Linear scaling computation of the Fock matrix. IX. Parallel computation of the Coulomb matrix

We present parallelization of a quantum-chemical tree-code [J. Chem. Phys. {\bf 106}, 5526 (1997)] for linear scaling computation of the Coulomb matrix. Equal time partition [J. Chem. Phys. {\bf 118}, 9128 (2003)] is used to load balance computation of the Coulomb matrix. Equal time partition is a measurement based algorithm for domain decomposition that exploits small variation of the density between self-consistent-field cycles to achieve load balance. Efficiency of the equal time partition is illustrated by several tests involving both finite and periodic systems. It is found that equal time partition is able to deliver 91 -- 98 % efficiency with 128 processors in the most time consuming part of the Coulomb matrix calculation. The current parallel quantum chemical tree code is able to deliver 63 -- 81% overall efficiency on 128 processors with fine grained parallelism (less than two heavy atoms per processor).Comment: 7 pages, 6 figure

About the ergodic regime in the analogical Hopfield neural networks. Moments of the partition function

In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage case, when the number of patterns is linearly diverging with the number of neurons. We study the infinite volume behavior of the normalized momenta of the partition function. We find a region in the parameter space where the free energy density in the infinite volume limit is self-averaging around its annealed approximation, as well as the entropy and the internal energy density. Moreover, we evaluate the corrections to their extensive counterparts with respect to their annealed expressions. The fluctuations of properly introduced overlaps, which act as order parameters, are also discussed.Comment: 15 page

SPHERICAL IMAGES FOR CULTURAL HERITAGE: SURVEY AND DOCUMENTATION WITH THE NIKON KM360

The work presented here focuses on the analysis of the potential of spherical images acquired with specific cameras for documentation and three-dimensional reconstruction of Cultural Heritage. Nowadays, thanks to the introduction of cameras able to generate panoramic images automatically, without the requirement of a stitching software to join together different photos, spherical images allow the documentation of spaces in an extremely fast and efficient way. In this particular case, the Nikon Key Mission 360 spherical camera was tested on the Tolentini's cloister, which used to be part of the convent of the close church and now location of the Iuav University of Venice. The aim of the research is based on testing the acquisition of spherical images with the KM360 and comparing the obtained photogrammetric models with data acquired from a laser scanning survey in order to test the metric accuracy and the level of detail achievable with this particular camera. This work is part of a wider research project that the Photogrammetry Laboratory of the Iuav University of Venice has been dealing with in the last few months; the final aim of this research project will be not only the comparison between 3D models obtained from spherical images and laser scanning survey's techniques, but also the examination of their reliability and accuracy with respect to the previous methods of generating spherical panoramas. At the end of the research work, we would like to obtain an operational procedure for spherical cameras applied to metric survey and documentation of Cultural Heritage

Spin Glass Computations and Ruelle's Probability Cascades

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.Comment: 20 page

On the Thermodynamic Limit in Random Resistors Networks

We study a random resistors network model on a euclidean geometry \bt{Z}^d. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per unit volume is finite almost surely and in the mean. Moreover, we show that for a particular thermodynamic limit the result is also independent of the boundary conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty', revised version to appear in Journal of Physics

From point cloud to digital fabrication: A tangible reconstruction of Ca' Venier dei Leoni, the Guggenheim Museum in Venice

The paper describes how new digital methodologies can be used within the field of Cultural Heritage, not only with the aim of documenting the actual state of an architecture but to review the past transformations it has undergone, conserving and representing these histories as well. The premise to conservation and enhancement of our Heritage is a deep study in terms of position, shape, colour, and also of the historical and artistic features. Survey methods have acquired data acquisition techniques in line with technological progress: today's electronic and IT technologies, that are the tools of modern Geomatics, allow the effective survey and representation of 3D objects, from architectural structures to sculptures or archaeological finds. Over the last few years, the methodologies of acquisition and integrated representation for 3D patrimony documentation have developed and consolidated considerably: the possibilities of the digital realm can augment the understanding and the valorisation of a monument. The specific case offered in the present paper, Ca' Venier dei Leoni, the palace where is the Guggenheim Museum in Venice, is a significant example. It suggests not only the theme of the "no longer existing", or better never built, but also the opportunity to formulate hypotheses regarding its implementation and the impact that the palace would have had in the Venetian contest

