Central limit theorem for crossings in randomly embedded graphs

We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$. Using Stein's method and size-bias coupling, we prove an upper bound on the Kolmogorov distance between the distribution of the number of crossings and a standard normal random variable. As an application, we establish central limit theorems, along with convergence rates, for the number of crossings in random matchings, path graphs, cycle graphs, and the disjoint union of triangles.Comment: 18 pages, 5 figures. This is a merger of arXiv:2104.01134 and arXiv:2205.0399

Lipid-Rich Variant of Urothelial Carcinoma Presenting as the Dominant Morphology in a Recurrent Tumor After Local Therapy

Objective: Rare co-existance of disease or pathology Background: The lipid-rich variant is a rare and aggressive type of urothelial carcinoma (UCa), with less than 40 cases reported in the literature. This variant usually presents as an advanced-stage primary tumor. Case Report: We report the case of a 61-year-old man with previous history of T1 high-grade conventional urothelial carcinoma treated with local therapy. The patient later presented with a new 6.5-cm exophytic bladder mass. Histopathological examination revealed a T2 urothelial carcinoma of the lipid-rich variant. Retrospective review of the previous biopsies confirmed conventional high-grade urothelial car0cinoma, but scattered rare individual or small clusters of cells that resemble the lipid-rich variant urothelial carcinoma were also noted. Conclusions: The findings in this case suggest that the differential sensitivity of conventional urothelial carcinoma to local therapy may have allowed the lipid-rich variant to predominate in the recurrence. Pathologists should be aware of the lipid-rich variant of urothelial carcinoma. The prognostic significance of rare lipoblast-like cells among predominantly conventional urothelial carcinoma may requires further study

Condyloma Acuminata Presenting as Isolated Papillary Lesions in the Prostatic Urethra

BACKGROUND A condyloma acuminatum is a sexually transmitted, human papillomavirus (HPV) associated, neoplasm. In men, it is predominantly found on external genitalia and rarely progresses more proximally than the distal penile urethra. Condyloma acuminata of the prostatic urethra are rare and are usually seen as an extension of, or in association with external lesions. Therefore, it is not typically considered in the differential diagnosis of isolated papillary lesions limited to the prostatic urethra. CASE REPORT A 62-year-old male with rheumatoid arthritis treated with abatacept presented to urology due to a history of intermittent bladder self-catheterization for urinary obstruction. He underwent a transurethral resection of the prostate and had incidental findings of papillary lesions restricted to the prostatic urethra that were presumed to be urothelial carcinoma. Microscopic examination established the diagnosis of condyloma acuminata, and low-risk HPV 6 and 11 were detected by in-situ hybridization. Subsequent cystoscopy showed marked growth and extension of condyloma acuminata to near the external meatus. After multiple treatments with intraurethral 5-fluorouracil, several small lesions remained in the bulbous urethra. With follow up for 2 years since diagnosis, the patient has not developed external condylomata. CONCLUSIONS A condyloma acuminatum might present as an isolated papillary growth in the prostatic urethra without clinical or historical evidence of a visible lesion on external genitalia. Immunosuppression and/or urethral instrumentation might be a risk factor for such a presentation. Urologists and pathologists should be aware of this rare possibility in order to avoid misdiagnosis, and ensure that the patient receives appropriate therapy

Synthesis of zeolite A using raw kaolin from Ethiopia and its application in removal of Cr(III) from tannery wastewater

BACKGROUND: The commercial production of zeolite A mainly involves costly synthetic chemicals. However, cheaper raw materials such as clay minerals, coal ashes, natural zeolites, solid wastes and industrial sludge have been tested. Based on this, the objective of the present study is synthesis of zeolite A from two sources of raw kaolins (Ansho and Bombowha) from Ethiopia and evaluation of its application in tannery wastewater treatment. RESULTS: The synthesis result indicated high crystallinity (>90%) of zeolite A using Ansho kaolin. Lower grade Bombowha kaolin yielded zeolite A with crystallinity of 80%. In the tannery wastewater treatment study, a real sample having chromium concentration of 2036 mg L-1 was treated, obtaining 99.8% removal and about 200 mg g-1 adsorption capacity of Cr(III) using 100 g L-1 and 5 g L-1 adsorbent dose, respectively. This indicated that the synthesized zeolite A has great potential for Cr(III) removal from tannery wastewater. CONCLUSION: In this study, zeolite A has been synthesized from two sources of kaolin from Ethiopia and has been evaluated in tannery wastewater treatment. The synthesis result indicated the formation of crystals of zeolite A with optimum crystallinity of 91% and the material exhibited chromium removal efficiency of 99.8%

Evaluation of ethyl tert-butyl ether biodegradation in a contaminated aquifer by compound specific isotope analysis and in situ microcosms

