Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities

In recent work, Chow, Huang, Li and Zhou introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When $N\ge 2$ is the number of vertices of the graph, they show that the corresponding Fokker-Planck equation is a system of $N$ nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. The different choices for inner products on the space of probability distributions result in different Fokker-Planck equations for the same process. Each of these Fokker-Planck equations has a unique global equilibrium, which is a Gibbs distribution. In this paper we study the {\em speed of convergence} towards global equilibrium for the solution of these Fokker-Planck equations on a graph, and prove that the convergence is indeed exponential. The rate as measured by the decay of the $L_2$ norm can be bound in terms of the spectral gap of the Laplacian of the graph, and as measured by the decay of (relative) entropy be bound using the modified logarithmic Sobolev constant of the graph. With the convergence result, we also prove two Talagrand-type inequalities relating relative entropy and Wasserstein metric, based on two different metrics introduced in [CHLZ] The first one is a local inequality, while the second is a global inequality with respect to the "lower bound metric" from [CHLZ]

Supervisory Efficiency and Collusion in a Multiple-Agent Hierarchy

We analyze a principal-supervisor-two-agent hierarchy with inefficient supervision. The su-pervisor may collects a wrong signal on each agent’s unobservable effort level. When reportingto the principal, the supervisor can collude with one or both agents to manipulate the signalin exchange for a bribe. In contract design, we identify a new trade-off between the loss fromsupervisor-agent collusion and the risk from inefficient supervision: Although allowing collu-sion makes shirking more attractive to the agents, it brings in a benefit because it can “correct”an incorrect negative signal when the agent has exerted effort. Such collusive supervision savesrisk premiums that the principal has to pay for incentive provision. We characterize the princi-pal’s optimal contract choice among no-supervision, collusion-proof, and collusive-supervisioncontracts. We show that the collusive-supervision contract dominates when the supervisory ef-ficiency is at an intermediate level

Experimental investigation of unsteadiness in transonic shock boundary layer interaction

Transonic shock wave/boundary layer interaction over a wall-mounted bump was investigated with specific focus on shock wave unsteadiness and identification of its source. A large separation bubble resulted of an interaction driven by a flow characterized by a peak Mach number of 1.365. Overall this particular type of transonic unsteadiness is characterized with low amplitude and relatively high frequency motion. Low frequency shock unsteadiness was optically estimated and matched spectral content of wall fluctuating pressure. A strong correlation between separation onset and reattachment zones suggested a model of bubble expansion/contraction at the reattachment point where upstream-traveling pressure waves are generated and cause the shock wave excursions

Dietary protein requirements of the New Zealand Black-footed Abalone (Haliotis iris, Martyn 1784)

The aim of this thesis is to evaluate the nutritional aspects of dietary protein for the New Zealand black-footed abalone (Haliotis iris) as an aquaculture species, and thus provide an affordable option for formulated feeds to be used in this abalone industry. Young (4 hours) and mature (7 days) and nine of twenty strains were mixed to each other microalgal biofilms were tested for their effectiveness on H. iris larval early developmental processes (attachment, metamorphosis, settlement and survival). Amino acid profiles and percent biofilm cover of microalgae also were monitored. Significantly better effects on attachment, metamorphosis, settlement and survival were found when abalone were exposed to mature microalgal biofilms compared to young biofilms, but few significant differences were found among biofilms composed of different microalgal species. Attachment and metamorphosis did not appear to be affected by differences in essential or non-essential amino acid profiles in the diets, but positive correlations were found between developmental processes and total amino acid content and percent biofilm cover. Similar results were also found in dual strains experiment. Nine commercially available protein sources (white fish, red fish, blood, meat and bone, casein, soybean, gluten, maize protein, Spirulina) were used as sole protein sources in formulated diets, which was fed to juvenile H. iris at 18 °C for five months. Juvenile abalone fed with diets containing white fish, red fish, casein, soybean and Spirulina had significantly better growth than those of fed other protein sources, thus indicating that these diets could be suitable as sole protein sources for H. iris formulated feeds. Abalone juveniles fed soybean diets (with extremely low methionine content) had similar growth results as those fed fish meal diets, and did not show a decrease in certain amino acid content (such as methionine) in their soft body tissues. However, dietary amino acid profiles did affect the amino acid profiles of both soft bodies and shells, which may have caused changes in shell bio-mineralization. Red fish protein had the best performance and it was therefore used to determine protein requirements under two different temperature regimes (13-21°C and 8-16°C) that simulated the temperature regimes of the South and North Islands in New Zealand. Six different dietary protein levels (0, 10, 20, 30, 40, and 45%) made from red fish meal were fed to juvenile abalone for four months. Growth performance increased steadily with increasing dietary protein. A second-order polynomial curve fit showed differences in protein requirements between the two temperature regimes, which were 42-53% in low temperatures and 38-39% in high temperature regimes. Shell morphology of previous two dietary experiments shown that: dietary protein sources and levels strongly affected H. iris shell morphology. Significantly wider, higher and heavier shells were found in animals fed casein diets. Both fish meal diets resulted in abalone with flatter and heavier shells. High dietary protein levels also promoted the enhancement of shell width and shell weight, and high temperature environments produced heavier and thicker shells. In conclusion, dietary protein is an important factor for H. iris aquaculture. The content of dietary protein strongly affects settlement of larvae and growth of juveniles in H. iris. Dietary amino acid profiles can change amino acid profiles in both soft bodies and shells, which may cause changes in shell morphology. A dietary protein content above 40%, as can be provided with red fish meal in formulated diets, is recommended to improve H. iris production. Raising dietary protein contents can effectively recover the decreased growth that results from a low cultivation water temperature regime

