On the maximal achievable accuracy in nonlinear filtering problems

The optimal filtering error for a class of nonlinear cone-bounded filtering problems is analyzed for the case of observation noise intensity tending to zero. A sufficient condition for the resulting optimal error covariance matrix to tend to zero is derived by relating the nonlinear filtering problems to linear ones. The results are specialized for the case of nonlinear autoregressive moving-average (ARMA) processes     

Bounds on the symmetric binary cutoff rate for dispersive Gaussianchannels

Bounds on the symmetric binary cutoff rate for a pulse amplitude modulated (PAM) signaling over dispersive Gaussian channels are evaluated and discussed. These easily calculable bounds can be used to estimate the reliable rate of information transmission and the error exponent behavior for binary (two-level) PAM schemes, operating through a prefiltered additive white Gaussian channel, the memory of which is long enough to make the exact evaluation of the cutoff rate formidable. The core of the bounding technique relies on a probabilistic interpretation of a fundamental theorem in matrix theory, regarding the logarithm of the largest eigenvalue of a nonnegative primitive matrix, commonly applied in large deviation problems. These bounds are calculated for some examples and their respective tightness is considered. Further potential applications of the proposed bounding technique are pointed out     

Universal denoising for the finite-input general-output channel

We consider the problem of reconstructing a finite-alphabet signal corrupted by a known memoryless channel with a general output alphabet. The goodness of the reconstruction is measured by a given loss function. We (constructively) establish the existence of a universal (sequence of) denoiser(s) attaining asymptotically the optimum distribution-dependent performance for any stationary source that may be generating the noiseless signal. We show, in fact, that there is a whole family of denoiser sequences with this property. These schemes are shown to be universal also in a semistochastic setting, where the only randomness assumed is that associated with the channel noise. The scheme is practical, requiring O(n/sup 1+/spl epsiv//) operations (for any /spl epsiv/>0) and working storage size sublinear in the input data length. This extends recent work that presented a discrete universal denoiser for recovering a discrete source corrupted by a discrete memoryless channel (DMC).     

On the capacity of associative memories with linear thresholdfunctions

Some important features of various known constructions of associative memories based on linear threshold functions are analyzed. Two important features are dealt with: (a) the ability to select an arbitrary set of desired memory vectors and design a network for this set; (b) the sizes and shapes of the domains of attraction of the desired memory vectors and their relation to various design parameters. The static capacity for randomly chosen desired memories is also analyzed. Two extremal examples of sets of desired memories are then analyzed in detail. For spectral schemes with randomly chosen O[N /ln N] memories, it is shown that almost all of the Hamming sphere around each memory is directly attracted     

On the parameters estimation of continuous-time ARMA processes from noisy observations

Recently, an iterative algorithm has been presented for estimating the parameters of partially observed continuous-time processes [1]. In this note we concentrate on continuous-time ARMA processes observed in white noise. A maximum a-posteriori (MAP) estimator is defined for the trajectory of the parameters' random process. This approach enables the MAP estimation of randomly slowly varying parameters, and extends the conventional treatment of time-invariant parameters. The iterative algorithm derived for the MAP estimation, increases the posterior probability of the parameters in each iteration, and converges to a stationary point of the posterior probability functional. Each iteration involves a standard linear smoother followed by a finite-dimensional linear system, and thus is easily implemented.     

Extending the range of rate constants available from BIACORE: interpreting mass transport-influenced binding data

Myelin-associated inhibitors of neurite growth play an important role in the regenerative failure after injury in the adult mammalian CNS. The application of the mAb IN-1, which efficiently neutralizes the NI-250/35 inhibitory proteins, alone or in combination with neurotrophin-3 (NT-3), has been shown to promote axonal regeneration when applied in acute injury models. To test whether IN-1 application can induce axonal growth also in a chronic injury model, we treated rats with IN-1 and NT-3 starting 2 or 8 weeks after injury. Rats underwent bilateral dorsal hemisection of the spinal cord at the age of 5-6 weeks. Regeneration of corticospinal (CST) fibers into the caudal spinal cord was observed in three of eight of those animals with a 2-week delay between lesion and treatment. CST fibers regenerated for 2-11.4 mm. In the control group sprouting occurred rostral to the lesion but no long-distance regeneration occurred. In animals where treatment started at 8 weeks after injury the longest fibers observed grew up to 2 mm into the caudal spinal cord. The results show that transected corticospinal axons retain the ability to regenerate at least for a few weeks after injury. Functional analysis of these animals showed a slight improvement of functional recovery.     

