A Meinardus theorem with multiple singularities

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journa

On orientational relief of inter-molecular potential and the structure of domain walls in fullerite C60

A simple planar model for an orientational ordering of threefold molecules on a triangular lattice modelling a close-packed (111) plane of fullerite is considered. The system has 3-sublattice ordered ground state which includes 3 different molecular orientations. There exist 6 kinds of orientational domains, which are related with a permutation or a mirror symmetry. Interdomain walls are found to be rather narrow. The model molecules have two-well orientational potential profiles, which are slightly effected by a presence of a straight domain wall. The reason is a stronger correlation between neighbour molecules in triangular lattice versus previously considered square lattice A considerable reduction (up to one order) of orientational interwell potential barrier is found in the core regions of essentially two-dimentional potential defects, such as a three-domain boundary or a kink in the domain wall. For ultimately uncorrelated nearest neighbours the height of the interwell barrier can be reduced even by a factor of 100.Comment: 11 pages, 13 figures, LaTeX, to appear in Low Temperature Physic

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

Mathematics education and technology

Recent international surveys such as the Organisation for Economic Co-operation and Development (OECD) report Students, Computers and Learning ( 2015) highlight the wide gap in students’ access to, and use of, technology in secondary mathematics in participating countries. The OECD “snapshot” methodology in which 15-year-old students were asked if they (or their teachers) had performed a range of mathematical tasks using computers in the month preceding their completion of the Programme for International Student Assessment (PISA) survey revealed low levels of technology use (see Fig. 1)

Small ball probability, Inverse theorems, and applications

Let $\xi$ be a real random variable with mean zero and variance one and $A={a_1,...,a_n}$ be a multi-set in $\R^d$. The random sum $$S_A := a_1 \xi_1 + ... + a_n \xi_n$$ where $\xi_i$ are iid copies of $\xi$ is of fundamental importance in probability and its applications. We discuss the small ball problem, the aim of which is to estimate the maximum probability that $S_A$ belongs to a ball with given small radius, following the discovery made by Littlewood-Offord and Erdos almost 70 years ago. We will mainly focus on recent developments that characterize the structure of those sets $A$ where the small ball probability is relatively large. Applications of these results include full solutions or significant progresses of many open problems in different areas.Comment: 47 page

MicroRNA-335-5p suppresses voltage-gated sodium channel expression and may be a target for seizure control

There remains an urgent need for new therapies for treatment-resistant epilepsy. Sodium channel blockers are effective for seizure control in common forms of epilepsy, but loss of sodium channel function underlies some genetic forms of epilepsy. Approaches that provide bidirectional control of sodium channel expression are needed. MicroRNAs (miRNA) are small noncoding RNAs which negatively regulate gene expression. Here we show that genome-wide miRNA screening of hippocampal tissue from a rat epilepsy model, mice treated with the antiseizure medicine cannabidiol, and plasma from patients with treatment-resistant epilepsy, converge on a single target-miR-335-5p. Pathway analysis on predicted and validated miR-335-5p targets identified multiple voltage-gated sodium channels (VGSCs). Intracerebroventricular injection of antisense oligonucleotides against miR-335-5p resulted in upregulation of Scn1a, Scn2a, and Scn3a in the mouse brain and an increased action potential rising phase and greater excitability of hippocampal pyramidal neurons in brain slice recordings, consistent with VGSCs as functional targets of miR-335-5p. Blocking miR-335-5p also increased voltage-gated sodium currents and SCN1A, SCN2A, and SCN3A expression in human induced pluripotent stem cell-derived neurons. Inhibition of miR-335-5p increased susceptibility to tonic-clonic seizures in the pentylenetetrazol seizure model, whereas adeno-associated virus 9-mediated overexpression of miR-335-5p reduced seizure severity and improved survival. These studies suggest modulation of miR-335-5p may be a means to regulate VGSCs and affect neuronal excitability and seizures. Changes to miR-335-5p may reflect compensatory mechanisms to control excitability and could provide biomarker or therapeutic strategies for different types of treatment-resistant epilepsy

Estimation of Fracture Toughness of Anisotropic Rocks by Semi-Circular Bend (SCB) Tests Under Water Vapor Pressure

