Products of Random Matrices

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted prior in statistical image analysis.Comment: 9 pages, 1 figur

Statistical Speech Segmentation in Tone Languages: The Role of Lexical Tones

First Published May 9, 2017Research has demonstrated distinct roles for consonants and vowels in speech processing. For example, consonants have been shown to support lexical processes, such as the segmentation of speech based on transitional probabilities (TPs), more effectively than vowels. Theory and data so far, however, have considered only non-tone languages, that is to say, languages that lack contrastive lexical tones. In the present work, we provide a first investigation of the role of consonants and vowels in statistical speech segmentation by native speakers of Cantonese, as well as assessing how tones modulate the processing of vowels. Results show that Cantonese speakers are unable to use statistical cues carried by consonants for segmentation, but they can use cues carried by vowels. This difference becomes more evident when considering tone-bearing vowels. Additional data from speakers of Russian and Mandarin suggest that the ability of Cantonese speakers to segment streams with statistical cues carried by tone-bearing vowels extends to other tone languages, but is much reduced in speakers of non-tone languages.The research leading to these results has received funding from: the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC [grant agreement 269502, PASCAL]; the Chilean CONICYT program PIA/BASAL [grant FB0003]; the Alexander von Humboldt Foundation; and the Basque Foundation for Science (Ikerbasque)

Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color

We study quantum frequency translation and two-color photon interference enabled by the Bragg scattering four-wave mixing process in optical fiber. Using realistic model parameters, we computationally and analytically determine the Green function and Schmidt modes for cases with various pump-pulse lengths. These cases can be categorized as either "non-discriminatory" or "discriminatory" in regards to their propensity to exhibit high-efficiency translation or high-visibility two-photon interference for many different shapes of input wave packets or for only a few input wave packets, respectively. Also, for a particular case, the Schmidt mode set was found to be nearly equal to a Hermite-Gaussian function set. The methods and results also apply with little modification to frequency conversion by sum-frequency conversion in optical crystals

Major flaws in conflict prevention policies towards Africa : the conceptual deficits of international actors’ approaches and how to overcome them

Current thinking on African conflicts suffers from misinterpretations oversimplification, lack of focus, lack of conceptual clarity, state-centrism and lack of vision). The paper analyses a variety of the dominant explanations of major international actors and donors, showing how these frequently do not distinguish with sufficient clarity between the ‘root causes’ of a conflict, its aggravating factors and its triggers. Specifically, a correct assessment of conflict prolonging (or sustaining) factors is of vital importance in Africa’s lingering confrontations. Broader approaches (e.g. “structural stability”) offer a better analytical framework than familiar one-dimensional explanations. Moreover, for explaining and dealing with violent conflicts a shift of attention from the nation-state towards the local and sub-regional level is needed.Aktuelle Analysen afrikanischer Gewaltkonflikte sind häufig voller Fehlinterpretationen (Mangel an Differenzierung, Genauigkeit und konzeptioneller Klarheit, Staatszentriertheit, fehlende mittelfristige Zielvorstellungen). Breitere Ansätze (z. B. das Modell der Strukturellen Stabilität) könnten die Grundlage für bessere Analyseraster und Politiken sein als eindimensionale Erklärungen. häufig differenzieren Erklärungsansätze nicht mit ausreichender Klarheit zwischen Ursachen, verschärfenden und auslösenden Faktoren. Insbesondere die richtige Einordnung konfliktverlängernder Faktoren ist in den jahrzehntelangen gewaltsamen Auseinandersetzungen in Afrika von zentraler Bedeutung. Das Diskussionspapier stellt die große Variationsbreite dominanter Erklärungsmuster der wichtigsten internationalen Geber und Akteure gegenüber und fordert einen Perspektivenwechsel zum Einbezug der lokalen und der subregionalen Ebene für die Erklärung und Bearbeitung gewaltsamer Konflikte

Owl and Lizard: Patterns of Head Pose and Eye Pose in Driver Gaze Classification

Accurate, robust, inexpensive gaze tracking in the car can help keep a driver safe by facilitating the more effective study of how to improve (1) vehicle interfaces and (2) the design of future Advanced Driver Assistance Systems. In this paper, we estimate head pose and eye pose from monocular video using methods developed extensively in prior work and ask two new interesting questions. First, how much better can we classify driver gaze using head and eye pose versus just using head pose? Second, are there individual-specific gaze strategies that strongly correlate with how much gaze classification improves with the addition of eye pose information? We answer these questions by evaluating data drawn from an on-road study of 40 drivers. The main insight of the paper is conveyed through the analogy of an "owl" and "lizard" which describes the degree to which the eyes and the head move when shifting gaze. When the head moves a lot ("owl"), not much classification improvement is attained by estimating eye pose on top of head pose. On the other hand, when the head stays still and only the eyes move ("lizard"), classification accuracy increases significantly from adding in eye pose. We characterize how that accuracy varies between people, gaze strategies, and gaze regions.Comment: Accepted for Publication in IET Computer Vision. arXiv admin note: text overlap with arXiv:1507.0476

The linear Fokker-Planck equation for the Ornstein-Uhlenbeck process as an (almost) nonlinear kinetic equation for an isolated N-particle system

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the infinite particle limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation.Comment: Minor revisions and corrections (including the title