The widespread and long-lived failings of academic economics are due to an over-reliance on largely inappropriate mathematical methods of analysis. This is an assessment I have long maintained. Many heterodox economists, however, appear to hold instead that the central problem is a form of political-economic ideology. Specifically, it is widely contended in heterodox circles that the discipline goes astray just because so many economists are committed to a portrayal of the market economy as a smoothly or efficiently functioning system or (...) some such, a portrayal that, whether sincerely held or otherwise, is inconsistent with the workings of social reality. Here I critically examine the contention that a form of political-economic ideology of this sort is the primary problem and assess its explanatory power. I conclude that the contention does not fare very well. I do not, though, deny that ideology of some sort has a major impact on the output of the modern economics academy. However it is of a different nature to the form typically discussed, and works in somewhat indirect and complex ways. Having raised the question of the impact of ideology I take the opportunity to explore its play in the economics academy more generally. (shrink)

Mathematical models provide explanations of limited power of specific aspects of phenomena. One way of articulating their limits here, without denying their essential powers, is in terms of contrastive explanation.

In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Endothelial cells which form the lining of neighbouring blood vessels respond to this chemotactic stimulus in a well-ordered sequence of events comprising, at minimum, of a degradation of their basement membrane, migration and proliferation. Capillary sprouts are formed which migrate towards the tumour eventually penetrating it and permitting vascular growth to take place. It (...) is during this stage of growth that the insidious process of invasion of surrounding tissues can and does take place. A model mechanism for angiogenesis is presented which includes the diffusion of the TAF into the surrounding host tissue and the response of the endothelial cells to the chemotactic stimulus. Numerical simulations of the model are shown to compare very well with experimental observations. The subsequent vascular growth of the tumour is discussed with regard to a classical reaction-diffusion pre-pattern model. (shrink)

Understanding the mechanisms and the time and spatial evolution of penumbra following an ischemic stroke is crucially important for developing therapeutics aimed at preventing this area from evolving towards infarction. To help in integrating the available data, we decided to build a formal model. We first collected and categorised the major available evidence from animal models and human observations and summarized this knowledge in a flow-chart with the potential key components of an evolving stroke. Components were grouped in ten sub-models (...) that could be modelled and tested independently: the sub-models of tissue reactions, ionic movements, oedema development, glutamate excitotoxicity, spreading depression, NO synthesis, inflammation, necrosis, apoptosis, and reperfusion. Then, we figured out markers, identified mediators and chose the level of complexity to model these sub-models. We first applied this integrative approach to build a model based on cytotoxic oedema development following a stroke. Although this model includes only three sub-models and would need to integrate more mechanisms in each of these sub-models, the characteristics and the time and spatial evolution of penumbra obtained by simulation are qualitatively and, to some extent, quantitatively consistent with those observed using medical imaging after a permanent occlusion or after an occlusion followed by a reperfusion. (shrink)

Herbert A. Simon's reply (Inquiry, Vol. 25, No. 3) to my criticism of his 1954 paper is not to the point. He fails to respond to some of my arguments and misconceives others. One of his misconceptions is that any mathematical deduction from empirical premises which are formulated mathematically will necessarily lead to empirically valid conclusions. This claim is particularly unwarrantable in Simon's case since his mathematical premise, the continuity of the reaction function, is empirically meaningless.

Darwin described biological species as groups of morphologically similar individuals. These groups of individuals can split into several subgroups due to natural selection, resulting in the emergence of new species. Some species can stay stable without the appearance of a new species, some others can disappear or evolve. Some of these evolutionary patterns were described in our previous works independently of each other. In this work we have developed a single model which allows us to reproduce the principal patterns in (...) Darwin’s diagram. Some more complex evolutionary patterns are also observed. The relation between Darwin’s definition of species, stated above, and Mayr’s definition of species is also discussed. (shrink)

Ever since Thomas Malthus used simple mathematics to model the evolution of food production vs the increasing human population of planet Earth and declared that we would very soon eat ourselves out of house and home, politicians have been falling hook, line and sinker for mathematical models. This paper examines how and why the mathematical modelling of complex systems has proved unreasonably effective in convincing mathematically illiterate politicians to take practical measures that have turned out to be disastrous. It then (...) suggests that mathematical modelling of the human brain is not a good strategy to pursue. (shrink)

