Two-batch liar games on a general bounded channel

We consider an extension of the 2-person R\'enyi-Ulam liar game in which lies are governed by a channel $C$, a set of allowable lie strings of maximum length $k$. Carole selects $x\in[n]$, and Paul makes $t$-ary queries to uniquely determine $x$. In each of $q$ rounds, Paul weakly partitions $[n]=A_0\cup >... \cup A_{t-1}$ and asks for $a$ such that $x\in A_a$. Carole responds with some $b$, and if $a\neq b$, then $x$ accumulates a lie $(a,b)$. Carole's string of lies for $x$ must be in the channel $C$. Paul wins if he determines $x$ within $q$ rounds. We further restrict Paul to ask his questions in two off-line batches. We show that for a range of sizes of the second batch, the maximum size of the search space $[n]$ for which Paul can guarantee finding the distinguished element is $\sim t^{q+k}/(E_k(C)\binom{q}{k})$ as $q\to\infty$, where $E_k(C)$ is the number of lie strings in $C$ of maximum length $k$. This generalizes previous work of Dumitriu and Spencer, and of Ahlswede, Cicalese, and Deppe. We extend Paul's strategy to solve also the pathological liar variant, in a unified manner which gives the existence of asymptotically perfect two-batch adaptive codes for the channel $C$.Comment: 26 page

Asymmetric binary covering codes

An asymmetric binary covering code of length n and radius R is a subset C of the n-cube Q_n such that every vector x in Q_n can be obtained from some vector c in C by changing at most R 1's of c to 0's, where R is as small as possible. K^+(n,R) is defined as the smallest size of such a code. We show K^+(n,R) is of order 2^n/n^R for constant R, using an asymmetric sphere-covering bound and probabilistic methods. We show K^+(n,n-R')=R'+1 for constant coradius R' iff n>=R'(R'+1)/2. These two results are extended to near-constant R and R', respectively. Various bounds on K^+ are given in terms of the total number of 0's or 1's in a minimal code. The dimension of a minimal asymmetric linear binary code ([n,R]^+ code) is determined to be min(0,n-R). We conclude by discussing open problems and techniques to compute explicit values for K^+, giving a table of best known bounds.Comment: 16 page

Age effects in first language attrition: speech perception by Korean-English bilinguals

This article has been awarded Open Materials and Open Data badges. All materials and data are publicly accessible via the Open Science Framework at https://osf.io/B2478 and at https://osf.io/G4C7Z. Learn more about the Open Practices badges from the Center for Open Science: https://osf.io/tvyxz/wiki.This study investigated how bilinguals’ perception of their first language (L1) differs according to age of reduced contact with L1 after immersion in a second language (L2). Twenty-one L1 Korean-L2 English bilinguals in the United States, ranging in age of reduced contact from 3 to 15 years, and 17 control participants in Korea were tested perceptually on three L1 contrasts differing in similarity to L2 contrasts. Compared to control participants, bilinguals were less accurate on L1-specific contrasts, and their accuracy was significantly correlated with age of reduced contact, an effect most pronounced for the contrast most dissimilar to L2. These findings suggest that the earlier bilinguals are extensively exposed to L2, the less likely they are to perceive L1 sounds accurately. However, this relationship is modulated by crosslinguistic similarity, and a turning point in L2 acquisition and L1 attrition of phonology appears to occur at around age 12.This research was supported by funding from the Ph.D. Program in Second Language Acquisition at the University of Maryland. The funding source was not involved in the design of the study, in the collection, analysis, and interpretation of data, in the writing of the manuscript, or in the decision to submit the manuscript for publication. We thank Dr. Youngkyu Kim at Ewha Womans University for his substantial support and Ms. Irene Jieun Ahn (formerly at Ewha Womans University and currently at Michigan State University) for her help during data collection in Korea. (Ph.D. Program in Second Language Acquisition at the University of Maryland

Random geometric graph diameter in the unit ball

This is the author's accepted manuscript

The Knowledge of Good

This book presents Robert S. Hartman’s formal theory of value and critically examines many other twentieth century value theorists in its light, including A.J. Ayer, Kurt Baier, Brand Blanshard, Paul Edwards, Albert Einstein, William K. Frankena, R.M. Hare, Nicolai Hartmann, Martin Heidegger, G.E. Moore, P.H. Nowell-Smith, Jose Ortega y Gasset, Charles Stevenson, Paul W. Taylor, Stephen E. Toulmin, and J.O. Urmson

Proof of Product Defect (Metallurgical Case)

This article describes some of the problems of proof encountered in the preparation of a unique product liability case. No single case regarding a defective hand tool was found which presented a standard of conduct by which the plaintiff could claim the defendant was negligent in causing the plaintiff his unfortunate injury-the loss of an eye