
Forcing Optimality and Brandt's Principle
Domenico Napoletani, Marco Panza, and Daniele C. Struppa
"In a series of previous papers...we described what we call the 'microarray paradigm' and we showed that there are scientific methodological motifs that structure the approach of data analysis to scientific problems. By 'microarray paradigm' we referred to the belief that sufficiently large data collected from a phenomenon allows answering any question about the phenomenon itself. Answers are then found through a process of automatic fitting of the data to models that do not carry any structural understanding beyond the actual solution of the problem. This is a process we suggested to label 'agnostic science'."

Forcing Optimality and Brandt's Principle
Domenico Napoletani, Marco Panza, and Daniele C. Struppa
We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. From these considerations, we extrapolate a principle for general data analysis methods, what we call ‘Brandt’s principle’, namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogenesis, are a natural setting for the application of this principle

A Complex Analysis Problem Book (Second Edition)
Daniel Alpay
This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration.
Benefits of the 2nd edition
Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

An Introduction to Superoscillatory Sequences
Fabrizio Colombo, Irene Sabadini, and Daniele C. Struppa
The notion of superoscillating functions, or more properly of superoscillatory sequences, is a byproduct of Aharonov's theory of weak measurements and weak values in quantum mechanics. Recently, many mathematicians and physicists have begun to pay attention to the mathematical significance of such objects, and have been able to begin a theory of superoscillatory behavior. Not surprisingly, this theory is based on some classical results in Fourier analysis, and it displays interesting connections with the theory of convolution equations. In this paper we will put these connections in a larger context, and show how to use this context to generate a large class of superoscillating sequences. As a concrete example we discuss the Cauchy problem with superoscillatory datum for the harmonic oscillator. Finally, we show how this theory can be generalized to the case of several variables.

Flipped Classroom Model: Effects on Performance, Attitudes and Perceptions in High School Algebra
Peter Esperanza, Khristin Fabian, and Criselda Toto
In this study, we evaluated student perceptions of the flipped classroom model and its effects to students’ performance and attitudes to mathematics. A randomized controlled trial with 91 high school algebra students was conducted. The experimental group participated in a yearlong intervention of the flipped classroom model while the control group followed the traditional lesson delivery. Results of the yearend evaluation of this model showed positive student perceptions. An analysis of covariance of the algebra posttest score with learning model as treatment factor and pretest as covariate resulted in a significant treatment effect at .05 level of significance. A pairedsample ttest by treatment group to compare pretest and posttest math attitude scores resulted in a significant decrease in the control groups’ value of mathematics while the experimental group had a significant positive change in their confidence and enjoyment of mathematics.

An Advanced Complex Analysis Problem Book: Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions
Daniel Alpay
This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

Preface to "Intertwingled: The Work and Influence of Ted Nelson"
Douglas R. Dechow and Daniele C. Struppa
This is the preface to "Intertwingled: The Work and Influence of Ted Nelson", which examines and honors the work and influence of the computer visionary and reimagines its meaning for the future. Emerging from a conference held in 2014 at Chapman University, it includes contributions from worldrenowned computer scientists and media figures.
The full text of this book is available on an open access basis at Springer.
The blog for the Intertwingled Conference can be read here.

Generalized Quaternionic Schur Functions in the Ball and HalfSpace and KreinLanger Factorization
Daniel Alpay, Fabrizio Colombo, and Irene Sabadini
In this paper we prove a new version of KreinLanger 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 SchauderTychonoff 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 SegalBargmann 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. LunaElizarrarás, 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. LunaElizarrarás, 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 IndoGangetic plains
Ramesh P. Singh
Dust storms are very common in the northern parts of India, and every year people living in the IndoGangetic plains suffer greatly. Dust storms affect daytoday lives of people living in the IndoGangetic 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 premonsoon season and their impacts on ocean, atmosphere, and meteorological parameters. Longterm 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 largescale life models but often require the use of technically complex lowerlevel 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 alife simulations and general enough to make our results applicable to various latticebased alife 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 latticebased simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for largescale latticebased alife 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, messagepassing, and hybridparallel platforms. MapReduce is an emerging distributed computing framework for largescale 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 natureinspired 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 MultiSensor 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 LithosphereAtmosphereIonosphere Coupling model, one of several paradigms used to explain our observations. Initial results for the period of20032009 are presented from our systematic hindcast validation studies. We present our findings of multisensor atmospheric precursory signals for two major earthquakes in Japan, M6.7 Niigataken Chuetsuoki 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 wellunderstood 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 SMPbased systems, such as multicore computers and multicore 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 divideandconquer methods; hence better understanding of merge sort parallelization can contribute to better understanding of divideandconquer parallelization in general. In this paper, we investigate three parallel mergesorts: shared memory merge sort that runs on SMP systems with OpenMP; messagepassing 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 divideandconquer algorithms for mainstream SMPbased 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 selfguided 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 etexts, detailed selfguided 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, Pythonbased selfguided labs.

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, usercentered 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 timeinvariant 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 nonpositive metric and the case of pairs of commuting nonselfadjoint operators.

QuasiCoisometric Realizations of Upper Triangular Matrices
Daniel Alpay and Y. Peretz
In this paper we study analogs of de BrangesRovnyak 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.
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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