A study of symbolic processing and computational aspects in helicopter dynamics

Even research models of helicopter dynamics often lead to a large number of equations of motion with periodic coefficients; and Floquet theory is a widely used mathematical tool for dynamic analysis. Presently, three approaches are used in generating the equations of motion. These are (1) general-purpose symbolic processors such as REDUCE and MACSYMA, (2) a special-purpose symbolic processor, DEHIM (Dynamic Equations for Helicopter Interpretive Models), and (3) completely numerical approaches. In this paper, comparative aspects of the first two purely algebraic approaches are studied by applying REDUCE and DEHIM to the same set of problems. These problems range from a linear model with one degree of freedom to a mildly non-linear multi-bladed rotor model with several degrees of freedom. Further, computational issues in applying Floquet theory are also studied, which refer to (1) the equilibrium solution for periodic forced response together with the transition matrix for perturbations about that response and (2) a small number of eigenvalues and eigenvectors of the unsymmetric transition matrix. The study showed the following: (1) compared to REDUCE, DEHIM is far more portable and economical, but it is also less user-friendly, particularly during learning phases; (2) the problems of finding the periodic response and eigenvalues are well conditioned.

Music and symbolic dynamics: the science behind an art

Music signals comprise of atomic notes drawn from a musical scale. The creation of musical sequences often involves splicing the notes in a constrained way resulting in aesthetically appealing patterns. We develop an approach for music signal representation based on symbolic dynamics by translating the lexicographic rules over a musical scale to constraints on a Markov chain. This source representation is useful for machine based music synthesis, in a way, similar to a musician producing original music. In order to mathematically quantify user listening experience, we study the correlation between the max-entropic rate of a musical scale and the subjective aesthetic component. We present our analysis with examples from the south Indian classical music system.

X-ray studies on crystalline complexes involving amino acids. IV. The structure of L-arginine L-ascorbate

L-Arginine ascorbate, C6HIsN40+.C6H706, a 1"1 crystalline complex between the amino acid arginineand the vitamin ascorbic acid, crystallizes in the monoclinic space group P21 with two formula units in a cell of dimensions a = 5.060 (8), b = 9.977 (9), c = 15.330 (13) A, fl = 97.5 (2) °. The structure was solved by the symbolic addition procedure and refined to an R of 0.067 for 1501 photographically observed reflec- tions. The conformation of the arginine molecule in the structure is different from any observed so far. The present structure provides the first description of the ascorbate anion unaffected by the geometrical constraints and disturbances imposed by the requirements of metal coordination. The lactone group and the deprotonated enediol group in the anion are planar and the side chain assumes a conformation which appears to be sterically the most favourable. In the crystals, the arginine molecules and the ascorbate anions aggregate separately into alternating layers. The molecules in the arginine layer are held together by interactions involving a-amino and ~t-carboxylate groups, a situation analogous to that found in proteins. The two layers of unlike molecules are interconnected primarily through the interactions of the side-chain guanidyl group of arginine with the ascorbate ion. These involve a specific ion-pair interaction accompanied by two convergent hydrogen bonds and another pair of nearly parallel hydrogen bonds.

Structural studies of analgesics and their interactions. II. The crystal structure of a 1:1 complex between antipyrine and salicyclic acid (salipyrine)

The complex crystallizes in the space group P21/c with four formula units in a unit cell of dimensions a= 12.747, b= 7.416, c= 17.894 A and/3= 90.2 °. The structure has been solved by the symbolic addition procedure using three-dimensional photographic data and refined to an R value of 0.079 for 2019 observed reflexions. The pyramidal nature of the two hetero nitrogen atoms in the antipyrine molecule is inter:nediate between that observed in free antipyrine and in some of its metal complexes. The molecule is more polar than that in crystals of free antipyrine but less so compared with that in metal complexes. In the salicylic acid molecule, the hydroxyl group forms an internal hydrogen bond with one of the oxygen atoms in the carboxyl group. The association between the salicylic acid and the antipyrine molecules is achieved through an intermolecular hydrogen bond with the other carboxyl oxygen atom in the salicylic acid molecule as the proton donor and the carboxyl oxygen atom of the antipyrine molecule as the acceptor.

