Covering a line segment with variable radius discs

The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc Covering Problem on a Line. The cost of each sensor includes a fixed component f, and a variable component that is a convex function of the diameter of the field-of- view area. When only one type of sensor or, in general, one type of disc, is available, then a simple polynomial algorithm solves the problem. When there are different types of sensors, the problem becomes hard. A branch-and-bound algorithm as well as an efficient heuristic are developed for the special case in which the variable cost component of each sensor is proportional to the square of the measure of the field-of-view area. The heuristic very often obtains the optimal solution as shown in extensive computational testing

Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

Axiomatic Characterization of the Mean Function on Trees

A mean of a sequence π = (x1, x2, . . . , xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean(π) = { x | x is a mean of π } is called the mean function on X. In this paper the mean function on finite trees is characterized axiomatically

Business process modelling and visualisation to support e-government decision making: Business/IS alignment

© 2017 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/978-3-319-57487-5_4.Alignment between business and information systems plays a vital role in the formation of dependent relationships between different departments in a government organization and the process of alignment can be improved by developing an information system (IS) according to the stakeholders’ expectations. However, establishing strong alignment in the context of the eGovernment environment can be difficult. It is widely accepted that business processes in the government environment plays a pivotal role in capturing the details of IS requirements. This paper presents a method of business process modelling through UML which can help to visualise and capture the IS requirements for the system development. A series of UML models have been developed and discussed. A case study on patient visits to a healthcare clinic in the context of eGovernment has been used to validate the models

A polynomial-time algorithm for optimizing over N-fold 4-block decomposable integer programs

In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any convex separable objective function. We conclude with two sample applications, stochastic integer programs with second-order dominance constraints and stochastic integer multi-commodity flows, which (for fixed blocks) can be solved in polynomial time in the number of scenarios and commodities and in the binary encoding length of the input data. In the proof of our main theorem we combine several non-trivial constructions from the theory of Graver bases. We are confident that our approach paves the way for further extensions

Improving Employment Standards and their Enforcement in Ontario: A Research Brief Addressing Options Identified in the Interim Report of the Changing Workplaces Review

The quality of employment available to Ontarians is a growing concern among legislators, policymakers, and the general public alike. There is widespread recognition that precarious employment and the challenges posed by the associated realignment of risks, costs and power relations between employees and employers require improvements to employees’ legislative protection. Ontario’s Changing Workplaces Review (CWR) affords us an opportunity to take stock of important changes taking place the province’s labour market. As the Terms of Reference introduced at the outset of the CWR note, “far too many workers are experiencing greater precariousness” in employment in Ontario today than in the recent past. Accordingly, with the aim of “creating decent work in Ontario, particularly [for] those who have been made vulnerable by changes in our economy and workplaces,” such terms directed the Special Advisors to investigate the dynamics underlying the magnitude of precariousness in the province’s labour market and to pose options for mitigating this fundamental social and economic problem through reforms to Ontario’s Labour Relations Act (LRA) and Employment Standards Act (ESA)

Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

Semaphorin 3F signaling actively retains neutrophils at sites of inflammation

Neutrophilic inflammation is central to disease pathogenesis, for example, in chronic obstructive pulmonary disease, yet the mechanisms that retain neutrophils within tissues remain poorly understood. With emerging evidence that axon guidance factors can regulate myeloid recruitment and that neutrophils can regulate expression of a class 3 semaphorin, SEMA3F, we investigated the role of SEMA3F in inflammatory cell retention within inflamed tissues. We observed that neutrophils upregulate SEMA3F in response to proinflammatory mediators and following neutrophil recruitment to the inflamed lung. In both zebrafish tail injury and murine acute lung injury models of neutrophilic inflammation, overexpression of SEMA3F delayed inflammation resolution with slower neutrophil migratory speeds and retention of neutrophils within the tissues. Conversely, constitutive loss of sema3f accelerated egress of neutrophils from the tail injury site in fish, whereas neutrophil-specific deletion of Sema3f in mice resulted in more rapid neutrophil transit through the airways, and significantly reduced time to resolution of the neutrophilic response. Study of filamentous-actin (F-actin) subsequently showed that SEMA3F-mediated retention is associated with F-actin disassembly. In conclusion, SEMA3F signaling actively regulates neutrophil retention within the injured tissues with consequences for neutrophil clearance and inflammation resolution