Semigroups with operation-compatible Green’s quasiorders

We call a semigroup on which the Green’s quasiorder ≤ J (≤ L, ≤ R) is operation-compatible, a ≤ J-compatible (≤ L-compatible, ≤ R-compatible) semigroup. We study the classes of ≤ J-compatible, ≤ L-compatible and ≤ R-compatible semigroups, using the smallest operation-compatible quasiorders containing Green’s quasiorders as a tool. We prove a number of results, including the following. The class of ≤ L-compatible (≤ R-compatible) semigroups is closed under taking homomorphic images. A regular periodic semigroup is ≤ J-compatible if and only if it is a semilattice of simple semigroups. Every negatively orderable semigroup can be embedded into a negatively orderable ≤ J-compatible semigroup

Nonexistence Certificates for Ovals in a Projective Plane of Order Ten

In 1983, a computer search was performed for ovals in a projective plane of order ten. The search was exhaustive and negative, implying that such ovals do not exist. However, no nonexistence certificates were produced by this search, and to the best of our knowledge the search has never been independently verified. In this paper, we rerun the search for ovals in a projective plane of order ten and produce a collection of nonexistence certificates that, when taken together, imply that such ovals do not exist. Our search program uses the cube-and-conquer paradigm from the field of satisfiability (SAT) checking, coupled with a programmatic SAT solver and the nauty symbolic computation library for removing symmetries from the search.Comment: Appears in the Proceedings of the 31st International Workshop on Combinatorial Algorithms (IWOCA 2020

Cognitive skills and literacy performance of Chinese adolescents with and without dyslexia

The present study sought to identify cognitive abilities that might distinguish Hong Kong Chinese adolescents with dyslexia and to assess how these abilities were associated with Chinese word reading, word dictation, and reading comprehension. The cognitive skills of interest were morphological awareness, visual-orthographic knowledge, rapid naming, and verbal working memory. A total of 90 junior secondary school students, 30 dyslexic, 30 chronological age controls, and 30 reading level controls was tested on a range of cognitive and literacy tasks. Dyslexic students were less competent than the control students in all cognitive and literacy measures. The regression analyses also showed that verbal working memory, rapid naming, morphological awareness, and visual-orthographic knowledge were significantly associated with literacy performance. Findings underscore the importance of these cognitive skills for Chinese literacy acquisition. Overall, this study highlights the persistent difficulties of Chinese dyslexic adolescents who seem to have multiple causes for reading and spelling difficulties

Brane-World Gravity

The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the \textit{d} extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak ($\sim$ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity "leaks" into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall--Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at \emph{low} energies -- the 5-dimensional Dvali--Gabadadze--Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.Comment: A major update of Living Reviews in Relativity 7:7 (2004) "Brane-World Gravity", 119 pages, 28 figures, the update contains new material on RS perturbations, including full numerical solutions of gravitational waves and scalar perturbations, on DGP models, and also on 6D models. A published version in Living Reviews in Relativit

Costs and benefits of orthographic inconsistency in reading:evidence from a cross-linguistic comparison

We compared reading acquisition in English and Italian children up to late primary school analyzing RTs and errors as a function of various psycholinguistic variables and changes due to experience. Our results show that reading becomes progressively more reliant on larger processing units with age, but that this is modulated by consistency of the language. In English, an inconsistent orthography, reliance on larger units occurs earlier on and it is demonstrated by faster RTs, a stronger effect of lexical variables and lack of length effect (by fifth grade). However, not all English children are able to master this mode of processing yielding larger inter-individual variability. In Italian, a consistent orthography, reliance on larger units occurs later and it is less pronounced. This is demonstrated by larger length effects which remain significant even in older children and by larger effects of a global factor (related to speed of orthographic decoding) explaining changes of performance across ages. Our results show the importance of considering not only overall performance, but inter-individual variability and variability between conditions when interpreting cross-linguistic differences

Immunological mechanism of action and clinical profile of disease-modifying treatments in multiple sclerosis.

Multiple sclerosis (MS) is a life-long, potentially debilitating disease of the central nervous system (CNS). MS is considered to be an immune-mediated disease, and the presence of autoreactive peripheral lymphocytes in CNS compartments is believed to be critical in the process of demyelination and tissue damage in MS. Although MS is not currently a curable disease, several disease-modifying therapies (DMTs) are now available, or are in development. These DMTs are all thought to primarily suppress autoimmune activity within the CNS. Each therapy has its own mechanism of action (MoA) and, as a consequence, each has a different efficacy and safety profile. Neurologists can now select therapies on a more individual, patient-tailored basis, with the aim of maximizing potential for long-term efficacy without interruptions in treatment. The MoA and clinical profile of MS therapies are important considerations when making that choice or when switching therapies due to suboptimal disease response. This article therefore reviews the known and putative immunological MoAs alongside a summary of the clinical profile of therapies approved for relapsing forms of MS, and those in late-stage development, based on published data from pivotal randomized, controlled trials