On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

Sibling Rivalry among Paralogs Promotes Evolution of the Human Brain

Geneticists have long sought to identify the genetic changes that made us human, but pinpointing the functionally relevant changes has been challenging. Two papers in this issue suggest that partial duplication of SRGAP2, producing an incomplete protein that antagonizes the original, contributed to human brain evolution

Maximum principle and mutation thresholds for four-letter sequence evolution

A four-state mutation-selection model for the evolution of populations of DNA-sequences is investigated with particular interest in the phenomenon of error thresholds. The mutation model considered is the Kimura 3ST mutation scheme, fitness functions, which determine the selection process, come from the permutation-invariant class. Error thresholds can be found for various fitness functions, the phase diagrams are more interesting than for equivalent two-state models. Results for (small) finite sequence lengths are compared with those for infinite sequence length, obtained via a maximum principle that is equivalent to the principle of minimal free energy in physics.Comment: 25 pages, 16 figure

Degeneracy Algorithm for Random Magnets

It has been known for a long time that the ground state problem of random magnets, e.g. random field Ising model (RFIM), can be mapped onto the max-flow/min-cut problem of transportation networks. I build on this approach, relying on the concept of residual graph, and design an algorithm that I prove to be exact for finding all the minimum cuts, i.e. the ground state degeneracy of these systems. I demonstrate that this algorithm is also relevant for the study of the ground state properties of the dilute Ising antiferromagnet in a constant field (DAFF) and interfaces in random bond magnets.Comment: 17 pages(Revtex), 8 Postscript figures(5color) to appear in Phys. Rev. E 58, December 1st (1998

Exercise does not influence development of phenotype in PLN p.(Arg14del) cardiomyopathy

BACKGROUND: Endurance and frequent exercise are associated with earlier onset of arrhythmogenic right ventricular cardiomyopathy (ARVC) and ventricular arrhythmias (VA) in desmosomal gene variant carriers. Individuals with the pathogenic c.40_42del; p.(Arg14del) variant in the PLN gene are frequently diagnosed with ARVC or dilated cardiomyopathy (DCM). The aim of this study was to evaluate the effect of exercise in PLN p.(Arg14del) carriers. METHODS: In total, 207 adult PLN p.(Arg14del) carriers (39.1% male; mean age 53 ± 15 years) were interviewed on their regular physical activity since the age of 10 years. The association of exercise with diagnosis of ARVC, DCM, sustained VA and hospitalisation for heart failure (HF) was studied. RESULTS: Individuals participated in regular physical activities with a median of 1661 metabolic equivalent of task (MET) hours per year (31.9 MET-hours per week) until clinical presentation. The 50% most and least active individuals had a similar frequency of sustained VA (18.3% vs 18.4%; p = 0.974) and hospitalisation for HF (9.6% vs 8.7%; p = 0.827). There was no relationship between exercise and survival free from (incident) sustained VA (p = 0.65), hospitalisation for HF (p = 0.81), diagnosis of ARVC (p = 0.67) or DCM (p = 0.39) during follow-up. In multivariate analyses, exercise was not associated with sustained VA or HF hospitalisation during follow-up in this relatively not-active cohort. CONCLUSION: There was no association between the amount of exercise and the susceptibility to develop ARVC, DCM, VA or HF in PLN p.(Arg14del) carriers. This suggested unaffected PLN p.(Arg14del) carriers can safely perform mild-moderate exercise, in contrast to desmosomal variant carriers and ARVC patients

Combination of simulation and model-checking for the analysis of autonomous vehicles’ behaviors: A case study

International audienceAutonomous vehicles’ behavioural analysis represents a major challenge in the automotive world. In order to ensure safety and fluidity of driving, various methods are available, in particular, simulation and formal verification. The analysis, however, has to cope with very complex environments depending on many parameters evolving in real time. In this context, none of the aforementioned approaches is fully satisfactory, which lead us to propose a combined methodology in order to point out suspicious behaviours more efficiently. We illustrate this approach by studying a non deterministic scenario involving a vehicle, which has to react to some perilous situation

