Discrete Painleve system and the double scaling limit of the matrix model for irregular conformal block and gauge theory

We study the partition function of the matrix model of finite size that realizes the irregular conformal block for the case of the ${\cal N}=2$ supersymmetric $SU(2)$ gauge theory with $N_f =2$. This model has been obtained in [arXiv:1008.1861 [hep-th]] as the massive scaling limit of the $\beta$ deformed matrix model representing the conformal block. We point out that the model for the case of $\beta =1$ can be recast into a unitary matrix model with log potential and show that it is exhibited as a discrete Painlev\'{e} system by the method of orthogonal polynomials. We derive the Painlev\'{e} II equation, taking the double scaling limit in the vicinity of the critical point which is the Argyres-Douglas type point of the corresponding spectral curve. By the $0$d-$4$d dictionary, we obtain the time variable and the parameter of the double scaled theory respectively from the sum and the difference of the two mass parameters scaled to their critical values.Comment: 12 pages; v2: references added; v3: accepted version for Physics Letters B; v4: minor corrections, published versio

Quantum information criteria for model selection in quantum state estimation

Quantum state estimation (or state tomography) is an indispensable task in quantum information processing. Because full state tomography that determines all elements of the density matrix is computationally demanding, one usually takes the strategy of assuming a certain model of quantum states and identifying the model parameters. However, it is difficult to make a valid assumption given little prior knowledge on a quantum state of interest, and thus we need a reasonable model selection method for quantum state estimation. Actually, in the classical statistical estimation theory, several types of information criteria have been established and widely used in practice for appropriately choosing a classical statistical model. In this study, we propose quantum information criteria for evaluating the quality of the estimated quantum state in terms of the quantum relative entropy, which is a natural quantum analogue of the classical information criterion defined in terms of Kullback-Leibler divergence. In particular, we derive two quantum information criteria depending on the type of estimator for the quantum relative entropy; one uses the log-likelihood and the other uses the classical shadow. The general role of information criteria is to predict the performance of an estimated model for unseen data, although it is a function of only sampled data; this generalization capability of the proposed quantum information criteria is evaluated in numerical simulations

The Molting Biomarker Metabolite N-acetylglucosamino-1,5-lactone in Female Urine of the Helmet Crab Telmessus cheiragonus

N-acetylglucosamino-1,5-lactone (NAGL) is a molting biomarker in the blue crab Callinectes sapidus. The concentration of this compound in urine is highest at the premolt stage. Since sexually mature premolt females release sex pheromone in their urine, NAGL is a candidate sex pheromone molecule in C. sapidus. This compound has not been reported in other species. In the present study, we quantified the concentration of NAGL in the urine of the helmet crab Telmessus cheiragonus, using nuclear magnetic resonance spectroscopy, and found that the concentration increases toward the day of molting and decreases after molting. However, the total amount of NAGL collected from individual animals was greatest two to five days after molting, because the amount of urine collected was the lowest at the premolt stage, and it increased after molting. The highest median concentration of NAGL in T. cheiragonas was 29 μmol l−1, which is 75% of the highest concentration reported in C. sapidus. This is the first report of NAGL as a molting biomarker in a species other than C. sapidus. We assume that NAGL is part of a pheromone bouquet in these two species

A Novel Hypoxia Imaging Endoscopy System

Measurement of tumor hypoxia is required for the diagnosis of tumor and the evaluation of therapeutic outcome. Currently, invasive and noninvasive techniques being exploited for tumor hypoxia measurement include polarographic needle electrodes, immunohistochemical (IHC) staining, magnetic resonance imaging (MRI), radionuclide imaging (positron emission tomography [PET] and single-photon emission computed tomography [SPECT]), optical imaging (bioluminescence and fluorescence), and hypoxia imaging endoscopy. This review provides a summary of the modalities available for assessment of tissue oxygenation as well as a discussion of current arguments for and against each modality, with a particular focus on noninvasive hypoxia imaging with emerging agents and new imaging technologies intended to detect molecular events associated with tumor hypoxia

One-Dimensional Transport Calculation of Energy- and Space-Distribution of Neutral Particles in a High Temperature Plasma

The transport equation for neutral particles in a high temperature plasma was numerically solved in a one-dimensional phase space. Close correlation has been found between the spectra of the emerging neutral flux and the plasma parameters. The numerical results show that the asymptotic temperature, which is determined from the calculated spectrum of the emerging neutral flux, varies from about 70 % to 95 % of the maximum ion temperature for the realizable plasma conditions. The reflection coefficient of the wall and the profile of the ion temperature of the plasma do not bring any important influence to the spectrum of emerging neutral flux

A Theoretical Analysis of Neutral Beam Probe for Measuring Ion Temperature of a Plasma

A theoretical basis of the neutral beam probe for measuring the local ion temperature of a plasma is given. The results of numerical calculations for some typical plasmas show that it is desirable to choose the beam energy in the region of 10 keV to 30 keV for plasmas of current and of next generation tokamaks. It is pointed out that the method of least squares can be applied to determine the local ion temperature from the measured data