Search

This study employed soft computing techniques, namely, support vector machine (SVM) and Gaussian process regression (GPR) techniques, to predict the properties of a scour hole [depth (ds) and length (Ls)] in a diversion channel flow system. The study considered different geometries of diversion channels (angles and bed widths) and different hydraulic conditions. Four kernel function models for each technique (polynomial kernel function, normalized polynomial kernel function, radial basis kernel, and the Pearson VII function kernel) were evaluated in this investigation. Root mean square error (RMSE) values are 8.3949 for training datasets and 11.6922 for testing datasets, confirming that the normalized polynomial kernel function-based GP outperformed other models in predicting Ls. Regarding predicting ds, the polynomial kernel function-based SVM outperforms other models, recording RMSE of 0.5175 for training datasets and 0.6019 for testing datasets. The sensitivity investigation of input parameters shows that the diversion angle had a major influence in predicting Ls and ds.

In this work, the fuzzy fractional two-point boundary value problems (FFTBVPs) are analyzed and solved using the fuzzy fractional homotopy analysis method (FF-HAM). Fuzzy set theory mixed with Caputo fractional derivative properties is utilized to produce a new formulation of the standard HAM in the fuzzy domain for the persistence of approximation series solutions for fuzzy fractional differential equations with boundary conditions. The FF-HAM provides a suitable way of controlling the convergence of the series solution through the advantage of the convergence control parameter, which plays a pivotal role in solving a wide range of mathematical problems. The convergence analysis algorithm has been described, along with a graphical representation of the FF-HAM of the proposed applications. The method produces high accuracy solutions with simple implementation for solving linear and nonlinear fuzzy fractional boundary value problems associated with physical application. Also, the obtained results are analyzed and compared with those present in the literature to show the efficiency of the FF-HAM.

In this work, the Optimal Homotopy Asymptotic Method (OHAM) is prolifically implemented to find the optimal solutions of fractional order of fuzzy differential equations. We inspect the competence of the method by examining fractional order time-dependent first order fuzzy initial value problems in the Caputo derivative sense. The concepts of fuzzy sets theory and fractional calculus were used to present a new general fuzzification formulation of the OHAM method followed by fuzzy analysis for the proposed fractional problems are presented in detail. OHAM is recognized as a feasible and convergent method for solving linear and nonlinear models, and it provides a convenient technique for controlling the convergence of approximate solutions optimally. The method's capability is demonstrated by obtaining approximate solutions to linear and nonlinear fuzzy initial value problems in various orders of fractional derivative. The numerical results acknowledge that OHAM is a feasible and transformation mechanism for solving linear and nonlinear fuzzy fractional initial value problems. Also, the results ensure that the method used was succinct, efficient, and simple to use, to deal with a more comprehensive fuzzy fractional differential equation.

BackgroundSpatial and single-cell transcriptomics have revealed significant heterogeneity in tumor and normal tissues. Each approach has its advantages: The Visium platform for spatial transcriptomics (ST) offers lower resolution than single-cell analysis, but histology enables the examination of cell morphology, tissue architecture, and potential cell-cell interactions. Single-cell transcriptomics (SC) provides high resolution, but manual cell-type annotation depends on incomplete scientific knowledge from heterogeneous experiments. When investigating poorly defined phenomena, such as the transition from normal tissue to cancer and metaplasia, researchers might overlook critical and unexpected findings in downstream analysis if they rely on pre-existing annotations to determine cell types, particularly in the context of phenotypic plasticity.ResultsWe employ our deep-transfer learning framework, DEGAS, to identify benign morphology glands in normal prostate tissue that are associated with poor progression-free survival in cancer patients and exhibit transcriptional signatures of carcinogenesis and de-differentiation. We confirm this finding in an additional ST dataset and use novel published methods to integrate SC data, showing that cells annotated as cancerous in the SC data map to regions of benign glands in another dataset. We pinpoint several genes, primarily MSMB, with expression closely correlated with progression-free survival scores, which are known markers of de-differentiation, and attribute their expression specifically to luminal epithelia, which are the presumed origin of most prostatic cancers.DiscussionOur work shows that morphologically normal epithelia can have transcriptional signatures like that of frank cancer, and that these tissues are associated with poor progression-free survival. We also highlight a critical gap in single-cell workflows: annotating continuous transitional phenomena like carcinogenesis with discrete labels can result in incomplete conclusions. Two approaches can help mitigate this issue: Tools like DEGAS and Scissor can provide a disease-association score for SC and ST data, independent of cell type and histology. Additionally, researchers should adopt a bidirectional approach, transferring histological labels from ST data to SC data using tools like RCTD, rather than only using SC cell-type assignments to annotate ST data. Employed together, these methods can offer valuable histology and disease-related information to better define tissue subtypes, especially epithelial cells in the process of carcinogenesis.ConclusionsDEGAS is a vital tool for generating clinically-oriented hypotheses from SC and ST data, which are heterogeneous, information-rich assays. In this study, we identify potential signatures of carcinogenesis in morphologically benign epithelia, which may be the precursors to cancer and high-grade pre-malignant lesions. Validating these genes as a panel may help identify patients at high risk for future cancer development, recurrence, and assist researchers in studying the biology of early carcinogenesis by detecting metaplastic changes before they are morphologically identifiable.

