Optimal local polynomial regression of noisy time varying signals

We address the problem of local-polynomial modeling of smooth time-varying signals with unknown functional form, in the presence of additive noise. The problem formulation is in the time domain and the polynomial coefficients are estimated in the pointwise minimum mean square error (PMMSE) sense. The choice of the window length for local modeling introduces a bias-variance tradeoff, which we solve optimally by using the intersection-of-confidence-intervals (ICI) technique. The combination of the local polynomial model and the ICI technique gives rise to an adaptive signal model equipped with a time-varying PMMSE-optimal window length whose performance is superior to that obtained by using a fixed window length. We also evaluate the sensitivity of the ICI technique with respect to the confidence interval width. Simulation results on electrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio (SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo performance analysis shows that the performance is comparable to the basic wavelet techniques. For 0 dB SNR, the adaptive window technique yields about 2-3dB higher SNR than wavelet regression techniques and for SNRs greater than 12dB, the wavelet techniques yield about 2dB higher SNR.

Finding a Box Representation for a Graph in $O(n^2\Delta^2\ln n)$ time

An axis-parallel box in $b$-dimensional space is a Cartesian product $R_1 \times R_2 \times \cdots \times R_b$ where $R_i$ (for $1 \leq i \leq b$) is a closed interval of the form $[a_i, b_i]$ on the real line. For a graph $G$, its boxicity is the minimum dimension $b$, such that $G$ is representable as the intersection graph of (axis-parallel) boxes in $b$-dimensional space. The concept of boxicity finds application in various areas of research like ecology, operation research etc. Chandran, Francis and Sivadasan gave an $O(\Delta n^2 \ln^2 n)$ randomized algorithm to construct a box representation for any graph $G$ on $n$ vertices in $\lceil (\Delta + 2)\ln n \rceil$ dimensions, where $\Delta$ is the maximum degree of the graph. They also came up with a deterministic algorithm that runs in $O(n^4 \Delta )$ time. Here, we present an $O(n^2 \Delta^2 \ln n)$ deterministic algorithm that constructs the box representation for any graph in $\lceil (\Delta + 2)\ln n \rceil$ dimensions.

Real-time Computer Simulation of Three Dimensional Elastostatics using the Finite Point Method

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

Time-frequency analysis of human motion during rhythmic exercises

Biomechanical signals due to human movements during exercise are represented in time-frequency domain using Wigner Distribution Function (WDF). Analysis based on WDF reveals instantaneous spectral and power changes during a rhythmic exercise. Investigations were carried out on 11 healthy subjects who performed 5 cycles of sun salutation, with a body-mounted Inertial Measurement Unit (IMU) as a motion sensor. Variance of Instantaneous Frequency (I.F) and Instantaneous Power (I.P) for performance analysis of the subject is estimated using one-way ANOVA model. Results reveal that joint Time-Frequency analysis of biomechanical signals during motion facilitates a better understanding of grace and consistency during rhythmic exercise.

Effect of dimerization on dynamics of spin-charge separation in Pariser-Parr-Pople model: A time-dependent density matrix renormalization group study

We investigate the effect of static electron-phonon coupling on real-time dynamics of spin and charge transport in pi-conjugated polyene chains. The polyene chain is modeled by the Pariser-Parr-Pople Hamiltonian with dimerized nearest-neighbor parameter t(0)(1 + delta) for short bonds and t(0)(1 - delta) for long bonds, and long-range electron-electron interactions. We follow the time evolution of the spin and charge using time-dependent density matrix renormalization group technique when a hole is injected at one end of the chain in its ground state. We find that spin and charge dynamics followed through spin and charge velocities depend both on chain length and extent of dimerization delta. Analysis of the results requires focusing on physical quantities such as average spin and charge polarizations, particularly in the large dimerization limit. In the dimerization range 0.0 <= delta <= 0.15, spin-charge dynamics is found to have a well-defined behavior, with spin-charge separation (measured as the ratio of charge velocity to spin velocity) as well as the total amount of charge and spin transported in a given time along the chain decreasing as dimerization increases. However, in the range 0.3 <= delta <= 0.5, it is observed that the dynamics of spin and charge transport becomes complicated. It is observed that, for large delta values, spin-charge separation is suppressed and the injected hole fails to travel the entire length of the chain.

