1,688 research outputs found
Magic number 7 2 in networks of threshold dynamics
Information processing by random feed-forward networks consisting of units
with sigmoidal input-output response is studied by focusing on the dependence
of its outputs on the number of parallel paths M. It is found that the system
leads to a combination of on/off outputs when , while for , chaotic dynamics arises, resulting in a continuous distribution of
outputs. This universality of the critical number is explained by
combinatorial explosion, i.e., dominance of factorial over exponential
increase. Relevance of the result to the psychological magic number
is briefly discussed.Comment: 6 pages, 5 figure
Harmonic maps from degenerating Riemann surfaces
We study harmonic maps from degenerating Riemann surfaces with uniformly
bounded energy and show the so-called generalized energy identity. We find
conditions that are both necessary and sufficient for the compactness in
and modulo bubbles of sequences of such maps.Comment: 27 page
Scalability and Total Recall with Fast CoveringLSH
Locality-sensitive hashing (LSH) has emerged as the dominant algorithmic
technique for similarity search with strong performance guarantees in
high-dimensional spaces. A drawback of traditional LSH schemes is that they may
have \emph{false negatives}, i.e., the recall is less than 100\%. This limits
the applicability of LSH in settings requiring precise performance guarantees.
Building on the recent theoretical "CoveringLSH" construction that eliminates
false negatives, we propose a fast and practical covering LSH scheme for
Hamming space called \emph{Fast CoveringLSH (fcLSH)}. Inheriting the design
benefits of CoveringLSH our method avoids false negatives and always reports
all near neighbors. Compared to CoveringLSH we achieve an asymptotic
improvement to the hash function computation time from to
, where is the dimensionality of data and is
the number of hash tables. Our experiments on synthetic and real-world data
sets demonstrate that \emph{fcLSH} is comparable (and often superior) to
traditional hashing-based approaches for search radius up to 20 in
high-dimensional Hamming space.Comment: Short version appears in Proceedings of CIKM 201
Small Universal Accepting Networks of Evolutionary Processors with Filtered Connections
In this paper, we present some results regarding the size complexity of
Accepting Networks of Evolutionary Processors with Filtered Connections
(ANEPFCs). We show that there are universal ANEPFCs of size 10, by devising a
method for simulating 2-Tag Systems. This result significantly improves the
known upper bound for the size of universal ANEPFCs which is 18.
We also propose a new, computationally and descriptionally efficient
simulation of nondeterministic Turing machines by ANEPFCs. More precisely, we
describe (informally, due to space limitations) how ANEPFCs with 16 nodes can
simulate in O(f(n)) time any nondeterministic Turing machine of time complexity
f(n). Thus the known upper bound for the number of nodes in a network
simulating an arbitrary Turing machine is decreased from 26 to 16
Exploiting lattice structures in shape grammar implementations
The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible
Coordination via Interaction Constraints I: Local Logic
Wegner describes coordination as constrained interaction. We take this
approach literally and define a coordination model based on interaction
constraints and partial, iterative and interactive constraint satisfaction. Our
model captures behaviour described in terms of synchronisation and data flow
constraints, plus various modes of interaction with the outside world provided
by external constraint symbols, on-the-fly constraint generation, and
coordination variables. Underlying our approach is an engine performing
(partial) constraint satisfaction of the sets of constraints. Our model extends
previous work on three counts: firstly, a more advanced notion of external
interaction is offered; secondly, our approach enables local satisfaction of
constraints with appropriate partial solutions, avoiding global synchronisation
over the entire constraints set; and, as a consequence, constraint satisfaction
can finally occur concurrently, and multiple parts of a set of constraints can
be solved and interact with the outside world in an asynchronous manner, unless
synchronisation is required by the constraints. This paper describes the
underlying logic, which enables a notion of local solution, and relates this
logic to the more global approach of our previous work based on classical
logic
Invariant Peano curves of expanding Thurston maps
We consider Thurston maps, i.e., branched covering maps
that are postcritically finite. In addition, we assume that is expanding in
a suitable sense. It is shown that each sufficiently high iterate of
is semi-conjugate to , where is equal to the
degree of . More precisely, for such an we construct a Peano curve
(onto), such that
(for all ).Comment: 63 pages, 12 figure
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