Lucky Cars and the Quicksort Algorithm

Quicksort is a classical divide-and-conquer sorting algorithm. It is a comparison sort that makes an average of $2(n+1)H_n - 4n$ comparisons on an array of size $n$ ordered uniformly at random, where $H_n = \sum_{i=1}^n\frac{1}{i}$ is the $n$th harmonic number. Therefore, it makes $n!\left[2(n+1)H_n - 4n\right]$ comparisons to sort all possible orderings of the array. In this article, we prove that this count also enumerates the parking preference lists of $n$ cars parking on a one-way street with $n$ parking spots resulting in exactly $n-1$ lucky cars (i.e., cars that park in their preferred spot). For $n\geq 2$, both counts satisfy the second order recurrence relation $f_n=2nf_{n-1}-n(n-1)f_{n-2}+2(n-1)!$ with $f_0=f_1=0$.Comment: 8 pages, and 2 figures, to appear in The American Mathematical Monthl

Sparse Graphical Designs via Linear Programming

Graphical designs are a framework for sampling and numerical integration of functions on graphs. In this note, we introduce a method to address the trade-off between graphical design sparsity and accuracy. We show how to obtain sparse graphical designs via linear programming and design objective functions that aim to maximize their accuracy. We showcase our approach using yellow taxicab data from New York City

Permutation Invariant Parking Assortments

We introduce parking assortments, a generalization of parking functions with cars of assorted lengths. In this setting, there are $n\in\mathbb{N}$ cars of lengths $\mathbf{y}=(y_1,y_2,\ldots,y_n)\in\mathbb{N}^n$ entering a one-way street with $m=\sum_{i=1}^ny_i$ parking spots. The cars have parking preferences $\mathbf{x}=(x_1,x_2,\ldots,x_n)\in[m]^n$, where $[m]:=\{1,2,\ldots,m\}$, and enter the street in order. Each car $i \in [n]$, with length $y_i$ and preference $x_i$, follows a natural extension of the classical parking rule: it begins looking for parking at its preferred spot $x_i$ and parks in the first $y_i$ contiguously available spots thereafter, if there are any. If all cars are able to park under the preference list $\mathbf{x}$, we say $\mathbf{x}$ is a parking assortment for $\mathbf{y}$. Parking assortments also generalize parking sequences, introduced by Ehrenborg and Happ, since each car seeks for the first contiguously available spots it fits in past its preference. Given a parking assortment $\mathbf{x}$ for $\mathbf{y}$, we say it is permutation invariant if all rearrangements of $\mathbf{x}$ are also parking assortments for $\mathbf{y}$. While all parking functions are permutation invariant, this is not the case for parking assortments in general, motivating the need for a characterization of this property. Although obtaining a full characterization for arbitrary $n\in\mathbb{N}$ and $\mathbf{y}\in\mathbb{N}^n$ remains elusive, we do so for $n=2,3$. Given the technicality of these results, we introduce the notion of minimally invariant car lengths, for which the only invariant parking assortment is the all ones preference list. We provide a concise, oracle-based characterization of minimally invariant car lengths for any $n\in\mathbb{N}$. Our results around minimally invariant car lengths also hold for parking sequences

CIBERER : Spanish national network for research on rare diseases: A highly productive collaborative initiative

Altres ajuts: Instituto de Salud Carlos III (ISCIII); Ministerio de Ciencia e Innovación.CIBER (Center for Biomedical Network Research; Centro de Investigación Biomédica En Red) is a public national consortium created in 2006 under the umbrella of the Spanish National Institute of Health Carlos III (ISCIII). This innovative research structure comprises 11 different specific areas dedicated to the main public health priorities in the National Health System. CIBERER, the thematic area of CIBER focused on rare diseases (RDs) currently consists of 75 research groups belonging to universities, research centers, and hospitals of the entire country. CIBERER's mission is to be a center prioritizing and favoring collaboration and cooperation between biomedical and clinical research groups, with special emphasis on the aspects of genetic, molecular, biochemical, and cellular research of RDs. This research is the basis for providing new tools for the diagnosis and therapy of low-prevalence diseases, in line with the International Rare Diseases Research Consortium (IRDiRC) objectives, thus favoring translational research between the scientific environment of the laboratory and the clinical setting of health centers. In this article, we intend to review CIBERER's 15-year journey and summarize the main results obtained in terms of internationalization, scientific production, contributions toward the discovery of new therapies and novel genes associated to diseases, cooperation with patients' associations and many other topics related to RD research

Berry Flesh and Skin Ripening Features in Vitis vinifera as Assessed by Transcriptional Profiling

