supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

modular feedback logic for discrete event systems we examine a modular approach to the synthesis of state feedback controls for the problem of maintaining a predicate on the state set of a discrete dynamic system invariant dynamical systems are modeled by automata together with a mechanism for enabling and disabling a subset of state transitions the basic problem of interest is to ensure by appropriate control action that a given predicate on the state set of the process remains invariantly true whenever it is initially satisfied assuming the predicate can be decomposed into the conjunction or disjunction of component predicates we determine conditions under which it is possible to synthesize the appropriate control in a modular fashion

on the spectral radius of a random matrix an upper bound without fourth moment consider a square matrix with independent and identically distributed entries of zero mean and unit variance it is well known that if the entries have a finite fourth moment then in high dimension with high probability the spectral radius is close to the square root of the dimension we conjecture that this holds true under the sole assumption of zero mean and unit variance in other words that there are no outliers in the circular law in this work we establish the conjecture in the case of symmetrically distributed entries with a finite moment of order larger than two the proof uses the method of moments combined with a novel truncation technique for cycle weights that might be of independent interest

generating 3d audio using a regularized hrtf hrir filter 3d sound is generated using an improved hrtf modeling technique for synthesizing hrtfs with varying degrees of smoothness and generalization a plurality n of spatial characteristic function sets are regularized or smoothed before combination with corresponding eigen filter functions and summed to provide an hrtf or hrir filter having improved smoothness in a continuous auditory space a trade off is allowed between accuracy in localization and smoothness by controlling the smoothness level of the regularizing models with a lambda factor improved smoothness in the hrtf filter allows the perception by the listener of a smoothly moving sound rendering free of annoying discontinuities creating clicks in the 3d sound

the infimal controllable and n observable superpredicate of a given predicate addresses a decentralized state feedback control problem in discrete event systems the problem requires that the set of reachable states in the closed loop system is in the given admissible range in particular the authors investigate the existence of the infimal solution that is the infimal controllable and n observable superpredicate of the minimally acceptable behavior

predicates and predicate transformers for supervisory control of discrete event dynamical systems discrete event systems are studied treating the state space as the fundamental modeling concept the control of discrete event systems using predicates and predicate transformers is treated predicates have the advantage that they can concisely characterize an infinite state space the notion of controllability of a predicate is defined and the supervisory predicate control problem is solved a closed form expression for the weakest controllable predicate is obtained the problem of controlling discrete event systems under incomplete state observation is also considered and observability of predicates is defined techniques for finding extremal solutions of boolean equations are used to derive minimally restrictive supervisors

outlier eigenvalues for deformed i i d random matrices we consider a square random matrix of size n of the form a y where a is deterministic and y has iid entries with variance 1 n under mild assumptions as n grows the empirical distribution of the eigenvalues of a y converges weakly to a limit probability measure beta on the complex plane this work is devoted to the study of the outlier eigenvalues i e eigenvalues in the complement of the support of beta even in the simplest cases a variety of interesting phenomena can occur as in earlier works we give a sufficient condition to guarantee that outliers are stable and provide examples where their fluctuations vary with the particular distribution of the entries of y or the jordan decomposition of a we also exhibit concrete examples where the outlier eigenvalues converge in distribution to the zeros of a gaussian analytic function

decentralized state feedback control of discrete event systems abstract in this paper we consider decentralized state feedback control of discrete event systems with a global control specification given by a predicate in this framework instead of a global state feedback each local state feedback controls a part of the system according to local information so that global behaviors satisfy the global control specification we introduce the notion of n observability of predicates and present necessary and sufficient conditions for the existence of a decentralized state feedback which achieves the global control specification

observations on a principal components analysis of head related transfer functions a recent principal components analysis kistler and wightman 1992 has shown that the transfer functions of the human external ear for a wide range of source locations can be expressed as weighted sums of a small number of basis vectors directional transfer functions obtained in this laboratory using substantially different measurement techniques yielded principal component basis vectors that are remarkably similar to those reported by kistler and wightman when this subject population was divided in half according to the overall physical sizes of subjects basis vectors computed for the subpopulation of smaller subjects were shifted systematically to higher frequencies relative to those computed for the subpopulation of larger subjects

control of vector discrete event systems i the base model a vector discrete event system vdes is a discrete event system model in which the system state is represented by a vector with integer components and state transitions by integer vector addition the authors investigate such structures from the viewpoint of control theory the objective is to specialize to vdes the general automation based control theory of p j ramadge and w m wonham 1987 and w m wonham and p j ramadge 1988 it is shown that within the vdes framework a useful class of control systems can be compactly modeled and some of the associated control problems of ramadge and wonham can be more efficiently solved

voice activity detection method and apparatus using the same free field to eardrum transfer functions fetf s are developed by comparing auditory data for points in three dimensional space for a model ear and auditory data collected for the same listening location with a microphone each fetf is represented as a weighted sum of frequency dependent functions obtained from an expansion of the measured fetf s covariance matrix spatial transformation characteristic functions stcf s are applied to transform the weighted frequency dependent factors to functions of spatial variables for azimuth and elevation a generalized spline model is fit to each stcf to filter out noise and permit interpolation of the stcf between measured points sound is reproduced for a selected direction by synthesizing the weighted frequency dependent factors with the smoothed and interpolated stcf s

