Organismic Supercategores: II. On Multistable Systems\ud \ud

The representation of biological systems in terms of organismic supercategories, introduced in previous papers by Baianu et al. (Bull. Math. Biophysics,30, 625–636;31, 59–70) is further discussed. To state more clearly this representation some new definitions are introduced. Also, some necessary changes in axiomatics are made. The conclusion is reached that any organismic supercategory has at least one superpushout, and this expresses the fact that biological systems are multistable. This way a connection between some results of Rashevsky’s theory of organismic sets and our results becomes obvious

Lie Calculus

We explain that general differential calculus and Lie theory have a common foundation: Lie Calculus is differential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher order theory naturally involves higher algebra (n-fold groupoids).(conceptual, topological) differential calculus, groupoids, higher algebra($n$-fold groupoids), Lie group, Lie groupoid, tangent groupoid, cubes of ringsComment: V2 : minor corrections; to appear in: Proceedings of 50. Seminar Sophus Lie, Banach Center Publications, Warsa

Interactive Data Exploration with Smart Drill-Down

We present {\em smart drill-down}, an operator for interactively exploring a relational table to discover and summarize "interesting" groups of tuples. Each group of tuples is described by a {\em rule}. For instance, the rule $(a, b, \star, 1000)$ tells us that there are a thousand tuples with value $a$ in the first column and $b$ in the second column (and any value in the third column). Smart drill-down presents an analyst with a list of rules that together describe interesting aspects of the table. The analyst can tailor the definition of interesting, and can interactively apply smart drill-down on an existing rule to explore that part of the table. We demonstrate that the underlying optimization problems are {\sc NP-Hard}, and describe an algorithm for finding the approximately optimal list of rules to display when the user uses a smart drill-down, and a dynamic sampling scheme for efficiently interacting with large tables. Finally, we perform experiments on real datasets on our experimental prototype to demonstrate the usefulness of smart drill-down and study the performance of our algorithms

Abstract Interpretation of Supermodular Games

Supermodular games find significant applications in a variety of models, especially in operations research and economic applications of noncooperative game theory, and feature pure strategy Nash equilibria characterized as fixed points of multivalued functions on complete lattices. Pure strategy Nash equilibria of supermodular games are here approximated by resorting to the theory of abstract interpretation, a well established and known framework used for designing static analyses of programming languages. This is obtained by extending the theory of abstract interpretation in order to handle approximations of multivalued functions and by providing some methods for abstracting supermodular games, in order to obtain approximate Nash equilibria which are shown to be correct within the abstract interpretation framework

Categorical Ontology of Complex Systems, Meta-Systems and Theory of Levels: The Emergence of Life, Human Consciousness and Society

Single cell interactomics in simpler organisms, as well as somatic cell interactomics in multicellular organisms, involve biomolecular interactions in complex signalling pathways that were recently represented in modular terms by quantum automata with ‘reversible behavior’ representing normal cell cycling and division. Other implications of such quantum automata, modular modeling of signaling pathways and cell differentiation during development are in the fields of neural plasticity and brain development leading to quantum-weave dynamic patterns and specific molecular processes underlying extensive memory, learning, anticipation mechanisms and the emergence of human consciousness during the early brain development in children. Cell interactomics is here represented for the first time as a mixture of ‘classical’ states that determine molecular dynamics subject to Boltzmann statistics and ‘steady-state’, metabolic (multi-stable) manifolds, together with ‘configuration’ spaces of metastable quantum states emerging from complex quantum dynamics of interacting networks of biomolecules, such as proteins and nucleic acids that are now collectively defined as quantum interactomics. On the other hand, the time dependent evolution over several generations of cancer cells --that are generally known to undergo frequent and extensive genetic mutations and, indeed, suffer genomic transformations at the chromosome level (such as extensive chromosomal aberrations found in many colon cancers)-- cannot be correctly represented in the ‘standard’ terms of quantum automaton modules, as the normal somatic cells can. This significant difference at the cancer cell genomic level is therefore reflected in major changes in cancer cell interactomics often from one cancer cell ‘cycle’ to the next, and thus it requires substantial changes in the modeling strategies, mathematical tools and experimental designs aimed at understanding cancer mechanisms. Novel solutions to this important problem in carcinogenesis are proposed and experimental validation procedures are suggested. From a medical research and clinical standpoint, this approach has important consequences for addressing and preventing the development of cancer resistance to medical therapy in ongoing clinical trials involving stage III cancer patients, as well as improving the designs of future clinical trials for cancer treatments.\ud \ud \ud KEYWORDS: Emergence of Life and Human Consciousness;\ud Proteomics; Artificial Intelligence; Complex Systems Dynamics; Quantum Automata models and Quantum Interactomics; quantum-weave dynamic patterns underlying human consciousness; specific molecular processes underlying extensive memory, learning, anticipation mechanisms and human consciousness; emergence of human consciousness during the early brain development in children; Cancer cell ‘cycling’; interacting networks of proteins and nucleic acids; genetic mutations and chromosomal aberrations in cancers, such as colon cancer; development of cancer resistance to therapy; ongoing clinical trials involving stage III cancer patients’ possible improvements of the designs for future clinical trials and cancer treatments. \ud \u

TEMPOS: A Platform for Developing Temporal Applications on Top of Object DBMS

This paper presents TEMPOS: a set of models and languages supporting the manipulation of temporal data on top of object DBMS. The proposed models exploit object-oriented technology to meet some important, yet traditionally neglected design criteria related to legacy code migration and representation independence. Two complementary ways for accessing temporal data are offered: a query language and a visual browser. The query language, namely TempOQL, is an extension of OQL supporting the manipulation of histories regardless of their representations, through fully composable functional operators. The visual browser offers operators that facilitate several time-related interactive navigation tasks, such as studying a snapshot of a collection of objects at a given instant, or detecting and examining changes within temporal attributes and relationships. TEMPOS models and languages have been formalized both at the syntactical and the semantical level and have been implemented on top of an object DBMS. The suitability of the proposals with regard to applications' requirements has been validated through concrete case studies

Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists

This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational Maps, Bidirectional Associative Memories and Fuzzy Associative Memories are defined here. The authors introduce 13 multi-expert models using the notion of fuzzy supermatrices. These models are described with illustrative examples. This book has three chapters. In the first chaper, the basic concepts about super matrices and fuzzy super matrices are recalled. Chapter two introduces the notion of fuzzy super matrices adn their properties. The final chapter introduces many super fuzzy multi expert models.Comment: 280 page