Rate of Convergence for Cardy’s Formula

We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to their limit given by the Cardy–Smirnov formula. We use this result to obtain new upper and lower bounds of e[superscript O(√log logR)] R[superscript -1/3] for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R [superscript −1/3+o(1)].Natural Sciences and Engineering Research Council of Canada. Postdoctoral ScholarshipNational Science Foundation (U.S.). Graduate Research Fellowship Program (Award 1122374

Spectral properties of random graphs with fixed equitable partition

We define a graph to be $S$-regular if it contains an equitable partition given by a matrix $S$. These graphs are generalizations of both regular and bipartite, biregular graphs. An $S$-regular matrix is defined then as a matrix on an $S$-regular graph consistent with the graph's equitable partition. In this paper we derive the limiting spectral density for large, random $S$-regular matrices as well as limiting functions of certain statistics for their eigenvector coordinates as a function of eigenvalue. These limiting functions are defined in terms of spectral measures on $S$-regular trees. In general, these spectral measures do not have a closed-form expression; however, we provide a defining system of polynomials for them. Finally, we explore eigenvalue bounds of $S$-regular graph, proving an expander mixing lemma, Alon-Bopana bound, and other eigenvalue inequalities in terms of the eigenvalues of the matrix $S$.Comment: 24 pages, 3 figure

Exact synthesis of multiqubit Clifford-cyclotomic circuits

Let $n\geq 8$ be an integer divisible by 4. The Clifford-cyclotomic gate set $\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \mathrm{diag}(1,\zeta_n)$, where $\zeta_n$ is a primitive $n$-th root of unity. In this note, we show that, when $n$ is a power of 2, a multiqubit unitary matrix $U$ can be exactly represented by a circuit over $\mathcal{G}_n$ if and only if the entries of $U$ belong to the ring $\mathbb{Z}[1/2,\zeta_n]$. We moreover show that $\log(n)-2$ ancillas are always sufficient to construct a circuit for $U$. Our results generalize prior work to an infinite family of gate sets and show that the limitations that apply to single-qubit unitaries, for which the correspondence between Clifford-cyclotomic operators and matrices over $\mathbb{Z}[1/2,\zeta_n]$ fails for all but finitely many values of $n$, can be overcome through the use of ancillas

Molecular elasticity and the geometric phase

We present a method for solving the Worm Like Chain (WLC) model for twisting semiflexible polymers to any desired accuracy. We show that the WLC free energy is a periodic function of the applied twist with period 4 pi. We develop an analogy between WLC elasticity and the geometric phase of a spin half system. These analogies are used to predict elastic properties of twist-storing polymers. We graphically display the elastic response of a single molecule to an applied torque. This study is relevant to mechanical properties of biopolymers like DNA.Comment: five pages, one figure, revtex, revised in the light of referee's comments, to appear in PR

Evidence of superficial knowledge regarding antibiotics and their use: Results of two cross-sectional surveys in an urban informal settlement in Kenya

<div><p>We assessed knowledge and practices related to antibiotic use in Kibera, an urban informal settlement in Kenya. Surveys was employed at the beginning (entry) and again at the end (exit) of a 5-month longitudinal study of AMR. Two-hundred households were interviewed at entry, of which 149 were also interviewed at exit. The majority (>65%) of respondents in both surveys could name at least one antibiotic, with amoxicillin and cotrimoxazole jointly accounting for 85% and 77% of antibiotics mentioned during entry and exit, respectively. More than 80% of respondents felt antibiotics should not be shared or discontinued following the alleviation of symptoms. Nevertheless, 66% and 74% of respondents considered antibiotics effective for treating colds and flu in the entry and exit surveys, respectively. There was a high (87%, entry; 70% exit) level of reported antibiotic use (past 12 months) mainly for colds/flu, coughs and fever, with >80% of respondents obtaining antibiotics from health facilities and pharmacies. Less than half of respondents remembered getting information on the correct use of antibiotics, although 100% of those who did reported improved attitudes towards antibiotic use. Clinicians and community pharmacists were highly trusted information sources. Paired household responses (n = 149) generally showed improved knowledge and attitudes by the exit survey although practices were largely unchanged. Weak agreement (κ = -0.003 to 0.22) between survey responses suggest both that unintended learning had not occurred, and that participant responses were not based on established knowledge or behaviors. Targeted public education regarding antibiotics is needed to address this gap.</p></div

Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.

BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362

WHO global research priorities for antimicrobial resistance in human health

The WHO research agenda for antimicrobial resistance (AMR) in human health has identified 40 research priorities to be addressed by the year 2030. These priorities focus on bacterial and fungal pathogens of crucial importance in addressing AMR, including drug-resistant pathogens causing tuberculosis. These research priorities encompass the entire people-centred journey, covering prevention, diagnosis, and treatment of antimicrobial-resistant infections, in addition to addressing the overarching knowledge gaps in AMR epidemiology, burden and drivers, policies and regulations, and awareness and education. The research priorities were identified through a multistage process, starting with a comprehensive scoping review of knowledge gaps, with expert inputs gathered through a survey and open call. The priority setting involved a rigorous modified Child Health and Nutrition Research Initiative approach, ensuring global representation and applicability of the findings. The ultimate goal of this research agenda is to encourage research and investment in the generation of evidence to better understand AMR dynamics and facilitate policy translation for reducing the burden and consequences of AMR