Task A, Analysis of C-W Data, Final Report

The object of this investigation is to obtain additional information concerning the effects of aurora on high frequency radio signals which is essential to a complete understanding of new modes of propagation that have tactical and strategic applications.Signal Corps Contract No. DA-36-039-SC-71137 Department of the Army Project No. 3-99-03-022 Signal Corps Project No. 182BLIST OF FIGURES -- [SECTION I] PURPOSE -- [SECTION II] ABSTRACT -- [SECTION III] PUBLICATIONS. LECTURES, REPORTS AND CONFERENCES -- [SECTION IV] FACTUAL DATA : 1. Signal Outage Time on Short Paths and Blackouts Compared for Years of High and Low Solar Activity. ; 2. Study of Possible Relations between Transmission over Long Paths and Ionospheric,Magnetic and Solar Phenomena. ; 3. Study of Fluctuation Indices. ; 4. Effects of Ionospheric Absorption and Irregularities on 4 Mc/s Short Path Transmission. ; 5. F2 Region Parameters at College for the Period June 1941 Through December 1956. ; 6. Tables of Monthly Medians Signal Strength June 1949-December 1950 and January 1954-October 1955. -- [SECTION V] OVERALL CONCLUSIONS -- [SECTION VI] RECOMMENDATIONS -- [SECTION VII] PERSONNELYe

Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps

In this Letter we propose a systematic approach for detecting and calculating preserved measures and integrals of a rational map. The approach is based on the use of cofactors and Discrete Darboux Polynomials and relies on the use of symbolic algebra tools. Given sufficient computing power, all rational preserved integrals can be found. We show, in two examples, how to use this method to detect and determine preserved measures and integrals of the considered rational maps.Comment: 8 pages, 1 Figur

Computer Simulation of the Cool Down of the ATLAS Liquid Argon Barrel Calorimeter

The ATLAS electromagnetic barrel calorimeter consists of a liquid argon detector with a total mass of 120 tonnes. This highly complicated structure, fabricated from copper, lead, stainless steel and glass-fiber reinforced epoxy will be placed in an aluminum cryostat. The cool down process of the detector will be limited by the maximum temperature differences accepted by the composite structure so as to avoid critical mechanical stresses. A computer program simulating the cool down of the detector by calculating the local heat transfer throughout a simplified model has been developed. The program evaluates the cool down time as a function of different contact gasses filling the spaces within the detector

Deep learning as optimal control problems

We briefly review recent work where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We report here new preliminary experiments with implicit symplectic Runge-Kutta methods. In this paper, we discuss ongoing and future research in this area

Structure-preserving deep learning

Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems involved in applying deep learning: most deep learning methods require the solution of hard optimisation problems, and a good understanding of the tradeoff between computational effort, amount of data and model complexity is required to successfully design a deep learning approach for a given problem. A large amount of progress made in deep learning has been based on heuristic explorations, but there is a growing effort to mathematically understand the structure in existing deep learning methods and to systematically design new deep learning methods to preserve certain types of structure in deep learning. In this article, we review a number of these directions: some deep neural networks can be understood as discretisations of dynamical systems, neural networks can be designed to have desirable properties such as invertibility or group equivariance, and new algorithmic frameworks based on conformal Hamiltonian systems and Riemannian manifolds to solve the optimisation problems have been proposed. We conclude our review of each of these topics by discussing some open problems that we consider to be interesting directions for future research

Lawrence Berkeley laboratory neutral-beam engineering test facility power-supply system

The Lawrence Berkeley Laboratory is upgrading the neutral beam source test facility (NBSTF) into a neutral beam engineering test facility (NBETF) with increased capabilities for the development of neutral beam systems. The NBETF will have an accel power supply capable of 170 kV, 70 A, 30 sec pulse length, 10% duty cycle; and the auxiliary power supplies required for the sources. This paper describes the major components, their ratings and capabilities, and the flexibility designed to accomodate the needs of source development

Backward error analysis and the substitution law for Lie group integrators

Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio

On post-Lie algebras, Lie--Butcher series and moving frames

Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on differential manifolds. They have been studied extensively in recent years, both from algebraic operadic points of view and through numerous applications in numerical analysis, control theory, stochastic differential equations and renormalization. Butcher series are formal power series founded on pre-Lie algebras, used in numerical analysis to study geometric properties of flows on euclidean spaces. Motivated by the analysis of flows on manifolds and homogeneous spaces, we investigate algebras arising from flat connections with constant torsion, leading to the definition of post-Lie algebras, a generalization of pre-Lie algebras. Whereas pre-Lie algebras are intimately associated with euclidean geometry, post-Lie algebras occur naturally in the differential geometry of homogeneous spaces, and are also closely related to Cartan's method of moving frames. Lie--Butcher series combine Butcher series with Lie series and are used to analyze flows on manifolds. In this paper we show that Lie--Butcher series are founded on post-Lie algebras. The functorial relations between post-Lie algebras and their enveloping algebras, called D-algebras, are explored. Furthermore, we develop new formulas for computations in free post-Lie algebras and D-algebras, based on recursions in a magma, and we show that Lie--Butcher series are related to invariants of curves described by moving frames.Comment: added discussion of post-Lie algebroid

Competition-induced stress does not explain deceptive alarm calling in tufted capuchin monkeys

Tactical deception has long attracted interest because it is often assumed to entail complex cognitive mechanisms. However, systematic evidence of tactical deception is rare and no study has attempted to determine whether such behaviours may be underpinned by relatively simple mechanisms. This study examined whether deceptive alarm calling among wild tufted capuchin monkeys, Cebus apella nigritus, feeding on contestable food resources can be potentially explained by a physiological mechanism, namely increased activation in the adrenocortex and the resulting production of glucocorticoids (GCs; ‘stress hormones’). This was tested experimentally in Iguazu? National Park, Argentina, by manipulating the potential for contest competition over food and noninvasively monitoring GC production through analysis of faecal hormone metabolites. If deceptive false alarms are indeed associated with adreno- cortical activity, it was predicted that the patterns of production of these calls would match the patterns of GC output, generally being higher in callers than noncallers in cases in which food is most contestable, and specifically being higher in callers on those occasions when a deceptive false alarm was produced. This hypothesis was not supported, as (1) GC output was significantly lower in association with the experimental introduction of contestable resources than in natural contexts wherein the potential for contest is lower, (2) within experimental contexts, there was a nonsignificant tendency for noncallers to show higher GC output than callers when food was most contestable, and (3) individuals did not show higher GC levels in cases in which they produced deceptive alarms relative to cases in which they did not. A learned association between the production of alarms and increased access to food may be the most likely cognitive explanation for this case of tactical deception, although unexplored physiological mechanisms also remain possible