Arbitrary Transition Research Articles

Diffusion Approximation for an Open Queueing Network with Limited Number of Customers and Time-Dependent Service

The object of this research is an open queueing network (QN) with a single class of customers, in which the total number of customers is limited. Service parameters are dependent on time, the routing of customers is determined by an arbitrary stochastic transition probability matrix, which is also depends on time. The service times of customers in each queue of the system is exponentially distributed with FIFO service, and it is assumed that a birth and death process generates and destroys the customers. The random vector, which determines the network state, forming a Markov random process is introduced. The purpose of the research is an asymptotic analysis of this Markov process, describing the queueing network state with a large number of customers, obtained from a system of differential equations, and used to find the mean relative number of customers in the network queues at any time. The results are illustrated with a specific example. This approach can be used tp model processes of customer service in the insurance companies, banks, logistics companies and other cyber-economical or service organizations.

Widely tunable Bi2Se3/transition metal dichalcogenide 2D heterostructures for write-read-erase-reuse applications

We present a method to tune the photoluminescence (PL) and exciton dynamics in a family of 2D heterostructures by controllably disrupting the interlayer coupling. Growing 1–3 layers of Bi2Se3 on arbitrary monolayer transition metal dichalcogenides (TMDs), including alloys, quenches the TMDs signature PL. Applying controlled doses of energy in air modulates the PL upward in small increments, while thermal annealing in Ar or N2 reverses those changes. This PL-tuning can even be accomplished locally using a low-power laser, allowing complex patterns with submicron features to written. We demonstrate this over a wide-range of emission energy values in the visible (1.5 eV < Eph < 2 eV), suggesting this family of 2D materials is well-suited for applications requiring ‘write-read-erase-reuse’ capability.

Deep Reactive Policies for Planning in Stochastic Nonlinear Domains

Recent advances in applying deep learning to planning have shown that Deep Reactive Policies (DRPs) can be powerful for fast decision-making in complex environments. However, an important limitation of current DRP-based approaches is either the need of optimal planners to be used as ground truth in a supervised learning setting or the sample complexity of high-variance policy gradient estimators, which are particularly troublesome in continuous state-action domains. In order to overcome those limitations, we introduce a framework for training DRPs in continuous stochastic spaces via gradient-based policy search. The general approach is to explicitly encode a parametric policy as a deep neural network, and to formulate the probabilistic planning problem as an optimization task in a stochastic computation graph by exploiting the re-parameterization of the transition probability densities; the optimization is then solved by leveraging gradient descent algorithms that are able to handle non-convex objective functions. We benchmark our approach against stochastic planning domains exhibiting arbitrary differentiable nonlinear transition and cost functions (e.g., Reservoir Control, HVAC and Navigation). Results show that DRPs with more than 125,000 continuous action parameters can be optimized by our approach for problems with 30 state fluents and 30 action fluents on inexpensive hardware under 6 minutes. Also, we observed a speedup of 5 orders of magnitude in the average inference time per decision step of DRPs when compared to other state-of-the-art online gradient-based planners when the same level of solution quality is required.

H-Infinity Fault Detection for Delta Operator Systems With Random Two-Channels Packet Losses and Limited Communication

This paper is concerned with the H-infinity fault detection for time-delays delta operator systems with random two-channels packet losses and limited communication. The considered networked control systems (NCSs) are modeled as the time-delays delta operator systems with random packet losses and limited communication, where the packet losses exist in sensor-to-controller (S-C link) or controller-to-actuator (C-A link), and the limited communication occurs in the controller-to-actuator link. The random two-channels packet losses are described by the Markov chain process and limited communication is transformed into system state by feedback control in time-delays delta operator systems. The above delta operator systems are modeled as the Markovian jump systems, and the designed method of H-infinity fault detection filter is proposed under arbitrary transition probabilities matrix. The sufficient conditions for the asymptotical stability of the residual systems with H-infinity performance for the considered delta operator systems are presented by Lyapunov-Krasovskii functional in delta domain, and the gain matrices of the designed fault detection filter can be easily determined by linear matrix inequalities (LMIs). Finally, comparative examples are provided to illustrate the effectiveness of the proposed method.

