Fundamental properties of N-valued logics are compared and eleven theorems are presented for their Logic Algebras, including Łukasiewicz–Moisil Logic Algebras represented in terms of categories and functors. For example, the Fundamental Logic Adjunction Theorem allows one to transfer certain universal, or global, properties of the Category of Boolean Algebras,, (which are well-understood) to the more general category \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal L}$$\end{document}Mn of Łukasiewicz–Moisil Algebras. Furthermore, the relationships of LMn-algebras (...) to other many-valued logical structures, such as the n-valued Post, MV and Heyting logic algebras, are investigated and several pertinent theorems are derived. Applications of Łukasiewicz–Moisil Algebras to biological problems, such as nonlinear dynamics of genetic networks – that were previously reported – are also briefly noted here, and finally, probabilities are precisely defined over LMn-algebras with an eye to immediate, possible applications in biostatistics. (shrink)

This rare publication continues an exploratory journey in relational biology, a study of biology in terms of the organization of networked connections in living systems. It builds on the author's two earlier monographs which looked at the epistemology of life and the ontogeny of life. Here the emphasis is on the intangibility of life, that the real nature of living systems is conveyed not by their tangible material basis but by their intangible inherent processes. Relational biology is the approach that (...) hails 'function dictates structure'; it is mathematics decoded into biological realizations. Therefore, the work begins with a concise introduction to category theory, equiping the reader with the mathematical metalanguage of relation biology. The book is organized around three parts: Part I is a comprehensive study of the most important functor in relational biology, the power set functor. The author lays the set-theoretic foundations of the functorial connections in relational biology, exploring relations, mappings, and set-valued mappings. In Part II, Natural Law receives a new mathematical formulation founded on two axioms: 'Everything is a set.' and 'Every process is a set-valued mapping.' The reader sees how Metabolism-Repair networks, equipped with set-valued processors, expand their role from models of biological entities to generic models of all natural systems. Part III expounds the various shades of invertibility in general, and the inversion of encoding to decoding in particular. A plethora of mathematical and biological examples illustrate the category-theoretic concepts of equivalence and adjunction. This book's algebraic approach to biological models will appeal to researchers and graduate students in mathematics, biology, and the philosophy of science. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

Fundamental properties of N-valued logics are compared and eleven theorems are presented for their Logic Algebras, including Łukasiewicz–Moisil Logic Algebras represented in terms of categories and functors. For example, the Fundamental Logic Adjunction Theorem allows one to transfer certain universal, or global, properties of the Category of Boolean Algebras,, (which are well-understood) to the more general category \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal L}$$\end{document}Mn of Łukasiewicz–Moisil Algebras. Furthermore, the relationships of LMn-algebras (...) to other many-valued logical structures, such as the n-valued Post, MV and Heyting logic algebras, are investigated and several pertinent theorems are derived. Applications of Łukasiewicz–Moisil Algebras to biological problems, such as nonlinear dynamics of genetic networks – that were previously reported – are also briefly noted here, and finally, probabilities are precisely defined over LMn-algebras with an eye to immediate, possible applications in biostatistics. (shrink)

A hypergroup, as a generalization of the notion of a group, was introduced by F. Marty in 1934. The first book in hypergroup theory was published by Corsini. Nowadays, hypergroups have found applications to many subjects of pure and applied mathematics, for example, in geometry, topology, cryptography and coding theory, graphs and hypergraphs, probability theory, binary relations, theory of fuzzy and rough sets and automata theory, physics, and also in biological inheritance.

This paper illustrates how Priestley duality can be used in the transfer of an optimal natural duality from a minimal generating algebra for a quasi-variety to other generating algebras. Detailed calculations are given for the quasi-variety \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{I}\mathbb{S}\mathbb{P}(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{4} )$$ \end{document} of Kleene algebras and the quasi-varieties \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$B$$ \end{document}n of pseudocomplemented distributive lattices (n ≥ 1).

