Tight bounds and conjectures for the isolation lemma

Given a hypergraph $H$ and a weight function $w: V \rightarrow \{1, \dots, M\}$ on its vertices, we say that $w$ is isolating if there is exactly one edge of minimum weight $w(e) = \sum_{i \in e} w(i)$. The Isolation Lemma is a combinatorial principle introduced in Mulmuley et. al (1987) which gives a lower bound on the number of isolating weight functions. Mulmuley used this as the basis of a parallel algorithm for finding perfect graph matchings. It has a number of other applications to parallel algorithms and to reductions of general search problems to unique search problems (in which there are one or zero solutions). The original bound given by Mulmuley et al. was recently improved by Ta-Shma (2015). In this paper, we show improved lower bounds on the number of isolating weight functions, and we conjecture that the extremal case is when $H$ consists of $n$ singleton edges. When $M \gg n$ our improved bound matches this extremal case asymptotically. We are able to show that this conjecture holds in a number of special cases: when $H$ is a linear hypergraph or is 1-degenerate, or when $M = 2$. We also show that it holds asymptotically when $M \gg n \gg 1$

Edge-coloring linear hypergraphs with medium-sized edges

Motivated by the Erd\H{o}s-Faber-Lov\'{a}sz (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We show that if the hyper-edge sizes are bounded between $i$ and $C_{i,\epsilon} \sqrt{n}$ inclusive, then there is a list edge coloring using $(1 + \epsilon) \frac{n}{i - 1}$ colors. The dependence on $n$ in the upper bound is optimal (up to the value of $C_{i,\epsilon}$)

Dynamics of Unitary Operators

We consider the iteration of a unitary operator on a separable Hilbert space and study the spreading rates of the associated discrete-time dynamical system relative to a given orthonormal basis. We prove lower bounds for the transport exponents, which measure the time-averaged spreading on a power-law scale, in terms of dimensional properties of the spectral measure associated with the unitary operator and the initial state. These results are the unitary analog of results established in recent years for the dynamics of the Schr\"odinger equation, which is a continuum-time dynamical system associated with a self-adjoint operator. We discuss how these general results may be studied by means of subordinacy theory in cases where the unitary operator is given by a CMV matrix. An example of particular interest in which this scenario arises is given by a time-homogeneous quantum walk on the integers. For the particular case of the time-homogeneous Fibonacci quantum walk, we illustrate how these components work together and produce explicit lower bounds for the transport exponents associated with this model.Comment: 27 page

Rational Expectations, the Expectations Hypothesis, and Treasury Bill Yields: An Econometric Analysis

This paper tests the joint hypothesis of rational expectations and the expectations model of the term structure for three- and six-month Treasury bills. Previous studies are extended in three directions. First, common efficient markets-rational expectations tests are compared, and it is shown that four of the five tests considered are asymptotically equivalent, and that the fifth is less restrictive than the other four. Second, the joint hypothesis is tested using weekly data for Treasury bills maturing in exactly 13 and 26 weeks beginning in 1970 and ending in 1979. In contrast, previous studies using comparable data have typically discarded 12/13 of the sample to form a nonoverlapping data set. Finally, a more complete set of possible determinants of time-varying term premiums is tested.

Information, Knowledge and Wisdom:The Epistemic Hierarchy andComputer-Based Information Systems

As we move further into the Information Age, and as its technology becomes moreand more pervasive, it is appropriate to consider exactly what information might be and what part it should play in the formation of belief and, perhaps, even knowledge. My goal is to contribute a little to lessening the confusion of definitions and to suggest a meter by which we can measure whether we know a thing presented by an information system, merely believe it, or simply have a piece of information and further, whether a computerized information system can be a valid tool for moving our thinking up the epistemic hierarchy.This paper will 1.) look at some contemporary definitions of information and test their fitness against a philosophical definition, 2) define and distinguish the formal requirements for knowledge as opposed to belief, 3.) examine a definition of knowledge and epistemic warrant adaptable to Information Systems, and 4.) evaluate how this criterion might assist our decision maker of the beginning of this paper

Towards A Professional Information Systems Ethic (Cyberethics)

Information Systems technology promises to transform our world. The pertinent ethical question is whether that transformation will be for good or for ill. Who will make the decisions, and upon what basis? Who will benefit? Who will be harmed? As computers and the software programs they run become more pervasive in modern life, there is a growing apprehension of the potential harm they can cause and an awareness that, in America, the professionals and semi-professionals whose programs influence our lives are a non-regulated, non-certified group, in large measure not bound by any code of conduct beyond their own conscience. Hence there are moves afoot in the United States and Canada (Gotterbarn, Kerr) to legislate formal licensing and certification for InformationSystems (IS) professionals. Unless national and international professional associations are able to police their own members, society at large may seize the reins. For professional, political, philosophical, and economic reasons, it is preferable to institute measures of self-governance. This paper surveys an eclectic literature in order to provide a framework for future research developing a system of professional ethical training and a self-governance system

Growth and productivity of juvenile banana prawns, Penaeus merguiensis in natural and laboratory systems

Abstract only.Growth and survival of Penaeus merguiensis juveniles were measured over four years in the Norman River estuary, south-eastern Gulf of Carpentaria. Growth in carapace length for the first 8-9 weeks after settlement was essentially linear and averaged 1.2 mm/week in summer at 29.5°C and 0.45 mm/week in winter at 19.5°C. A comparison of different cohorts under varying temperatures and salinities indicated that growth was temperature- but not salinity-dependent. Survival of newly settled postlarvae varied seasonally and was highest in spring (October-November). In the laboratory, a study of moulting rate and moult increment at 15, 20, 25, 30 and 35°C demonstrated that the optimal temperature for growth was 25-30°C. Survival of juveniles was also highest at intermediate temperatures. Effects of salinity and food ration amounts are discussed

Return On Goodwill

Goodwill represents value not recorded until a company is purchased by another company. The value of goodwill comes from intangibles such as location, superior market position or the skill and learning of management. Goodwill is the difference between the purchase price of a company and the fair value of its assets. The residual nature of goodwill makes measurement of its contribution to performance difficult.  Two questions flow from this. The first is whether the contribution of goodwill is measurable. The second question is whether the contribution of goodwill varies from industry to industry. One way to measure contribution is return on assets.  This study analyses 38,519 years of company operations in 48 industries and compares the return of companies with and without goodwill. For some, but not all industries, return on assets for companies with goodwill was higher that for companies without goodwill.  The contributions of this study are to demonstrate whether goodwill contributes to performance and to analyze variability of performance by industry