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There has been a great deal of interest in the last few years for neural networks (NNs) with values in multidimensional domains. The most popular models are complex-valued neural networks (CVNNs), followed by quaternion-valued neural networks (QVNNs), and, more recently, by Clifford-valued neural networks (ClVNNs). However, also very recently, a different type of NNs were put forward, namely octonion-valued neural networks (OVNNs). OVNNs are defined on the 8D octonion algebra, and they are not a special type of ClVNNs, because Clifford numbers are associative, whereas octonions are not. Moreover, beside the complex and quaternion algebras, the only other normed division algebra over the reals is the algebra of octonions, which makes OVNNs a direct generalization of CVNNs and QVNNs from this point of view, raising interest for applications handling high-dimensional data. On the other hand, systems defined on time scales were proposed as a generalization of both discrete time and continuous time systems, or any type of hybrid combination between the two. Finally, time delays appear as a consequence of implementing NNs in real life circuits. Taking all these into consideration, this paper studies the fundamental properties of exponential stability and exponential synchronization for OVNNs with leakage and mixed delays defined on time scales. In order to avoid the problems raised by the non-associativity of the octonion algebra, the OVNN model is decomposed into a real-valued one. Then, two different Lyapunov-type functionals are defined and the particularities of time scale calculus are used in order to deduce sufficient conditions expressed as scalar and linear matrix inequalities (LMIs) for the exponential stability of the proposed models, based on Halanay-type inequalities suitable for time scale systems. Afterwards, a state feedback controller is used to deduce sufficient criteria given as scalar inequalities and LMIs for the exponential synchronization of the same type of models. The generality of the model, given by the definition on the algebra of octonions, the use of different types of delays, and the definition on time scales represent an important advantage. Also, for less general models, it is possible to particularize the obtained results. With the aim to demonstrate each of the paper's four theorems, four numerical examples are provided. [ABSTRACT FROM AUTHOR]

Pulmonary complications (PC) are common after esophagectomy and their impact on long-term survival is not defined yet. The present study aimed to assess the effect of postoperative PCs on long-term survival after esophagectomy for cancer. Systematic review of the literature through February 1, 2023, was performed. The included studies evaluated the effect of PC on long-term survival. Primary outcome was long-term overall survival (OS). Cancer-specific survival (CSS) and disease-free survival (DFS) were secondary outcomes. Restricted mean survival time difference (RMSTD), hazard ratio (HR), and 95% confidence intervals (CI) were used as pooled effect size measures. Eleven studies were included (3423 patients). Overall, 674 (19.7%) patients developed PC. The RMSTD analysis shows that at 60-month follow-up, patients not experiencing PC live an average of 8.5 (95% CI 6.2–10.8; p < 0.001) months longer compared with those with PC. Similarly, patients not experiencing postoperative PC seem to have significantly longer CSS (8 months; 95% CI 3.7–12.3; p < 0.001) and DFS (5.4 months; 95% CI 1.6–9.1; p = 0.005). The time-dependent HRs analysis shows a reduced mortality hazard in patients without PC at 12 (HR 0.6, 95% CI 0.51–0.69), 24 (HR 0.64, 95% CI 0.55–0.73), 36 (HR 0.67, 95% CI 0.55–0.79), and 60 months (HR 0.69, 95% CI 0.51–0.89). This study suggests a moderate clinical impact of PC on long-term OS, CSS, and DFS after esophagectomy. Patients not experiencing PC seem to have a significantly reduced mortality hazard up to 5 years of follow-up. [ABSTRACT FROM AUTHOR]

