Quantum Spectral Curve for AdS3/CFT2: a proposal

We conjecture the Quantum Spectral Curve equations for string theory on AdS3× S3× T4 with RR charge and its CFT2 dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS5 and AdS4 cases, but contains a critical new feature — the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.

$${\mathcal {N}}=1$$ super topological recursion

We introduce the notion of $${\mathcal {N}}=1$$ N = 1 abstract super loop equations and provide two equivalent ways of solving them. The first approach is a recursive formalism that can be thought of as a supersymmetric generalization of the Eynard–Orantin topological recursion, based on the geometry of a local super spectral curve. The second approach is based on the framework of super Airy structures. The resulting recursive formalism can be applied to compute correlation functions for a variety of examples related to 2d supergravity.

Comparison of Spectral and Perfusion Computed Tomography Imaging in the Differential Diagnosis of Peripheral Lung Cancer and Focal Organizing Pneumonia

ObjectiveTo investigate the spectral and perfusion computed tomography (CT) findings of peripheral lung cancer (PLC) and focal organizing pneumonia (FOP) and to compare the accuracy of spectral and perfusion CT imaging in distinguishing PLC from FOP.Materials and MethodsPatients who were suspected of having lung tumor and underwent “one-stop” chest spectral and perfusion CT, with their diagnosis confirmed pathologically, were prospectively enrolled from September 2020 to March 2021. Patients who were suspected of having lung tumor and underwent “one-stop” chest spectral and perfusion CT, with their diagnosis confirmed pathologically, were prospectively enrolled from September 2020 to March 2021. A total of 57 and 35 patients with PLC and FOP were included, respectively. Spectral parameters (CT40keV, CT70keV, CT100keV, iodine concentration [IC], water concentration [WC], and effective atomic number [Zeff]) of the lesions in the arterial and venous phases were measured in both groups. The slope of the spectral curve (K70keV) was calculated. The perfusion parameters, including blood volume (BV), blood flow (BF), mean transit time (MTT), and permeability surface (PS), were measured simultaneously in both groups. The differences in the spectral and perfusion parameters between the groups were examined. Receiver operating characteristic (ROC) curves were generated to calculate and compare the area under the curve (AUC), sensitivity, specificity, and accuracy of both sets of parameters in both groups.ResultsThe patients’ demographic and clinical characteristics were similar in both groups (P > 0.05). In the arterial and venous phases, the values of spectral parameters (CT40keV, CT70keV, spectral curve K70keV, IC, and Zeff) were greater in the FOP group than in the PLC group (P < 0.05). In contrast, the values of the perfusion parameters (BV, BF, MTT, and PS) were smaller in the FOP group than in the PLC group (P < 0.05). The AUC of the combination of the spectral parameters was larger than that of the perfusion parameters. For the former imaging method, the AUC, sensitivity, and specificity were 0.89 (95% confidence interval [CI]: 0.82–0.96), 0.86, and 0.83, respectively. For the latter imaging method, the AUC, sensitivity, and specificity were 0.80 (95% CI: 0.70–0.90), 0.71, and 0.83, respectively. There was no significant difference in AUC between the two imaging methods (P > 0.05).ConclusionSpectral and perfusion CT both has the capability to differentiate PLC and FOP. However, compared to perfusion CT imaging, spectral CT imaging has higher diagnostic efficiency in distinguishing them.

Kasteleyn Theorem, Geometric Signatures and KP-II Divisors on Planar Bipartite Networks in the Disk

Maximal minors of Kasteleyn sign matrices on planar bipartite graphs in the disk count dimer configurations with prescribed boundary conditions, and the weighted version of such matrices provides a natural parametrization of the totally non–negative part of real Grassmannians (Postnikov et al. J. Algebr. Combin. 30(2), 173–191, 2009; Lam J. Lond. Math. Soc. (2) 92(3), 633–656, 2015; Lam 2016; Speyer 2016; Affolter et al. 2019). In this paper we provide a geometric interpretation of such variant of Kasteleyn theorem: a signature is Kasteleyn if and only if it is geometric in the sense of Abenda and Grinevich (2019). We apply this geometric characterization to explicitly solve the associated system of relations and provide a new proof that the parametrization of positroid cells induced by Kasteleyn weighted matrices coincides with that of Postnikov boundary measurement map. Finally we use Kasteleyn system of relations to associate algebraic geometric data to KP multi-soliton solutions. Indeed the KP wave function solves such system of relations at the nodes of the spectral curve if the dual graph of the latter represents the soliton data. Therefore the construction of the divisor is automatically invariant, and finally it coincides with that in Abenda and Grinevich (Sel. Math. New Ser. 25(3), 43, 2019; Abenda and Grinevich 2020) for the present class of graphs.

