Approximating Threshold Circuits by Rational Functions

AbstractMotivated by the problem of understanding the limitations of threshold networks for representing boolean functions, we consider size-depth trade-offs for threshold circuits that compute the parity function. Using a fundamental result in the theory of rational approximation, we show how to approximate small threshold circuits by rational functions of low degree. We apply this result to establish an almost optimal lower bound of Ω(n2/ln2n) on the number of edges of any depth-2 threshold circuit with polynomially bounded weights that computes the parity function. We also prove that any depth-3 threshold circuit with polynomially bounded weights requires Ω(n1.2/ln5/3n) edges to compute parity. On the other hand, we give a construction of a depth d threshold circuit that computes parity with n1+1/Θ(φd) edges where φ = (1 + √5)/2 is the golden ratio. We conjecture that there are no linear size bounded depth threshold circuits for computing parity

Linking Distributive and Procedural Justice to Employee Engagement Through Social Exchange: A Field Study in India

Research linking justice perceptions to employee outcomes has referred to social exchange as its central theoretical premise. We tested a conceptual model linking distributive and procedural justice to employee engagement through social exchange mediators, namely, perceived organizational support and psychological contract, among 238 managers and executives from manufacturing and service sector firms in India. Findings suggest that perceived organizational support mediated the relationship between distributive justice and employee engagement, and both perceived organizational support and psychological contract mediated the relationship between procedural justice and employee engagement. Theoretical and practical implications with respect to organizational functions are discussed

Professionals and volunteers

In sociological research on relationships between professionals and volunteers, professionals are often contrasted with volunteers as abstracted, distinct and homogeneous groups. Focusing on healthcare in selected modern societies, and adopting a neo-Weberian and complementary boundary work perspective, this essay argues the landscape is more complex than between paid groups with exclusionary social closure and the unwaged in the market. First, diversification exists within health professions themselves based on social closure, with hierarchies and differential scopes of practice. Second, unpaid volunteers vary in responsibility depending on factors like employment sector and social background, including qualifications and experience. Third, in the paid workforce, there are interstitial non-professionalised health occupations, such as the neglected, lower educated health support workers, forming the largest, most heterogeneous healthcare labour force. Drawing on studies of healthcare, it is argued that recognising the diversification and interplay between professionals, volunteers and support workers is vital for enhancing health policy.</p

Critical approaches in qualitative educational research:The relation of some theoretical and methodological approaches to these issues

A local property reconstructor for a graph property is an algorithm which, given oracle access to the adjacency list of a graph that is “close” to having the property, provides oracle access to the adjacency matrix of a “correction” of the graph, i.e. a graph which has the property and is close to the given graph. For this model, we achieve local property reconstructors for the properties of connectivity and k-connectivity in undirected graphs, and the property of strong connectivity in directed graphs. Along the way, we present a method of transforming a local reconstructor (which acts as a “adjacency matrix oracle” for the corrected graph) into an “adjacency list oracle”. This allows us to recursively use our local reconstructor for (k − 1)-connectivity to obtain a local reconstructor for k-connectivity. We also extend this notion of local reconstruction to parametrized graph properties (for instance, having diameter at most D for some parameter D) and require that the corrected graph has the property with parameter close to the original. We obtain a local reconstructor for the low diameter property, where if the original graph is close to having diameter D, then the corrected graph has diameter roughly 2D. We also exploit a connection between local property reconstruction and property testing, observed by Brakerski, to obtain new tolerant property testers for all of the aforementioned properties. Except for the one for connectivity, these are the first tolerant property testers for these properties.National Science Foundation (U.S.) (Grant CCF-0829672)National Science Foundation (U.S.) (Grant CCF-1065125)National Science Foundation (U.S.) (Grant CCF-6922462)National Science Foundation (U.S.) (NSF-STC Award 0939370)National Science Foundation (U.S.). Graduate Research Fellowshi

The Disagreement Power of an Adversary

At the heart of distributed computing lies the fundamental result that the level of agreement that can be obtained in an asynchronous shared memory model where t processes can crash is exactly t + 1. In other words, an adversary that can crash any subset of size at most t can prevent the processes from agreeing on t values. But what about the rest (22n − n) adversaries that might crash certain combination of processes and not others? Given any adversary, what is its disagreement power? i.e., the biggest k for which it can prevent processes from agreeing on k values. This paper answers this question. We present a general characterization of adversaries that enables to directly derive their disagreement power. We use our characterization to also close the question of the weakest failure detector for k-set agreement. So far, the result has been obtained for two extreme cases: consensus and n − 1-set agreement. We answer this question for any k and any adversary