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.
Skin infections caused by microorganisms such as Staphylococcus aureus, Escherichia coli, and Pseudomonas aeruginosa represent a significant public health challenge, particularly due to increasing antimicrobial resistance associated with conventional antibiotic therapies. As an alternative, natural compounds have been explored, highlighting kombucha fermented with yerba mate (KYM), which is known for its antimicrobial, antioxidant, and probiotic properties. In this study, nanoemulsification was investigated as a strategy to protect KYM bioactive compounds and enhance their bioavailability and therapeutic efficacy. During KYM preparation, the effects of light exposure and fermentation time were evaluated, along with pH and total phenolic content. Nanoemulsions were formulated using Tween 80 (R) and Span 80 (R) as surfactants, based on hydrophilic-lipophilic balance (HLB) calculations, to incorporate KYM. The nanoemulsions were characterized in terms of droplet size, physical stability, FTIR-ATR, fluorescence properties, and storage stability. Antimicrobial activity determination, irritability assays and histopathological evaluation were also conducted. The results revealed no significant differences between light and dark treatments during KYM preparation, indicating that light exposure did not significantly affect the total phenolic content of the medium. The nanoemulsions containing 80% KYM presented suitable physicochemical properties, with droplet sizes below 350 nm, low polydispersity, and stability maintained for 28 days at 4 degrees C and 25 degrees C. Infrared and fluorescence spectroscopy suggested the formation of an organized structure with the incorporation of KYM bioactives. The incorporation of KYM significantly enhanced the in vitro antimicrobial activity against S. aureus, E. coli, and P. aeruginosa, achieving inhibition levels of 92% to 100%. Irritation and histopathological assays showed a non-irritant and biocompatible profile of the formulations. Overall, nanoemulsions containing yerba-mate kombucha represent a stable and effective natural delivery system with promising potential for the prevention and topical treatment of skin infections.
Introduction/Justification: The Estrogen Receptor (ER) has a crucial role in the treatment and prognosis of breast cancer. Its status is determined by the percentage of tumor cell nuclei positive for ER on immunohistochemistry: negative (<1%) or positive (>1%). ER-positive tumors tend to exhibit slower growth, better response to hormone therapy, and lower recurrence rates. Recently, tumors with 1%–10% ER expression (ER-low) have been recognized as having intermediate biological behavior and response to hormone therapy. Given the recent understanding of these data, a gap remains regarding their clinical and epidemiological profile, which prompted the present study. Methods: Cross-sectional study based on medical records from the Hospital Universitário Polydoro Ernani de São Thiago (HU/UFSC) between December 2019 and 2024. Were excluded: male patients; ductal carcinoma in situ; metastatic, bilateral, or recurrent tumors; inaccessible or incomplete records. Results: Among 279 identified patients, 176 comprised the final sample. Estrogen Receptor (ER) positivity was 81.81%, progesterone receptor (PR) positivity was 67.61%, while HER2 negativity was 18.93%. ER-low occurred in 3 patients (1.89%). Among ER-low cases, PR positivity (66.66%) and HER2 negativity (66.66%) predominated. Mean age was similar in the total sample (56.84 years) and ER-low cases (54.33 years). Menopause predominated in ER-positive tumors (ER-low: 66.66%; ER-high: 66.38%), while premenopause predominated in ER-negative patients (56.66%). According to the 8th edition of the American Joint Committee on Cancer (AJCC), ER-low cases were mainly stage III (66.66%). Tumor size T3–T4 occurred in 33.33% of ER-low tumors, intermediate between ER-negative (58.06%) and ER-high (18.69%). Regional lymph node stage N2–N3 occurred in 33.33% of ER-low, higher than ER-negative (19.35%) and ER-high (13.11%). Conclusion: The frequency of ER-low was low (1.89%), but associated with more aggressive disease than other ER-positive tumors, and potentially associated with a worse prognosis.
