Balanced Families of Perfect Hash Functions and Their Applications

The construction of perfect hash functions is a well-studied topic. In this paper, this concept is generalized with the following definition. We say that a family of functions from $[n]$ to $[k]$ is a $\delta$-balanced $(n,k)$-family of perfect hash functions if for every $S \subseteq [n]$, $|S|=k$, the number of functions that are 1-1 on $S$ is between $T/\delta$ and $\delta T$ for some constant $T>0$. The standard definition of a family of perfect hash functions requires that there will be at least one function that is 1-1 on $S$, for each $S$ of size $k$. In the new notion of balanced families, we require the number of 1-1 functions to be almost the same (taking $\delta$ to be close to 1) for every such $S$. Our main result is that for any constant $\delta > 1$, a $\delta$-balanced $(n,k)$-family of perfect hash functions of size $2^{O(k \log \log k)} \log n$ can be constructed in time $2^{O(k \log \log k)} n \log n$. Using the technique of color-coding we can apply our explicit constructions to devise approximation algorithms for various counting problems in graphs. In particular, we exhibit a deterministic polynomial time algorithm for approximating both the number of simple paths of length $k$ and the number of simple cycles of size $k$ for any $k \leq O(\frac{\log n}{\log \log \log n})$ in a graph with $n$ vertices. The approximation is up to any fixed desirable relative error

Some results on (a:b)-choosability

A solution to a problem of Erd\H{o}s, Rubin and Taylor is obtained by showing that if a graph $G$ is $(a:b)$-choosable, and $c/d > a/b$, then $G$ is not necessarily $(c:d)$-choosable. Applying probabilistic methods, an upper bound for the $k^{th}$ choice number of a graph is given. We also prove that a directed graph with maximum outdegree $d$ and no odd directed cycle is $(k(d+1):k)$-choosable for every $k \geq 1$. Other results presented in this article are related to the strong choice number of graphs (a generalization of the strong chromatic number). We conclude with complexity analysis of some decision problems related to graph choosability

Admission Control to Minimize Rejections and Online Set Cover with Repetitions

We study the admission control problem in general networks. Communication requests arrive over time, and the online algorithm accepts or rejects each request while maintaining the capacity limitations of the network. The admission control problem has been usually analyzed as a benefit problem, where the goal is to devise an online algorithm that accepts the maximum number of requests possible. The problem with this objective function is that even algorithms with optimal competitive ratios may reject almost all of the requests, when it would have been possible to reject only a few. This could be inappropriate for settings in which rejections are intended to be rare events. In this paper, we consider preemptive online algorithms whose goal is to minimize the number of rejected requests. Each request arrives together with the path it should be routed on. We show an $O(\log^2 (mc))$-competitive randomized algorithm for the weighted case, where $m$ is the number of edges in the graph and $c$ is the maximum edge capacity. For the unweighted case, we give an $O(\log m \log c)$-competitive randomized algorithm. This settles an open question of Blum, Kalai and Kleinberg raised in \cite{BlKaKl01}. We note that allowing preemption and handling requests with given paths are essential for avoiding trivial lower bounds

The political economy of Food subsidy reform in Egypt

Subsidies Egypt ,Food aid ,Food policy ,Food relief Government policy Cost effectiveness ,Poor Government policy ,

Multilateral development banks and environmental policymaking in Central and Eastern Europe