IntroductionMelanoma is the fifth most common cancer in US, and the incidence is increasing 1.4% annually. The overall survival rate for early-stage disease is 99.4%. However, melanoma can recur years later (in the same region of the body or as distant metastasis), and results in a dramatically lower survival rate. Currently there is no reliable method to predict tumor recurrence and metastasis on early primary tumor histological images.MethodsTo identify rapid, accurate, and cost-effective predictors of metastasis and survival, in this work, we applied various interpretable machine learning approaches to analyze melanoma histopathological H&E images. The result is a set of image features that can help clinicians identify high-risk-of-metastasis patients for increased clinical follow-up and precision treatment. We use simple models (i.e., logarithmic classification and KNN) and “human-interpretable” measures of cell morphology and tissue architecture (e.g., cell size, staining intensity, and cell density) to predict the melanoma survival on public and local Stage I–III cohorts as well as the metastasis risk on a local cohort.ResultsWe use penalized survival regression to limit features available to downstream classifiers and investigate the utility of convolutional neural networks in isolating tumor regions to focus morphology extraction on only the tumor region. This approach allows us to predict survival and metastasis with a maximum F1 score of 0.72 and 0.73, respectively, and to visualize several high-risk cell morphologies.DiscussionThis lays the foundation for future work, which will focus on using our interpretable pipeline to predict metastasis in Stage I & II melanoma.

A reaction-diffusion system can be represented by the Gray-Scott model. In this study, we discuss a one-dimensional time-fractional Gray-Scott model with Liouville-Caputo, Caputo-Fabrizio-Caputo, and Atangana-Baleanu-Caputo fractional derivatives. We utilize the fractional homotopy analysis transformation method to obtain approximate solutions for the time-fractional Gray-Scott model. This method gives a more realistic series of solutions that converge rapidly to the exact solution. We can ensure convergence by solving the series resultant. We study the convergence analysis of fractional homotopy analysis transformation method by determining the interval of convergence employing the ℏ u , v -curves and the average residual error. We also test the accuracy and the efficiency of this method by comparing our results numerically with the exact solution. Moreover, the effect of the fractionally obtained derivatives on the reaction-diffusion is analyzed. The fractional homotopy analysis transformation method algorithm can be easily applied for singular and nonsingular fractional derivative with partial differential equations, where a few terms of series solution are good enough to give an accurate solution.

Background The definitive diagnosis of melanocytic neoplasia using solely histopathologic evaluation can be challenging. Novel techniques that objectively confirm diagnoses are needed. This study details the development and validation of a melanoma prediction model from spatially resolved multivariate protein expression profiles generated by Imaging Mass Spectrometry (IMS). Methods Three board-certified dermatopathologists blindly evaluated 333 samples. Samples with triply concordant diagnoses were included in this study, divided into a training set (n = 241) and a test set (n = 92). Both the training and test sets included various representative subclasses of unambiguous nevi and melanomas. A prediction model was developed from the training set using a linear support vector machine (SVM) classification model. Results We validated the prediction model on the independent test set of 92 specimens (75 classified correctly, two misclassified, and 15 indeterminate). IMS detects melanoma with a sensitivity of 97.6% and a specificity of 96.4% when evaluating each unique spot. IMS predicts melanoma at the sample level with a sensitivity of 97.3% and a specificity of 97.5%. Indeterminate results were excluded from sensitivity and specificity calculations. Conclusion This study provides evidence that IMS-based proteomics results are highly concordant to diagnostic results obtained by careful histopathologic evaluation from a panel of expert dermatopathologists. This article is protected by copyright. All rights reserved.