Background Ripening of fleshy fruit is a complex developmental process involving the differentiation of tissues with separate functions. During grapevine berry ripening important processes contributing to table and wine grape quality take place, some of them flesh- or skin-specific. In this study, transcriptional profiles throughout flesh and skin ripening were followed during two different seasons in a table grape cultivar ‘Muscat Hamburg’ to determine tissue-specific as well as common developmental programs. Methodology/Principal Findings Using an updated GrapeGen Affymetrix GeneChip® annotation based on grapevine 12×v1 gene predictions, 2188 differentially accumulated transcripts between flesh and skin and 2839 transcripts differentially accumulated throughout ripening in the same manner in both tissues were identified. Transcriptional profiles were dominated by changes at the beginning of veraison which affect both pericarp tissues, although frequently delayed or with lower intensity in the skin than in the flesh. Functional enrichment analysis identified the decay on biosynthetic processes, photosynthesis and transport as a major part of the program delayed in the skin. In addition, a higher number of functional categories, including several related to macromolecule transport and phenylpropanoid and lipid biosynthesis, were over-represented in transcripts accumulated to higher levels in the skin. Functional enrichment also indicated auxin, gibberellins and bHLH transcription factors to take part in the regulation of pre-veraison processes in the pericarp, whereas WRKY and C2H2 family transcription factors seems to more specifically participate in the regulation of skin and flesh ripening, respectively. Conclusions/Significance A transcriptomic analysis indicates that a large part of the ripening program is shared by both pericarp tissues despite some components are delayed in the skin. In addition, important tissue differences are present from early stages prior to the ripening onset including tissue-specific regulators. Altogether, these findings provide key elements to understand berry ripening and its differential regulation in flesh and skin.This study was financially supported by GrapeGen Project funded by Genoma España within a collaborative agreement with Genome Canada. The authors also thank The Ministerio de Ciencia e Innovacion for project BIO2008-03892 and a bilateral collaborative grant with Argentina (AR2009-0021). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewe

Mortality from gastrointestinal congenital anomalies at 264 hospitals in 74 low-income, middle-income, and high-income countries: a multicentre, international, prospective cohort study

Summary Background Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. Methods We did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung’s disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. Findings We included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung’s disease) from 264 hospitals (89 in high-income countries, 166 in middleincome countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58·0%) were male. Median gestational age at birth was 38 weeks (IQR 36–39) and median bodyweight at presentation was 2·8 kg (2·3–3·3). Mortality among all patients was 37 (39·8%) of 93 in low-income countries, 583 (20·4%) of 2860 in middle-income countries, and 50 (5·6%) of 896 in high-income countries (p<0·0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90·0%] of ten in lowincome countries, 97 [31·9%] of 304 in middle-income countries, and two [1·4%] of 139 in high-income countries; p≤0·0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2·78 [95% CI 1·88–4·11], p<0·0001; middle-income vs high-income countries, 2·11 [1·59–2·79], p<0·0001), sepsis at presentation (1·20 [1·04–1·40], p=0·016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4–5 vs ASA 1–2, 1·82 [1·40–2·35], p<0·0001; ASA 3 vs ASA 1–2, 1·58, [1·30–1·92], p<0·0001]), surgical safety checklist not used (1·39 [1·02–1·90], p=0·035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1·96, [1·41–2·71], p=0·0001; parenteral nutrition 1·35, [1·05–1·74], p=0·018). Administration of parenteral nutrition (0·61, [0·47–0·79], p=0·0002) and use of a peripherally inserted central catheter (0·65 [0·50–0·86], p=0·0024) or percutaneous central line (0·69 [0·48–1·00], p=0·049) were associated with lower mortality. Interpretation Unacceptable differences in mortality exist for gastrointestinal congenital anomalies between lowincome, middle-income, and high-income countries. Improving access to quality neonatal surgical care in LMICs will be vital to achieve Sustainable Development Goal 3.2 of ending preventable deaths in neonates and children younger than 5 years by 2030

Leishmania Uses Mincle to Target an Inhibitory ITAM Signaling Pathway in Dendritic Cells that Dampens Adaptive Immunity to Infection

C-type lectin receptors sense a diversity of endogenous and exogenous ligands that may trigger differential responses. Here, we have found that human and mouse Mincle bind to a ligand released by Leishmania, a eukaryote parasite that evades an effective immune response. Mincle-deficient mice had milder&nbsp;dermal pathology and a tenth of the parasite burden&nbsp;compared to wild-type mice after Leishmania major&nbsp;intradermal ear infection. Mincle deficiency enhanced adaptive immunity against the&nbsp;parasite, correlating with increased activation, migration, and priming by Mincle-deficient dendritic cells (DCs). Leishmania triggered a Mincle-dependent inhibitory axis characterized by SHP1 coupling to the FcRγ chain. Selective loss of SHP1 in CD11c+ cells phenocopies enhanced adaptive immunity to Leishmania. In conclusion, Leishmania shifts Mincle to an inhibitory ITAM (ITAMi) configuration that impairs DC activation. Thus, ITAMi can be exploited for immune evasion by a pathogen and may represent a paradigm for ITAM-coupled receptors sensing self and non-self