Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe (...) a general model that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science. (shrink)

Philosophers of science have recently focused on the scientific activity of modeling phenomena, and explicated several of its properties, as well as the activities embedded into it. A first approach to modeling has been elaborated in terms of representing a target system: yet other epistemic functions, such as producing data or detecting phenomena, are at least as relevant. Additional useful distinctions have emerged, such as the one between phenomenological and mechanistic models. In biological sciences, besides mathematical models, models (...) now come in three forms: in vivo, in vitro and in silico. Each has been investigated separately, and many specific problems they raised have been laid out. Another relevant distinction is disciplinary: do models differ in significant ways according to the discipline involved—medicine or biology, evolutionary biology or earth science? Focusing on either this threefold distinction or the disciplinary boundaries reveals that they might not be sufficient from a philosophical perspective. On the contrary, focusing on the interaction between these various kinds of models, some interesting forms of explanation come to the fore, as is exemplified by the papers included in this issue. On the other hand, a focus on the use of models, rather than on their content, shows that the distinction between biological and medical models is theoretically sound. (shrink)

Philosophers of science have recently focused on the scientific activity of modeling phenomena, and explicated several of its properties, as well as the activities embedded into it. A first approach to modeling has been elaborated in terms of representing a target system: yet other epistemic functions, such as producing data or detecting phenomena, are at least as relevant. Additional useful distinctions have emerged, such as the one between phenomenological and mechanistic models. In biological sciences, besides mathematical models, models (...) now come in three forms: in vivo, in vitro and in silico. Each has been investigated separately, and many specific problems they raised have been laid out. Another relevant distinction is disciplinary: do models differ in significant ways according to the discipline involved—medicine or biology, evolutionary biology or earth science? Focusing on either this threefold distinction or the disciplinary boundaries reveals that they might not be sufficient from a philosophical perspective. On the contrary, focusing on the interaction between these various kinds of models, some interesting forms of explanation come to the fore, as is exemplified by the papers included in this issue. On the other hand, a focus on the use of models, rather than on their content, shows that the distinction between biological and medical models is theoretically sound. (shrink)

Philosophers of science have recently focused on the scientific activity of modeling phenomena, and explicated several of its properties, as well as the activities embedded into it. A first approach to modeling has been elaborated in terms of representing a target system: yet other epistemic functions, such as producing data or detecting phenomena, are at least as relevant. Additional useful distinctions have emerged, such as the one between phenomenological and mechanistic models. In biological sciences, besides mathematical models, models (...) now come in three forms: in vivo, in vitro and in silico. Each has been investigated separately, and many specific problems they raised have been laid out. Another relevant distinction is disciplinary: do models differ in significant ways according to the discipline involved—medicine or biology, evolutionary biology or earth science? Focusing on either this threefold distinction or the disciplinary boundaries reveals that they might not be sufficient from a philosophical perspective. On the contrary, focusing on the interaction between these various kinds of models, some interesting forms of explanation come to the fore, as is exemplified by the papers included in this issue. On the other hand, a focus on the use of models, rather than on their content, shows that the distinction between biological and medical models is theoretically sound. (shrink)

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)

The epistemic value of models has traditionally been approached from a representational perspective. This paper argues that the artifactual approach evades the problem of accounting for representation and better accommodates the modal dimension of modeling. From an artifactual perspective, models are viewed as erotetic vehicles constrained by their construction and available representational tools. The modal dimension of modeling is approached through two case studies. The first portrays mathematical modeling in economics, while the other discusses the modeling (...) practice of synthetic biology, which exploits and combines models in various modes and media. Neither model intends to represent any actual target system. Rather, they are constructed to study possible mechanisms through the construction of a model system with built-in dependencies. (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)

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)

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.

Inquiries into the nature of scientific modeling have tended to focus their attention on mathematical models and, relatedly, to think of nonconcrete models as mathematical structures. The arguments of this article are arguments for rethinking both tendencies. Nonmathematical models play an important role in the sciences, and our account of scientific modeling must accommodate that fact. One key to making such accommodations, moreover, is to recognize that one kind of thing we use the term ‘model’ to refer to (...) is a collection of propositions. (shrink)

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)

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 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)

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)

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)

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.

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)

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)

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)

Mathematical modeling can ground communication and reciprocal enrichment among fields of knowledge whose domains are very different. We propose a new mathematical model applicable in biology, specified into ecology and evolutionary biology, and in cultural transmission studies, considered as a branch of economics. Main inspiration for the model are some biological concepts we call “eco-phenotypic” such as development, plasticity, reaction norm, phenotypic heritability, epigenetics, and niche construction. “Physiology” is a core concept we introduce and translate differently in the biological (...) and cultural domains. The model is ecological in that it aims at describing and studying organisms and populations that perform living, intended as a thermodynamic, matter-energy process concerning resources gathering, usage, and depletion in a spatiotemporal context with given characteristics, as well as with multiplication and space occupation. The model also supports evolution, intended as a dynamics including cumulative change in the features of unique organisms that are connected into breeding populations. The model is then applicable to the economics of cultural transmission in which individuals form their attitudes and patterns of behavior under a complex system of influences derived from their “cultural parents”, other members of the society, and the environment. On the side of biology, an innovative goal is to integrate in a single model all the eco-phenotypic concepts as well as both evolution and ecology. On the side of cultural transmission, eco-phenotypic modeling seems more appropriate in capturing some aspects of cultural systems which are modeled away in the earlier framework based on Mendelian population genetics. (shrink)

