Single machine slack due-window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activity

In this paper, we consider the slack due-window assignment model and study a single machine scheduling problem of linear time-dependent deteriorating jobs and a deteriorating maintenance activity. The cost for each job consists of four components: earliness, tardiness, window location and window size. The objective is to schedule the jobs and to assign the maintenance activity and due-windows such that the total cost among all the jobs is minimized. A polynomial-time algorithm with the running time not exceeding $O(n^2logn)$ to give a solution to this problem is introduced, where $n$ is the number of jobs.Comment: Submitted - Under Revie

Bit Flipping Moment Balancing Schemes for Insertion, Deletion and Substitution Error Correction

In this paper, two moment balancing schemes, namely a variable index scheme and a fixed index scheme, for either single insertion/deletion error correction or multiple substitution error correction are introduced for coded sequences originally developed for correcting substitution errors only. By judiciously flipping bits of the original substitution error correcting code word, the resulting word is able to correct either a reduced number of substitution errors or a single insertion/deletion error. The number of flips introduced by the two schemes can be kept small compared to the code length. It shows a practical value of applying the schemes to a long substitution error correcting code for a severe channel where substitution errors dominate but insertion/deletion errors can occur with a low probability. The new schemes can be more easily implemented in an existing coding system than any previously published moment balancing templates since no additional parity bits are required which also means the code rate remains same and the existing substitution error correcting decoder requires no changes. Moreover, the work extends the class of Levenshtein codes capable of correcting either single substitution or single insertion/deletion errors to codes capable of correcting either multiple substitution errors or single insertion/deletion error

Long-Bone Fracture Detection using Artificial Neural Networks based on Line Features of X-ray Images

Two line-based fracture detection scheme are developed and discussed, namely Standard line-based fracture detection and Adaptive Differential Parameter Optimized (ADPO) line-based fracture detection. The purpose for the two line-based fracture detection schemes is to detect fractured lines from X-ray images using extracted features based on recognised patterns to differentiate fractured lines from non-fractured lines. The difference between the two schemes is the detection of detailed lines. The ADPO scheme optimizes the parameters of the Probabilistic Hough Transform, such that granule lines within the fractured regions are detected, whereas the Standard scheme is unable to detect them. The lines are detected using the Probabilistic Hough Function, in which the detected lines are a representation of the image edge objects. The lines are given in the form of points, (x,y), which includes the starting and ending point. Based on the given line points, 13 features are extracted from each line, as a summary of line information. These features are used for fracture and non-fracture classification of the detected lines. The classification is carried out by the Artificial Neural Network (ANN). There are two evaluations that are employed to evaluate both the entirety of the system and the ANN. The Standard Scheme is capable of achieving an average accuracy of 74.25%, whilst the ADPO scheme achieved an average accuracy of 74.4%. The ADPO scheme is opted for over the Standard scheme, however it can be further improved with detected contours and its extracted features

On the global dynamics of the inhomogeneous Boltzmann equations without angular cutoff: Hard potentials and Maxwellian molecules

This is the first one of two papers on the global dynamics of the original Boltzmann equations without angular cutoff on the torus. We address the problem for the hard potentials and Maxwellian molecules in the present paper. The case of soft potentials is left to a forthcoming paper. The key to solve the problem is the energy-entropy method which characterizes the propagation of the regularity, $H$-theorem and the interplay between the energy and the entropy. Our main results are as follows: (i) We present a unified framework to prove the well-posedness for the original Boltzmann equation for both angular cutoff and without cutoff in weighted Sobolev spaces with polynomial weights. As a consequence, we obtain an explicit formula for the asymptotics of the equation from angular cutoff to non-cutoff. (ii) We describe the global dynamics of the equation under the almost optimal assumption on the solution which makes sure that the Boltzmann collision operator behaves like a fractional Laplace operator for the velocity variable. More precisely, we obtain the propagation of the regularity for the solution and a new mechanism for the convergence of the solution to its equilibrium with quantitative estimates. (iii) We prove that any global and smooth solution to the equation is stable, i.e., any perturbed solution will remain close to the reference solution if initially they are close to each other

Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality

In this note we explored the holographic relative entropy in the presence of the 5d Chern-Simons term, which introduces a mixed gauge-gravity anomaly to the dual CFT. The theory trivially satisfies an entanglement first law. However, to quadratic order in perturbations of the stress tensor $T$ and current density $J$, there is a mixed contribution to the relative entropy bi-linear in $T$ and $J$, signalling a potential violation of the positivity of the relative entropy. Miraculously, the term vanishes up to linear order in a derivative expansion. This prompted a closer inspection on a different consistency check, that involves time-delay of a graviton propagating in a charged background, scattered via a coupling supplied by the Chern-Simons term. The analysis suggests that the time-delay can take either sign, potentially violating causality for any finite value of the CS coupling.Comment: 21 pages, Details added, typos fixed, references updated; version to appear in JHE

A Predation Behavior Model Based on Game Theory

This article adopts game theory to build a model for explaining the predation behavior of animals.We assume that both the prey and the preydator have two stratigies in this game,the active one and the passive one.By calculating the outcome and the income of energy in different stratigies, we find the solution to analyze the different evolution path of both the prey and the predator.A simulation result approximately represents the correctness of our model.Comment: 5 pages,1 figure,1 tabl

Optimal Scheduling of Multiple Sensors over Lossy and Bandwidth Limited Channels

This work considers the sensor scheduling for multiple dynamic processes. We consider $n$ linear dynamic processes, the state of each process is measured by a sensor, which transmits their local state estimates over wireless channels to a remote estimator with certain communication costs. In each time step, only a portion of the sensors is allowed to transmit data to the remote estimator and the packet might be lost due to unreliability of the wireless channels. Our goal is to find a scheduling policy which coordinates the sensors in a centralized manner to minimize the total expected estimation error of the remote estimator and the communication costs. We formulate the problem as a Markov decision process. We develop an algorithm to check whether there exists a deterministic stationary optimal policy. We show the optimality of monotone policies, which saves computational effort of finding an optimal policy and facilitates practical implementation. Nevertheless, obtaining an exact optimal policy still suffers from curse of dimensionality when the number of processes are large. We further provide an index-based heuristics to avoid brute force computation. Numerical examples are presented to illustrate our theoretical results.Comment: Correct versio

Nonlinearity enhancement in optomechnical system

The nonlinearity is an important feature in the field of optomechanics. Employing atomic coherence, we put forward a scheme to enhance the nonlinearity of the cavity optomechanical system. The effective Hamiltonian is derived, which shows that the nonlinear strength can be enhanced by increasing the number of atoms at certain range of parameters. We also numerically study the nonlinearity enhancement beyond the effective Hamiltonian. Furthermore, we investigate the potential usage of the nonlinearity in performing quantum nondemolition (QND) measurement of the bosonic modes. Our results show that the present system exhibits synchronization, and the nonlinear effects provide us an effective method in performing QND.Comment: 6 pages, 4figure

Radiation tolerance of opto-electronic components proposed for space-based quantum key distribution

Plasma in low earth orbit can damage electronic components and potentially jeopardise the scientific missions in space. Predicting the accumulated damage and understanding the components' radiation tolerance are important to mission planning. In this manuscript we report on the observed radiation tolerance of single photon detectors and a liquid crystal polarization rotator. We conclude that an uncooled Si APD could continue to operate from more than a month up to beyond the lifetime of the satellite depending on the orbit. The polarization rotator was also unaffected by the exposed dosage.Comment: 4 pages, 2 figures, accepted by Journal of Modern Optic

Robust fermionic-mode entanglement of a nanoelectronic system in non-Markovian environments

A maximal steady-state fermionic entanglement of a nanoelectronic system is generated in finite temperature non-Markovian environments. The fermionic entanglement dynamics is presented by connecting the exact solution of the system with an appropriate definition of fermionic entanglement. We prove that the two understandings of the dissipationless non-Markovian dynamics, namely the bound state and the modified Laplace transformation are completely equivalent. For comparison, the steady-state entanglement is also studied in the wide-band limit and Born-Markovian approximation. When the environments have a finite band structure, we find that the system presents various kinds of relaxation processes. The final states can be: thermal or thermal-like states, quantum memory states and oscillating quantum memory states. Our study provide an analytical way to explore the non-Markovian entanglement dynamics of identical fermions in a realistic setting, i.e., finite temperature reservoirs with a cutoff spectrum