GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

Soft-spring wall based non-periodic boundary conditions for non-equilibrium molecular dynamics of dense fluids

Non-equilibrium molecular dynamics (MD) simulations require imposition of non-periodic boundary conditions (NPBCs) that seamlessly account for the effect of the truncated bulk region on the simulated MD region. Standard implementation of specular boundary conditions in such simulations results in spurious density and force fluctuations near the domain boundary and is therefore inappropriate for coupled atomistic-continuum calculations. In this work, we present a novel NPBC model that relies on boundary atoms attached to a simple cubic lattice with soft springs to account for interactions from particles which would have been present in an untruncated full domain treatment. We show that the proposed model suppresses the unphysical fluctuations in the density to less than 1% of the mean while simultaneously eliminating spurious oscillations in both mean and boundary forces. The model allows for an effective coupling of atomistic and continuum solvers as demonstrated through multiscale simulation of boundary driven singular flow in a cavity. The geometric flexibility of the model enables straightforward extension to nonplanar complex domains without any adverse effects on dynamic properties such as the diffusion coefficient. (c) 2015 AIP Publishing LLC.

A Family of Domains Associated with mu-Synthesis

We introduce a family of domains-which we call the -quotients-associated with an aspect of -synthesis. We show that the natural association that the symmetrized polydisc has with the corresponding spectral unit ball is also exhibited by the -quotient and its associated unit `` -ball''. Here, is the structured singular value for the case Specifically: we show that, for such an E, the Nevanlinna-Pick interpolation problem with matricial data in a unit `` -ball'', and in general position in a precise sense, is equivalent to a Nevanlinna-Pick interpolation problem for the associated -quotient. Along the way, we present some characterizations for the -quotients.

Exploring Viral Phenomenon as an Innovative Trajectory

The viral phenomenon has garnered a great deal of attention in the recent years. Although evidence of viral success exists the underlying factors leading to the phenomenon and its measurement still remains a grey area which needs to be explored. The viral phenomenon for a product or information and its distinction based on growth curve trajectory has not been rigorously explored in the previous works. This paper aims to understand the viral phenomenon that makes products or information go viral. The viral phenomenon trajectories that distinguish the viral from a non-viral phenomenon are demonstrated. The curve fitting methodology for viral phenomenon is adopted which has not been looked into in the previous works. TED talks are analyzed to understand the diffusion pattern, essentially one or more spike, within a time period. Insights drawn indicate the characteristic viral growth trajectories and its implication on innovation.

Lower bounds on Ricci flow invariant curvatures and geometric applications

We consider Ricci flow invariant cones C in the space of curvature operators lying between the cones ``nonnegative Ricci curvature'' and ``nonnegative curvature operator''. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies R + epsilon I is an element of C at the initial time, then it satisfies R + epsilon I is an element of C on some time interval depending only on the scalar curvature control. This allows us to link Gromov-Hausdorff convergence and Ricci flow convergence when the limit is smooth and R + I is an element of C along the sequence of initial conditions. Another application is a stability result for manifolds whose curvature operator is almost in C. Finally, we study the case where C is contained in the cone of operators whose sectional curvature is nonnegative. This allows us to weaken the assumptions of the previously mentioned applications. In particular, we construct a Ricci flow for a class of (not too) singular Alexandrov spaces.