Quantitative assessments of when infectious disease outbreaks end are crucial, as resources targeted towards outbreak responses typically remain in place until outbreaks are declared over. Recent improvements and innovations in mathematical approaches for determining when outbreaks end provide public health authorities with more confidence when making end-of-outbreak declarations. Although quantitative analyses of outbreaks have a long history, more complex mathematical and statistical methodologies for analysing outbreak data were developed early in the 20th century and continue to be refined. Historically, such (...) methodologies focused primarily on factors affecting the early and middle phases of an outbreak, with less attention given to determining how and when outbreaks end. This review discusses mathematical modelling methods from the last 20 years that have been developed for determining the ends of infectious disease outbreaks, and considers factors that affect the accuracy of such determinations. When disease surveillance systems provide timely and representative data to inform models, the timings of end-of-outbreak declarations can be fine-tuned to allow outbreaks to be declared over quickly and with a low risk of being incorrect. Premature declarations that outbreaks are over can undermine earlier achievements in disease control and may result in a resurgence of cases, but unnecessary delays in declaring outbreaks over can cause significant economic and social harm. Appropriate declarations that balance the benefits of relaxing control measures against the risk of a surge in cases allow public health resources to be conserved (and economic and social pressures to be reduced) while limiting the potential for additional transmission. (shrink)

This research investigates how pre-service teachers aim to bring awareness of environmental sustainability while learning mathematical modelling to their 5th-grade students. Theoretical perspectives from socio-critical modelling research can involve engaging students in societal issues, including focusing on action. Thematic coding of a mandatory task by a group of pre-service teachers, where they design, implement, and reflect on a modelling activity during practicum, is used to analyse how they combine environmental and mathematical aims. The findings show that the pre-service teachers emphasise (...) the authenticity of tasks and data, engage students in actions in littering, reflect on students’ critique of assumptions, and focus on the meaning-making of environmental numbers using students’ everyday language. Implications to teacher education suggest that teachers can combine focusing on environmental sustainability through mathematics education. Further, teacher education can support pre-service teachers and students in actions through socio-critical modelling activities. (shrink)

Although every emerging infectious disease occurs in a unique context, the behaviour of previous pandemics offers an insight into the medium- and long-term outcomes of the current threat. Where an informative historical analogue exists, epidemiologists and policymakers should consider how the insights of the past can inform current forecasts and responses.

In recognition memory paradigms, emotional details are often recognised better than neutral ones, but at the cost of memory for peripheral details. We previously provided evidence that, when periph...

This chapter contains sections titled: Why Use Mathematical Models? Theory‐based Models Data‐based Modeling Computational Approaches Conclusions Notes.

Open peer commentary on the article “Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld’s Conceptual Analysis” by Victor V. Cifarelli & Volkan Sevim. Upshot: Problem solving is an enormous field of study, where so-called “problems” can end up having very little in common. One of the least studied categories of problems is open-ended mathematical modeling research. Cifarelli and Sevim’s framework - although not developed for this purpose - may be a useful lens (...) for studying the development of mathematical modelers and researchers in applied mathematics. (shrink)

This dissertation challenges two prevalent views on the topic of scientific explanation: that science explains by revealing causal mechanisms, and that science explains by unifying our knowledge of the world. ;My methodological strategy is to compare our best current philosophical accounts of scientific explanation with evidence from contemporary scientific research. In particular, I focus on evidence from dynamical explanations, that is, explanations which appeal to nonlinear dynamical modeling for their force. Nonlinear dynamical modeling is a type of mathematical (...) modeling which is used by scientists in many different disciplines, including population biology, ecology, physics, and psychology. ;Chapter 1 argues that dynamical explanations are a philosophically important class of explanations, based on their prevalence and their close relationship with the semantic view of theories. ;Chapters 2 and 3 conclude that extant causal and unification accounts encounter serious difficulties when applied to dynamical explanations. Chapter 2 argues that causal relevance is neither a necessary nor a sufficient condition for explanatory relevance. Chapter 3 clarifies and evaluates different claims about the unifying power of science. Here, I argue that dynamical explanations provide some support for the thesis that unification is constitutive of explanation. However, dynamical explanations also indicate that some of the intuitions embodied in extant unification accounts are untenable. ;Chapter 4 concludes by advancing diagnostic criticisms of existing causal and unification accounts. I explore the relationships between dynamical explanations and three conceptions of scientific explanation, as well as the relationships between different types of inference and scientific understanding. I suggest that philosophers look to cognitive science and the semantic view of theories for aid in constructing a viable positive account of explanation. ;The technical appendix introduces several key definitions and concepts of dynamical systems theory. (shrink)

The aim of this article is to show how a tumor can modify energy substrates fluxes in the brain to support its own growth. To address this question we use a modeling approach to explain brain nutrient kinetics. In particular we set up a system of 17 equations for oxygen, lactate, glucose concentrations and cells number in the brain. We prove the existence and uniqueness of nonnegative solutions and give bounds on the solutions. We also provide numerical simulations.