The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

On the chromatic number of random geometric graphs

Given independent random points X_1,...,X_n\in\eR^d with common probability distribution $\nu$, and a positive distance $r=r(n)>0$, we construct a random geometric graph $G_n$ with vertex set $\{1,...,n\}$ where distinct $i$ and $j$ are adjacent when \norm{X_i-X_j}\leq r. Here \norm{.} may be any norm on \eR^d, and $\nu$ may be any probability distribution on \eR^d with a bounded density function. We consider the chromatic number $\chi(G_n)$ of $G_n$ and its relation to the clique number $\omega(G_n)$ as $n \to \infty$. Both McDiarmid and Penrose considered the range of $r$ when $r \ll (\frac{\ln n}{n})^{1/d}$ and the range when $r \gg (\frac{\ln n}{n})^{1/d}$, and their results showed a dramatic difference between these two cases. Here we sharpen and extend the earlier results, and in particular we consider the `phase change' range when $r \sim (\frac{t\ln n}{n})^{1/d}$ with $t>0$ a fixed constant. Both McDiarmid and Penrose asked for the behaviour of the chromatic number in this range. We determine constants $c(t)$ such that $\frac{\chi(G_n)}{nr^d}\to c(t)$ almost surely. Further, we find a "sharp threshold" (except for less interesting choices of the norm when the unit ball tiles $d$-space): there is a constant $t_0>0$ such that if $t \leq t_0$ then $\frac{\chi(G_n)}{\omega(G_n)}$ tends to 1 almost surely, but if $t > t_0$ then $\frac{\chi(G_n)}{\omega(G_n)}$ tends to a limit $>1$ almost surely.Comment: 56 pages, to appear in Combinatorica. Some typos correcte

Classic McEliece Implementation with Low Memory Footprint

The Classic McEliece cryptosystem is one of the most trusted quantum-resistant cryptographic schemes. Deploying it in practical applications, however, is challenging due to the size of its public key. In this work, we bridge this gap. We present an implementation of Classic McEliece on an ARM Cortex-M4 processor, optimized to overcome memory constraints. To this end, we present an algorithm to retrieve the public key ad-hoc. This reduces memory and storage requirements and enables the generation of larger key pairs on the device. To further improve the implementation, we perform the public key operation by streaming the key to avoid storing it as a whole. This additionally reduces the risk of denial of service attacks. Finally, we use these results to implement and run TLS on the embedded device

The Netherlands Arrhythmogenic Cardiomyopathy Registry:design and status update

BACKGROUND: Clinical research on arrhythmogenic cardiomyopathy (ACM) is typically limited by small patient numbers, retrospective study designs, and inconsistent definitions. AIM: To create a large national ACM patient cohort with a vast amount of uniformly collected high-quality data that is readily available for future research. METHODS: This is a multicentre, longitudinal, observational cohort study that includes (1) patients with a definite ACM diagnosis, (2) at-risk relatives of ACM patients, and (3) ACM-associated mutation carriers. At baseline and every follow-up visit, a medical history as well information regarding (non-)invasive tests is collected (e. g. electrocardiograms, Holter recordings, imaging and electrophysiological studies, pathology reports, etc.). Outcome data include (non-)sustained ventricular and atrial arrhythmias, heart failure, and (cardiac) death. Data are collected on a research electronic data capture (REDCap) platform in which every participating centre has its own restricted data access group, thus empowering local studies while facilitating data sharing. DISCUSSION: The Netherlands ACM Registry is a national observational cohort study of ACM patients and relatives. Prospective and retrospective data are obtained at multiple time points, enabling both cross-sectional and longitudinal research in a hypothesis-generating approach that extends beyond one specific research question. In so doing, this registry aims to (1) increase the scientific knowledge base on disease mechanisms, genetics, and novel diagnostic and treatment strategies of ACM; and (2) provide education for physicians and patients concerning ACM, e. g. through our website ( www.acmregistry.nl ) and patient conferences