A 60-year-old female presented with a large, left upper eyelid mass that had rapidly expanded in the 3 months prior to presentation. She had a presumed chalazion excised from the same area 1.5 years ago, but no pathology was investigated. On examination, she had a palpebral mass measuring 4.5 cm x 3.5 cm that abutted the globe with extensive conjunctival involvement. Neuroimaging demonstrated lesions concerning for parotid gland metastases. An incisional biopsy demonstrated synaptophysin-positive small blue cells concerning for neuroendocrine carcinoma. The patient underwent orbital exenteration with parotidectomy and radical neck dissection. The excised mass was found to have distinct neuroendocrine carcinoma cells intermingled with sebaceous carcinoma cells, a combination not previously reported.

River discharge links the hydrologic and geologic cycles in addition to climate components; therefore, it forms an important source of hydraulic and hydrologic quantity. The ability to quantify river discharge accurately is very important for estimating water availability and distribution for better water resources management. In this study, the performance of ARIMA, random forest (RF), the M5P and Bagged M5P (BM5P) methods, for modeling the daily discharge of the Baitarani Riverwere compared and evaluated against measured values. Fifteen different input combinations under two groups (i.e., discharge and rainfall) were considered, and a suitable modeling approach with appropriate model input combination is proposed on the basis of various goodness fit parameters. Four statistical assessment methods implemented to determine the best performing models include the correlation coefficient (CC), Mean square error (MSE), Root mean square error (RMSE) and Scattering Index (SI).The outcomes of this study indicated that the Bagged M5P modeling approach is outperforming than ARIMA, RF and M5P. This model recorded up to 0.8676, 10.7279, 39.836 m3/s and 0.9599 for (CC), (MAE), (RMSE) and (SI), respectively, for testing data set.

This work aims to propose a new simple robust power series formula with its truncation error to approximate the Caputo fractional-order operator $ D_{a}^{\alpha}y(t) $ of order $ m-1 < \alpha < m $, where $ m\in\mathbb{N} $. The proposed formula, which are derived with the help of the weighted mean value theorem, is expressed ultimately in terms of a fractional-order series and its reminder term. This formula is used successfully to provide approximate solutions of linear and nonlinear fractional-order differential equations in the form of series solution. It can be used to determine the analytic solutions of such equations in some cases. Some illustrative numerical examples, including some linear and nonlinear problems, are provided to validate the established formula.

Accumulation of the sediment in the stream of the diversion channels adversely affects its operational systems. Diversion channels are often constructed perpendicular to the main river. In this study, the water flow and sediment transport in the diversion channel with different angles were investigated in an attempt to maximize water discharge and minimize sediment discharge. A physical model with movable bed was used to simulate water and sediment flow with five diversion angles (θ) between (30°–90°). Moreover, three bed width ratios (Br) (the relation between diversion to main channel bed width) between 30% and 50% and five total discharges between (7.25 L/s to 12.25 L/s) were considered for each case of (θ). The results showed, up to 10%, increasing in proportion discharge ratios for 30 and 45 diversion angles compared with 90° diversion angle. The results also showed that the lowest diversion sediment concentration was provided by the (θ) of 30°. Across all scenarios, the average proportion concentration reduction was 64%, compared with 90° diversion angle. Closer observation of the diversion system mechanism confirmed that decreased (θ) result in decreased sediment concentrations in the diversion channels. In conclusion, the diversion channel water and sediment discharge could be effectively managed by changing the (θ) to 30° or 45° instead of 90°.

