and use more parameters, but generate more regular structures, with smaller, limited fan-in and significantly smaller depth (propagation delay), and may be better suited for VLSI implementations. When the number of inputs or outputs is not very small compared to the size of the training set, however, a strictly layered topology is seen to yield an overall better performance.

Collision detection is one of the most important tools that has been used widely in animation and simulation especially in computer games and medical simulation purpose. One of the critical issues in collision detection system is to actually prepared what kind of technique that is suitable for virtual environment to adapt collision detection system installed. Hence, this research paper described a detailed review on collision detection algorithm mainly in narrow phase collision detection phase.

We present a novel and fast algorithm to estimate penetration depth (PD) between two polyhedral models. Given two overlapping polyhedra, it computes the minimal translational distance to separate them using a combination of discretized computations and hierarchical refinement. The algorithm computes pairwise Minkowski sums of decomposed convex pieces, performs closest point query using rasterization hardware, and refines the estimated PD by incremental walking. It uses bounding volume hierarchies, model simplification, and culling algorithms to further accelerate the computation and refines the estimated PD in a hierarchical manner. We highlight its performance on complex models.

In many emerging applications, data streams are monitored in a network environment. Due to limited communication bandwidth and other resource constraints, a critical and practical demand is to online compress data streams continuously with quality guarantee. Although many data compression and digital signal processing methods have been developed to reduce data volume, their super-linear time and more-than-constant space complexity prevents them from being applied directly on data streams, particularly over resource-constrained sensor networks. In this paper, we tackle the problem of online quality guaranteed compression of data streams using fast linear approximation (i.e., using line segments to approximate a time series). Technically, we address two versions of the problem which explore quality guarantees in different forms. We develop online algorithms with linear time complexity and constant cost in space. Our algorithms are optimal in the sense they generate the minimum number of segments that approximate a time series with the required quality guarantee. To meet the resource constraints in sensor networks, we also develop a fast algorithm which creates connecting segments with very simple computation. The low cost nature of our methods leads to a unique edge on the applications of massive and fast streaming environment, low bandwidth networks, and heavily constrained nodes in computational power. We implement and evaluate our methods in the application of an acoustic wireless sensor network.

In this paper, we apply a newly developed method to solve boundary value problems for differential equations to solve optimal space guidance problems in a fast and accurate fashion. The method relies on the least-squares solution of differential equations via orthogonal polynomials expansion and constrained expression as derived via Theory of Connection (ToC). The application of the optimal control theory to derive the first order necessary conditions for optimality, yields a Two-Point Boundary Value Problem (TPBVP) that must be solved to find state and costate. Combining orthogonal polynomials expansion and ToC, we solve the TPBVP for a class of optimal guidance problems including energy-optimal landing on planetary bodies and fixed-time optimal intercept for a target-interceptor scenario. The performance analysis in terms of accuracy shows the potential of the proposed methodology as applied to optimal guidance problems.

In this paper, we show the optimality of a certain class of disturbance-affine control policies in the context of one-dimensional, constrained, multi-stage robust optimization. Our results cover the finite horizon case, with minimax (worst-case) objective, and convex state costs plus linear control costs. We develop a new proof methodology, which explores the relationship between the geometrical properties of the feasible set of solutions and the structure of the objective function. Apart from providing an elegant and conceptually simple proof technique, the approach also entails very fast algorithms for the case of piecewise affine state costs, which we explore in connection with a classical inventory management application.

Abstract: We discuss in this paper a method of finding skyline or non-dominated points in a set $ P $ of $ n_P $ points with respect to a set $ S $ of $ n_S $ sites. A point $ p_i\ in P $ is non-dominated if and only if for each $ p_j\ in P $, $ j\ not= i $, there exists at least one point $ s\ in S $ that is closer to $ p_i $ than $ p_j $. We reduce this problem of determining non-dominated points to the problem of finding sites that have non-empty cells in an additive Voronoi diagram with a convex distance function. The weights of the additive Voronoi ...

