9,850 research outputs found
Dynamic safety assessment of a nonlinear pumped-storage generating system in a transient process
This paper focuses on a pumped-storage generating system with a reversible Francis turbine and presents an innovative framework for safety assessment in an attempt to overcome their limitations. Thus the aim is to analyze the dynamic safety process and risk probability of the above nonlinear generating system. This study is carried out based on an existing pumped-storage power station. In this paper we show the dynamic safety evaluation process and risk probability of the nonlinear generating system using Fisher discriminant method. A comparison analysis for the safety assessment is performed between two different closing laws, namely the separate mode only to include a guide vane and the linkage mode that includes a guide vane and a ball valve. We find that the most unfavorable condition of the generating system occurs in the final stage of the load rejection transient process. It is also
demonstrated that there is no risk to the generating system with the linkage mode but the risk probability of the separate mode is 6 percent. The results obtained are in good agreement with the actual operation of hydropower stations. The developed framework may not only be adopted for the applications of the pumped-storage generating system with a reversible Francis turbine but serves as the basis for the safety assessment of various engineering applications.National Natural Science Foundation of ChinaFundamental Research Funds for the Central UniversitiesScientific research funds of Northwest A&F UniversityScience Fund for Excellent Young Scholars from Northwest A&F University and Shaanxi Nova progra
Search via Quantum Walk
We propose a new method for designing quantum search algorithms for finding a
"marked" element in the state space of a classical Markov chain. The algorithm
is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of
the Markov chain. The main new idea is to apply quantum phase estimation to the
quantum walk in order to implement an approximate reflection operator. This
operator is then used in an amplitude amplification scheme. As a result we
considerably expand the scope of the previous approaches of Ambainis (2004) and
Szegedy (2004). Our algorithm combines the benefits of these approaches in
terms of being able to find marked elements, incurring the smaller cost of the
two, and being applicable to a larger class of Markov chains. In addition, it
is conceptually simple and avoids some technical difficulties in the previous
analyses of several algorithms based on quantum walk.Comment: 21 pages. Various modifications and improvements, especially in
Section
Quantum walks can find a marked element on any graph
We solve an open problem by constructing quantum walks that not only detect
but also find marked vertices in a graph. In the case when the marked set
consists of a single vertex, the number of steps of the quantum walk is
quadratically smaller than the classical hitting time of any
reversible random walk on the graph. In the case of multiple marked
elements, the number of steps is given in terms of a related quantity
which we call extended hitting time.
Our approach is new, simpler and more general than previous ones. We
introduce a notion of interpolation between the random walk and the
absorbing walk , whose marked states are absorbing. Then our quantum walk
is simply the quantum analogue of this interpolation. Contrary to previous
approaches, our results remain valid when the random walk is not
state-transitive. We also provide algorithms in the cases when only
approximations or bounds on parameters (the probability of picking a
marked vertex from the stationary distribution) and are
known.Comment: 50 page
A multi-phenotypic cancer model with cell plasticity
The conventional cancer stem cell (CSC) theory indicates a hierarchy of CSCs
and non-stem cancer cells (NSCCs), that is, CSCs can differentiate into NSCCs
but not vice versa. However, an alternative paradigm of CSC theory with
reversible cell plasticity among cancer cells has received much attention very
recently. Here we present a generalized multi-phenotypic cancer model by
integrating cell plasticity with the conventional hierarchical structure of
cancer cells. We prove that under very weak assumption, the nonlinear dynamics
of multi-phenotypic proportions in our model has only one stable steady state
and no stable limit cycle. This result theoretically explains the phenotypic
equilibrium phenomena reported in various cancer cell lines. Furthermore,
according to the transient analysis of our model, it is found that cancer cell
plasticity plays an essential role in maintaining the phenotypic diversity in
cancer especially during the transient dynamics. Two biological examples with
experimental data show that the phenotypic conversions from NCSSs to CSCs
greatly contribute to the transient growth of CSCs proportion shortly after the
drastic reduction of it. In particular, an interesting overshooting phenomenon
of CSCs proportion arises in three-phenotypic example. Our work may pave the
way for modeling and analyzing the multi-phenotypic cell population dynamics
with cell plasticity.Comment: 29 pages,6 figure
Classification of chirp signals using hierarchical bayesian learning and MCMC methods
This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning together with Markov chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of the observed data conditional on each class from a set of training samples. Unfortunately, this estimation requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning that estimates the class conditional probability densities using MCMC methods. The performance of this implementation is first studied via an academic example for which the class conditional densities are known. The problem of classifying chirp signals is then addressed by using a similar hierarchical Bayesian learning implementation based on a Metropolis-within-Gibbs algorithm
On analog quantum algorithms for the mixing of Markov chains
The problem of sampling from the stationary distribution of a Markov chain
finds widespread applications in a variety of fields. The time required for a
Markov chain to converge to its stationary distribution is known as the
classical mixing time. In this article, we deal with analog quantum algorithms
for mixing. First, we provide an analog quantum algorithm that given a Markov
chain, allows us to sample from its stationary distribution in a time that
scales as the sum of the square root of the classical mixing time and the
square root of the classical hitting time. Our algorithm makes use of the
framework of interpolated quantum walks and relies on Hamiltonian evolution in
conjunction with von Neumann measurements.