Thermally stable low current consuming gallium and germanium chalcogenides for consumer and automotive memory applications

The phase change technology behind rewritable optical disks and the latest generation of electronic memories has provided clear commercial and technological advances for the field of data storage, by virtue of the many well known attributes, in particular scaling, cycling endurance and speed, that chalcogenide materials offer. While the switching power and current consumption of established germanium antimony telluride based memory cells are a major factor in chip design in real world applications, often the thermal stability of the device can be a major obstacle in the path to the full commercialisation. In this work we describe our research in material discovery and characterization for the purpose of identifying more thermally stable chalcogenides for applications in PCRAM

On the Lyapunov functional of Leslie-Gower predator-prey models with time-delay and Holling's functional responses

The global stability on the dynamical behavior of the Leslie-Gower predator-prey system with delayed prey specific growth is analyzed by constructing the corresponding Lyapunov functional. Three different types of famous Holling's functional responses are considered in the present study. The sufficient conditions for the global stability analysis of the unique positive equilibrium point are derived accordingly. A numerical example is presented to illustrate the effect of different Holling-Type functional responses on the global stability of the Leislie-Gower predator-prey model

The Taiwanese National Language (guoyu) Movement of the 1950s : with a consideration of the Chinese Language Standardization Movement following the Founding of People\u27s Republic of China

北岡正子教授退休記念

Equilibrium Analysis of Channel Structure Strategies in Uncertain Environment

Abstract In this paper, we consider a pricing decision problem with two competing supply chains which distribute differentiated but competing products in the same market. Each chain can be vertically integrated or decentralized based on the choice of the manufacturer. The manufacturing costs, sales costs and consumer demands are characterized as uncertain variables, whose distributions are estimated by experienced experts. Meanwhile, uncertainty theory and game theory are employed to formulate the pricing decision problems. The equilibrium behaviors (how the supply chain members make their own pricing decisions on wholesale prices and retailer markups) at operational level under three possible scenarios are derived. Numerical experiments are also given to explore the impacts of the parameters’ uncertain degrees on supply chain members’ pricing decisions. The results demonstrate that the supply chain uncertain factors have great influences on equilibrium prices. In addition, we also evaluate the effects of competing intensity (substitutability) of the two products on the strategy behaviors, vertically integrated channel strategy versus decentralized strategy, of the manufacturers. It is found that the manufacturers are better off to distribute their products through a decentralized channel rather than an integrated one when the substitutability is greater than some value. Besides, the uncertain factors in the supply chain might reduce the value contrast to the one in deterministic case. Some other interesting managerial highlights are also provided in this paper

Metalloporphyrin-incorporated diphosphine ligands for metal ion-binding

Poster: no. P48Diphosphine ligands have been widely used in organometallic chemistry and catalysis.1 By incorporation of functional units such as metallomacrocycles, the resulting functionalized diphosphines could exhibit unusual properties or binding behavior. In this study, we prepared several examples of ruthenium porphyrin phosphine complexes [RuII(Por)(dppm)2] (1; Por = TTP, 4-MeO-TPP, F20-TPP; dppm = bis(diphenylphosphino)methane) by a similar method to that previously reported for their congeners.2 Reaction of complexes 1 with a number of metal …published_or_final_versio