Unimodality for free L\'evy processes

We will prove that: (1) A symmetric free L\'evy process is unimodal if and only if its free L\'evy measure is unimodal; (2) Every free L\'evy process with boundedly supported L\'evy measure is unimodal in sufficiently large time. (2) is completely different property from classical L\'evy processes. On the other hand, we find a free L\'evy process such that its marginal distribution is not unimodal for any time $s>0$ and its free L\'evy measure does not have a bounded support. Therefore, we conclude that the boundedness of the support of free L\'evy measure in (2) cannot be dropped. For the proof we will (almost) characterize the existence of atoms and the existence of continuous probability densities of marginal distributions of a free L\'evy process in terms of L\'evy--Khintchine representation.Comment: 20 pages. To appear in Annales de l'Institut Henri Poincar\'e (B) Probabilit\'es et Statistique

On the Law of Free Subordinators

We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supported on [0,\infty), called the free regular measures. We prove that the class of free regular measures is closed under the free multiplicative convolution, t-th boolean power for $0\leq t\leq 1$, t-th free multiplicative power for $t\geq 1$ and weak convergence. In addition, we show that a symmetric distribution is freely infinitely divisible if and only if its square can be represented as the free multiplicative convolution of a free Poisson and a free regular measure. This gives two new explicit examples of distributions which are infinitely divisible with respect to both classical and free convolutions: \chi^2(1) and F(1,1). Another consequence is that the free commutator operation preserves free infinite divisibility.Comment: 16 page

The normal distribution is freely selfdecomposable

The class of selfdecomposable distributions in free probability theory was introduced by Barndorff-Nielsen and the third named author. It constitutes a fairly large subclass of the freely infinitely divisible distributions, but so far specific examples have been limited to Wigner's semicircle distributions, the free stable distributions, two kinds of free gamma distributions and a few other examples. In this paper, we prove that the (classical) normal distributions are freely selfdecomposable. More generally it is established that the Askey-Wimp-Kerov distribution $\mu_c$ is freely selfdecomposable for any $c$ in $[-1,0]$. The main ingredient in the proof is a general characterization of the freely selfdecomposable distributions in terms of the derivative of their free cumulant transform.Comment: 22 page

A STRIPAK component Strip regulates neuronal morphogenesis by affecting microtubule stability

During neural development, regulation of microtubule stability is essential for proper morphogenesis of neurons. Recently, the striatin-interacting phosphatase and kinase (STRIPAK) complex was revealed to be involved in diverse cellular processes. However, there is little evidence that STRIPAK components regulate microtubule dynamics, especially in vivo. Here, we show that one of the core STRIPAK components, Strip, is required for microtubule organization during neuronal morphogenesis. Knockdown of Strip causes a decrease in the level of acetylated α-tubulin in Drosophila S2 cells, suggesting that Strip influences the stability of microtubules. We also found that Strip physically and genetically interacts with tubulin folding cofactor D (TBCD), an essential regulator of α- and β-tubulin heterodimers. Furthermore, we demonstrate the genetic interaction between strip and Down syndrome cell adhesion molecule (Dscam), a cell surface molecule that is known to work with TBCD. Thus, we propose that Strip regulates neuronal morphogenesis by affecting microtubule stability.This work was supported by grants from the Japanese Ministry of Education, Science, Sports, Culture and Technology (MEXT), the Japan Society for the Promotion of Science and the Japan Science and Technology Agency (to C.S., M.O., M.M. and T.C.)

Follistatin-like 5 is expressed in restricted areas of the adult mouse brain: Implications for its function in the olfactory system

Follistatin‐like 5 (Fstl5), a member of the follistatin family of genes, encodes a secretory glycoprotein. Previous studies revealed that other members of this family including Fstl1 and Fstl3 play an essential role in development, homeostasis, and congenital disorders. However, the in vivo function of Fstl5 is poorly understood. To gain insight into the function of Fstl5 in the mouse central nervous system, we examined the Fstl5 expression pattern in the adult mouse brain. The results of in situ hybridization analysis showed a highly restricted pattern of Fstl5, namely, with localization in the olfactory system, hippocampal CA3 area and granular cell layer of the cerebellum. Restricted expression in the olfactory system suggests a possible role for Fstl5 in maintaining odor perception

Drosophila Strip serves as a platform for early endosome organization during axon elongation

Early endosomes are essential for regulating cell signalling and controlling the amount of cell surface molecules during neuronal morphogenesis. Early endosomes undergo retrograde transport (clustering) before their homotypic fusion. Small GTPase Rab5 is known to promote early endosomal fusion, but the mechanism linking the transport/clustering with Rab5 activity is unclear. Here we show that Drosophila Strip is a key regulator for neuronal morphogenesis. Strip knockdown disturbs the early endosome clustering, and Rab5-positive early endosomes become smaller and scattered. Strip genetically and biochemically interacts with both Glued (the regulator of dynein-dependent transport) and Sprint (the guanine nucleotide exchange factor for Rab5), suggesting that Strip is a molecular linker between retrograde transport and Rab5 activation. Overexpression of an active form of Rab5 in strip-mutant neurons suppresses the axon elongation defects. Thus, Strip acts as a molecular platform for the early endosome organization that has important roles in neuronal morphogenesis.This work was supported by grants from the National Institute of General Medical Science of the National Institutes of Health (R01-GM085232 to V.I.G.), the National Institutes of Health (R01-DC005982 to L.L.), the Japanese Ministry of Education, Science, Sports, Culture, and Technology (MEXT), the Japan Society for the Promotion of Science, and the Japan Science and Technology Agency (to C.S., K.T., Y.Y., M.M., and T.C.)

Aldosterone to Potassium Ratio after Adrenocorticotropin Stimulation in Unilateral Primary Aldosteronism Diagnosis

Article信州医学雑誌 68(3): 159-168(2020)journal articl

Periostin as a novel biomarker for postoperative recurrence of chronic rhinosinitis with nasal polyps

We previously reported that chronic rhinosinusitis with nasal polyps (CRSwNP) was subdivided into four chronic rhinosinusitis (CRS) subtypes using the JESREC scoring system. We sought to identify the gene expression profile and biomarkers related with CRSwNP by RNA-sequence. RNA-sequencing was performed to identify differentially expressed genes between nasal polyps (NPs) and inferior turbinate mucosa from 6 patients with CRSwNP, and subsequently, quantitative real-time PCR was performed to verify the results. ELISA was performed to identify possible biomarkers for postoperative recurrence. In the RNA-sequencing results, periostin (POSTN) expression was the highest in NP. We focused on POSTN and investigated the protein level of POSTN by immunohistochemistry and ELISA. POSTN was diffusely expressed in moderate and severe eosinophilic CRS using immunohistochemistry, and its staining pattern was associated with the severity of the phenotype of the CRSwNP (P < 0.05). There was a significant difference between the POSTN high/low groups for postoperative recurrence when the cutoff point was set at 115.5 ng/ml (P = 0.0072). Our data suggests that the protein expression level of POSTN was associated with the severity of CRSwNP, and serum POSTN can be a novel biomarker for postoperative recurrence of CRSwNP