BackgroundLaser photocoagulation and/or intravitreal anti-vascular endothelial growth factor (anti-VEGF) injections constitute the current standard treatment for retinopathy of prematurity (ROP). This systematic review and meta-analysis aimed to assess the efficacy and safety of anti-VEGF monotherapy for ROP treatment using the Grading of Recommendations Assessment, Development and Evaluation (GRADE) approach.MethodsWe searched the Medline, Embase, and Cochrane Central Register of Controlled Trials (CENTRAL) databases. We included randomized controlled trials (RCTs) that compared intravitreal anti-VEGF monotherapy (e.g., bevacizumab, ranibizumab, aflibercept, and pegaptanib) with laser photocoagulation in preterm infants with ROP. We evaluated the rates of recurrence, treatment switching, retreatment, adverse events, and mortality. The risk ratio (RR) was used to represent dichotomous outcomes. Data were pooled using the inverse variance weighting method. The quality of evidence was assessed using the GRADE approach. Risk of bias was assessed using the Revised Cochrane risk of bias tool for randomized trials.ResultsSeven RCTs (n = 579; 1,158 eyes) were deemed eligible. Three RCTs had an overall low risk of bias, three had some concerns, and one had an overall high risk of bias. The pooled effect estimate showed a statistically significant reduction in adverse events in favor of anti-VEGF monotherapy [RR = 0.17, 95% confidence interval (CI) 0.07–0.44]. The pooled analysis showed no significant difference between the anti-VEGF and laser groups in terms of recurrence rate (RR = 1.56, 95% CI 0.23–10.54), treatment switching (RR = 2.92, 95% CI 0.40–21.05), retreatment (RR = 1.56, 95% CI 0.35–6.96), and mortality rate (RR = 1.28, 95% CI 0.48–3.41).ConclusionOverall, intravitreal anti-VEGF monotherapy was associated with fewer adverse events than laser therapy, rated as high quality of evidence according to the GRADE criteria. Pooled analysis revealed no significant difference between the two arms with respect to the recurrence rate, treatment switching, retreatment, and mortality rate, with quality of evidence ranging from moderate to very low as per the GRADE approach.Systematic Review Registration[https://www.crd.york.ac.uk/prospero/#recordDetails], identifier [CRD42021270077].

Chondromyxoid metaplasia can rarely lead to the formation of a distinctive tumor-like proliferation in the plantar foot. This is thought to represent a reactive or reparative process, possibly due to chronic trauma. For the unwary dermatopathologist, this could represent a diagnostic challenge. Herein, we review the clinical, histopathological, and molecular presentation of an athletic 17-year-old boy with a soft tissue mass arising in the right plantar foot. Microscopic examination showed a relatively circumscribed proliferation of spindle cells with abundant chondromyxoid stroma, hyalinization, and diffuse ERG reactivity. We also review characteristics of this entity that help differentiate it from clinical and histopathologic mimics and postulate possible links with soft tissue chondromas and immature chondroid choristoma.

Extranodal NK/T-cell lymphoma (NKTCL) is a rarely occurring non-Hodgkin lymphoma with predilection for the nasal cavity. Cutaneous involvement, rarely occurring and often aggressive in behavior, may present as nodular mass-forming lesions with or without ulceration. Histologically, lesions are characterized by an atypical dermal lymphoid infiltrate with angioinvasion and associated necrosis. Fortuitously, Epstein-Barr virus (EBV) infection, implicated in the pathogenesis of this entity, serves as a useful diagnostic marker (i.e. EBER in situ hybridization). We present a 54-year-old-man who initially presented with two ulcerations on the right lower leg which progressed despite antibiotic therapy. Histologic examination demonstrated dense lymphoid infiltrates exhibiting epidermotropism, angiocentricity and angioinvasion extending into the deep dermis. Immunohistochemical staining demonstrated expression of CD2, CD3, CD8, TIA-1, perforin, and granzyme-B, consistent with a cytotoxic T-cell phenotype. Additionally, CD56 was positive, confirming the presence of a coexistent NK cell phenotype. Testing also demonstrated significant CD30 expression, and molecular analysis was positive for TCR gene rearrangement. These findings, in conjunction with EBER in situ hybridization positivity, confirmed a diagnosis of extranodal NKTCL. We aim to increase awareness of this rarely occurring lymphoma with cutaneous involvement. CD30 expression in NKTCL raises the possibility of targeted treatment with brentuximab.

This research focuses on the approximate solutions of second-order fuzzy differential equations with fuzzy initial condition with two different methods depending on the properties of the fuzzy set theory. The methods in this research based on the Optimum homotopy asymptotic method (OHAM) and homotopy analysis method (HAM) are used implemented and analyzed to obtain the approximate solution of second-order nonlinear fuzzy differential equation. The concept of topology homotopy is used in both methods to produce a convergent series solution for the propped problem. Nevertheless, in contrast to other destructive approaches, these methods do not rely upon tiny or large parameters. This way we can easily monitor the convergence of approximation series. Furthermore, these techniques do not require any discretization and linearization relative with numerical methods and thus decrease calculations more that can solve high order problems without reducing it into a first-order system of equations. The obtained results of the proposed problem are presented, followed by a comparative study of the two implemented methods. The use of the methods investigated and the validity and applicability of the methods in the fuzzy domain are illustrated by a numerical example. Finally, the convergence and accuracy of the proposed methods of the provided example are presented through the error estimates between the exact solutions displayed in the form of tables and figures.

