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  From Velocities to Fluxions

  Marco Panza

  "Though the De Methodis results, for its essential structure and content, from a re-elaboration of a previous unfinished treatise composed in the Fall of 1666—now known, after Whiteside, as The October 1666 tract on fluxions ([22], I, pp. 400-448)—, the introduction of the term ‘fluxion’ goes together with an important conceptual change concerned with Newton’s understanding of his own achievements. I shall argue that this change marks a crucial step in the origins of analysis, conceived as an autonomous mathematical theory."

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  Distributed Simulated Annealing with MapReduce

  Atanas Radenski

  Simulated annealing’s high computational intensity has stimulated researchers to experiment with various parallel and distributed simulated annealing algorithms for shared memory, message-passing, and hybrid-parallel platforms. MapReduce is an emerging distributed computing framework for large-scale data processing on clusters of commodity servers; to our knowledge, MapReduce has not been used for simulated annealing yet. In this paper, we investigate the applicability of MapReduce to distributed simulated annealing in general, and to the TSP in particular. We (i) design six algorithmic patterns of distributed simulated annealing with MapReduce, (ii) instantiate the patterns into MR implementations to solve a sample TSP problem, and (iii) evaluate the solution quality and the speedup of the implementations on a cloud computing platform, Amazon’s Elastic MapReduce. Some of our patterns integrate simulated annealing with genetic algorithms. The paper can be beneficial for those interested in the potential of MapReduce in computationally intensive nature-inspired methods in general and simulated annealing in particular.

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  Difference Equations in Spaces of Regular Functions: A Tribute To Salvatore Pincherle

  Irene Sabadini and Daniele C. Struppa

  Pincherle studies the surjectivity of a difference operator with constant coefficients in the space of holomorphic functions. In this paper, we discuss how this work can be rephrased in the context of modern functional analysis and we conclude by extending his results and we show that difference equations act surjectively on the space of quaternionic regular functions.

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  Lamberto Cattabriga and the Theory of Linear Constant Coefficients Partial Differential Equations

  Daniele C. Struppa

  This article focuses on the contributions of Cattabriga and De Giorgi to the study of surjectivity of linear constant coefficients partial differential equations on spaces of real analytic functions. Their contributions are placed in the context of the concurrent development of the general theory of Analytically Uniform spaces due to Ehrenpreis.

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  A Complex Analysis Problem Book

  Daniel Alpay

  This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises show the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.

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  Atmospheric Signals Associated with Major Earthquakes. A Multi-Sensor Approach

  Dimitar Ouzounov, Sergey Pulinets, Kasumi Hattori, Menas Kafatos, and Patrick Taylor

  We are studying the possibility of a connection between atmospheric observation recorded by several ground and satellites as earthquakes precursors. Our main goal is to search for the existence and cause of physical phenomenon related to prior earthquake activity and to gain a better understanding of the physics of earthquake and earthquake cycles. The recent catastrophic earthquake in Japan in March 2011 has provided a renewed interest in the important question of the existence of precursory signals preceding strong earthquakes. We will demonstrate our approach based on integration and analysis of several atmospheric and environmental parameters that were found associated with earthquakes. These observations include: thermal infrared radiation, radon! ion activities; air temperature and humidity and a concentration of electrons in the ionosphere. We describe a possible physical link between atmospheric observations with earthquake precursors using the latest Lithosphere-Atmosphere-Ionosphere Coupling model, one of several paradigms used to explain our observations. Initial results for the period of2003-2009 are presented from our systematic hind-cast validation studies. We present our findings of multi-sensor atmospheric precursory signals for two major earthquakes in Japan, M6.7 Niigata-ken Chuetsu-oki of July16, 2007 and the latest M9.0 great Tohoku earthquakes of March 11,2011.

