97,796 research outputs found
Revisiting LFSMs
Linear Finite State Machines (LFSMs) are particular primitives widely used in
information theory, coding theory and cryptography. Among those linear
automata, a particular case of study is Linear Feedback Shift Registers (LFSRs)
used in many cryptographic applications such as design of stream ciphers or
pseudo-random generation. LFSRs could be seen as particular LFSMs without
inputs.
In this paper, we first recall the description of LFSMs using traditional
matrices representation. Then, we introduce a new matrices representation with
polynomial fractional coefficients. This new representation leads to sparse
representations and implementations. As direct applications, we focus our work
on the Windmill LFSRs case, used for example in the E0 stream cipher and on
other general applications that use this new representation.
In a second part, a new design criterion called diffusion delay for LFSRs is
introduced and well compared with existing related notions. This criterion
represents the diffusion capacity of an LFSR. Thus, using the matrices
representation, we present a new algorithm to randomly pick LFSRs with good
properties (including the new one) and sparse descriptions dedicated to
hardware and software designs. We present some examples of LFSRs generated
using our algorithm to show the relevance of our approach.Comment: Submitted to IEEE-I
Collective stability of networks of winner-take-all circuits
The neocortex has a remarkably uniform neuronal organization, suggesting that
common principles of processing are employed throughout its extent. In
particular, the patterns of connectivity observed in the superficial layers of
the visual cortex are consistent with the recurrent excitation and inhibitory
feedback required for cooperative-competitive circuits such as the soft
winner-take-all (WTA). WTA circuits offer interesting computational properties
such as selective amplification, signal restoration, and decision making. But,
these properties depend on the signal gain derived from positive feedback, and
so there is a critical trade-off between providing feedback strong enough to
support the sophisticated computations, while maintaining overall circuit
stability. We consider the question of how to reason about stability in very
large distributed networks of such circuits. We approach this problem by
approximating the regular cortical architecture as many interconnected
cooperative-competitive modules. We demonstrate that by properly understanding
the behavior of this small computational module, one can reason over the
stability and convergence of very large networks composed of these modules. We
obtain parameter ranges in which the WTA circuit operates in a high-gain
regime, is stable, and can be aggregated arbitrarily to form large stable
networks. We use nonlinear Contraction Theory to establish conditions for
stability in the fully nonlinear case, and verify these solutions using
numerical simulations. The derived bounds allow modes of operation in which the
WTA network is multi-stable and exhibits state-dependent persistent activities.
Our approach is sufficiently general to reason systematically about the
stability of any network, biological or technological, composed of networks of
small modules that express competition through shared inhibition.Comment: 7 Figure
MATEX: A Distributed Framework for Transient Simulation of Power Distribution Networks
We proposed MATEX, a distributed framework for transient simulation of power
distribution networks (PDNs). MATEX utilizes matrix exponential kernel with
Krylov subspace approximations to solve differential equations of linear
circuit. First, the whole simulation task is divided into subtasks based on
decompositions of current sources, in order to reduce the computational
overheads. Then these subtasks are distributed to different computing nodes and
processed in parallel. Within each node, after the matrix factorization at the
beginning of simulation, the adaptive time stepping solver is performed without
extra matrix re-factorizations. MATEX overcomes the stiff-ness hinder of
previous matrix exponential-based circuit simulator by rational Krylov subspace
method, which leads to larger step sizes with smaller dimensions of Krylov
subspace bases and highly accelerates the whole computation. MATEX outperforms
both traditional fixed and adaptive time stepping methods, e.g., achieving
around 13X over the trapezoidal framework with fixed time step for the IBM
power grid benchmarks.Comment: ACM/IEEE DAC 2014. arXiv admin note: substantial text overlap with
arXiv:1505.0669
Trajectories entropy in dynamical graphs with memory
In this paper we investigate the application of non-local graph entropy to
evolving and dynamical graphs. The measure is based upon the notion of Markov
diffusion on a graph, and relies on the entropy applied to trajectories
originating at a specific node. In particular, we study the model of
reinforcement-decay graph dynamics, which leads to scale free graphs. We find
that the node entropy characterizes the structure of the network in the two
parameter phase-space describing the dynamical evolution of the weighted graph.
We then apply an adapted version of the entropy measure to purely memristive
circuits. We provide evidence that meanwhile in the case of DC voltage the
entropy based on the forward probability is enough to characterize the graph
properties, in the case of AC voltage generators one needs to consider both
forward and backward based transition probabilities. We provide also evidence
that the entropy highlights the self-organizing properties of memristive
circuits, which re-organizes itself to satisfy the symmetries of the underlying
graph.Comment: 15 pages one column, 10 figures; new analysis and memristor models
added. Text improve
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