The Selberg integral and Young books

The Selberg integral is an important integral first evaluated by Selberg in 1944. Stanley found a combinatorial interpretation of the Selberg integral in terms of permutations. In this paper, new combinatorial objects "Young books" are introduced and shown to have a connection with the Selberg integral. This connection gives an enumeration formula for Young books. It is shown that special cases of Young books become standard Young tableaux of various shapes: shifted staircases, squares, certain skew shapes, and certain truncated shapes. As a consequence, product formulas for the number of standard Young tableaux of these shapes are obtained.Comment: 13 pages, 11 figure

The Selberg integral and Young books

The Selberg integral is an important integral first evaluated by Selberg in 1944. Stanley found a combinatorial interpretation of the Selberg integral in terms of permutations. In this paper, new combinatorial objects "Young books'' are introduced and shown to have a connection with the Selberg integral. This connection gives an enumeration formula for Young books. It is shown that special cases of Young books become standard Young tableaux of various shapes: shifted staircases, squares, certain skew shapes, and certain truncated shapes. As a consequence, enumeration formulas for standard Young tableaux of these shapes are obtained

Effect of Multiple Quantum Well Periods on Structural Properties and Performance of Extended Short-Wavelength Infrared LEDs

We present research on the role of multiple quantum well periods in extended short-wavelength infrared InGaAs/InAsPSb type-I LEDs. The fabricated LEDs consisted of 6, 15, and 30 quantum well periods, and we evaluated the structural properties and device performance through a combination of theoretical simulations and experimental characterization. The strain and energy band offset was precisely controlled by carefully adjusting the composition of the InAsPSb quaternary material, achieving high valence and conduction band offsets of 350 meV and 94 meV, respectively. Our LEDs demonstrated a high degree of relaxation of 94-96 %. Additionally, we discovered that the temperature-dependent dark current characterization attributed to generation-recombination and trap-assign tunneling, with trap-assign tunneling being more dominant at lower current injections. Electroluminescence analysis revealed that the predominant emission mechanism of the LEDs originated from localized exciton and free exciton radiative recombination, which the 30 quantum wells LED exhibited the highest contribution of the localized exciton/free exciton radiative recombination. We observed that increasing the quantum well periods from 6 to 15 led to an increase in the 300 K electroluminescence intensity of the LED. However, extending the quantum well period to 30 resulted in a decline in emission intensity due to the degradation of the epitaxial film quality

Lithium normalizes ASD-related neuronal, synaptic, and behavioral phenotypes in DYRK1A-knockin mice

Dyrk1A deficiency is linked to various neurodevelopmental disorders, including developmental delays, intellectual disability (ID) and autism spectrum disorders (ASD). Haploinsufficiency of Dyrk1a in mice reportedly leads to ASD-related phenotypes. However, the key pathological mechanisms remain unclear and human DYRK1A mutations remain uncharacterized in mice. Here, we generated and studied Dyrk1a-knockin mice carrying a human ASD patient mutation (Ile48LysfsX2; Dyrk1a-I48K mice). These mice display severe microcephaly, social and cognitive deficits, dendritic shrinkage, excitatory synaptic deficits, and altered phospho-proteomic patterns enriched for multiple signaling pathways and synaptic proteins. Early chronic lithium treatment of newborn mutant mice rescues the brain volume, behavior, dendritic, synaptic, and signaling/synapse phospho-proteomic phenotypes at juvenile and adult stages. These results suggest that signaling/synaptic alterations contribute to the phenotypic alterations seen in Dyrk1a-I48K mice, and that early correction of these alterations by lithium treatment has long-lasting effects in preventing juvenile and adult-stage phenotypes

Clinical and Radiographic Features of Adult-onset Ankylosing Spondylitis in Korean Patients: Comparisons between Males and Females

