An exact sequence for Milnor's K-theory with applications to quadratic forms

We construct a four-term exact sequence which provides information on the kernel and cokernel of the multiplication by a pure symbol in Milnor's K-theory mod 2 of fields of characteristic zero. As an application we establish, for fields of characteristics zero, the validity of three conjectures in the theory of quadratic forms - the Milnor conjecture on the structure of the Witt ring, the Khan-Rost-Sujatha conjecture and the J-filtration conjecture. The first version of this paper was written in the spring of 1996

Sizing Up Repo

We measure the repo funding extended by money market funds (MMF) and securities lenders to the shadow banking system, including quantities, haircuts, and repo rates by type of underlying collateral. We find that repo played only a small role in funding private sector assets prior to the crisis, as most repos are backed by Treasury and Agency collateral. Repo with private sector collateral contracts during the crisis, but the magnitude is relatively insignificant compared with the contraction in asset-backed commercial paper (ABCP). While relatively small in aggregate, the contraction in repo particularly affected key dealer banks with large exposures to private sector securities, which then had knock-on effects on security markets, and led these dealer banks to resort to the Fed's emergency lending programs. We also find that haircuts in MMF-to-dealer repo rise less than the dealer-to-dealer or dealer-to-hedge fund repo haircuts reported in earlier papers. This finding suggests that the contraction in repo led dealers to take defensive actions, given their own capital and liquidity problems, raising credit terms to their borrowers. The picture that emerges from these findings looks less like a traditional bank run of depositors and more like a credit crunch among dealer banks.

Extremal black holes in D=4 Gauss-Bonnet gravity

We show that four-dimensional Einstein-Maxwell-Dilaton-Gauss-Bonnet gravity admits asymptotically flat black hole solutions with a degenerate event horizon of the Reissner-Nordstr\"om type $AdS_2\times S^2$. Such black holes exist for the dilaton coupling constant within the interval $0\leq a^2<a^2_{\rm cr}$. Black holes must be endowed with an electric charge and (possibly) with magnetic charge (dyons) but they can not be purely magnetic. Purely electric solutions are constructed numerically and the critical dilaton coupling is determined $a_{\rm cr}\simeq 0.488219703$. For each value of the dilaton coupling $a$ within this interval and for a fixed value of the Gauss--Bonnet coupling $\alpha$ we have a family of black holes parameterized by their electric charge. Relation between the mass, the electric charge and the dilaton charge at both ends of the allowed interval of $a$ is reminiscent of the BPS condition for dilaton black holes in the Einstein-Maxwell-Dilaton theory. The entropy of the DGB extremal black holes is twice the Bekenstein-Hawking entropy.Comment: New material and references added, errors corrected including higher decimals in a_cr, figures improve

Fast Glare Detection in Document Images

Glare is a phenomenon that occurs when the scene has a reflection of a light source or has one in it. This luminescence can hide useful information from the image, making text recognition virtually impossible. In this paper, we propose an approach to detect glare in images taken by users via mobile devices. Our method divides the document into blocks and collects luminance features from the original image and black-white strokes histograms of the binarized image. Finally, glare is detected using a convolutional neural network on the aforementioned histograms and luminance features. The network consists of several feature extraction blocks, one for each type of input, and the detection block, which calculates the resulting glare heatmap based on the output of the extraction part. The proposed solution detects glare with high recall and f-score.Comment: 4 pages, Workshop on Industrial Applications of Document Analysis and Recognition 201

Global solutions for higher-dimensional stretched small black holes

Small black holes in heterotic string theory have vanishing horizon area at the supergravity level, but the horizon is stretched to the finite radius $AdS_2 \times S^{D-2}$ geometry once higher curvature corrections are turned on. This has been demonstrated to give good agreement with microscopic entropy counting. Previous considerations, however, were based on the classical local solutions valid only in the vicinity of the event horizon. Here we address the question of global existence of extremal black holes in the $D$-dimensional Einstein-Maxwell-Dilaton theory with the Gauss-Bonnet term introducing a variable dilaton coupling $a$ as a parameter. We show that asymptotically flat black holes exist only in a bounded region of the dilaton couplings $0 < a < a_{\rm cr}$ where $a_{\rm cr}$ depends on $D$. For $D \geq 5$ (but not for $D = 4$) the allowed range of $a$ includes the heterotic string values. For $a > a_{\rm cr}$ numerical solutions meet weak naked singularities at finite radii $r = r_{\rm cusp}$ (spherical cusps), where the scalar curvature diverges as $|r - r_{\rm cusp}|^{-1/2}$. For $D \geq 7$ cusps are met in pairs, so that solutions can be formally extended to asymptotically flat infinity choosing a suitable integration variable. We show, however, that radial geodesics cannot be continued through the cusp singularities, so such a continuation is unphysical.Comment: 26 pages, 19 figures, minor correction

NEW APPROACH FOR REMOTE DETECTION OF HUMAN EMOTIONS

Various instrumental methods have been developed for observing human emotions in psychology, the neurosciences, and machine learning studies. These methods are mostly directed to detecting individual, personal emotions. The focus of this study is developing instrumental methods for remote detection of human emotions, both individual and collective. A new antenna device has been added to the Electrophotonic Imaging/Gas Discharge Visualization camera system. Examples of data are explored from a water blessing ritual, healing workshop training, musical performance, geophysical measurements during a solar eclipse, and a shamanic ceremony. These preliminary indications demonstrate a potential for mapping the effects of human emotions. We propose an international collaborative project for a Geoactive Zones Database: developing maps of energy parameters for sacral subjects and a program for study of their influence on the human psycho-physiological condition; in relation with both the environmental situation, and the health and psycho-types of people