Tooteko: A case study of augmented reality for an accessible cultural heritage. Digitization, 3D printing and sensors for an audio-tactile experience

Tooteko is a smart ring that allows to navigate any 3D surface with your finger tips and get in return an audio content that is relevant in relation to the part of the surface you are touching in that moment. Tooteko can be applied to any tactile surface, object or sheet. However, in a more specific domain, it wants to make traditional art venues accessible to the blind, while providing support to the reading of the work for all through the recovery of the tactile dimension in order to facilitate the experience of contact with art that is not only "under glass." The system is made of three elements: A high-tech ring, a tactile surface tagged with NFC sensors, and an app for tablet or smartphone. The ring detects and reads the NFC tags and, thanks to the Tooteko app, communicates in wireless mode with the smart device. During the tactile navigation of the surface, when the finger reaches a hotspot, the ring identifies the NFC tag and activates, through the app, the audio track that is related to that specific hotspot. Thus a relevant audio content relates to each hotspot. The production process of the tactile surfaces involves scanning, digitization of data and 3D printing. The first experiment was modelled on the facade of the church of San Michele in Isola, made by Mauro Codussi in the late fifteenth century, and which marks the beginning of the Renaissance in Venice. Due to the absence of recent documentation on the church, the Correr Museum asked the Laboratorio di Fotogrammetria to provide it with the aim of setting up an exhibition about the order of the Camaldolesi, owners of the San Michele island and church. The Laboratorio has made the survey of the facade through laser scanning and UAV photogrammetry. The point clouds were the starting point for prototypation and 3D printing on different supports. The idea of the integration between a 3D printed tactile surface and sensors was born as a final thesis project at the Postgraduate Mastercourse in Digital Architecture of the University of Venice (IUAV) in 2012. Now Tooteko is now a start up company based in Venice, Italy

GEOMATICS TECHNIQUES FOR THE ENHANCEMENT AND PRESERVATION OF CULTURAL HERITAGE

Abstract. The deep knowledge of Cultural Heritage, with historical research and interpretative analysis of materials, is fundamental to know the state of conservation and to plan potential restoration interventions. In the last years, thanks to the fast and continuous technological development, the metrical survey had a significant increase in this particular field: in fact, 3D digital acquisition allows to study some aspects otherwise difficult to investigate in a detailed way.In this research, we will explain the methodology used for the ceiling's survey of the Sala Capitolare of the Scuola Grande di San Rocco in Venice, focusing on the support structure of Tintoretto's paintings, anchored to a wooden system of Palladian trusses. The complexity of this Venetian architecture, its considerable dimension, the richness of decorations and the particular lighting conditions provided the opportunity of thinking about unconventional choices to apply from time to time and they required the integration of different methodologies: the laser scanning survey and the photogrammetric acquisition, together with a topographic network, allowed to obtain an adequate metric result for the study of the structure in its entirety. Furthermore, it was also decided to test image acquisition with a spherical camera for the documentation of the analysed architecture: this type of information, more related to a viewable aspect than to a metric one, can be presented together with traditional 2D representations to ensure a better enhancement of the achieved results.</p

How glassy are neural networks?

In this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one of a bipartite spin glass (whose parties consist of Ising and Gaussian spins respectively), we give a complete control of the whole annealed region. The strategy explored is based on an interpolation between the bipartite system and two independent spin glasses built respectively by dichotomic and Gaussian spins: Critical line, behavior of the principal thermodynamic observables and their fluctuations as well as overlap fluctuations are obtained and discussed. Then, we move further, extending such an equivalence beyond the critical line, to explore the broken ergodicity phase under the assumption of replica symmetry and we show that the quenched free energy of this (analogical) Hopfield model can be described as a linear combination of the two quenched spin-glass free energies even in the replica symmetric framework

Local Spin Glass Order in 1D

We study the behavior of one dimensional Kac spin glasses as function of the interaction range. We verify by Montecarlo numerical simulations the crossover from local mean field behavior to global paramagnetism. We investigate the behavior of correlations and find that in the low temperature phase correlations grow at a faster rate then the interaction range. We completely characterize the growth of correlations in the vicinity of the mean-field critical region