Optimal control and numerical methods for hybrid stochastic SIS models

This work focuses on optimal controls of a class of stochastic SIS epidemic models under regime switching. By assuming that a decision maker can influence the infectivity period, our aim is to minimize the expected discounted cost due to illness, medical treatment, and the adverse effect on the society. In addition, a model with the incorporation of vaccination is proposed. Numerical schemes are developed by approximating the continuous-time dynamics using Markov chain approximation methods. It is demonstrated that the approximation schemes converge to the optimal strategy as the mesh size goes to zero. Numerical examples are provided to illustrate our results.     

Chemical bonding in representative astrophysically relevant neutral,cation, and anion HCnH chains

Most existing studies assign a polyynic and cumulenic character of chemical bonding in carbon-based chains relying on values of the bond lengths. Building on our recent work, in this paper we add further evidence on the limitations of such an analysis and demonstrate the significant insight gained via natural bond analysis. Presently reported results include atomic charges, natural bond order and valence indices obtained from ab initio computations for representative members of the astrophysically relevant neutral and charged HC_2k/2k+1H chain family. They unravel a series of counter-intuitive aspects and/or help naive intuition in properly understanding microscopic processes, e.g., electron removal from or electron attachment to a neutral chain. Demonstrating that the Wiberg indices adequately quantify the chemical bonding structure of the HC_2k/2k+1H chains—while the often heavily advertised Mayer indices do not—represents an important message conveyed by the present study.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains

There has been some substantial research about the connections between quantum chaos and quantum correlations in many-body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin-1/2 chains are compared. The CC and QD between nearest-neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite-size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis.     

An inequality connecting entropy distance,Fisher Information and large deviations

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.     

Tuning Emission Wavelength of Polymorphous Crystal via Controllable Alkyl Chain Stacking and Its Vapor- and Thermo-Responsive Fluorescence

Tuning fluorescence colour of solid-state materials has become a topic of increasing interest for both fundamental mechanism study and practical applications such as sensors, optical recording and security printing. In this work, a fluorescent colour tuneable molecule BA-C16 is rationally designed and facilely synthesized by attaching flexible long alkyl chains to 2-hydroxybenzophenone azine ( BA ), which shows both aggregation-induced emission (AIE) and excited-state intramolecular proton transfer (ESIPT) characteristics. Compared to BA , the simple introduction of long alkyl chains in BA-C16 leads to an emission wavelength redshift from 542 to 558 nm. This strategy of extending emission wavelength is rarely reported, and is ascribed to the enlarged through-space π-conjugation between interplanar molecules in the aggregate of BA-C16 . Three crystals of BA-C16 are obtained with green, yellowish green and yellow emission. According to characterization by X-ray crystallography, X-ray powder diffraction and differential scanning calorimetry, alkyl chains play an important role in inducing different stacking modes of the three crystals, which further leads to polymorph-dependent fluorescence colour. BA-C16 exhibits tuneable solid-state fluorescence upon vapor fumigation, or annealing based on a transition between a “near-monomer” crystalline state and a “dimer” crystalline state. BA-C16 is further applied for rewritable fluorescence printing tuned by vapor- and thermal-treatment.