Variations on Twins in Permutations

Let $\pi$ be a permutation of the set $[n]=\{1,2,\dots, n\}$. Two disjoint order-isomorphic subsequences of $\pi$ are called twins. How long twins are contained in every permutation? The well known Erdős-Szekeres theorem implies that there is always a pair of twins of length $\Omega(\sqrt{n})$. On the other hand, by a simple probabilistic argument Gawron proved that for every $n\geqslant 1$ there exist permutations with all twins having length $O(n^{2/3})$. He conjectured that the latter bound is the correct size of the longest twins guaranteed in every permutation. We support this conjecture by showing that almost all permutations contain twins of length $\Omega(n^{2/3}/\log n^{1/3})$. Recently, Bukh and Rudenko have tweaked our proof and removed the log-factor. For completeness, we also present our version of their proof (see Remark 2 below on the interrelation between the two proofs). In addition, we study several variants of the problem with diverse restrictions imposed on the twins. For instance, if we restrict attention to twins avoiding a fixed permutation $\tau$, then the corresponding extremal function equals $\Theta(\sqrt{n})$, provided that $\tau$ is not monotone. In case of block twins (each twin occupies a segment) we prove that it is $(1+o(1))\frac{\log n}{\log\log n}$, while for random permutations it is twice as large. For twins that jointly occupy a segment (tight twins), we prove that for every $n$ there are permutations avoiding them on all segments of length greater than $24$.

Testing overidentifying restrictions with many instruments and heteroskedasticity using regularized Jackknife IV

This paper proposes a new overidentifying restrictions test in a linear model when the number of instruments (possibly weak) may be smaller or larger than the sample size n or even infinite in a heteroskedastic framework. The proposed J test combines two techniques: the Jackknife method and the regularization technique which consists in stabilizing the projection matrix. We theoretically show that our new test achieves the asymptotically correct size in the presence of many instruments. The simulation results demonstrate that our modified J statistic test has better empirical properties in small samples than existing J tests. We also propose a regularized F-test to assess the strength of the instruments, which is robust to heteroskedasticity and many instruments.

An Autocrine Negative Feedback Loop Inhibits Dictyostelium discoideum Proliferation through Pathways Including IP3/Ca 2+

Many mammalian tissues such as the liver have the remarkable ability to regulate their size and have their cells stop proliferating when the tissue reaches the correct size. One possible mechanism involves the cells secreting a signal that they all sense, and a high level of the signal tells the cells that there are enough of them and to stop proliferating.

An assessment of radiation use, knowledge and concerns in trainee cardiologists in Ireland

Objective To evaluate knowledge, routine use and concerns of trainee cardiologists in the Republic of Ireland regarding radiation use in the cardiac catheterization laboratory. Methods We handed out a Radiation Questionnaire to cardiology trainees in February 2020 at the Irish Cardiac Society “Spring Meeting”. The questionnaire assessed radiation protection use amongst trainees and tested knowledge of X-ray basics. Results Many trainees report inadequate access to properly sized lead protection, and infrequent dosimeter usage. Over one-third of trainees report musculoskeletal issues from wearing leads, the majority of whom use correct size lead <60% of the time. 33.3% report radiation concerns will affect their decision making regarding subspeciality training, but notably 83.3% of females and only 19% of males surveyed report this, showing this is a bigger issue for females in cardiology. Less than half of trainees feel adequately educated about radiation. Conclusion Our assessment show deficiencies in the provision and use of personal protective equipment to trainees, highlights extra radiation concerns of female cardiology trainees, and notes gaps in knowledge in radiation use. Advances in knowledge Our assessment highlights deficiencies in the education of cardiology trainees regarding ionizing radiation, and suggests this area needs to be improved upon.

Improving the Power Supply Performance in Rural Smart Grids with Photovoltaic DG by Optimizing Fuse Selection

The recent increase in the use of renewable sources in electrical systems has transformed the electrical distribution network with the subsequent implementation of the distributed generation (DG) concept. The high penetration level of photovoltaic units increases their injected fault current that may result in a lack of coordination of fuse reclosers in distribution networks. One of the main protection devices that is generally used in rural distribution networks is the fuse. A correct size selection is key for ensuring good operation and coordination with other protection devices. The DG implementation makes the selection above more difficult, as the current flow both in steady state and in case of short-circuit is subject to alterations. A new protection fuse selection method for distribution networks with implemented DG is proposed in this paper with the aim of ensuring an effective coordination between them, avoiding untimely behaviors. Different case studies have been analyzed (for diverse locations of DG in the network with various penetration levels which represent 25%, 50%, 75%, and 100% of the total installed load), using an IEEE 13-node test feeder. Besides, a new model to analyze fuse performance is proposed in this work. This model has proven to fit the manufacturer’s data well, with a maximum error of 2% within the normal trip current values.

