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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Extreme Development of Dragon Fruit Agriculture with Nighttime Lighting in Southern Vietnam

Shenyue Jia, Son V. Nghiem, Seung-Hee Kim, Laura Krauser, Andrea E. Gaughan, Forest R. Stevens, Menas Kafatos, and Khanh D. Ngo

Dragon fruit is widely grown in Southeast Asia and other tropical or subtropical regions. As a high-value cash crop ideal for exportation, dragon fruit cultivation has boomed during the past decade in southern Vietnam. Light supplementing during the winter months using artificial lighting sources is a widely adopted cultivation technique to boost productivity in the major dragon fruit planting regions of Vietnam. The application of electric lighting at night leads to a significant increase of nighttime light (NTL) observable by satellite sensors. The strong seasonality signal of NTL in dragon fruit cultivation enables identifying dragon fruit plantations using NTL images. We employed Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) monthly nighttime imagery from 2012 to 2019 to extract the growing area of dragon fruit in Bình Thuận Province, the largest dragon fruit growing region of Vietnam. The Breakpoint for Additive Seasonal Trend (B-FAST) analysis was applied to calculate the seasonality of NTL inside the dragon fruit plantations and distinguish them from the background. The results indicated that the dragon fruit cultivation strongly increased after 2014 and reached a plateau after 2017. In recent years, dragon fruit cultivation has experienced a slight decrease due to market fluctuations. We applied a buffer analysis over the largest dragon fruit cultivation area in Bình Thuận to analyze the spatial trend of the expansion of dragon fruit planting. Our results suggest that the dragon fruit cultivation of Bình Thuận has expanded to cover most inter-hill plains, reaching a spatial extent capacity due to the topographical constraints, and thus has begun to encroach into the low-elevation foothill area. In the case of emergency lock-down orders in February 2020 during the COVID-19 pandemic, NTL used for dragon fruit cultivation changed heterogeneously in space and time, driven by market price and shipping limitations far away from the local restrictions. Under the dual rural-urban hot spot situation with strong and contemporary developments of both dragon fruit agriculture and the urban tourism industry, building structures were detected densely in the city and gradually dispersed well into the rural landscape in Bình Thuận. The outcomes of this study will be valuable for local policymakers to better understand of the available area for dragon fruit cultivation and achieve better-coordinated cultivation planning against future fluctuations of the global market while providing insights and new understanding into the dual hot-spot developments valuable for planning rural-urban change strategies.
Earthquake Precursors in the Atmosphere and Ionosphere

Sergey Pulinets, Dimitar Ouzounov, Alexander Karelin, and Kyrill Boyarchuk

This book discusses how the increased emanation of radon and other gases from the Earth’s crust in the vicinity of active tectonic faults triggers a chain of physical processes and chemical reactions in the atmospheric boundary layer and the Earth’s ionosphere over an earthquake area several days/hours before strong seismic shocks occur. It presents the two main concepts involved in this mechanism: atmosphere ionization and the global electric circuit. The Lithosphere-Atmosphere-Ionosphere Coupling (LAIC) concept is strongly supported by experimental data showing the atmospheric and ionospheric precursors for major recent earthquakes including 2004 Sumatra; 2008 Sichuan, China; 2011 Tohoku, Japan; and 2015 Nepal. The book not only addresses the theoretical considerations but also includes information on experimental techniques used for precursor observations based on the space-borne systems. Providing practical methods of precursor identification and interpretation, it is an excellent textbook for graduate courses in geophysics, earthquake science, atmospheric physics and remote sensing. Moreover, it offers a wealth of information for scientists and experts from governmental and international agencies working in the fields of natural-disaster mitigation, response and recovery.
On the Representation of Boolean Magmas and Boolean Semilattices

Peter Jipsen, M. Eyad Kurd-Misto, and James Wimberley

A magma is an algebra with a binary operation ·, and a Boolean magma is a Boolean algebra with an additional binary operation · that distributes over all finite Boolean joins. We prove that all square-increasing (x ≤ x²) Boolean magmas are embedded in complex algebras of idempotent (x = x²) magmas. This solves a problem in a recent paper [3] by C. Bergman. Similar results are shown to hold for commutative Boolean magmas with an identity element and a unary inverse operation, or with any combination of these properties.

