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

Equation-Free Dynamic Renormalization: Self-Similarity in Multidimensional Particle System Dynamics

We present an equation-free dynamic renormalization approach to the computational study of coarse-grained, self-similar dynamic behavior in multidimensional particle systems. The approach is aimed at problems for which evolution equations for coarse-scale observables (e.g. particle density) are not explicitly available. Our illustrative example involves Brownian particles in a 2D Couette flow; marginal and conditional Inverse Cumulative Distribution Functions (ICDFs) constitute the macroscopic observables of the evolving particle distributions.Comment: 7 pages, 5 figure

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

Survival Outcomes and Patterns of Recurrence After Adjuvant Vaginal Cuff Brachytherapy and Chemotherapy in Early-Stage Uterine Serous Carcinoma

Background: Uterine serous carcinoma (USC) is a relatively rare histology that portends a poor prognosis. The optimal adjuvant therapy for early-stage USC remains controversial; however, adjuvant vaginal cuff brachytherapy (VB) and chemotherapy is a commonly utilized strategy. Objectives: We sought to characterize predictors of survival endpoints and determine recurrence patterns in women with early-stage USC who received adjuvant VB and chemotherapy. Methods: We queried our prospectively maintained database for patients with 2009 FIGO stages I-II USC who underwent adequate surgical staging at our institution and received adjuvant chemotherapy with carboplatin and paclitaxel along with VB. We excluded women with synchronous malignancies. Overall survival (OS), disease-specific survival (DSS), and recurrence-free survival (RFS) were assessed by Kaplan-Meier and log-rank tests. Univariate (UVA) and multivariate analyses (MVA) were performed to identify statistically significant predictors of survival endpoints. Variables with P\u3c0.1 on UVA were included in a MVA and any variable with P\u3c0.05 was considered statistically significant. Results: We identified 77 women who met our inclusion criteria who underwent surgical staging between 1991 and 2018. The median follow-up time was 36 months (range 6-125). The median age was 66 years. Of the cohort, 70% were FIGO stage IA, 17% were stage IB, and 13% were stage II. The median number of dissected lymph nodes (LN) was 22. There were 10 women (13%) diagnosed with a recurrence with a median time to recurrence of 12.0 months. The main site of initial recurrence was distant in seven patients (70%) with the remaining recurrences being pelvic/para-aortic. The 5-year RFS for patients who experienced a distant recurrence was 87% (95% Confidence Interval [CI] 0.75-0.94). For the entire cohort, 5-year OS, DSS, and RFS were 83% (95% CI 0.68-0.91), 92% (95% CI 0.78-0.97), and 83% (95% CI 0.71-0.91), respectively. The sole predictor of 5-year OS on UVA was receipt of omentectomy (P=0.09). The predictors of 5-year DSS on UVA were presence of positive peritoneal cytology (P=0.03), number of LN examined (Hazard Ratio [HR] 1.10, 95% CI 1.00-1.21, P=0.05), and number of para-aortic LN examined (HR 1.16 [95% CI 1.01-1.32], P=0.03). The sole independent predictor of DSS was the presence of positive peritoneal cytology (HR 0.03 [95% CI 0.00-0.72], P=0.03). Predictors of five-year RFS on UVA were robotic vs open surgery technique (P=0.06), presence of positive peritoneal cytology (P=0.01), percent myometrial invasion (HR 5.59 [95% CI 0.84-37.46], P=0.08), and presence of lymphovascular space invasion (LVSI) (P=0.05). Conclusions: Five-year survival outcomes were promising in this cohort of women with early-stage USC treated with adjuvant chemotherapy and VB; however, this study shows that the predominant pattern of relapse in this population is distant, suggesting the need to optimize systemic therapy. Possible predictors of worse outcomes include positive peritoneal cytology, deep myometrial invasion, and presence of LVSI. Multi-institutional pooled analyses are warranted to confirm our study results

Metatarsophalangeal joint pain in psoriatic arthritis: a cross-sectional study

Methods. Thirty-four consecutive patients with PsA (mean age 45.3 years, 65% female, mean disease duration 9.9 years) and 22 control participants (mean age 37.9 years, 64% female) underwent clinical and US examination to determine the presence of pain, swelling, synovitis, erosions, effusions and submetatarsal bursae at the MTP joints. Mean barefoot peak plantar pressures were determined at each MTP joint. Levels of pain, US-determined pathology and peak pressures were compared between groups. Binary logistic regression was used to identify demographic, clinical examination-derived, US-derived and plantar pressure predictors of pain at the MTP joints in the PsA group. Results. The presence of pain, deformity, synovitis, erosions (P < 0.001) and submetatarsal bursae and peak plantar pressure at MTP 3 (P < 0.05) were significantly higher in the PsA group. MTP joint pain in PsA was independently predicted by high BMI, female gender and the presence of joint subluxation, synovitis and erosion. Conclusion. These results suggest local inflammatory and structural factors, together with systemic factors (gender, BMI), are predominantly responsible for painful MTP joints in PsA, with no clear role for plantar pressure characteristics

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