Computing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets

In this paper we describe a singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. Singly exponential algorithms for computing the zero-th Betti number, and the Euler-Poincar\'e characteristic, were known before. No singly exponential algorithm was known for computing any of the individual Betti numbers other than the zero-th one. We also give algorithms for obtaining semi-algebraic descriptions of the semi-algebraically connected components of any given real algebraic or semi-algebraic set in single-exponential time improving on previous results

An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions

We prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of semi-algebraically connected components of the realizations of all realizable sign conditions of a family of real polynomials. More precisely, we prove that the number of semi-algebraically connected components of the realizations of all realizable sign conditions of a family of $s$ polynomials in $\R[X_1,...,X_k]$ whose degrees are at most $d$ is bounded by $$\frac{(2d)^k}{k!}s^k + O(s^{k-1}).$$ This improves the best upper bound known previously which was $${1/2}\frac{(8d)^k}{k!}s^k + O(s^{k-1}).$$ The new bound matches asymptotically the lower bound obtained for families of polynomials each of which is a product of generic polynomials of degree one.Comment: 19 pages. Bibliography has been updated and a few more references have been added. This is the final version of this paper which will appear in Combinatoric

How to measure mood in nutrition research

© 2014 The Authors. Mood is widely assessed in nutrition research, usually with rating scales. A core assumption is that positive mood reinforces ingestion, so it is important to measure mood well. Four relevant theoretical issues are reviewed: (i) the distinction between protracted and transient mood; (ii) the distinction between mood and emotion; (iii) the phenomenology of mood as an unstable tint to consciousness rather than a distinct state of consciousness; (iv) moods can be caused by social and cognitive processes as well as physiological ones. Consequently, mood is difficult to measure and mood rating is easily influenced by non-nutritive aspects of feeding, the psychological, social and physical environment where feeding occurs, and the nature of the rating system employed. Some of the difficulties are illustrated by reviewing experiments looking at the impact of food on mood. The mood-rating systems in common use in nutrition research are then reviewed, the requirements of a better mood-rating system are described, and guidelines are provided for a considered choice of mood-rating system including that assessment should: have two main dimensions; be brief; balance simplicity and comprehensiveness; be easy to use repeatedly. Also mood should be assessed only under conditions where cognitive biases have been considered and controlled

Patent Licensing and the Research University

We construct a dynamic model of university research that allows us to examine recent concerns that financial incentives associated with university patent licensing are detrimental to the traditional mission of US research universities. We assume a principal-agent framework in which the university administration is the principal and a faculty researcher is the agent. Whether or not the researcher remains in the university, and if so her choice of the amount of time to spend on basic and applied research, is complicated by the fact that she earns license income and prestige both inside and outside the university. Thus in contrast to usual principal agent models the participation constraint is endogenous. This, plus the fact that current research affects future knowledge stocks, allows us to show that it is far from obvious that licensing will damage basic research and education.

DECISION MAKING UNDER CATASTROPHIC RISK AND LEARNING: THE CASE OF THE POSSIBLE COLLAPSE OF THE WEST ANTARCTIC ICE SHEET

A collapse of the West-Antarctic Ice Sheet (WAIS) would cause a sea level rise of 5-6 metres, perhaps even within one hundred years, with catastrophic consequences. The probability of such a collapse is small but increasing with the rise of the atmospheric concentrations of greenhouse gas and the resulting climate change. This paper investigates how the potential collapse of the WAIS affects the optimal rate of greenhouse gas emission control. We design a decision and learning tree in which decision are made about emission reduction at regular intervals. At the same time, the decision makers receive new information on the probability of a WAIS collapse and the severity of its impacts. The probability of a WAIS collapse is endogenous and contingent on greenhouse gas concentrations. We solve this optimisation problem by backward induction. We find that a potential WAIS collapse substantially bring the date of the optimal emission reduction forward and increases its amount if the probability is high enough, if the impacts are high enough, or if the decision maker is risk averse enough. We also find that, as soon as a WAIS collapse is a foregone fact, emission reduction falls to free up resource to prepare for adapting to the inevitable.Decision making under uncertainty, West-Antarctic ice sheet

Smuggling, Camouflaging, and Market Structure

We examine how market structure and enforcement affect smuggling and welfare in a model where smuggling is camouflaged by legal sales. Conditions are given for when some, but not necessarily all, firms smuggle. With camouflaging, the market price is below the price when all sales are legal, so smuggling improves welfare if the price effect outweighs excess smuggling cost. This welfare effect is directly related to the degree of competition. Increased enforcement in this model potentially reduces welfare. The model is shown to be consistent with evidence on cigarette smuggling in the United States for 1975-1982.

