3,909 research outputs found
On Time Synchronization Issues in Time-Sensitive Networks with Regulators and Nonideal Clocks
Flow reshaping is used in time-sensitive networks (as in the context of IEEE
TSN and IETF Detnet) in order to reduce burstiness inside the network and to
support the computation of guaranteed latency bounds. This is performed using
per-flow regulators (such as the Token Bucket Filter) or interleaved regulators
(as with IEEE TSN Asynchronous Traffic Shaping). Both types of regulators are
beneficial as they cancel the increase of burstiness due to multiplexing inside
the network. It was demonstrated, by using network calculus, that they do not
increase the worst-case latency. However, the properties of regulators were
established assuming that time is perfect in all network nodes. In reality,
nodes use local, imperfect clocks. Time-sensitive networks exist in two
flavours: (1) in non-synchronized networks, local clocks run independently at
every node and their deviations are not controlled and (2) in synchronized
networks, the deviations of local clocks are kept within very small bounds
using for example a synchronization protocol (such as PTP) or a satellite based
geo-positioning system (such as GPS). We revisit the properties of regulators
in both cases. In non-synchronized networks, we show that ignoring the timing
inaccuracies can lead to network instability due to unbounded delay in per-flow
or interleaved regulators. We propose and analyze two methods (rate and burst
cascade, and asynchronous dual arrival-curve method) for avoiding this problem.
In synchronized networks, we show that there is no instability with per-flow
regulators but, surprisingly, interleaved regulators can lead to instability.
To establish these results, we develop a new framework that captures industrial
requirements on clocks in both non-synchronized and synchronized networks, and
we develop a toolbox that extends network calculus to account for clock
imperfections.Comment: ACM SIGMETRICS 2020 Boston, Massachusetts, USA June 8-12, 202
A General Framework for the Derivation of Regular Expressions
The aim of this paper is to design a theoretical framework that allows us to
perform the computation of regular expression derivatives through a space of
generic structures. Thanks to this formalism, the main properties of regular
expression derivation, such as the finiteness of the set of derivatives, need
only be stated and proved one time, at the top level. Moreover, it is shown how
to construct an alternating automaton associated with the derivation of a
regular expression in this general framework. Finally, Brzozowski's derivation
and Antimirov's derivation turn out to be a particular case of this general
scheme and it is shown how to construct a DFA, a NFA and an AFA for both of
these derivations.Comment: 22 page
Superdiffusive, heterogeneous, and collective particle motion near the jamming transition in athermal disordered materials
We use computer simulations to study the microscopic dynamics of an athermal
assembly of soft particles near the fluid-to-solid, jamming transition.
Borrowing tools developed to study dynamic heterogeneity near glass
transitions, we discover a number of original signatures of the jamming
transition at the particle scale. We observe superdiffusive, spatially
heterogeneous, and collective particle motion over a characteristic scale which
displays a surprising non-monotonic behavior across the transition. In the
solid phase, the dynamics is an intermittent succession of elastic deformations
and plastic relaxations, which are both characterized by scale-free spatial
correlations and system size dependent dynamic susceptibilities. Our results
show that dynamic heterogeneities in dense athermal systems and glass-formers
are very different, and shed light on recent experimental reports of
`anomalous' dynamical behavior near the jamming transition of granular and
colloidal assemblies
Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials: The Regular Case
Let and be
two sets of nonlinear polynomials over
( being a field). We consider the computational problem of finding
-- if any -- an invertible transformation on the variables mapping
to . The corresponding equivalence problem is known as {\tt
Isomorphism of Polynomials with one Secret} ({\tt IP1S}) and is a fundamental
problem in multivariate cryptography. The main result is a randomized
polynomial-time algorithm for solving {\tt IP1S} for quadratic instances, a
particular case of importance in cryptography and somewhat justifying {\it a
posteriori} the fact that {\it Graph Isomorphism} reduces to only cubic
instances of {\tt IP1S} (Agrawal and Saxena). To this end, we show that {\tt
IP1S} for quadratic polynomials can be reduced to a variant of the classical
module isomorphism problem in representation theory, which involves to test the
orthogonal simultaneous conjugacy of symmetric matrices. We show that we can
essentially {\it linearize} the problem by reducing quadratic-{\tt IP1S} to
test the orthogonal simultaneous similarity of symmetric matrices; this latter
