Subsets of finite groups exhibiting additive regularity

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In particular, we show that any sum set must exhibit higher-order regularity and that an abelian sum set is necessarily a reversible difference set. We next develop several general construction techniques under the hypothesis that the over-riding group contains a normal subgroup of order 2. Finally, by exploiting properties of dihedral groups and Frobenius groups, several infinite classes of sum sets and partial sum sets are introduced

Ranking Multi-Attribute Entities - A Possible Inexpensive Alternative to AHP

A poster discussing a possible alternative to Analytic Hierarchy Process

The Overdue Death of a Dinosaur or It’s Time to End “Tax Bracket” GPA Grading

This paper presents a continuous alternative to the discrete grading system currently used by virtually all schools and colleges throughout the country. In order to most accurately reflect the nuances of academic achievement of a student, a continuous grading policy is superior to a discrete policy. Such a scheme is presented here. The ubiquity of computational aids, particularly Excel, makes such an alternative both viable and trivial

“R22” – An Unbreakable, Un-hackable, Friend-to-Friend Encryption System

This project begins a discussion of creating a secure “friend-to-friend” messaging scheme that involves only ordinary computers on the “surface web, does not depend on the difficulty of factoring, is impervious to any kind of deliberate or accidental backdoors, does not use any third party random number generators, and is unbreakable in any reasonable amount of time

Two New Grading Options: Scaling and Importance

Two new tools for adjusting student grades to more accurately reflect the nuances of student performance, to account for misjudgments in the design of assignments, and to account for the effects of “too-easy” or “too-demanding” grading are introduced. These are called scaling and importance. They are defined and their effects are illustrated

Validating Predictions of Unobserved Quantities

The ultimate purpose of most computational models is to make predictions, commonly in support of some decision-making process (e.g., for design or operation of some system). The quantities that need to be predicted (the quantities of interest or QoIs) are generally not experimentally observable before the prediction, since otherwise no prediction would be needed. Assessing the validity of such extrapolative predictions, which is critical to informed decision-making, is challenging. In classical approaches to validation, model outputs for observed quantities are compared to observations to determine if they are consistent. By itself, this consistency only ensures that the model can predict the observed quantities under the conditions of the observations. This limitation dramatically reduces the utility of the validation effort for decision making because it implies nothing about predictions of unobserved QoIs or for scenarios outside of the range of observations. However, there is no agreement in the scientific community today regarding best practices for validation of extrapolative predictions made using computational models. The purpose of this paper is to propose and explore a validation and predictive assessment process that supports extrapolative predictions for models with known sources of error. The process includes stochastic modeling, calibration, validation, and predictive assessment phases where representations of known sources of uncertainty and error are built, informed, and tested. The proposed methodology is applied to an illustrative extrapolation problem involving a misspecified nonlinear oscillator

Scheduling Electric Power Restoration

After Tropical Storm Irene and the Halloweensnowstorm, everybody understands the need for rapid restoration of electric power. Optimal job scheduling is an NP-complete problem, which means, in ordinary English, that the only known solution is a full enumeration of all possible schedules. As near as we can tell, CL&P uses either a "First Come, First Served" (FCFS) policy or an "Outside In" policy for scheduling their crews. FCFS means that the jobs are scheduled in the order that they're called in, and "Outside In" means that crews are sent to the borders of affected areas and they then work their way in to the center of an affected area. This last method is equivalent to what's called the "Nearest Neighbor" algorithm, which is equivalent to "Shortest Travel Time First" scheduling. The authors wondered whether a scheduling algorithm known as "Longest Remaining Job First" (LRJF) might produce better results. LRJF is a "near-optimal" algorithm, apparently discovered by Prof. Todd in the early 90s, that when used for scheduling jobs for parallel processing, results in faster job completion times

Performance Predictors for Evidence-based Education for Highly Inclusive Colleges

This paper presents initial results of students’ and employers’ expectations of college graduates for the purpose of increasing our graduates’ marketability in consonance with President Obama’s recent call for a new, jobs-related rating system for colleges. It also includes an initial proposal for defining and measuring key process predictors (KPPs) that can guide us to continuously refine classroom performance expectations of both faculty and students toward achieving higher retention, graduation, and employment rates

Multimodal Frontostriatal Connectivity Underlies Individual Differences in Self-Esteem

A heightened sense of self-esteem is associated with a reduced risk for several types of affective and psychiatric disorders, including depression, anxiety and eating disorders. However, little is known about how brain systems integrate self-referential processing and positive evaluation to give rise to these feelings. To address this, we combined diffusion tensor imaging (DTI) and functional magnetic resonance imaging (fMRI) to test how frontostriatal connectivity reflects long-term trait and short-term state aspects of self-esteem. Using DTI, we found individual variability in white matter structural integrity between the medial prefrontal cortex and the ventral striatum was related to trait measures of self-esteem, reflecting long-term stability of self-esteem maintenance. Using fMRI, we found that functional connectivity of these regions during positive self-evaluation was related to current feelings of self-esteem, reflecting short-term state self-esteem. These results provide convergent anatomical and functional evidence that self-esteem is related to the connectivity of frontostriatal circuits and suggest that feelings of self-worth may emerge from neural systems integrating information about the self with positive affect and reward. This information could potentially inform the etiology of diminished self-esteem underlying multiple psychiatric conditions and inform future studies of evaluative self-referential processing

The Probability of Winning at Solitaire: A Preliminary Description of a State-Transition Approach

This paper is the very beginning of a proposal of an approach that may offer a method for solving a currently unsolved problem - calculating the probability of winning at Solitaire. We describe the game as a series of state transitions, from an initial state to a winning state. The state variables and allowable transitions are described, and a list of “next steps” is given. It is hoped that this approach may prove fruitful