In programs of acoustic survey, the amount of data collected and the lack of automatic routines for their classification and interpretation can represent a serious obstacle to achieving quick results. To overcome these obstacles, we are proposing an ecosemiotic model of data mining, ecoacoustic event detection and identification, that uses a combination of the acoustic complexity indices and automatically extracts the ecoacoustic events of interest from the sound files. These events may be indicators of environmental functioning at the scale of (...) individual vocal species, the acoustic community, the sound marks, or the soundscape. The EEDI model is represented by three procedural steps: 1) selecting acoustic data according to environmental variables, 2) detecting the events by creating an ecoacoustic event space produced by plotting ACIft and its evenness, 3) identifying events according to the level of correlation between the acoustic signature of the detected events and an ad hoc library of previously identified events. The EEDI procedure can be extensively used in basic and applied research. In particular, EEDI may be used in long-term monitoring programs to assess the effect of climate change on individual vocal species behavior, population, and acoustic community dynamics. The EEDI model can be also used to investigate acoustic human intrusion in natural systems and the effect in urban areas. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Convention for Protection of Human Rights and Dignity of the Human Being with Regard to the Application of Biology and Biomedicine: Convention on Human Rights and BiomedicineCouncil of EuropePreambleThe Member States of the Council of Europe, the other States and the European Community signatories hereto,Bearing in mind the Universal Declaration of Human Rights proclaimed by the General Assembly of the United Nations on 10 December 1948;Bearing in mind the (...) Convention for the Protection of Human Rights and Fundamental Freedoms of 4 November 1950;Bearing in mind the European Social Charter of 18 October 1961;Bearing in mind the International Covenant on Civil and Political Rights and the International Covenant on Economic, Social and Cultural Rights of 16 December 1966;Bearing in mind the Convention for the Protection of Individuals with Regard to Automatic Processing of Personal Data of 28 January 1981;Bearing also in mind the Convention on the Rights of the Child of 20 November 1989;Considering that the aim of the Council of Europe is the achievement of a greater unity between its members and that one of the methods by which that aim is to be pursued is the maintenance and further realisation of human rights and fundamental freedoms;Conscious of the accelerating developments in biology and medicine;Convinced of the need to respect the human being both as an individual and as a member of the human species and recognising the importance of ensuring the dignity of the human being; [End Page 277]Conscious that the misuse of biology and medicine may lead to acts endangering human dignity;Affirming that progress in biology and medicine should be used for the benefit of present and future generations;Stressing the need for international co-operation so that all humanity may enjoy the benefits of biology and medicine;Recognising the importance of promoting a public debate on the questions posed by the application of biology and medicine and the responses to be given thereto;Wishing to remind all members of society of their rights and responsibilities;Taking account of the work of the Parliamentary Assembly in this field, including Recommendation 1160 (1991) on the preparation of a Convention on bioethics;Resolving to take such measures as are necessary to safeguard human dignity and the fundamental rights and freedoms of the individual with regard to the application of biology and medicine;Have agreed as follows:Chapter IGeneral provisionsArticle 1. (Purpose and object)Parties to this Convention shall protect the dignity and identity of all human beings and guarantee everyone, without discrimination, respect for their integrity and other rights and fundamental freedoms with regard to the application of biology and medicine.Each Party shall take in its internal law the necessary measures to give effect to the provisions of this Convention.Article 2. (Primacy of the human being)The interests and welfare of the human being shall prevail over the sole interest of society or science.Article 3. (Equitable access to health care)Parties, taking into account health needs and available resources, shall take appropriate measures with a view to providing, within their jurisdiction, equitable access to health care of appropriate quality. [End Page 278]Article 4. (Professional standards)Any intervention in the health field, including research, must be carried out in accordance with relevant professional obligations and standards.Chapter IIConsentArticle 5. (General rule)An intervention in the health field may only be carried out after the person concerned has given free and informed consent to it.This person shall beforehand be given appropriate information as to the purpose and nature of the intervention as well as on its consequences and risks.The person concerned may freely withdraw consent at any time.Article 6. (Protection of persons not able to consent)1. Subject to Articles 17 and 20 below, an intervention may only be carried out on a person who does not have the capacity to consent, for his or her direct benefit.2. Where, according to law, a minor does not have the capacity to consent to an intervention, the intervention may only be carried out with the authorisation of his or her representative or an authority or a person or... (shrink)

The extended reduced Kies distribution, which is an asymmetric flexible extension of the reduced Kies distribution, is the subject of this research. Some of its most basic mathematical properties are deduced from its formal definitions. We computed the ExRKD parameters using eight well-known methods. A full simulation analysis was done that allows the study of these estimators’ asymptotic behavior. The efficiency and applicability of the ExRKD are investigated via the modeling of COVID-19 and milk data sets, which demonstrates that the (...) ExRKD delivers a better match to the data sets when compared to competing models. (shrink)

This paper illustrates how Priestley duality can be used in the transfer of an optimal natural duality from a minimal generating algebra for a quasi-variety to other generating algebras. Detailed calculations are given for the quasi-variety of Kleene algebras and the quasi-varieties n of pseudocomplemented distributive lattices (n 1).

