Efficient QR Decomposition Using Low Complexity Column-wise Givens Rotation (CGR)

QR decomposition (QRD) is a widely used Numerical Linear Algebra (NLA) kernel with applications ranging from SONAR beamforming to wireless MIMO receivers. In this paper, we propose a novel Givens Rotation (GR) based QRD (GR QRD) where we reduce the computational complexity of GR and exploit higher degree of parallelism. This low complexity Column-wise GR (CGR) can annihilate multiple elements of a column of a matrix simultaneously. The algorithm is first realized on a Two-Dimensional (2 D) systolic array and then implemented on REDEFINE which is a Coarse Grained run-time Reconfigurable Architecture (CGRA). We benchmark the proposed implementation against state-of-the-art implementations to report better throughput, convergence and scalability.

Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

Spontaneous Lorentz violation: the case of infrared QED

It is by now clear that the infrared sector of quantum electrodynamics (QED) has an intriguingly complex structure. Based on earlier pioneering work on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the U(1) charge group of QED to the ``Sky'' group incorporating the well-known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality (Balachandran and Vaidya, Eur Phys J Plus 128:118, 2013). It was shown that the ``Sky'' group is generated by the algebra of angle-dependent charges and a study of its superselection sectors has revealed a manifest description of spontaneous breaking of the Lorentz symmetry. We further elaborate this approach here and investigate in some detail the properties of charged particles dressed by the infrared photons. We find that Lorentz violation due to soft photons may be manifestly codified in an angle-dependent fermion mass, modifying therefore the fermion dispersion relations. The fact that the masses of the charged particles are not Lorentz invariant affects their spin content, and time dilation formulas for decays should also get corrections.

Non-Abelian gauge redundancy and entropic ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 x 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.

L-infinity norms of holomorphic modular forms in the case of compact quotient

We prove a sub-convex estimate for the sup-norm of L-2-normalized holomorphic modular forms of weight k on the upper half plane, with respect to the unit group of a quaternion division algebra over Q. More precisely we show that when the L-2 norm of an eigenfunction f is one, parallel to f parallel to(infinity) <<(epsilon) k(1/2-1/33+epsilon) for any epsilon > 0 and for all k sufficiently large.

Co-Exploration of NLA Kernels and Specification of Compute Elements in Distributed Memory CGRAs

Coarse Grained Reconfigurable Architectures (CGRA) are emerging as embedded application processing units in computing platforms for Exascale computing. Such CGRAs are distributed memory multi- core compute elements on a chip that communicate over a Network-on-chip (NoC). Numerical Linear Algebra (NLA) kernels are key to several high performance computing applications. In this paper we propose a systematic methodology to obtain the specification of Compute Elements (CE) for such CGRAs. We analyze block Matrix Multiplication and block LU Decomposition algorithms in the context of a CGRA, and obtain theoretical bounds on communication requirements, and memory sizes for a CE. Support for high performance custom computations common to NLA kernels are met through custom function units (CFUs) in the CEs. We present results to justify the merits of such CFUs.

A Generalization of Gravity

I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to Cayley's hyperdeterminants. The resulting diff-invariant actions give rise to geometric theories that go beyond the metric paradigm (even metric-less theories are possible), and contain Einstein gravity as a special case. Examples contain theories with generalizeations of Riemannian geometry. The 0-tensor case is related to dilaton gravity. These theories can give rise to new types of spontaneous Lorentz breaking and might be relevant for ``dark'' sector cosmology.

Action of Hopf on the twisted modular Hecke operator

Let Gamma subset of SL2(Z) be a principal congruence subgroup. For each sigma is an element of SL2(Z), we introduce the collection A(sigma)(Gamma) of modular Hecke operators twisted by sigma. Then, A(sigma)(Gamma) is a right A(Gamma)-module, where A(Gamma) is the modular Hecke algebra introduced by Connes and Moscovici. Using the action of a Hopf algebra h(0) on A(sigma)(Gamma), we define reduced Rankin-Cohen brackets on A(sigma)(Gamma). Moreover A(sigma)(Gamma) carries an action of H 1, where H 1 is the Hopf algebra of foliations of codimension 1. Finally, we consider operators between the levels A(sigma)(Gamma), sigma is an element of SL2(Z). We show that the action of these operators can be expressed in terms of a Hopf algebra h(Z).