Dissecting Ubiquitin Folding Using the Self-Organized Polymer Model

Folding of Ubiquitin (Ub), a functionally important protein found in eukaryotic organisms, is investigated at low and neutral pH at different temperatures using simulations of the coarse-grained self-organized-polymer model with side chains (SOP-SC). The melting temperatures (T-m's), identified with the peaks in the heat capacity curves, decrease as pH decreases, in qualitative agreement with experiments. The calculated radius of gyration, showing dramatic variations with pH, is in excellent agreement with scattering experiments. At T-m Ub folds in a two-state manner at low and neutral pH. Clustering analysis of the conformations sampled in equilibrium folding trajectories at T-m with multiple transitions between the folded and unfolded states, shows a network of metastable states connecting the native and unfolded states. At low and neutral pH, Ub folds with high probability through a preferred set of conformations resulting in a pH-dependent dominant folding pathway. Folding kinetics reveal that Ub assembly at low pH occurs by multiple pathways involving a combination of nucleation-collapse and diffusion collision mechanism. The mechanism by which Ub folds is dictated by the stability of the key secondary structural elements responsible for establishing long-range contacts and collapse of Ub. Nucleation collapse mechanism holds if the stability of these elements are marginal, as would be the case at elevated temperatures. If the lifetimes associated with these structured microdomains are on the order of hundreds of microseconds, then Ub folding follows the diffusion collision mechanism with intermediates, many of which coincide with those found in equilibrium. Folding at neutral pH is a sequential process with a populated intermediate resembling that sampled at equilibrium. The transition state structures, obtained using a P-fold analysis, are homogeneous and globular with most of the secondary and tertiary structures being native-like. Many of our findings for both the thermodynamics and kinetics of folding are not only in agreement with experiments but also provide missing details not resolvable in standard experiments. The key prediction that folding mechanism varies dramatically with pH is amenable to experimental tests.

Multiple Spectral Peak Tracking for Heart Rate Monitoring from Photoplethysmography Signal During Intensive Physical Exercise

We propose a multiple initialization based spectral peak tracking (MISPT) technique for heart rate monitoring from photoplethysmography (PPG) signal. MISPT is applied on the PPG signal after removing the motion artifact using an adaptive noise cancellation filter. MISPT yields several estimates of the heart rate trajectory from the spectrogram of the denoised PPG signal which are finally combined using a novel measure called trajectory strength. Multiple initializations help in correcting erroneous heart rate trajectories unlike the typical SPT which uses only single initialization. Experiments on the PPG data from 12 subjects recorded during intensive physical exercise show that the MISPT based heart rate monitoring indeed yields a better heart rate estimate compared to the SPT with single initialization. On the 12 datasets MISPT results in an average absolute error of 1.11 BPM which is lower than 1.28 BPM obtained by the state-of-the-art online heart rate monitoring algorithm.

Power Allocation in MIMO Wiretap Channel with Statistical CSI and Finite-Alphabet Input

In this paper, we consider the problem of power allocation in MIMO wiretap channel for secrecy in the presence of multiple eavesdroppers. Perfect knowledge of the destination channel state information (CSI) and only the statistical knowledge of the eavesdroppers CSI are assumed. We first consider the MIMO wiretap channel with Gaussian input. Using Jensen's inequality, we transform the secrecy rate max-min optimization problem to a single maximization problem. We use generalized singular value decomposition and transform the problem to a concave maximization problem which maximizes the sum secrecy rate of scalar wiretap channels subject to linear constraints on the transmit covariance matrix. We then consider the MIMO wiretap channel with finite-alphabet input. We show that the transmit covariance matrix obtained for the case of Gaussian input, when used in the MIMO wiretap channel with finite-alphabet input, can lead to zero secrecy rate at high transmit powers. We then propose a power allocation scheme with an additional power constraint which alleviates this secrecy rate loss problem, and gives non-zero secrecy rates at high transmit powers.

Isolated singularities of polyharmonic operator in even dimension

We consider the equation Delta(2)u = g(x, u) >= 0 in the sense of distribution in Omega' = Omega\textbackslash {0} where u and -Delta u >= 0. Then it is known that u solves Delta(2)u = g(x, u) + alpha delta(0) - beta Delta delta(0), for some nonnegative constants alpha and beta. In this paper, we study the existence of singular solutions to Delta(2)u = a(x) f (u) + alpha delta(0) - beta Delta delta(0) in a domain Omega subset of R-4, a is a nonnegative measurable function in some Lebesgue space. If Delta(2)u = a(x) f (u) in Omega', then we find the growth of the nonlinearity f that determines alpha and beta to be 0. In case when alpha = beta = 0, we will establish regularity results when f (t) <= Ce-gamma t, for some C, gamma > 0. This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (N >= 5) with a specific weight function a(x) = |x|(sigma). Later, we discuss its analogous generalization for the polyharmonic operator.