This paper illustrates how Priestley duality can be used in the transfer of an optimal natural duality from a minimal generating algebra for a quasi-variety to other generating algebras. Detailed calculations are given for the quasi-variety \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{I}\mathbb{S}\mathbb{P}(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{4} )$$ \end{document} of Kleene algebras and the quasi-varieties \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$B$$ \end{document}n of pseudocomplemented distributive lattices (n ≥ 1).

Most philosophical systems of ethics are based upon the reciprocity principle as expressed by the Golden Rule: “Do unto others as you would have them do unto you!” The same idea underlies Kant's categorical imperative: “Act always on such a maxim as thou canst at the same time will to be a universal law!” Here, the individual act is generalized into, and considered as the specific application of the general law of ethics.

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...) Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...) Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

Cardiovascular modelling has been a major research subject for the last decade. Different cardiac models have been developed at a cellular level as well as at the whole organ level. Most of these models are defined by a comprehensive cellular modelling using continuous formalisms or by a tissue-level modelling often based on discrete formalisms. Nevertheless, both views still suffer from difficulties that reduce their clinical applications: the first approach requires heavy computational resources while the second one is not able (...) to reproduce certain pathologies.This paper presents an original methodology trying to gather advantages from both approaches, by means of a hybrid model mixing discrete and continuous formalisms. This method has been applied to define a hybrid model of cardiac action potential propagation on a 2D grid of endocardial cells, combining cellular automata and a set of cells defined by the Beeler-Reuter model. For simulations under physiological and ischemic conditions, results show that the action potential propagation as well as electrogram reconstructions are consistent with clinical diagnosis. Finally, the advantage of the proposed approach is discussed within the frame of cardiac modelling and simulation. (shrink)

The Streptococcus pyogenes CRISPR‐Cas system has gained widespread application as a genome editing and gene regulation tool as simultaneous cellular delivery of the Cas9 protein and guide RNAs enables recognition of specific DNA sequences. The recent discovery that Cas9 can also bind and cleave RNA in an RNA‐programmable manner indicates the potential utility of this system as a universal nucleic acid‐recognition technology. RNA‐targeted Cas9 (RCas9) could allow identification and manipulation of RNA substrates in live cells, empowering the study of cellular (...) gene expression, and could ultimately spawn patient‐ and disease‐specific diagnostic and therapeutic tools. Here we describe the development of RCas9 and compare it to previous methods for RNA targeting, including engineered RNA‐binding proteins and other types of CRISPR‐Cas systems. We discuss potential uses ranging from live imaging of transcriptional dynamics to patient‐specific therapies and applications in synthetic biology. (shrink)

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition result (...) involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

Phytomorphology — if concerned with development — often concentrates on correlative changes of form and neglects the aspects of age, time and clock, although the plant's spatial and temporal organisation are intimately interconnected. Common age as measured in physical time by a physical process is compared to biological age as measured by a biological clock based on a biological process. A typical example for a biological clock on the organ level is, for example, a shoot. Its (...) biological age is measured by the biological time unit of a plastochron, which itself is defined by the cyclic-periodic initiation of the leaves. In a controlled environment biological age may replace physical age. However, biological and physical age are not necessarily linearly convertible into each other. In stationary or steady state conditions the repetitive initiation of any organ, unit or module of an articulate plant or plant modular system may define the biological time unit. A linear — monotonous biological process, e.g. axis elongation, may also define a biological time unit as a certain amount of additional growth, e.g. of length. One may speak of periodical and of continuous plastochron or, perhaps, of plastochron and rheochron. A precise measure of biological age is the generalized plastochron index applying to any modular system and module respectively. However, one should be aware that it is based on two clocks, one of them referring to the periodic process of module initiation for counting the integer plastochrons and the other to the continuous plastochron of module growth for the determination of the fraction of one plastochron. The application of the concepts is restricted to phases of stationary or steady state growth and development. In certain cases of non-stationary or non-steady state conditions a normalized-age concept may apply. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

