Six Permutation Patterns Force Quasirandomness

A sequence $\pi_1,\pi_2,\dots$ of permutations is said to be "quasirandom" if the induced density of every permutation $\sigma$ in $\pi_n$ converges to $1/|\sigma|!$ as $n\to\infty$. We prove that $\pi_1,\pi_2,\dots$ is quasirandom if and only if the density of each permutation $\sigma$ in the set $$\{123,321,2143,3412,2413,3142\}$$ converges to $1/|\sigma|!$. Previously, the smallest cardinality of a set with this property, called a "quasirandom-forcing" set, was known to be between four and eight. In fact, we show that there is a single linear expression of the densities of the six permutations in this set which forces quasirandomness and show that this is best possible in the sense that there is no shorter linear expression of permutation densities with positive coefficients with this property. In the language of theoretical statistics, this expression provides a new nonparametric independence test for bivariate continuous distributions related to Spearman's $\rho$.Comment: 27 pages, 1 figure, 5 appendices included as ancillary file

Extremal Bounds for Three-Neighbour Bootstrap Percolation in Dimensions Two and Three

For $r\geq1$, the $r$-neighbour bootstrap process in a graph $G$ starts with a set of infected vertices and, in each time step, every vertex with at least $r$ infected neighbours becomes infected. The initial infection percolates if every vertex of $G$ is eventually infected. We exactly determine the minimum cardinality of a set that percolates for the $3$-neighbour bootstrap process when $G$ is a $3$-dimensional grid with minimum side-length at least $11$. We also characterize the integers $a$ and $b$ for which there is a set of cardinality $\frac{ab+a+b}{3}$ that percolates for the $3$-neighbour bootstrap process in the $a\times b$ grid; this solves a problem raised by Benevides, Bermond, Lesfari and Nisse [HAL Research Report 03161419v4, 2021].Comment: 45 page

Performance Evaluation of Bluetooth Low Energy Communication

Bluetooth Low Energy (BLE), also known as Bluetooth Smart is the new power efficient version of Bluetooth. With the massive increase in the use of IoT devices, their compatibility and suitability for use with BLE, it has become an important protocol for communication. The performance of the protocol in terms of throughput, however, remains untested. Several parameters like connection interval, packet size per connection interval, data length extension and others constitute the implementation of the BLE protocol on a device. These parameters directly or indirectly effect the throughput of devices communicating over BLE. In this paper, we evaluated BLE performance by performing experiments to calculate throughput with varying values of connection interval and MTU size of application payload. We provide experimental values of throughput and compare it with the theoretically expected results and discuss the pattern and aberration found

Overview and Evaluation of Conceptual Strategies for Accessing CPU-Dependent Execution Resources in Grid Infrastructures

The emergence of many-core and massively-parallel computational accelerators (e.g., GPGPUs) has led to user demand for such resources in grid infrastructures. A widely adopted approach for discovering and accessing such resources has, however, yet to emerge.  GPGPUs are an example of a larger class of computational resources, characterized in part by dependence on an allocated CPU. This paper terms such resources "CPU-Dependent Execution Resources" (CDERs). Five conceptual strategies for discovering and accessing CDERs are described and evaluated against key criteria, and all five strategies are compliant with GLUE 1.3, GLUE 2.0, or both. From this evaluation, two of the presented strategies clearly emerge as providing the greatest flexibility for publishing both static and dynamic CDER information and identifying CDERs that satisfy specific job requirements. Furthermore, a two-phase approach to job-submission is proposed for those jobs requiring access to CDERs. The approach is compatible with existing grid services.  Examples are provided to illustrate job submission under each strategy

Ectopy on a single 12‐lead ECG, incident cardiac myopathy, and death in the community

