An approximate isoperimetric inequality for r-sets

10 pages10 pages10 pages10 pagesWe prove a vertex-isoperimetric inequality for [n]^(r), the set of all r-element subsets of {1,2,...,n}, where x,y \in [n]^(r) are adjacent if |x \Delta y|=2. Namely, if \mathcal{A} \subset [n]^(r) with |\mathcal{A}|=\alpha {n \choose r}, then the vertex-boundary b(\mathcal{A}) satisfies |b(\mathcal{A})| \geq c\sqrt{\frac{n}{r(n-r)}} \alpha(1-\alpha) {n \choose r}, where c is a positive absolute constant. For \alpha bounded away from 0 and 1, this is sharp up to a constant factor (independent of n and r).The research of the first author was supported by EPSRC grant EP/G056730/1; the research of the third author was supported in part by ERC grant 239696 and EPSRC grant EP/G056730/1

HESS Opinions: "Climate, hydrology, energy, water: recognizing uncertainty and seeking sustainability"

Since 1990 extensive funds have been spent on research in climate change. Although Earth Sciences, including climatology and hydrology, have benefited significantly, progress has proved incommensurate with the effort and funds, perhaps because these disciplines were perceived as “tools” subservient to the needs of the climate change enterprise rather than autonomous sciences. At the same time, research was misleadingly focused more on the “symptom”, i.e. the emission of greenhouse gases, than on the “illness”, i.e. the unsustainability of fossil fuel-based energy production. Unless energy saving and use of renewable resources become the norm, there is a real risk of severe socioeconomic crisis in the not-too-distant future. A framework for drastic paradigm change is needed, in which water plays a central role, due to its unique link to all forms of renewable energy, from production (hydro and wave power) to storage (for time-varying wind and solar sources), to biofuel production (irrigation). The extended role of water should be considered in parallel to its other uses, domestic, agricultural and industrial. Hydrology, the science of water on Earth, must move towards this new paradigm by radically rethinking its fundamentals, which are unjustifiably trapped in the 19thcentury myths of deterministic theories and the zeal to eliminate uncertainty. Guidance is offered by modern statistical and quantum physics, which reveal the intrinsic character of uncertainty/entropy in nature, thus advancing towards a new understanding and modelling of physical processes, which is central to the effective use of renewable energy and water resources

Conditional Acceptability for Random Variables

Acceptable random variables introduced by Giuliano Antonini et al. (J. Math. Anal. Appl. 338:1188-1203, 2008) form a class of dependent random variables that contains negatively dependent random variables as a particular case. The concept of acceptability has been studied by authors under various versions of the definition, such as extended acceptability or wide acceptability. In this paper, we combine the concept of acceptability with the concept of conditioning, which has been the subject of current research activity. For conditionally acceptable random variables, we provide a number of probability inequalities that can be used to obtain asymptotic results

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove

A note on hitting maximum and maximal cliques with a stable set

It was recently proved that any graph satisfying $\omega > \frac 23(\Delta+1)$ contains a stable set hitting every maximum clique. In this note we prove that the same is true for graphs satisfying $\omega \geq \frac 23(\Delta+1)$ unless the graph is the strong product of $K_{\omega/2}$ and an odd hole. We also provide a counterexample to a recent conjecture on the existence of a stable set hitting every sufficiently large maximal clique.Comment: 7 pages, two figures, accepted to J. Graph Theor

Integrated modelling of cost-effective siting and operation of flow-control infrastructure for river ecosystem conservation

Wetland and floodplain ecosystems along many regulated rivers are highly stressed, primarily due to a lack of environmental flows of appropriate magnitude, frequency, duration, and timing to support ecological functions. In the absence of increased environmental flows, the ecological health of river ecosystems can be enhanced by the operation of existing and new flow-control infrastructure (weirs and regulators) to return more natural environmental flow regimes to specific areas. However, determining the optimal investment and operation strategies over time is a complex task due to several factors including the multiple environmental values attached to wetlands, spatial and temporal heterogeneity and dependencies, nonlinearity, and time-dependent decisions. This makes for a very large number of decision variables over a long planning horizon. The focus of this paper is the development of a nonlinear integer programming model that accommodates these complexities. The mathematical objective aims to return the natural flow regime of key components of river ecosystems in terms of flood timing, flood duration, and interflood period. We applied a 2-stage recursive heuristic using tabu search to solve the model and tested it on the entire South Australian River Murray floodplain. We conclude that modern meta-heuristics can be used to solve the very complex nonlinear problems with spatial and temporal dependencies typical of environmental flow allocation in regulated river ecosystems. The model has been used to inform the investment in, and operation of, flow-control infrastructure in the South Australian River Murray.<br /

Perpetrating Cyber Dating Abuse: A Brief Report on the Role of Aggression, Romantic Jealousy and Gender

There is increasing evidence that the use of elec-tronic communication technology (ECT) is being integrated into romantic relationships, which can be used as a medium to control a romantic partner. Most research focuses on the vic-tims of cyber dating abuse, however, we focused on the factors that predict perpetration of cyber dating abuse. We explored whether aggression (verbal aggression, physical aggression, anger and hostility), romantic jealousy (emotional, cognitive and behavioral jealousy), and gender predicted perpetration of cyber dating abuse (n = 189). We found that hostility, behav-ioral jealousy and gender significantly predicted perpetration of cyber dating abuse. The findings of this study contribute to our understanding of the psychological factors that drive cyber dating abuse in romantic relationships

MINERALOGY AND PETROLOGY OF THE BRNJICA GRANITOIDS (EASTERN SERBIA)

The Variscan Brnjica granitoids in East Serbia, occurring in the Kucaj Terrane of the Carpatho-Balkanides, are composed of hornblende - biotite tonalité (TON), biotite granodiorite (GRD), twomica granite (TMG) and leucogranite (LG). The rocks analyzed are slightly peraluminous. A preplate collision tectonic environment is supported based on the R1-R2 discrimination diagram. A two-step mixing plus fractional crystallization (MFC) process is considered responsible for the evolution of the Brnjica granitoids. In the 1st step, the parental magma (having the composition of the more basic TON) is forming the mineral assemblage Pl596Biio.3Hbio.7Mto.7Titi.oQzi7.7 by 44% crystallization, and at the same time is mixed (r=0.1) with a magma similar to TMG to give a melt similar to the composition of the less evolved GRD. In the 2nd step, 60% crystallization (Pl39oKfi oBÌ25oZr06Api aMti 4Titi 0QZ303) of the less evolved GRD and a simultaneous mixing with the same acid magma (TMG) but with higher r (0.6) is needed for the genesis of GRD group. The TON could originate in the crust by melting of amphibolites and basalts under various P-T conditions while the granites could be crustal melts produced by melting of amphibolites, gneisses, graywackes and pelites. Pressure of 2.3 to 4.1 kb and temperatures from 626 to 813 °C were calculated for TON, using hornblende and co-existing hornblende and plagioclase compositions respectively

Relational consequences of compulsive Internet use: A longitudinal study among newlyweds

This article examines how compulsive Internet use and marital well-being are related to each other. We suggest that they are negatively related and explore whether compulsive Internet use predicts marital well-being or vice versa. The relation between compulsive Internet use and marital well-being is tested in a two-wave prospective study among 190 newlywed couples. The results suggest that (a) compulsive Internet use predicts marital well-being, and not vice versa, (b) that this is a within- rather than a cross-partner effect, and (c) that the frequency of Internet use may be positively related to marital well-being. The results are discussed in terms of the mechanisms that underlie the link between compulsive Internet use and relationship quality