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.

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.

Protein sequence design on the basis of topology optimization techniques -Using continuous modeling of discrete amino acid types

The notion of optimization is inherent in protein design. A long linear chain of twenty types of amino acid residues are known to fold to a 3-D conformation that minimizes the combined inter-residue energy interactions. There are two distinct protein design problems, viz. predicting the folded structure from a given sequence of amino acid monomers (folding problem) and determining a sequence for a given folded structure (inverse folding problem). These two problems have much similarity to engineering structural analysis and structural optimization problems respectively. In the folding problem, a protein chain with a given sequence folds to a conformation, called a native state, which has a unique global minimum energy value when compared to all other unfolded conformations. This involves a search in the conformation space. This is somewhat akin to the principle of minimum potential energy that determines the deformed static equilibrium configuration of an elastic structure of given topology, shape, and size that is subjected to certain boundary conditions. In the inverse-folding problem, one has to design a sequence with some objectives (having a specific feature of the folded structure, docking with another protein, etc.) and constraints (sequence being fixed in some portion, a particular composition of amino acid types, etc.) while obtaining a sequence that would fold to the desired conformation satisfying the criteria of folding. This requires a search in the sequence space. This is similar to structural optimization in the design-variable space wherein a certain feature of structural response is optimized subject to some constraints while satisfying the governing static or dynamic equilibrium equations. Based on this similarity, in this work we apply the topology optimization methods to protein design, discuss modeling issues and present some initial results.

Topology Optimization of Micromachined Structures with Surface Micromachining Manufacturing Constraints

Topology optimization methods have been shown to have extensive application in the design of microsystems. However, their utility in practical situations is restricted to predominantly planar configurations due to the limitations of most microfabrication techniques in realizing structures with arbitrary topologies in the direction perpendicular to the substrate. This study addresses the problem of synthesizing optimal topologies in the out-of-plane direction while obeying the constraints imposed by surface micromachining. A new formulation that achieves this by defining a design space that implicitly obeys the manufacturing constraints with a continuous design parameterization is presented in this paper. This is in contrast to including manufacturing cost in the objective function or constraints. The resulting solutions of the new formulation obtained with gradient-based optimization directly provide the photolithographic mask layouts. Two examples that illustrate the approach for the case of stiff structures are included.

Comparison Of If Estimation Methods For Noise Robustness

Non-stationary signal modeling is a well addressed problem in the literature. Many methods have been proposed to model non-stationary signals such as time varying linear prediction and AM-FM modeling, the later being more popular. Estimation techniques to determine the AM-FM components of narrow-band signal, such as Hilbert transform, DESA1, DESA2, auditory processing approach, ZC approach, etc., are prevalent but their robustness to noise is not clearly addressed in the literature. This is critical for most practical applications, such as in communications. We explore the robustness of different AM-FM estimators in the presence of white Gaussian noise. Also, we have proposed three new methods for IF estimation based on non-uniform samples of the signal and multi-resolution analysis. Experimental results show that ZC based methods give better results than the popular methods such as DESA in clean condition as well as noisy condition.

A comparative study of speaker adaptation methods

For the problem of speaker adaptation in speech recognition, the performance depends on the availability of adaptation data. In this paper, we have compared several existing speaker adaptation methods, viz. maximum likelihood linear regression (MLLR), eigenvoice (EV), eigenspace-based MLLR (EMLLR), segmental eigenvoice (SEV) and hierarchical eigenvoice (HEV) based methods. We also develop a new method by modifying the existing HEV method for achieving further performance improvement in a limited available data scenario. In the sense of availability of adaptation data, the new modified HEV (MHEV) method is shown to perform better than all the existing methods throughout the range of operation except the case of MLLR at the availability of more adaptation data.

Edge-based connected component approach for skew correction of complex document images

Skew correction of complex document images is a difficult task. We propose an edge-based connected component approach for robust skew correction of documents with complex layout and content. The algorithm essentially consists of two steps - an 'initialization' step to determine the image orientation from the centroids of the connected components and a 'search' step to find the actual skew of the image. During initialization, we choose two different sets of points regularly spaced across the the image, one from the left to right and the other from top to bottom. The image orientation is determined from the slope between the two succesive nearest neighbors of each of the points in the chosen set. The search step finds succesive nearest neighbors that satisfy the parameters obtained in the initialization step. The final skew is determined from the slopes obtained in the 'search' step. Unlike other connected component based methods, the proposed method does not require any binarization step that generally precedes connected component analysis. The method works well for scanned documents with complex layout of any skew with a precision of 0.5 degrees.

A model based factorization approach for dense 3D recovery from monocular video

Feature track matrix factorization based methods have been attractive solutions to the Structure-front-motion (Sfnl) problem. Group motion of the feature points is analyzed to get the 3D information. It is well known that the factorization formulations give rise to rank deficient system of equations. Even when enough constraints exist, the extracted models are sparse due the unavailability of pixel level tracks. Pixel level tracking of 3D surfaces is a difficult problem, particularly when the surface has very little texture as in a human face. Only sparsely located feature points can be tracked and tracking error arc inevitable along rotating lose texture surfaces. However, the 3D models of an object class lie in a subspace of the set of all possible 3D models. We propose a novel solution to the Structure-from-motion problem which utilizes the high-resolution 3D obtained from range scanner to compute a basis for this desired subspace. Adding subspace constraints during factorization also facilitates removal of tracking noise which causes distortions outside the subspace. We demonstrate the effectiveness of our formulation by extracting dense 3D structure of a human face and comparing it with a well known Structure-front-motion algorithm due to Brand.

