8,068 research outputs found
Pattern synchronization in two-dimensional cellular spaces
This paper presents an algorithm for synchronizing (firing) an arbitrary, finite, connected pattern of cells in a potentially infinite two-dimensional grid of identical finite state cells. Earlier solution times have been quadratic in m, where m is the edge length of the smallest square enclosing the pattern. A linear solution is formulated
On Factor Universality in Symbolic Spaces
The study of factoring relations between subshifts or cellular automata is
central in symbolic dynamics. Besides, a notion of intrinsic universality for
cellular automata based on an operation of rescaling is receiving more and more
attention in the literature. In this paper, we propose to study the factoring
relation up to rescalings, and ask for the existence of universal objects for
that simulation relation. In classical simulations of a system S by a system T,
the simulation takes place on a specific subset of configurations of T
depending on S (this is the case for intrinsic universality). Our setting,
however, asks for every configurations of T to have a meaningful interpretation
in S. Despite this strong requirement, we show that there exists a cellular
automaton able to simulate any other in a large class containing arbitrarily
complex ones. We also consider the case of subshifts and, using arguments from
recursion theory, we give negative results about the existence of universal
objects in some classes
Intrinsically universal one-dimensional quantum cellular automata in two flavours
We give a one-dimensional quantum cellular automaton (QCA) capable of
simulating all others. By this we mean that the initial configuration and the
local transition rule of any one-dimensional QCA can be encoded within the
initial configuration of the universal QCA. Several steps of the universal QCA
will then correspond to one step of the simulated QCA. The simulation preserves
the topology in the sense that each cell of the simulated QCA is encoded as a
group of adjacent cells in the universal QCA. The encoding is linear and hence
does not carry any of the cost of the computation. We do this in two flavours:
a weak one which requires an infinite but periodic initial configuration and a
strong one which needs only a finite initial configuration. KEYWORDS: Quantum
cellular automata, Intrinsic universality, Quantum computation.Comment: 27 pages, revtex, 23 figures. V3: The results of V1-V2 are better
explained and formalized, and a novel result about intrinsic universality
with only finite initial configurations is give
Complexity Measures from Interaction Structures
We evaluate new complexity measures on the symbolic dynamics of coupled tent
maps and cellular automata. These measures quantify complexity in terms of
-th order statistical dependencies that cannot be reduced to interactions
between units. We demonstrate that these measures are able to identify
complex dynamical regimes.Comment: 11 pages, figures improved, minor changes to the tex
Coupled Maps with Growth and Death: An Approach to Cell Differentiation
An extension of coupled maps is given which allows for the growth of the
number of elements, and is inspired by the cell differentiation problem. The
growth of elements is made possible first by clustering the phases, and then by
differentiating roles. The former leads to the time sharing of resources, while
the latter leads to the separation of roles for the growth. The mechanism of
the differentiation of elements is studied. An extension to a model with
several internal phase variables is given, which shows differentiation of
internal states. The relevance of interacting dynamics with internal states
(``intra-inter" dynamics) to biological problems is discussed with an emphasis
on heterogeneity by clustering, macroscopic robustness by partial
synchronization and recursivity with the selection of initial conditions and
digitalization.Comment: LatexText,figures are not included. submitted to PhysicaD
(1995,revised 1996 May
High-Frequency network activity, global increase in Neuronal Activity, and Synchrony Expansion Precede Epileptic Seizures In Vitro
How seizures start is a major question in epilepsy research. Preictal EEG changes occur in both human patients and animal models, but their underlying mechanisms and relationship with seizure initiation remain unknown. Here we demonstrate the existence, in the hippocampal CA1 region, of a preictal state characterized by the progressive and global increase in neuronal activity associated with a widespread buildup of low-amplitude high-frequency activity (HFA) (100 Hz) and reduction in system complexity.HFAis generated by the firing of neurons, mainly pyramidal cells, at much lower frequencies. Individual cycles ofHFAare generated by the near-synchronous (within 5 ms) firing of small numbers of pyramidal cells. The presence of HFA in the low-calcium model implicates nonsynaptic synchronization; the presence of very similar HFA in the high-potassium model shows that it does not depend on an absence of synaptic transmission. Immediately before seizure onset, CA1 is in a state of high sensitivity in which weak depolarizing or synchronizing perturbations can trigger seizures. Transition to seizure is haracterized by a rapid expansion and fusion of the neuronal populations responsible for HFA, associated with a progressive slowing of HFA, leading to a single, massive, hypersynchronous cluster generating the high-amplitude low-frequency activity of the seizure
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