On the negative Pell equation

Using a recent breakthrough of Smith, we improve the results of Fouvry and Kl\"uners on the solubility of the negative Pell equation. Let $\mathcal{D}$ denote the set of fundamental discriminants having no prime factors congruent to $3$ modulo $4$. Stevenhagen conjectured that the density of $D$ in $\mathcal{D}$ such that the negative Pell equation $x^2-Dy^2=-1$ is solvable with $x,y\in\mathbb{Z}$ is $58.1\%$, to the nearest tenth of a percent. By studying the distribution of the $8$-rank of narrow class groups $\mathrm{CL}^+(D)$ of $\mathbb{Q}(\sqrt{D})$, we prove that the infimum of this density is at least $53.8\%$

Terahertz active spatial filtering through optically tunable hyperbolic metamaterials

We theoretically consider infrared-driven hyperbolic metamaterials able to spatially filtering terahertz radiation. The metamaterial is a slab made of alternating semiconductor and dielectric layers whose homogenized uniaxial response, at terahertz frequencies, shows principal permittivities of different signs. The gap provided by metamaterial hyperbolic dispersion allows the slab to stop spatial frequencies within a bandwidth tunable by changing the infrared radiation intensity. We numerically prove the device functionality by resorting to full wave simulation coupled to the dynamics of charge carries photoexcited by infrared radiation in semiconductor layers.Comment: 3 pages, 4 figures. Submitted for publication on Applied Physics Letter

Ultra High Throughput Sequencing in Human DNA Variation Detection: A Comparative Study on the NDUFA3-PRPF31 Region

BACKGROUND: Ultra high throughput sequencing (UHTS) technologies find an important application in targeted resequencing of candidate genes or of genomic intervals from genetic association studies. Despite the extraordinary power of these new methods, they are still rarely used in routine analysis of human genomic variants, in part because of the absence of specific standard procedures. The aim of this work is to provide human molecular geneticists with a tool to evaluate the best UHTS methodology for efficiently detecting DNA changes, from common SNPs to rare mutations. METHODOLOGY/PRINCIPAL FINDINGS: We tested the three most widespread UHTS platforms (Roche/454 GS FLX Titanium, Illumina/Solexa Genome Analyzer II and Applied Biosystems/SOLiD System 3) on a well-studied region of the human genome containing many polymorphisms and a very rare heterozygous mutation located within an intronic repetitive DNA element. We identify the qualities and the limitations of each platform and describe some peculiarities of UHTS in resequencing projects. CONCLUSIONS/SIGNIFICANCE: When appropriate filtering and mapping procedures are applied UHTS technology can be safely and efficiently used as a tool for targeted human DNA variations detection. Unless particular and platform-dependent characteristics are needed for specific projects, the most relevant parameter to consider in mainstream human genome resequencing procedures is the cost per sequenced base-pair associated to each machine

The effect of sun-dried raisins (Vitis vinifera L.) on the in vitro composition of the gut microbiota

Modulation of the human gut microbiota has proven to have beneficial effects on host health. Sun-dried raisins exhibited prebiotic potential

“Silver Linings Graybook”: A Comparative Study of Age-friendly Development in Hong Kong and Manchester

In face of global population ageing, the World Health Organization (WHO) launched the Age-friendly Movement in 2006 and developed the WHO age-friendly framework that is being widely adopted around the world. Although there is an extensive body of literature on age-friendly development following the WHO movement, limited discussion was on the process at the neighbourhood level, particularly in relation to the interplay of different stakeholders. To fill in this research gap, this study adopted a neo-institutionalist lens with elements of street-level bureaucracy in comparing the process of how age-friendliness is being enacted at the neighbourhood scale in Manchester and Hong Kong, through a comparative case study approach. This is the one of the first truly international comparisons on age-friendly cities of western and non-western contexts. Data was collected through document analysis, in-depth interviews and participatory observation. The findings of this thesis document the process of age-friendliness at the neighbourhood level, with rich detail on the interplay of the different stakeholders involved. The major contribution of these findings is bringing a new perspective in understanding age-friendly processes by introducing the role of street-level bureaucrats (SLB), who are the determining agent in shaping how age-friendliness is being enacted at the neighbourhood level. Moreover, the findings in both cases also suggest an interdependent relationship between the processes at the city and neighbourhood levels. This thesis also suggests that the role of academics can be strengthened through a collaborative partnership of different stakeholders in developing age-friendliness at the community level. Finally, by contrasting the two case studies, it is shown that the ways of interpreting age-friendliness among different stakeholders vary place by place. This thesis hence concludes by suggesting age-friendliness as a fluid concept that should be embraced with a flexible mindset

Assessment of Hypertension Using Clinical Electrocardiogram Features: A First-Ever Review

