Hoffman polynomials of nonnegative irreducible matrices and strongly connected digraphs

AbstractFor a nonnegative n×n matrix A, we find that there is a polynomial f(x)∈R[x] such that f(A) is a positive matrix of rank one if and only if A is irreducible. Furthermore, we show that the lowest degree such polynomial f(x) with tr f(A)=n is unique. Thus, generalizing the well-known definition of the Hoffman polynomial of a strongly connected regular digraph, for any irreducible nonnegative n×n matrix A, we are led to define its Hoffman polynomial to be the polynomial f(x) of minimum degree satisfying that f(A) is positive and has rank 1 and trace n. The Hoffman polynomial of a strongly connected digraph is defined to be the Hoffman polynomial of its adjacency matrix. We collect in this paper some basic results and open problems related to the concept of Hoffman polynomials

New algebraic relationships between tight binding models

In this thesis, we present a new perspective on tight binding models. Utilising the rich algebraic toolkit provided by a combination of graph and matrix theory allows us to explore tight binding systems related through polynomial relationships. By utilising ring operations of weighted digraphs through intermediate König digraph representations, we establish a polynomial algebra over finite and infinite periodic graphs, analogous to polynomial operations on adjacency matrices. Exploring the microscopic and macroscopic behaviour of polynomials in a graph-theoretic setting, we reveal elegant relationships between the symmetrical, topological, and spectral properties of a parent graph G and its family of child graphs p(G). Drawing a correspondence between graphs and tight binding models, we investigate deep-rooted connections between different quantum systems, providing a fresh angle from which to view established tight binding models. Finally, we visit topological chains, demonstrate how their properties relate to more trivial underlying chains through effective “square root” operations, and provide new insights into their spectral characteristics

Applying system dynamics modelling to building resilient logistics : a case of the Humber Ports Complex

This research employs system dynamics modelling to analyse the structural behaviour of the interactions between Disaster Preparedness, Environment Instability, and Resilience in maritime logistics chain as a response to policy change, or strategic risk management interventions, at ports on the Humber Estuary.Port authorities, logistics operators, agencies, transporters, and researchers have revealed that disasters lead to interruptions in free flow of supply chains, and has the potential to disrupt the overall performance of a logistics chain. There is strong evidence about the rise in frequency, magnitude, and disruption potentials of catastrophic events in recent times (e.g. 9/11 attack, the Japanese earthquake/Tsunami and the aftermath nuclear disaster, Hurricanes Katrina and Haiyan, Super Storm Sandy, and many more). However, it appears that risk managers are not able to anticipate the outcomes of risk management decisions, and how those strategic interventions can affect the future of the logistics chain. Management appears to misjudge (or miscalculate) risks, perhaps due to the assumed complexity, the unpredictability of associated disruptions, and sometimes due to individual managerial approach to risk management. The uncertainties and states assumed notwithstanding, investors and regulators have become increasingly intolerant for risk mismanagement. Shipowners and port authorities tend to managing cost instead of managing risk. Hence they appear to invest little time and fewer resources in managing disruptions in their logistics chains even though they seem to frequently conduct risk assessments. We suggest that disaster preparedness that leads to resilience in maritime logistics chain is the best alternative to preventing or reducing the impacts of disruptions from catastrophes.We aim at improving current level of understanding the sources of disruptions in port/maritime logistics system through analysing the interdependencies between key variables. The dynamic models from this research have revealed that there is strong influence relationships (interdependencies) between Disaster Preparedness, Environment Instability, and Resilience. We found that potential sources of disruptions along the spokes of maritime logistics system can be port physics related, however the subtle triggering factors appear to be port size related. We also found that policy interventions geared towards risk management have the potential to produce unintended consequences basically due to unacknowledged conditions. Thus the relevance of the research and the SD models was to provide strategic policy makers with real-time decision evaluation tool that can provide justification for acceptance or rejection of a risk management intervention prior to decision implementation

A grammar of the Pendau language

This dissertation is a basic description of Pendau, a previously undescribed Western Malayo-Polynesian language in the Tomini-Tolitoli group found in Central Sulawesi, Indonesia. This description relies heavily on natural language data for its documentation. Most of the description covers concerns in the typological functional framework which also provides a means to organize the data. Chapter 1 gives a brief ethnographic background and introduces the linguistic context and background to Pendau. Very little had been known about Pendau until this current research. Chapter 2 describes the phonetics and the basic phonology of Pendau in essentially a structuralist framework. However it includes acoustic analyses of stress (non-phonemic pitch-accent with low to high tone), vowel formants, and the glottal stop (which is often manifested as creaky voice). Chapter 3 builds on chapter 2 by examining the phonology in a generative framework and looks at the phonological processes via lexical phonology. The most outstanding feature of phonology in Pendau is the extensive use of vowel harmony in many prefixes. Chapter 4 discusses the morphology of Pendau and the complicated stem forming morphology. At the morphological level I take a non-morphemic view and integrate a kind of word and paradigm approach in connection with lexical phonology and autosegmental phonology. Word classes are introduced in chapter 5, and chapter 6 introduces basic clausal syntax and includes a discussion of grammatical relations. Both of these chapters are fundamental to understanding the description in later parts of the dissertation. Chapter 7 discusses nominal phrases. Chapter 8 discusses prepositional and instrumental phrases. Chapter 9 describes the seven canonical verb classes and miscellaneous verb morphology. Chapter 10 describes transitivity altering operations which include causatives, applicatives, reciprocals, and a special equative construction. Chapter 11 describes directional verbs and their use as directional serial verbs. Chapter 12 describes the importance of voice and introduces the use of inverse voice which contrasts with the other transitive voice construction, active voice. Tense, aspect, and mode are described in chapter 13. Auxiliaries, adverbs, and negation are described in chapter 14. Chapter 15 describes clause combinations and complex sentences, and includes comparatives, complementation, quotation margin formulas, relative clauses, interclausal relators and propositional relations, and discourse connectors. Chapter 16 describes the use of imperatives and interrogatives. Finally, at the discourse level I integrate several discourse methods with the strongest emphases coming from Longacre and Givon. Chapter 17 describes some discourse features of cohesion and prominence. This includes fronting, leftdislocation, repetition, and topic continuity. In chapter 18 I follow Longacre's approach to discourse analysis and describe structures of different genres in Pendau. Three interlinearized texts are included in the appendices. The other appendices provide supporting data, figures, tables and charts

Complexity in Economic and Social Systems

There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

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.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp