On Randomized Algorithms for Matching in the Online Preemptive Model

We investigate the power of randomized algorithms for the maximum cardinality matching (MCM) and the maximum weight matching (MWM) problems in the online preemptive model. In this model, the edges of a graph are revealed one by one and the algorithm is required to always maintain a valid matching. On seeing an edge, the algorithm has to either accept or reject the edge. If accepted, then the adjacent edges are discarded. The complexity of the problem is settled for deterministic algorithms. Almost nothing is known for randomized algorithms. A lower bound of $1.693$ is known for MCM with a trivial upper bound of $2$. An upper bound of $5.356$ is known for MWM. We initiate a systematic study of the same in this paper with an aim to isolate and understand the difficulty. We begin with a primal-dual analysis of the deterministic algorithm due to McGregor. All deterministic lower bounds are on instances which are trees at every step. For this class of (unweighted) graphs we present a randomized algorithm which is $\frac{28}{15}$-competitive. The analysis is a considerable extension of the (simple) primal-dual analysis for the deterministic case. The key new technique is that the distribution of primal charge to dual variables depends on the "neighborhood" and needs to be done after having seen the entire input. The assignment is asymmetric: in that edges may assign different charges to the two end-points. Also the proof depends on a non-trivial structural statement on the performance of the algorithm on the input tree. The other main result of this paper is an extension of the deterministic lower bound of Varadaraja to a natural class of randomized algorithms which decide whether to accept a new edge or not using independent random choices

An extension and application of the Leontief pollution model for waste generation and disposal in Scotland

Solid waste generation, treatment and disposal are important policy concerns for the Scottish Parliament. As a result of the Environment Act 1995, a National Waste Strategy for Scotland was introduced with the general aim of reducing the amount of waste produced and dealing with what is produced in more sustainable ways. This implies the need for an empirical framework to inform policymakers regarding the relationship between economic activity and waste generation, treatment and disposal and the likely impacts of any policy actions or other disturbances on all types of sustainability indicators. In this paper we report on a study to develop an extended input-output (IO) system of the type originally proposed in the seminal paper by Leontief (1970). This involves extending the standard IOaccounts to take account of pollution or waste generation as an additional output accompanying production and consumption activities in the economy and of the activity required to clean up (or prevent) these unwanted outputs. The extension of IO tables to take account of pollution/waste generation is relatively widespread in the literature. It is usually achieved through the introduction of physical pollution/waste-output coefficients, and has been previously applied to Scotland for the case ofair pollution (see McNicoll & Blackmore, 1993, McGregor et al, 2001). Such an approach allows us to examine the impact of the economy on the environment, in terms of the amount of pollution/waste emitted as a result of economic activity. However, it does not allow us to track the feedback from the environment to the economy in terms of the resources used in environmental cleaning. If we areinterested in this aspect, we need to identify the input structure of any pollution abatement or waste disposal activities and identify columns in the IO tables representing cleaning activities

An economics of wellbeing: what would economics look like if it were focussed on human wellbeing?

This paper makes a number of fundamental proposals to reconsider economics by putting human wellbeing at the centre. It emerges from a pluralist perspective in economics and the ontological, conceptual, axiomatic and methodological propositions that are made lead to the construction of what we call an inclusive economy matrix (IEM).In particular, the paper draws on heterodox economics to redefine the scope of economics, economic agency, rational behaviour and put emphasis on wellbeing rather than welfare. Furthermore, from the acknowledgement of human wellbeing as a three-dimensional concept, the economic aggregation problem is reconsidered and the methodological implications discussed.The IEM is proposed as a comprehensive and robust analytical framework that gives space to bring social equity and sustainable development considerations forward as a priori concerns for economic development. As such, the IEM can serve as a point of departure for formulating new research questions, exploring new relationships between human wellbeing and economic development, and building economic models that bring us closer to people’s realities on the ground

