We introduce the Method of Ellipcenters (ME) for unconstrained minimization. At the cost of two gradients per iteration and a line search, we compute the next iterate by setting it as the centre of an elliptical interpolation. The idea behind the ellipse built in each step is to emulate the original level curve of the objective function constrained to a suitable two-dimensional affine space, which is determined by the current iterate and two appropriate gradient vectors. We present the method for general unconstrained minimization and carry out a convergence analysis for the case where the objective function is quadratic. In this context, ME enjoys linear convergence with the rate being at least as good as the linear rate of the steepest descent (gradient) method with optimal step. In our experiments, however, ME was much faster than the gradient method with optimal step size. Moreover, ME seems highly competitive in comparison to several well-established algorithms. The efficiency in terms of both time and number of iterations is stressed even more for ill-conditioned problems.
This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow capture ill-conditioning of the underlying optimization problem. In the first article on ME, we were able to prove that it converges with linear rate when the objective function is quadratic and strongly convex, while here we derive convergence for any differentiable strongly convex objective. This investigation was inspired by the great performance of ME in quadratic minimization against steepest descent with exact line search, FISTA, Barzilai-Borwein and Conjugate Gradient. The experiments we carry out now, make ME even more attractive from the numerical point of view. On top of that, the theory seems promising for quite more general settings.
Breakthroughs in language and vision have motivated increasingly general foundation models for time series and physical dynamics, where evidence is promising but less mature. In safety-critical Cyber-Physical Systems (CPS), globally parameterized dynamics models must remain valid through regime shifts, degradation, and lifecycle updates while supporting traceable assurance evidence. We argue that shared global parameters couple adaptation, frequency-sensitive fault representation, and verification evidence in ways that obstruct retained regime knowledge and bounded analysis. For systems whose operating conditions can be covered by a finite set of locally valid models, assurance evidence should be organized around those bounded models and their explicit composition, not around a single globally adapted model; increasing scale cannot supply explicit validity boundaries. HYDRA is a reference architecture for this position: frozen local specialists, runtime arbitration, and explicit coverage-gap monitoring. It illustrates how modular auditability and formal analysis of bounded components support Certifiable State Integrity, while whole-system certification, switching guarantees, and empirical validation remain separate obligations.
Yerba-mate kombucha-loaded nanoemulsions were developed as a strategy to protect bioactive compounds and enhance their bioavailability and therapeutic efficacy for potential use in topical treatment of skin infections.
The article explores the application of the ESA-B (Economic Social Environmental and Buildings) model using the USAT (Urban Sustainability Assessment Tool) to assess the integrated sustainability of a neighborhood and a commercial building in Lagoa da Conceição, Florianópolis/SC. The aim is to present how the tool works and its possibilities. In the urban context, the tool analyzes sustainable planning, in items such as soil permeability, land use and the quality of the natural environment. For the building, it evaluates practices such as the reuse of materials, water and energy efficiency and integration with the surroundings. The preliminary results highlight the predictions of the ESA-B model in integrating sustainability at different scales, providing a detailed diagnosis applicable to urban policies and business practices presented in the format of the USAT tool. In addition, the limitations of the study and the possibilities for improving the tool are discussed, with a focus on expanding the database and adapting it to local specificities.
