Mathematical sciences : operator theory and mathematical physics

Issued as Final report, Project no. G-37-60

Democratic Fair Allocation of Indivisible Goods

We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which all agents in each group must agree that their group's share is fair. Under this strict requirement, fair allocations exist only for small groups. We introduce the concept of democratic fairness, which aims to satisfy a certain fraction of the agents in each group. This concept is better suited to large groups such as cities or countries. We present protocols for democratic fair allocation among two or more arbitrarily large groups of agents with monotonic, additive, or binary valuations. For two groups with arbitrary monotonic valuations, we give an efficient protocol that guarantees envy-freeness up to one good for at least $1/2$ of the agents in each group, and prove that the $1/2$ fraction is optimal. We also present other protocols that make weaker fairness guarantees to more agents in each group, or to more groups. Our protocols combine techniques from different fields, including combinatorial game theory, cake cutting, and voting.Comment: Appears in the 27th International Joint Conference on Artificial Intelligence and the 23rd European Conference on Artificial Intelligence (IJCAI-ECAI), 201

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

Strategic Review of Tropical Fisheries Management

This project addresses the constraints to tropical fisheries development with sustainable exploitation through a strategic assessment of tropical fisheries management with the following purposes: (1) To evaluate relevant research methods for the development of assessment models appropriate to the circumstances of tropical coastal fisheries; and (2) To evaluate the utility of existing strategies for the implementation of management advice. The report consists of three substantive chapters. Chapter 2 contains a detailed socio-economic assessment of various instruments and implementation strategies applicable to tropical capture fisheries. In Chapter 3, a detailed assessment of the fisheries for tropical large marine ecosystems has been conducted using a technique developed by FAO (Granger & Garcia 1996). The data used were the FAO statistics published regularly by FAO. This analysis has been conducted for each of the tropical large marine ecosystems and indicates that there is the potential for increased fishing in a number of these ecosystems. One of the clear requirements identified in Chapter 2 and implicit in Chapter 3, is that there is a significant need for simple and robust fisheries assessment methods which can estimate the potential of a particular resource, its capacity in terms of the level of fishing effort and its current status ie whether it is currently exploited sustainably or not. In Chapter 4, these problems are addressed directly and, using two approaches, significant simplification of fishery methods is developed. In the first approach, simple empirical relationships between the life history parameters of a species are used to develop models of potential yield which can be determined by a simple assessment of fish growth. In the second approach, optimal life history theory is applied to the key demographic parameters of exploited fish populations and using estimates of the Beverton & Holt invariants a significant simplifying of the basic stock assessment equations is developed

The Development Gap Between the CIS and EU

Current report aims to identify major existing gaps in the five socio-economic dimensions (economic, human, openness, environmental, and institutional) and to reveal those gaps which could potentially hinder social and economic integration of neighbor states with the EU. To achieve this, the authors aim to assess the existing trends in the size of the gaps across countries and problem areas, taking into consideration the specific origin of the gap between EU15/EU12, on the one hand, and FSU republics, EU candidates and West Balkan countries, on the other hand. The paper is structured as follows: 1. A review of literature on the determinants of growth and development and the analysis of the catching up process between countries or groups of countries. 2. An analysis of the historic roots and origins of the development gap, and its evolvement over time. 3. A review of literature sources, draft analysis of primary statistical data, and qualitative explanations of gaps and divergences in selected development issues across the following socio-economic dimensions: level of economic development and convergence rates based on Real GDP (application of methodology testing ß and ? convergence to the set of countries analyzed); • quality of life and its components (poverty, inequality, health status and health care, access to fresh water and sanitation facilities, subjective perceptions of well-being); • human capital and labor market development, including level of education and public spending on education, its accessibility and quality, main differences in labor market development (employment participation rates and levels of unemployment, new jobs creation and labor protection legislation); • innovation potential, including R&D, information and communication technologies, and institutional environment; • openness and trade potential, including trade in goods and services, FDI stocks, trade regime and performance in logistics and infrastructure; THE DEVELOPMENT GAP BETWEEN THE CIS AND EU 15 CASE Network Reports No. 81 • environmental performance in terms of environmental stresses, efforts aimed at their reduction, and institutional capacity; • business climate, political institutions, and other institutional indicators (econometric analysis). 4. A test econometric analysis of development gaps across selected dimensions by using a Principal Components Method (PCM). The results are further presented in the form of ranks of countries analyzed reflecting their distances from EU15 in respective aggregate averages. Special attention is paid to gender-related development issues. Respective issues in human capital and labor market study, as well as variables included into PCM analysis were supplemented with relative gender data. Several conclusions finalize the report.EU, CIS, development gap, GDP, convergence, quality of life, human capital, innovation, environment, institutions, Principal Components Method