Philosophy can shed light on mathematical modeling and the juxtaposition of modeling and empirical data. This paper explores three philosophical traditions of the structure of scientific theory—Syntactic, Semantic, and Pragmatic—to show that each illuminates mathematical modeling. The Pragmatic View identifies four critical functions of mathematical modeling: (1) unification of both models and data, (2) model fitting to data, (3) mechanism identification accounting for observation, and (4) prediction of future observations. Such facets are explored using a recent (...) exchange between two groups of mathematical modelers in plant biology. Scientific debate can arise from different modeling philosophies. (shrink)

We provide a mathematical study of a model of energy metabolism and hemodynamics of glioma allowing a better understanding of metabolic modifications leading to anaplastic transformation from low grade glioma.This mathematical analysis allows ultimately to unveil the solution to a viability problem which seems quite pertinent for applications to medecine.

This volume represents a magnum opus by Wolfgang Weidlich, summarizing his long work in the area of sociodynamics. It lays out the origins and development of his ideas on this topic, presents a variety of applications drawn from his previous work, and offers some new insights and suggestions. For those acquainted with Professor Weidlich’s work it is a satisfying summing up. For those unacquainted with it, the book provides a good overview and discussion of what is involved in it, both (...) its weaknesses and its strengths. It has a definite predecessor, Weidlich’s 1983 book with his frequent coauthor, Günter Haag, Concepts and Models of a Quantitative Sociology, but goes well beyond the arguments and models presented in that volume. (shrink)

In international relations theory, there is a long history of Richardson-like modeling of the evolution of military capability. Usually, such models are deterministic and predictive and do not allow for the representation of the transition from competitive peace to shooting war. More recently, models have been developed which attempt to represent the evolution of relationship between nations. The relationship between nations, varying from friendship to hostility, is taken to be synonymous with the intent of nations towards each other, varying (...) from good will to malice. Generally, these relationship models do not include capability though common sense would indicate that capability and mutual intent should profoundly influence each other. A model is presented here which combines these two fundamental attributes of international relations and attempts to represent the outbreak of war in the world system by the onset of deterministic chaos in the extended model. (shrink)

In this paper, a mathematical model of the respiratory mechanics is used to reproduce experimental signal waveforms acquired from three newborn lambs. As the main challenge is to determine specific lamb parameters, a sensitivity analysis has been realized to find the most influent parameters, which are identified using an evolutionary algorithm. Results show a close match between experimental and simulated pressure and flow waveforms obtained during spontaneous ventilation and pleural pressure variations acquired during the application of positive pressure, since root (...) mean square errors equal to 0.0119, 0.0052 and 0.0094. The identified parameters were discussed in light of previous knowledge of respiratory mechanics in the newborn. (shrink)

The current WSN is vulnerable to a variety of malicious attacks, resulting in the decline of its comprehensive performance. Multihop routing involves a number of safety and privacy issues. Problems such as snooping, sinkhole, manipulation, cloning, wormhole, spoofing, and so on affect the integrity, availability, and confidentiality of the WSNs. Therefore, this paper mainly studies the mathematical modeling of WSN multiattack behavior discrimination based on the incidence matrix. The WSN node model is used to collect relevant data and mark (...) and map the disguised data, so as to determine the characteristics of multiattack behavior and establish the WSN multiattack behavior discrimination model based on the incidence matrix. The experimental results show that the designed multiattack behavior discrimination model can distinguish the attack type according to the characteristics, has high recognition ability, can spend a short time to effectively distinguish the attack behavior, has a low false positive rate, and can effectively improve the antiattack ability of the WSN. (shrink)

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal (...) and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models. (shrink)

Mathematical modelling has played an increasingly prominent role in public health responses, for example by offering estimates of how infectious disease incidence over time may be affected by the adoption of certain policies and interventions. In this paper, we call for greater research and reflection into the ethics of mathematical modeling in public health. First, we present some promising ways of framing the ethics of mathematical modeling that have been offered in the very few publications specifically devoted to (...) this subject. Second, to draw out some issues that have not yet been sufficiently considered, we bring in the case of mathematical modeling in voluntary medical male circumcision (VMMC) initiatives for HIV prevention in Africa. We argue that greater attention should be paid to ethical considerations in mathematical modeling, particularly as its use is becoming more widespread and its potential impacts are becoming greater in the ‘big data’ era, as witnessed during the COVID-19 pandemic. (shrink)

This study on the cambium of Pinus sylvestris L. examines the intrusive growth of fusiform cambial initials and its possible contribution to the tangential and radial expansions of the cambial cylinder. The location and extent of intrusive growth of the fusiform initials were determined by microscopic observations and by mathematical modeling. In order to meet the required circumferential expansion of the cambial cylinder, the fusiform initials grow in groups by means of a symplastic rather than intrusive growth, leaving no (...) room for the assumption that intrusive growth of the initials takes place between radial walls and has a direct role in the increase of the cambial circumference. Therefore, it is postulated that the fusiform initials grow intrusively between the tangential walls of the neighboring initials and their immediate derivatives and not between the radial walls of the adjacent initials as per common belief. (shrink)

Professor Aubert's ?three?stage rocket? (Inquiry, Vol. 26 [1983], No. 1) has reached periodic orbit. His comments on my earlier reply to his critique of my election predictions paper simply repeat arguments I have already refuted. In this note, I limit myself largely to pointing out Professor Aubert's misconceptions of what my position actually is. I find no reasons for revising the views stated in my original election predictions paper, nor any reasons for thinking that paper violated norms of scientific method (...) that prevail in the natural sciences. (shrink)

The constantly accelerating progress of contemporary natural science is indissolubly associated with the development and use of mathematics and with the processes of mathematical modeling of the phenomena of nature. The essence of this diverse and highly fertile interaction of mathematics and natural science and the dialectics of this interaction can only be disclosed through analysis of the nature of theoretical notions in general. Today, above all in the ranks of materialistically minded researchers, it is generally accepted that theory (...) possesses a value of its own. Contrary to positivist concepts of the nature of our knowledge, the meaning and significance of theory do not consist merely of the recording of experimental data, their classification and notation in abbreviated form. The meaning of theory is considerably more significant and is revealed, above all, in its explanatory and predictive functions. Contemporary theoretical knowledge is quite advanced and comprises a highly complex system, relatively self-contained and capable of internal development. Mathematics is the most interesting and distinctive phenomenon in the system of theoretical knowledge, in the system of science in general. It is in its dialectical development that the internal force and dynamics of the development of theory, in the very broadest sense of that word, find expression. Paul Lafargue tells us that Karl Marx held that "science only attains perfection when it succeeds in making use of mathematics" . In many fields of research the formulation of new ideas and concepts rests upon mathematics, its concepts and notions, and "is suggested" by the latter. "Mathematics," writes F. Dyson, "is the main source of the notions and principles out of which new theories are created" . The basic significance of mathematics to theory has been noted by outstanding thinkers over the course of the entire history of development of science. Today the expressive phrase, "the mathematization of knowledge," has come into general currency as a description of the principal direction of growth of theoretical notions in natural science. However, with respect to the growth of modern theoretical physics in general, the statement that it develops primarily by the method of the mathematical hypothesis has general validity. For example, the principal findings and discoveries of quantum theory and particle physics, starting from the corpuscularwave dualism and terminating with the omega minus hyperon and hypothetical quarks, were obtained or made "at the tip of a mathematician's pen.". (shrink)

In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that the (...) hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically. (shrink)

Current mathematical models are notoriously unreliable in describing the time evolution of unexpected social phenomena, from financial crashes to revolution. Can such events be forecast? Can we compute probabilities about them? Can we model them? This book investigates and attempts to answer these questions through GOdel's two incompleteness theorems, and in doing so demonstrates how influential GOdel is in modern logical and mathematical thinking. Many mathematical models are applied to economics and social theory, while GOdel's theorems are able to predict (...) their limitations for more accurate analysis and understanding of national and international events. This unique discussion is written for graduate level mathematicians applying their research to the social sciences, including economics, social studies and philosophy, and also for formal logicians and philosophers of science. (shrink)

