Explicit incidence bounds over general finite fields

Let $\mathbb{F}_{q}$ be a finite field of order $q=p^k$ where $p$ is prime. Let $P$ and $L$ be sets of points and lines respectively in $\mathbb{F}_{q} \times \mathbb{F}_{q}$ with $|P|=|L|=n$. We establish the incidence bound $I(P,L) \leq \gamma n^{3/2 - 1/12838}$, where $\gamma$ is an absolute constant, so long as $P$ satisfies the conditions of being an `antifield'. We define this to mean that the projection of $P$ onto some coordinate axis has no more than half-dimensional interaction with large subfields of $\mathbb{F}_q$. In addition, we give examples of sets satisfying these conditions in the important cases $q=p^2$ and $q=p^4$

An assessment of PERT as a technique for schedule planning and control

The PERT technique including the types of reports which can be computer generated using the NASA/LaRC PPARS System is described. An assessment is made of the effectiveness of PERT on various types of efforts as well as for specific purposes, namely, schedule planning, schedule analysis, schedule control, monitoring contractor schedule performance, and management reporting. This assessment is based primarily on the author's knowledge of the usage of PERT by NASA/LaRC personnel since the early 1960's. Both strengths and weaknesses of the technique for various applications are discussed. It is intended to serve as a reference guide for personnel performing project planning and control functions and technical personnel whose responsibilities either include schedule planning and control or require a general knowledge of the subject

Causal Interfaces

The interaction of two binary variables, assumed to be empirical observations, has three degrees of freedom when expressed as a matrix of frequencies. Usually, the size of causal influence of one variable on the other is calculated as a single value, as increase in recovery rate for a medical treatment, for example. We examine what is lost in this simplification, and propose using two interface constants to represent positive and negative implications separately. Given certain assumptions about non-causal outcomes, the set of resulting epistemologies is a continuum. We derive a variety of particular measures and contrast them with the one-dimensional index.Comment: 20 pages, 3 figure

Non-linear Plank Problems and polynomial inequalities

We study lower bounds for the norm of the product of polynomials and their applications to the so called \emph{plank problem.} We are particularly interested in polynomials on finite dimensional Banach spaces, in which case our results improve previous works when the number of polynomials is large.Comment: 19 page

Program Synthesis using Natural Language

Interacting with computers is a ubiquitous activity for millions of people. Repetitive or specialized tasks often require creation of small, often one-off, programs. End-users struggle with learning and using the myriad of domain-specific languages (DSLs) to effectively accomplish these tasks. We present a general framework for constructing program synthesizers that take natural language (NL) inputs and produce expressions in a target DSL. The framework takes as input a DSL definition and training data consisting of NL/DSL pairs. From these it constructs a synthesizer by learning optimal weights and classifiers (using NLP features) that rank the outputs of a keyword-programming based translation. We applied our framework to three domains: repetitive text editing, an intelligent tutoring system, and flight information queries. On 1200+ English descriptions, the respective synthesizers rank the desired program as the top-1 and top-3 for 80% and 90% descriptions respectively

Limiting conditional distributions for birth-death processes

In a recent paper one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on whether or not the process is evanescent. In the former case we shall relax the condition that absorption is certain. Furthermore, we shall allow for the possibility that the minimal process might be explosive, so that the transition rates alone will not necessarily determine the birth-death process uniquely. Although we shall be concerned mainly with the minimal process, our most general results hold for any birth-death process whose transition probabilities satisfy both the backward and the forward Kolmogorov differential equations

Identifying the NMSSM by the interplay of LHC and ILC

The interplay between the LHC and the $e^+ e^-$ International Linear Collider (ILC) with $\sqrt{s}=500$ GeV might be crucial for the discrimination between the minimal and next-to-minimal supersymmetric standard model. We present an NMSSM scenario, where the light neutralinos have a significant singlino component, that cannot be distinguished from the MSSM by cross sections and mass measurements. Mass and mixing state predictions for the heavier neutralinos from the ILC analysis at different energy stages and comparison with observation at the LHC, lead to clear identification of the particle character and identify the underlying supersymmetric model.Comment: 8 pages, 2 eps figures, revtex4 style Contribution to the `2005 International Linear Collider Workshop - Stanford, U.S.A.

Enumeration of points, lines, planes, etc

One of the earliest results in enumerative combinatorial geometry is the following theorem of de Bruijn and Erd\H{o}s: Every set of points $E$ in a projective plane determines at least $|E|$ lines, unless all the points are contained in a line. Motzkin and others extended the result to higher dimensions, who showed that every set of points $E$ in a projective space determines at least $|E|$ hyperplanes, unless all the points are contained in a hyperplane. Let $E$ be a spanning subset of a $d$-dimensional vector space. We show that, in the partially ordered set of subspaces spanned by subsets of $E$, there are at least as many $(d-k)$-dimensional subspaces as there are $k$-dimensional subspaces, for every $k$ at most $d/2$. This confirms the "top-heavy" conjecture of Dowling and Wilson for all matroids realizable over some field. The proof relies on the decomposition theorem package for $\ell$-adic intersection complexes.Comment: 18 pages, major revisio