Following a previous article published in Biological Theory, in this study we present a mathematical theory for a science of qualities as directly perceived by living organisms, and based on morphological patterns. We address a range of qualitative phenomena as observables of a psychological system seen as an impredicative system. The starting point of our study is the notion that perceptual phenomena are projections of underlying invariants, objects that remain unchanged when transformations of a certain class under consideration are (...) applied. The study develops with the observables, the entailed total order and metric, whence the algebra and the geometry of such a science, presenting a formal phenomenological model for phenomena that are not rigidly Euclidean. We show how non-Euclidean perception can have many useful Euclidean formalizations, as well as locally-homeomorphic-to-Euclidean-space models. The mathematical models we provide are tested on the basis of results from experimental psychology, in particular from the field of color, time, and space perception. (shrink)

Recent sequencing of the metazoan Oikopleura dioica genome has provided important insights, which challenges the current understanding of eukaryotic genome evolution. Many genomic features of O. dioica show deviation from the commonly observed trends in other eukaryotic genomes. For instance, O. dioica has a rapidly evolving, highly compact genome with a divergent intron‐exon organization. Additionally, O. dioica lacks the minor spliceosome and key DNA repair pathway genes. Even with a compact genome, O. dioica contains tandem repeats, comparable to other eukaryotes, (...) and shows lineage‐specific expansion of certain protein domains. Here, we review its genomic features in the context of current knowledge, discuss implications for contemporary biology and identify areas for further research. Analysis of the O. dioica genome suggests that non‐adaptive forces such as elevated mutation rates might influence the evolution of genome architecture. The knowledge of unique genomic features and splicing mechanisms in O. dioica may be exploited for synthetic biology applications, such as generation of orthogonal splicing systems. (shrink)

Choice Outstanding Academic Title, 1996. In hundreds of articles by experts from around the world, and in overviews and "road maps" prepared by the editor, The Handbook of Brain Theory and Neural Networkscharts the immense progress made in recent years in many specific areas related to two great questions: How does the brain work? and How can we build intelligent machines? While many books have appeared on limited aspects of one subfield or another of brain theory and neural networks, the (...) Handbookcovers the entire sweep of topics—from detailed models of single neurons, analyses of a wide variety of biological neural networks, and connectionist studies of psychology and language, to mathematical analyses of a variety of abstract neural networks, and technological applications of adaptive, artificial neural networks. The excitement, and the frustration, of these topics is that they span such a broad range of disciplines including mathematics, statistical physics and chemistry, neurology and neurobiology, and computer science and electrical engineering as well as cognitive psychology, artificial intelligence, and philosophy. Thus, much effort has gone into making the Handbookaccessible to readers with varied backgrounds while still providing a clear view of much of the recent, specialized research in specific topics. The heart of the book, part III, comprises of 267 original articles by leaders in the various fields, arranged alphabetically by title. Parts I and II, written by the editor, are designed to help readers orient themselves to this vast range of material. Part I, Background, introduces several basic neural models, explains how the present study of brain theory and neural networks integrates brain theory, artificial intelligence, and cognitive psychology, and provides a tutorial on the concepts essential for understanding neural networks as dynamic, adaptive systems. Part II, Road Maps, provides entry into the many articles of part III through an introductory "Meta-Map" and twenty-three road maps, each of which tours all the Part III articles on the chosen theme. (shrink)

Choice Outstanding Academic Title, 1996. In hundreds of articles by experts from around the world, and in overviews and "road maps" prepared by the editor, The Handbook of Brain Theory and Neural Networks charts the immense progress made in recent years in many specific areas related to great questions: How does the brain work? How can we build intelligent machines? While many books discuss limited aspects of one subfield or another of brain theory and neural networks, the Handbook covers the (...) entire sweep of topics—from detailed models of single neurons, analyses of a wide variety of biological neural networks, and connectionist studies of psychology and language, to mathematical analyses of a variety of abstract neural networks, and technological applications of adaptive, artificial neural networks. Expository material makes the book accessible to readers with varied backgrounds while still offering a clear view of the recent, specialized research on specific topics. (shrink)

The main aim of the paper is to solve a problem posed in Di Nola et al. (Multiple Val. Logic 8:715–750, 2002) whether every pseudo BL-algebra with two negations is good, i.e. whether the two negations commute. This property is intimately connected with possessing a state, which in turn is essential in quantum logical applications. We approach the solution by describing the structure of pseudo BL-algebras and pseudo hoops as important families of quantum structures. We show when a (...) pseudo hoop can be embedded into the negative cone of the reals. We give an equational base characterizing representable pseudo hoops. We also describe some subvarieties: normal-valued, and varieties where each maximal filter is normal. We produce some noncommutative covers and extend the area where each algebra is good. Finally, we show that there are uncountably many subvarieties of pseudo BL-algebras having members that are not good. (shrink)

