A Filtration on the Cohomology Rings of Regular Nilpotent Hessenberg Varieties

Let n be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in GL(n, C) / B such that its associated graded ring has graded pieces (i.e., homogeneous components) isomorphic to rings which are related to the cohomology rings of Hessenberg varieties in GL(n- 1 , C) / B, showing the inductive nature of these rings. In previous work, the first two authors, together with Abe and Masuda, gave an explicit presentation of these cohomology rings in terms of generators and relations. We introduce a new set of polynomials which are closely related to the relations in the above presentation and obtain a sequence of equivalence relations they satisfy; this allows us to derive our filtration. In addition, we obtain the following three corollaries. First, we give an inductive formula for the Poincaré polynomial of these varieties. Second, we give an explicit monomial basis for the cohomology rings of regular nilpotent Hessenberg varieties with respect to the presentation mentioned above. Third, we derive a basis of the set of linear relations satisfied by the images of the Schubert classes in the cohomology rings of regular nilpotent Hessenberg varieties. Finally, our methods and results suggest many directions for future work; in particular, we propose a definition of “Hessenberg Schubert polynomials” in the context of regular nilpotent Hessenberg varieties, which generalize the classical Schubert polynomials. We also outline several open questions pertaining to them

Parameter identification of nonlinear viscoelastic model with impact area parameter for sport surface by using multi-intensity multi-area impact test

AbstractIn previous studies, we proposed various models of material and methods for identifying the parameters of these models by multi-intensity impact test. Especially, the exponential funtion type nonlinear Voigt model shows an excellent accuracy for identifying the property of material behavior. Although other papers show that this model is applicable to the case of varying impact duration and various temperatures, we have not yet discussed how the properties would change as the impact area changed. The purpose of this study is to propose an identification technique of nonlinear Voigt model with hysteresis and dependence on impact area by multi-intensity multi-area impact test. The nonlinear elastic element of this model is expressed by the exponential function based on displacement and impact area. And the nonlinear viscous element of the model is expressed by the product of the exponential function based on displacement and the exponential function based on velocity

Structural Parameterizations of Vertex Integrity

The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected components small. In this paper, we initiate a systematic study of structural parameterizations of the problem of computing the unweighted/weighted vertex integrity. As structural graph parameters, we consider well-known parameters such as clique-width, treewidth, pathwidth, treedepth, modular-width, neighborhood diversity, twin cover number, and cluster vertex deletion number. We show several positive and negative results and present sharp complexity contrasts.Comment: 21 pages, 6 figures, WALCOM 202

Spinal Surgery after Bilateral Subthalamic Stimulation for Patients with Parkinson's Disease: A Retrospective Outcome Analysis of Pain and Functional Control

Parkinson's disease (PD) patients often suffer from spinal diseases requiring surgeries, although the risk of complications is high. There are few reports on outcomes after spinal surgery for PD patients with deep brain stimulation (DBS). The objective of this study was to explore the data on spinal surgery for PD patients with precedent DBS. We evaluated 24 consecutive PD patients with 28 spinal surgeries from 2007 to 2017 who received at least a 2-year follow-up. The characteristics and outcomes of PD patients after spinal surgery were compared to those of 156 non-PD patients with degenerative spinal diseases treated in 2013-2017. Then, the characteristics, outcomes, and spinal alignment of PD patients receiving DBS were analyzed in degenerative spinal/ lumbar diseases. The mean age at the time of spinal surgery was 68 years. The Hoehn and Yahr score regarding PD was stage 1 for 8 patients, stage 2 for 2 patients, stage 3 for 8 patients, stage 4 for 10 patients, and stage 5 for 0 patient. The median preoperative L-DOPA equivalent daily dose was 410 mg. Thirteen patients (46%) received precedent subthalamic nucleus (STN) DBS. Lumbar lesions with pain were common, and operation and anesthesia times were long in PD patients. Pain and functional improvement of PD patients persisted for 2 years after surgery with a higher complication rate than for non-PD patients. PD patients with STN DBS maintained better lumbar lordosis for 2 years after spinal surgery. STN DBS significantly maintained spinal alignment with subsequent pain and functional amelioration 2 years after surgery. The outcomes of spinal surgery for PD patients might be favorably affected by thorough treatment for PD including DBS

Functional relevance of the precuneus in verbal politeness.

Non-competitive and non-threatening aspects of social hierarchy, such as politeness, are universal among human cultures, and might have evolved from ritualized submission in primates; however, these behaviors have rarely been studied. Honorific language is a type of polite linguistic communication that plays an important role in human social interactions ranging from everyday conversation to international diplomacy. Here, functional magnetic resonance imaging (fMRI) revealed selective precuneus activation during a verbal politeness judgment task, but not other linguistic-judgment or social-status recognition tasks. The magnitude of the activation was correlated with the task performance. Functional suppression of the activation using cathodal transcranial direct-current stimulation reduced performance in the politeness task. These results suggest that the precuneus is an essential hub of the verbal politeness judgment

Diagnostic approach for patients with unidentified fever according to the classical criteria of fever of unknown origin in the field of autoimmune disorders

ArticleImmunological medicine. 42(4): 176-184 (2019)journal articl

Long-term maintenance of the mucosal healing induced by azacitidine therapy in a patient with intestinal Behçet's-like disease accompanied with myelodysplastic syndrome involving trisomy 8

ArticleImmunological medicine. 42(3): 135-141 (2019)journal articl

Intermediate-luminosity Type IIP SN 2021gmj: a low-energy explosion with signatures of circumstellar material

We present photometric, spectroscopic and polarimetric observations of the intermediate-luminosity Type IIP supernova (SN) 2021gmj from 1 to 386 days after the explosion. The peak absolute V-band magnitude of SN 2021gmj is -15.5 mag, which is fainter than that of normal Type IIP SNe. The spectral evolution of SN 2021gmj resembles that of other sub-luminous supernovae: the optical spectra show narrow P-Cygni profiles, indicating a low expansion velocity. We estimate the progenitor mass to be about 12 Msun from the nebular spectrum and the 56Ni mass to be about 0.02 Msun from the bolometric light curve. We also derive the explosion energy to be about 3 x 10^{50} erg by comparing numerical light curve models with the observed light curves. Polarization in the plateau phase is not very large, suggesting nearly spherical outer envelope. The early photometric observations capture the rapid rise of the light curve, which is likely due to the interaction with a circumstellar material (CSM). The broad emission feature formed by highly-ionized lines on top of a blue continuum in the earliest spectrum gives further indication of the CSM at the vicinity of the progenitor. Our work suggests that a relatively low-mass progenitor of an intermediate-luminosity Type IIP SN can also experience an enhanced mass loss just before the explosion, as suggested for normal Type IIP SNe.Comment: 18 pages, 16 figures, resubmitted to MNRAS after addressing referee comment