In order to investigate the influence of water vapor pressure in the surrounding environment on mode I fracture toughness (KIc) of rocks, semi-circular bend (SCB) tests under various water vapor pressures were conducted. Water vapor is one of the most effective agents which promote stress corrosion of rocks. The range of water vapor pressure used was 10−2 to 103 Pa, and two anisotropic rock types, African granodiorite and Korean granite, were used in this work. The measurement of elastic wave velocity and observation of thin sections of these rocks were performed to investigate the microstructures of the rocks. It was found that the distribution of inherent microcracks and grains have a preferred orientation. Two types of specimens in different orientations, namely Type-1 and Type-3, were prepared based on the anisotropy identified by the differences in the elastic wave velocity. KIc of both rock types was dependent on the water vapor pressure in the surrounding environment and decreased with increasing water vapor pressure. It was found that the degree of the dependence is influenced by the orientation and density of inherent microcracks. The experimental results also showed that KIc depended on the material anisotropy. A fracture process was discussed on the basis of the geometry of fractures within fractured specimens visualized by the X-ray computed tomography (CT) method. It was concluded that the dominant factor causing the anisotropy of KIc is the distribution of grains rather than inherent microcracks in these rocks

Additive QTLs on three chromosomes control flowering time in woodland strawberry (Fragaria vesca L.)

Flowering time is an important trait that affects survival, reproduction and yield in both wild and cultivated plants. Therefore, many studies have focused on the identification of flowering time quantitative trait locus (QTLs) in different crops, and molecular control of this trait has been extensively investigated in model species. Here we report the mapping of QTLs for flowering time and vegetative traits in a large woodland strawberry mapping population that was phenotyped both under field conditions and in a greenhouse after flower induction in the field. The greenhouse experiment revealed additive QTLs in three linkage groups (LG), two on both LG4 and LG7, and one on LG6 that explain about half of the flowering time variance in the population. Three of the QTLs were newly identified in this study, and one co-localized with the previously characterized FvTFL1 gene. An additional strong QTL corresponding to previously mapped PFRU was detected in both field and greenhouse experiments indicating that gene(s) in this locus can control the timing of flowering in different environments in addition to the duration of flowering and axillary bud differentiation to runners and branch crowns. Several putative flowering time genes were identified in these QTL regions that await functional validation. Our results indicate that a few major QTLs may control flowering time and axillary bud differentiation in strawberries. We suggest that the identification of causal genes in the diploid strawberry may enable fine tuning of flowering time and vegetative growth in the closely related octoploid cultivated strawberry.Peer reviewe

Heterogeneity in Health Insurance Coverage Among US Latino Adults

We sought to determine the differences in observed and unobserved factors affecting rates of health insurance coverage between US Latino adults and US Latino adults of Mexican ancestry. Our hypothesis was that Latinos of Mexican ancestry have worse health insurance coverage than their non-Mexican Latino counterparts. The National Health Interview Survey (NHIS) database from 1999–2007 consists of 33,847 Latinos. We compared Latinos of Mexican ancestry to non-Mexican Latinos in the initial descriptive analysis of health insurance coverage. Disparities in health insurance coverage across Latino categories were later analyzed in a multivariable logistic regression framework, which adjusts for confounding variables. The Blinder-Oaxaca technique was applied to parse out differences in health insurance coverage into observed and unobserved components. US Latinos of Mexican ancestry consistently had lower rates of health insurance coverage than did US non-Mexican Latinos. Approximately 65% of these disparities can be attributed to differences in observed characteristics of the Mexican ancestry population in the US (e.g., age, sex, income, employment status, education, citizenship, language and health condition). The remaining disparities may be attributed to unobserved heterogeneity that may include unobserved employment-related information (e.g., type of employment and firm size) and behavioral and idiosyncratic factors (e.g., risk aversion and cultural differences). This study confirmed that Latinos of Mexican ancestry were less likely to have health insurance than were non-Mexican Latinos. Moreover, while differences in observed socioeconomic and demographic factors accounted for most of these disparities, the share of unobserved heterogeneity accounted for 35% of these differences