65,137 research outputs found
Self-stabilizing network orientation algorithms in arbitrary rooted networks
Network orientation is the problem of assigning different labels to the edges at each processor, in a globally consistent manner. A self-stabilizing protocol guarantees that the system will arrive at a legitimate state in finite time, irrespective of the initial state of the system. Two deterministic distributed network orientation protocols on arbitrary rooted, asynchronous networks are proposed in this work. Both protocols set up a chordal sense of direction in the network. The protocols are self-stabilizing, meaning that starting from an arbitrary state, the protocols are guaranteed to reach a state in which every processor has a valid node label and every link has a valid edge label. The first protocol assumes an underlying depth-first token circulation protocol; it orients the network as the token is passed among the nodes and stabilizes in O(n) steps after the token circulation stabilizes, where n is the number of processors in the network. The second protocol is designed on an underlying spanning tree protocol and stabilizes in O(h) time, after the spanning tree is constructed, where h is the height of the spanning tree. Although the second protocol assumes the existence of a spanning tree of the rooted network, it orients all edges--both tree and non-tree edges--of the network
Abelian networks IV. Dynamics of nonhalting networks
An abelian network is a collection of communicating automata whose state
transitions and message passing each satisfy a local commutativity condition.
This paper is a continuation of the abelian networks series of Bond and Levine
(2016), for which we extend the theory of abelian networks that halt on all
inputs to networks that can run forever. A nonhalting abelian network can be
realized as a discrete dynamical system in many different ways, depending on
the update order. We show that certain features of the dynamics, such as
minimal period length, have intrinsic definitions that do not require
specifying an update order.
We give an intrinsic definition of the \emph{torsion group} of a finite
irreducible (halting or nonhalting) abelian network, and show that it coincides
with the critical group of Bond and Levine (2016) if the network is halting. We
show that the torsion group acts freely on the set of invertible recurrent
components of the trajectory digraph, and identify when this action is
transitive.
This perspective leads to new results even in the classical case of sinkless
rotor networks (deterministic analogues of random walks). In Holroyd et. al
(2008) it was shown that the recurrent configurations of a sinkless rotor
network with just one chip are precisely the unicycles (spanning subgraphs with
a unique oriented cycle, with the chip on the cycle). We generalize this result
to abelian mobile agent networks with any number of chips. We give formulas for
generating series such as where is the number of recurrent chip-and-rotor configurations with
chips; is the diagonal matrix of outdegrees, and is the adjacency
matrix. A consequence is that the sequence completely
determines the spectrum of the simple random walk on the network.Comment: 95 pages, 21 figure
Techniques for the Synthesis of Reversible Toffoli Networks
This paper presents novel techniques for the synthesis of reversible networks
of Toffoli gates, as well as improvements to previous methods. Gate count and
technology oriented cost metrics are used. Our synthesis techniques are
independent of the cost metrics. Two new iterative synthesis procedure
employing Reed-Muller spectra are introduced and shown to complement earlier
synthesis approaches. The template simplification suggested in earlier work is
enhanced through introduction of a faster and more efficient template
application algorithm, updated (shorter) classification of the templates, and
presentation of the new templates of sizes 7 and 9. A novel ``resynthesis''
approach is introduced wherein a sequence of gates is chosen from a network,
and the reversible specification it realizes is resynthesized as an independent
problem in hopes of reducing the network cost. Empirical results are presented
to show that the methods are effective both in terms of the realization of all
3x3 reversible functions and larger reversible benchmark specifications.Comment: 20 pages, 5 figure
Architecture and Design of Medical Processor Units for Medical Networks
This paper introduces analogical and deductive methodologies for the design
medical processor units (MPUs). From the study of evolution of numerous earlier
processors, we derive the basis for the architecture of MPUs. These specialized
processors perform unique medical functions encoded as medical operational
codes (mopcs). From a pragmatic perspective, MPUs function very close to CPUs.
Both processors have unique operation codes that command the hardware to
perform a distinct chain of subprocesses upon operands and generate a specific
result unique to the opcode and the operand(s). In medical environments, MPU
decodes the mopcs and executes a series of medical sub-processes and sends out
secondary commands to the medical machine. Whereas operands in a typical
computer system are numerical and logical entities, the operands in medical
machine are objects such as such as patients, blood samples, tissues, operating
rooms, medical staff, medical bills, patient payments, etc. We follow the
functional overlap between the two processes and evolve the design of medical
computer systems and networks.Comment: 17 page
Efficient data processing and quantum phenomena: Single-particle systems
We study the relation between the acquisition and analysis of data and
quantum theory using a probabilistic and deterministic model for photon
polarizers. We introduce criteria for efficient processing of data and then use
these criteria to demonstrate that efficient processing of the data contained
in single events is equivalent to the observation that Malus' law holds. A
strictly deterministic process that also yields Malus' law is analyzed in
detail. We present a performance analysis of the probabilistic and
deterministic model of the photon polarizer. The latter is an adaptive
dynamical system that has primitive learning capabilities. This additional
feature has recently been shown to be sufficient to perform event-by-event
simulations of interference phenomena, without using concepts of wave
mechanics. We illustrate this by presenting results for a system of two chained
Mach-Zehnder interferometers, suggesting that systems that perform efficient
data processing and have learning capability are able to exhibit behavior that
is usually attributed to quantum systems only.Comment: http://www.compphys.net/dl
Optimisation in âSelf-modellingâ Complex Adaptive Systems
When a dynamical system with multiple point attractors is released from an arbitrary initial condition it will relax into a configuration that locally resolves the constraints or opposing forces between interdependent state variables. However, when there are many conflicting interdependencies between variables, finding a configuration that globally optimises these constraints by this method is unlikely, or may take many attempts. Here we show that a simple distributed mechanism can incrementally alter a dynamical system such that it finds lower energy configurations, more reliably and more quickly. Specifically, when Hebbian learning is applied to the connections of a simple dynamical system undergoing repeated relaxation, the system will develop an associative memory that amplifies a subset of its own attractor states. This modifies the dynamics of the system such that its ability to find configurations that minimise total system energy, and globally resolve conflicts between interdependent variables, is enhanced. Moreover, we show that the system is not merely ârecallingâ low energy states that have been previously visited but âpredictingâ their location by generalising over local attractor states that have already been visited. This âself-modellingâ framework, i.e. a system that augments its behaviour with an associative memory of its own attractors, helps us better-understand the conditions under which a simple locally-mediated mechanism of self-organisation can promote significantly enhanced global resolution of conflicts between the components of a complex adaptive system. We illustrate this process in random and modular network constraint problems equivalent to graph colouring and distributed task allocation problems
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