Introduction and allegro for violin and orchestra

Thesis (M.A.)--Boston Universit

A Note on the Sparing Number of the Sieve Graphs of Certain Graphs

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer (IASI) of a given graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. An IASI $f$ of a graph $G$ is said to be a weak IASI of $G$ if $|f^+(uv)|=\max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. A graph which admits a weak IASI may be called a weak IASI graph. The sparing number of a graph $G$ is the minimum number of edges with singleton set-labels required for a graph $G$ to admit a weak IASI. In this paper, we introduce the notion of $k$-sieve graphs of a given graph and study their sparing numbers.Comment: 9 pages, 3 figures, Publishe

On the Continuous CNN Problem

In the (discrete) CNN problem, online requests appear as points in $\mathbb{R}^2$. Each request must be served before the next one is revealed. We have a server that can serve a request simply by aligning either its $x$ or $y$ coordinate with the request. The goal of the online algorithm is to minimize the total $L_1$ distance traveled by the server to serve all the requests. The best known competitive ratio for the discrete version is 879 (due to Sitters and Stougie). We study the continuous version, in which, the request can move continuously in $\mathbb{R}^2$ and the server must continuously serve the request. A simple adversarial argument shows that the lower bound on the competitive ratio of any online algorithm for the continuous CNN problem is 3. Our main contribution is an online algorithm with competitive ratio $3+2 \sqrt{3} \approx 6.464$. Our analysis is tight. The continuous version generalizes the discrete orthogonal CNN problem, in which every request must be $x$ or $y$ aligned with the previous request. Therefore, Our result improves upon the previous best competitive ratio of 9 (due to Iwama and Yonezawa)

Biomass production and management practices in mixed crop-livestock systems in the west African Sahel: Opportunities and constraints

The Sahel is characterized by a marked inter-annual climate variability and has experienced a number of food security crises following the severe droughts during the 1970s and 1980s. Due to recent challenges such as rapid population growth, climate change, environmental concerns and market changes which cause major impacts to their production systems, the sahelian people have been shifting and adapting their production systems and the way they live to cope with uncertainties. The objective of the present report is to review the various biomass production and management issues in the mixed crop-livestock systems in West African Sahel. An elaborated literature survey of peer reviewed papers mostly, was conducted. The studies were based on the Sahel scale research, more specifically research that had been published on the West African Sahel, including studies published between 1990s and 2016. Results show that many factors have contributed to the changes, among which, rainfall variability, population growth, human induced-activities, land tenure systems and the effects of globalization. Various biomass production and management practices are employed in West African Sahel for both on-farm and off-farm biomass improvements. Some of the best practices are mulching, soil and water conservation techniques, composting, farmer managed natural regeneration, agroforestry, etc. These practices have overall contributed to increase agricultural productivity, ecosystem services provisioning and have sometime deepened the difference between men and women, rich and poor, young and old people. Most of the constraints associated with large adoption of the best practices in the Sahel are land tenure systems, the huge gap between inputs and output investment costs but, the climate conventions are offering new opportunities that will ultimately contribute to positive changes. This will be possible only when land tenure systems in the region are reinforced, institutional linkages are strengthened, and new information systems are used to inform farmers on climate issues and new agricultural practices

An integer programming approach to the Hospitals/Residents problem with ties

The classical Hospitals/Residents problem (HR) models the assignment of junior doctors to hospitals based on their preferences over one another. In an instance of this problem, a stable matching M is sought which ensures that no blocking pair can exist in which a resident r and hospital h can improve relative to M by becoming assigned to each other. Such a situation is undesirable as it could naturally lead to r and h forming a private arrangement outside of the matching. The original HR model assumes that preference lists are strictly ordered. However in practice, this may be an unreasonable assumption: an agent may find two or more agents equally acceptable, giving rise to ties in its preference list. We thus obtain the Hospitals/Residents problem with Ties (HRT). In such an instance, stable matchings may have different sizes and MAX HRT, the problem of finding a maximum cardinality stable matching, is NP-hard. In this paper we describe an Integer Programming (IP) model for MAX HRT. We also provide some details on the implementation of the model. Finally we present results obtained from an empirical evaluation of the IP model based on real-world and randomly generated problem instances