3-tuples have at most 7 prime factors infinitely often

Let $L_1$, $L_2$ $L_3$ be integer linear functions with no fixed prime divisor. We show there are infinitely many $n$ for which the product $L_1(n)L_2(n)L_3(n)$ has at most 7 prime factors, improving a result of Porter. We do this by means of a weighted sieve based upon the Diamond-Halberstam-Richert multidimensional sieve.Comment: 13 Page

User's Privacy in Recommendation Systems Applying Online Social Network Data, A Survey and Taxonomy

Recommender systems have become an integral part of many social networks and extract knowledge from a user's personal and sensitive data both explicitly, with the user's knowledge, and implicitly. This trend has created major privacy concerns as users are mostly unaware of what data and how much data is being used and how securely it is used. In this context, several works have been done to address privacy concerns for usage in online social network data and by recommender systems. This paper surveys the main privacy concerns, measurements and privacy-preserving techniques used in large-scale online social networks and recommender systems. It is based on historical works on security, privacy-preserving, statistical modeling, and datasets to provide an overview of the technical difficulties and problems associated with privacy preserving in online social networks.Comment: 26 pages, IET book chapter on big data recommender system

An Introduction to Temporal Optimisation using a Water Management Problem

Optimisation problems usually take the form of having a single or multiple objectives with a set of constraints. The model itself concerns a single problem for which the best possible solution is sought. Problems are usually static in the sense that they do not consider changes over time in a cumulative manner. Dynamic optimisation problems to incorporate changes. However, these are memoryless in that the problem description changes and a new problem is solved - but with little reference to any previous information. In this paper, a temporally augmented version of a water management problem which allows farmers to plan over long time horizons is introduced. A climate change projection model is used to predict both rainfall and temperature for the Murrumbidgee Irrigation Area in Australia for up to 50 years into the future. Three representative decades are extracted from the climate change model to create the temporal data sets. The results confirm the utility of the temporal approach and show, for the case study area, that crops that can feasibly and sustainably be grown will be a lot fewer than the present day in the challenging water-reduced conditions of the future

Cost Escalation in Nuclear Power

This report is concerned with the escalation of capital costs of nuclear central station power plants between the early 1960s and the present. The report presents an historical overview of the development of the nuclear power industry and cost escalation in the industry, using existing data on orders and capital costs. New data are presented on regulatory delays in the licensing process, derived from a concurrent study being carried on in the Social Science group at Caltech. The conclusions of the study are that nuclear capital costs have escalated more rapidly than the GNP deflator or the construction industry price index. Prior to 1970, cost increases are related to bottleneck problems in the nuclear construction and supplying industries and the regulatory process; intervenors play only a minor role in cost escalation. After 1970, generic changes introduced into the licensing process by intervenors (including environmental impact reviews, antitrust reviews, more stringent safety standards) dominate the cost escalation picture, with bottlenecks of secondary importance. Recent increases in the time from application for a construction permit to commercial operation are related not only to intervenor actions, but also to suspensions, cancellations or postponements of construction by utilities due to unfavorable demand or financing conditions

Integrating continuous differential evolution with discrete local search for meander line RFID antenna design

The automated design of meander line RFID antennas is a discrete self-avoiding walk(SAW) problem for which efficiency is to be maximized while resonant frequency is to beminimized. This work presents a novel exploration of how discrete local search may beincorporated into a continuous solver such as differential evolution (DE). A prior DE algorithmfor this problem that incorporates an adaptive solution encoding and a bias favoringantennas with low resonant frequency is extended by the addition of the backbite localsearch operator and a variety of schemes for reintroducing modified designs into the DEpopulation. The algorithm is extremely competitive with an existing ACO approach and thetechnique is transferable to other SAW problems and other continuous solvers. The findingsindicate that careful reintegration of discrete local search results into the continuous populationis necessary for effective performance

A Computational Comparison of Evolutionary Algorithms for Water Resource Planning for Agricultural and Environmental Purposes

The use of water resources for agricultural purposes, particularly in arid and semi-arid regions, is a matter of increasing concern across the world. Optimisation techniques can play an important role in improving the allocation of land to different crops, based on a utility function (such as net revenue) and the water resources needed to support these. Recent work proposed a model formulation for an agricultural region in the Murrumbidgee Irrigation Area of the Murray-Darling River basin in Australia, and found that the well-known NSGA-II technique could produce sensible crop mixes while preserving ground and surface water for environmental purposes. In the present study we apply Differential Evolution using two different solution representations, one of which explores the restricted space in which no land is left fallow. The results improve on those of the prior NSGA-II and demonstrate that a combination of solution representations allows Differential Evolution to more thoroughly explore the multiobjective space of profit versus environment

On thermodynamic and quantum fluctuations of cosmological constant

We discuss from the condensed-matter point of view the recent idea that the Poisson fluctuations of cosmological constant about zero could be a source of the observed dark energy. We argue that the thermodynamic fluctuations of Lambda are much bigger. Since the amplitude of fluctuations is proportional to V^{-1/2}, where V is the volume of the Universe, the present constraint on the cosmological constant provides the lower limit for V, which is much bigger than the volume within the cosmological horizon.Comment: 4 pages, version submitted to JETP Letter