20 research outputs found
Low-Dimensional Topology of Information Fusion
We provide an axiomatic characterization of information fusion, on the basis
of which we define an information fusion network. Our construction is
reminiscent of tangle diagrams in low dimensional topology. Information fusion
networks come equipped with a natural notion of equivalence. Equivalent
networks `contain the same information', but differ locally. When fusing
streams of information, an information fusion network may adaptively optimize
itself inside its equivalence class. This provides a fault tolerance mechanism
for such networks.Comment: 8 pages. Conference proceedings version. Will be superceded by a
journal versio
Computing with Coloured Tangles
We suggest a diagrammatic model of computation based on an axiom of
distributivity. A diagram of a decorated coloured tangle, similar to those that
appear in low dimensional topology, plays the role of a circuit diagram.
Equivalent diagrams represent bisimilar computations. We prove that our model
of computation is Turing complete, and that with bounded resources it can
moreover decide any language in complexity class IP, sometimes with better
performance parameters than corresponding classical protocols.Comment: 36 pages,; Introduction entirely rewritten, Section 4.3 adde
Tsirelson's Bound Prohibits Communication Through a Disconnected Channel
Why does nature only allow nonlocal correlations up to Tsirelson's bound and
not beyond? We construct a channel whose input is statistically independent of
its output, but through which communication is nevertheless possible if and
only if Tsirelson's bound is violated. This provides a statistical
justification for Tsirelson's bound on nonlocal correlations in a bipartite
setting.Comment: 9 pages, 2 figures. Title and abstract modified, exposition
simplifie
Computing by nowhere increasing complexity
A cellular automaton is presented whose governing rule is that the Kolmogorov
complexity of a cell's neighborhood may not increase when the cell's present
value is substituted for its future value. Using an approximation of this
two-dimensional Kolmogorov complexity the underlying automaton is shown to be
capable of simulating logic circuits. It is also shown to capture trianry logic
described by a quandle, a non-associative algebraic structure. A similar
automaton whose rule permits at times the increase of a cell's neighborhood
complexity is shown to produce animated entities which can be used as
information carriers akin to gliders in Conway's game of life
Subgradient-Based Markov Chain Monte Carlo Particle Methods for Discrete-Time Nonlinear Filtering
This work shows how a carefully designed instrumental distribution can improve the performance of a Markov chain Monte Carlo (MCMC) filter for systems with a high state dimension. We propose a special subgradient-based kernel from which candidate moves are drawn. This facilitates the implementation of the filtering algorithm in high dimensional settings using a remarkably small number of particles. We demonstrate our approach in solving a nonlinear non-Gaussian high-dimensional problem in comparison with a recently developed block particle filter and over a dynamic compressed sensing (l1 constrained) algorithm. The results show high estimation accuracy