Computing the Cassels-Tate Pairing for Jacobian Varieties of Genus Two Curves

Let J be the Jacobian variety of a genus two curve defined over a number field K. The main focus of this thesis is on computing the Cassels-Tate pairing on the 2-Selmer group of J. We start by studying the Cassels-Tate pairing when J admits a Richelot isogeny φ : J → J. Suppose all points in J[2] are defined over K. We compute the Cassels-Tate pairing ⟨ , ⟩CT on Selφ(J)×Selφ(J) following the Weil pairing definition of the Cassels-Tate pairing. We then study the pairing ⟨ , ⟩CT on Sel2(J) × Sel2(J) following the homogeneous space definition of the Cassels-Tate pairing. For ε,η ∈ Sel2(J), we compute ⟨ε,η⟩CT both in the case where all points in J[2] are defined over K and in the case where the twisted Kummer surface Kη has a K-rational point. In both cases, we give a computable formula for ⟨ε,η⟩CT and a practical algorithm for computation when K = Q. In all cases, we calculate examples for which computing the Cassels-Tate pairing improves the rank bound of J obtained by carrying out standard de- scent calculations. We also give techniques to reduce the degree of the number field needed in the algorithm for computation

Computing the Cassels-Tate pairing on the 2-Selmer group of a genus 2 Jacobian

We describe a method for computing the Cassels-Tate pairing on the 2-Selmer group of the Jacobian of a genus 2 curve. This can be used to improve the upper bound coming from 2-descent for the rank of the group of rational points on the Jacobian. Our method remains practical regardless of the Galois action on the Weierstrass points of the genus 2 curve. It does however depend on being able to find a rational point on a certain twisted Kummer surface. The latter does not appear to be a severe restriction in practice. In particular, we have used our method to unconditionally determine the ranks of all genus 2 Jacobians in the L-functions and modular forms database (LMFDB).Comment: 48 page

Flame Boundary Measurement Using an Electrostatic Sensor Array

Flame boundary is an important geometrical characteristic for the evaluation of flame properties such as heat release rate and radiation. Reliable and accurate measurement of flame boundary is desirable for the prediction of flame structure and the optimization of combustion systems. Such measurement will inform the designers and operators of the combustion systems. This paper presents for the first time a study of using an electrostatic sensor array for flame boundary measurement. The electrostatic sensor is placed in the vicinity of the flame to sense its movement through charge transfer. The principle, design, implementation and assessment of a measurement system based on this methodology are introduced. Comparative experimental investigations with a digital camera conducted on a laboratory-scale combustion test rig show that the electrostatic sensor can respond to the variation of the distance between the electrode and the flame boundary. Reconstruction of the flame boundary is achieved using a set of distance measurements obtained from a sensor array. For diffusion flames over the range of fuel flow rate 0.60-0.80 L/min and premixed flames over the range of equivalence ratio 1.27-3.81, experimental results show that the measurement system is capable of providing reliable measurement of the flame boundary. The correlation coefficients under all test conditions are mostly larger than 0.96, the mean relative errors within 7.4% and the relative root mean square errors within 0.09. More accurate flame boundary measurements are achieved for diffusion flames. In addition, the overall polarity of charges in a flame can be determined from the polarity of the sensor signal

TROPHY: A Topologically Robust Physics-Informed Tracking Framework for Tropical Cyclones

