92 research outputs found

    Counting Labelled Trees with Given Indegree Sequence

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    For a labelled tree on the vertex set [n]:={1,2,...,n}[n]:=\{1,2,..., n\}, define the direction of each edge ijij to be i→ji\to j if i<ji<j. The indegree sequence of TT can be considered as a partition λ⊹n−1\lambda \vdash n-1. The enumeration of trees with a given indegree sequence arises in counting secant planes of curves in projective spaces. Recently Ethan Cotterill conjectured a formula for the number of trees on [n][n] with indegree sequence corresponding to a partition λ\lambda. In this paper we give two proofs of Cotterill's conjecture: one is `semi-combinatorial" based on induction, the other is a bijective proof.Comment: 10 page

    A q-analogue of spanning trees : nilpotent transformations over finite fields

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 67).The main result of this work is a q-analogue relationship between nilpotent transformations and spanning trees. For example, nilpotent endomorphisms on an n-dimensional vector space over Fq is a q-analogue of rooted spanning trees of the complete graph Kn. This relationship is based on two similar bijective proofs to calculate the number of spanning trees and nilpotent transformations, respectively. We also discuss more details about this bijection in the cases of complete graphs, complete bipartite graphs, and cycles. It gives some refinements of the q-analogue relationship. As a corollary, we find the total number of nilpotent transformations with some restrictions on Jordan block sizes.by Jingbin Yin.Ph.D

    Segawa syndrome caused by TH gene mutation and its mechanism

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    Dopa-responsive dystonia (DRD), also known as Segawa syndrome, is a rare neurotransmitter disease. The decrease in dopamine caused by tyrosine hydroxylase (TH) gene mutation may lead to dystonia, tremor and severe encephalopathy in children. Although the disease caused by recessive genetic mutation of the tyrosine hydroxylase (TH) gene is rare, we found that the clinical manifestations of seven children with tyrosine hydroxylase gene mutations are similar to dopa-responsive dystonia. To explore the clinical manifestations and possible pathogenesis of the disease, we analyzed the clinical data of seven patients. Next-generation sequencing showed that the TH gene mutation in three children was a reported homozygous mutation (c.698G&gt;A). At the same time, two new mutations of the TH gene were found in other children: c.316_317insCGT, and c.832G&gt;A (p.Ala278Thr). We collected venous blood from four patients with Segawa syndrome and their parents for real-time quantitative polymerase chain reaction analysis of TH gene expression. We predicted the structure and function of proteins on the missense mutation iterative thread assembly refinement (I-TASSER) server and studied the conservation of protein mutation sites. Combined with molecular biology experiments and related literature analysis, the qPCR results of two patients showed that the expression of the TH gene was lower than that in 10 normal controls, and the expression of the TH gene of one mother was lower than the average expression level. We speculated that mutation in the TH gene may clinically manifest by affecting the production of dopamine and catecholamine downstream, which enriches the gene pool of Segawa syndrome. At the same time, the application of levodopa is helpful to the study, diagnosis and treatment of Segawa syndrome

    Potential of Core-Collapse Supernova Neutrino Detection at JUNO

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    JUNO is an underground neutrino observatory under construction in Jiangmen, China. It uses 20kton liquid scintillator as target, which enables it to detect supernova burst neutrinos of a large statistics for the next galactic core-collapse supernova (CCSN) and also pre-supernova neutrinos from the nearby CCSN progenitors. All flavors of supernova burst neutrinos can be detected by JUNO via several interaction channels, including inverse beta decay, elastic scattering on electron and proton, interactions on C12 nuclei, etc. This retains the possibility for JUNO to reconstruct the energy spectra of supernova burst neutrinos of all flavors. The real time monitoring systems based on FPGA and DAQ are under development in JUNO, which allow prompt alert and trigger-less data acquisition of CCSN events. The alert performances of both monitoring systems have been thoroughly studied using simulations. Moreover, once a CCSN is tagged, the system can give fast characterizations, such as directionality and light curve

    Detection of the Diffuse Supernova Neutrino Background with JUNO

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    As an underground multi-purpose neutrino detector with 20 kton liquid scintillator, Jiangmen Underground Neutrino Observatory (JUNO) is competitive with and complementary to the water-Cherenkov detectors on the search for the diffuse supernova neutrino background (DSNB). Typical supernova models predict 2-4 events per year within the optimal observation window in the JUNO detector. The dominant background is from the neutral-current (NC) interaction of atmospheric neutrinos with 12C nuclei, which surpasses the DSNB by more than one order of magnitude. We evaluated the systematic uncertainty of NC background from the spread of a variety of data-driven models and further developed a method to determine NC background within 15\% with {\it{in}} {\it{situ}} measurements after ten years of running. Besides, the NC-like backgrounds can be effectively suppressed by the intrinsic pulse-shape discrimination (PSD) capabilities of liquid scintillators. In this talk, I will present in detail the improvements on NC background uncertainty evaluation, PSD discriminator development, and finally, the potential of DSNB sensitivity in JUNO

    Real-time Monitoring for the Next Core-Collapse Supernova in JUNO

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    Core-collapse supernova (CCSN) is one of the most energetic astrophysical events in the Universe. The early and prompt detection of neutrinos before (pre-SN) and during the SN burst is a unique opportunity to realize the multi-messenger observation of the CCSN events. In this work, we describe the monitoring concept and present the sensitivity of the system to the pre-SN and SN neutrinos at the Jiangmen Underground Neutrino Observatory (JUNO), which is a 20 kton liquid scintillator detector under construction in South China. The real-time monitoring system is designed with both the prompt monitors on the electronic board and online monitors at the data acquisition stage, in order to ensure both the alert speed and alert coverage of progenitor stars. By assuming a false alert rate of 1 per year, this monitoring system can be sensitive to the pre-SN neutrinos up to the distance of about 1.6 (0.9) kpc and SN neutrinos up to about 370 (360) kpc for a progenitor mass of 30M⊙M_{\odot} for the case of normal (inverted) mass ordering. The pointing ability of the CCSN is evaluated by using the accumulated event anisotropy of the inverse beta decay interactions from pre-SN or SN neutrinos, which, along with the early alert, can play important roles for the followup multi-messenger observations of the next Galactic or nearby extragalactic CCSN.Comment: 24 pages, 9 figure
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