Information Compression, Intelligence, Computing, and Mathematics

This paper presents evidence for the idea that much of artificial intelligence, human perception and cognition, mainstream computing, and mathematics, may be understood as compression of information via the matching and unification of patterns. This is the basis for the "SP theory of intelligence", outlined in the paper and fully described elsewhere. Relevant evidence may be seen: in empirical support for the SP theory; in some advantages of information compression (IC) in terms of biology and engineering; in our use of shorthands and ordinary words in language; in how we merge successive views of any one thing; in visual recognition; in binocular vision; in visual adaptation; in how we learn lexical and grammatical structures in language; and in perceptual constancies. IC via the matching and unification of patterns may be seen in both computing and mathematics: in IC via equations; in the matching and unification of names; in the reduction or removal of redundancy from unary numbers; in the workings of Post's Canonical System and the transition function in the Universal Turing Machine; in the way computers retrieve information from memory; in systems like Prolog; and in the query-by-example technique for information retrieval. The chunking-with-codes technique for IC may be seen in the use of named functions to avoid repetition of computer code. The schema-plus-correction technique may be seen in functions with parameters and in the use of classes in object-oriented programming. And the run-length coding technique may be seen in multiplication, in division, and in several other devices in mathematics and computing. The SP theory resolves the apparent paradox of "decompression by compression". And computing and cognition as IC is compatible with the uses of redundancy in such things as backup copies to safeguard data and understanding speech in a noisy environment

Can You hear the Shape of a Market? Geometric Arbitrage and Spectral Theory

Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the 'instantaneous arbitrage capability' generated by the market itself. The cashflow bundle is the vector bundle associated to this stochastic principal fibre bundle for the natural choice of the vector space fibre. The cashflow bundle carries a stochastic covariant differentiation induced by the connection on the principal fibre bundle. The link between arbitrage theory and spectral theory of the connection Laplacian on the vector bundle is given by the zero eigenspace resulting in a parametrization of all risk neutral measures equivalent to the statistical one. This indicates that a market satisfies the (NFLVR) condition if and only if $0$ is in the discrete spectrum of the connection Laplacian on the cash flow bundle or of the Dirac Laplacian of the twisted cash flow bundle with the exterior algebra bundle. We apply this result by extending Jarrow-Protter-Shimbo theory of asset bubbles for complete arbitrage free markets to markets not satisfying the (NFLVR). Moreover, by means of the Atiyah-Singer index theorem, we prove that the Euler characteristic of the asset nominal space is a topological obstruction to the the (NFLVR) condition, and, by means of the Bochner-Weitzenb\"ock formula, the non vanishing of the homology group of the cash flow bundle is revealed to be a topological obstruction to (NFLVR), too. Asset bubbles are defined, classified and decomposed for markets allowing arbitrage.Comment: arXiv admin note: substantial text overlap with arXiv:1406.6805, arXiv:0910.167

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Toward the Integration of Economics and Outdoor Recreation Management

The general theme of this bulletin is that improved management of public-sector recreational resources is a multidisciplinary task. To this end, we attempt to integrate elements of outdoor recreation management theory and economics. The bulletin is written for both resource managers and researchers. For the former, our intent is to emphasize the importance of being aware of economic implications-at least conceptually-of management actions that influence the character and availability of recreational opportunities. To researchers involved in developing recreation management theory, we draw attention to the parallel between recreation management theory and the traditional managerial economic model of the firm. To economists, particularly those involved in developing and applying nonmarket valuation techniques, we draw attention to the types of decisions faced by resource managers. We argue that the most important resource allocation issues are of the incremental variety, so nonmarket valuation should also yield incremental values. These values alone, however, are not sufficient economic input into rational public choice analysis. The missing link , or nexus, between outdoor recreation management theory and economic analysis is the integration of supply and demand, as called for by traditional managerial economics. Collaborative research to develop recreation supply response functions akin to agricultural production functions is an essential step that is missing from both literatures. Theoretical and applied work assume greater practical importance if they feed information into this broadened framework. It is our hope that this bulletin will bring the disciplines closer to that realization

Aggregate Shocks vs Reallocation Shocks: an Appraisal of the Applied Literature

This paper critically appraises the di erent approaches that have characterized the literature on the macroeconomic e ects of job reallocations from Lilien's seminal work to recent developments rooted in structural general equilibrium models, nonlinear econometric techniques and the concepts of job creation and destruction. Despite a ourishing of empirical analysis no unifying theoretical framework has obtained consensus in the scienti c debate. We face a corpus of research which is heterogeneous in variables' selection and experimental design. This widespread heterogeneity makes the evaluation of results a daunting task. Reliability of outcomes becomes almost impossible to assess when, even within models of the same generation, the lack of a rigorous theoretical background hinders well de ned experimental design and makes comparisons di cult. The strong pace at which the empirical literature on the macroeconomic e ects of job reallocations has been growing in recent years suggests that a general assessment of the state of the art is valuable and maybe indispensable. As a guiding principle for our excursion we track down the methodological development of the proposed solutions to the crucial problem of observational equivalence. We do not linger on speci c econometric methods nor on strictly theoretical issues not relevant to our main purpose. We draw the conclusion that the asymmetric and non-directional nature of allocative shocks, which holds the key to the solution of the problem, is better captured by multivariate, non-linear, dynamic econometric models and numerical simulation techniques. Davis and Haltiwanger's perspective on job creation and destruction seems to us of paramount importance for future research because of its potential to encompass a wealth of micro-level data sets within a rigorous analytical framework.Sectoral shifts, methodology, measurement, assessment