A self-similar process arising from a random walk with random environment in random scenery

In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an i.i.d. scenery along its path. We assume that the scenery is in the domain of attraction of a stable distribution and prove that the resulting observations satisfy a limit theorem. The resulting limit process is a self-similar stochastic process with non-trivial dependencies.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ234 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The extremes of a random scenery as seen by a random walk in a random environment

A random walk performs a motion in an iid-environment and observes an iid-scenery along its path. Assuming the scenery is in the domain of attraction of an extreme-value distribution, we prove a limit-theorem for the observed extremes.

Operator semi-self-similar processes and their space-scaling matrices

Wide sense operator semi-self-similar processes are investigated with a focus on the class of space-scaling matrices of the processes. The existence of the exponent of the semi-self-similarity is also shown but the situation is different from the case of operator self-similar processes.Operator semi-self-similar process Exponent of semi-self-similarity Operator semistable distribution

Remarks on kernel Bayes’ rule

<p>The kernel Bayes’ rule has been proposed as a nonparametric kernel-based method to realize Bayesian inference in reproducing kernel Hilbert spaces. However, we demonstrate both theoretically and experimentally that the way of incorporating the prior in the kernel Bayes’ rule is unnatural. In particular, we show that under some reasonable conditions, the posterior in the kernel Bayes’ rule is completely unaffected by the prior, which seems to be irrelevant in the context of Bayesian inference. We consider that this phenomenon is in part due to the fact that the assumptions in the kernel Bayes’ rule do not hold in general.</p

The diagnosis of a metastatic breast tumor from ovarian cancer by the succession of a p53 mutation: a case report

Abstract Background Metastatic breast tumors from other organs are very rare. We herein describe the case of a patient with a metastatic breast tumor due to ovarian cancer who was diagnosed by the succession of a p53 mutation. Case presentation The patient was a 59-year-old woman with sigmoid colon stenosis. Diagnostic imaging revealed a pelvic mass, multiple liver tumors, ascites, and multiple swollen para-aortic lymph nodes, suggesting an advanced ovarian tumor. Transverse loop colostomy and partial resection of the greater omentum was performed followed by six cycles of paclitaxel with carboplatin chemotherapy (TC therapy). Her cancer almost disappeared, with the exception of a small tumor in her pelvis. Simple hysterectomy with bilateral salpingo-oophorectomy was performed. Two years and 5 months after the second surgery, a mass was detected in her right breast and simple mastectomy was performed. A histological examination of the tumors from the first surgery revealed infiltrating papillary adenocarcinoma and the solid nest proliferation of atypical cells with comedo necrosis and psammoma bodies. The findings of an immunohistochemical analysis were as follows: cancer antigen 125 (CA125 (+)), cytokeratin 7 (CK7 (+)), cytokeratin 20 (CK20 (−)), p53 (+) and CDX2 (−), estrogen receptor (ER (slightly +)), progesterone receptor (PR (slightly +)), and human epidermal growth factor receptor 2 (HER2 (1+)). The breast tumors presented similar morphological features (ER (−), PR (−), HER2 (−), CA125 (+), CK7 (+), CK20 (−), p53 (+), mammaglobin (−), and GCDFP15 (−)), which were not characteristic of breast cancer. A direct sequencing analysis of p53 revealed a p.V173M mutation in exon 5 in both the breast tumor and the ovarian cancer. It was not detected in normal tissue, suggesting that the breast tumors were metastatic serous adenocarcinomas from ovarian cancer. Conclusions A direct sequencing mutation analysis of p53 was useful for distinguishing the primary tumor from the metastatic tumor. We should resect metastatic breast tumors to the extent that is possible because the prognosis of such patients is relatively good

Solitary Fibrous Tumor of the Prostate: A Case Report and Literature Review

Solitary fibrous tumors (SFTs) usually occur in the pleura and account for two-thirds of all cases; however, SFTs occurring in the prostate are extremely rare. Approximately 25 cases have been reported in the literature to date. This study reports the case of a 43-year-old man referred to our hospital with the chief complaint of a pelvic tumor after careful examination. The tumor marker levels were within normal limits. T2-weighted magnetic resonance imaging revealed a tumor, demonstrating primarily low signal intensity. It showed a capsule-like rim at the left lobe of the prostate, suggesting that the tumor was partially invading the rectal wall. Histopathological examination of needle-core biopsies showed spindle cell neoplasm with small and fusiform cells, strongly expressing signal transducer and activator of transcription 6 (STAT6) with a ramifying vascular network. Therefore, the clinical diagnosis of the patient was SFT of the prostate and robot-assisted radical prostatectomy was performed. Histopathological examination revealed that the tumor was composed of spindle cells with patternless and staghorn patterns. Immunohistochemical analysis showed a strong expression of STAT6. Furthermore, the tumor was partially positive for CD34. Therefore, the patient was diagnosed with SFT of the prostate. Two years after the initial diagnosis, the patient was alive with normal erectile function, continence status, and no evidence of the disease

Solitary Fibrous Tumor of the Prostate: A Case Report and Literature Review

Solitary fibrous tumors (SFTs) usually occur in the pleura and account for two-thirds of all cases; however, SFTs occurring in the prostate are extremely rare. Approximately 25 cases have been reported in the literature to date. This study reports the case of a 43-year-old man referred to our hospital with the chief complaint of a pelvic tumor after careful examination. The tumor marker levels were within normal limits. T2-weighted magnetic resonance imaging revealed a tumor, demonstrating primarily low signal intensity. It showed a capsule-like rim at the left lobe of the prostate, suggesting that the tumor was partially invading the rectal wall. Histopathological examination of needle-core biopsies showed spindle cell neoplasm with small and fusiform cells, strongly expressing signal transducer and activator of transcription 6 (STAT6) with a ramifying vascular network. Therefore, the clinical diagnosis of the patient was SFT of the prostate and robot-assisted radical prostatectomy was performed. Histopathological examination revealed that the tumor was composed of spindle cells with patternless and staghorn patterns. Immunohistochemical analysis showed a strong expression of STAT6. Furthermore, the tumor was partially positive for CD34. Therefore, the patient was diagnosed with SFT of the prostate. Two years after the initial diagnosis, the patient was alive with normal erectile function, continence status, and no evidence of the disease