Increasingly, molecular methods are being utilized in the workup of melanocytic neoplasms. To this end, we sought to correlate data from a single nucleotide polymorphism (SNP) array platform based on molecular inversion probes with clinical data. Copy number variation (CNV) data were obtained on 95 melanocytic tumors (6 ordinary nevi, 15 atypical nevi, 34 ambiguous neoplasms, and 40 melanomas) from 92 patients. The average number of significant CNVs was 0 for nevi, 0.6 for atypical nevi (range 0–3), 2.8 for ambiguous neoplasms (range 0–17), and 18.1 for melanomas (range 0–69). Clinical follow-up data were available in 57 of 95 lesions (56 of 92 patients). Tumors from patients with adverse events demonstrated an average number of CNVs of 24.5 (range 6–69) as compared with 7.9 (range 0–35) among tumors without an associated adverse event (p ≤ 0.001). No adverse events were observed in nevi including atypical nevi. Adverse events were found in 2 of 19 ambiguous neoplasms and 10 of 32 melanomas with follow up. In these two latter groups of neoplasms, the correlation between adverse events and the average number of CNVs remained statistically significant even when controlled for Breslow depth (21.5 versus 8.7, p value = 0.036). No neoplasm with adverse events had ≤3 CNVs. These results provide further evidence that SNP array testing for CNVs may be helpful in the classification and prognostication of ambiguous neoplasms. Based on these results, an algorithmic approach to challenging melanocytic neoplasms using CNV data is suggested, using as cutoff of >3 CNVs with some caveats, as the threshold for a positive result. Future clinical validation, using a larger cohort of relevant tumors, will be necessary.

Multi-proxy signature schemes (MPSS) allow n proxy signers to generate a valid signature on behalf of the original signer. A new efficient self-certified MPSS with message recovery based on the Ell...

In this paper we consider the homotopy analysis transform method (HATM) to solve the time fractional order Korteweg-de Vries (KdV) and Korteweg-de Vries-Burger’s (KdVB) equations. The HATM is a combination of the Laplace decomposition method (LDM) and the homotopy analysis method (HAM). The fractional derivatives are defined in the Caputo sense. This method gives the solution in the form of a rapidly convergent series with h-curves are used to determine the intervals of convergent. Averaged residual errors are used to find the optimal values of h. It is found that the optimal h accelerates the convergence of the HATM, with the rate of convergence depending on the parameters in the KdV and KdVB equations. The HATM solutions are compared with exact solutions and excellent agreement is found.

This article introduces some new straightforward and yet powerful formulas in the form of series solutions together with their residual errors for approximating the Riemann-Liouville fractional derivative operator. These formulas are derived by utilizing some of forthright computations, and by utilizing the so-called weighted mean value theorem (WMVT). Undoubtedly, such formulas will be extremely useful in establishing new approaches for several solutions of both linear and nonlinear fractionalorder differential equations. This assertion is confirmed by addressing several linear and nonlinear problems that illustrate the effectiveness and the practicability of the gained findings.

Background Pediatric Drug reaction with eosinophilia and systemic symptoms (DRESS) is an uncommon disease that can be difficult to diagnose. This case series and literature review highlights the clinical features of pediatric DRESS and underscores the differential diagnoses, culprit medications, and need for clinical follow-up to detect associated autoimmune sequelae. Objective To describe the clinical and laboratory features of pediatric DRESS, identify associated culprit medications, and discuss the natural history of disease. Methods Ten cases of pediatric DRESS were identified in the electronic medical record by searching the inpatient dermatology consultation list at Indiana University between 2013 and 2018. Clinical and laboratory data were collected including demographics, differential diagnoses, culprit medications, resolution of disease, and autoimmune sequelae. Results Pediatric patients with DRESS presented at a mean age of 11.5 years and demonstrated a mean time from drug initiation to onset of symptoms of 4 weeks. The most common inciting drugs included antibiotics (62.5%) followed by antiepileptics (37.5%). Rash and transaminitis resolved by 3 weeks, and 20% of patients, all female, developed autoimmune sequelae including Hashimoto's thyroiditis and an undifferentiated connective tissue disorder and occurred at an average of 14.5 weeks after diagnosis. Limitations This was a small retrospective study of an uncommon clinical diagnosis at a single institution. Conclusions Pediatric DRESS was most commonly caused by antibiotics which are being increasingly recognized in the literature as the predominant culprit medications. The development of autoimmune sequelae is a notable consequence that can present weeks after illness and may preferentially affect female patients.