Compressed Sensing Technology for Spectral Reconstruction Based on Maximum Entropy Criterion

In order to choose the related sampling ratio in the information-poor and information-rich spectral fragments, this paper attempts to recover the spectral reflectance by compressed sensing technology based on maximum entropy criterion. The maximum entropy threshold method is the criterion that the optimal threshold is determined to segment the information content of spectral curves. The spectral reflectance in each sub-spectral fragment is reconstructed by compressed sensing. The wavelet orthogonal matrix performs a sparse representation of each segmented spectral curve. Undersampling spectral curve be collected by random gaussian measurement matrix. The orthogonal matching pursuit algorithm recovers sparse original signals from undersampling observed signals. In this paper, the four standard color blocks of Munsell and the spectral curves of five types of ground objects in the hyperspectral data set are used as the exper-imental objects. The reconstructed results are evaluated by spectral curve reconstruction, root mean square error and information entropy difference. The experimental results show that our approach improves the reconstruction accuracy of spectral reflectance effectively, compared with the traditional method.

Spectral Curves for the Derivative Nonlinear Schrödinger Equations

Currently, in nonlinear optics, models associated with various types of the nonlinear Schrödinger equation (scalar (NLS), vector (VNLS), derivative (DNLS)), as well as with higher and mixed equations from the corresponding hierarchies are usually studied. Typical tools for solving the problem of propagation of optical nonlinear waves are the forward and inverse nonlinear Fourier transforms. One of the methods for reconstructing a periodic nonlinear signal is based on the use of spectral data in the form of spectral curves. In this paper, we study the properties of the spectral curves for all the derivatives NLS equations simultaneously. For all the main DNLS equations (DNLSI, DNLSII, DNLSIII), we have obtained unified Lax pairs, unified hierarchies of evolutionary and stationary equations, as well as unified equations of spectral curves of multiphase solutions. It is shown that stationary and evolutionary equations have symmetries, the presence of which leads to the existence of holomorphic involutions on spectral curves. Because of this symmetry, spectral curves of genus g are covers over other curves of genus M and N=g−M, where M is a number of phase of solutions. We also showed that the number of the genus g of the spectral curve is related to the number of phases M of the solution of one of the two formulas: g=2M or g=2M+1. The third section provides examples of the simplest solutions.

Identification of Typical Solid Hazardous Chemicals Based on Hyperspectral Imaging

The identification of hazardous chemicals based on hyperspectral imaging is an important emergent means for the prevention of explosion accidents and the early warning of secondary hazards. In this study, we used a combination of spectral curve matching based on full-waveform characteristics and spectral matching based on spectral characteristics to identify the hazardous chemicals, and proposed a method to quantitatively characterize the matching degree of the spectral curves of hazardous chemicals. The results showed that the four hazardous chemicals, sulfur, red phosphorus, potassium permanganate, and corn starch had bright colors, distinct spectral curve characteristics, and obvious changes in reflectivity, which were easy to identify. Moreover, the matching degree of their spectral curves was positively correlated with their reflectivity. However, the spectral characteristics of carbon powder, strontium nitrate, wheat starch, and magnesium–aluminum alloy powder were not obvious, with no obvious characteristic peaks or trends of change in reflectivity. Except for the reflectivity and the matching degree of the carbon powder being maintained at a low level, the reflectivity of the remaining three samples was relatively close, so that it was difficult to identify with the spectral curves alone, and color information should be considered for further identification.

Differentiation of Vulnerable Carotid Plaques by Analysis of Calcium Content and Spectral Curve Slope using Gemstone Spectral Imaging

Growing evidence indicates that vulnerable carotid plaque rupture is an important cause of stroke. However, fewer studies have been conducted to investigate the role of a novel gemstone spectral imaging (GSI) in assessment of vulnerable carotid plaque. In this study, we analyzed GSI data including calcium content of carotid atherosclerotic plaque and spectral curve slope, as well as serum high-sensitivity C-reactive protein (Hs-CRP), monocyte chemotactic protein-1 (MCP-1) levels in patients with carotid atherosclerotic plaque using the GSI-computed tomographic angiography (CTA) and immunoturbidimetry. The patients with unstable plaques demonstrated a significantly lower calcium content and higher spectral curve slope than the stable plaques group. In addition, the patients with unstable plaque showed an increase in Hs-CRP levels and MCP-1 levels compared with the stable plaque and normal controls (NC) group. The alternation in GSI calcium content and spectral curve slope reflects a close link between calcification and plaque instability, while derangement of Hs-CRP and MCP-1 is involved in the formation or development of vulnerable plaques. Taken together, our results strongly support the feasibility of using these serological and newly discovered imaging parameters as multiple potential biomarkers relevant to plaque vulnerability or stroke progression.