2,347 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Towards Autopoietic Computing
A key challenge in modern computing is to develop systems that address
complex, dynamic problems in a scalable and efficient way, because the
increasing complexity of software makes designing and maintaining efficient and
flexible systems increasingly difficult. Biological systems are thought to
possess robust, scalable processing paradigms that can automatically manage
complex, dynamic problem spaces, possessing several properties that may be
useful in computer systems. The biological properties of self-organisation,
self-replication, self-management, and scalability are addressed in an
interesting way by autopoiesis, a descriptive theory of the cell founded on the
concept of a system's circular organisation to define its boundary with its
environment. In this paper, therefore, we review the main concepts of
autopoiesis and then discuss how they could be related to fundamental concepts
and theories of computation. The paper is conceptual in nature and the emphasis
is on the review of other people's work in this area as part of a longer-term
strategy to develop a formal theory of autopoietic computing.Comment: 10 Pages, 3 figure
Quantum hypercomputation based on the dynamical algebra su(1,1)
An adaptation of Kieu's hypercomputational quantum algorithm (KHQA) is
presented. The method that was used was to replace the Weyl-Heisenberg algebra
by other dynamical algebra of low dimension that admits infinite-dimensional
irreducible representations with naturally defined generalized coherent states.
We have selected the Lie algebra , due to that this algebra
posses the necessary characteristics for to realize the hypercomputation and
also due to that such algebra has been identified as the dynamical algebra
associated to many relatively simple quantum systems. In addition to an
algebraic adaptation of KHQA over the algebra , we
presented an adaptations of KHQA over some concrete physical referents: the
infinite square well, the infinite cylindrical well, the perturbed infinite
cylindrical well, the P{\"o}sch-Teller potentials, the Holstein-Primakoff
system, and the Laguerre oscillator. We conclude that it is possible to have
many physical systems within condensed matter and quantum optics on which it is
possible to consider an implementation of KHQA.Comment: 25 pages, 1 figure, conclusions rewritten, typing and language errors
corrected and latex format changed minor changes elsewhere and
Making dynamic modelling effective in economics
Mathematics has been extremely effective in physics, but not in economics beyond finance. To establish economics as science we should follow the Galilean method and try to deduce mathematical models of markets from empirical data, as has been done for financial markets. Financial markets are nonstationary. This means that 'value' is subjective. Nonstationarity also means that the form of the noise in a market cannot be postulated a priroi, but must be deduced from the empirical data. I discuss the essence of complexity in a market as unexpected events, and end with a biological speculation about market growth.Economics; fniancial markets; stochastic process; Markov process; complex systems
A Non-Probabilistic Model of Relativised Predictability in Physics
Little effort has been devoted to studying generalised notions or models of
(un)predictability, yet is an important concept throughout physics and plays a
central role in quantum information theory, where key results rely on the
supposed inherent unpredictability of measurement outcomes. In this paper we
continue the programme started in [1] developing a general, non-probabilistic
model of (un)predictability in physics. We present a more refined model that is
capable of studying different degrees of "relativised" unpredictability. This
model is based on the ability for an agent, acting via uniform, effective
means, to predict correctly and reproducibly the outcome of an experiment using
finite information extracted from the environment. We use this model to study
further the degree of unpredictability certified by different quantum
phenomena, showing that quantum complementarity guarantees a form of
relativised unpredictability that is weaker than that guaranteed by
Kochen-Specker-type value indefiniteness. We exemplify further the difference
between certification by complementarity and value indefiniteness by showing
that, unlike value indefiniteness, complementarity is compatible with the
production of computable sequences of bits.Comment: 10 page
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