On the basis of previous studies in relational biology and the phenomenological calculus, in my contribution I outline the mathematical foundations of biological perception generally, and visual perception specifically. In this approach, the premise is that objects in nature are not directly accessible, and that real manifestations are projections of these invariant objects. The morphology of observables is mathematically entailed by the duality of projections and projectors in a bilinear algebra that is the phenomenological calculus. The relationships between what (...) is not directly accessible (which can be defined as noumena) and phenomena may be explicated in terms of metabolism and repair, whence a geometric theory of the perceived, the visible in particular, may be formulated in the category-theoretic language of relational biology. (shrink)

Philosophical analysis of ecological theories has lagged behind the study of evolutionary theory. The semantic conception of scientific theories, which has been employed successfully in the analysis of evolutionary theory, is adopted here to analyse ecological theory. Two general problems in ecology are discussed. One arises from the continued use of covering law models in ecology, and the other concerns the applicability of ecological theory in conservation biology. The semantic conception of ecological theories is used to resolve these problems.

Over the last decade the modeling and the storage of biological data has been a topic of wide interest for scientists dealing with biological and biomedical research. Currently most data is still stored in text files which leads to data redundancies and file chaos.In this paper we show how to use relational modeling techniques and relational database technology for modeling and storing biological sequence data, i.e. for data maintained in collections like EMBL or SWISS-PROT to better serve (...) the needs for these application domains. (shrink)

The technique of covers is now well established in semigroup theory. The idea is, given a semigroup S, to find a semigroup having a better understood structure than that of S, and an onto morphism of a specific kind from to S. With the right conditions on , the behaviour of S is closely linked to that of . If S is finite one aims to choose a finite . The celebrated results for inverse semigroups of McAlister in the 1970s (...) form the flagship of this theory.Weakly left quasi-ample semigroups form a quasivariety (of algebras of type(2, 1)), properly containing the classes of groups, and of inverse, left ample, and weakly left ample semigroups. We show how the existence of finite proper covers for semigroups in this quasivariety is a consequence of Ashs powerful theorem for pointlike sets. Our approach is to obtain a cover of a weakly left quasi-ample semigroup S as a subalgebra of S × G, where G is a group. It follows immediately from the fact that weakly left quasi-ample semigroups form a quasivariety, that is weakly left quasi-ample. We can then specialise our covering results to the quasivarieties of weakly left ample, and left ample semigroups. The latter have natural representations as (2, 1)-subalgebras of partial (one-one) transformations, where the unary operation takes a transformation to the identity map in the domain of . In the final part of this paper we consider representations of weakly left quasi-ample semigroups. (shrink)

George Boole published the pamphlet The Mathematical Analysis of Logic in 1847. He believed that logic should belong to a universal mathematics that would cover both quantitative and nonquantitative research. With his pamphlet, Boole signalled an important change in symbolic logic: in contrast with his predecessors, his thinking was exclusively extensional. Notwithstanding the innovations introduced he accepted all traditional Aristotelean syllogisms. Nevertheless, some criticisms have been raised concerning Boole’s view of Aristotelean logic as the solution of algebraic equations. In order (...) to circumvent such criticisms, we show here how Boole’s conclusions may be deduced from the axioms and inference rules proposed in his pamphlet, from which Aristotle’s deductions in Prior Analytics (including those that are completed through an impossibility) can be stated as theorems. We clarify his method for dealing with both universal and particular premises by means of his symbol v and demystify some criticisms concerning the way he expressed particular premises. Boole’s conclusions for some of those premises for which according to Aristotle there is no deduction are also discussed. The deductive system presented here has the potential to provide a new perspective on Boole’s approach to logic in The Mathematical Analysis of Logic. (shrink)