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Political Science, 1999.Includes bibliographical references (p. 298-312).The dissertation is a comparative study of three multilateral development banks (MDBs)-the World Bank, European Bank for Reconstruction and Development (EBRD), and European Investment Bank (EIB)-and their struggles to operationalize and implement relatively new environmental mandates. MDBs are increasingly being relied upon to address environmental issues in their activities, while at the same time facing criticism for allegedly promoting serious environmental degradation in borrowing countries. The dissertation focuses on the activities of these banks in Central and Eastern Europe, where the fall of the Iron Curtain revealed the most polluted countries in Europe, and where these MDBs are among the top donors. There is significant variation in the degree to which these MDBs have incorporated environmental goals into their work. The World Bank has played an important role in providing policy support for environmental reform in the region, while financing the largest scope of "green" projects of the three banks. The EIB has responded to its environmental goals in minimal ways, and the EBRD has an intermediate position between the other two. I argue that external pressure from major shareholder countries, usually supported or pushed by NGOs, is a key factor determining the depth of an MDB's commitment to new mandates, such as the environment. However, shareholder commitment is a necessary but not sufficient condition in explaining the banks' environmental behavior. Governance structures for all three banks are diffuse, and, as a result, institutional design and incentive systems play critical roles in how environmental objectives are translated into activities. In all three cases, the banks' internal incentive systems are poorly aligned with their environmental goals, and even where institutional variables are structured to promote greater awareness of environmental issues within the banks, they do not always work as envisioned. Theoretically, the dissertation argues that different causal variables matter at different stages of the policy process. Neorealist approaches have the most explanatory power in accounting for how environmental ideas are brought to the MDBs, but are insufficient in explaining outcomes. Approaches drawn from institutionalist and organizational theories, in turn, provide guidance in analyzing the mechanisms by which environmental objectives are translated into practice. The argument calls for a better integration of international relations theories emphasizing the importance of shareholder politics with theories that focus on how institutional arrangements shape behavior.by Tamar L. Gutner.Ph.D

A scoping review of frameworks in empirical studies and a review of dissemination frameworks

BACKGROUND: The field of dissemination and implementation (D&I) research has grown immensely in recent years. However, the field of dissemination research has not coalesced to the same degree as the field of implementation research. To advance the field of dissemination research, this review aimed to (1) identify the extent to which dissemination frameworks are used in dissemination empirical studies, (2) examine how scholars define dissemination, and (3) identify key constructs from dissemination frameworks. METHODS: To achieve aims 1 and 2, we conducted a scoping review of dissemination studies published in D&I science journals. The search strategy included manuscripts published from 1985 to 2020. Articles were included if they were empirical quantitative or mixed methods studies about the dissemination of information to a professional audience. Studies were excluded if they were systematic reviews, commentaries or conceptual papers, scale-up or scale-out studies, qualitative or case studies, or descriptions of programs. To achieve aim 1, we compiled the frameworks identified in the empirical studies. To achieve aim 2, we compiled the definitions from dissemination from frameworks identified in aim 1 and from dissemination frameworks identified in a 2021 review (Tabak RG, Am J Prev Med 43:337-350, 2012). To achieve aim 3, we compile the constructs and their definitions from the frameworks. FINDINGS: Out of 6017 studies, 89 studies were included for full-text extraction. Of these, 45 (51%) used a framework to guide the study. Across the 45 studies, 34 distinct frameworks were identified, out of which 13 (38%) defined dissemination. There is a lack of consensus on the definition of dissemination. Altogether, we identified 48 constructs, divided into 4 categories: process, determinants, strategies, and outcomes. Constructs in the frameworks are not well defined. IMPLICATION FOR D&I RESEARCH: This study provides a critical step in the dissemination research literature by offering suggestions on how to define dissemination research and by cataloging and defining dissemination constructs. Strengthening these definitions and distinctions between D&I research could enhance scientific reproducibility and advance the field of dissemination research

A unique coral biomineralization pattern has resisted 40 million years of major ocean chemistry change

Today coral reefs are threatened by changes to seawater conditions associated with rapid anthropogenic global climate change. Yet, since the Cenozoic, these organisms have experienced major fluctuations in atmospheric CO2 levels (from greenhouse conditions of high pCO2 in the Eocene to low pCO2 ice-house conditions in the Oligocene-Miocene) and a dramatically changing ocean Mg/Ca ratio. Here we show that the most diverse, widespread, and abundant reef-building coral genus Acropora (20 morphological groups and 150 living species) has not only survived these environmental changes, but has maintained its distinct skeletal biomineralization pattern for at least 40 My: Well-preserved fossil Acropora skeletons from the Eocene, Oligocene, and Miocene show ultra-structures indistinguishable from those of extant representatives of the genus and their aragonitic skeleton Mg/Ca ratios trace the inferred ocean Mg/Ca ratio precisely since the Eocene. Therefore, among marine biogenic carbonate fossils, well-preserved acroporid skeletons represent material with very high potential for reconstruction of ancient ocean chemistry