5,379 research outputs found
Asymptotic Consensus Without Self-Confidence
This paper studies asymptotic consensus in systems in which agents do not
necessarily have self-confidence, i.e., may disregard their own value during
execution of the update rule. We show that the prevalent hypothesis of
self-confidence in many convergence results can be replaced by the existence of
aperiodic cores. These are stable aperiodic subgraphs, which allow to virtually
store information about an agent's value distributedly in the network. Our
results are applicable to systems with message delays and memory loss.Comment: 13 page
Byzantine Approximate Agreement on Graphs
Consider a distributed system with n processors out of which f can be Byzantine faulty. In the approximate agreement task, each processor i receives an input value x_i and has to decide on an output value y_i such that
1) the output values are in the convex hull of the non-faulty processors\u27 input values,
2) the output values are within distance d of each other.
Classically, the values are assumed to be from an m-dimensional Euclidean space, where m >= 1.
In this work, we study the task in a discrete setting, where input values with some structure expressible as a graph. Namely, the input values are vertices of a finite graph G and the goal is to output vertices that are within distance d of each other in G, but still remain in the graph-induced convex hull of the input values. For d=0, the task reduces to consensus and cannot be solved with a deterministic algorithm in an asynchronous system even with a single crash fault. For any d >= 1, we show that the task is solvable in asynchronous systems when G is chordal and n > (omega+1)f, where omega is the clique number of G. In addition, we give the first Byzantine-tolerant algorithm for a variant of lattice agreement. For synchronous systems, we show tight resilience bounds for the exact variants of these and related tasks over a large class of combinatorial structures
An Overview of Transience Bounds in Max-Plus Algebra
We survey and discuss upper bounds on the length of the transient phase of
max-plus linear systems and sequences of max-plus matrix powers. In particular,
we explain how to extend a result by Nachtigall to yield a new approach for
proving such bounds and we state an asymptotic tightness result by using an
example given by Hartmann and Arguelles.Comment: 13 pages, 2 figure
Universal scaling at non-thermal fixed points of a two-component Bose gas
Quasi-stationary far-from-equilibrium critical states of a two-component Bose
gas are studied in two spatial dimensions. After the system has undergone an
initial dynamical instability it approaches a non-thermal fixed point. At this
critical point the structure of the gas is characterised by ensembles of
(quasi-)topological defects such as vortices, skyrmions and solitons which give
rise to universal power-law behaviour of momentum correlation functions. The
resulting power-law spectra can be interpreted in terms of
strong-wave-turbulence cascades driven by particle transport into
long-wave-length excitations. Scaling exponents are determined on both sides of
the miscible-immiscible transition controlled by the ratio of the intra-species
to inter-species couplings. Making use of quantum turbulence methods, we
explain the specific values of the exponents from the presence of transient
(quasi-)topological defects.Comment: 13 pages, 12 figure
On the Tightness of Bounds for Transients of Weak CSR Expansions and Periodicity Transients of Critical Rows and Columns of Tropical Matrix Powers
We study the transients of matrices in max-plus algebra. Our approach is
based on the weak CSR expansion. Using this expansion, the transient can be
expressed by , where is the weak CSR threshold and
is the time after which the purely pseudoperiodic CSR terms start to dominate
in the expansion. Various bounds have been derived for and ,
naturally leading to the question which matrices, if any, attain these bounds.
In the present paper we characterize the matrices attaining two particular
bounds on , which are generalizations of the bounds of Wielandt and
Dulmage-Mendelsohn on the indices of non-weighted digraphs. This also leads to
a characterization of tightness for the same bounds on the transients of
critical rows and columns. The characterizations themselves are generalizations
of those for the non-weighted case.Comment: 42 pages, 9 figure
Unfaithful Glitch Propagation in Existing Binary Circuit Models
We show that no existing continuous-time, binary value-domain model for
digital circuits is able to correctly capture glitch propagation. Prominent
examples of such models are based on pure delay channels (P), inertial delay
channels (I), or the elaborate PID channels proposed by Bellido-D\'iaz et al.
We accomplish our goal by considering the solvability/non-solvability border of
a simple problem called Short-Pulse Filtration (SPF), which is closely related
to arbitration and synchronization. On one hand, we prove that SPF is solvable
in bounded time in any such model that provides channels with non-constant
delay, like I and PID. This is in opposition to the impossibility of solving
bounded SPF in real (physical) circuit models. On the other hand, for binary
circuit models with constant-delay channels, we prove that SPF cannot be solved
even in unbounded time; again in opposition to physical circuit models.
Consequently, indeed none of the binary value-domain models proposed so far
(and that we are aware of) faithfully captures glitch propagation of real
circuits. We finally show that these modeling mismatches do not hold for the
weaker eventual SPF problem.Comment: 23 pages, 15 figure
Superfluid Turbulence: Nonthermal Fixed Point in an Ultracold Bose Gas
Nonthermal fixed points of far-from-equilibrium dynamics of a dilute
degenerate Bose gas are analysed in two and three spatial dimensions. For such
systems, universal power-law distributions, previously found within a
nonperturbative quantum-field theoretic approach, are shown to be related to
vortical dynamics and superfluid turbulence. The results imply an
interpretation of the momentum scaling at the nonthermal fixed points in terms
of independent vortex excitations of the superfluid. Long-wavelength acoustic
excitations on the top of these are found to follow a non-thermal power law.
The results shed light on fundamental aspects of superfluid turbulence and have
strong potential implications for related phenomena studied, e.g., in
early-universe inflation or quark-gluon plasma dynamics.Comment: 5 pages, 5 figure
Weak CSR expansions and transience bounds in max-plus algebra
This paper aims to unify and extend existing techniques for deriving upper
bounds on the transient of max-plus matrix powers. To this aim, we introduce
the concept of weak CSR expansions: A^t=CS^tR + B^t. We observe that most of
the known bounds (implicitly) take the maximum of (i) a bound for the weak CSR
expansion to hold, which does not depend on the values of the entries of the
matrix but only on its pattern, and (ii) a bound for the CS^tR term to
dominate. To improve and analyze (i), we consider various cycle replacement
techniques and show that some of the known bounds for indices and exponents of
digraphs apply here. We also show how to make use of various parameters of
digraphs. To improve and analyze (ii), we introduce three different kinds of
weak CSR expansions (named after Nachtigall, Hartman-Arguelles, and Cycle
Threshold). As a result, we obtain a collection of bounds, in general
incomparable to one another, but better than the bounds found in the
literature.Comment: 32 page
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