A Boolean semilattice is a Boolean magma where · is associative, commutative, and square-increasing. Let SL be the class of semilattices and let S(SL⁺) be all subalgebras of complex algebras of semilattices. All members of S(SL⁺) are Boolean semilattices and we investigate the question of which Boolean semilattices are representable, i.e., members of S(SL⁺). There are 79 eight-element integral Boolean semilattices that satisfy a list of currently known axioms of S(SL⁺). We show that 72 of them are indeed members of S(SL⁺), leaving the remaining 7 as open problems.
Quaternionic de Branges Spaces and Characteristic Operator Function

Daniel Alpay, Fabrizio Colombo, and Irene Sabadini

This work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed.
Commutative Doubly-Idempotent Semirings Determined by Chains and by Preorder Forests

Natanael Alpay and Peter Jipsen

A commutative doubly-idempotent semiring (cdi-semiring) (S,V,·,0,1) is a semilattice (S,V,0) with x V 0 = x and a semilattices (S,·,1) with identity 1 such that x0 = 0, and x(y V z) = xy V xz holds for all x, y, z ϵ S. Bounded distributive lattices are cdi-semirings that satisfy xy = x ^ y, and the variety of cdi-semirings covers the variety of bounded distributive lattices. Chajda and Länger showed in 2017 that the variety of all cdi-semirings is generated by a 3-element cdi-semiring. We show that there are seven cdi-semirings with a V-semilattice of height less than or equal to 2. We construct all cdi-semirings for which their multiplicative semilattice is a chain with n + 1 elements, and we show that up to isomorphism the number of such algebras is the nth Catalan number C_n = (1/(n+1)) (2n/n ) . We also show that cdi-semirings with a complete atomic Boolean V-semilattice on the set of atoms A are determined by singleton-rooted preorder forests on the set A. From these results we obtain efficient algorithms to construct all multiplicatively linear cdisemirings of size n and all Boolean cdi-semirings of size 2n.
Michele Sce's Works in Hypercomplex Analysis

Fabrizio Colombo, Irene Sabadini, and Daniele C. Struppa

"This book presents English translations of Michele Sce’s most important works, originally written in Italian during the period 1955-1973, on hypercomplex analysis and algebras of hypercomplex numbers. Despite their importance, these works are not very well known in the mathematics community because of the language they were published in. Possibly the most remarkable instance is the so-called Fueter-Sce mapping theorem, which is a cornerstone of modern hypercomplex analysis, and is not yet understood in its full generality."
Weakening Relation Algebras and FL²-algebras

Nikolaos Galatos and Peter Jipsen

FL²-algebras are lattice-ordered algebras with two sets of residuated operators. The classes RA of relation algebras and GBI of generalized bunched implication algebras are subvarieties of FL²-algebras. We prove that the congruences of FL²-algebras are determined by the congruence class of the respective identity elements, and we characterize the subsets that correspond to this congruence class. For involutive GBI-algebras the characterization simplifies to a form similar to relation algebras.

For a positive idempotent element p in a relation algebra A, the double division conucleus image p/A/p is an (abstract) weakening relation algebra, and all representable weakening relation algebras (RWkRAs) are obtained in this way from representable relation algebras (RRAs). The class S(dRA) of subalgebras of {p/A/p∶ A ϵ RA; 1 ≤ p² = p ϵ A} is a discriminator variety of cyclic involutive GBI-algebras that includes RA. We investigate S(dRA) to find additional identities that are valid in all RWkRAs. A representable weakening relation algebra is determined by a chain if and only if it satisfies 0 ≤ 1, and we prove that the identity 1 ≤ 0 holds only in trivial members of S(dRA).
Shortcut to Superconductivity: Superconducting Electronics via COMSOL Modeling

Armen Gulian

"This accessible textbook offers a novel, concept-led approach to superconducting electronics, using the COMSOL Multiphysics software to help describe fundamental principles in an intuitive manner.