Boundary Representations of \u03bb-Harmonic and Polyharmonic Functions on Trees

On a countable tree T, allowing vertices with infinite degree, we consider an arbitrary stochastic irreducible nearest neighbour transition operator P. We provide a boundary integral representation for general eigenfunctions of P with eigenvalue λ ∈ C. This is possible whenever λ is in the resolvent set of P as a self-adjoint operator on a suitable ℓ2-space and the diagonal elements of the resolvent (“Green function”) do not vanish at λ. We show that when P is invariant under a transitive (not necessarily fixed-point-free) group action, the latter condition holds for all λ≠ 0 in the resolvent set. These results extend and complete previous results by Cartier, by Figà-Talamanca and Steger, and by Woess. For those eigenvalues, we also provide an integral representation of λ-polyharmonic functions of any order n, that is, functions f: T to mathbb {C} for which (λ ⋅ I − P)nf = 0. This is a far-reaching extension of work of Cohen et al., who provided such a representation for the simple random walk on a homogeneous tree and eigenvalue λ = 1. Finally, we explain the (much simpler) analogous results for “forward only” transition operators, sometimes also called martingales on trees.

Flatness and structural analysis as a constructive framework for private communication

This paper deals with the use of control theoretical concepts, essentially flatness, along with structural analysis, in the context of private communication. A new and systematic methodology to design a cryptographic architecture belonging to the special class of ciphers called Self Synchronizing Stream Ciphers (SSSC) is proposed. Till now, the constructions of SSSC were based on automata with finite input memory involving shifts or triangular functions (T-functions) as state transition functions. Besides, only ad-hoc approaches were available in the literature. The contribution of this paper is to propose a general framework to design SSSC involving dynamical systems taking the form of switched linear systems over finite fields with arbitrary state transition functions. An example of cipher with complete specifications is given. Its implementation on a small scale breeding of an ICS-SCADA equipment is described.

Adaptable Energy Systems Integration by Modular, Standardized and Scalable System Architectures: Necessities and Prospects of Any Time Transition

Energy conversion and distribution of heat and electricity is characterized by long planning horizons, investment periods and depreciation times, and it is thus difficult to plan and tell the technology that optimally fits for decades. Uncertainties include future energy prices, applicable subsidies, regulation, and even the evolution of market designs. To achieve higher adaptability to arbitrary transition paths, a technical concept based on integrated energy systems is envisioned and described. The problem of intermediate steps of evolution is tackled by introducing a novel paradigm in urban infrastructure design. It builds on standardization, modularization and economies of scale for underlying conversion units. Building on conceptual arguments for such a platform, it is then argued how actors like (among others) municipalities and district heating system operators can use this as a practical starting point for a manageable and smooth transition towards more environmental friendly supply technologies, and to commit to their own pace of transition (bearable investment/risk). Merits are not only supported by technical arguments but also by strategical and societal prospects like technology neutrality and availability of real options.

Stable lattice Boltzmann model for Maxwell equations in media.

38, 1710 (2014)AMMODL0307-904X10.1016/j.apm.2013.09.009] and apply an extension that treats the effects of polarization and magnetization separately. We show simulations of simple examples in which EM waves travel into media to quantify error scaling, stability, accuracy, and time scaling. For conductive media, we use the Strang splitting and check the simulations accuracy at the example of the skin effect. Like pure EM propagation, the error for the static limits, which are constructed with a current density added in a first-order scheme, can be less than 1%. The presented method is an easily implemented alternative for the stabilization of simulation for EM waves propagating in spatially complex structured media properties and arbitrary transitions.

Effect of electron transition kinetics on the photomotor velocity

An expression for the average velocity of a semiconductor photomotor has been obtained. A threelevel model of the electron subsystem of a photomotor with arbitrary transition rate constants was considered, and the time dependences of the occupation of its electronic levels were calculated. Variation of the occupation of the levels with time determines the time dependence of the potential energy and the average velocity of the photomotor motion along the polar substrate. The optimum conditions of laser photoexcitation and the kinetic characteristics of electron transitions in the photomotor that provide the maximum velocity of its directional motion were determined.

A Nearly-Black-Box Online Algorithm for Joint Parameter and State Estimation in Temporal Models

Online joint parameter and state estimation is a core problem for temporal models.Most existing methods are either restricted to a particular class of models (e.g., the Storvik filter) or computationally expensive (e.g., particle MCMC). We propose a novel nearly-black-box algorithm, the Assumed Parameter Filter (APF), a hybrid of particle filtering for state variables and assumed density filtering for parameter variables.It has the following advantages:(a) it is online and computationally efficient;(b) it is applicable to both discrete and continuous parameter spaces with arbitrary transition dynamics.On a variety of toy and real models, APF generates more accurate results within a fixed computation budget compared to several standard algorithms from the literature.

