Approximation Algorithms for Route Planning with Nonlinear Objectives

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs to capture a penalty for early arrival. It is known that as nonlinearity arises, the problem becomes NP-hard and little is known about computing optimal solutions when in addition there is no monotonicity guarantee. We show that an approximately optimal non-simple path can be efficiently computed under some natural constraints. In particular, we provide a fully polynomial approximation scheme under hop constraints. Our approximation algorithm can extend to run in pseudo-polynomial time under a more general linear constraint that sometimes is useful. As a by-product, we show that our algorithm can be applied to the problem of finding a path that is most likely to be on time for a given deadline.Comment: 9 pages, 2 figures, main part of this paper is to be appear in AAAI'1

Enhanced optical Kerr effect method for a detailed characterization of the third order nonlinearity of 2D materials applied to graphene

Using an enhanced optically heterodyned optical Kerr effect method and a theoretical description of the interactions between an optical beam, a single layer of graphene, and its substrate, we provide experimental answers to questions raised by theoretical models of graphene third-order nonlinear optical response. In particular, we measure separately the time response of the two main tensor components of the nonlinear susceptibility, we validate the assumption that the out-of plane tensor components are small, and we quantify the optical impact of the substrate on the measured coefficients. Our method can be applied to other 2D materials, as it relies mainly on the small ratio between the thickness and the wavelength.Comment: 7 pages, 4 figure

A Binomial Distribution With Dependent Trials And Its Use in Stochastic Model Evaluation

A model of Markov dependent trials is considered that leads to a generalization of the binomial distribution in the context of evaluating models of a time series by exploiting the sequential nature of model-based predictions. Adopting an evaluation method similar in nature to that suggested by Xekalaki & Katti (1984), the behaviour of the model is assigned a score that reflects the concordance or discordance of predicted and observed values for each of a sequence of points in time. The resulting series of scores leads to a final rating which is considered as a measure of the predictive ability of the model. The Markov dependent distribution is used to develop exact theory for the construction of confidence intervals and for testing hypotheses pertaining to the forecasting protential of a model. Some asymptotic theory is also developed.Model evaluation, Model validation, Dependent Bernouli trials, Forecasting models

Metabolic scavenging by cancer cells: when the going gets tough, the tough keep eating

Cancer is fundamentally a disease of uncontrolled cell proliferation. Tumour metabolism has emerged as an exciting new discipline studying how cancer cells obtain the necessary energy and cellular ‘building blocks’ to sustain growth. Glucose and glutamine have long been regarded as the key nutrients fuelling tumour growth. However, the inhospitable tumour microenvironment of certain cancers, like pancreatic cancer, causes the supply of these nutrients to be chronically insufficient for the demands of proliferating cancer cells. Recent work has shown that cancer cells are able to overcome this nutrient insufficiency by scavenging alternative substrates, particularly proteins and lipids. Here, we review recent work identifying the endocytic process of macropinocytosis and subsequent lysosomal processing as an important substrate-acquisition route. In addition, we discuss the impact of hypoxia on fatty acid metabolism and the relevance of exogenous lipids for supporting tumour growth as well as the routes by which tumour cells can access these lipids. Together, these cancer-specific scavenging pathways provide a promising opportunity for therapeutic intervention

On a Distribution Arising in the Context of Comparative Model Performance Evaluation Problems

The paper deals with a distribution that arises as the distribution of a sample statistic used to compare the predictive ability of two competing linear models. It is defined as the distribution of the ratio of two correlated gamma variables and its probabilities are tabulated in order that they become readily available for practical useModel selection, Bivariate gamma distribution, F distribution

A Predictive Model Evaluation and Selection Approach - The Correlated Gamma Ratio Distribution

In this paper, an evaluation method is suggested for selecting one of two competing models based on certain predictive ability ratings. The main focus is on the case of linear models that are not necessarily nested. In the context of such models, the test procedure is based on a sample statistic whose distribution is shown to arise as the distribution of the ratio of two correlated gamma variables termed as the Correlated Gamma Ration Distribution. Percentage points of this distribution are obtained. The procedure is illustrated on real data.Model selection, Bivariate gamma distribution, F distribution, Correlated gamma-ratio distribution, Predictive ability