Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure

Alcohol-related cerebellar degeneration: not all down to toxicity?

Background: Alcohol-related cerebellar degeneration is one of the commonest acquired forms of cerebellar ataxia. The exact pathogenic mechanisms by which alcohol leads to cerebellar damage remain unknown. Possible autoreactive immune mediated mechanisms have not been explored previously. In this study, we aim to investigate the potential role of alcohol-induced immune mediated cerebellar degeneration. Methods: Patients with ataxia and a history of alcohol misuse were recruited from the Ataxia and Hepatology tertiary clinics at Sheffield Teaching Hospitals NHS Trust. We determined the pattern of cerebellar involvement both on clinical (SARA score) and imaging (MRI volumetry and MR spectroscopy) parameters. In addition, HLA genotyping, serological markers for gluten-related disorders and serological reactivity on rat cerebellar tissue using indirect immunohistochemistry were assessed. Results: Thirty-eight patients were included in the study all of whom had ataxia. The gait (97 %), stance (89 %) and heel-shin slide (89 %) were the predominant SARA elements affected. MRI volumetric and spectroscopy techniques demonstrated significant structural, volumetric and functional deficits of the cerebellum with particular involvement of the cerebellar vermis. Circulating anti-gliadin antibodies were detected in 34 % patients vs. 12 % in healthy controls. Antibodies to transglutaminase 6 (TG6) were detected in 39 % of patients and 4 % of healthy control subjects. Using immunohistochemistry, Purkinje cell and/or granular layer reactivity was demonstrated in 71 % of patient sera. Conclusions: Alcohol induced tissue injury to the CNS leading to cerebellar degeneration may also involve immune mediated mechanisms, including sensitisation to gluten

Antagonistic Bacterial Interactions Help Shape Host-Symbiont Dynamics within the Fungus-Growing Ant-Microbe Mutualism

Conflict within mutually beneficial associations is predicted to destabilize relationships, and theoretical and empirical work exploring this has provided significant insight into the dynamics of cooperative interactions. Within mutualistic associations, the expression and regulation of conflict is likely more complex than in intraspecific cooperative relationship, because of the potential presence of: i) multiple genotypes of microbial species associated with individual hosts, ii) multiple species of symbiotic lineages forming cooperative partner pairings, and iii) additional symbiont lineages. Here we explore complexity of conflict expression within the ancient and coevolved mutualistic association between attine ants, their fungal cultivar, and actinomycetous bacteria (Pseudonocardia). Specifically, we examine conflict between the ants and their Pseudonocardia symbionts maintained to derive antibiotics against parasitic microfungi (Escovopsis) infecting the ants' fungus garden. Symbiont assays pairing isolates of Pseudonocardia spp. associated with fungus-growing ants spanning the phylogenetic diversity of the mutualism revealed that antagonism between strains is common. In contrast, antagonism was substantially less common between more closely related bacteria associated with Acromyrmex leaf-cutting ants. In both experiments, the observed variation in antagonism across pairings was primarily due to the inhibitory capabilities and susceptibility of individual strains, but also the phylogenetic relationships between the ant host of the symbionts, as well as the pair-wise genetic distances between strains. The presence of antagonism throughout the phylogenetic diversity of Pseudonocardia symbionts indicates that these reactions likely have shaped the symbiosis from its origin. Antagonism is expected to prevent novel strains from invading colonies, enforcing single-strain rearing within individual ant colonies. While this may align ant-actinomycete interests in the bipartite association, the presence of single strains of Pseudonocardia within colonies may not be in the best interest of the ants, because increasing the diversity of bacteria, and thereby antibiotic diversity, would help the ant-fungus mutualism deal with the specialized parasites

Nonlocal observables and lightcone-averaging in relativistic thermodynamics

The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred class of hyperplanes in spacetime. (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems. These ambiguities led, for example, to various proposals for the Lorentz transformation law of temperature. Traditional 'isochronous' formulations of relativistic thermodynamics are neither theoretically satisfactory nor experimentally feasible. Here, we demonstrate how these deficiencies can be resolved by defining thermodynamic quantities with respect to the backward-lightcone of an observation event. This approach yields novel, testable predictions and allows for a straightforward-extension of thermodynamics to General Relativity. Our theoretical considerations are illustrated through three-dimensional relativistic many-body simulations.Comment: typos in Eqs. (12) and (14) corrected, minor additions in the tex

Solution NMR assignment of the C-terminal domain of human chTOG

The microtubule regulatory protein colonic and hepatic tumor overexpressed gene (chTOG), also known as cytoskeleleton associated protein 5 (CKAP5) plays an important role in organizing the cytoskeleton and in particular in the assembly of k-fibres in mitosis. Recently, we dissected the hitherto poorly understood C-terminus of this protein by discovering two new domains—a cryptic TOG domain (TOG6) and a smaller, helical domain at the very C-terminus. It was shown that the C-terminal domain is important for the interaction with the TACC domain in TACC3 during the assembly of k-fibres in a ternary complex that also includes clathrin. Here we now present the solution NMR assignment of the chTOG C-terminal domain which confirms our earlier prediction that it is mainly made of α-helices. However, the appearance of the 1H–15N HSQC spectrum is indicative of the presence of a considerable amount of unstructured and possibly flexible portions of protein in the domain

Pioglitazone and risk of bladder cancer among diabetic patients in France: a population-based cohort study

Abstract Aims/hypothesis Previous studies have suggested an increased risk of bladder cancer with pioglitazone exposure. We aimed to investigate the association between pioglitazone exposure and bladder cancer in France. Methods This cohort study involved use of data from the French national health insurance information system (Système National d'Information Inter-régimes de l'Assurance Maladie; SNIIRAM) linked with the French hospital discharge database (Programme de Médicalisation des Systèmes d'Information; PMSI). The cohort included patients aged 40 to 79 years who filled a prescription for a glucose-lowering drug in 2006. The cohort was followed for up to 42 months. Pioglitazone exposure was modelled as a time-dependent variable and defined by having filled at least two prescriptions over a 6-month period. Incident cases of bladder cancer were identified by a discharge diagnosis of bladder cancer combined with specific aggressive treatment. Statistical analyses involved a multivariate Cox model adjusted for age, sex and exposure to other glucose-lowering drugs. Results The cohort included 1,491,060 diabetic patients, 155,535 of whom were exposed to pioglitazone. We found 175 cases of bladder cancer among exposed patients and 1,841 among non-exposed patients. Incidence rates were 49.4 and 42.8 per 100,000 person-years, respectively. Pioglitazone exposure was significantly associated with bladder cancer incidence (adjusted HR 1.22 [95% CI 1.05, 1.43

A unifying mathematical framework for experimental TCR-pMHC kinetic constants

Receptor binding and triggering are central in Immunology as T cells activated through their T cell receptors (TCR) by protein antigens orchestrate immune responses. In order to understand receptor-ligand interactions, many groups working with different experimental techniques and assays have generated a vast body of knowledge during the last decades. However, in recent years a type of assays, referred to as two-dimensional or membrane-to-membrane, has questioned our current understanding of the role of different kinetic constants (for instance, on- versus off-rate constants) on TCR-ligand interaction and subsequent T cell activation. Here we present a general mathematical framework that provides a unifying umbrella to relate fundamental and effective (or experimentally determined) kinetic constants, as well as describe and compare state-of-the-art experimental methods. Our framework is able to predict the correlations between functional output, such as 1/EC50, and effective kinetic constants for a range of different experimental assays (in two and three dimensions). Furthermore, our approach can be applied beyond Immunology, and serve as a “translation method” for the biochemical characterization of receptor-ligand interactions