Pebbling and Branching Programs Solving the Tree Evaluation Problem

We study restricted computation models related to the Tree Evaluation Problem}. The TEP was introduced in earlier work as a simple candidate for the (*very*) long term goal of separating L and LogDCFL. The input to the problem is a rooted, balanced binary tree of height h, whose internal nodes are labeled with binary functions on [k] = {1,...,k} (each given simply as a list of k^2 elements of [k]), and whose leaves are labeled with elements of [k]. Each node obtains a value in [k] equal to its binary function applied to the values of its children, and the output is the value of the root. The first restricted computation model, called Fractional Pebbling, is a generalization of the black/white pebbling game on graphs, and arises in a natural way from the search for good upper bounds on the size of nondeterministic branching programs (BPs) solving the TEP - for any fixed h, if the binary tree of height h has fractional pebbling cost at most p, then there are nondeterministic BPs of size O(k^p) solving the height h TEP. We prove a lower bound on the fractional pebbling cost of d-ary trees that is tight to within an additive constant for each fixed d. The second restricted computation model we study is a semantic restriction on (non)deterministic BPs solving the TEP - Thrifty BPs. Deterministic (resp. nondeterministic) thrifty BPs suffice to implement the best known algorithms for the TEP, based on black (resp. fractional) pebbling. In earlier work, for each fixed h a lower bound on the size of deterministic thrifty BPs was proved that is tight for sufficiently large k. We give an alternative proof that achieves the same bound for all k. We show the same bound still holds in a less-restricted model, and also that gradually weaker lower bounds can be obtained for gradually weaker restrictions on the model.Comment: Written as one of the requirements for my MSc. 29 pages, 6 figure

Uniqueness of zero-temperature metastate in disordered Ising ferromagnets

We study ground states of Ising models with random ferromagnetic couplings, proving the triviality of all zero-temperature metastates. This unexpected result sheds a new light on the properties of these systems, putting strong restrictions on their possible ground state structure. Open problems related to existence of interface-supporting ground states are stated and an interpretation of the main result in terms of first-passage and random surface models in a random environment is presented

Correcting Errors in the Bostrom/Kulczycki Simulation Arguments

Both patched versions of the Bostrom/Kulczycki simulation argument contain serious objective errors, discovered while attempting to formalize them in predicate logic. The English glosses of both versions involve badly misleading meanings of vague magnitude terms, which their impressiveness benefits from. We fix the errors, prove optimal versions of the arguments, and argue that both are much less impressive than they originally appeared. Finally, we provide a guide for readers to evaluate the simulation argument for themselves, using well-justified settings of the argument parameters that have simple, accurate statements in English, which are easier to understand and critique than the statements in the original paper

2011 Outlook Report

To assess the outlook for grantmaking in Minnesota in 2011, the Minnesota Council on Foundations (MCF) conducted its 2011 Outlook Report survey in October and November of 2010. The survey asked grantmakers to predict how their 2011 giving will compare to 2010. A total of 118 organizations responded, representing about 65 percent of annual grantmaking in the state. Foundation giving is expected to stabilize in 2011 following two years in which grantmakers anticipated declines. According to MCF's 2011 Outlook Report survey, indicators also signal that Minnesota grantmakers are more optimistic about their giving in 2011 than they were at this time last year

Giving in Minnesota 2009 Edition Summary

This summary reports highlights of the Minnesota Council on Foundations' Giving in Minnesota, 2009 Edition research report, the most comprehensive analysis of charitable giving in the state. The 2009 edition features Minnesota giving in 2007, the most recent year for which comprehensive data are available. This report includes information about overall giving by foundations, corporations and individuals in Minnesota, along with detailed grantmaking trends by the Giving in Minnesota sample, which is comprised of 100 of the state's largest grantmakers based on grants paid

2010 Outlook Report

To assess the outlook for grantmaking in Minnesota in 2010, the Minnesota Council on Foundations (MCF) conducted its 2010 Outlook Report survey in October and November of 2009. The survey asked MCF members and other large grantmakers in the state to predict how their 2010 giving will compare to 2009. In all, 125 organizations responded, representing about 70 percent of annual grantmaking in the state

Giving in Minnesota, 2010 Edition

The Minnesota Council on Foundations has produced its Giving in Minnesota, 2010 Edition research report, the most comprehensive analysis of charitable giving in the state. The 2010 edition features Minnesota giving in 2008, the most recent year for which comprehensive data are available. This report includes information about overall giving by foundations, corporations and individuals in Minnesota, along with detailed grantmaking trends by the Giving in Minnesota sample, which is comprised of 100 of the state's largest grantmakers based on grants paid