Topology-based denoising of chaos

In this article, we propose a denoising algorithm to denoise a time series y(i) = x(i) + e(i), where {x(i)} is a time series obtained from a time- T map of a uniformly hyperbolic or Anosov flow, and {e(i)} a uniformly bounded sequence of independent and identically distributed (i.i.d.) random variables. Making use of observations up to time n, we create an estimate of x(i) for i<n. We show under typical limiting behaviours of the orbit and the recurrence properties of x(i), the estimation error converges to zero as n tends to infinity with probability 1.

Theory and Algorithms for Hop-Count-Based Localization with Random Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes in a region of Euclidean space. Following deployment, the nodes self-organize into a mesh topology with a key aspect being self-localization. Having obtained a mesh topology in a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this work, we analyze this approximation through two complementary analyses. We assume that the mesh topology is a random geometric graph on the nodes; and that some nodes are designated as anchors with known locations. First, we obtain high probability bounds on the Euclidean distances of all nodes that are h hops away from a fixed anchor node. In the second analysis, we provide a heuristic argument that leads to a direct approximation for the density function of the Euclidean distance between two nodes that are separated by a hop distance h. This approximation is shown, through simulation, to very closely match the true density function. Localization algorithms that draw upon the preceding analyses are then proposed and shown to perform better than some of the well-known algorithms present in the literature. Belief-propagation-based message-passing is then used to further enhance the performance of the proposed localization algorithms. To our knowledge, this is the first usage of message-passing for hop-count-based self-localization.

Orientational relaxation in a random dipolar lattice: Wave-number and frequency dependence

In order to understand the role of translational modes in the orientational relaxation in dense dipolar liquids, we have carried out a computer ''experiment'' where a random dipolar lattice was generated by quenching only the translational motion of the molecules of an equilibrated dipolar liquid. The lattice so generated was orientationally disordered and positionally random. The detailed study of orientational relaxation in this random dipolar lattice revealed interesting differences from those of the corresponding dipolar liquid. In particular, we found that the relaxation of the collective orientational correlation functions at the intermediate wave numbers was markedly slower at the long times for the random lattice than that of the liquid. This verified the important role of the translational modes in this regime, as predicted recently by the molecular theories. The single-particle orientational correlation functions of the random lattice also decayed significantly slowly at long times, compared to those of the dipolar liquid.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

A Global Constraint On Relative Rotation To Avoid Lumped Compliant Mechanisms In Topology Optimization

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint oil the following benchmark problems - displacement inverter and gripper.

A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background: A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data. Results: The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification. Conclusion: A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

Speeding up AdaBoost Classifier with Random Projection

The development of techniques for scaling up classifiers so that they can be applied to problems with large datasets of training examples is one of the objectives of data mining. Recently, AdaBoost has become popular among machine learning community thanks to its promising results across a variety of applications. However, training AdaBoost on large datasets is a major problem, especially when the dimensionality of the data is very high. This paper discusses the effect of high dimensionality on the training process of AdaBoost. Two preprocessing options to reduce dimensionality, namely the principal component analysis and random projection are briefly examined. Random projection subject to a probabilistic length preserving transformation is explored further as a computationally light preprocessing step. The experimental results obtained demonstrate the effectiveness of the proposed training process for handling high dimensional large datasets.

Topology-Guided Tessellation Of Quadratic Elements

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological representations of piecewise-linear functions may be applied directly to the piecewise-quadratic function. In particular, the tessellation is used for computing the Reeb graph, a topological data structure that provides a succinct representation of level sets of the function.

On The Topology Of Manifolds With Positive Isotropic Curvature

We show that a closed orientable Riemannian n-manifold, n >= 5, with positive isotropic curvature and free fundamental group is homeomorphic to the connected sum of copies of Sn-1 x S-1.