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  Shared Memory, Message Passing, and Hybrid Merge Sorts for Standalone and Clustered SMPs

  Atanas Radenski

  While merge sort is well-understood in parallel algorithms theory, relatively little is known of how to implement parallel merge sort with mainstream parallel programming platforms, such as OpenMP and MPI, and run it on mainstream SMP-based systems, such as multi-core computers and multi-core clusters. This is misfortunate because merge sort is not only a fast and stable sort algorithm, but it is also an easy to understand and popular representative of the rich class of divide-and-conquer methods; hence better understanding of merge sort parallelization can contribute to better understanding of divide-and-conquer parallelization in general. In this paper, we investigate three parallel merge-sorts: shared memory merge sort that runs on SMP systems with OpenMP; message-passing merge sort that runs on computer clusters with MPI; and combined hybrid merge sort, with both OpenMP and MPI, that runs on clustered SMPs. We have experimented with our parallel merge sorts on a dedicated Rocks SMP cluster and on a virtual SMP luster in the Amazon Elastic Compute Cloud. In our experiments, shared memory merge sort with OpenMP has achieved best speedup. We believe that we are the first ones to concurrently experiment with - and compare – shared memory, message passing, and hybrid merge sort. Our results can help in the parallelization of specific practical merge sort routines and, even more important, in the practical parallelization of other divide-and-conquer algorithms for mainstream SMP-based systems.

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  What More There Is in Early-Modern Algebra than its Literal Formalism

  Marco Panza

  "There are two views about early-modern algebra very often endorsed (either explicitly or implicitly). The former is that in early-modern age, algebra and geometry were different branches of mathematics and provided alternative solutions for many problems. The latter is that early-modern algebra essentially resulted from the adoption of a new literal formalism. My present purpose is to question the latter. In doing that, I shall also implicitly undermine the former."

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  Isaac Barrow and the Bounds of Geometry

  Marco Panza

  I discuss two examples advanced by Barrow in his Lectiones Mathematicæ in order to argue for the (foundational) primacy of geometry over arithmetic.

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  Digital CS1 Study Pack Based on Moodle and Python

  Atanas Radenski

  We believe that CS1 courses can be made more attractive to students:

  • by teaching a highly interactive scripting language – Python
  • by using an open source course management system - such as Moodle - to make all course resources available in a comprehensive digital study pack, and
  • by offering detailed self-guided online labs

  We have used Moodle [1] and Python [2] to develop a "Python First" digital study pack [3] which comprises a wealth of new, original learning modules: extensive e-texts, detailed self-guided labs, numerous sample programs, quizzes, and slides. Our digital study pack pedagogy is described in recent ITiCSE and SIGCSE papers [4, 5]. “Python First” digital packs instances have already been adopted by instructors at several universities. This demonstration reveals instructor and student perspectives to the "Python First" digital pack. In particular, we demonstrate how instructors can use standard Moodle functionality to customize and manage digital packs. We also demonstrate several Moodlesupported, Python-based self-guided labs.

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  Nombres. Eléments de mathématiques pour philosophes

  Marco Panza

  Livre tiré des notes de cours de mathématiques pour philosophes (première année de Deug) tenus à Nantes entre 1993 et 2001

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  Some Sober Conceptions of Mathematical Truth

  Marco Panza

  It is not sufficient to supply an instance of Tarski’s schema, ⌈“p” is true if and only if p⌉ for a certain statement in order to get a definition of truth for this statement and thus fix a truth-condition for it. A definition of the truth of a statement x of a language L is a bi-conditional whose two members are two statements of a meta-language L’. Tarski’s schema simply suggests that a definition of truth for a certain segment x of a language L consists in a statement of the form: ⌈v(x) is true if and only if τ(x)⌉, where ⌈v(x)⌉ is the name of x in L’ and τ(x) is a function τ: S → S’ (S and S’ being the sets of the statements respectively of L end L’) which associates to x the statement of L’ expressed by the same sentence as that which expresses x in L. In order to get a definition of truth for x and thus fix a truth-condition for it, one has thus to specify the function τ. A conception of truth for a certain class X of mathematical statements is a general condition imposed on the truth-conditions for the statements of this class. It is advanced when the nature of the function τ is specified for the statements belonging to X. It is sober when there is no need to appeal to a controversial ontology in order to describe the conditions under which the statement τ(x) is assertible. Four sober conceptions of truth are presented and discussed.