Based on a course taught by the author and aimed primarily at engineering students, the book explains concepts effectively and efficiently, uncovering the “shortcut” to understanding each topic, enabling readers to quickly grasp the underlying essence. The book is divided into two main parts; the first part provides a general introduction to key topics encountered in superconductivity, illustrated using COMSOL simulations based on time-dependent Ginzburg-Landau equations and avoiding any deeply mathematical derivations. It includes numerous worked examples and problem sets with tips and solutions."
Interrogating Regulatory Mechanisms in Signaling Proteins by Allosteric Inhibitors and Activators: A Dynamic View Through the Lens of Residue Interaction Networks

Lindy Astl, Amanda Tse, and Gennady M. Verkhivker

Computational studies of allosteric interactions have witnessed a recent renaissance fueled by the growing interest in modeling of the complex molecular assemblies and biological networks. Allosteric interactions in protein structures allow for molecular communication in signal transduction networks. In this chapter, we discuss recent developments in understanding of allosteric mechanisms and interactions of protein systems, particularly in the context of structural, functional, and computational studies of allosteric inhibitors and activators. Computational and experimental approaches and advances in understanding allosteric regulatory mechanisms are reviewed to provide a systematic and critical view of the current progress in the development of allosteric modulators and highlight most challenging questions in the field. The abundance and diversity of genetic, structural, and biochemical data underlies the complexity of mechanisms by which targeted and personalized drugs can combat mutational profiles in protein kinases. Structural and computational studies of protein kinases have generated in recent decade significant insights that allowed leveraging knowledge about conformational diversity and allosteric regulation of protein kinases in the design and discovery of novel kinase drugs. We discuss recent developments in understanding multilayered allosteric regulatory machinery of protein kinases and provide a systematic view of the current state in understanding molecular basis of allostery mediated by kinase inhibitors and activators. In conclusion, we highlight the current status and future prospects of computational biology approaches in bridging the basic science of protein kinases with the discovery of anticancer therapies.
Logics for Rough Concept Analysis

Giuseppe Greco, Peter Jipsen, Krishna Manoorkar, Alessandra Palmigiano, and Apostolos Tzimoulis

Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough algebra counterparts of certain subclasses of rough formal contexts, and introduce proper display calculi for the logics associated with these varieties which are sound, complete, conservative and with uniform cut elimination and subformula property. These calculi modularly extend the multi-type calculi for rough algebras to a ‘nondistributive’ (i.e. general lattice-based) setting.
On the Structure of Generalized Effect Algebras and Separation Algebras

Sarah Alexander, Peter Jipsen, and Nadiya Upegui

Separation algebras are models of separation logic and effect algebras are models of unsharp quantum logics. We investigate these closely related classes of partial algebras as well as their noncommutative versions and the subclasses of (generalized) (pseudo-)orthoalgebras. We present an orderly algorithm for constructing all nonisomorphic generalized pseudoeffect algebras with n elements and use it to compute these algebras with up to 10 elements.
Introduction to Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations: A Volume Dedicated to Heinz Langer

Daniel Alpay and Bernd Kirstein

"This volume is a tribute to Heinz Langer on the occasion of his eightieth birthday. Two earlier OT volumes (namely, volume 106 and volume 163; see [19] and [35] respectively) were dedicated to Heinz, the first one on the occasion of his sixtieth birthday, and the second one on the occasion of his retirement...The first named editor (DA) worked very hard on Heinz’ papers (and in particular on the above-mentioned series of papers with M.G. Krein) during his doctoral studies [1] at the Weizmann Institute in Israel."
Multiparameter Assessment of Pre‐Earthquake Atmospheric Signals

