An inverse problem of the flux for minimal surfaces

For a complete minimal surface in the Euclidean 3-space, the so-called flux vector corresponds to each end. The flux vectors are balanced, i.e., the sum of those over all ends are zero. Consider the following inverse problem: For each balanced n vectors, find an n-end catenoid which attains given vectors as flux. Here, an n-end catenoid is a complete minimal surface of genus 0 with ends asymptotic to the catenoids. In this paper, the problem is reduced to solving algebraic equation. Using this reduction, it is shown that, when n=4, the inverse problem for 4-end catenoid has solutions for almost all balanced 4 vectors. Further obstructions for n-end catenoids with parallel flux vectors are also discussed.Comment: 28 pages, AMSLaTeX 1.1, with 8 figures, To appear in Indiana University Mathematics Journa

CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regression

In causal inference about two treatments, Conditional Average Treatment Effects (CATEs) play an important role as a quantity representing an individualized causal effect, defined as a difference between the expected outcomes of the two treatments conditioned on covariates. This study assumes two linear regression models between a potential outcome and covariates of the two treatments and defines CATEs as a difference between the linear regression models. Then, we propose a method for consistently estimating CATEs even under high-dimensional and non-sparse parameters. In our study, we demonstrate that desirable theoretical properties, such as consistency, remain attainable even without assuming sparsity explicitly if we assume a weaker assumption called implicit sparsity originating from the definition of CATEs. In this assumption, we suppose that parameters of linear models in potential outcomes can be divided into treatment-specific and common parameters, where the treatment-specific parameters take difference values between each linear regression model, while the common parameters remain identical. Thus, in a difference between two linear regression models, the common parameters disappear, leaving only differences in the treatment-specific parameters. Consequently, the non-zero parameters in CATEs correspond to the differences in the treatment-specific parameters. Leveraging this assumption, we develop a Lasso regression method specialized for CATE estimation and present that the estimator is consistent. Finally, we confirm the soundness of the proposed method by simulation studies

Alkane inducible proteins in Geobacillus thermoleovorans B23

<p>Abstract</p> <p>Background</p> <p>Initial step of β-oxidation is catalyzed by acyl-CoA dehydrogenase in prokaryotes and mitochondria, while acyl-CoA oxidase primarily functions in the peroxisomes of eukaryotes. Oxidase reaction accompanies emission of toxic by-product reactive oxygen molecules including superoxide anion, and superoxide dismutase and catalase activities are essential to detoxify them in the peroxisomes. Although there is an argument about whether primitive life was born and evolved under high temperature conditions, thermophilic archaea apparently share living systems with both bacteria and eukaryotes. We hypothesized that alkane degradation pathways in thermophilic microorganisms could be premature and useful to understand their evolution.</p> <p>Results</p> <p>An extremely thermophilic and alkane degrading <it>Geobacillus thermoleovorans </it>B23 was previously isolated from a deep subsurface oil reservoir in Japan. In the present study, we identified novel membrane proteins (P16, P21) and superoxide dismutase (P24) whose production levels were significantly increased upon alkane degradation. Unlike other bacteria acyl-CoA oxidase and catalase activities were also increased in strain B23 by addition of alkane.</p> <p>Conclusion</p> <p>We first suggested that peroxisomal β-oxidation system exists in bacteria. This eukaryotic-type alkane degradation pathway in thermophilic bacterial cells might be a vestige of primitive living cell systems that had evolved into eukaryotes.</p

Synthetic Control Methods by Density Matching under Implicit Endogeneity

Synthetic control methods (SCMs) have become a crucial tool for causal inference in comparative case studies. The fundamental idea of SCMs is to estimate counterfactual outcomes for a treated unit by using a weighted sum of observed outcomes from untreated units. The accuracy of the synthetic control (SC) is critical for estimating the causal effect, and hence, the estimation of SC weights has been the focus of much research. In this paper, we first point out that existing SCMs suffer from an implicit endogeneity problem, which is the correlation between the outcomes of untreated units and the error term in the model of a counterfactual outcome. We show that this problem yields a bias in the causal effect estimator. We then propose a novel SCM based on density matching, assuming that the density of outcomes of the treated unit can be approximated by a weighted average of the densities of untreated units (i.e., a mixture model). Based on this assumption, we estimate SC weights by matching moments of treated outcomes and the weighted sum of moments of untreated outcomes. Our proposed method has three advantages over existing methods. First, our estimator is asymptotically unbiased under the assumption of the mixture model. Second, due to the asymptotic unbiasedness, we can reduce the mean squared error for counterfactual prediction. Third, our method generates full densities of the treatment effect, not only expected values, which broadens the applicability of SCMs. We provide experimental results to demonstrate the effectiveness of our proposed method

Di-neutron correlations in 6He through Coulomb breakup reactions

The internal correlations of binary subsystems not only in the ground state but also in excited states of 6He are investigated through the Coulomb breakup reaction. For the excited states, to investigate the internal correlations, the twodimensional energy distributions of the E1 strength are calculated with respect to the relative energy in the binary subsystems, and the importance of the final state interactions are discussed. For the ground state, the E1 strength distributions are calculated by using two types of wave functions with and without strong di-neutron correlations, and the contributions from the di-neutron correlations are investigated

Coulomb Breakup Reactions in Complex-Scaled Solutions of the Lippmann-Schwinger Equation

We propose a new method to describe three-body breakups of nuclei, in which the Lippmann-Schwinger equation is solved combining with the complex scaling method. The complex-scaled solutions of the Lippmann-Schwinger equation (CSLS) enables us to treat boundary conditions of many-body open channels correctly and to describe a many-body breakup amplitude from the ground state. The Coulomb breakup cross section from the 6He ground state into 4He+n+n three-body decaying states as a function of the total excitation energy is calculated by using CSLS, and the result well reproduces the experimental data. Furthermore, the two-dimensional energy distribution of the E1 transition strength is obtained and an importance of the 5He(3/2-) resonance is confirmed. It is shown that CSLS is a promising method to investigate correlations of subsystems in three-body breakup reactions of the weakly-bound nuclei.Comment: 12 pages, 6 figures, submitted to Progress of Theoretical Physics; section 2.4 added, 2 equations added, 1 equation replace