The complexity of counting models of linear-time temporal logic

We determine the complexity of counting models of bounded size of specifications expressed in linear-time temporal logic. Counting word-models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of nondeterministic polynomial space Turing machines, if the bound is given in binary. Counting tree-models is as hard as counting accepting runs of nondeterministic exponential time Turing machines, if the bound is given in unary. For a binary encoding of the bound, the problem is at least as hard as counting accepting runs of nondeterministic exponential space Turing machines, and not harder than counting accepting runs of nondeterministic doubly-exponential time Turing machines. Finally, counting arbitrary transition systems satisfying a formula is #P-hard and not harder than counting accepting runs of nondeterministic polynomial time Turing machines with a PSPACE oracle, if the bound is given in unary. If the bound is given in binary, then counting arbitrary models is as hard as counting accepting runs of nondeterministic exponential time Turing machines.

Loops, projective invariants, and the realization of the Borromean topological link in quantum mechanics

All the typical global quantum mechanical observables are complex relative phases obtained by interference phenomena. They are described by means of some global geometric phase factor, which is thought of as the “memory” of a quantum system undergoing a “cyclic evolution” after coming back to its original physical state. The origin of a geometric phase factor can be traced to the local phase invariance of the transition probability assignment in quantum mechanics. Beyond this invariance, transition probabilities also remain invariant under the operation of complex conjugation. Most important, geometric phase factors distinguish between unitary and antiunitary transformations in terms of complex conjugation. These two types of invariance functions as an anchor point to investigate the role of loops and based loops in the state space of a quantum system as well as their links and interrelations. We show that arbitrary transition probabilities can be calculated using projective invariants of loops in the space of rays. The case of the double slit experiment serves as a model for this purpose. We also represent the action of one-parameter unitary groups in terms of oppositely oriented-based loops at a fixed ray. In this context, we explain the relation among observables, local Boolean frames of projectors, and one-parameter unitary groups. Next, we exploit the non-commutative group structure of oriented-based loops in 3-d space and demonstrate that it carries the topological semantics of a Borromean link. Finally, we prove that there exists a representation of this group structure in terms of one-parameter unitary groups that realizes the topological linking properties of the Borromean link.

Diffusion approximation of the network with limited number of same type customers and time dependent service parameters

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

RNA folding pathways in stop motion.

We introduce a method for predicting RNA folding pathways, with an application to the most important RNA tetraloops. The method is based on the idea that ensembles of three-dimensional fragments extracted from high-resolution crystal structures are heterogeneous enough to describe metastable as well as intermediate states. These ensembles are first validated by performing a quantitative comparison against available solution nuclear magnetic resonance (NMR) data of a set of RNA tetranucleotides. Notably, the agreement is better with respect to the one obtained by comparing NMR with extensive all-atom molecular dynamics simulations. We then propose a procedure based on diffusion maps and Markov models that makes it possible to obtain reaction pathways and their relative probabilities from fragment ensembles. This approach is applied to study the helix-to-loop folding pathway of all the tetraloops from the GNRA and UNCG families. The results give detailed insights into the folding mechanism that are compatible with available experimental data and clarify the role of intermediate states observed in previous simulation studies. The method is computationally inexpensive and can be used to study arbitrary conformational transitions.

Quantifying Noisy Attractors: From Heteroclinic to Excitable Networks

Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical connection between “nodes''). Such network attractors can display a high degree of sensitivity to noise both in terms of the regions of phase space visited and in terms of the sequence of transitions around the network. The two types of network are intimately related---one can directly bifurcate to the other. In this paper we attempt to quantify the effect of additive noise on such network attractors. Noise increases the average rate at which the networks are explored and can result in “macroscopic” random motion around the network. We perform an asymptotic analysis of local behavior of an escape model near heteroclinic/excitable nodes in the limit of noise $\eta\rightarrow 0^+$ as a model for the mean residence time $T$ near equilibria. The heteroclinic network case has $T$ proportional to $-\ln\eta$ while the excitable network has $T$ given by a Kramers' law, proportional to $\exp (B/\eta^2)$. There is singular scaling behavior (where $T$ is proportional to $1/\eta$) at the bifurcation between the two types of network. We also explore transition probabilities between nodes of the network in the presence of anisotropic noise. For low levels of noise, numerical results suggest that a (heteroclinic or excitable) network can approximately realize any set of transition probabilities and any sufficiently large mean residence times at the given nodes. We show that this can be well modeled in our example network by multiple independent escape processes, where the direction of first escape determines the transition. This suggests that it is feasible to design noisy network attractors with arbitrary Markov transition probabilities and residence times.