Quantum stochastic calculus associated with quadratic quantum noises

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie dagger-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Ito formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus. (C) 2016 AIP Publishing LLC.

Counting zero kernel pairs over a finite field

Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field. We give a new and elementary proof of the same formula by solving the equivalent problem of determining the number of so called zero kernel pairs over a finite field. We show that the problem is, equivalent to certain other enumeration problems and outline a connection with some recent results of Guo and Yang on the natural density of rectangular unimodular matrices over F-qx]. We also propose a new conjecture on the density of unimodular matrix polynomials. (C) 2016 Elsevier Inc. All rights reserved.

Análisis espacial y multitemporal de la cobertura y uso del suelo con base en imágenes de satélites en la subcuenca Río Dipilto, Nueva Segovia, Nicaragua (1993, 2000, 2011)

La cuantificación del cambio de uso del suelo presenta aún altos niveles de incertidumbre, lo que repercute por ejemplo en la estimación de las emisiones de CO 2 . En este estudio se desarrollaron métodos, basados en imágenes de satélite y trabajo de campo, para estimar la tasa de cambio de la cobertura y uso del suelo, y las emisiones de CO 2 en la subcuenca río Dipilto, Nueva Segovia. La superficie de los tipos de vegetación se determinó con imágenes Landsat. Se utilizaron datos de carbono de nueve parcelas de muestreo en bosque de pino que fueron correlacionadas, para establecer un modelo de regresión lineal con el objetivo de estimar el Stock de Carbono. La sobreposición y algebra de mapas se utilizó para el escenario de emisiones de CO 2 . El análisis con imágenes de los años 1993, 2000 y 2011 reveló que durante es tos 18 años la velocidad a la que se perdieron los bosques latifoliados cerrado fue variable. Durante los primeros 7 años (1993 a 2000) se registró un aumento de 99.95 ha , que corresponde a una tasa de deforestación de - 1.45 % anual. Durante los últimos once años (2000 a 2011) esta cantidad cambió totalmente, ya que se eliminaron 331.76 h a , que corresponde a una tasa de deforestación anual de 3.41 %. Finalmente considerando el periodo de análisis, se transformaron más de 232.01 h a por año, correspondiente a u na tasa de deforestación anual de 1.55 %. La imagen de 2011 demostró que las reservas o Stock de C oscila entre 40 - 150 t/ha. Este intervalo de valores fue estimado por un modelo de regresión con razonable ajuste (R2 = 0.73 ), cuyas variables independientes fueron la reflectancia de las distintas bandas como índices de vegetación e infrarrojo cercano. Las pérdidas de C se estimaron en intervalos 1 - 191 t/h a en 20.76% del área. El 32.85% del área se mantuvo estable y 46.39% ganancias de 1 - 210 t/ha. La combinación de imágenes de resolución espacial media como son las de la serie Landsat para definir trayectorias de cambio de la cobertura del suelo, es una opción viable para la solución de interrogantes relacionadas con el cambio climático, tales como la estimación de las emisiones de CO 2 derivadas del cambio de uso del suelo.

Evaluación de la influencia de la fertilización en el vivero sobre la calidad de la planta de Pinus oocarpa Schiede y su desarrollo inicial en campo

