There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper proposes a very tractable approach to modeling changes in regime. The parameters of an autoregression are viewed as the outcome of a discrete-state Markov process. For example, the mean growth rate of a nonstationary series may be subject to occasional, discrete shifts. The econometrician is presumed not to observe these shifts directly, but instead must draw probabilistic inference about whether and when they may have occurred based on the observed behavior of the series. The paper presents an algorithm for drawing such probabilistic inference in the form of a nonlinear iterative filter

A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

Forecasting with artificial neural networks: the state of the art

Recurrence plots for the analysis of complex systems

SUMMARY Objective: Anterior thalamus (AN) has been shown to mediate seizures in both focal and generalized models. Specific regional increase in AN serotonergic activity was observed following AN-DBS in our pentylenetetrazol (PTZ) rodent model of acute seizures, and this increase may inhibit seizures and contribute to the mechanism of anticonvulsant DBS. Methods: Anesthetized rats with AN-directed dialysis cannula with scalp/depth EEG were infused with PTZ at 5.5 mg/(kg min) until an EEG seizure occurred. Eight experimental groups of AN-dialysis infusion were evaluated: controls (dialysate-only), 10 and 100 mM serotonin 5-HT7 agonist 5-carboxamidotryptamine (5-CT), 1, 10 and 100 mM serotonin antagonist methysergide (METH), AN-DBS, and 100 mM METH + AN-DBS. Results: Latency for seizures in control animals was 3120 770 s (S.D.); AN-DBS delayed onset to 5018 1100 (p < 0.01). AN-directed 5-CT increased latency in dose-dependent fashion: 3890 430 and 4247 528 (p < 0.05). Methysergide had an unexpected protective effect at low-dose (3908 550, p < 0.05) but not at 100 mM (2687 1079). The anticonvulsant action of AN-DBS was blocked by prior dialysis using 100 mM METH. Surface EEG burst count and nonlinear analysis (H-Statistic) noted significant (p < 0.05) increased pre-ictal epileptiform bursts in 5-CT, methysergide, but not DBS group compared to control. Conclusion: Increased serotonergic activity in AN raised PTZ seizure threshold, similar to DBS, but without preventing cortical bursting. 5-Carboxamidotryptamine, a 5-HT7 agonist, demonstrated dosedependent seizure inhibition. Methysergide proved to have an inverse, dose-dependent agonist property, antagonizing the action of AN-DBS at the highest dose. Anticonvulsant AN-DBS may in part act to selectively alter serotonin neurotransmission to raise seizure threshold.

/pdf/anticonvulsant-serotonergic-and-deep-brain-stimulation-in-1n45p2lxiy.pdf

Anticonvulsant serotonergic and deep brain stimulation in anterior thalamus

Certain types of non-linear transformations of stochastic signal processes have proven useful in engineering applications. A form of processing called hard clipping (or hard limiting) has frequently been used in electronic systems which work in “real time” in order to reduce the number of information bits which the system has to process. With hard clipping only one binary digit is used per sample value of an input signal X(t). However, information is lost about X(t) and the spectrum which is calculated from the clipped signal is a distorted form of the original signal spectrum. By a sine transformation of the sample covariance of the clipped process, a consistent estimator is derived for the spectral density of X(t). The asymptotic variance-covariance function is calculated for this estimator.

Estimation of Spectra After Hard Clipping of Gaussian Processes

Most array signal processing systems use delay‐and‐sum beamforming to estimate source bearings. This paper demonstrates the close relationship between beamforming and frequency–wavenumber spectrum analysis. The latter approach has computational advantages over beamforming when the noise is spatially correlated. The wavenumber approach is used to derive the array response of a general linear or planar array to plane wave signals. The statistical properties of the maximum‐likelihood estimators of source bearing and amplitude are presented for an array with many elements. Optimal array design is also discussed.

/pdf/frequency-wavenumber-array-processing-tf7reyo7n6.pdf

Frequency-wavenumber array processing

When a towed array of hydrophones is significantly nonlinear due to bending, ordinary linear array beamforming gives a biased estimate of the true source bearing. By processing the array as a sequence of smaller aperture subarrays and then computing the mean of the subarray bearings, the variation due to bending is reduced and a reasonably precise estimate is obtained if the average bending angle with respect to the nominal axis is small. The median and mean subarray bearings are analyzed for a theoretical statistical model and are tested using artificial data for various sinusoidal array geometries.Subject Classification: 60.20; 30.82.

/pdf/bearing-estimation-using-a-large-towed-array-3ovtm33r9h.pdf

Bearing estimation using a large towed array

Suppose that we have the distances to p + 1 targets obtained from a moving platform at discrete times with the ( p + 1)st target being a reference beacon. Assume that the distances are measured with an additive error which has a zero mean and that the errors are uncorrelated in time and space. Given the knowledge of the error structure, the position of the reference target, and the set of the successive simultaneous ranges, we present a statistical method for accurately determining the positions of the remaining targets in a computationally reasonable manner, assuming that the platform positions satisfy a certain constraint. Alternatively, reversing the roles of targets and observer, the method can be used to track a moving target platform using ranges simultaneously measured from p observers whose fixed positions are known, provided that there is a ( p + 1)st observer at a known position. As long as the target track is sufficiently variable, the discrete-time range data can be used to estimate the position of the p observers and the target track. In practice the method could be used to refine the location estimates of the observers based on successive simultaneous range measurements of the target while tracking the target. If {\sl two} observer positions {sl are known}, {sl no constraint} has to be put on the target track. The technique is analyzed using several artificial data sets for one reference target (or observer). We show that when the error is small we obtain an accurate map of ten fixed targets from 500 platform locations, and the map is also reasonably accurate even when the mean error is 70 percent of the average true distance. We also analyze another model that has 14 targets observed from 1000 locations but where the location of two of these targets are known. In any of the scenerios, as the number of successive range measurements whose errors are uncorrelated grows to infinity, the coordinate estimates of the p target (observer) locations converges in probability to the true coordinates.

Melvin J. Hinich

Papers

Anticonvulsant serotonergic and deep brain stimulation in anterior thalamus

Estimation of Spectra After Hard Clipping of Gaussian Processes

Frequency-wavenumber array processing

Bearing estimation using a large towed array

A method for locating targets using range only