Germline mutations in BRCA1-associated protein 1 (BAP1) are associated with several neoplasms, including BAP1-inactivated melanocytic tumors (BIMTs). BIMTs are classically described as biphenotypic melanocytic proliferations with BAP1-deficient large epithelioid and rhabdoid melanocytes showing various degrees of cytologic atypia. This morphology has been traditionally classified as "spitzoid" despite the various differences between these lesions and the more classic Spitz nevi. Herein, we report a case of an otherwise healthy 11-year-old female patient with a family history of several malignancies who presented with multiple pink to brown papules. Histologic and immunohistochemical evaluation identified three lesions with loss of nuclear BAP1 staining. The histologic spectrum of these lesions included junctional spitzoid cells within a triphenotypic proliferation and a separate lesion composed entirely of dermal small to medium-sized epithelioid melanocytes with maturation. BAP1 gene sequencing revealed a germline frameshift pathogenic BAP1 mutation, denoted c.1717delC. This case provides further evidence that not all BIMTs conform to classic morphological criteria and that the morphologic spectrum includes lesions resembling conventional nevi. As BIMTs can serve as an early marker of the BAP1 hereditary tumor predisposition syndrome, we believe a need exists for a more comprehensive combined clinical and pathological approach for BIMT identification.

The profound characteristics of factoring problems and chaotic maps are utilized in this article to produce a new identity-based cryptographic scheme. These characteristics include random b...

Dedifferentiated metastatic melanoma can pose a significant diagnostic challenge, especially if the history of primary melanoma is not known or is remote. BRAF and NRAS mutations are common melanoma driver mutations that are usually sequenced to evaluate for treatment targets. We evaluated whether BRAF and NRAS mutational testing could contribute to the diagnosis of dedifferentiated metastatic melanoma when immunostains are negative. Seven patients with melanoma who had an additional diagnosis of poorly differentiated sarcoma with negative melanocytic immunostains were tested for BRAF and NRAS mutations. Three patients showed identical BRAF mutations in the melanoma and the poorly differentiated sarcoma and hence were re-classified as metastatic dedifferentiated melanoma. In these three patients, there was an average delay of 7 months before appropriate testing, workup and treatment for metastatic melanoma was initiated. Two of these patients currently have stable metastatic disease and show sustained therapeutic response to melanoma-specific treatment including BRAF inhibitors. BRAF mutational analysis should therefore be considered in cases of poorly differentiated sarcoma, especially if there is a known history of melanoma or with unusual localization of disease. The administration of melanoma-specific treatments in such dedifferentiated cases can show therapeutic response, highlighting the importance of rendering accurate diagnoses on such cases.

In this paper, a numerical procedure called multistage optimal homotopy asymptotic method (MOHAM) is introduced to solve multi-pantograph equations with time delay. It was shown that the MOHAM algorithm rapidly provides accurate convergent approximate solutions of the exact solution using only one term. A comparative study between the proposed method, the homotopy perturbation method (HPM) and the Taylor matrix method are presented. The obtained results revealed that the method is of higher accuracy, effective and easy to use.

The hyperchaotic system is a condition of phenomenal uncertainty in which at least two Lyapunov exponents are present in the system. For the analytical solution of the hyperchaotic Zhou system, the multistage homotopy analysis approach is used in this article. The solution constructs a convergent series in terms of the exponential combination and polynomial functions that use a few terms of this series to obtain higher accuracy. To demonstrate the efficiency of the proposed method, the residual error is presented.

