Modular symbols and Hecke operators

We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and Robert MacPherson.Comment: 11 pp, 2 figures, uses psfrag.st

Development of an electronically-scanned pressure module for operation at cryogenic temperatures

Pressure and temperature characteristics were measured for a number of multichannel electronically scanned pressure sensors. The tests were made on commercially available units designed to operate in a controlled temperature environment. Measurements of zero shift, sensitivity, and nonlinearity for each transducer were taken over a temperature range from 100 K to 340 K using a computer controlled data acquisition system. The units tested failed to meet accuracy specifications over the complete temperature range, which was expected. However, the sensors showed acceptable and predictable behavior over the temperature range from approximately -40 C (233 K) to 70 C (343 K). It was determined that a combination of local heating and accurate temperature monitoring can result in a device that can be compensated for temperature as well as its other physical properties. The design of a prototype for operation in a cryogenic environment is proposed, and a method for compensation is developed

Development and evaluation of silent reading exercises for grade one,

Thesis (M.A.)--Boston Universit

The dynamics of surges in the 3 February 2015 avalanches in Vallee de la Sionne

Five avalanches were artificially released at the Vallée de la Sionne test site in the west of Switzerland on 3 February 2015 and recorded by the GEOphysical flow dynamics using pulsed Doppler radAR Mark 3 radar system. The radar beam penetrates the dilute powder cloud and measures reflections from the underlying denser avalanche features allowing the tracking of the flow at 111 Hz with 0.75 m downslope resolution. The data show that the avalanches contain many internal surges. The large or “major” surges originate from the secondary release of slabs. These slabs can each contain more mass than the initial release, and thus can greatly affect the flow dynamics, by unevenly distributing the mass. The small or “minor” surges appear to be a roll wave-like instability, and these can greatly influence the front dynamics as they can repeatedly overtake the leading edge. We analyzed the friction acting on the fronts of minor surges using a Voellmy-like, simple one-dimensional model with frictional resistance and velocity-squared drag. This model fits the data of the overall velocity, but it cannot capture the dynamics and especially the slowing of the minor surges, which requires dramatically varying effective friction. Our findings suggest that current avalanche models based on Voellmy-like friction laws do not accurately describe the physics of the intermittent frontal region of large mixed avalanches. We suggest that these data can only be explained by changes in the snow surface, such as the entrainment of the upper snow layers and the smoothing by earlier flow fronts

Fitting Voronoi Diagrams to Planar Tesselations

Given a tesselation of the plane, defined by a planar straight-line graph $G$, we want to find a minimal set $S$ of points in the plane, such that the Voronoi diagram associated with $S$ "fits" \ $G$. This is the Generalized Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered recently in \cite{Baner12}. Here we give an algorithm that solves this problem with a number of points that is linear in the size of $G$, assuming that the smallest angle in $G$ is constant.Comment: 14 pages, 8 figures, 1 table. Presented at IWOCA 2013 (Int. Workshop on Combinatorial Algorithms), Rouen, France, July 201

Information capacity in the weak-signal approximation

We derive an approximate expression for mutual information in a broad class of discrete-time stationary channels with continuous input, under the constraint of vanishing input amplitude or power. The approximation describes the input by its covariance matrix, while the channel properties are described by the Fisher information matrix. This separation of input and channel properties allows us to analyze the optimality conditions in a convenient way. We show that input correlations in memoryless channels do not affect channel capacity since their effect decreases fast with vanishing input amplitude or power. On the other hand, for channels with memory, properly matching the input covariances to the dependence structure of the noise may lead to almost noiseless information transfer, even for intermediate values of the noise correlations. Since many model systems described in mathematical neuroscience and biophysics operate in the high noise regime and weak-signal conditions, we believe, that the described results are of potential interest also to researchers in these areas.Comment: 11 pages, 4 figures; accepted for publication in Physical Review

Universal geometric approach to uncertainty, entropy and information

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique "ensemble volume" is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon bounds in quantum and classical information theory; a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles; a geometric derivation of semi-classical uncertainty relations; a new means for defining classical and quantum localization for arbitrary evolution processes; a geometric interpretation of relative entropy; and a new proposed definition for the spot-size of an optical beam. Advantages of the ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10) of published version

Many Roads to Synchrony: Natural Time Scales and Their Algorithms

We consider two important time scales---the Markov and cryptic orders---that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the epsilon-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabilistic property of a process. Rather, it is a topological property and, moreover, it is not computable from any finite-state model other than the epsilon-machine. Via an exhaustive survey, we close by demonstrating that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes. We draw out the roles played in statistical mechanical spin systems by these two complementary length scales.Comment: 17 pages, 16 figures: http://cse.ucdavis.edu/~cmg/compmech/pubs/kro.htm. Santa Fe Institute Working Paper 10-11-02

Analisis Open Government dan E-Government di Indonesia Berdasarkan Kerangka Kerja SDGs: Studi Kasus Desa Melung, Kabupaten Banyumas

This research paper aims to analyze the readiness of local government in Indonesia in order to fulfill the Sustainable Development Goals (SDGs) initiated by the United Nations for rural area level. The author analyzes the open government readiness in Melung Village, Banyumas Districts, Central Java, as a specific case to see the strategy and application of e-government model that was conducted by the government. This paper argues despite the location in the rural area, the government of Melung Village has utilized the system based on the SDGs framework, such as an action to replace paper-based administration into electronic government. This effort was taken to improve the efficiency of public services based on quality and accountability which leads to more active government participation in sharing information with its citizen. Nevertheless, the local government of Melung Village efforts were not good enough since they still need assistance from government and state-owned company. Therefore, the result of the research might strengthen local government institutional and able to fulfill the development goals as is set in SDGs framework