Asymptotic extremal combinatorics deals with questions that in the language of model theory can be re-stated as follows. For finite models M, N of an universal theory without constants and function symbols (like graphs, digraphs or hypergraphs), let p(M, N) be the probability that a randomly chosen sub-model of N with |M| elements is isomorphic to M. Which asymptotic relations exist between the quantities p(M₁, N),...,p(Mh, N), where M₁,...,Mh are fixed "template" models and |N| grows to infinity? In this paper (...) we develop a formal calculus that captures many standard arguments in the area, both previously known and apparently new. We give the first application of this formalism by presenting a new simple proof of a result by Fisher about the minimal possible density of triangles in a graph with given edge density. (shrink)

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the (...) mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences. (shrink)

This work deals with the expressive power of logics on finite graphs with access to an additional "arbitrary" linear order. The queries that can be expressed this way are the order-invariant queries for the logic. For the standard logics used in computer science, such as first-order logic, it is known that access to an arbitrary linear order increases the expressiveness of the logic. However, when we look at the separating examples, we find that they have satisfying models whose Gaifman Graph (...) is complex -unbounded in valence and in treewidth. We thus explore the expressiveness of order-invariant queries over well-behaved graphs. We prove that first-order order-invariant queries over strings and trees have no additional expressiveness over first-order logic in the original signature. We also prove new upper bounds on order-invariant queries over bounded treewidth and bounded valence graphs. Our results make use of a new technique of independent interest: the application of algebraic characterizations of definability to show collapse results. (shrink)

Catastrophe Theory was developed in an attempt to provide a form of Mathematics particularly apt for applications in the biological sciences. It was claimed that while it could be applied in the more conventional physical way, it could also be applied in a new metaphysical way, derived from the Structuralism of Saussure in Linguistics and Lévi-Strauss in Anthropology.Since those early beginnings there have been many attempts to apply Catastrophe Theory to Biology, but these hopes cannot be said to (...) have been fully realised. (shrink)

Different approaches have been proposed in order to achieve knowledge integration for coronary care monitoring applications, usually in the form of expert systems. The clinical impact of these expert systems, which are based only on "shallow" knowledge, has not been remarkable due to the difficulties associated with the construction and maintenance of a complete knowledge base. Model-based systems represent an alternative to these problems because they allow efficient integration of the "deep" knowledge on the underlying physiological phenomena being monitored. (...) In this work, a brief review of existing model-based systems for cardiac rhythm interpretation is presented, followed by the description of a new system forCardiac Arrhythmia Recognition by Model-Based ECG Matching (CARMEM). Fundamental characteristics of CARMEM are presented; in particular, its ability to provide on-line parameter adaptation to simulate complex rhythms and to match observed ECG signals. The proposed model can be useful for the explanation of the origin of cardiac arrhythmias and contribute towards their robust characterization in the context of coronary care units. (shrink)

We investigate degree of satisfiability questions in the context of Heyting algebras and intuitionistic logic. We classify all equations in one free variable with respect to finite satisfiability gap, and determine which common principles of classical logic in multiple free variables have finite satisfiability gap. In particular we prove that, in a finite non-Boolean Heyting algebra, the probability that a randomly chosen element satisfies $x \vee \neg x = \top $ is no larger than $\frac {2}{3}$. Finally, we generalize (...) our results to infinite Heyting algebras, and present their applications to point-set topology, black-box algebras, and the philosophy of logic. (shrink)

Given the recent explosion of interest in applications of evolutionary biology to understanding human psychology, we think it timely to assure better understanding of modern evolutionary theory among the psychologists who might be using it. We find it necessary to do so because of the very reducd version of evolutionary theorizing that has been incorporated into much of evolutionary psychology so far. Our aim here is to clarify why the use of a reduced version of evolutionary genetics will lead (...) to faulty science and to indicate where other resources of evolutionary biology can be found that might elevate the standard of the evolutionary component of evolutionary psychology. (shrink)

This paper examines an issue that is becoming increasingly relevant as the pressures of a warming planet, changing climate and changing ecosystems ramp up. The broad context for the paper is the intragenerational, intergenerational, and interspecies equity implications of changing the climate and the value orientations of adapting to such change. In addition, the need to stabilize the planetary climate by urgent mitigation of change factors is a foundational ethical assumption. In order to avoid further animal and plant extinctions, or (...) at the very least, their increased vulnerability to becoming rare and endangered; the systematic assisted colonization of “at risk” species is being seriously considered by scientists and managers of biodiversity. The more practical aspects of assisted colonization have been covered in the conservation biology literature; however, the ethical implications of such actions have not been extensively examined. Our discussion of the value issues, using a novel case study approach, will rectify the limited ethical analysis of the issue of assisted colonization of species in the face of climate change pressures. Beyond sustainability ethics, both animal and environmental ethical approaches will be used and intrinsic versus instrumental value orientations in the literature shall form the basis of our discussion. After the application of all the ethical approaches to the case studies, we conclude that without mitigation and the prospect of a future stable climate, assisted colonization will be involved in an inherently unethical process and a “move and lose it” outcome. With mitigation, there is wide-ranging ethical support for assisted colonization. (shrink)

