Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow

We prove several differential Harnack inequalities for positive solutions to nonlinear backward heat equations with different potentials coupled with the Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear heat equation under the $\varepsilon$-Ricci flow on a closed surface. These new Harnack inequalities extend the previous differential Harnack inequalities for linear heat equations with potentials under the Ricci flow.Comment: 17 pages. New explanations added; Final versio

Analysis of dynamic system optimal assignment with departure time choice

Most analyses on dynamic system optimal (DSO) assignment are done by using the control theory with an outflow traffic model. On the one hand, this control theoretical formulation provides some attractive mathematical properties for analysis. On the other hand, however, this kind of formulation often ignores the importance of ensuring proper flow propagation. Moreover, the outflow models have also been extensively criticized for their implausible traffic behaviour. This paper aims to provide another framework for analysing a DSO assignment problem based upon sound traffic models. The assignment problem we considered aims to minimize the total system cost in a network by seeking an optimal inflow profile within a fixed planning horizon. This paper first summarizes the requirements on a plausible traffic model and reviews three common traffic models. The necessary conditions for the optimization problem are then derived using a calculus of variations technique. Finally, a simple working example and some concluding remarks are given

System optimizing flow and externalities in time-dependent road networks

This paper develops a framework for analysing and calculating system optimizing flow and externalities in time-dependent road networks. The externalities are derived by using a novel sensitivity analysis of traffic models. The optimal network flow is determined by solving a state-dependent optimal control problem, which assigns traffic such that the total system cost of the network system is minimized. This control theoretic formulation can work with general travel time models and cost functions. Deterministic queue is predominantly used in dynamic network models. The analysis in this paper is more general and is applied to calculate the system optimizing flow for Friesz’s whole link traffic model. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

Departure from the onset-onset rule

Using a signal-detection task, the generality of Turvey's (1973) onset-onset rule was tested in four experiments. After seeing, in succession, (1) one or two letters (target display), (2) a multiletter detection display, and (3) a mask display, subjects decided whether or not the letter or letters in the target display reappeared in the succeeding detection display at different levels of detection-display duration in various situations. The subjects' sensitivity was inconsistent with the onset-onset rule. More specifically, sensitivity increased with increases in display duration within a fixed stimulus onset asynchrony of 150 msec. Display duration, however, had no effect on response bias. Nor was there any interaction between display duration and display size in terms of either sensitivity or response bias. The more complicated relationship between display duration and display size does not invalidate the departure from the onset-onset rule

Analysis of dynamic system optimum and externalities with departure time choice

This paper aims to analyse the dynamic system optimal assignment with departure time choice, which is an important, yet underdeveloped area. The main contribution of this paper is the necessary conditions and the sensitivity analysis for dynamic system optimizing flow. Following this, we revisit the issue of dynamic externality in a more plausible way. We showed that how the externality can be derived and interpreted from the control theoretic formulation and the sensitivity analysis of traffic flow. To solve the system optimal assignment, we propose a dynamic programming solution approach. We present numerical calculations and discuss the characteristics of the results. In particular, we contrast the system optimal assignment with its equilibrium counterpart in terms of the amount of travel generated, flow profiles, and travel costs

The Distribution of Integral Points on the Wonderful Compactification by Height

We study the asymptotic distribution of S-integral points of bounded height on partial bi-equivariant compactifications of semi-simple groups of adjoint type.Comment: arXiv admin note: text overlap with arXiv:1102.2162 by other author

Continuity and change: Challenging the disposable Chinese city

The newly outward‐looking economic stance that China adopted in the 1980s was reflected by a Western‐style building boom. As widely spaced towers replaced traditional courtyard‐based environments, urban legibility was lost – and the new buildings were not designed to last. In recent years there has been a backlash: adaptive reuse is now encouraged, as are loose‐fit approaches to new design for greater durability. California‐based architect Renee Y Chow traces these shifts, and highlights projects that have sought to redress the balance – including one by her own practice, Studio URBIS