Kinematics and dynamics of Jansen leg mechanism: A bond graph approach

The Jansen mechanism is a one degree-of-freedom, planar, 12-link, leg mechanism that can be used in mobile robotic applications and in gait analysis. This paper presents the kinematics and dynamics of the Jansen leg mechanism. The forward kinematics, accomplished using circle intersection method, determines the trajectories of various points on the mechanism in the chassis (stationary link) reference frame. From the foot point trajectory, the step length is shown to vary linearly while step height varies non-linearly with change in crank radius. A dynamic model for the Jansen leg mechanism is proposed using bond graph approach with modulated multiport transformers. For given ground reaction force pattern and crank angular speed, this model helps determine the motor torque profile as well as the link and joint stresses. The model can therefore be used to rate the actuator torque and in design of the hardware and controller for such a system. The kinematics of the mechanism can also be obtained from this dynamic model. The proposed model is thus a useful tool for analysis and design of systems based on the Jansen leg mechanism. (C) 2015 Elsevier B.V. All rights reserved.

Speaker verification based on the fusion of speech acoustics and inverted articulatory signals

We propose apractical, feature-level and score-level fusion approach by combining acoustic and estimated articulatory information for both text independent and text dependent speaker verification. From a practical point of view, we study how to improve speaker verification performance by combining dynamic articulatory information with the conventional acoustic features. On text independent speaker verification, we find that concatenating articulatory features obtained from measured speech production data with conventional Mel-frequency cepstral coefficients (MFCCs) improves the performance dramatically. However, since directly measuring articulatory data is not feasible in many real world applications, we also experiment with estimated articulatory features obtained through acoustic-to-articulatory inversion. We explore both feature level and score level fusion methods and find that the overall system performance is significantly enhanced even with estimated articulatory features. Such a performance boost could be due to the inter-speaker variation information embedded in the estimated articulatory features. Since the dynamics of articulation contain important information, we included inverted articulatory trajectories in text dependent speaker verification. We demonstrate that the articulatory constraints introduced by inverted articulatory features help to reject wrong password trials and improve the performance after score level fusion. We evaluate the proposed methods on the X-ray Microbeam database and the RSR 2015 database, respectively, for the aforementioned two tasks. Experimental results show that we achieve more than 15% relative equal error rate reduction for both speaker verification tasks. (C) 2015 Elsevier Ltd. All rights reserved.

Weakly corrected numerical solutions to stochastically driven nonlinear dynamical systems

A method to weakly correct the solutions of stochastically driven nonlinear dynamical systems, herein numerically approximated through the Eule-Maruyama (EM) time-marching map, is proposed. An essential feature of the method is a change of measures that aims at rendering the EM-approximated solution measurable with respect to the filtration generated by an appropriately defined error process. Using Ito's formula and adopting a Monte Carlo (MC) setup, it is shown that the correction term may be additively applied to the realizations of the numerically integrated trajectories. Numerical evidence, presently gathered via applications of the proposed method to a few nonlinear mechanical oscillators and a semi-discrete form of a 1-D Burger's equation, lends credence to the remarkably improved numerical accuracy of the corrected solutions even with relatively large time step sizes. (C) 2015 Elsevier Inc. All rights reserved.