There also exists a different notion for quantum mixing: the problem of
sampling from the limiting distribution of quantum walks, defined in a
time-averaged sense. In this scenario, the quantum mixing time is defined as
the time required to sample from a distribution that is close to this limiting
distribution. Recently we provided an upper bound on the quantum mixing time
for Erd\"os-Renyi random graphs [Phys. Rev. Lett. 124, 050501 (2020)]. Here, we
also extend and expand upon our findings therein. Namely, we provide an
intuitive understanding of the state-of-the-art random matrix theory tools used
to derive our results. In particular, for our analysis we require information
about macroscopic, mesoscopic and microscopic statistics of eigenvalues of
random matrices which we highlight here. Furthermore, we provide numerical
simulations that corroborate our analytical findings and extend this notion of
mixing from simple graphs to any ergodic, reversible, Markov chain.Comment: The section concerning time-averaged mixing (Sec VIII) has been
updated: Now contains numerical plots and an intuitive discussion on the
random matrix theory results used to derive the results of arXiv:2001.0630
On the deformation chirality of real cubic fourfolds
According to our previous results, the conjugacy class of the involution
induced by the complex conjugation in the homology of a real non-singular cubic
fourfold determines the fourfold up to projective equivalence and deformation.
Here, we show how to eliminate the projective equivalence and to obtain a pure
deformation classification, that is how to respond to the chirality question:
which cubics are not deformation equivalent to their image under a mirror
reflection. We provide an arithmetical criterion of chirality, in terms of the
eigen-sublattices of the complex conjugation involution in homology, and show
how this criterion can be effectively applied taking as examples -cubics
(that is those for which the real locus has the richest topology) and
-cubics (the next case with respect to complexity of the real locus). It
happens that there is one chiral class of -cubics and three chiral classes
of -cubics, contrary to two achiral classes of -cubics and three
achiral classes of -cubics.Comment: 25 pages, 8 figure
Finding a marked node on any graph by continuous-time quantum walk
Spatial search by discrete-time quantum walk can find a marked node on any
ergodic, reversible Markov chain quadratically faster than its classical
counterpart, i.e.\ in a time that is in the square root of the hitting time of
. However, in the framework of continuous-time quantum walks, it was
previously unknown whether such general speed-up is possible. In fact, in this
framework, the widely used quantum algorithm by Childs and Goldstone fails to
achieve such a speedup. Furthermore, it is not clear how to apply this
algorithm for searching any Markov chain . In this article, we aim to
reconcile the apparent differences between the running times of spatial search
algorithms in these two frameworks. We first present a modified version of the
Childs and Goldstone algorithm which can search for a marked element for any
ergodic, reversible by performing a quantum walk on its edges. Although
this approach improves the algorithmic running time for several instances, it
cannot provide a generic quadratic speedup for any . Secondly, using the
framework of interpolated Markov chains, we provide a new spatial search
algorithm by continuous-time quantum walk which can find a marked node on any
in the square root of the classical hitting time. In the scenario where
multiple nodes are marked, the algorithmic running time scales as the square
root of a quantity known as the extended hitting time. Our results establish a
novel connection between discrete-time and continuous-time quantum walks and
can be used to develop a number of Markov chain-based quantum algorithms.Comment: This version deals only with new algorithms for spatial search by
continuous-time quantum walk (CTQW) on ergodic, reversible Markov chains.
Please see arXiv:2004.12686 for results on the necessary and sufficient
conditions for the optimality of the Childs and Goldstone algorithm for
spatial search by CTQ
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