Dimitar Ouzounov, Sergey Pulinets, Jann-Yenq Liu, Katsumi Hattori, and Peng Han

We apply interdisciplinary observation to study earthquake processes, their physics, and the phenomena that precede their energy release. Our approach is based on multisensor observations of short-term pre-earthquake phenomena preceding large earthquakes (M>6). The integrated satellite and terrestrial framework is our method for validation and is based on a sensor web of several physical and environmental parameters (satellite thermal infrared radiation (STIR), electron concentration in the ionosphere, air temperature, and relative humidity measurements) that were associated with earthquakes. The scientific rationale for multidisciplinary analysis is founded on the concept lithosphere-atmosphere-ionosphere coupling. To check the predictive potential of pre-earthquake signals we validate in retrospective and prospective modes. Our validation processes consist of two steps: (a) a retrospective analysis preformed over three different regions with high seismic activity (M 6.0 Napa of 2014, M 6.0 Taiwan of 2016, and M 7.9 Kumamoto, Japan of 2016); (b) testing of Molchan's error diagram (MED) for STIR and differential total electron content anomalous events over Japan and Taiwan. Our findings suggest that: (a) pre-earthquake signals (with 1-30 days time lag) follow a general temporal-spatial evolution pattern; (b) pre-earthquake atmospheric anomalies can provide short-term predictive information for the occurrence of major earthquakes in the tested regions.
Lithosphere–Atmosphere–Ionosphere–Magnetosphere Coupling—A Concept for Pre‐Earthquake Signals Generation

Sergey Pulinets, Dimitar Ouzounov, Alexander Karelin, and Dmitry Davidenko

"The physics of earthquake genesis at the latest stage of a seismic cycle has always been the subject of scientific interest and discussion. In such discussion and in model development, however, only solid Earth processes have been contemplated. Development of satellite technologies brought new insight to the problem: new types of anomalies in the atmosphere and ionosphere were discovered that appear a few days/weeks before the main shock within the zone of earthquake preparation. These anomalies were thoroughly investigated, and results of the research have demonstrated a high statistical confidence warrants their identification as short-term earthquake precursors. In this chapter we seek to clarify how information and energy are transported from underground to the upper and lower layers of the atmosphere, including near-Earth space. Owing to the interdisciplinary character of the model, it is very difficult to create a common code for all its physical and spatial domains. That is why the material presented here should be considered conceptual rather than modeling output. As an example, if the boundary layer plasmachemistry instrumentation is applied, for ionospheric anomalies the electromagnetism approach is adopted. This conceptual approach, however, proved to be valid not only for earthquakes but also for other natural and technological disasters where air ionization occurs."
Preface to Natural Hazards: Earthquakes, Volcanoes, and Landslides

Ramesh Singh and Darius Bartlett

A preface to Natural Hazards: Earthquakes, Volcanoes, and Landslides, edited by Ramesh Singh and Darius Bartlett, that gives an overview of the book and the contributions of each chapter.
Beyond Wavefunctions: A Time-Symmetric Nonlocal Ontology for Quantum Mechanics

Yakir Aharonov, Eliahu Cohen, and Avshalom C. Elitzur

"We take Agassi's attitude to QM as an invitation to present some insights we have gained during our research in this field. Following is a highly non-technical account of a few works which we believe begins to merge into a novel and rich picture of physical reality."
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
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'."
Bernstein-type Inequalities for Bicomplex Polynomials

Irene Sabadini, Adrian Vajiac, and Mihaela Vajiac

This paper considers the well-known Bernstein and Erdős–Lax inequalities in the case of bicomplex polynomials. We shall prove that the validity of these inequalities depends on the norm in use and we consider the cases of the Euclidean, Lie, dual Lie and hyperbolic-valued norms. In particular, we show that in the case of the Euclidean norm the inequalities holds keeping the same relation with the degree of the polynomial that holds in the classical complex case, but we have to enlarge the radius of the ball. In the case of the dual Lie norm both the relation with the degree and the radius of the ball have to be changed. Finally, we prove that the exact analogs of the two inequalities hold when considering the Lie norm and the hyperbolic-valued norm. In the case of these two norms we also show the validity of the maximum modulus principle for bicomplex holomorphic functions.
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 year-long intervention of the flipped classroom model while the control group followed the traditional lesson delivery. Results of the year-end evaluation of this model showed positive student perceptions. An analysis of covariance of the algebra post-test score with learning model as treatment factor and pre-test as covariate resulted in a significant treatment effect at .05 level of significance. A paired-sample t-test by treatment group to compare pre-test and post-test 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.
Mathematics Is Physics

Matthew S. Leifer

In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within ..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics.

This version of the essay contains an addendum responding to Slyvia Wenmackers' essay and comments that were made on the FQXi website.
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 re-imagines its meaning for the future. Emerging from a conference held in 2014 at Chapman University, it includes contributions from world-renowned 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.