Interlocked permutations

The zero-error capacity of channels with a countably infinite input alphabet formally generalises Shannon's classical problem about the capacity of discrete memoryless channels. We solve the problem for three particular channels. Our results are purely combinatorial and in line with previous work of the third author about permutation capacity.Comment: 8 page

Skewincidence

We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewincidence if there is a coordinate i for which x_i=y_{i+1}=1 or vice versa. We give rather sharp bounds on the maximum number of binary sequences of length n any pair of which has a skewincidence

Witness sets

Given a set C of binary n-tuples and c in C, how many bits of c suffice to distinguish it from the other elements in C? We shed new light on this old combinatorial problem and improve on previously known bounds.Comment: Coding theory and applications, Espagne (2008

On Bounded Weight Codes

The maximum size of a binary code is studied as a function of its length N, minimum distance D, and minimum codeword weight W. This function B(N,D,W) is first characterized in terms of its exponential growth rate in the limit as N tends to infinity for fixed d=D/N and w=W/N. The exponential growth rate of B(N,D,W) is shown to be equal to the exponential growth rate of A(N,D) for w <= 1/2, and equal to the exponential growth rate of A(N,D,W) for 1/2< w <= 1. Second, analytic and numerical upper bounds on B(N,D,W) are derived using the semidefinite programming (SDP) method. These bounds yield a non-asymptotic improvement of the second Johnson bound and are tight for certain values of the parameters

Exact equations for smoothed Wigner transforms and homogenization of wave propagation

The Wigner Transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features counterintuitive 'interference terms', which often make computation impractical. In this connection, we propose the use of the smoothed Wigner Transform (SWT), and derive new, exact equations for it, covering a broad class of wave propagation problems. Equations for spectrograms are included as a special case. The 'taming' of the interference terms by the SWT is illustrated, and an asymptotic model for the Schroedinger equation is constructed and numerically verified.Comment: 16 pages, 8 figure

Ambiguities in the up quark mass

It has long been known that no physical singularity is encountered as up quark mass is adjusted from small positive to negative values as long as all other quarks remain massive. This is tied to an additive ambiguity in the definition of the quark mass. This calls into question the acceptability of attempts to solve the strong CP problem via a vanishing mass for the lightest quark.Comment: 9 pages, 1 figure. Revision as will appear in Physical Review Letters. Simplified renormalization group discussion and title change requested by PR

Bayesian Estimation of Mixture Models with Prespecified Elements to Compare Drug Resistance in Treatment-Naïve and Experienced Tuberculosis Cases

We propose a Bayesian approach for estimating branching tree mixture models to compare drug-resistance pathways (i.e. patterns of sequential acquisition of resistance to individual antibiotics) that are observed among Mycobacterium tuberculosis isolates collected from treatment-naïve and treatment-experienced patients. Resistant pathogens collected from treatment-naïve patients are strains for which fitness costs of resistance were not sufficient to prevent transmission, whereas those collected from treatment-experienced patients reflect both transmitted and acquired resistance, the latter of which may or may not be associated with lower transmissibility. The comparison of the resistance pathways constructed from these two groups of drug-resistant strains provides insight into which pathways preferentially lead to the development of multiple drug resistant strains that are transmissible. We apply the proposed statistical methods to data from worldwide surveillance of drug-resistant tuberculosis collected by the World Health Organization over 13 years

Suppression of the postoperative neutrophil leucocytosis following neoadjuvant chemoradiotherapy for rectal cancer and implications for surgical morbidity

Objective: The extent to which neoadjuvant chemoradio- therapy for rectal cancer influences postoperative morbid- ity is controversial. This study investigated whether this treatment suppresses the normal perioperative inflamma- tory response and explored the clinical implications. Method: Prospective databases were queried to identify 37 consecutive study patients undergoing definitive surgery following 5-FU ⁄ capecitabine-based chemoradio- therapy and 35 consecutive untreated control patients operated upon for rectal or rectosigmoid cancer. Preop- erative (< 10 days) and postoperative (< 24 h) neutrophil counts, along with morbidity data, were confirmed retrospectively. Univariate and multivariate analyses assessed the apparent effect of chemoradiotherapy on change in neutrophil count. The latter’s association with postoperative morbidity was then examined. Results: Sufficient data were available for 34 study and 27 control patients. Repeated-measures ANCOVA revealed significant differences between their periopera- tive neutrophil counts (P = 0.02). Of the other charac- teristics which differed between the groups, only age and tumour location were prognostically significant regarding perioperative change in neutrophil count. Accounting for relevant covariates, chemoradiotherapy was significantly associated with a suppressed perioper- ative neutrophil leucocytosis. Local postoperative com- plications affected 25 of 61 patients, who had lower perioperative neutrophil increases than their counter- parts (P = 0.016). Conclusion: Chemoradiotherapy appears to suppress the perioperative inflammatory response, thereby increasing susceptibility to local postoperative complications