method and apparatus for regularizing measured hrtf for smooth 3d digital audio the present invention provides an improved hrtf modeling technique for synthesizing hrtfs with varying degrees of smoothness and generalization a plurality n of spatial characteristic function sets are regularized or smoothed before combination with corresponding eigen filter functions and summed to provide an hrtf or hrir filter having improved smoothness in a continuous auditory space a trade off is allowed between accuracy in localization and smoothness by controlling the smoothness level of the regularizing models with a lambda factor improved smoothness in the hrtf filter allows the perception by the listener of a smoothly moving sound rendering free of annoying discontinuities creating clicks in the 3d sound

think globally act locally decentralized supervisory control decentralized supervisory control is investigated by considering problem formulations that model systems whose specifications are given as global constraints but whose solution is described by local controllers a necessary and sufficient condition is given for the existence of a solution to the problem of finding decentralized supervisors that ensure that the behavior of the closed loop system lies in a given range where the range of behavior can be described by regular languages it can be effectively tested whether the decentralized control problem is solvable in this case a procedure is given to compute the associated supervisors

method and apparatus for identifying speech in telephone signals method and apparatus for identifying telephone signals which are produced by a human voice the method includes determining a measure of the energy of predetermined frequency bins of the frequency spectrum of the signal for a frame comprised of a predetermined number of consecutive samples of the signal if the signal is an analog signal averaging the measure of the energy of the predetermined frequency bins over a predetermined number of frames to provide a frame group average energy measure determining the sum of the absolute value of the difference between the frame group average energy measure for all pairs of frame groups which are consecutive in time and comparing the sum with a predetermined amount to identify the signal as having been produced by a human voice if the sum exceeds the predetermined amount

on the eigenvalue problem for toeplitz band matrices abstract a formula is given for the characteristic polynomial of an n th order toeplitz band matrix with bandwidth k n in terms of the zeros of a k th degree polynomial with coefficients independent of n the complexity of the formula depends on the bandwidth k and not on the order n also given is a formula for eigenvectors in terms of the same zeros and k coefficients which can be obtained by solving a k k homogeneous system

random regularization of brown spectral measure abstract we generalize a recent result of haagerup namely we show that a convolution with a standard gaussian random matrix regularizes the behavior of fuglede kadison determinant and brown spectral distribution measure in this way it is possible to establish a connection between the limit eigenvalues distributions of a wide class of random matrices and the brown measure of the corresponding limits

how many zeros of a random polynomial are real we provide an elementary geometric derivation of the kac integral formula for the expected number of real zeros of a random polynomial with independent standard normally distributed coefficients we show that the expected number of real zeros is simply the length of the moment curve 1 t tn projected onto the surface of the unit sphere divided by the probability density of the real zeros is proportional to how fast this curve is traced out we then relax kac s assumptions by considering a variety of random sums series and distributions and we also illustrate such ideas as integral geometry and the fubini study metric

a model of head related transfer functions based on principal components analysis and minimum phase reconstruction free field to eardrum transfer functions hrtfs were measured from both ears of 10 subjects with sound sources at 265 different positions a principal components analysis of the resulting 5300 hrtf magnitude functions revealed that the hrtfs can be modeled as a linear combination of five basic spectral shapes basis functions and that this representation accounts for approximately 90 of the variance in the original hrtf magnitude functions hrtf phase was modeled by assuming that hrtfs are minimum phase functions and that interaural phase differences can be approximated by a simple time delay subjects judgments of the apparent directions of headphone presented sounds that had been synthesized from the modeled hrtfs were nearly identical to their judgments of sounds synthesized from measured hrtfs with fewer than five basis functions used in the model a less faithful reconstruction of the hrtf was produced and the frequency of large localization errors increased dramatically

outliers of random perturbations of toeplitz matrices with finite symbols consider an n times n toeplitz matrix t n with symbol varvec a lambda sum ell d 2 d 1 a ell lambda ell perturbed by an additive noise matrix n gamma e n where the entries of e n are centered i i d random variables of unit variance and gamma 1 2 it is known that the empirical measure of eigenvalues of the perturbed matrix converges weakly as n rightarrow infty to the law of varvec a u where u is distributed uniformly on mathbb s 1 in this paper we consider the outliers i e eigenvalues that are at a positive n independent distance from varvec a mathbb s 1 we prove that there are no outliers outside mathrm spec t varvec a the spectrum of the limiting toeplitz operator with probability approaching one as n rightarrow infty in contrast in mathrm spec t varvec a setminus varvec a mathbb s 1 the process of outliers converges to the point process described by the zero set of certain random analytic functions the limiting random analytic functions can be expressed as linear combinations of the determinants of finite sub matrices of an infinite dimensional matrix whose entries are i i d having the same law as that of e n the coefficients in the linear combination depend on the roots of the polynomial p z varvec a lambda varvec a lambda z lambda d 2 and semi standard young tableaux with shapes determined by the number of roots of p z varvec a lambda 0 that are greater than one in moduli

voice activity detector for half duplex audio communication system a method 501 502 of detecting voice in an audio signal comprises the steps of determining an average peak value 703 ap representing an envelope of the audio signal determining a running instance of audio signal standard deviation 702 which corresponds to one of a number of overlapping time intervals and updating a power density function pdf by adding instances of noise to the pdf if the average peak of the audio signal exceeds the current level of the audio signal by a certain amount and if the current standard deviation value falls below a threshold for a predetermined time interval a noise floor nf is located based on the mean value of the pdf 501 and if the audio signal sustains a power level exceeding the noise floor voice activity is determined to be present in the audio signal 502 the pdf is updated by a low confidence factor 1206 if all of the standard deviation values calculated during a certain period of time are below the threshold value and by a high confidence factor 1204 if all standard deviation values within a certain longer period of time period are below the threshold value