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  Triplet Superconductors: Exploitable Basis for Scaleable Quantum Computing

  Kent S. Wood, Huey-Daw Wu, Frank F. Golf, Hiroshi Yaguchi, Yoshiteru Maeno, and Armen Gulian

  Triplet-pairing superconductors with broken time-reversal symmetry such as ruthenates, Sr₂RuO₄, have potential application as a basis for quantum computing (QC). The prerequisite here is the requirement of achieving superconductivity in single domain mesoscopic samples. One possible fabrication approach is application of thin film technologies. Initially some attempts were made by other groups to achieve epitaxial Sr₂RuO₄ films by pulsed laser deposition, but they failed. We propose an alternative method that makes small pieces of the material from larger crystals without destroying the crystal Meanwhile, experimental demonstration of quantum dynamics of triplet superconductors, such as Sr₂RuO₄, requires small structures on the order of the size of a single domain. QC done using triplet state superconductivity is potentially advantageous because the qubit is only a tiny piece of metal, yet a complete QC system can be implemented building upon this kind of qubit as the foundation. The supporting technology for initiation, entanglement and readout is described. Some of it involves application of ferromagnetic components, used in gate mechanisms. Ultimately, the approach presented here brings together triplet superconductivity in mesoscopic structures with ferromagnetic techniques.

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  Nonequilibrium Electrons and Phonons in Superconductors: Selected Topics in Superconductors

  Armen Gulian and Gely F. Zharkov

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  The Origins of Analytical Mechanics in 18th Century

  Marco Panza

  An overview of the history of analytical mechanics in 18th century.

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  Mathematisation of the Science of Motion and the Birth of Analytical Mechanics : A Historiographical Note

  Marco Panza

  Usually, one speaks of mathematization of a natural or social science to mean that mathematics comes to be a tool of such a science: the language of mathematics is used to formulate its results, and/or some mathematical techniques is employed to obtain these results.

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  Massive Date Sets Issues in Earth Observing

  Ruixin Yang and Menas Kafatos

  Current and next decade global Earth observing, other remote sensing and related climate analysis data collected by space and operational U.S. agencies such as NASA and NOAA, the European ESA, the Japanese NASDA and other international agency missions of India, China, Russia, etc. will reach unprecedented data volumes, exceeding many petabytes. This is rushing in a new era in Earth system science. Along with the technology and data volumes afforded by remote sensing, there has been an unprecedented increase of capabilities in distributed data systems in the last few years. The existence of the Internet and the World Wide Web afford users access to data at diverse distributed sites that would had been very difficult in the past and only available to specialists. These data can be accessed by a variety of scientists, applications experts and the general public. Yet, the unprecedented large volumes of such missions are also presenting formidable challenges to wide user access and require both higher bandwidths of future Internet systems as well as more focused, user-centered data productions. Specialized data productions are best achieved in federated data systems. The large data volumes present a challenge of access, storage and distribution. What is most important is not just the volume of the data itself but the information they contain. A data system's usefulness is related to the ease that its users can search and access products and as such obtain information on the actual content of data before proceeding to order large volumes of data sets which may or may not serve their needs. Here we explore different functionalities in distributed Earth observing data systems and associated interoperability options. As an example, we examine options in the Earth Science Information Partners Federation (ESIPs) funded by NASA to extend the usage of NASA remote sensing data holdings. Results of several interoperability options applicable to federated systems are also presented. We also examine challenges presented by the use of regional remote sensing missions such as hyperspectral imaging.

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  The Schur Algorithm, Reproducing Kernel Spaces and System Theory

  Daniel Alpay

  The same positive functions (in the sense of reproducing kernel spaces) appear in a natural way in two different domains, namely the modeling of time-invariant dissipative linear systems and the theory of linear operators. We use the associated reproducing kernel Hilbert spaces to study the relationships between these domains. The inverse scattering problem plays a key role in the exposition. The reproducing kernel approach allows us to tackle in a natural way more general cases, such as nonstationary systems, the case of a non-positive metric and the case of pairs of commuting nonself-adjoint operators.