The radial evolution of solar wind speeds

The WSA-ENLIL model predicts significant evolution of the solar wind speed. Along a flux tube the solar wind speed at 1.0 AU and beyond is found to be significantly altered from the solar wind speed in the outer corona at 0.1 AU, with most of the change occurring within a few tenths of an AU from the Sun. The evolution of the solar wind speed is most pronounced during solar minimum for solar wind with observed speeds at 1.0 AU between 400 and 500 km/s, while the fastest and slowest solar wind experiences little acceleration or deceleration. Solar wind ionic charge state observations made near 1.0 AU during solar minimum are found to be consistent with a large fraction of the intermediate-speed solar wind having been accelerated or decelerated from slower or faster speeds. This paper sets the groundwork for understanding the evolution of wind speed with distance, which is critical for interpreting the solar wind composition observations near Earth and throughout the inner heliosphere. We show from composition observations that the intermediate-speed solar wind (400-500 km/s) represents a mix of what was originally fast and slow solar wind, which implies a more bimodal solar wind in the corona than observed at 1.0 AU

Remediation and the Development of Modernist Forms in The Western Home

This chapter will proceed in four parts. First, we will articulate our argument for reading The Western Home Monthly through the lens of modernism by exploring the links that have been drawn recently between modernism, the middlebrow, and new media studies. Second, we will outline the method through which The Western Home Monthly was digitized and the tools we used in our analysis. The third section will demonstrate how our distant reading methods helped us to better understand the formal dimensions of the magazine, particularly in terms of the influence of advertising and increasing formal fragmentation. In our fourth section we will analyse a single issue of The Western Home Monthly, showing how a combination of distant and close readings helps us to understand the place of an agrarian middlebrow magazine within the transnational and intermedial phenomenon of modernist culture

Sublinear Estimation of Weighted Matchings in Dynamic Data Streams

This paper presents an algorithm for estimating the weight of a maximum weighted matching by augmenting any estimation routine for the size of an unweighted matching. The algorithm is implementable in any streaming model including dynamic graph streams. We also give the first constant estimation for the maximum matching size in a dynamic graph stream for planar graphs (or any graph with bounded arboricity) using $\tilde{O}(n^{4/5})$ space which also extends to weighted matching. Using previous results by Kapralov, Khanna, and Sudan (2014) we obtain a $\mathrm{polylog}(n)$ approximation for general graphs using $\mathrm{polylog}(n)$ space in random order streams, respectively. In addition, we give a space lower bound of $\Omega(n^{1-\varepsilon})$ for any randomized algorithm estimating the size of a maximum matching up to a $1+O(\varepsilon)$ factor for adversarial streams

Sustainable care: theorising the wellbeing of caregivers to older persons

The term ‘care crisis’ is invoked to denote chronic system failures and bad outcomes for the people involved. We present a comprehensive wellbeing framework and illustrate its practicality with evidence of negative outcomes for those who provide care. We find evidence of substantial material and relational wellbeing failures for family carers and for care workers, while there has been little interest in carers’ views of their ability to live the life that they most value. Understanding and improving wellbeing outcomes for carers is an essential component of sustainable care, which requires the wellbeing of the different actors in care arrangements

Time series forecasting for dynamic environments: The DyFor Genetic Program model

Copyright © 2007 IEEESeveral studies have applied genetic programming (GP) to the task of forecasting with favorable results. However, these studies, like those applying other techniques, have assumed a static environment, making them unsuitable for many real-world time series which are generated by varying processes. This study investigates the development of a new ldquodynamicrdquo GP model that is specifically tailored for forecasting in nonstatic environments. This dynamic forecasting genetic program (DyFor GP) model incorporates features that allow it to adapt to changing environments automatically as well as retain knowledge learned from previously encountered environments. The DyFor GP model is tested for forecasting efficacy on both simulated and actual time series including the U.S. Gross Domestic Product and Consumer Price Index Inflation. Results show that the performance of the DyFor GP model improves upon that of benchmark models for all experiments. These findings highlight the DyFor GP's potential as an adaptive, nonlinear model for real-world forecasting applications and suggest further investigations.Neal Wagner, Zbigniew Michalewicz, Moutaz Khouja, and Rob Roy McGrego