Non-Gaussian Lévy noises are present in many models for understanding underlining principles of physics, finance, biology and more. In this work, we consider the Fokker-Planck equation(FPE) due to one-dimensional asymmetric Lévy motion, which is a nonlocal partial differential equation. We present an accurate numerical quadrature for the singular integrals in the nonlocal FPE and develop a fast summation method to reduce the order of the complexity from O(J 2) to O(J log J) in one time-step, where J is the number of unknowns. We also provide conditions under which the numerical schemes satisfy maximum principle. Our numerical method is validated by comparing with exact solutions for special cases. We also discuss the properties of the probability density functions and the effects of various factors on the solutions, including the stability index, the skewness parameter, the drift term, the Gaussian and non-Gaussian noises and the domain size.

This paper addresses the problem of computing robust trajectories against uncertainties in the robot model. Based on the notion of closed-loop state sensitivity introduced in [1], [2] for identifying deviations of the closed-loop trajectories of any robot/controller pair against variations of uncertain parameters in the robot model, uncertainty tubes can be derived for bounded parameter variations [3]. Such tubes were integrated within a motion planner named SAMP [4] to produce robust global plans, emphasizing the generation of low sensitivity trajectories. However, a bottleneck of this method remains the very high computational cost of the uncertainty tubes. In this paper, we mitigate this problem by proposing a novel framework that first incorporates a Long Short-Term Memory [5] (LSTM) neural network (NN) to provide fast and accurate uncertainty tubes estimation, and then reduces tracking errors at given points on the trajectory. We validate our framework on a full 3D-quadrotor UAV model performing a 'ring-recovering' task requiring high accuracy. Our results show the computational gain of the LSTM-based robust planning and that the subsequent optimization stage significantly improves the accuracy of the trajectory execution.

Prototype design and testing is an indispensable stage of any project development in many fields of activity, such as aeronautical, spatial, automotive industries or architecture. Scientists and engineers rely on prototyping for a visual confirmation and validation of both their ideas and concepts. Using computers for designing digital prototypes is not a new idea since CAD applications are nowadays widely used. In this paper we present how new advances in 3D interaction and real time visualisation research domains lead to the development of a collaborative and really interactive system for virtual prototyping. This work is supported by the European Community through the ESPRIT programme 4. ! &quot;

We establish new functional relations for the dilogarithm involving two variables, which adhere the properties of Polylogarithm. We also considered several closely-related identities such as (for example) polylogarithm (also known as Jonqui`ere’s function), Euler dilogarithm function and Clausen’s function.

Universal designated verifier signatures (UDVS) were introduced in 2003 by Steinfeld et al. to allow signature holders to monitor the verification of a given signature in the sense that any plain signature can be publicly turned into a signature which is only verifiable by some specific designated verifier. Privacy issues, like non-dissemination of digital certificates, are the main motivations to study such primitives. In this paper, we propose two fairly efficient UDVS schemes which are secure (in terms of unforgeability and anonymity) in the standard model (i.e. without random oracles). Their security relies on algorithmic assumptions which are much more classical than assumptions involved in the two only known UDVS schemes in standard model to date. The latter schemes, put forth by Zhang et al. in 2005 and Vergnaud in 2006, rely on the Strong Diffie-Hellman assumption and the strange-looking knowledge of exponent assumption (KEA). Our schemes are obtained from Waters's signature and they do not need the KEA assumption. They are also the first random oracle-free constructions with the anonymity property.

This paper describes a fast algorithm for estimating formation permeability from Stoneley wave logs. The procedure uses a simplified Biot‐Rosenbaum model formulation. The input to the inversion is the Stoneley‐wave spectral amplitudes at each receiver position, the bore‐hole fluid properties (velocity and density), the borehole caliper log, the formation density and porosity (from log data), and the compressional and shear velocities for the interval of interest. The model uses the borehole caliper and elastic properties to compute the Stoneley wave excitation (that is, predicted amplitude without permeability effects) as a function of frequency, and the porosity and permeability to compute the fluid flow amplitude reduction. This method also uses a reference depth of known permeability and compares amplitude variations at other depths relative to the reference depth. The permeability value obtained from the inversion represents the best fit over all receivers and all relevant frequ...