Real-time density matrix renormalization group dynamics of spin and charge transport in push-pull polyenes and related systems

In this paper we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes [D-(CH)(x)-A] chains, also known as push-pull polyenes. We employ a long-range correlated model Hamiltonian for the D-(CH)(x)-A system, and time-dependent density matrix renormalization group technique for time propagating the wave packet obtained by injecting a hole at a terminal site, in the ground state of the system. Our studies reveal that the end groups do not affect spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these push-pull systems with donor-acceptor substituted polymethine imine (PMI), D-(CHN)(x)-A, systems in which besides electron affinities, the nature of p(z) orbitals in conjugation also alternate from site to site. We note that spin and charge dynamics in the PMIs are very different from that observed in the case of push-pull polyenes, and within the time scale of our studies, transport of spin and charge leads to the formation of a ``quasi-static'' state.

Possibility of chaos in interval friction experiments of martensites

Wuttig and Suzuki's model on anelastic nonlinearities in solids in the vicinity of martensite transformations is analysed numerically. This model shows chaos even in the absence of applied forcing field as a function of a temperature dependent parameter. Even though the model exhibits sustained oscillations as a function of the amplitude of the forcing term, it does not exactly capture the features of the experimental time series. We have improved the model by adding a symmetry breaking term. The improved model shows period doubling bifurcation as a function of the amplitude of the forcing term. The solutions of our improved model shows good resemblance with the nonsymmetric period four oscillation seen in the experiment. (C) 1999 Elsevier Science B.V. All rights reserved.

Cubicity and Bandwidth

A unit cube in (or a k-cube in short) is defined as the Cartesian product R (1) x R (2) x ... x R (k) where R (i) (for 1 a parts per thousand currency sign i a parts per thousand currency sign k) is a closed interval of the form a (i) , a (i) + 1] on the real line. A k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that two vertices in G are adjacent if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G is the minimum k such that G has a k-cube representation. From a geometric embedding point of view, a k-cube representation of G = (V, E) yields an embedding such that for any two vertices u and v, ||f(u) - f(v)||(a) a parts per thousand currency sign 1 if and only if . We first present a randomized algorithm that constructs the cube representation of any graph on n vertices with maximum degree Delta in O(Delta ln n) dimensions. This algorithm is then derandomized to obtain a polynomial time deterministic algorithm that also produces the cube representation of the input graph in the same number of dimensions. The bandwidth ordering of the graph is studied next and it is shown that our algorithm can be improved to produce a cube representation of the input graph G in O(Delta ln b) dimensions, where b is the bandwidth of G, given a bandwidth ordering of G. Note that b a parts per thousand currency sign n and b is much smaller than n for many well-known graph classes. Another upper bound of b + 1 on the cubicity of any graph with bandwidth b is also shown. Together, these results imply that for any graph G with maximum degree Delta and bandwidth b, the cubicity is O(min{b, Delta ln b}). The upper bound of b + 1 is used to derive upper bounds for the cubicity of circular-arc graphs, cocomparability graphs and AT-free graphs in terms of the maximum degree Delta.

Time-Temperature Scaling of Conductivity Spectra of Organic Plastic Crystalline Conductors

Organic plastic crystalline soft matter ion conductors are interesting alternatives to liquid electrolytes in electrochemical storage devices such as Lithium-ion batteries. The solvent dynamics plays a major role in determining the ion transport in plastic crystalline ion conductors. We present here an analysis of the frequency-dependent ionic conductivity of succinonitrile-based plastic crystalline ion conductors at varying salt composition (0.005 to 1 M) and temperature (-20 to 60 degrees C) using time-temperature superposition principle (TTSP). The main motivation of the work has been to establish comprehensive insight into the ion transport mechanism from a single method viz, impedance spectroscopy rather than employing cluster of different characterization methods probing various length and time scales. The TTSP remarkably aids in explicit identification of the extent of the roles of solvent dynamics and ion-ion interactions on the effective conductivity of the orientationally disordered plastic crystalline ion conductors.