Fair Influence Maximization: A Welfare Optimization Approach

Several behavioral, social, and public health interventions, such as suicide/HIV prevention or community preparedness against natural disasters, leverage social network information to maximize outreach. Algorithmic influence maximization techniques have been proposed to aid with the choice of "peer leaders" or "influencers" in such interventions. Yet, traditional algorithms for influence maximization have not been designed with these interventions in mind. As a result, they may disproportionately exclude minority communities from the benefits of the intervention. This has motivated research on fair influence maximization. Existing techniques come with two major drawbacks. First, they require committing to a single fairness measure. Second, these measures are typically imposed as strict constraints leading to undesirable properties such as wastage of resources. To address these shortcomings, we provide a principled characterization of the properties that a fair influence maximization algorithm should satisfy. In particular, we propose a framework based on social welfare theory, wherein the cardinal utilities derived by each community are aggregated using the isoelastic social welfare functions. Under this framework, the trade-off between fairness and efficiency can be controlled by a single inequality aversion design parameter. We then show under what circumstances our proposed principles can be satisfied by a welfare function. The resulting optimization problem is monotone and submodular and can be solved efficiently with optimality guarantees. Our framework encompasses as special cases leximin and proportional fairness. Extensive experiments on synthetic and real world datasets including a case study on landslide risk management demonstrate the efficacy of the proposed framework.Comment: The short version of this paper appears in the proceedings of AAAI-2

Special Libraries, March 1977

Volume 68, Issue 3https://scholarworks.sjsu.edu/sla_sl_1977/1002/thumbnail.jp

The Impact of Financial Inclusion on the Nigerian Economy

Financial inclusion remains a critical issue for developing economies such as Nigeria, where the focus of the government is to bring all economic units into the pool of the country's financial system. The rate of financial inclusion is an economic yardstick that cannot be discounted and one which remains a clear focal point of different inter-governmental efforts and policy. On one hand, there is the realisation that a low rate of financial inclusion means that a huge percentage of the population rarely has access to the kind of financial services that can take them out of poverty. As a contemporary discourse, this research seeks to assess the impact of financial inclusion on the development of the economy; arguing on the premise that proxy indicators in existing research have failed to provide a clear picture on the impact of financial inclusion on the economy, thereby failing to provide stakeholders with a strong motivation to pursue financial inclusiveness in the country. The focus of the study is to assess the effect of financial inclusion on income inequality and economic growth. To achieve this objective the study leverages on data spanning a period of 34 years (1981 to 2016), based on data generated from the Central Bank of Nigeria Statistical Bulletin and the World Bank Development Indicators. Using the Error Correction Mechanism (ECM),Unit Root Analysis and the Co-Integration analytical framework, the findings indicated that the short and longrun relationship between financial inclusion and economic growth in Nigeria show that the current values of the variables were not significant. Regarding the relationship between financial inclusion and income inequality in Nigeria, the short-run result revealed that only the past values of loans to rural areas and number of commercial bank branches appears to be significant, while at the long-run, the lagged value of gross domestic product per capital, commercial bank deposits and loans to rural areas were found to be statistically significant. The study further notes that financial inclusiveness was a precursor for economic growth in Nigeria. It is on this basis that the study recommends among others that; there is the need to increase loans to the rural areas by at least 50% this can be done through moral suasion to boost the economic activities in the rural areas, improve their aggregate demand, and ultimately their standard of living. There is also the need to engage more workforce in the rural areas to close the inequality gap prevalent in the country