Hypertension affects an estimated 1.4 billion people and is a major cause of morbidity and mortality worldwide. Early diagnosis and intervention can potentially decrease cardiovascular events later in life. However, blood pressure (BP) measurements take time and require training for health care professionals. The measurements are also inconvenient for patients to access, numerous daily variables affect BP values, and only a few BP readings can be collected per session. This leads to an unmet need for an accurate, 24-h continuous, and portable BP measurement system. Electrocardiograms (ECGs) have been considered as an alternative way to measure BP and may meet this need. This review summarizes the literature published from January 1, 2010, to January 1, 2020, on the use of only ECG wave morphology to monitor BP or identify hypertension. From 35 articles analyzed (9 of those with no listed comorbidities and confounders), the P wave, QTc intervals and TpTe intervals may be promising for this purpose. Unfortunately, with the limited number of articles and the variety of participant populations, we are unable to make conclusions about the effectiveness of ECG-only BP monitoring. We provide 13 recommendations for future ECG-only BP monitoring studies and highlight the limited findings in pregnant and pediatric populations. With the advent of convenient and portable ECG signal recording in smart devices and wearables such as watches, understanding how to apply ECG-only findings to identify hypertension early is crucial to improving health outcomes worldwide

Sequence randomness and polymer collapse transitions

Contrary to expectations based on Harris' criterion, chain disorder with frustration can modify the universality class of scaling at the theta transition of heteropolymers. This is shown for a model with random two-body potentials in 2D on the basis of exact enumeration and accurate Monte Carlo results. When frustration grows beyond a certain finite threshold, the temperature below which disorder becomes relevant coincides with the theta one and scaling exponents definitely start deviating from those valid for homopolymers.Comment: 4 pages, 4 eps figure

Early and Highly Suppressive ART are Main Factors Associated with Low Viral Reservoir in European Perinatally HIV Infected Children

Abstract BACKGROUND: Future strategies aiming to achieve HIV-1 remission are likely to target individuals with small reservoir size. SETTING: We retrospectively investigated factors associated with HIV-1 DNA levels in European, perinatally HIV-infected children starting ART <6 months of age. METHODS: Total HIV-1 DNA was measured from 51 long-term suppressed children 6.3 years (median) after initial viral suppression. Factors associated with log10 total HIV-1 DNA were analyzed using linear regression. RESULTS: At ART initiation, children were aged median [IQR] 2.3 [1.2,4.1] months, CD4% 37 [24,45] %, CD8% 28 [18,36] %, log10 plasma viral load (VL) 5.4 [4.4,5.9] copies/ml. Time to viral suppression was 7.98 [4.6,19.3] months. Following suppression, 13 (25%) children had suboptimal response [ 652 consecutive VL50-400 followed by VL<50] and/or experienced periods of virological failure [ 652 consecutive VL 65400 followed by VL<50]. Median total HIV-1 DNA was 43 [6,195] copies/10 PBMC.Younger age at therapy initiation was associated with lower total HIV-1 DNA (adjusted coefficient [AC] 0.12 per month older, p=0.0091), with a month increase in age at ART start being associated with a 13% increase in HIV DNA. Similarly, a higher proportion of time spent virally suppressed (AC 0.10 per 10% higher, p=0.0022) and absence of viral failure/suboptimal response (AC 0.34 for those with fail/ suboptimal response, p=0.0483) were associated with lower total HIV-1 DNA. CONCLUSION: Early ART initiation and a higher proportion of time suppressed are linked with lower total HIV-1 DNA. Early ART start and improving adherence in perinatally HIV-1 infected children minimize the size of viral reservoir.This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial License 4.0 (CCBY-NC), where it is permissible to download, share, remix, transform, and buildup the work provided it is properly cited. The work cannot be used commercially without permission from the journal

Testing simplified protein models of the hPin1 WW domain

The WW domain of the human Pin1 protein for its simple topology and the large amount of experimental data is an ideal candidate to assess theoretical approaches to protein folding. The purpose of the present work is to compare the reliability of the chemically-based Sorenson/Head-Gordon (SHG) model and a standard native centric model in reproducing through molecular dynamics simulations some of the well known features of the folding transition of this small domain. Our results show that the G\={o} model correctly reproduces the cooperative, two-state, folding mechanism of the WW-domain, while the SHG model predicts a transition occurring in two stages: a collapse followed by a structural rearrangement. The lack of a cooperative folding in the SHG simulations appears to be related to the non-funnel shape of the energy landscape featuring a partitioning of the native valley in sub-basins corresponding to different chain chiralities. However the SHG approach remains more reliable in estimating the $\Phi$-values with respect to G\={o}-like description. This may suggest that the WW-domain folding process is stirred by energetic and topological factors as well, and it highlights the better suitability of chemically-based models in simulating mutations.Comment: RevTex4: 12 pages and 13 eps-figure file