Mathematics, Physics, and Computer Science Faculty Books and Book Chapters

Below you may find selected books and book chapters from Mathematics, Physics, and Computer Science faculty in the Schmid College of Science and Technology.

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"It from Bit" and the Quantum Probability Rule

Matthew S. Leifer

I argue that, on the subjective Bayesian interpretation of probability, "it from bit" requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as noncontextuality, is required. I outline the prospects for a derivation of noncontextuality within this approach and argue that it requires a realist approach to physics, or "bit from it". I then explain why this does not conflict with "it from bit". This version of the essay includes an addendum responding to the open discussion that occurred on the FQXi website. It is otherwise identical to the version submitted to the contest.
Generalized Quaternionic Schur Functions in the Ball and Half-Space and Krein-Langer Factorization

Daniel Alpay, Fabrizio Colombo, and Irene Sabadini

In this paper we prove a new version of Krein-Langer factorization theorem in the slice hyperholomorphic setting which is more general than the one proved in [8]. We treat both the case of functions with κ negative squares defined on subsets of the quaternionic unit ball or on subsets of the half space of quaternions with positive real part. A crucial tool in the proof of our results is the Schauder-Tychonoff theorem and an invariant subspace theorem for contractions in a Pontryagin space.
The Fock Space in the Slice Hyperholomorphic Setting

Daniel Alpay, Fabrizio Colombo, Irene Sabadini, and Guy Salomon

In this paper we introduce and study some basic properties of the Fock space (also known as Segal-Bargmann space) in the slice hyperholomorphic setting. We discuss both the case of slice regular functions over quaternions and also the case of slice monogenic functions with values in a Clifford algebra. In the specific setting of quaternions, we also introduce the full Fock space. This paper can be seen as the beginning of the study of infinite dimensional analysis in the quaternionic setting.
Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis

Daniel Alpay, M. E. Luna-Elizarrarás, Michael Shapiro, and Daniele C. Struppa

"With the goal of providing the foundations for a rigorous study of modules of bicomplex holomorphic functions, we develop here a general theory of functional analysis with bicomplex scalars."
Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis

D. Alpay, M. E. Luna-Elizarrarás, M. Shapiro, and Daniele C. Struppa

This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this may serve for many different developments, just like the usual functional analysis with complex scalars and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schur analysis.
Dust Storms and Their Influence on Atmospheric Parameters Over the Indo-Gangetic plains

Ramesh P. Singh

Dust storms are very common in the northern parts of India, and every year people living in the Indo-Gangetic plains suffer greatly. Dust storms affect day-to-day lives of people living in the Indo-Gangetic plains (IGP) and impact their health. The atmospheric and meteorological parameters are highly influenced by the dust storms and are found to affect the air quality that creates a big health threat and also affects the weather conditions. In this chapter, we discuss use of satellite remote sensing data in monitoring the dust events which occur every year during pre-monsoon season and their impacts on ocean, atmosphere, and meteorological parameters. Long-term effects of such dust storms on the climate of the northern parts of India are discussed. Such dust storms can be easily monitored using satellite data that can be used in issuing warning to the people so that they would not be exposed to such strong dust storms.
Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Atanas Radenski

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.
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.
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.
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.
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.
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.
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.
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.
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.
Nonequilibrium Electrons and Phonons in Superconductors: Selected Topics in Superconductors

Armen Gulian and Gely F. Zharkov
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.
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.
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.
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.
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.
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.
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.
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.
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.