Ischemia at the anastomotic site is thought to be a protagonist in the development of anastomosis-related complications while different strategies to overcome this problem have been reported. Gastric ischemic conditioning (GIC) prior to esophagectomy has been described with this intent. Evaluate the effect of GIC on anastomotic complications after esophagectomy. Scopus, Web of Science, MEDLINE, and PubMed were investigated up to March 31st, 2023. We considered articles that appraised short-term outcomes after GIC vs. no GIC in patients undergoing esophagectomy. Anastomotic leak (AL), anastomotic stricture (AS), and gastric conduit necrosis (GCN) were primary outcomes. Risk ratio (RR) and standardized mean difference (SMD) were used as pooled effect size measures, whereas 95% confidence intervals (95% CIs) were used to calculate related inference. Fourteen studies (1760 patients) were included. Of those, 732 (41.6%) underwent GIC, while 1028 (58.4%) underwent one-step esophagectomy. Compared with no GIC, GIC was related to a reduced RR for AL (R RR = 0.63; 95% CI 0.47–0.86; p < 0.01) and AS (RR = 0.51; 95% CI 0.29–0.91; p = 0.02), whereas no differences were found for GCN (RR = 0.56; 95% CI 0.19–1.61; p = 0.28). Postoperative pneumonia (RR = 1.09; p = 0.99), overall complications (RR = 0.87; p = 0.19), operative time (SMD − 0.58; p = 0.07), hospital stay (SMD 0.66; p = 0.09), and 30-day mortality (RR = 0.69; p = 0.22) were comparable. GIC prior to esophagectomy seems associated with a reduced risk for AL and AS. Further studies are necessary to identify the subset of patients who can benefit from this procedure, the optimal technique, and the timing of GIC prior to esophagectomy. [ABSTRACT FROM AUTHOR]

This paper presents the deduction of the enhanced gradient descent, conjugate gradient, scaled conjugate gradient, quasi-Newton, and Levenberg-Marquardt methods for training quaternion-valued feedforward neural networks, using the framework of the HR calculus. The performances of these algorithms in the real- and complex-valued cases led to the idea of extending them to the quaternion domain, also. Experiments done using the proposed training methods on time series prediction applications showed a significant performance improvement over the quaternion gradient descent algorithm. [ABSTRACT FROM AUTHOR]

We will propose a new algorithm for finding critical points of cost functions defined on a differential manifold. We will lift the initial cost function to a manifold that can be embedded in a Riemannian manifold (Euclidean space) and will construct a vector field defined on the ambient space whose restriction to the embedded manifold is the gradient vector field of the lifted cost function. The advantage of this method is that it allows us to do computations in Cartesian coordinates instead of using local coordinates and covariant derivatives on the initial manifold. We will exemplify the algorithm in the case of SO(3) averaging problems and will rediscover a few well known results that appear in literature. [ABSTRACT FROM AUTHOR]

The risk of cardiovascular disease is increased in patients with rheumatoid arthritis compared with the general population owing to the influence of traditional and non-traditional risk factors. Inflammation has a pivotal contribution and can accelerate the atherosclerotic process. Although dampening inflammation with DMARDs should theoretically abrogate this process, evidence suggests that these drugs can also promote atherosclerosis directly and indirectly, hence adding to an increased cardiovascular burden. However, the extent and direction of the effects largely differ across drugs. Understanding how these drugs influence endothelial damage and vascular repair mechanisms is key to understanding these outcomes. NSAIDs and glucocorticoids can increase the cardiovascular risk. Conversely, conventional, biologic and targeted DMARDs control inflammation and reduce this risk, although some of these drugs can also aggravate traditional factors or thrombotic events. Given these data, the fundamental objective for clinicians should be disease control, in an individualized approach that considers the most appropriate drug for each patient, taking into account joint and cardiovascular outcomes. This Review provides a comprehensive analysis of the effects of DMARDs and other approved drugs on cardiovascular involvement in rheumatoid arthritis, from a clinical and mechanistic perspective, with a roadmap to inform the research agenda. [ABSTRACT FROM AUTHOR]

A Correction to this paper has been published: https://doi.org/10.1038/s41584-021-00616-z. [ABSTRACT FROM AUTHOR]