An ontological approach as a tool for managing the processes of constructing mathematical models based on interval data and further use of these models for solving applied problems is proposed in this article. Mathematical models built using interval data analysis are quite effective in many applications, as they have “guaranteed” predictive properties, which are determined by the accuracy of experimental data. However, the application of mathematical modeling methods is complicated by the lack of software tools for the implementation of (...) procedures for constructing this type of mathematical models, creating an ontological model that operates by the categories of the subject area of mathematical modeling, regardless of the modeling object proposed in this article. This approach has made it possible to generate tools for mathematical modeling of various objects based on the interval data analysis for any software development environment selected by the user. The technology of creating the software on the basis of the developed ontological superstructure for mathematical modeling using the interval data for different objects, as well as various forms of user interface implementation, is presented in this article. A number of schemes, which illustrate the technology of using the ontological approach of mathematical modeling based on interval data, are presented, and the features of its interpretation when solving environmental monitoring problems are described. (shrink)

Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized eigenvalues problem of sparse matrices, with automatic parallelization of calculations on modern parallel computers with graphics processors. Peculiarities of realization of parallel algorithms for different structures of sparse matrices are presented. The times of solving the problem of stability of composite materialsusing a three-dimensional model of "finite size fibers" on computers of different architectures are given. In mathematical modeling of physical (...) and technical processes in many cases there is a need to solve problems of algebraic problem of eigenvalues with sparse matrices of large volumes. In particular, such problems arise in the analysis of the strength of structures in civil and industrial construction, aircraft construction, electric welding, etc. The solving to these problems is to determine the eigenvalues and eigenvectors of sparse matrices of different structure. The efficiency of solving these problems largely depends on the effectiveness of mathematical modeling of the problem as a whole. Continuous growth of task parameters, calculation of more complete models of objects and processes on computers require an increase in computer productivity. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. Today, this problem is solved by using powerful supercomputers of hybrid architecture, such as computers with multicore processors and graphics processors, which combine MIMD and SIMD architectures. But the potential of high-performance computers can be used to the fullest only with algorithmic software that takes into account both the properties of the task and the features of the hybrid architecture. Complicating the architecture of modern high-performance supercomputers of hybrid architecture, which are actively used for mathematical modeling means a significant complication of efficient use of these resources in creating parallel algorithms and programs. here are problems with the creation of algorithmic software with automatic execution of stages of work, which are associated with the efficient use of computing resources, ways to store and process sparse matrices, analysis of the reliability of computer results. This makes it possible to significantly increase the efficiency of mathematical modeling of practical problems on modern high-performance computers, as well as free users from the problems of parallelization of complex problems. he developed algorithmic software automatically implements all stages of parallel computing and processing of sparse matrices on a hybrid computer. It was used at the Institute of Mechanics named after S.P. Tymoshenko NAS of Ukraine in modeling the strength problems of composite material. A significant improvement in the time characteristics of mathematical modeling was obtained. Problems of mathematical modeling of the properties of composite materials has an important role in designing the processes of deformation and destruction of products in various subject areas. Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized problem of eigen values of sparse matrices of different structure of large orders, with automatic parallelization of calculations on modern parallel computers with graphics processors. The main methodological principles and features of implementation of parallel algorithms for different structures of sparse matrices are presented, which ensure effective implementation of multilevel parallelism of a hybrid system and reduce data exchange time during the computational process. As an example of these approaches, a hybrid algorithm of the iteration method in subspace for tape and block-diagonal matrices with a frame for computers of hybrid architecture is given. Peculiarities of data decomposition for matrices of profile structure at realization of parallel algorithms are considered. The proposed approach provides automatic determination of the required topology of the hybrid computer and the optimal amount of resources for the organization of an efficient computational process. The results of testing the developed algorithmic software for problems from the collection of the University of Florida, as well as the times of solving the problem of stability of composite materials using a three-dimensional model of "finite size fibers" on computers of different architectures. The results show a significant improvement in the time characteristics of solving problems. (shrink)

The paper deals with the problems in the electric power industry, do not allow us to ensure a sufficient level of competitiveness of the industry and each individual subject of the electric power industry, the threatens national security, in particular, the economic security of the state, and creates barriers to maintaining the sustainable development of territories. It is proposed to use the economic and mathematical modeling allowed us to determine the high importance of human resources in the final results (...) of the electric power company, which makes it possible to consider the optimization of investment funds from the position of strengthening the focus of management processes in the field of personnel development. (shrink)

