High resolution pole-zero analysis of Parkinsonian speech

High resolution analysis of voiced speech signals in Parkinsonian patients using a pitch synchronous pole-zero model is introduced. A modified estimation error is defined leading to an accurate and consistent determination of the excitation instants of the model. An infinite resolution in determining these instants, despite the finite sampling interval, is achieved by mapping the discrete (digitized) problem into a continuous one. The proposed analysis was found to be useful in analyzing Parkinsonian speech where the goal was to detect and quantify the Parkinsonian tremor and rigidity from sustained voiced sounds.     

The primal-dual algorithm as a constraint-set-manipulation device

A general primal—dual algorithm for linearly constrained optimization problems is formulated in which the dual variables are updated by a dual algorithmic operator. Convergence is proved under the assumption that the dual algorithmic operator implies asymptotic feasibility of the primal iterates with respect to the linear constraints. A general result relating the minimal values of an infinite sequence of constrained problems to the minimal value of a limiting problem (constrained by the limit of the sequence of constraints sets) is established and invoked. The applicability of the general theory is demonstrated by analyzing a specific dual algorithmic operator. This leads to the MART algorithm for constrained entropy maximization used in image reconstruction from projections.     

Some Low Distortion Metric Ramsey Problems

In this note we consider the metric Ramsey problem for the normed spaces $\ell_p$. Namely, given some $1\le p \le \infty$ and $\alpha \ge 1$, and an integer $n$, we ask for the largest $m$ such that every $n$-point metric space contains an $m$-point subspace which embeds into $\ell_p$ with distortion at most $ \alpha$. In [1] it is shown that in the case of $\ell_2$, the dependence of $m$ on $\alpha$ undergoes a phase transition at $\alpha =2$. Here we consider this problem for other $\ell_p$, and specifically the occurrence of a phase transition for $p\neq 2$. It is shown that a phase transition does occur at $\alpha=2$ for every $p\in [1,2]$. For $p > 2$ we are unable to determine the answer, but estimates are provided for the possible location of such a phase transition. We also study the analogous problem for isometric embedding and show that for every $1 < p < \infty$ there are arbitrarily large metric spaces, no four points of which embed isometrically in $\ell_p$.     

Using EMG to anticipate head motion for virtual-environment applications

In virtual environment (VE) applications, where virtual objects are presented in a see-through head-mounted display, virtual images must be continuously stabilized in space in response to user's head motion. Time delays in head-motion compensation cause virtual objects to "swim" around instead of being stable in space which results in misalignment errors when overlaying virtual and real objects. Visual update delays are a critical technical obstacle for implementing head-mounted displays in applications such as battlefield simulation/training, telerobotics, and telemedicine. Head motion is currently measurable by a head-mounted 6-degrees-of-freedom inertial measurement unit. However, even given this information, overall VE-system latencies cannot be reduced under about 25 ms. We present a novel approach to eliminating latencies, which is premised on the fact that myoelectric signals from a muscle precede its exertion of force, thereby limb or head acceleration. We thus suggest utilizing neck-muscles' myoelectric signals to anticipate head motion. We trained a neural network to map such signals onto equivalent time-advanced inertial outputs. The resulting network can achieve time advances of up to 70 ms.     

Exactly solvable model for driven dissipative systems

We introduce a solvable stochastic model inspired by granular gases for driven dissipative systems. We characterize far from equilibrium steady states of such systems through the non-Boltzmann energy distribution and compare different measures of effective temperatures. As an example we demonstrate that fluctuation-dissipation relations hold, however, with an effective temperature differing from the effective temperature defined from the average energy.     

Proximity Function Minimization Using Multiple Bregman Projections, with Applications to Split Feasibility and Kullback–Leibler Distance Minimization

Problems in signal detection and image recovery can sometimes be formulated as a convex feasibility problem (CFP) of finding a vector in the intersection of a finite family of closed convex sets. Algorithms for this purpose typically employ orthogonal or generalized projections onto the individual convex sets. The simultaneous multiprojection algorithm of Censor and Elfving for solving the CFP, in which different generalized projections may be used at the same time, has been shown to converge for the case of nonempty intersection; still open is the question of its convergence when the intersection of the closed convex sets is empty.Motivated by the geometric alternating minimization approach of Csiszár and Tusnády and the product space formulation of Pierra, we derive a new simultaneous multiprojection algorithm that employs generalized projections of Bregman to solve the convex feasibility problem or, in the inconsistent case, to minimize a proximity function that measures the average distance from a point to all convex sets. We assume that the Bregman distances involved are jointly convex, so that the proximity function itself is convex. When the intersection of the convex sets is empty, but the closure of the proximity function has a unique global minimizer, the sequence of iterates converges to this unique minimizer. Special cases of this algorithm include the Expectation Maximization Maximum Likelihood (EMML) method in emission tomography and a new convergence result for an algorithm that solves the split feasibility problem.     

An Automated System for ST Segment and Arrhythmia Analysis in Exercise Radionuclide Ventriculography

A computer-based system for interpretation of the electrocardiogram (ECG) in the diagnosis of arrhythmia and ST segment abnormality in an exercise system is presented. The system was designed for inclusion in a gamma camera so that ECG diagnosis could be combined with the diagnostic capability of radionuclide ventriculography. Digitized data are analyzed in a beat-by-beat mode and a contextual diagnosis of underlying rhythm is provided. Each beat is assigned a beat code based on a combination of waveform analysis and RR interval measurement. The waveform analysis employs a new correlation coefficient formula which corrects for baseline wander. Selective signal averaging, in which only normal beats are included, is done for an improved signal-to-noise ratio prior to ST segment analysis. Template generation, R wave detection, QRS window size, baseline correction, and continuous updating of heart rate have all been automated. ST level and slope measurements are computed on signal-averaged data. Arrhythmia analysis of 13 passages of abnormal rhythm by computer was found to be correct in 98.4 percent of all beats. 25 passages of exercise data, 1-5 min in length, were evaluated by the cardiologist and found to be in agreement in 95.8 percent in measurements of ST level and 91.7 percent in measurements of ST slope.     

The decomposition of trees into subtrees

A necessary condition for the decomposition of a tree T into subtrees, each isomorphic to a tree from a given set of trees is presented. We also present a characterization of the set of trees for which the condition is sufficient. Many examples are given.