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

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 classical (set-theoretic) concept of structure has become essential for every contemporary account of a scientific theory, but also for the metatheoretical accounts dealing with the adequacy of such theories and their methods. In the latter category of accounts, and in particular, the structural metamodels designed for the applicability of mathematics have struggled over the last decade to justify the use of mathematical models in sciences beyond their 'indispensability' in terms of either method or concepts/entities. In this paper, I (...) argue that these metamodels employ structures of different natures and epistemologies, and this diversity does pose a serious problem to the intended justification. (shrink)

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins (...) by explaining in simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability, combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one, but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.". (shrink)

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

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)

This study provides a basic introduction to agent-based modeling (ABM) as a powerful blend of classical and constructive mathematics, with a primary focus on its applicability for social science research. The typical goals of ABM social science researchers are discussed along with the culture-dish nature of their computer experiments. The applicability of ABM for science more generally is also considered, with special attention to physics. Finally, two distinct types of ABM applications are summarized in order to illustrate concretely (...) the duality of ABM: Real-world systems can not only be simulated with verisimilitude using ABM; they can also be efficiently and robustly designed and constructed on the basis of ABM principles. (shrink)

Estimation of the repartition of asynchronous cells in the cell cycle can be explained by two hypotheses:– - the cells are supposed to be distributed into three groups: cells with a 2c DNA content (G0/1 phase), cells with a 4c DNA content (G2+M phase) and cells with a DNA content ranging from 2c to 4c (S phase); – - there is a linear relationship between the amount of fluorescence emitted by the fluorescent probe which reveals the DNA and the DNA (...) content. According to these hypotheses, the cell cycle can be represented by the following equation. (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)

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)

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 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)

Among the universal attributes of homo sapiens, several have become established as special fields of study—language, art and music, religion, and political economy. But mathematics, another universal attribute of our species, is still modeled separately by logicians, historians, neuroscientists, and others. Could it be integrated into “mathematics studies,” a coherent, many-faceted branch of empirical science? Could philosophers facilitate such a unification? Some philosophers of mathematics identify themselves with “positions” on the nature of mathematics. Those “positions” could (...) more productively serve as models of mathematics. (shrink)

This paper brings together Thompson's naive action explanation with interventionist modeling of causal structure to show how they work together to produce causal models that go beyond current modeling capabilities, when applied to specifically selected systems. By deploying well-justified assumptions about rationalization, we can strengthen existing causal modeling techniques' inferential power in cases where we take ourselves to be modeling causal systems that also involve actions. The internal connection between means and end exhibited in naive action (...) explanation has a modal strength like that of distinctively mathematical explanation, rather than that of causal explanation. Because it is stronger than causation, it can be treated as if it were merely causal in a causal model without thereby overextending the justification it can provide for inferences. This chapter introduces and demonstrate the usage of the Rationalization condition in causal modeling, where it is apt for the system(s) being modeled, and to provide the basics for incorporating R variables into systems of variables and R arrows into DAGs. Use of the Rationalization condition supplements causal analysis with action analysis where it is apt. (shrink)

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of (...) the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction. (shrink)

The aim of this article was to discuss the modeling and control method of quadrotor unmanned aerial vehicle. In the process of modeling, mechanism modeling and experimental testing are combined, especially the motor and propeller are modeled in detail. Through the understanding of the body structure and flight principle of the quadrotor UAV, the Newton–Euler method is used to analyze the dynamics of the quadrotor UAV, and the mathematical model of the UAV is established under the small (...) angle rotation. Process identifier is used to control it. First, the attitude angle of the model is controlled by PID, and based on this, the speed in each direction is controlled by PID. Then, the PID control of the four rotor aircraft with the center of gravity offset is simulated by MATLAB. The results show that the pitch angle and roll angle can be controlled by 5 degrees together without center of gravity deviation, and the PID can effectively control the control quantity and achieve the desired effect in a short time. Classical BP algorithm, classical GA-BP algorithm, and improved GA-BP algorithm were trained, respectively, with a total of 150 sets of training data, training function uses Levenberg-Marquardt, and performance function uses mean squared error. In the background of the same noise, the improved GA-BP algorithm has the highest detection rate, classical GA-BP algorithm is the second, and classical BP algorithm is the worst. The simulation results show that the PID control law can effectively control the attitude angle and speed of the rotor UAV in the case of center of gravity deviation. (shrink)

This research project investigated manifestations of critical thinking in pupils 10 to 12 years of age during their group discussions held in the context of Philosophy for Children Adapted to Mathematics. The objective of the research project was to examine, through the pupils' discussions, the development of dialogical critical thinking processes. The research was conducted during an entire school year. The research method was based on the Grounded Theory approach; the material used consisted of transcripts of verbal exchanges among (...) the pupils. Analysis of the transcripts revealed that: critical thinking appears to the extent that a 'dia-logue' is established among pupils; on the cognitive level, dialogical critical thinking is comprised of four thinking modes: logical, creative, responsible and meta-cognitive; and on the epistemological level, dialogical critical thinking is only manifested in a context where egocentricity of perspective and relativism of beliefs are transcended. (shrink)