On Optimal Harvesting in Stochastic Environments: Optimal Policies in a Relaxed Model

This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff structure of the price rate function (the price decreases as the population increases), no optimal harvesting policy exists. This paper establishes a relaxed formulation of the harvesting model in such a manner that existence of an optimal relaxed harvesting policy can not only be proven but also identified. The analysis embeds the harvesting problem in an infinite-dimensional linear program over a space of occupation measures in which the initial position enters as a parameter and then analyzes an auxiliary problem having fewer constraints. In this manner upper bounds are determined for the optimal value (with the given initial position); these bounds depend on the relation of the initial population size to a specific target size. The more interesting case occurs when the initial population exceeds this target size; a new argument is required to obtain a sharp upper bound. Though the initial population size only enters as a parameter, the value is determined in a closed-form functional expression of this parameter.Comment: Key Words: Singular stochastic control, linear programming, relaxed contro

Transition from fractal to non-fractal scalings in growing scale-free networks

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameter $q$. Interestingly, we show that by adjusting $q$, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from `large' to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.Comment: 7 pages, 3 figures, definitive version accepted for publication in EPJ

Role of fractal dimension in random walks on scale-free networks

Fractal dimension is central to understanding dynamical processes occurring on networks; however, the relation between fractal dimension and random walks on fractal scale-free networks has been rarely addressed, despite the fact that such networks are ubiquitous in real-life world. In this paper, we study the trapping problem on two families of networks. The first is deterministic, often called $(x,y)$-flowers; the other is random, which is a combination of $(1,3)$-flower and $(2,4)$-flower and thus called hybrid networks. The two network families display rich behavior as observed in various real systems, as well as some unique topological properties not shared by other networks. We derive analytically the average trapping time for random walks on both the $(x,y)$-flowers and the hybrid networks with an immobile trap positioned at an initial node, i.e., a hub node with the highest degree in the networks. Based on these analytical formulae, we show how the average trapping time scales with the network size. Comparing the obtained results, we further uncover that fractal dimension plays a decisive role in the behavior of average trapping time on fractal scale-free networks, i.e., the average trapping time decreases with an increasing fractal dimension.Comment: Definitive version published in European Physical Journal

Mushy Zone Morphology During Directional Solidification of Pb-5.8 Wt Pct Sb Alloy

The Pb-5.8 wt pet Sb alloy was directionally solidified with a positive thermal gradient of 140 K cm(-1) at a growth speed ranging from 0.8 to 30 mu m s(-1), and then it was quenched to retain the mushy zone morphology. The morphology of the mushy zone along its entire length has been characterized by using a serial sectioning and three-dimensional image reconstruction technique. Variation in the cellular/dendritic shape factor, hydraulic radius of the interdendritic region, and fraction solid along the mushy zone length has been studied. A comparison with predictions from theoretical models indicates that convection remarkably reduces the primary dendrite spacing while its influence on the dendrite tip radius is not as significant

Effect of Magnetic-Field on the Microstructure and Macrosegregation in Directionally Solidified Pb-Sn Alloys

An investigation into the influence of a transverse magnetic field (0.45 T) on the mushy zone morphology and macrosegregation in directionally solidified hypoeutectic Pb-Sn alloy shows that the field has no influence on the morphology of dendritic arrays. The field does, however, cause severe distortion in the cellular array morphology. Cellular arrayed growth with the magnetic field results in an extensive channel formation in the mushy zone, as opposed to the well-aligned and uniformly distributed cells formed in the absence of the field. The channels are produced due to the anisotropy in the thermosolutal convection caused by the magnetic field. Macrosegregation, however, along the length of the directionally solidified samples is not influenced by this magnetic field for either the cellular or dendritic arrays

Studying Kaon-pion S-wave scattering in K-matrix formalism

We generalize our previous work on \pi\pi scattering to K\pi scattering, and re-analyze the experiment data of K\pi scattering below 1.6 GeV. Without any free parameter, we explain K\pi I=3/2 S-wave phase shift very well by using t-channel rho and u-channel K^* meson exchange. With the t-channel and u-channel meson exchange fixed as the background term, we fit the K\pi I=1/2 S-wave data of the LASS experiment quite well by introducing one or two s-channel resonances. It is found that there is only one s-channel resonance between K\pi threshold and 1.6 GeV, i.e., K_0^*(1430) with a mass around 1438~1486 MeV and a width about 346 MeV, while the t-channel rho exchange gives a pole at (450-480i) MeV for the amplitude.Comment: REVTeX4 file, 11 pages and 3 figure

Quantum Inequalities for the Electromagnetic Field

A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential, and the sampling function used to weight the energy integrals is left arbitrary up to the constraints that it be a positive, continuous function of unit area and that it decays at infinity. Examples of the quantum inequality are developed for Minkowski spacetime, Rindler spacetime and the Einstein closed universe.Comment: 19 pages, 1 table and 1 figure. RevTex styl

Analysis of the intraspinal calcium dynamics and its implications on the plasticity of spiking neurons

The influx of calcium ions into the dendritic spines through the N-metyl-D-aspartate (NMDA) channels is believed to be the primary trigger for various forms of synaptic plasticity. In this paper, the authors calculate analytically the mean values of the calcium transients elicited by a spiking neuron undergoing a simple model of ionic currents and back-propagating action potentials. The relative variability of these transients, due to the stochastic nature of synaptic transmission, is further considered using a simple Markov model of NMDA receptos. One finds that both the mean value and the variability depend on the timing between pre- and postsynaptic action-potentials. These results could have implications on the expected form of synaptic-plasticity curve and can form a basis for a unified theory of spike time-dependent, and rate based plasticity.Comment: 14 pages, 10 figures. A few changes in section IV and addition of a new figur

Time Dependence of Tip Morphology during Cellular/Dendritic Arrayed Growth

Succinonitrile-1.9 wt pct acetone has been directionally solidified in 0.7 X 0.7-cm-square cross section pyrex ampoules in order to observe the cell/dendrite tip morphologies, not influenced by the 'wall effects', which are present during growth in the generally used thin (about 200 gm) crucibles. The tips do not maintain a steady-state shape, as is generally assumed. Instead, they fluctuate within a shape envelope. The extent of fluctuation increases with decreasing growth speed, as the micro structure changes from the dendritic to cellular. The influence of natural convection has been examined by comparing these morphologies with those grown, without convection, in the thin ampoules

In-plane fluxon in layered superconductors with arbitrary number of layers

I derive an approximate analytic solution for the in-plane vortex (fluxon) in layered superconductors and stacked Josephson junctions (SJJ's) with arbitrary number of layers. The validity of the solution is verified by numerical simulation. It is shown that in SJJ's with large number of thin layers, phase/current and magnetic field of the fluxon are decoupled from each other. The variation of phase/current is confined within the Josephson penetration depth, $\lambda_J$, along the layers, while magnetic field decays at the effective London penetration depth, $\lambda_c \gg \lambda_J$. For comparison with real high-$T_c$ superconducting samples, large scale numerical simulations with up to 600 SJJ's and with in-plane length up to 4000 $\lambda_J$%, are presented. It is shown, that the most striking feature of the fluxon is a Josephson core, manifesting itself as a sharp peak in magnetic induction at the fluxon center.Comment: 4 pages, 4 figures. Was presented in part at the First Euroconference on Vortex Matter in Superconductors (Crete, September 1999