Dictionary-Learning-Based Post-Filter for HMM-Based Speech Synthesis

Oversmoothing of speech parameter trajectories is one of the causes for quality degradation of HMM-based speech synthesis. Various methods have been proposed to overcome this effect, the most recent ones being global variance (GV) and modulation-spectrum-based post-filter (MSPF). However, there is still a significant quality gap between natural and synthesized speech. In this paper, we propose a two-fold post-filtering technique to alleviate to a certain extent the oversmoothing of spectral and excitation parameter trajectories of HMM-based speech synthesis. For the spectral parameters, we propose a sparse coding-based post-filter to match the trajectories of synthetic speech to that of natural speech, and for the excitation trajectory, we introduce a perceptually motivated post-filter. Experimental evaluations show quality improvement compared with existing methods.

Numerical analysis of segmented-electrode Orbitraps

Simple geometries which are possible alternatives for the Orbitrap are studied in this paper. We have taken up for numerical investigation two segmented-electrode structures, ORB1 and ORB2, to mimic the electric field of the Orbitrap. In the ORB1, the inner spindle-like electrode and the outer barrel-like electrode of the Orbitrap have been replaced by 35 rings and 35 discs of fixed radii, respectively. In this structure two segmented end cap electrodes have been added. In this geometry, different potentials are applied to the different electrodes keeping top-bottom symmetry intact. In the second geometry, ORB2, the inner and outer electrodes of the Orbitrap were replaced by an approximate step structure which follows the profile of the Orbitrap electrodes. In the present study 45 steps have been used. In the ORB2, like the Orbitrap, the inner electrode is held at a negative potential and the outer electrode is at ground potential. For the purpose of comparing the performance of ORB1 and ORB2 with that of the Orbitrap, the following studies have been undertaken: (1) variation of electric potential, (2) computation of ion trajectories, (3) simulation of image currents. These studies have been carried out using both 2D and 3D Boundary Element Method (BEM), the 3D BEM was developed specifically for this study. It has been seen in these investigations that ORB1 and ORB2 have performance similar to that of the Orbitrap, with the performance of the ORB1 being seen to be marginally superior to that of the ORB2. It has been shown that with proper optimization, geometries containing far fewer electrodes can be used as mass analyzers. A novel technique of optimization of the electric field has been proposed with the objective of minimizing the dependence of axial frequency of ion motion on the initial position of an ion. The results on the optimization of 9 and 15 segmented-electrode traps having the same design as ORB1 show that it can provide accurate mass analysis. (C) 2015 Elsevier B.V. All rights reserved.

Numerical analysis of segmented-electrode Orbitraps

Simple geometries which are possible alternatives for the Orbitrap are studied in this paper. We have taken up for numerical investigation two segmented-electrode structures, ORB1 and ORB2, to mimic the electric field of the Orbitrap. In the ORB1, the inner spindle-like electrode and the outer barrel-like electrode of the Orbitrap have been replaced by 35 rings and 35 discs of fixed radii, respectively. In this structure two segmented end cap electrodes have been added. In this geometry, different potentials are applied to the different electrodes keeping top-bottom symmetry intact. In the second geometry, ORB2, the inner and outer electrodes of the Orbitrap were replaced by an approximate step structure which follows the profile of the Orbitrap electrodes. In the present study 45 steps have been used. In the ORB2, like the Orbitrap, the inner electrode is held at a negative potential and the outer electrode is at ground potential. For the purpose of comparing the performance of ORB1 and ORB2 with that of the Orbitrap, the following studies have been undertaken: (1) variation of electric potential, (2) computation of ion trajectories, (3) simulation of image currents. These studies have been carried out using both 2D and 3D Boundary Element Method (BEM), the 3D BEM was developed specifically for this study. It has been seen in these investigations that ORB1 and ORB2 have performance similar to that of the Orbitrap, with the performance of the ORB1 being seen to be marginally superior to that of the ORB2. It has been shown that with proper optimization, geometries containing far fewer electrodes can be used as mass analyzers. A novel technique of optimization of the electric field has been proposed with the objective of minimizing the dependence of axial frequency of ion motion on the initial position of an ion. The results on the optimization of 9 and 15 segmented-electrode traps having the same design as ORB1 show that it can provide accurate mass analysis. (C) 2015 Elsevier B.V. All rights reserved.