Suitability of a point-contact SAW-based stiffness transducer for biomedical applications

Methods of diagnosis in Biomedical applications can be broadly divided into contact and non-contact based methods. So far, ultrasound based methods have been found to be most favorable for non-contact, non-invasive diagnosis, especially in the case of tissue stiffness analysis. We report here, the fabrication and characterization details of a new contact based transducer system for qualitative determination of the stiffnesses of non-piezoelectric substrates using the phenomenon of Surface Acoustic Waves (SAW). Preliminary trials to study the functionality of this system were carried out on various metallic and non-metallic substrates, and the results were found to be satisfactory. To confirm the suitability of this system for biomedical applications, similar trials have been conducted on tissue mimicking phantoms with varying degrees of stiffness.

Site characterization model using least-square support vector machine and relevance vector machine based on corrected SPT data (N-c)

Statistical learning algorithms provide a viable framework for geotechnical engineering modeling. This paper describes two statistical learning algorithms applied for site characterization modeling based on standard penetration test (SPT) data. More than 2700 field SPT values (N) have been collected from 766 boreholes spread over an area of 220 sqkm area in Bangalore. To get N corrected value (N,), N values have been corrected (Ne) for different parameters such as overburden stress, size of borehole, type of sampler, length of connecting rod, etc. In three-dimensional site characterization model, the function N-c=N-c (X, Y, Z), where X, Y and Z are the coordinates of a point corresponding to N, value, is to be approximated in which N, value at any half-space point in Bangalore can be determined. The first algorithm uses least-square support vector machine (LSSVM), which is related to aridge regression type of support vector machine. The second algorithm uses relevance vector machine (RVM), which combines the strengths of kernel-based methods and Bayesian theory to establish the relationships between a set of input vectors and a desired output. The paper also presents the comparative study between the developed LSSVM and RVM model for site characterization. Copyright (C) 2009 John Wiley & Sons,Ltd.

Accelerated gradient based diffuse optical tomographic image reconstruction

Purpose: Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). Methods: DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Results: Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. Conclusions: We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data. (C) 2011 American Association of Physicists in Medicine. DOI: 10.1118/1.3531572]

Coupled electrostatic-elastic analysis for topology optimization using material interpolation

In this paper, we present a novel analytical formulation for the coupled partial differential equations governing electrostatically actuated constrained elastic structures of inhomogeneous material composition. We also present a computationally efficient numerical framework for solving the coupled equations over a reference domain with a fixed finite-element mesh. This serves two purposes: (i) a series of problems with varying geometries and piece-wise homogeneous and/or inhomogeneous material distribution can be solved with a single pre-processing step, (ii) topology optimization methods can be easily implemented by interpolating the material at each point in the reference domain from a void to a dielectric or a conductor. This is attained by considering the steady-state electrical current conduction equation with a `leaky capacitor' model instead of the usual electrostatic equation. This formulation is amenable for both static and transient problems in the elastic domain coupled with the quasi-electrostatic electric field. The procedure is numerically implemented on the COMSOL Multiphysics (R) platform using the weak variational form of the governing equations. Examples have been presented to show the accuracy and versatility of the scheme. The accuracy of the scheme is validated for the special case of piece-wise homogeneous material in the limit of the leaky-capacitor model approaching the ideal case.

Finite data performance of MUSIC and minimum norm methods

In the direction of arrival (DOA) estimation problem, we encounter both finite data and insufficient knowledge of array characterization. It is therefore important to study how subspace-based methods perform in such conditions. We analyze the finite data performance of the multiple signal classification (MUSIC) and minimum norm (min. norm) methods in the presence of sensor gain and phase errors, and derive expressions for the mean square error (MSE) in the DOA estimates. These expressions are first derived assuming an arbitrary array and then simplified for the special case of an uniform linear array with isotropic sensors. When they are further simplified for the case of finite data only and sensor errors only, they reduce to the recent results given in [9-12]. Computer simulations are used to verify the closeness between the predicted and simulated values of the MSE.

Partial instantiation methods for inference in first-order logic

Satisfiability algorithms for propositional logic have improved enormously in recently years. This improvement increases the attractiveness of satisfiability methods for first-order logic that reduce the problem to a series of ground-level satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolution-based methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (1) extending it to logic with functions, (2) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (3) simplifying it to obtain further speedup. We provide a similar development for a "dual" partial instantiation approach defined by Hooker and suggest a primal-dual strategy. We prove correctness of the primal and dual algorithms for full first-order logic with functions, as well as termination on unsatisfiable formulas. We also report some preliminary computational results.

Subspace Based Speech Enhancement Using Gaussian Mixture Model

Traditional subspace based speech enhancement (SSE)methods use linear minimum mean square error (LMMSE) estimation that is optimal if the Karhunen Loeve transform (KLT) coefficients of speech and noise are Gaussian distributed. In this paper, we investigate the use of Gaussian mixture (GM) density for modeling the non-Gaussian statistics of the clean speech KLT coefficients. Using Gaussian mixture model (GMM), the optimum minimum mean square error (MMSE) estimator is found to be nonlinear and the traditional LMMSE estimator is shown to be a special case. Experimental results show that the proposed method provides better enhancement performance than the traditional subspace based methods.Index Terms: Subspace based speech enhancement, Gaussian mixture density, MMSE estimation.