En la finca San Nicolás ubicada en el municipio de San Fernando, departamento de Nueva Segovia, Nicaragua, se realizó el estudio con la plantas de la especie de pino (Pinus oocarpa) con el objetivo de analizar el efecto de la fertilización en el vivero sobre la calidad de la planta de estas plantas y su desarrollo inicial en plantación. Este estudio se desarrolló en dos etapas, la primera en vivero donde se evaluaron tres niveles de fertilización: F0 (sin fertilización), F1 (100 gr. de 18-46-0 en 5 lt de agua (20 cc por planta), a un mes después de la germinación) y F2 (Una segunda fertilización dos meses después de la primera con la misma dosis); las variables evaluadas en esta etapa fueron altur a, diámetro y peso de la planta con las cuales se determinaron los índices de calidad de plantas y la segunda etapa, en plantación donde se evaluó su desempeño en los primeros cuatro meses en plantación tomando en cuenta su sobrevivencia, incremento en altura y diámetro y la condición fitosanitaria. Las plantas con mayor fertilización presentaron mayor altura, diámetro y biomasa aérea y radical en vivero que las plantas con una y sin fertilización. La fertilización en vivero influyó en la calidad de las plantas resultando las plantas con doble fertilización con un índice de calidad de Dickson de 1.66, siendo estas las de mejor calidad; el índice de lignificación influyó en la sobre vivencia de las plantas en plantación donde la mejor lignificadas fueron las plantas sin fertilización que presentaron un valor de 31.08%, las cuales en plantación fueron las plantas con mayor porcentaje de sobrevivencia durante el periodo de evaluación con 97.90%, así mismo estas plantas fueron las que mejor estado fitosanitario presentaron. Las plantas que presentaron un incremento más ace lerado tanto en diámetro como en altura en la etapa inicial de plantación fueron las plantas que en vivero obtuvieron la menor calidad con valores de incremento periódico mensual en altura y diámetro de 6.81 y 0.94 respectivamente. La fertilización produce plantas más grandes, con mayores contenidos de nutrientes y una mayor capacidad de producción de nuevas raíces, sin embargo su capacidad de resistir estrés a la hora de ser trasladadas a la plantación, disminuye, afectando el comportamiento de esta.

Generalized rayleigh principle and its applications

In this paper, we mainly deal with cigenvalue problems of non-self-adjoint operator. To begin with, the generalized Rayleigh variational principle, the idea of which was due to Morse and Feshbach, is examined in detail and proved more strictly in mathematics. Then, other three equivalent formulations of it are presented. While applying them to approximate calculation we find the condition under which the above variational method can be identified as the same with Galerkin's one. After that we illustrate the generalized variational principle by considering the hydrodynamic stability of plane Poiseuille flow and Bénard convection. Finally, the Rayleigh quotient method is extended to the cases of non-self-adjoint matrix in order to determine its strong eigenvalne in linear algebra.

Guide to best practices for ocean CO2 measurements

CHAP 1 - Introduction to the Guide CHAP 2 - Solution chemistry of carbon dioxide in sea water CHAP 3 - Quality assurance CHAP 4 - Recommended standard operating procedures (SOPs) SOP 1 - Water sampling for the parameters of the oceanic carbon dioxide system SOP 2 - Determination of total dissolved inorganic carbon in sea water SOP 3a - Determination of total alkalinity in sea water using a closed-cell titration SOP 3b - Determination of total alkalinity in sea water using an open-cell titration SOP 4 - Determination of p(CO2) in air that is in equilibrium with a discrete sample of sea water SOP 5 - Determination of p(CO2) in air that is in equilibrium with a continuous stream of sea water SOP 6a - Determination of the pH of sea water using a glass/reference electrode cell SOP 6b - Determination of the pH of sea water using the indicator dye m-cresol purple SOP 7 - Determination of dissolved organic carbon and total dissolved nitrogen in sea water SOP 7 en Español - Determinacion de carbono organico disuelto y nitrogeno total disuelto en agua de mar SOP 11 - Gravimetric calibration of the volume of a gas loop using water SOP 12 - Gravimetric calibration of volume delivered using water SOP 13 - Gravimetric calibration of volume contained using water SOP 14 - Procedure for preparing sodium carbonate solutions for the calibration of coulometric CT measurements SOP 21 - Applying air buoyancy corrections SOP 22 - Preparation of control charts SOP 23 - Statistical techniques used in quality assessment SOP 24 - Calculation of the fugacity of carbon dioxide in the pure gas or in air CHAP 5 - Physical and thermodynamic data Errata - to the hard copy of the Guide to best practices for ocean CO2 measurements