The objective of this study was to investigate clinical and radiographic features and gender differences in Korean patients with adult-onset ankylosing spondylitis. Multicenter cross-sectional studies were conducted in the rheumatology clinics of 13 Korean tertiary referral hospitals. All patients had a confirmed diagnosis of ankylosing spondylitis according to the modified New York criteria. Clinical, laboratory, and radiographic features were evaluated and disease activities were assessed using the Bath ankylosing spondylitis disease activity index. Five hundred and five patients were recruited. The male to female ratio was 6.1:1. Average age at symptom onset was 25.4±8.9 yr and average disease duration was 9.6±6.8 yr. Males manifested symptoms at a significantly earlier age. HLA-B27 was more frequently positive in males. Hips were more commonly affected in males, and knees in females. When spinal mobility was measured using tragus-to-wall distance and the modified Schober's test, females had significantly better results. Radiographic spinal changes, including bamboo spine and syndesmophytes, were more common in males after adjustment of confounding factors. In conclusion, we observed significant gender differences in radiographic spinal involvement as well as other clinical manifestations among Korea patients with adult-onset ankylosing spondylitis. These findings may influence the timing of the diagnosis and the choice of treatment

Prediction of major depressive disorder following beta-blocker therapy in patients with cardiovascular diseases

Incident depression has been reported to be associated with poor prognosis in patients with cardiovascular disease (CVD), which might be associated with beta-blocker therapy. Because early detection and intervention can alleviate the severity of depression, we aimed to develop a machine learning (ML) model predicting the onset of major depressive disorder (MDD). A model based on L1 regularized logistic regression was trained against the South Korean nationwide administrative claims database to identify risk factors for the incident MDD after beta-blocker therapy in patients with CVD. We identified 50,397 patients initiating beta-blockers for CVD, with 774 patients developing MDD within 365 days after initiating beta-blocker therapy. An area under the receiver operating characteristic curve (AUC) of 0.74 was achieved. A history of non-selective beta-blockers and factors related to anxiety disorder, sleeping problems, and other chronic diseases were the most strong predictors. AUCs of 0.62–0.71 were achieved in the external validation conducted on six independent electronic health records and claims databases in the USA and South Korea. In conclusion, an ML model that identifies patients at high-risk for incident MDD was developed. Application of ML to identify susceptible patients for adverse events of treatment may serve as an important approach for personalized medicine

Observation of γγ → ττ in proton-proton collisions and limits on the anomalous electromagnetic moments of the τ lepton

The production of a pair of τ leptons via photon–photon fusion, γγ → ττ, is observed for the f irst time in proton–proton collisions, with a significance of 5.3 standard deviations. This observation is based on a data set recorded with the CMS detector at the LHC at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb−1. Events with a pair of τ leptons produced via photon–photon fusion are selected by requiring them to be back-to-back in the azimuthal direction and to have a minimum number of charged hadrons associated with their production vertex. The τ leptons are reconstructed in their leptonic and hadronic decay modes. The measured fiducial cross section of γγ → ττ is σfid obs = 12.4+3.8 −3.1 fb. Constraints are set on the contributions to the anomalous magnetic moment (aτ) and electric dipole moments (dτ) of the τ lepton originating from potential effects of new physics on the γττ vertex: aτ = 0.0009+0.0032 −0.0031 and |dτ| < 2.9×10−17ecm (95% confidence level), consistent with the standard model

The Selberg integral and Young books

The Selberg integral is an important integral first evaluated by Selberg in 1944. Stanley found a combinatorial interpretation of the Selberg integral in terms of permutations. In this paper, new combinatorial objects "Young books'' are introduced and shown to have a connection with the Selberg integral. This connection gives an enumeration formula for Young books. It is shown that special cases of Young books become standard Young tableaux of various shapes: shifted staircases, squares, certain skew shapes, and certain truncated shapes. As a consequence, enumeration formulas for standard Young tableaux of these shapes are obtained.L’intégrale de Selberg est une partie intégrante importante abord évaluée par Selberg en 1944. Stanley a trouvé une interprétation combinatoire de la Selberg aide en permutations. Dans ce papier, de nouveaux objets combinatoires “livres de Young” sont introduits et présentés à avoir un lien avec l’intégrale de Selberg. Cette connexion donne une formule d'énumération pour les livres de Young. Il est démontré que des cas spéciaux de livres de Young deviennent tableaux standards de Young de formes diverses: escaliers décalés, places, certaines formes gauches et certaines formes tronquées. En conséquence, l’énumération des formules pour tableaux standards de Young de ces formes sont obtenues