Background Existing literature on post-endoscopic retrograde cholangiopancreatography (ERCP) complications in patients with liver transplant remains scarce and largely inconsistent. We therefore aimed to systematically review and analyze the literature on complication rates associated with ERCP in patients with liver transplant. Methods We performed a comprehensive literature search in PubMed, PubMed Central, Embase, and ScienceDirect databases from inception through March 2020 to identify all the studies that evaluated post-ERCP complications in patients with liver transplant. Effect estimates from the individual studies were extracted and combined using the random effect, generic inverse variance method of DerSimonian and Laird, and a pooled odds ratio (OR) and event rates were calculated. Forest plots were generated, and publication bias was assessed for using conventional techniques. Results Fourteen studies with a total of 1,787 patients were analyzed. In total, 3,192 ERCPs were performed on these patients. The pooled all-complication rate was 5.2% (95% confidence interval (CI): 0.035 - 0.075). Procedural complications analyzed included post-ERCP pancreatitis 3.4% (95% CI: 0.025 - 0.047), bleeding 1.1% (95% CI: 0.006 - 0.020), infections 0.2% (95% CI: 0.025 - 0.047), and cholangitis 0.8% (95% CI: 0.004 - 0.020). No cases of periprocedural death were reported. The pooled OR for post-ERCP pancreatitis in patients with liver transplant compared to patients without liver transplant was 1.289 (95% CI: 0.455 - 3.653, P = 0.633, I2 = 72.88%). Conclusion Post-ERCP complication rates in liver transplant patients are comparable to the general population and hence, peri-procedural evaluation and management may follow the current standards of care in this patient population.

Background PRAME (PReferentially expressed Antigen in Melanoma) immunohistochemistry has demonstrated high specificity for unequivocal melanomas; however, its utility in ambiguous melanocytic neoplasms has yet to be fully elucidated. Methods Cases of challenging melanocytic neoplasms were subclassified into one of three categories: challenging, favor benign (FB), challenging, cannot be subclassified (CCS), or challenging, favor malignant (FM). Using a previously published system, whereby cases with diffuse staining (>75%) were considered positive, scoring of PRAME was performed. Additionally, tumors with hotspot staining were also considered positive. Results Sixteen out of 85 tumors showed positive staining representing 5% of FB tumors, 24% of CCS tumors, and 47% of FM. In FB and CCS tumors, positive staining was mainly encountered in atypical intraepidermal melanocytic proliferations and spitzoid neoplasms. The specificity of positive PRAME staining was 95% and its concordance with the final diagnostic interpretation was 75%. Conclusions PRAME positivity is more common in neoplasms favored to be malignant by histopathologic evaluation. Its clinical utility may include early diagnosis of incipient melanoma in situ. Rarely, benign melanocytic neoplasms could show diffuse expression of PRAME, and additional studies are needed to determine optimal utilization. Lastly, hotspot staining may increase its sensitivity without much compromise in specificity.

In this study, we introduce an efficient computational method to obtain an approximate solution of the time-dependent Emden-Fowler type equations. The method is based on the 2D-Bernstein polynomials (2D-BPs) and their operational matrices. In the cases of time-dependent Lane&ndash, Emden type problems and wave-type equations which are the special cases of the problem, the method converts the problem to a linear system of algebraic equations. If the problem has a nonlinear part, the final system is nonlinear. We analyzed the error and give a theorem for the convergence. To estimate the error for the numerical solutions and then obtain more accurate approximate solutions, we give the residual correction procedure for the method. To show the effectiveness of the method, we apply the method to some test examples. The method gives more accurate results whenever increasing n,m for linear problems. For the nonlinear problems, the method also works well. For linear and nonlinear cases, the residual correction procedure estimates the error and yields the corrected approximations that give good approximation results. We compare the results with the results of the methods, the homotopy analysis method, homotopy perturbation method, Adomian decomposition method, and variational iteration method, on the nodes. Numerical results reveal that the method using 2D-BPs is more effective and simple for obtaining approximate solutions of the time-dependent Emden-Fowler type equations and the method presents a good accuracy.

In this article, we proposed an efficient method to solve the delay Fractional Bagley-Torvik equation. The proposed method is capable of reducing the volume of the computational work as compared to the classical techniques while still maintaining the high accuracy of the numerical result; the size reduction amounts to an improvement of the performance of the approach. Our concern was to provide an analytic solution to the Bagley-Torvik equation using a relatively new analytical technique, the homotopy-Sumudu transformation method. The method does not need to calculate the fractional derivatives or integrations in each term. The results compared with implicit hybrid one-step method yield the efficiency of the presented algorithm. Also, the calculations involved in the method are very simple and straightforward.