Deriving Matrix Concentration Inequalities from Kernel Couplings

This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for concentration of measure, as introduced by Chatterjee. Recent work of Mackey et al. uses these techniques to analyze random matrices with additive structure, while the enhancements in this paper cover a wider class of matrix-valued random elements. In particular, these ideas lead to a bounded differences inequality that applies to random matrices constructed from weakly dependent random variables. The proofs require novel trace inequalities that may be of independent interest.Comment: 29 page

Reading and Misreading: Schumann's Accompaniments to Bach's Sonatas and Partitas for Solo Violin

The piano accompaniments Robert Schumann wrote for J. S. Bach's solo violin works can be read as a commentary by one major composer on another's works. These accompaniments misread Bach's intentions in obvious ways (e.g., that solo violin is not a viable performance vehicle), and interpret rhythmic, harmonic, thematic/motivic, and formal structures in a manner clearly at odds with early eighteenth-century conceptions. Comparing these works with Schumann's accompaniments, eighteenth century arrangements of some movements (including some by Bach), and keeping in mind the theoretical frameworks of various eras allows us to gain insights into how our own stylistic biases affect what we hear in music of past eras

Time Course of the Increase in the Myocardial Slow Inward Current after a Photochemically Generated Concentration Jump of Intracellular cAMP

Voltage-clamped atrial trabeculae from bullfrog hearts were exposed to membrane-permeant photolyzable o-nitrobenzyl esters of cAMP and cGMP. UV flashes produced intracellular concentration jumps of cAMP or cGMP. With the cAMP derivative, flashes resulted in an increased slow inward current (Isi), producing a broadened action potential. The Isi reached a maximum 10-30 sec after the flash and decreased over the next 60-300 sec. The first increases were observable within 150 msec; this value is an upper limit imposed by the instrumentation. Responses to flashes lasted longer at higher drug concentrations and in the presence of the phosphodiesterase inhibitor papaverine; effects of flashes developed and decreased faster at higher temperature. Although the amplitude of the Isi was increased, its waveform and voltage sensitivity were not affected. Intracellular concentration jumps of cAMP failed to affect the muscarinic K+ conductance. There were no observable effects of cGMP concentration jumps. The data confirm (i) that cAMP regulates the Isi and (ii) that the 5- to 10-sec delay between application of ß-agonists and the onset of positive inotropic effects, observed in previous studies, has been correctly ascribed to events prior to the interaction between cAMP and protein kinase

Efron–Stein inequalities for random matrices

This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron–Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs

Aplicacion, Registro y Pago de los Ttributos En la Empresa Uno la Virgen de la ciudad de Matagalpa, en el periodo 2016

El presente Seminario de Graduación está centrado en los Tributos aplicados por las empresas de la ciudad de Matagalpa en el año 2016, tomándose como punto de referencia la Gasolinera UNO La Virgen S.A. El propósito principal es evaluar la aplicación, registro y pago de los Impuestos en la Gasolinera UNO La Virgen S.A, en el periodo 2016, debido a que los impuestos son siempre una obligación que es establecida por la Ley para con los contribuyentes. Este tema se considera de mucha importancia ya que el correcto registro, aplicación y pago de los Tributos está regido por las leyes tributarias y como contribuyente lo ideal es cumplir con cada uno de estos rubros al pie de la letra, y así, evitar posibles sanciones, además permitirá a individuos interesados en la temática obtener un mayor conocimiento sobre la recaudación de impuestos en Matagalpa. Como conclusiones se ha podido apreciar que la Gasolinera UNO La Virgen S.A, es una empresa dedicada al comercio, por lo tanto aplica tributos nacionales y municipales, de acuerdo a nuestro criterio, la empresa realiza sus registros contables de manera correcta, aplicando las tarifas establecidas en los diferentes reglamentos y decretos, mientras sus declaraciones las realiza siguiendo lo citado en cada ley y sus pagos los lleva a cabo a través de la Ventanilla Electrónica Tributaria para Impuestos Nacionales, visitas a la Alcaldía Municipal para los Municipales y a través del SIE para las contribuciones de INS

Control Of Flexible Structures-2 (COFS-2) flight control, structure and gimbal system interaction study

The second Control Of Flexible Structures Flight Experiment (COFS-2) includes a long mast as in the first flight experiment, but with the Langley 15-m hoop column antenna attached via a gimbal system to the top of the mast. The mast is to be mounted in the Space Shuttle cargo bay. The servo-driven gimbal system could be used to point the antenna relative to the mast. The dynamic interaction of the Shuttle Orbiter/COFS-2 system with the Orbiter on-orbit Flight Control System (FCS) and the gimbal pointing control system has been studied using analysis and simulation. The Orbiter pointing requirements have been assessed for their impact on allowable free drift time for COFS experiments. Three fixed antenna configurations were investigated. Also simulated was Orbiter attitude control behavior with active vernier jets during antenna slewing. The effect of experiment mast dampers was included. Control system stability and performance and loads on various portions of the COFS-2 structure were investigated. The study indicates possible undesirable interaction between the Orbiter FCS and the flexible, articulated COFS-2 mast/antenna system, even when restricted to vernier reaction jets

A photoisomerizable muscarinic antagonist. Studies of binding and of conductance relaxations in frog heart

These experiments employ the photoisomerizable compound, 3,3'-bis- [alpha-(trimethylammonium)methyl]azobenzene (Bis-Q), to study the response to muscarinic agents in frog myocardium. In homogenates from the heart, trans-Bis-Q blocks the binding of [3H]-N-methylscopolamine to muscarinic receptors. In voltage-clamped atrial trabeculae, trans- Bis-Q blocks the agonist-induced potassium conductance. The equilibrium dose-response curve for carbachol is shifted to the right, suggesting competitive blockade. Both the biochemical and electrophysiological data yield a dissociation constant of 4-5 microM for trans-Bis-Q; the cis configuration is severalfold less potent as a muscarinic blocker. Voltage-clamped preparations were exposed simultaneously to carbachol and Bis-Q and were subjected to appropriately filtered flashes (less than 1 ms duration) from a xenon flashlamp. Trans leads to cis and cis leads to trans photoisomerizations cause small (less than 20%) increases and decreases, respectively, in the agonist-induced current. The relaxation follows an S-shaped time course, including an initial delay or period of zero slope. The entire waveform is described by [1 - exp(-kt)]n. At 23 degrees C, k is approximately 3 s-1 and n is 2. Neither k nor n is affected when: (a) [Bis-Q] is varied between 5 and 100 microM; (b) [carbachol] is varied between 1 and 50 microM; (c) carbachol is replaced by other agonists (muscarine, acetylcholine, or acetyl-beta-methylcholine); or (d) the voltage is varied between the normal resting potential and a depolarization of 80 mV. However, in the range of 13-30 degrees C, k increases with temperature; the Q10 is between 2 and 2.5. In the same range, n does not change significantly. Like other investigators, we conclude that the activation kinetics of the muscarinic K+ conductance are not determined by ligand-receptor binding, but rather by a subsequent sequence of two (or more) steps with a high activation energy

Matrix concentration inequalities via the method of exchangeable pairs

This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein's method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix generalizations of the classical inequalities due to Hoeffding, Bernstein, Khintchine and Rosenthal. The same technique delivers bounds for sums of dependent random matrices and more general matrix-valued functions of dependent random variables.Comment: Published in at http://dx.doi.org/10.1214/13-AOP892 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Efron–Stein inequalities for random matrices

This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron–Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs