On isolation of singular zeros of multivariate analytic systems

We give a separation bound for an isolated multiple root $x$ of a square multivariate analytic system $f$ satisfying that an operator deduced by adding $Df(x)$ and a projection of $D^2f(x)$ in a direction of the kernel of $Df(x)$ is invertible. We prove that the deflation process applied on $f$ and this kind of roots terminates after only one iteration. When $x$ is only given approximately, we give a numerical criterion for isolating a cluster of zeros of $f$ near $x$. We also propose a lower bound of the number of roots in the cluster.Comment: 17 page

The NumericalCertification package in Macaulay2

The package \texttt{NumericalCertification} implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regular solutions, the package implements Smale's $\alpha$-theory and Krawczyk method. For a singular solution, we implement soft verification using the iterative deflation method. We demonstrate the functionalities of the package focusing on interaction with current numerical solvers in \texttt{Macaulay2}.Comment: 10 page

On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials

The generalized Nash equilibrium problem (GNEP) is a kind of game to find strategies for a group of players such that each player's objective function is optimized. Solutions for GNEPs are called generalized Nash equilibria (GNEs). In this paper, we propose a numerical method for finding GNEs of GNEPs of polynomials based on the polyhedral homotopy continuation and the Moment-SOS hierarchy of semidefinite relaxations. We show that our method can find all GNEs if they exist, or detect the nonexistence of GNEs, under some genericity assumptions. Some numerical experiments are made to demonstrate the efficiency of our method.Comment: 25 pages, Version to appear in Journal of Scientific Computin

Taboos related to food culture at the 13th–14th-century Mongols

This article reviews the characteristics of terms used by the Mongols to express taboos concerning food and examines their food-related culture based on sources from the Mongolian Empire (Plano Carpini’s Historia Mongalorum, Marco Polo’s Il milione, Chinggis Khan’s Yeke Jasag, Rashīd ad-Dīn’s Jāmiʿ al-tawārīkh, and the Yuan Dynasty’s 飮食須知 Yin shi xu zhi). The Mongols left behind fairly strict food-related taboos in the form of eating habits. To better understand Mongolia’s food-related taboo expressions, we have examined five mediaeval sources written in various languages in which diverse food taboos are recorded

Implementing real polyhedral homotopy

We implement a real polyhedral homotopy method using three functions. The first function provides a certificate that our real polyhedral homotopy is applicable to a given system; the second function generates binomial systems for a start system; the third function outputs target solutions from the start system obtained by the second function. This work realizes the theoretical contributions in \cite{ergur2019polyhedral} as easy to use functions, allowing for further investigation into real homotopy algorithms.Comment: 10 page

Recognition of Transmembrane Protein 39A as a Tumor-Specific Marker in Brain Tumor

Transmembrane protein 39A (TMEM39A) belongs to the TMEM39 family. TMEM39A gene is a susceptibility locus for multiple sclerosis. In addition, TMEM39A seems to be implicated in systemic lupus erythematosus. However, any possible involvement of TMEM39A in cancer remains largely unknown. In the present report, we provide evidence that TMEM39A may play a role in brain tumors. Western blotting using an anti-TMEM39A antibody indicated that TMEM39A was overexpressed in glioblastoma cell lines, including U87-MG and U251-MG. Deep-sequencing transcriptomic profiling of U87-MG and U251-MG cells revealed that TMEM39A transcripts were upregulated in such cells compared with those of the cerebral cortex. Confocal microscopic analysis of U251-MG cells stained with anti-TMEM39A antibody showed that TMEM39A was located in dot-like structures lying close to the nucleus. TMEM39A probably located to mitochondria or to endosomes. Immunohistochemical analysis of glioma tissue specimens indicated that TMEM39A was markedly upregulated in such samples. Bioinformatic analysis of the Rembrandt knowledge base also supported upregulation of TMEM39A mRNA levels in glioma patients. Together, the results afford strong evidence that TMEM39A is upregulated in glioma cell lines and glioma tissue specimens. Therefore, TMEM39A may serve as a novel diagnostic marker of, and a therapeutic target for, gliomas and other cancers

Murine Model of Buckwheat Allergy by Intragastric Sensitization with Fresh Buckwheat Flour Extract

Food allergies affect about 4% of the Korean population, and buckwheat allergy is one of the most severe food allergies in Korea. The purpose of the present study was to develop a murine model of IgE-mediated buckwheat hypersensitivity induced by intragastric sensitization. Young female C3H/HeJ mice were sensitized and challenged intragastricly with fresh buckwheat flour (1, 5, 25 mg/dose of proteins) mixed in cholera toxin, followed by intragastric challenge. Anaphylactic reactions, antigen-specific antibodies, splenocytes proliferation assays and cytokine productions were evaluated. Oral buckwheat challenges of sensitized mice provoked anaphylactic reactions such as severe scratch, perioral/periorbital swellings, or decreased activity. Reactions were associated with elevated levels of buckwheat-specific IgE antibodies. Splenocytes from buckwheat allergic mice exhibited significantly greater proliferative responses to buckwheat than non-allergic mice. Buckwheat-stimulated IL-4, IL-5, and INF-γ productions were associated with elevated levels of buckwheat-specific IgE in sensitized mice. In this model, 1 mg and 5 mg dose of sensitization produced almost the same degree of Th2-directed immune response, however, a 25 mg dose showed blunted antibody responses. In conclusion, we developed IgE-mediated buckwheat allergy by intragastric sensitization and challenge, and this model could provide a good tool for future studies