Generation of optimum random pinhole arrays for multiple imaging

Through an analysis using the transfer function of a pinhole camera, the multiple imaging characteristics of photographic diffusers described by Grover and Tremblay [Appl. Opt.21,4500(1982)] is studied. It is found that only one pinhole diameter satisfies the optimum imaging condition for best contrast transfer at any desired spatial frequency. A simple method of generating random pinhole arrays with a controlled pinhole diameter is described. These pinhole arrays are later used to generate high frequency sinusoidal gratings from a coarse grid. The contrast in the final gratings is found to be reasonably high.

A Nonlinear System Under Combined Periodic and Random Excitation

The anharmonic oscillator under combined sinusoidal and white noise excitation is studied using the Gaussian closure approximation. The mean response and the steady-state variance of the system is obtained by the WKBJ approximation and also by the Fokker Planck equation. The multiple steadystate solutions are obtained and their stability analysis is presented. Numerical results are obtained for a particular set of system parameters. The theoretical results are compared with a digital simulation study to bring out the usefulness of the present approximate theory.

Helix-coil stability constants for amino acids in nonaqueous solvents. Studies of random poly(-benzyl-L-glutamate-co-L-alanine) and poly(-benzyl-L-glutamate-co-L-leucine) in a mixed solvent

The host-guest technique has been applied to the determination of the helix-coil stability constants of two naturally occurring amino acids, L-alanine and L-leucine, in a nonaqueous solvent system. Random copolymers containing L-alanine and L-leucine, respectively, as guest residues and -benzyl-L-glutamate as the host residue were synthesized. The polymers were fractionated and characterized for their amino acid content, molecular weight, and helix-coil transition behavior in a dichloroacetic acid (DCA)-1,2-dichloroethane (DCE) mixture. Two types of helix-coil transitions were carried out on the copolymers: solvent-induced transitions in DCA-DCE mixtures at 25°C and thermally induced transitions in a 82:18 (wt %) DCA-DCE mixture. The thermally induced transitions were analyzed by statistical mechanical methods to determine the Zimm-Bragg parameters, and s, of the guest residues. The experimental data indicate that, in the nonaqueous solvent, the L-alanine residue stabilizes the -helical conformation more than the L-leucine residue does. This is in contrast to their behavior in aqueous solution, where the reverse is true. The implications of this finding for the analysis of helical structures in globular proteins are discussed.

Application of various viscosity theories to the viscosity data of methyl methacrylate-acrylonitrile random copolymersstar

Values of Ko, Flory constant related to unperturbed dimensions, are evaluated for methyl methacrylate-acrylonitrile random copolymers using Flory-Fox, Kurata-Stockmayer and Inagaki-Ptitsyn methods and compared with the Ko values obtained by Stockmayer-Fixman method. Ko values are seen to be less in solvents which have large a (Mark-Houwink exponent) values. A correlation between Ko and a is developed to arrive at a more reliable estimate of Ko for this copolymer system.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

Behaviour of methylmethacrylate-acrylonitrile random copolymers in dilute solution

Studies on the dilute solution properties of methylmethacrylate-acrylonitrile random copolymers of three different compositions, 0.236, 0.5 and 0.74 mole fraction (m.f.) of acrylonitrile (AN) designated as MAa, MAb and MAc, respectively, have been made in good solvents and theta solvents. MAa has been studied in benzene (Bz) and ethylacetate (EAc). MAb in acetonitrile (MeCN), dimethyl sulphoxide (DMSO) and a binary solvent mixture of Bz and dimentyl formamide (DMF) in the volume ratio 6.5:1 designated as BM1 and MAc in MeCN, DMSO and Bz + DMF in the volume ratio 1.667:1 designated as BM2. The Mark-Houwink exponent ‘a’ reveals that Bz is a theta solvent for MAa at 20°C. For MAb and MAc, BM1 and BM2, respectively have ‘a’ values of 0.5 at all three temperatures studied (30°, 40° and 50°C). It is not clear whether they represent theta states or preferential adsorption plays a role complicating the behaviour in solution. The values of A2 are very low in MeCN considering that it is a very good solvent for the copolymer, ‘a’ values for MAb and MAc being 0.75 and 0.7, respectively.