On the least squares tap adjustment algorithm in adaptive digitalecho cancellers

Fast recursive algorithms for updating coefficients in digital echo cancellers can be derived from the well-known method of least squares. Unless zero initial conditions are assumed, the exact initialization of these algorithms is yet unknown. For random data of more than twice the order of the filter, the existence of a unique least squares solution is proven. A constructive recursive procedure in time and order for computing the pseudoinverse solution for the initial steps is derived. Since the data matrix is composed of integers, this technique facilitates the implementation of stable tap-update algorithms     

Modeling the reversible kinetics of neutrophil aggregation under hydrodynamic shear

Neutrophil emigration into inflamed tissue is mediated by beta 2-integrin and L-selectin adhesion receptors. Homotypic neutrophil aggregation is also dependent on these molecules, and it provides a model system in which to study adhesion dynamics. In the current study we formulated a mathematical model for cellular aggregation in a linear shear field based on Smoluchowski's two-body collision theory. Neutrophil suspensions activated with chemotactic stimulus and sheared in a cone-plate viscometer rapidly aggregate. Over a range of shear rates (400-800 s-1), approximately 90% of the single cells were recruited into aggregates ranging from doublets to groupings larger than sextuplets. The adhesion efficiency fit to these kinetics reached maximum levels of > 70%. Formed aggregates remained intact and resistant to shear up to 120 s, at which time they spontaneously dissociated back to singlets. The rate of cell disaggregation was linearly proportional to the applied shear rate, and it was approximately 60% lower for doublets as compared to larger aggregates. By accounting for the time-dependent changes in adhesion efficiency, disaggregation rate, and the effects of aggregate geometry, we succeeded in predicting the reversible kinetics of aggregation over a wide range of shear rates and cell concentrations. The combination of viscometry with flow cytometry and mathematical analysis as presented here represents a novel approach to differentiating between the effects of hydrodynamics and the intrinsic biological processes that control cell adhesion.     

Source coding, large deviations, and approximate pattern matching

We present a development of parts of rate-distortion theory and pattern-matching algorithms for lossy data compression, centered around a lossy version of the asymptotic equipartition property (AEP). This treatment closely parallels the corresponding development in lossless compression, a point of view that was advanced in an important paper of Wyner and Ziv in 1989. In the lossless case, we review how the AEP underlies the analysis of the Lempel-Ziv algorithm by viewing it as a random code and reducing it to the idealized Shannon code. This also provides information about the redundancy of the Lempel-Ziv algorithm and about the asymptotic behavior of several relevant quantities. In the lossy case, we give various versions of the statement of the generalized AEP and we outline the general methodology of its proof via large deviations. Its relationship with Barron (1985) and Orey's (1985, 1986) generalized AEP is also discussed. The lossy AEP is applied to (i) prove strengthened versions, of Shannon's(1948, 1974) direct source-coding theorem and universal coding theorems; (ii) characterize the performance of "mismatched" codebooks in lossy data compression; ( iii) analyze the performance of pattern-matching algorithms for lossy compression (including Lempel-Ziv schemes); and (iv) determine the first-order asymptotic of waiting times between stationary processes. A refinement to the lossy AEP is then presented, and it is used to (i) prove second-order (direct and converse) lossy source-coding theorems, including universal coding theorems; (ii) characterize which sources are quantitatively easier to compress; (iii) determine the second-order asymptotic of waiting times between stationary processes; and (iv) determine the precise asymptotic behavior of longest match-lengths between stationary processes. Finally, we discuss extensions of the above framework and results to random fields