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  Quasi-Coisometric Realizations of Upper Triangular Matrices

  Daniel Alpay and Y. Peretz

  In this paper we study analogs of de Branges-Rovnyak spaces and prove a realization theorem in the setting of upper triangular matrices.

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  Derivation of Secure Parallel Applications by Means of Module Embedding

  Atanas Radenski

  An enhancement to modular languages called module embedding facilitates the development and utilization of secure generic parallel algorithms.

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  Inner Region Accretion Flows onto Black Holes

  Menas Kafatos and Prasad Subramanian

  We examine here the inner region accretion flows onto black holes. A variety of models are presented. We also discuss viscosity mechanisms under a variety of circumstances, for standard accretion disks onto galactic black holes and supermassive black holes and hot accretion disks. Relevant work is presented here on unified aspects of disk accretion onto supermassive black holes and the possible coupling of thick disks to beams in the inner regions. We also explore other accretion flow scenarios. We conclude that a variety of scenarios yield high temperatures in the inner flows and that viscosity is likely not higher than alpha ∼ 0.01.

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  The Non-local Universe: The New Physics and Matters of the Mind

  Robert Nadeau and Menas Kafatos

  Classical physics states that physical reality is local, or that a measurement at one point in space cannot cannot influence what occurs at another beyond a fairly short distance. Until recently this seemed like an immutable truth in nature. However, in 1997 experiments were conducted in which light particles (photons) originated under certain conditions and traveled in opposite directions to detectors located about seven miles apart. The amazing results indicated that the photons "interacted" or "communicated" with one another instantly or "in no time," leading to the revelation that physical reality is non-local--a discovery that Robert Nadeau and Menas Kafatos view as "the most momentous in the history of science."

  In pursuing this groundbreaking argument, the authors provide a fascinating history of developments that led to the discovery of non-locality and the sometimes heated debate between the great scientists responsible for these discoveries. What this new knowledge reveals, the authors conclude, is that the connection between mind and nature is far more intimate than we previously dared to imagine. What they offer is a revolutionary look at the implications of non-locality, implications that reach deep into that most intimate aspect of humanity--consciousness.

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  Development and Utilization of Parallel Generic Algorithms for Scientific Computations

  Atanas Radenski, Andrew Vann, and Boyana Norris

  We develop generic parallel algorithms as extensible modules that encapsulate related classes and parallel methods. Extensible modules define common parallel structures, such as meshes, pipelines, or master-server networks in problem-independent manner. Such modules can be extended with sequential domain-specific code in order to derive particular parallel applications. In this paper, we first outline the essence of extensible modules. Then, we focus on a case study of the cellular automaton, a message-parallel generic algorithm from which we derive diverse parallel scientific applications.

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  Parallel Probabilistic Computations on a Cluster of Workstations

  Atanas Radenski, Andrew Vann, and Boyana Norris

  Probabilistic algorithms are computationally intensive approximate methods for solving intractable problems. Probabilistic algorithms are excellent candidates for cluster computations because they require little communication and synchronization. It is possible to specify a common parallel control structure as a generic algorithm for probabilistic cluster computations. Such a generic parallel algorithm can be glued together with domain-specific sequential algorithms in order to derive approximate parallel solutions for different intractable problems.

  In this paper we propose a generic algorithm for probabilistic computations on a cluster of workstations. We use this generic algorithm to derive specific parallel algorithms for two discrete optimization problems: the knapsack problem and the traveling, salesperson problem. We implement the algorithms on clusters of Sun Ultra SPARC-1 workstations using PVM, the parallel virtual machine software package. Finally, we measure the parallel efficiency of the cluster implementation.

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  Is Oberon as Simple as Possible?

  Atanas Radenski

  The design of the programming language Oberon was led by the quote by Albert Einstein: 'make it as simple as possible, but not simpler'. The objective of this paper is to analyze some design solutions and propose alternatives which could both simplify and strengthen the language without making it simpler than possible. The paper introduces one general concept, the module type, which can be used to represent records, modules, and eventually procedures. Type extension is redefined in terms of component nesting and incomplete designators. As a result, type extension supports multiple inheritance.