Boundary interpolation for slice hyperholomorphic Schur functions

A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers $\kappa_1, \ldots, \kappa_N$, quaternions $p_1, \ldots, p_N$ all of modulus $1$, so that the $2$-spheres determined by each point do not intersect and $p_u \neq 1$ for $u = 1,\ldots, N$, and quaternions $s_1, \ldots, s_N$, we wish to find a slice hyperholomorphic Schur function $s$ so that $$\lim_{\substack{r\rightarrow 1\\ r\in(0,1)}} s(r p_u) = s_u\quad {\rm for} \quad u=1,\ldots, N,$$ and $$\lim_{\substack{r\rightarrow 1\\ r\in(0,1)}}\frac{1-s(rp_u)\overline{s_u}}{1-r}\le\kappa_u,\quad {\rm for} \quad u=1,\ldots, N.$$ Our arguments relies on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces

Coarse-graining the dynamics of coupled oscillators

We present an equation-free computational approach to the study of the coarse-grained dynamics of {\it finite} assemblies of {\it non-identical} coupled oscillators at and near full synchronization. We use coarse-grained observables which account for the (rapidly developing) correlations between phase angles and oscillator natural frequencies. Exploiting short bursts of appropriately initialized detailed simulations, we circumvent the derivation of closures for the long-term dynamics of the assembly statistics.Comment: accepted for publication in Phys. Rev. Let

Recurrence Risk Stratification for Women with FIGO Stage I Uterine Endometrioid Carcinoma Who Underwent Surgical Lymph Node Evaluation

Purpose/Objective(s): To estimate the recurrence risk based on the number of prognostic factors in women with FIGO stage I uterine endometrioid carcinoma (EC) in a large cohort of patients who underwent surgical staging including surgical lymph node evaluation (SLNE) and were managed with no adjuvant therapy. Materials/Methods: We queried our in-house prospectively maintained uterine cancer database for patients with FIGO stage I EC underwent surgical staging including SLNE between 1/1990-12/2020. Patients with synchronous ovarian and breast cancer diagnosis were excluded as well as those who received adjuvant therapy of any form. Patient\u27s demographics and pathologic variables were analyzed. We used multivariate analysis (MVA) with Stepwise Model Selection to determine risk factors for 5-year recurrence-free survival (RFS). Study population was then stratified based on the number of risk factors identified (0, 1 or 2). The resultant groups were compared for RFS, disease-specific survival (DSS) and overall survival (OS) using log-rank test and Kaplan-Meier curves. Additionally, independent predictors of DSS and overall OS were estimated. Results: 706 patients were identified who met our inclusion criteria with a median age of 60 years (range, 30-93) and a median follow-up of 120 months. All patients had at least pelvic SLNE with a median number of examined lymph node (LN) of 8 (range, 1-66): 66 patients (11%) had a sentinel LN sampling and 43% had paraaortic SLNE. 639 patients (91%) were stage IA and lymphovascular space invasion (LVSI) was detected in 6% (n=41). Recurrence was diagnosed in 44 patients (6%). Independent predictors of 5-year RFS include age ≥ 60 years (p=0.038), grade 2 vs. 1 (p=0.003), and grade 3 vs 1 (p\u3c0.001). 5-year RFS for group-0 (age \u3c 60 years and grade 1) was 98% vs. 92% for group-1 (either: age ≥ 60 years or grade 2/3) vs 84% for group-2 (both: age ≥ 60 years and grade 2/3), respectively (p\u3c0.001). 5- year DSS for the three groups was (100% vs 98% vs 95%, p=0.012) and 5-year OS was (98% vs 90% vs 81%, p\u3c0.001), respectively. On MVA, stage IB vs IA was deterministic for DSS (p=0.02); whereas age ≥ 60 years (p\u3c0.001) and grade 3 vs grade 1 (p=0.004) were predictors for worse OS. Conclusion: In patients with stage I endometrioid carcinoma who had surgical staging including SLNE and no adjuvant therapy, only age ≥ 60 years and high tumor grade were independent predictors of cancer recurrence and hence can be used to quantify individualized recurrence risk. Surprisingly, LVSI was not an independent prognostic factor in this study cohort with SLNE

The Automation of the Extraction of Evidence masked by Steganographic Techniques in WAV and MP3 Audio Files

