In this paper we prove a theorem concerning the relative strength of \R,P„\k and \R,qn\k summability methods, k > 1 , that generalizes a result of Bosanquet [1].

The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven to be a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing bounds on proof space, and establishing size-space trade-offs. The typical approach has been to encode the pebble game played on a graph as a CNF formula...

The reinforcing bar deformation patterns currently used in the U.S. were established over 45 years ago. In the interim, material properties and design procedures have changed, resulting in more congested reinforcement, the use of higher strength materials, and the application of coatings to provide corrosion protection. Based on an improved understanding of the interaction between reinforcing s...

We give exponential size lower bounds for bounded-depth Frege proofs of variants of the bijective (‘onto’) version of the pigeonhole principle, even given additional axiom schemas for modular counting principles. As a consequence we show that for bounded-depth Frege systems the general injective version of the pigeonhole principle is exponentially more powerful than its bijective version. Furth...

Categorization is the process by which the brain segregates continuously variable stimuli into discrete groups. We report that patterns of neural population activity in the owl optic tectum (OT) categorize stimuli based on their relative strengths into "strongest" versus "other." The category boundary shifts adaptively to track changes in the absolute strength of the strongest stimulus. This po...

Subjects studied either an 8- or 16-word list and later recalled the items while a voice key recorded each response latency. The trials were partitioned by recall total in order to examine the means and distributions of both latencies and interresponse times as a function of recall total. Each analysis was consistent with the view that an item's absolute strength determines whether it is recall...

Context-aware applications have been gaining huge interest in the last few years. With cell phones becoming ubiquitous computing devices, cell phone localization has become an important research problem. Database Correlation Method (DCM) is a positioning technology that based on a database of a premeasured location dependent variable such as Received Signal Strength (RSS). DCM has shown superio...

This paper is the result of an investigation into applying statistical tools and methodologies to the discovery of digital evidence. Multiple statistical methods were reviewed; the two most useful are presented here. It is important to note that this paper represents an inquiry into the value of applied mathematical analysis to digital forensics investigations. Readers are encouraged to explore...

Split cuts are among the most important and well-understood cuts for general mixed-integer programs. In this paper we consider some recent generalizations of split cuts and compare their relative strength. More precisely, we compare the elementary closures of split, cross, crooked cross and general multi-branch split cuts as well as cuts obtained from multi-row and basic relaxations. We present...