Memory‐Efficient Simulation of Frequency‐DependentQ

Memory‐variable methods have been widely applied to approximate frequency‐independent quality factor Q in numerical simulation of wave propagation. The frequency‐independent model is often appropriate for frequencies up to about 1 Hz but at higher frequencies is inconsistent with some regional studies of seismic attenuation. We apply the memory‐variable approach to frequency‐dependent Q models that are constant below, and follow a power‐law above, a chosen transition frequency. We present numerical results for the corresponding memory‐variable relaxation times and weights, obtained by nonnegative least‐squares fitting of the Q ( f ) function, for a range of exponent values; these times and weights can be scaled to an arbitrary transition frequency and a power‐law prefactor, respectively. The resulting memory‐variable formulation can be used with numerical wave‐propagation solvers based on methods such as finite differences (FDs) or spectral elements and may be implemented in either conventional or coarse‐grained form. In the coarse‐grained approach, we fit effective Q for low‐ Q values (<200) using a nonlinear inversion technique and use an interpolation formula to find the corresponding weighting coefficients for arbitrary Q . A 3D staggered‐grid FD implementation closely approximates the frequency–wavenumber solution to both a half‐space and a layered model with a shallow dislocation source for Q as low as 20 over a bandwidth of two decades. We compare the effects of different power‐law exponents using a finite‐fault source model of the 2008 M w 5.4 Chino Hills, California, earthquake and find that Q ( f ) models generally better fit the strong‐motion data than the constant Q models for frequencies above 1 Hz. Online Material: Figures comparing finite difference and frequency–wavenumber seismograms for an elastic layered‐model point source simulation. Median spectral acceleration centered at 1 s and Fourier amplitude centered at 0.25 and 2.25 Hz for strong ground motion recordings and synthetics from the Chino Hills earthquake.

Event-Based Control and Scheduling Codesign: Stochastic and Robust Approaches

With the advent of networked embedded control systems (NECSs) new opportunities and challenges have arisen. Among others, the challenges result mostly from variable communication delays, access constraints, and resource constraints. An event-based control and scheduling (EBCS) codesign strategy for NECSs involving a set of continuous-time LTI plants is proposed in this paper addressing all aforementioned challenges. A novel representation of the network-induced delay as an uncertain variable belonging to a finite set of different bounded intervals is further proposed. The transition from one bounded interval to another can be arbitrary or according to a stochastic process. Regarding the type of the transition and the resulting discrete-time switched polytopic system of the NECS, two versions of the EBCS problem are introduced: A robust EBCS problem under arbitrary transition and a stochastic EBCS problem under stochastic transition. Global uniform practical stability with guaranteed performance (measured by a quadratic cost function) is guaranteed for both versions after formulating them as LMI optimization problems. The effectiveness of the proposed EBCS strategy is illustrated along with a comparison between its versions for a set of mobile robots. Notably, the EBCS strategy is generally applicable to discrete-time switched polytopic systems.

Slant Field Plate Model for Field-Effect Transistors

The simplified field plate model for field-effect transistors previously introduced is further developed to allow arbitrary transition angles between gate and field plate or adjacent field plates. The model shows that transition angles less than 30° (measured from the surface) can result in significant improvements in electric field management.

Modifications on the surface layer scheme in RegCM4.3.5-CLM

The surface layer scheme in the Land Surface Model (CLM3.5) is revised for the new version of Regional Climate Model (RegCM4.3.5). In the original scheme, the stable and unstable regimes are divided into four pieces and the criteria that used for divisions are arbitrary and abrupt transitions between different pieces exist. In the modification, for the unstable conditions, the similarity functions are a blend of the widely used Paulson type expressions for near-neutral stratification plus a parameterization that takes into account highly convective conditions. For the stable regime, the formulations proposed by Cheng and Brutsaert are applied, which cover a wide range of stable stratification. The revised scheme is able to apply over a wider range of atmospheric stabilities than the old one without jump in different regimes, and the restrictions artificially imposed on certain variables in the old surface layer scheme are removed or suppressed. The old and revised schemes are tested over the East Asian domain with 10-year simulations. Two schemes present quite different flux simulations. Compared with observations, simulated surface variables biases are substantially decreased using the revised scheme. Impacts of the revised scheme on the simulation of several important surface variables, heat fluxes and precipitation are analyzed.

Magnetic entropy calculation for a second-order ferromagnetic phase transition

In this paper, we present a new calculation method of magnetic entropy in an arbitrary second-order ferromagnetic phase transition system. Based on the Arrott–Noakes relation (H/M)1/γ = (T-TC)/TC+(M/M1)1/β, the Gibbs energy can be rewritten as a new form where the critical exponents are naturally included. Correspondingly, the magnetic entropy (SM) is presented as: [Formula: see text]. Thus, the magnetic entropy change (ΔSM) can be deduced as [Formula: see text] which is consistent exactly with the previous report [V. Franco et al., Appl. Phys. Lett.89 (2006) 222512]. In addition, the conventional calculation method of magnetic entropy can be treated as a particular form of this calculation method. Furthermore, the obtained magnetic entropy change from experimental measurement are consistent with the theoretical value deduced from the present method.