6,268 research outputs found
Coordination and Control of Distributed Discrete Event Systems under Actuator and Sensor Faults
We investigate the coordination and control problems of distributed discrete
event systems that are composed of multiple subsystems subject to potential
actuator and/or sensor faults. We model actuator faults as local
controllability loss of certain actuator events and sensor faults as
observability failure of certain sensor readings, respectively. Starting from
automata-theoretic models that characterize behaviors of the subsystems in the
presence of faulty actuators and/or sensors, we establish necessary and
sufficient conditions for the existence of actuator and sensor fault tolerant
supervisors, respectively, and synthesize appropriate local post-fault
supervisors to prevent the post-fault subsystems from jeopardizing local safety
requirements. Furthermore, we apply an assume-guarantee coordination scheme to
the controlled subsystems for both the nominal and faulty subsystems so as to
achieve the desired specifications of the system. A multi-robot coordination
example is used to illustrate the proposed coordination and control
architecture.Comment: 33 pages; 20 figures; 1 tabl
Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes sytstem with competitive kinetics
In this paper, we study the rates of convergence of supposedly given global
bounded classical solutions to a two-species chemotaxis-Navier-Stokes system
with Lotka-Volterra competitive kinetics. Except in one case where the rate of
convergence for the fluid component is expressed in terms of the Poincare
constant and the model parameters, all other rates of convergence are shown to
be expressible only in terms of the model parameters and the underlying space
dimension.Comment: 16 pages, submitte
Ramanujan-type Congruences for -Regular Partitions Modulo and
Let be the number of -regular partitions of . Recently,
Hou et al established several infinite families of congruences for
modulo , where and . In this
paper, by the vanishing property given by Hou et al, we show an infinite family
of congruence for modulo . Moreover, for and
, we obtain three infinite families of congruences for modulo
and by the theory of Hecke eigenforms.Comment: 13 page
Formal residue and computer proofs of combinatorial identities
The coefficient of x^{-1} of a formal Laurent series f(x) is called the
formal residue of f(x). Many combinatorial numbers can be represented by the
formal residues of hypergeometric terms. With these representations and the
extended Zeilberger's algorithm, we generate recurrence relations for
summations involving combinatorial sequences such as Stirling numbers. As
examples, we give computer proofs of several known identities and derive some
new identities. The applicability of this method is also studied.Comment: 14 page
Critical mass on the Keller-Segel system with signal-dependent motility
This paper is concerned with the global boundedness and blowup of solutions
to the Keller-Segel system with density-dependent motility in a two-dimensional
bounded smooth domain with Neumman boundary conditions. We show that if the
motility function decays exponentially, then a critical mass phenomenon similar
to the minimal Keller-Segel model will arise. That is there is a number
, such that the solution will globally exist with uniform-in-time bound
if the initial cell mass (i.e. -norm of the initial value of cell density)
is less than , while the solution may blow up if the initial cell mass is
greater than
Global stabilization of the full attraction-repulsion Keller-Segel system
We are concerned with the following full Attraction-Repulsion Keller-Segel
(ARKS) system \begin{equation}\label{ARKS}\tag{} \begin{cases} u_t=\Delta
u-\nabla\cdot(\chi u\nabla v)+\nabla\cdot(\xi u\nabla w), &x\in \Omega, ~~t>0,
v_t=D_1\Delta v+\alpha u-\beta v,& x\in \Omega, ~~t>0,
w_t=D_2\Delta w+\gamma u-\delta w, &x\in \Omega, ~~t>0,\\
u(x,0)=u_0(x),~v(x,0)= v_0(x), w(x,0)= w_0(x) & x\in \Omega, \end{cases}
\end{equation} in a bounded domain with smooth boundary
subject to homogeneous Neumann boundary conditions. %The parameters
and are positive. By
constructing an appropriate Lyapunov functions, we establish the boundedness
and asymptotical behavior of solutions to the system \eqref{ARKS} with large
initial data. Precisely, we show that if the parameters satisfy
for all positive parameters and
, the system \eqref{ARKS} has a unique global classical solution
, which converges to the constant steady state
as
, where .
Furthermore, the decay rate is exponential if . This paper provides
the first results on the full ARKS system with unequal chemical diffusion rates
(i.e. ) in multi-dimensions.Comment: 20 page
Implementations of two-photon four-qubit Toffoli and Fredkin gates assisted by nitrogen-vacancy centers
It is desirable to implement an efficient quantum information process
demanding fewer quantum resources. We designed two compact quantum circuits for
determinately implementing four-qubit Toffoli and Fredkin gates on
single-photon systems in both the polarization and spatial degrees of freedom
(DoFs) via diamond nitrogen-vacancy (NV) centers in resonators. The gates are
heralded by the electron spins associated with the diamond NV centers. In
contrast to the ones with one DoF, our implementations reduce the quantum
resource and are robust against the decoherence. Evaluations of fidelities and
efficiencies of our gates show that our schemes may be implemented with current
technology.Comment: 9 pages,5 figure
Two faces of greedy leaf removal procedure on graphs
The greedy leaf removal (GLR) procedure on a graph is an iterative removal of
any vertex with degree one (leaf) along with its nearest neighbor (root). Its
result has two faces: a residual subgraph as a core, and a set of removed
roots. While the emergence of cores on uncorrelated random graphs was solved
analytically, a theory for roots is ignored except in the case of
Erd\"{o}s-R\'{e}nyi random graphs. Here we analytically study roots on random
graphs. We further show that, with a simple geometrical interpretation and a
concise mean-field theory of the GLR procedure, we reproduce the
zero-temperature replica symmetric estimation of relative sizes of both minimal
vertex covers and maximum matchings on random graphs with or without cores.Comment: 39 pages, 5 figures, and 3 table
Optimal Disruption of Complex Networks
The collection of all the strongly connected components in a directed graph,
among each cluster of which any node has a path to another node, is a typical
example of the intertwining structure and dynamics in complex networks, as its
relative size indicates network cohesion and it also composes of all the
feedback cycles in the network. Here we consider finding an optimal strategy
with minimal effort in removal arcs (for example, deactivation of directed
interactions) to fragment all the strongly connected components into tree
structure with no effect from feedback mechanism. We map the optimal network
disruption problem to the minimal feedback arc set problem, a
non-deterministically polynomial hard combinatorial optimization problem in
graph theory. We solve the problem with statistical physical methods from spin
glass theory, resulting in a simple numerical method to extract sub-optimal
disruption arc sets with significantly better results than a local heuristic
method and a simulated annealing method both in random and real networks. Our
results has various implications in controlling and manipulation of real
interacted systems.Comment: 22 pages, 11 figure
Statistical physics of hard combinatorial optimization: The vertex cover problem
Typical-case computation complexity is a research topic at the boundary of
computer science, applied mathematics, and statistical physics. In the last
twenty years the replica-symmetry-breaking mean field theory of spin glasses
and the associated message-passing algorithms have greatly deepened our
understanding of typical-case computation complexity. In this paper we use the
vertex cover problem, a basic nondeterministic-polynomial (NP)-complete
combinatorial optimization problem of wide application, as an example to
introduce the statistical physical methods and algorithms. We do not go into
the technical details but emphasize mainly the intuitive physical meanings of
the message-passing equations. A nonfamiliar reader shall be able to understand
to a large extent the physics behind the mean field approaches and to adjust
them in solving other optimization problems.Comment: 17 pages. A mini-review to be published in Chinese Physics
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