Tropical cyclones (TCs) are among the most destructive weather systems. Realistically and efficiently detecting and tracking TCs are critical for assessing their impacts and risks. Recently, a multilevel robustness framework has been introduced to study the critical points of time-varying vector fields. The framework quantifies the robustness of critical points across varying neighborhoods. By relating the multilevel robustness with critical point tracking, the framework has demonstrated its potential in cyclone tracking. An advantage is that it identifies cyclonic features using only 2D wind vector fields, which is encouraging as most tracking algorithms require multiple dynamic and thermodynamic variables at different altitudes. A disadvantage is that the framework does not scale well computationally for datasets containing a large number of cyclones. This paper introduces a topologically robust physics-informed tracking framework (TROPHY) for TC tracking. The main idea is to integrate physical knowledge of TC to drastically improve the computational efficiency of multilevel robustness framework for large-scale climate datasets. First, during preprocessing, we propose a physics-informed feature selection strategy to filter 90% of critical points that are short-lived and have low stability, thus preserving good candidates for TC tracking. Second, during in-processing, we impose constraints during the multilevel robustness computation to focus only on physics-informed neighborhoods of TCs. We apply TROPHY to 30 years of 2D wind fields from reanalysis data in ERA5 and generate a number of TC tracks. In comparison with the observed tracks, we demonstrate that TROPHY can capture TC characteristics that are comparable to and sometimes even better than a well-validated TC tracking algorithm that requires multiple dynamic and thermodynamic scalar fields

A loss-of-function allele of OsHMA3 associated with high cadmium accumulation in shoots and grain of Japonica rice cultivars

This article is protected by copyright. All rights reserved.Peer reviewedPostprin

Do Not Think Carefully? Re-examining the Effect of Unconscious Thought on Deception Detection

Several recent studies have examined the effect of unconscious thinking on deception detection with the hypothesis that unconscious thought increases the ability to discriminate between truth and deception, but these studies yielded conflicting results. The present study aimed to re-examine the effect of unconscious thinking and extend it by adopting both verbal and non-verbal/paraverbal stimuli. We hypothesized that unconscious thought leads to a higher accuracy rate than immediate decision and conscious thought when judging non-verbal/paraverbal stimuli, but not when judging verbal stimuli. In Study 1, we compared unconscious thought with immediate decision by using both video and audio stimuli. In Study 2, we compared unconscious thought with conscious thought by using both video and text stimuli. The results showed that when detecting deception vs. truth, (1) unconscious thought was not better than immediate decision on deception detection in both audio and video conditions (Study 1), and (2) unconscious thought was not better than conscious thought in both video and text conditions (Study 2). The Bayes factor of both studies also showed substantial evidence for null hypothesis (H0) relative to alternative hypothesis (H1). The implications and limitations of the present study are discussed

Measurement of Charge Density in Methane Fired Diffusion and Premixed Flames Using Electrostatic Probes

The charge density in a flame contains important information about the combustion processes that is difficult to obtain due to fast, complex, and highly exothermic reactions. This paper presents a study of using electrostatic probes to measure the charge density in methane fired diffusion and premixed flames. The sensing principle, practical design, and performance assessment of the electrostatic probe are presented. Comparative experimental studies with a reference ion-current sensor carried out on a combustion test rig indicate that the fluctuation of the signal from the electrostatic probe arises from the variation in the charge density in a flame. A dimensionless index, combining the average of local peak values in the electrostatic signal with the flame oscillation frequency, is adopted as an indicator of the charge density. Experimental results demonstrate that the charge density in a methane diffusion flame has an increasing trend with the fuel flowrate varying from 0.80 L/min to 1.20 L/min. The charge density in a methane-air premixed flame yields a decreasing trend with the equivalence ratio ranging from 0.54 to 0.75, then increases and reaches a local peak at the equivalence ratio of 1.03, and continues to increase when the equivalence ratio varies from 1.03 to 3.50. The charge density in the inner cone is higher than that in the outer cone for diffusion and premixed flames. The results obtained suggest that the developed electrostatic probe and the index can be used to indicate the charge density in diffusion and premixed flames

NAV Inflation and Impact on Performance in China

Our study is among the first to examine the net asset value (NAV) inflation practices of fund managers in China, finding that equity funds bolster their portfolios at quarter-end and especially year-end. In support of the NAV inflation hypothesis in China, we further document the following: (1) NAV inflation is more profound for the worst-performing fund managers and (2) the stocks in which fund managers hold larger stakes exhibit a more marked pattern of price inflation around quarter- and year-ends than do other stocks. We also find that closed-end funds in China engage in NAV inflation at quarter- and year-ends