BackgroundAtrial fibrillation and heart failure are 2 of the most common diseases, yet ready means to identify individuals at risk are lacking. The 12-lead ECG is one of the most accessible tests in medicine. Our objective was to determine whether a premature atrial contraction observed on a standard 12-lead ECG would predict atrial fibrillation and mortality and whether a premature ventricular contraction would predict heart failure and mortality.Methods and resultsWe utilized the CHS (Cardiovascular Health) Study, which followed 5577 participants for a median of 12 years, as the primary cohort. The ARIC (Atherosclerosis Risk in Communities Study), the replication cohort, captured data from 15 792 participants over a median of 22 years. In the CHS, multivariable analyses revealed that a baseline 12-lead ECG premature atrial contraction predicted a 60% increased risk of atrial fibrillation (hazard ratio, 1.6; 95% CI, 1.3-2.0; P<0.001) and a premature ventricular contraction predicted a 30% increased risk of heart failure (hazard ratio, 1.3; 95% CI, 1.0-1.6; P=0.021). In the negative control analyses, neither predicted incident myocardial infarction. A premature atrial contraction was associated with a 30% increased risk of death (hazard ratio, 1.3; 95% CI, 1.1-1.5; P=0.008) and a premature ventricular contraction was associated with a 20% increased risk of death (hazard ratio, 1.2; 95% CI, 1.0-1.3; P=0.044). Similarly statistically significant results for each analysis were also observed in ARIC.ConclusionsBased on a single standard ECG, a premature atrial contraction predicted incident atrial fibrillation and death and a premature ventricular contraction predicted incident heart failure and death, suggesting that this commonly used test may predict future disease

Tumour inflammatory infiltrate predicts survival following curative resection for node-negative colorectal cancer

<b>Background</b>: A pronounced tumour inflammatory infiltrate is known to confer a good outcome in colorectal cancer. Klintrup and colleagues reported a structured assessment of the inflammatory reaction at the invasive margin scoring low grade or high grade. The aim of the present study was to examine the prognostic value of tumour inflammatory infiltrate in node-negative colorectal cancer. <b>Methods</b>: Two hundred patients had undergone surgery for node-negative colorectal cancer between 1997 and 2004. Specimens were scored with Jass’ and Klintrup’s criteria for peritumoural infiltrate. Pathological data were taken from the reports at that time. <b>Results</b>: Low-grade inflammatory infiltrate assessed using Klintrup’s criteria was an independent prognostic factor in node-negative disease. In patients with a low-risk Petersen Index (n = 179), low-grade infiltrate carried a threefold increased risk of cancer death. Low-grade infiltrate was related to increasing T stage and an infiltrating margin. <b>Conclusion</b>: Assessment of inflammatory infiltrate using Klintrup’s criteria provides independent prognostic information on node-negative colorectal cancer. A high-grade local inflammatory response may represent effective host immune responses impeding tumour growth

Effectiveness of measures to eradicate Staphylococcus aureus carriage in patients with community-associated skin and soft-tissue infections: A randomized trial

BACKGROUND: Despite a paucity of evidence, decolonization measures are prescribed for outpatients with recurrent Staphylococcus aureus skin and soft tissue infections (SSTI). OBJECTIVE: Compare the effectiveness of four regimens for eradicating S. aureus carriage. DESIGN: Open-label, randomized controlled trial. Colonization status and recurrent SSTI were ascertained at one and four months. SETTING: Barnes-Jewish and St. Louis Children’s Hospitals, St. Louis, Missouri, 2007–2009. PARTICIPANTS: Three hundred patients with community-onset SSTI and S. aureus colonization in the nares, axilla, or inguinal folds. INTERVENTIONS: Participants were randomized to receive no therapeutic intervention (controls) or perform one of three 5-day regimens: 2% mupirocin ointment applied to the nares twice daily, intranasal mupirocin plus daily 4% chlorhexidine body washes, or intranasal mupirocin plus daily dilute bleach water baths. RESULTS: Among 244 participants with one-month colonization data, modified intention-to-treat analysis revealed S. aureus eradication in 38% of participants in the education only (control) group; 56% in the mupirocin group (p=0.03 vs. controls); 55% in the mupirocin/chlorhexidine group (p=0.05); and 63% in the mupirocin/bleach group (p=0.006). Of 229 participants with four-month colonization data, eradication rates were 48% in controls; 56% for mupirocin only (p=0.40 vs. controls); 54% for mupirocin/chlorhexidine (p=0.51); and 71% for mupirocin/bleach (p=0.02). At one and four months, respectively, recurrent SSTI was reported by 20% and 36% of participants. CONCLUSIONS: An inexpensive regimen of dilute bleach baths, intranasal mupirocin, and hygiene education effectively eradicated S. aureus over four months. High rates of recurrent SSTI suggest factors other than endogenous colonization as important determinants of infection