Antiforensics techniques and particularly steganography and cryptography have become increasingly pressing issues that affect the current digital forensics practice, both techniques are widely researched and developed as considered in the heart of the modern digital era but remain double edged swords standing between the privacy conscious and the criminally malicious, dependent on the severity of the methods deployed. This paper advances the automation of hidden evidence extraction in the context of audio files enabling the correlation between unprocessed evidence artefacts and extreme Steganographic and Cryptographic techniques using the Least Significant Bits extraction method (LSB). The research generates an in-depth review of current digital forensic toolkit and systems and formally address their capabilities in handling steganography-related cases, we opted for experimental research methodology in the form of quantitative analysis of the efficiency of detecting and extraction of hidden artefacts in WAV and MP3 audio files by comparing standard industry software. This work establishes an environment for the practical implementation and testing of the proposed approach and the new toolkit for extracting evidence hidden by Cryptographic and Steganographic techniques during forensics investigations. The proposed multi-approach automation demonstrated a huge positive impact in terms of efficiency and accuracy and notably on large audio files (MP3 and WAV) which the forensics analysis is time-consuming and requires significant computational resources and memory. However, the proposed automation may occasionally produce false positives (detecting steganography where none exists) or false negatives (failing to detect steganography that is present) but overall achieve a balance between detecting hidden data accurately along with minimising the false alarms.Comment: Wires Forensics Sciences Under Revie

Multifocal Metachronous Giant Cell Tumor: Case Report and Review of the Literature

Introduction. Giant cell tumors (GCTs) of bone are known for their local aggressiveness and high recurrence rate. There are rare cases of multicentric GCT and most are synchronous. We herein review metachronous multicentric GCT reported in the literature. Material and Methods. A MEDLINE, Cochrane, and Google Scholar search was done to collect all cases of multicentric metachronous GCT specifying the clinical, radiological, and histological characteristics of each location and its treatment. Results. A total of 37 multifocal giant cell tumors were found in the literature. 68% of cases of multicentric giant cell tumors occur in less than 4 years following treatment of the first lesion. Thirty-seven cases of multifocal metachronous GCT were identified in the literature until 2012. Patients with multicentric GCT tend to be younger averaging 23. There is a slight female predominance in metachronous GCT. The most common site of the primary GCT is around the knee followed by wrist and hand and feet. Recurrence rate of multicentric GCT is 28.5%. Conclusion. Multicentric giant cell tumor is rare. The correct diagnosis relies on correlation of clinical and radiographic findings with confirmation of the diagnosis by histopathologic examination

Sensitivity analysis and variance reduction in a stochastic NDT problem

In this paper, we present a framework to deal with uncertainty quantification in case where the ranges of variability of the random parameters are ill-known. Namely the physical properties of the corrosion product (magnetite) which frequently clogs the tube support plate of steam generator, which is inaccessible in nuclear power plants. The methodology is based on Polynomial Chaos (PC) for the direct approach and on Bayesian inference for the inverse approach. The direct Non-Intrusive Spectral Projection (NISP) method is first employed by considering prior probability densities and therefore constructing a PC surrogate model of the large-scale NDT finite element model. To face the prohibitive computational cost underlying the high dimensional random space, an adaptive sparse grid technique is applied on NISP resulting in drastic time reduction. The PC surrogate model, with reduced dimensionality, is used as a forward model in the Bayesian procedure. The posterior probability densities are then identified by inferring from few noisy experimental data. We demonstrate effectiveness of the approach by identifying the most influential parameter in the clogging detection as well as a variability range reduction

Clinical Study One-Haptic Fixation of Posterior Chamber Intraocular Lenses without Scleral Flaps

is properly cited. Purpose. To assess visual results and complications of a modified technique of posterior chamber intraocular lenses (PC IOLs) in aphakic eyes without scleral flaps. Methods. Modified one-haptic scleral fixation was performed in one eye each of 25 patients with aphakia and insufficient capsule support. Follow-up period was six months. Outcome measures included best-corrected visual acuity, intraocular pressure (IOP), and postoperative complications. Results. The study included 15 males and 10 females. The preoperative best-corrected visual acuity (BCVA) ranged from 5/60 to 6/9. The operation time ranged from 25 to 45 minutes (mean 35.25 ± 5.34 min). Anterior vitrectomy was performed in 12 cases (48%). There was no major IOL decentration. The final BCVA ranged from 6/36 to 6/9. Seven cases (28%) showed postoperative glaucoma, five cases (20%) had temporary hypotony, and hyphema in 2 eyes (8%). No cases of suture erosion, postoperative endophthalmitis, retinal detachment, or IOL dislocation were detected. Conclusion. This technique of one-haptic scleral fixation of posterior chamber IOLs is a good choice in presence of insufficient capsule support. It reduces the operation time, achieves the IOL stability, and minimizes postoperative suture-related complications