problem was shown by Chistov, Ivanyos and Karpinski to be equivalent to finding
an invertible matrix in the linear space of matrices over and to compute the square root in a matrix
algebra. While computing square roots of matrices can be done efficiently using
numerical methods, it seems difficult to control the bit complexity of such
methods. However, we present exact and polynomial-time algorithms for computing
the square root in for various fields (including
finite fields). We then consider \\#{\tt IP1S}, the counting version of {\tt
IP1S} for quadratic instances. In particular, we provide a (complete)
characterization of the automorphism group of homogeneous quadratic
polynomials. Finally, we also consider the more general {\it Isomorphism of
Polynomials} ({\tt IP}) problem where we allow an invertible linear
transformation on the variables \emph{and} on the set of polynomials. A
randomized polynomial-time algorithm for solving {\tt IP} when
is presented. From an algorithmic point
of view, the problem boils down to factoring the determinant of a linear matrix
(\emph{i.e.}\ a matrix whose components are linear polynomials). This extends
to {\tt IP} a result of Kayal obtained for {\tt PolyProj}.Comment: Published in Journal of Complexity, Elsevier, 2015, pp.3
Response Function of Coarsening Systems
The response function of domain growth processes, and in particular the
violation of the fluctuation-dissipation theorem, are studied both analytically
and numerically. In the asymptotic limit of large times, the
fluctuation-dissipation ratio , which quantifies this violation, tends to
one if and to zero if , corresponding to the fast (`bulk') and
slow (`domain-wall') responses, respectively. In this paper, we focus on the
pre-asymptotic behavior of the domain-wall response. This response is shown to
scale with the typical domain length as for dimension ,
and as for . Numerical results confirming this analysis
are presented
Some Combinatorial Operators in Language Theory
Multitildes are regular operators that were introduced by Caron et al. in
order to increase the number of Glushkov automata. In this paper, we study the
family of the multitilde operators from an algebraic point of view using the
notion of operad. This leads to a combinatorial description of already known
results as well as new results on compositions, actions and enumerations.Comment: 21 page
Calculation of Contraction Coefficient under Sluice Gates and Application to Discharge Measurement
The contraction coefficient under sluice gates on flat beds is studied for both free flow and submerged conditions based on the principle of momentum conservation, relying on an analytical determination of the pressure force exerted on the upstream face of the gate together with the energy equation. The contraction coefficient varies with the relative gate opening and the relative submergence, especially at large gate openings. The contraction coefficient may be similar in submerged flow and free flow at small openings but not at large openings, as shown by some experimental results. An application to discharge measurement is also presented
Nonequilibrium dynamics and fluctuation-dissipation relation in a sheared fluid
The nonequilibrium dynamics of a binary Lennard-Jones mixture in a simple
shear flow is investigated by means of molecular dynamics simulations. The
range of temperature investigated covers both the liquid, supercooled and
glassy states, while the shear rate covers both the linear and nonlinear
regimes of rheology. The results can be interpreted in the context of a
nonequilibrium, schematic mode-coupling theory developed recently, which makes
the theory applicable to a wide range of soft glassy materials. The behavior of
the viscosity is first investigated. In the nonlinear regime, strong
shear-thinning is obtained. Scaling properties of the intermediate scattering
functions are studied. Standard `mode-coupling properties' of factorization and
time-superposition hold in this nonequilibrium situation. The
fluctuation-dissipation relation is violated in the shear flow in a way very
similar to that predicted theoretically, allowing for the definition of an
effective temperature Teff for the slow modes of the fluid. Temperature and
shear rate dependencies of Teff are studied using density fluctuations as an
observable. The observable dependence of Teff is also investigated. Many
different observables are found to lead to the same value of Teff, suggesting
several experimental procedures to access Teff. It is proposed that tracer
particle of large mass may play the role of an `effective thermometer'. When
the Einstein frequency of the tracers becomes smaller than the inverse
relaxation time of the fluid, a nonequilibrium equipartition theorem holds.
This last result gives strong support to the thermodynamic interpretation of
Teff and makes it experimentally accessible in a very direct way.Comment: Version accepted for publication in Journal of Chemical Physic
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