Cubicity, degeneracy, and crossing number

A $k$-box $B=(R_1,...,R_k)$, where each $R_i$ is a closed interval on the real line, is defined to be the Cartesian product $R_1\times R_2\times ...\times R_k$. If each $R_i$ is a unit length interval, we call $B$ a $k$-cube. Boxicity of a graph $G$, denoted as $\boxi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-boxes. Similarly, the cubicity of $G$, denoted as $\cubi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-cubes. It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan: Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/ 0607092, 2006.] that, for a graph $G$ with maximum degree $\Delta$, $\cubi(G)\leq \lceil 4(\Delta +1)\log n\rceil$. In this paper, we show that, for a $k$-degenerate graph $G$, $\cubi(G) \leq (k+2) \lceil 2e \log n \rceil$. Since $k$ is at most $\Delta$ and can be much lower, this clearly is a stronger result. This bound is tight. We also give an efficient deterministic algorithm that runs in $O(n^2k)$ time to output a $8k(\lceil 2.42 \log n\rceil + 1)$ dimensional cube representation for $G$. An important consequence of the above result is that if the crossing number of a graph $G$ is $t$, then $\boxi(G)$ is $O(t^{1/4}{\lceil\log t\rceil}^{3/4})$ . This bound is tight up to a factor of $O((\log t)^{1/4})$. We also show that, if $G$ has $n$ vertices, then $\cubi(G)$ is $O(\log n + t^{1/4}\log t)$. Using our bound for the cubicity of $k$-degenerate graphs we show that cubicity of almost all graphs in $\mathcal{G}(n,m)$ model is $O(d_{av}\log n)$, where $d_{av}$ denotes the average degree of the graph under consideration. model is O(davlogn).

Joint data detection and dominant singular mode estimation in time varying reciprocal MIMO systems

This paper proposes an algorithm for joint data detection and tracking of the dominant singular mode of a time varying channel at the transmitter and receiver of a time division duplex multiple input multiple output beamforming system. The method proposed is a modified expectation maximization algorithm which utilizes an initial estimate to track the dominant modes of the channel at the transmitter and the receiver blindly; and simultaneously detects the un known data. Furthermore, the estimates are constrained to be within a confidence interval of the previous estimate in order to improve the tracking performance and mitigate the effect of error propagation. Monte-Carlo simulation results of the symbol error rate and the mean square inner product between the estimated and the true singular vector are plotted to show the performance benefits offered by the proposed method compared to existing techniques.

Dependence of electron recombination time and light to electricity conversion efficiency on shape of the nanocrystal light sensitizer

Tunability of electron recombination time and light to electricity conversion efficiency to superior values in semiconductor sensitized solar cells via optimized design of nanocrystal light sensitizer shape is discussed here.

Inference for the Component and System Lifetime Distribution of a k-unit Parallel System Based on System Data

In this paper, we consider the inference for the component and system lifetime distribution of a k-unit parallel system with independent components based on system data. The components are assumed to have identical Weibull distribution. We obtain the maximum likelihood estimates of the unknown parameters based on system data. The Fisher information matrix has been derived. We propose -expectation tolerance interval and -content -level tolerance interval for the life distribution of the system. Performance of the estimators and tolerance intervals is investigated via simulation study. A simulated dataset is analyzed for illustration.

Polynomial time and parameterized approximation algorithms for boxicity

The boxicity (cubicity) of a graph G, denoted by box(G) (respectively cub(G)), is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes (cubes) in ℝ k . The problem of computing boxicity (cubicity) is known to be inapproximable in polynomial time even for graph classes like bipartite, co-bipartite and split graphs, within an O(n 0.5 − ε ) factor for any ε > 0, unless NP = ZPP. We prove that if a graph G on n vertices has a clique on n − k vertices, then box(G) can be computed in time n22O(k2logk) . Using this fact, various FPT approximation algorithms for boxicity are derived. The parameter used is the vertex (or edge) edit distance of the input graph from certain graph families of bounded boxicity - like interval graphs and planar graphs. Using the same fact, we also derive an O(nloglogn√logn√) factor approximation algorithm for computing boxicity, which, to our knowledge, is the first o(n) factor approximation algorithm for the problem. We also present an FPT approximation algorithm for computing the cubicity of graphs, with vertex cover number as the parameter.

On existence of periodic solutions for stable interval plants with odd, sector type nonlinearities

In several systems, the physical parameters of the system vary over time or operating points. A popular way of representing such plants with structured or parametric uncertainties is by means of interval polynomials. However, ensuring the stability of such systems is a robust control problem. Fortunately, Kharitonov's theorem enables the analysis of such interval plants and also provides tools for design of robust controllers in such cases. The present paper considers one such case, where the interval plant is connected with a timeinvariant, static, odd, sector type nonlinearity in its feedback path. This paper provides necessary conditions for the existence of self sustaining periodic oscillations in such interval plants, and indicates a possible design algorithm to avoid such periodic solutions or limit cycles. The describing function technique is used to approximate the nonlinearity and subsequently arrive at the results. Furthermore, the value set approach, along with Mikhailov conditions, are resorted to in providing graphical techniques for the derivation of the conditions and subsequent design algorithm of the controller.