Concentration of Measure Inequalities for Toeplitz Matrices with Applications

We derive Concentration of Measure (CoM) inequalities for randomized Toeplitz matrices. These inequalities show that the norm of a high-dimensional signal mapped by a Toeplitz matrix to a low-dimensional space concentrates around its mean with a tail probability bound that decays exponentially in the dimension of the range space divided by a quantity which is a function of the signal. For the class of sparse signals, the introduced quantity is bounded by the sparsity level of the signal. However, we observe that this bound is highly pessimistic for most sparse signals and we show that if a random distribution is imposed on the non-zero entries of the signal, the typical value of the quantity is bounded by a term that scales logarithmically in the ambient dimension. As an application of the CoM inequalities, we consider Compressive Binary Detection (CBD).Comment: Initial Submission to the IEEE Transactions on Signal Processing on December 1, 2011. Revised and Resubmitted on July 12, 201

Sparsity and Incoherence in Compressive Sampling

We consider the problem of reconstructing a sparse signal $x^0\in\R^n$ from a limited number of linear measurements. Given $m$ randomly selected samples of $U x^0$, where $U$ is an orthonormal matrix, we show that $\ell_1$ minimization recovers $x^0$ exactly when the number of measurements exceeds $$m\geq \mathrm{Const}\cdot\mu^2(U)\cdot S\cdot\log n,$$ where $S$ is the number of nonzero components in $x^0$, and $\mu$ is the largest entry in $U$ properly normalized: $\mu(U) = \sqrt{n} \cdot \max_{k,j} |U_{k,j}|$. The smaller $\mu$, the fewer samples needed. The result holds for ``most'' sparse signals $x^0$ supported on a fixed (but arbitrary) set $T$. Given $T$, if the sign of $x^0$ for each nonzero entry on $T$ and the observed values of $Ux^0$ are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about this many samples

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The Teaching of Ethics in the Militar

Compressive system identification of LTI and LTV ARX models: The limited data set case

In this paper, we consider identifying Auto Regressive with eXternal input (ARX) models for both Linear Time-Invariant (LTI) and Linear Time-Variant (LTV) systems. We aim at doing the identification from the smallest possible number of observations. This is inspired by the field of Compressive Sensing (CS), and for this reason, we call this problem Compressive System Identification (CSI). In the case of LTI ARX systems, a system with a large number of inputs and unknown input delays on each channel can require a model structure with a large number of parameters, unless input delay estimation is performed. Since the complexity of input delay estimation increases exponentially in the number of inputs, this can be difficult for high dimensional systems. We show that in cases where the LTI system has possibly many inputs with different unknown delays, simultaneous ARX identification and input delay estimation is possible from few observations, even though this leaves an apparently ill-conditioned identification problem. We discuss identification guarantees and support our proposed method with simulations. We also consider identifying LTV ARX models. In particular, we consider systems with parameters that change only at a few time instants in a piecewise-constant manner where neither the change moments nor the number of changes is known a priori. The main technical novelty of our approach is in casting the identification problem as recovery of a block-sparse signal from an underdetermined set of linear equations. We suggest a random sampling approach for LTV identification, address the issue of identifiability and again support our approach with illustrative simulations

Reformulation of Article 185 Paragraph 1 Indonesia Criminal Procedure Code Related to Legal Certainty of the Use De Auditu Witnesses as a Legislative Evidence

The juridical implication of the emergence of the Constitutional Court Decision Number 65/PUU-VIII/2010 is expanding the meaning of witness. However, related to this, some things appear to be big problems related to legal certainty in the use of de auditu witnesses. Meanwhile, in the Criminal Procedure Code, the use of de auditu witnesses is very much against Article 185 paragraph 1 and its explanations. This research is normative legal research with approaches through the statue, cases, conceptual, comparative approaches and by using analytical techniques, namely teleological interpretation, and extensive interpretation and in this normative legal research approach using legal certainty theory, legal hierarchy theory, and relevance theory in evidence whose purpose is to find answers regarding that, in fact, testimonium de auditu can be used in criminal justice in Indonesia with the conditions specified in the decision of the constitutional court and the conditions specified in the Criminal Procedure Code, but before that Article 185 paragraph, 1 and its explanations must be reformulated to create certainty law. Keywords: Reformulation, Legal Certainty, Testimonium De Auditu DOI: 10.7176/JLPG/112-20 Publication date:August 31st 202

Joint Elastic Side-Scattering Lidar and Raman Lidar Measurements of Aerosol Optical Properties in South East Colorado

We describe an experiment, located in south-east Colorado, USA, that measured aerosol optical depth profiles using two Lidar techniques. Two independent detectors measured scattered light from a vertical UV laser beam. One detector, located at the laser site, measured light via the inelastic Raman backscattering process. This is a common method used in atmospheric science for measuring aerosol optical depth profiles. The other detector, located approximately 40km distant, viewed the laser beam from the side. This detector featured a 3.5m2 mirror and measured elastically scattered light in a bistatic Lidar configuration following the method used at the Pierre Auger cosmic ray observatory. The goal of this experiment was to assess and improve methods to measure atmospheric clarity, specifically aerosol optical depth profiles, for cosmic ray UV fluorescence detectors that use the atmosphere as a giant calorimeter. The experiment collected data from September 2010 to July 2011 under varying conditions of aerosol loading. We describe the instruments and techniques and compare the aerosol optical depth profiles measured by the Raman and bistatic Lidar detectors.Comment: 34 pages, 16 figure

Compressive imaging spectrometers using coded apertures

Abstract: We describe a novel method to track targets in a large field of view. This method simultaneously images multiple, encoded sub-fields of view onto a common focal plane. Sub-field encoding enables target tracking by creating a unique connection between target characteristics in superposition space and the target's true position in real space. This is accomplished without reconstructing a conventional image of the large field of view. Potential encoding schemes include spatial shift, rotation, and magnification. We discuss each of these encoding schemes, but the main emphasis of the paper and all examples are based on one-dimensional spatial shift encoding. System performance is evaluated in terms of two criteria: average decoding time and probability of decoding error. We study these performance criteria as a function of resolution in the encoding scheme and signal-to-noise ratio. Finally, we include simulation and experimental results demonstrating our novel tracking method