The Trade and FDI Effects of EMU Enlargement

This paper considers the nature and the distribution of trade and FDI effects of a potential enlargement of the European Monetary Union (EMU) to the ten countries that obtained EU membership in 2004. One-way and two-way error component gravity models are estimated using a dataset of unbalanced panel data that combines bilateral trade flows among 29 countries and the distribution of outward FDI stocks among these countries. The results reveal a complementarity between trade and investment and a relationship between trade and exchange rate volatility that depends on the sign of bilateral trade balances. Using a simulation-based technique, we find that estimates of FDI effects of EMU range between 18.5 percent for Poland and 30 percent for Hungary.EMU, exchange rate volatility, foreign investment, trade diversion, vertical integration

The Applicability of the Distribution Coefficient, KD, Based on Non-Aggregated Particulate Samples from Lakes with Low Suspended Solids Concentrations

Separate phases of metal partitioning behaviour in freshwater lakes that receive varying degrees of atmospheric contamination and have low concentrations of suspended solids were investigated to determine the applicability of the distribution coefficient, KD. Concentrations of Pb, Ni, Co, Cu, Cd, Cr, Hg and Mn were determined using a combination of filtration methods, bulk sample collection and digestion and Inductively Coupled Plasma-Mass Spectrometry (ICP-MS). Phytoplankton biomass, suspended solids concentrations and the organic content of the sediment were also analysed. By distinguishing between the phytoplankton and (inorganic) lake sediment, transient variations in KD were observed. Suspended solids concentrations over the 6-month sampling campaign showed no correlation with the KD (n = 15 for each metal, p > 0.05) for Mn (r2 = 0.0063), Cu (r2 = 0.0002, Cr (r2 = 0.021), Ni (r2 = 0.0023), Cd (r2 = 0.00001), Co (r2 = 0.096), Hg (r2 = 0.116) or Pb (r2 = 0.164). The results implied that colloidal matter had less opportunity to increase the dissolved (filter passing) fraction, which inhibited the spurious lowering of KD. The findings conform to the increasingly documented theory that the use of KD in modelling may mask true information on metal partitioning behaviour. The root mean square error of prediction between the directly measured total metal concentrations and those modelled based on the separate phase fractions were ± 3.40, 0.06, 0.02, 0.03, 0.44, 484.31, 80.97 and 0.1 μg/L for Pb, Cd, Mn, Cu, Hg, Ni, Cr and Co respectively. The magnitude of error suggests that the separate phase models for Mn and Cu can be used in distribution or partitioning models for these metals in lake water

Food choice by people with intellectual disabilities at day centres: A qualitative study

People with intellectual disabilities experience a range of health inequalities. It is important to investigate possible contributory factors that may lead to these inequalities. This qualitative study identified some difficulties for healthy eating in day centres. (1) Service users and their family carers were aware of healthy food choices but framed these as diets for weight loss rather than as everyday eating. (2) Paid carers and managers regarded the principle of service user autonomy and choice as paramount, which meant that they felt limited in their capacity to influence food choices, which they attributed to the home environment. (3) Carers used food as a treat, a reward and for social bonding with service users. (4) Service users’ food choices modelled other service users’ and carers’ choices at the time. It is suggested that healthy eating should be made more of a priority in day care, with a view to promoting exemplarily behaviour that might influence food choice at home

A Rare Case of Hemophagocytic Lymphohistiocytosis of Unknown Etiology

Hemophagocytic lymphohistiocytosis (HLH) is an uncommon cytokine storm syndrome marked which can cause high mortality. In adults, acquired HLH usually has an underlying infectious, autoimmune or malignant process that triggers the syndrome. In this case report, we present a 64-year old Caucasian male presenting with productive cough, fevers, weight loss and altered mental status who was ultimately found to have HLH of unknown etiology