The phenomenological calculus is a relational paradigm for complex systems, closely related in substance and spirit to Robert Rosen’s own approach. Its mathematical language is multilinear algebra. The epistemological exploration continues in this paper, with the expansion of the phenomenological calculus into the realm of anisotropy.

The uniqueness of Psychiatry as a medical speciality lies in the fact that aside from tackling what it considers as illnesses, it has perchance to comment on and tackle many issues of social relevance as well. Whether this is advisable or not is another matter; but such a process is inevitable due to the inherent nature of the branch and the problems it deals with. Moreover this is at the root of the polarization of psychiatry into opposing psychosocial and (...) class='Hi'>biological schools. This gets reflected in their visualization of scope, in definitions and in methodology as well. Whilst healthy criticism of one against the other school is necessary, there should be caution against hasty application of one's frame of reference to an approach that does not intend to follow, or conform to, one's methodology. This should be done within the referential framework of the school critically evaluated, with due consideration for its methods and concepts. Similarly, as at present, there is no evidence to prove one or the other of these approaches as better, aside from personal choice. We can say so even if there is a strong paradigm shift towards the biological at present. A renaissance of scientific psychoanalysis coupled with a perceptive neurobiology which can translate those insights into testable hypotheses holds the greatest promise for psychiatry in the future. This suggests the need for unification of diverse appearing approaches to get a more comprehensive and enlightened worldview. It requires a highly integrative capacity. Just as a physicist thinks simultaneously in terms of particles and waves, a psychiatrist must think of motives, emotions and desires in the same breath as neurobiology, genetics and psychopharmacology. However, the integration must be attempted without destroying the internal cohesiveness of the individual schools. This will give a fair chance for polarization in which a single proper approach in psychiatry could emerge, which may be a conglomerate of diverse appearing approaches of today, or one which supersedes the rest. A synthesis of cognitive psychology and neuroscience offers the greatest promise at present. (shrink)

How fast? How strong? How many? So what? Why do numbers matter in biology? Chromatin binding proteins are forever in motion, exchanging rapidly between bound and free pools. How do regulatory systems whose components are in constant flux ensure stability and flexibility? This review explores the application of quantitative and mathematical approaches to mechanisms of epigenetic regulation. We discuss methods for measuring kinetic parameters and protein quantities in living cells, and explore the insights that have been gained by quantifying and (...) modelling dynamics of chromatin binding proteins. (shrink)

Despite the presumed frequency of conflicts of interest in scientific peer review, there is a paucity of data in the literature reporting on the frequency and type of conflicts that occur, particularly with regard to the peer review of basic science applications. To address this gap, the American Institute of Biological Sciences conducted a retrospective analysis of conflict of interest data from the peer review of 282 biomedical research applications via several onsite review panels. The overall conflicted-ness (...) of these panels was significantly lower than that reported for regulatory review. In addition, the majority of identified conflicts were institutional or collaborative in nature. No direct financial conflicts were identified, although this is likely due to the relatively basic science nature of the research. It was also found that 65 % of identified conflicts were manually detected by AIBS staff searching reviewer CVs and application documents, with the remaining 35 % resulting from self-reporting. The lack of self-reporting may be in part attributed to a lack of perceived risk of the conflict. This result indicates that many potential conflicts go unreported in peer review, underscoring the importance of improving detection methods and standardizing the reporting of reviewer and applicant conflict of interest information. (shrink)

We present a method for rejecting competing models from noisy time-course data that does not rely on parameter inference. First we characterize ordinary differential equation models in only measurable variables using differential-algebra elimination. This procedure gives input-output equations, which serve as invariants for time series data. We develop a model comparison test using linear algebra and statistics to reject incorrect models from their invariants. This algorithm exploits the dynamic properties that are encoded in the structure of the model equations without (...) recourse to parameter values, and, in this sense, the approach is parameter-free. We demonstrate this method by discriminating between different models from mathematical biology. (shrink)