Conflicts within the tsetse fly belt revealed a strong correlation between the dynamics of bovine trypanosomosis and the insurgency involving farmers and herders in Nigeria and parts of West Africa. This study examined the history, causes and influence of farmers-herdsmen conflicts on banditry, terrorism and food security as it relates to the epidemiology of African animal trypanosomosis (AAT). A combination of literature database searches, semi-structured questionnaires, and mathematical modeling was employed. The study found that transhumance contributes significantly to conflicts (...) between farmers and herdsmen. An average of 6.46 persons per attack were reported between 2005 and 2021. Only 8.4 $$\%$$ (95 $$\%$$ CI: 5.0 $$-$$ 12.9) of farmers and 18.2 $$\%$$ (95 $$\%$$ CI: 12.4 $$-$$ 25.4) of herdsmen have engaged in conflict resolution efforts. The study shows that both conflict and the spread of trypanosomosis can be effectively controlled when $$R_0 < 1$$, ensuring that the sub-population remains in the basin of attraction of the trypanosomosis-conflict-free equilibrium ( $$T_{0c}$$ ). The partial derivative of the basic reproduction number, $$R_0$$, with respect to improved conflict resolution, suggests that halting transhumance can prevent a portion of the cattle recruitment rate ( $$\Lambda_c$$ ) from becoming infected with AAT. Climate change exacerbates these issues, leading to settlement and resettlement strategies within the fly belt regions. The model indicates that the basic reproduction number can only be reduced to less than one ( $$R_0 < 1$$ ) to become globally asymptotically stable if there is effective conflict resolution involving both farmers and herders. The study advocates for the establishment of ranching in tsetse-free zones with adequate social amenities, improved marketing strategies for animals and animal products led by government agencies through public-private partnerships, the banning of open grazing, and strict enforcement of policies against violators. (shrink)

This research aims at establishing the impact of information and communication technologies (ICT) on e-commerce development of industrial enterprises by means of economic and mathematical modelling. The goal was achieved using the following methods: theoretical generalization, analysis and synthesis (to critically analyse the scientific approaches of scientists regarding the expediency of using mathematical models in the context of enterprises’ e-commerce development), target, comparison and grouping (to reveal innovative methodological approach to assessing ICT impact on e-commerce development of industrial enterprises), tabular, (...) analytical and integral method (for summarizing the analysis results of enterprises readiness to implement ICT, ICT use in the activities of industrial enterprises of Ukraine and the analysis of e-commerce development), mathematical modelling (to build a regression model determining impact of changes in ICT use on the market share occupied by industrial enterprises), generalization (to determine promising directions of e-commerce developing of industrial enterprises). The implementation of a comprehensive approach to understanding the importance of ICT influence on e-commerce development of industrial enterprises will ensure acceleration of the digitalization of business processes, will contribute to the speed increase of enterprises response to customer requests, and increase the market share occupied by enterprises. A new vision of directions for developing e-commerce of industrial enterprises is suggested, which are determined by the need for enterprise rebranding, the development of e-commerce tools and technologies, the importance of outsourcing service automation and promotion of subscription trade. ICT is considered as integration factor that determines prospects for e-commerce development of industrial enterprises and contributes to increasing efficiency of online business management. Research results demonstrate that the use of economic and mathematical modelling is an important tool for assessing ICT impact, and its absence can negatively affect the accuracy and validity of online business management. (shrink)

Modelling with Words is an emerging modelling methodology closely related to the paradigm of Computing with Words introduced by Lotfi Zadeh. This book is an authoritative collection of key contributions to the new concept of Modelling with Words. A wide range of issues in systems modelling and analysis is presented, extending from conceptual graphs and fuzzy quantifiers to humanist computing and self-organizing maps. Among the core issues investigated are - balancing predictive accuracy and high level transparency in learning - scaling (...) linguistic algorithms to high-dimensional data problems - integrating linguistic expert knowledge with knowledge derived from data - identifying sound and useful inference rules - integrating fuzzy and probabilistic uncertainty in data modelling. (shrink)

We live in an information society where the usage, creation, distribution, manipulation, and integration of information is a significant activity. Computations allow us to process information from various sources in various forms and use the derived knowledge in improving efficiency and resilience in our interactions with each other and with our environment. The general theory of information tells us that information to knowledge is as energy is to matter. Energy has the potential to create or modify material structures and information (...) has the potential to create or modify knowledge structures. In this paper, we analyze computations as a vital technological phenomenon of contemporary society which allows us to process and use information. This analysis allows building classifications of computations based on their characteristics and explication of new types of computations. As a result, we extend the existing typologies of computations by delineating novel forms of information representations. While the traditional approach deals only with two dimensions of computation—symbolic and sub-symbolic, here we describe additional dimensions, namely, super-symbolic computation, hybrid computation, fused computation, blended computation, and symbiotic computation. (shrink)

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection (...) of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper. (shrink)