Inferring neuronal network connectivity from spike data: A temporal data mining approach

Understanding the functioning of a neural system in terms of its underlying circuitry is an important problem in neuroscience. Recent d evelopments in electrophysiology and imaging allow one to simultaneously record activities of hundreds of neurons. Inferring the underlying neuronal connectivity patterns from such multi-neuronal spike train data streams is a challenging statistical and computational problem. This task involves finding significant temporal patterns from vast amounts of symbolic time series data. In this paper we show that the frequent episode mining methods from the field of temporal data mining can be very useful in this context. In the frequent episode discovery framework, the data is viewed as a sequence of events, each of which is characterized by an event type and its time of occurrence and episodes are certain types of temporal patterns in such data. Here we show that, using the set of discovered frequent episodes from multi-neuronal data, one can infer different types of connectivity patterns in the neural system that generated it. For this purpose, we introduce the notion of mining for frequent episodes under certain temporal constraints; the structure of these temporal constraints is motivated by the application. We present algorithms for discovering serial and parallel episodes under these temporal constraints. Through extensive simulation studies we demonstrate that these methods are useful for unearthing patterns of neuronal network connectivity.

A constraint Jacobian based approach for static analysis of pantograph masts

This paper presents a constraint Jacobian matrix based approach to obtain the stiffness matrix of widely used deployable pantograph masts with scissor-like elements (SLE). The stiffness matrix is obtained in symbolic form and the results obtained agree with those obtained with the force and displacement methods available in literature. Additional advantages of this approach are that the mobility of a mast can be evaluated, redundant links and joints in the mast can be identified and practical masts with revolute joints can be analysed. Simulations for a hexagonal mast and an assembly with four hexagonal masts is presented as illustrations.

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The beam mode

Using asymptotics, the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell vibrating in the beam mode (viz. circumferential wave order n = 1) are studied. Initially, the uncoupled wavenumbers of the acoustic fluid and the cylindrical shell structure are discussed. Simple closed form expressions for the structural wavenumbers (longitudinal, torsional and bending) are derived using asymptotic methods for low- and high-frequencies. It is found that at low frequencies the cylinder in the beam mode behaves like a Timoshenko beam. Next, the coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter mu due to the coupling. An asymptotic expansion involving mu is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (as modifications to the uncoupled wavenumbers) separately for low- and high-frequency ranges and further, within each frequency range, for large and small values of mu. Only the flexural wavenumber, the first rigid duct acoustic cut-on wavenumber and the first pressure-release acoustic cut-on wavenumber are considered. The general trend found is that for small mu, the coupled wavenumbers are close to the in vacuo structural wavenumber and the wavenumbers of the rigid-acoustic duct. With increasing mu, the perturbations increase, until the coupled wavenumbers are better identified as perturbations to the pressure-release wavenumbers. The systematic derivation for the separate cases of small and large mu gives more insight into the physics and helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. This method of asymptotics is simple to implement using a symbolic computation package (like Maple). (C) 2008 Elsevier Ltd. All rights reserved.

Structural Studies Of Analgesics And Their Interactions .1. Crystal And Molecular-Structure Of Antipyrine

The complex crystallizes in the space group P21/c with four formula units in a unit cell of dimensionsa= 12.747, b= 7.416, c= 17.894 A and/3= 90.2 °. The structure has been solved by the symbolic addition procedure using three dimensional photographic data and refined to an R value of 0.079 for 2019 observed reflexions. The pyramidal nature of the two hetero nitrogen atoms in the antipyrine molecule is inter:nediate between that observed in free antipyrine and in some of its metal complexes. The molecule is more polar than that in crystals of free antipyrine but less so compared with that in metal complexes. In the salicylic acid molecule, the hydroxyl group forms an internal hydrogen bond with one of the oxygen atoms in the carboxyl group. The association between the salicylic acid and the antipyrine molecules is achieved through an intermolecular hydrogen bond with the other carboxyl oxygen atom in the salicylic acid molecule as the proton donor and the carboxyl oxygen atom of the antipyrine molecule as the acceptor

Kinematics of pantograph masts

This paper deals with the kinematics of pantograph masts. Pantograph masts have widespread use in space application as deployable structures. They are over constrained mechanisms with degree-of-freedom, evaluated by the Grübler–Kutzback formula, as less than one. In this paper, a numerical algorithm is used to evaluate the degree-of-freedom of pantograph masts by obtaining the null space of a constraint Jacobian matrix. In the process redundant joints in the masts are obtained. A method based on symbolic computation, to obtain the closed-form kinematics equations of triangular and box shaped pantograph masts, is presented. In the process, the various configurations such masts can attain during deployment, are obtained. The closed-form solution also helps in identifying the redundant joints in the masts. The symbolic computations involving the Jacobian matrix also leads to a method to evaluate the global degree-of-freedom for these masts.

Variable Elimination in Linear Constraints

Gauss and Fourier have together provided us with the essential techniques for symbolic computation with linear arithmetic constraints over the reals and the rationals. These variable elimination techniques for linear constraints have particular significance in the context of constraint logic programming languages that have been developed in recent years. Variable elimination in linear equations (Guassian Elimination) is a fundamental technique in computational linear algebra and is therefore quite familiar to most of us. Elimination in linear inequalities (Fourier Elimination), on the other hand, is intimately related to polyhedral theory and aspects of linear programming that are not quite as familiar. In addition, the high complexity of elimination in inequalities has forces the consideration of intricate specializations of Fourier's original method. The intent of this survey article is to acquaint the reader with these connections and developments. The latter part of the article dwells on the thesis that variable elimination in linear constraints over the reals extends quite naturally to constraints in certain discrete domains.

A Flat Concurrent Prolog compiler for PARAM

We describe a compiler for the Flat Concurrent Prolog language on a message passing multiprocessor architecture. This compiler permits symbolic and declarative programming in the syntax of Guarded Horn Rules, The implementation has been verified and tested on the 64-node PARAM parallel computer developed by C-DAC (Centre for the Development of Advanced Computing, India), Flat Concurrent Prolog (FCP) is a logic programming language designed for concurrent programming and parallel execution, It is a process oriented language, which embodies dataflow synchronization and guarded-command as its basic control mechanisms. An identical algorithm is executed on every processor in the network, We assume regular network topologies like mesh, ring, etc, Each node has a local memory, The algorithm comprises of two important parts: reduction and communication, The most difficult task is to integrate the solutions of problems that arise in the implementation in a coherent and efficient manner. We have tested the efficacy of the compiler on various benchmark problems of the ICOT project that have been reported in the recent book by Evan Tick, These problems include Quicksort, 8-queens, and Prime Number Generation, The results of the preliminary tests are favourable, We are currently examining issues like indexing and load balancing to further optimize our compiler.

Knowledge-based clustering

In the knowledge-based clustering approaches reported in the literature, explicit know ledge, typically in the form of a set of concepts, is used in computing similarity or conceptual cohesiveness between objects and in grouping them. We propose a knowledge-based clustering approach in which the domain knowledge is also used in the pattern representation phase of clustering. We argue that such a knowledge-based pattern representation scheme reduces the complexity of similarity computation and grouping phases. We present a knowledge-based clustering algorithm for grouping hooks in a library.

A computational procedure to generate difference equations from differential equations

In this paper we have developed methods to compute maps from differential equations. We take two examples. First is the case of the harmonic oscillator and the second is the case of Duffing's equation. First we convert these equations to a canonical form. This is slightly nontrivial for the Duffing's equation. Then we show a method to extend these differential equations. In the second case, symbolic algebra needs to be used. Once the extensions are accomplished, various maps are generated. The Poincare sections are seen as a special case of such generated maps. Other applications are also discussed.

Temporal Logics of Repeating Values

Various logical formalisms with the freeze quantifier have been recently considered to model computer systems even though this is a powerful mechanism that often leads to undecidability. In this article, we study a linear-time temporal logic with past-time operators such that the freeze operator is only used to express that some value from an infinite set is repeated in the future or in the past. Such a restriction has been inspired by a recent work on spatio-temporal logics that suggests such a restricted use of the freeze operator. We show decidability of finitary and infinitary satisfiability by reduction into the verification of temporal properties in Petri nets by proposing a symbolic representation of models. This is a quite surprising result in view of the expressive power of the logic since the logic is closed under negation, contains future-time and past-time temporal operators and can express the nonce property and its negation. These ingredients are known to lead to undecidability with a more liberal use of the freeze quantifier. The article also contains developments about the relationships between temporal logics with the freeze operator and counter automata as well as reductions into first-order logics over data words.

Border basis detection is NP-complete

Border basis detection (BBD) is described as follows: given a set of generators of an ideal, decide whether that set of generators is a border basis of the ideal with respect to some order ideal. The motivation for this problem comes from a similar problem related to Grobner bases termed as Grobner basis detection (GBD) which was proposed by Gritzmann and Sturmfels (1993). GBD was shown to be NP-hard by Sturmfels and Wiegelmann (1996). In this paper, we investigate the computational complexity of BBD and show that it is NP-complete.