Multiplicative noise: A mechanism leading to nonextensive statistical mechanics

A large variety of microscopic or mesoscopic models lead to generic results that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based on $S_1\equiv -k \int du p(u) \ln p(u)$). Similarly, other classes of models point toward nonextensive statistical mechanics (based on $S_q \equiv k [1-\int du [p(u)]^q]/[q-1]$, where the value of the entropic index $q\in\Re$ depends on the specific model). We show here a family of models, with multiplicative noise, which belongs to the nonextensive class. More specifically, we consider Langevin equations of the type $\dot{u}=f(u)+g(u)\xi(t)+\eta(t)$, where $\xi(t)$ and $\eta(t)$ are independent zero-mean Gaussian white noises with respective amplitudes $M$ and $A$. This leads to the Fokker-Planck equation $\partial_t P(u,t) = -\partial_u[f(u) P(u,t)] + M\partial_u\{g(u)\partial_u[g(u)P(u,t)]\} + A\partial_{uu}P(u,t)$. Whenever the deterministic drift is proportional to the noise induced one, i.e., $f(u) =-\tau g(u) g'(u)$, the stationary solution is shown to be $P(u, \infty) \propto \bigl\{1-(1-q) \beta [g(u)]^2 \bigr\}^{\frac{1}{1-q}}$ (with $q \equiv \frac{\tau + 3M}{\tau+M}$ and $\beta=\frac{\tau+M}{2A}$). This distribution is precisely the one optimizing $S_q$ with the constraint $_q \equiv \{\int du [g(u)]^2[P(u)]^q \}/ \{\int du [P(u)]^q \}=$constant. We also introduce and discuss various characterizations of the width of the distributions.Comment: 3 PS figure

Surgical outcomes of patients with diffuse-type tenosynovial giant-cell tumours: an international, retrospective, cohort study

Background: Diffuse-type tenosynovial giant-cell tumour is a rare, locally aggressive, and difficult-to-treat soft tissue tumour. Clinical and surgical outcomes depend on multiple factors, including preoperative diagnostic assessment, the localisation and extent of disease, and possibly the choice of treatment modalities by orthopaedic surgeons. We did a retrospective cohort study to characterise global surgical treatment protocols, and assess surgical outcomes, complications, and functional results in patients with diffuse-type tenosynovial giant-cell tumours. Methods: In this international, multicentre, retrospective cohort study, we included consecutive patients treated in 31 sarcoma reference centres between Jan 1, 1990, and Dec 31, 2017. Eligible patients were of any age and had histologically proven diffuse-type tenosynovial giant-cell tumour of large joints. Patient data were retrieved from the local databases of participating centres. Patients with localised-type tenosynovial giant-cell tumour were excluded. In the analysis, we only included patients with complete core criteria data regarding admission status, date of treatment, type of treatment at participating centre, and first local recurrence after treatment. We used a non-parametric method to estimate recurrence-free survival at 3, 5, and 10 years after initial surgical resection in a tertiary centre. We used a multivariate Cox regression model to estimate the effect of risk factors. We also present subgroup analyses of disease status at presentation (primary vs recurrent disease)and recurrence-free survival by surgery type (open surgery vs arthroscopic synovectomy), and prespecified risk factors were tested in a univariate and multivariable analyses, with an endpoint of first local recurrence after treatment in a tertiary centre. Findings: Data collection for these analyses occurred between January, 2016, and May, 2018. We received the records of 1192 patients, of which 966 (81%)were surgically treated and had complete information on core criteria. 445 patients were admitted with therapy-naive disease of the knee and were primarily treated in a tertiary centre. Since patients with wait and see treatment do not have a starting date of treatment, these patients were excluded in the calculation of median follow-up time for all patients. For this calculation we used time of surgery as a starting date. 758 (64%)of 1192 patients had knee involvement and 628 (54%)of 1163 patients with complete data on type of surgery had one-staged open synovectomy. At a median follow-up of 54 months (IQR 27\u201397), recurrent disease developed in 425 (44%)of all 966 surgically treated cases, and recurrence-free survival was 62% (95% CI 59\u201365)at 3 years, 55% (51\u201358)at 5 years, and 40% (35\u201345)at 10 years. Surgical complications were reported in 105 (12%)of 906 patients who had complete data on surgical complications. Pain improved after surgical treatment in 255 (59%)of 434 patients and swelling improved in 328 (72%)of 453 patients who had complete data. Interpretation: This study of patients with diffuse-type tenosynovial giant-cell tumour provides a comprehensive and up-to-date disease overview, assessing the clinical profile and management of the disease in multiple specialised referral centres. Surgical treatment of diffuse-type tenosynovial giant cell tumours is not a definitive treatment for every patient because it involves a high risk for local recurrent disease and a relatively high risk for postoperative complications. After surgical treatment in treatment-naive patients, risk factors for recurrent disease in individual patients were not identified in what we believe is the largest cohort to date. Funding: Daiichi Sankyo

Surgical Treatment of Localized-Type Tenosynovial Giant Cell Tumors of Large Joints

Contains fulltext : 208133.pdf (publisher's version ) (Closed access)Background: Localized-type tenosynovial giant cell tumor (TGCT) is a rare, neoplastic disease with only limited data supporting treatment protocols. We describe treatment protocols and evaluate their oncological outcome, complications, and functional results in a large multicenter cohort of patients. A secondary study aim was to identify factors associated with local recurrence after surgical treatment. Methods: Patients with histologically proven localized TGCT of a large joint were included if they had been treated between 1990 and 2017 in 1 of 31 tertiary sarcoma centers. Of 941 patients with localized TGCT, 62% were female. The median age at initial treatment was 39 years, and the median duration of follow-up was 34 months. Sixty-seven percent of the tumors affected the knee, and the primary treatment at the tertiary center was 1-stage open resection in 73% of the patients. Proposed factors for predicting a first local recurrence after treatment in the tertiary center were tested in a univariate analysis, and those that demonstrated significance were subsequently included in a multivariate analysis. Results: The localized TGCT recurred in 12% of all cases, with local-recurrence-free rates at 3, 5, and 10 years of 88%, 83%, and 79%, respectively. The strongest factor for predicting recurrent disease was a prior recurrence (p < 0.001). Surgical treatment decreased pain and swelling in 71% and 85% of the patients, respectively, and such treatment was associated with complications in 4% of the patients. Univariate and multivariate analyses of the patients who had not undergone therapy previously yielded positive associations between local recurrence and a tumor size of >= 5 cm versus <5 cm (hazard ratio [HR] = 2.50; 95% confidence interval [CI] = 1.32 to 4.74; p = 0.005). Arthroscopy (versus open surgery) was significantly associated with tumor recurrence in the univariate analysis (p = 0.04) but not in the multivariate analysis (p = 0.056). Conclusions: Factors associated with recurrence after resection of localized-type TGCT were larger tumor size and initial treatment with arthroscopy. Relatively low complication rates and good functional outcomes warrant an open approach with complete resection when possible to reduce recurrence rates in high-risk patients

Characteristics, management, and outcomes of patients with left‐sided infective endocarditis complicated by heart failure: a substudy of the ESC‐EORP EURO‐ENDO (European infective endocarditis) registry

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