Arabidopsis sepals: A model system for the emergent process of morphogenesis

During development, Arabidopsis thaliana sepal primordium cells grow, divide and interact with their neighbours, giving rise to a sepal with the correct size, shape and form. Arabidopsis sepals have proven to be a good system for elucidating the emergent processes driving morphogenesis due to their simplicity, their accessibility for imaging and manipulation, and their reproducible development. Sepals undergo a basipetal gradient of growth, with cessation of cell division, slow growth and maturation starting at the tip of the sepal and progressing to the base. In this review, I discuss five recent examples of processes during sepal morphogenesis that yield emergent properties: robust size, tapered tip shape, laminar shape, scattered giant cells and complex gene expression patterns. In each case, experiments examining the dynamics of sepal development led to the hypotheses of local rules. In each example, a computational model was used to demonstrate that these local rules are sufficient to give rise to the emergent properties of morphogenesis.

A new primer set for amplification of ITS-rDNA in Ditylenchus destructor

A technique was developed for the identification of Ditylenchus destructor nematode belonging to the Ditylenchus genus, based on the use of different primers for polymerase chain reaction (PCR). Two universal ribosomal primers were amplified to the internal transcribed spacer region ITS-rDNA. The sequencing of PCR products confirmed the polymorphism between species. The primers were sensitive to generate a particular band of the correct size (300bp) from the DNA template of a single, separate D. destructor stage of development. Screening populations of D. destructor from Iran and the Russian Federation have tested the reliability of the primers, and the expected size of the band was produced for all test populations. Ditylenchus destructor closely related species have also been tested and no specific band was amplified. Such results showed that the primers currently developed are useful for quantifying the D. destructo r density in potato tuber.

Charting the unknown currents of cellular flows and forces

ABSTRACTOne of the central questions in developmental biology concerns how cells become organized into tissues of the correct size, shape and polarity. This organization depends on the implementation of a cell's genetic information to give rise to specific and coordinated cell behaviors, including cell division and cell shape change. The execution of these cell behaviors requires the active generation of mechanical forces. However, understanding how force generation is controlled and, importantly, coordinated among many cells in a tissue was little explored until the early 2000s. Suzanne Eaton was one of the pioneers in this emerging field of developmental tissue mechanics. As we briefly review here, she connected the quantitative analysis of cell behaviors with genetic assays, and integrated physical modeling with measurements of mechanical forces to reveal fundamental insights into epithelial morphogenesis at cell- and tissue-level scales.

Control of Drosophila wing size by morphogen range and hormonal gating

The stereotyped dimensions of animal bodies and their component parts result from tight constraints on growth. Yet, the mechanisms that stop growth when organs reach the right size are unknown. Growth of the Drosophila wing—a classic paradigm—is governed by two morphogens, Decapentaplegic (Dpp, a BMP) and Wingless (Wg, a Wnt). Wing growth during larval life ceases when the primordium attains full size, concomitant with the larval-to-pupal molt orchestrated by the steroid hormone ecdysone. Here, we block the molt by genetically dampening ecdysone production, creating an experimental paradigm in which the wing stops growing at the correct size while the larva continues to feed and gain body mass. Under these conditions, we show that wing growth is limited by the ranges of Dpp and Wg, and by ecdysone, which regulates the cellular response to their signaling activities. Further, we present evidence that growth terminates because of the loss of two distinct modes of morphogen action: 1) maintenance of growth within the wing proper and 2) induced growth of surrounding “pre-wing” cells and their recruitment into the wing. Our results provide a precedent for the control of organ size by morphogen range and the hormonal gating of morphogen action.

USING THE CORRECT SIZE OF AMPLATZ SHEATH DURING PERCUTANEOUS NEPHROLITHOTOMY – A NOVEL METHOD.

Purpose- To choose appropriate size Amplatz sheath, during percutaneous nephrolithotomy (PCNL) based on retrograde nephrogram (RGP). Material and methods -Standard PCNL ,in prone position ,was performed in 20 patients. All patients had placement of Amplatz sheath based on retrograde nephrostogram study, all patients after surgery had nephrostomy tube for draining collecting system. The preoperative and postoperative renal parameters ,hemoglobin ,mean operating time and mean hospitalisation stay was measured. Results- There was no significant difference in the pre and postoperative hemoglobin and creatinine levels . Median operating time was 60.5 mins (45 to 98 mins).The median hospitalisation stay was 4.6 days( 3 to 7 days).There was no intraoperative pelvic wall or infundibular injury. Conclusion- Choosing correct size Amplatz sheath decreases the incidence of bleeding and renal function impairment.