Ethyl tert-butyl ether (ETBE) is an upcoming groundwater pollutant in Europe whose environmental fate has been less investigated thus far. In the present study, we investigated the in situ biodegradation of ETBE in a fuel-contaminated aquifer using compound-specific stable isotope analysis (CSIA) and in situ microcosms in combination with total lipid fatty acid (TLFA)-stable isotope probing (SIP). In a first field investigation, CSIA revealed no significant carbon isotope fractionation but low hydrogen isotope fractionation of up to +14 ¿ along the prevailing anoxic ETBE plume suggesting biodegradation of ETBE. Ten months later, oxygen injection was conducted to enhance the biodegradation of petroleum hydrocarbons (PH) at the field site. Within the framework of this remediation measure, in situ microcosms loaded with [13C6]-ETBE (BACTRAP®s) were exposed for 119 days in selected groundwater wells to assess the biodegradation of ETBE by TLFA-SIP under the following conditions: (i) ETBE as main contaminant; (ii) ETBE as main contaminant subjected to oxygen injection; (iii) ETBE plus other PH; (iv) ETBE plus other PH subjected to oxygen injection. Under all conditions investigated, significant 13C-incorporation into microbial total lipid fatty acids extracted from the in situ microcosms was found, providing clear evidence of ETBE biodegradation

Improved copper–epoxy adhesion by laser micro- and nano-structuring of copper surface for thermal applications

The objective of this work is the enhancement of metal-to-metal bonding to provide high thermal conductivity together with electrical insulation, to be used as heat sinks at room and cryo-genic temperatures. High thermal conductive metal (copper) and epoxy resin (Stycast 2850FT) were used in this study, with the latter also providing the required electrical insulation. The copper surface was irradiated with laser to induce micro- and nano-patterned structures that result in an improvement of the adhesion between the epoxy and the copper. Thus, copper-to-copper bonding strength was characterized by means of mechanical tensile shear tests. The effect of the laser processing on the thermal conductivity properties of the Cu/epoxy/Cu joint at different temperatures, from 10 to 300 K, is also reported. Using adequate laser parameters, it is possible to obtain high bonding strength values limited by cohesive epoxy fracture, together with good thermal conductivity at ambient and cryogenic temperatures. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Angiography with optical coherence tomography as a biomarker in multiple sclerosis

Purpose To investigate superficial retinal microvascular plexuses detected by optical coherence tomography angiography (OCT-A) in multiple sclerosis (MS) subjects and compare them with healthy controls. Methods A total of 92 eyes from 92 patients with relapsing-remitting MS and 149 control eyes were included in this prospective observational study. OCT-A imaging was performed using Triton Swept-Source OCT (Topcon Corporation, Japan). The vessel density (VD) percentage in the superficial retinal plexus and optic disc area (6 x 6 mm grid) was measured and compared between groups. Results MS patients showed a significant decrease VD in the superior (p = 0.005), nasal (p = 0.029) and inferior (p = 0.040) parafoveal retina compared with healthy subjects. Patients with disease durations of more than 5 years presented lower VD in the superior (p = 0.002), nasal (p = 0.017) and inferior (p = 0.022) parafoveal areas compared with healthy subjects. Patients with past optic neuritis episodes did not show retinal microvasculature alterations, but patients with an EDSS score of less than 3 showed a significant decrease in nasal (p = 0.024) and superior (p = 0.006) perifoveal VD when compared with healthy subjects. Conclusions MS produces a decrease in retinal vascularization density in the superficial plexus of the parafoveal retina. Alterations in retinal vascularization observed in MS patients are independent of the presence of optic nerve inflammation. OCT-A has the ability to detect subclinical vascular changes and is a potential biomarker for diagnosing the presence and progression of MS

Diagnostic ability and capacity of optical coherence tomography-angiography to detect retinal and vascular changes in patients with fibromyalgia

Background. To evaluate the neuroretina and retinal vasculature of fibromyalgia (FM) patients and calculate a linear discriminant function (LDF) to improve retinal parameters’ contribution to FM diagnosis. Methods. Fifty FM patients and 232 healthy controls underwent retinal evaluation using swept-source optical coherence tomography (SS-OCT) angiography (Triton plus; Topcon) and spectral domain OCT (SD-OCT) (Spectralis; Heidelberg). The macular (m) and peripapillary (p) retinal nerve fibre layer (RNFL) and ganglion cell layer (GCL) were assessed, as was the macular vascular density. A logistic regression analysis was performed, and an LDF was calculated to evaluate OCT’s contribution to FM diagnosis. Results. With Triton OCT, the patients presented pRNFL thinning in the temporal sector (). Spectralis OCT measurements showed decreased pRNFL in patients in the following sectors: superonasal, ; nasal, ; inferonasal, ; temporal, ; and inferotemporal, . No significant differences were observed in the macular vascular plexus between patients and controls. However, vascular density in the superior sector showed a strong inverse correlation with disease duration (r = −0.978, ). The LDF calculated for Spectralis OCT yielded an area under the ROC curve of 0.968. Conclusions. FM patients present RNFL thinning observable using SS- and SD-OCT. However, these patients show similar vascular density in the macular area to healthy controls. The LDF that combines several RNFL parameters obtained using Spectralis OCT gives this device a powerful ability to differentiate between healthy individuals and individuals with FM