CONTACT GEOMETRY OF SECOND ORDER II

This is the continuation of our previous paper “Contact Geometry of Second Order I” , where we have formulated the contact equivalence of systems of second order partial differential equations for a scalar function as the geometry of PD manifolds of second order. In this paper, we will discuss the Two Step Reduction procedure in Contact Geometry of Second Order. In fact we establish the Second Reduction Theorem for PD manifolds (R;D1,D2) of second order admitting the first order covariant systems ˜N . Utilizing the covariant system ˜N , we construct the intermediate object (W;C:,N), called the IG manifold of corank r, as a submanifold of the Involutive Grassmann bundle Ir(J) over the contact manifold (J,C), where J = R/Ch (D1). We will seek the condition when the equivalence of (R;D1,D2) is reducible to that of (W;C∗,N). Moreover, when Ch (N) is non-trivial, the equivalence of (W;C∗,N) is further reducible to that of (Y ;D∗ N,DN), where Y = W/Ch (N). This theorem gives a sufficient condition for the existence of higher dimensional characteristics of (R;D1,D2). By analyzing the construction parts of the Two Step Reduction procedure, we will show several examples of Parabolic Geometries, which are, through the Second Reduction Theorem, associated with the geometry of PD manifolds of second order

PARABOLIC GEOMETRIES ASSOCIATED WITH DIFFERENTIAL EQUATIONS OF FINITE TYPE

We present here classes of parabolic geometries arising naturally from Seashi’s principle to form good classes of linear differential equations of finite type, which generalize the cases of second and third order ODE for scalar function. We will explicitly describe the symbols of these differential equations. The model equations of these classes admit nonlinear contact transformations and their symmetry algebras (the Lie algebra of infinitesimal contact transformations preserving these equations) become finite dimensional and simple

Drapeau theorem for differential systems

Generalizing the theorem for Goursat flags, we will characterize those flags which are obtained by “Rank 1 Prolongation” from the space of 1 jets for 1 independent and m dependent variables

CHANGE OF MOVEMENT IN THE PELVIS DUE TO FATIGUE IN LONG-DISTANCE RUNNING- A CASE STUDY

The purpose of this study was to clarify the three-dimensional movement of the pelvis due to fatigue in long-distance running. Four collegiate long-distance runners participated in this study as subjects and ran 4000m with a 5000m race pace. Subject D, whose running pace was significantly slowest, showed a significant decrease in stride length, stride frequency, and pelvis rotation angle at the end of the 4000m run. Furthermore, Subject D showed a significant increase in pelvis elevation. These factors suggested that to maintain the range of motion of pelvis rotation and to keep the pelvis elevation movement minimal is a very important factor in maintaining running speed and attaining high performance in long-distance running

Neural Activity Changes Underlying the Working Memory Deficit in Alpha-CaMKII Heterozygous Knockout Mice

The alpha-isoform of calcium/calmodulin-dependent protein kinase II (α-CaMKII) is expressed abundantly in the forebrain and is considered to have an essential role in synaptic plasticity and cognitive function. Previously, we reported that mice heterozygous for a null mutation of α-CaMKII (α-CaMKII+/−) have profoundly dysregulated behaviors including a severe working memory deficit, which is an endophenotype of schizophrenia and other psychiatric disorders. In addition, we found that almost all the neurons in the dentate gyrus (DG) of the mutant mice failed to mature at molecular, morphological and electrophysiological levels. In the present study, to identify the brain substrates of the working memory deficit in the mutant mice, we examined the expression of the immediate early genes (IEGs), c-Fos and Arc, in the brain after a working memory version of the eight-arm radial maze test. c-Fos expression was abolished almost completely in the DG and was reduced significantly in neurons in the CA1 and CA3 areas of the hippocampus, central amygdala, and medial prefrontal cortex (mPFC). However, c-Fos expression was intact in the entorhinal and visual cortices. Immunohistochemical studies using arc promoter driven dVenus transgenic mice demonstrated that arc gene activation after the working memory task occurred in mature, but not immature neurons in the DG of wild-type mice. These results suggest crucial insights for the neural circuits underlying spatial mnemonic processing during a working memory task and suggest the involvement of α-CaMKII in the proper maturation and integration of DG neurons into these circuits

Characterization of an active LINE-1 in the naked mole-rat genome.

Naked mole-rats (NMRs, Heterocephalus glaber) are the longest-living rodent species. A reason for their long lifespan is pronounced cancer resistance. Therefore, researchers believe that NMRs have unknown secrets of cancer resistance and seek to find them. Here, to reveal the secrets, we noticed a retrotransposon, long interspersed nuclear element 1 (L1). L1s can amplify themselves and are considered endogenous oncogenic mutagens. Since the NMR genome contains fewer L1-derived sequences than other mammalian genomes, we reasoned that the retrotransposition activity of L1s in the NMR genome is lower than those in other mammalian genomes. In this study, we successfully cloned an intact L1 from the NMR genome and named it NMR-L1. An L1 retrotransposition assay using the NMR-L1 reporter revealed that NMR-L1 was active retrotransposon, but its activity was lower than that of human and mouse L1s. Despite lower retrotrasposition activity, NMR-L1 was still capable of inducing cell senescence, a tumor-protective system. NMR-L1 required the 3' untranslated region (UTR) for retrotransposition, suggesting that NMR-L1 is a stringent-type of L1. We also confirmed the 5' UTR promoter activity of NMR-L1. Finally, we identified the G-quadruplex structure of the 3' UTR, which modulated the retrotransposition activity of NMR-L1. Taken together, the data indicate that NMR-L1 retrotranspose less efficiently, which may contribute to the cancer resistance of NMRs

Radioligand Assay-Based Detection of Antibodies against SARS-CoV-2 in Hospital Workers Treating Patients with Severe COVID-19 in Japan.

This study aimed to clarify whether infection by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is prevalent among the staff of a hospital providing treatment to patients with severe coronavirus disease 2019 (COVID-19) using radioligand assay (RLA). One thousand samples from the staff of a general hospital providing treatment to patients with severe COVID-19 were assayed for SARS-CoV-2 nucleocapsid protein (N) IgG using RLA. Nine patients with COVID-19 who had been treated in inpatient settings and had already recovered were used as control subjects, and 186 blood donor samples obtained more than 10 years ago were used as negative controls. Four of the 1000 samples showed apparently positive results, and approximately 10 or more samples showed slightly high counts. Interestingly, a few among the blood donor samples also showed slightly high values. To validate the results, antibody examinations using ELISA and neutralizing antibody tests were performed on 21 samples, and chemiluminescence immunoassay (CLIA) was performed on 201 samples, both resulting in a very high correlation. One blood donor sample showed slightly positive results in both RLA and CLIA, suggesting a cross-reaction. This study showed that five months after the pandemic began in Japan, the staff of a general hospital with a tertiary emergency medical facility had an extremely low seroprevalence of the antibodies against SARS-CoV-2. Further investigation will be needed to determine whether the slightly high results were due to cross-reactions or a low titer of anti-SARS-CoV-2 antibodies. The quantitative RLA was considered sensitive enough to detect low titers of antibodies