Coderivative-Based Newton Methods in Structured Nonconvex and Nonsmooth Optimization

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and generalized differentiation. The objective functions belong to a broad class of prox-regular functions with specification to constrained optimization of nonconvex structured sums. We also develop a novel line search method, which is an extension of the proximal gradient algorithm while allowing us to globalize the proposed coderivative-based Newton methods by incorporating the machinery of forward-backward envelopes. Further applications and numerical experiments are conducted for the $\ell_0$-$\ell_2$ regularized least-square model appearing in statistics and machine learning

Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems

In this paper, we present new schemes to synchronize different dimensional chaotic and hyperchaotic systems. Based on coexistence of generalized synchronization (GS) and inverse generalized synchronization (IGS), a new type of hybrid chaos synchronization is constructed. Using Lyapunov stability theory and stability theory of linear continuous-time systems, some sufficient conditions are derived to prove the coexistence of generalized synchronization and inverse generalized synchronization between 3D master chaotic system and 4D slave hyperchaotic system. Finally, two numerical examples are illustrated with the aim to show the effectiveness of the approaches developed herein

Variational and Strong Variational Convexity in Infinite-Dimensional Variational Analysis

This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by Rockafellar, the importance of them has been already recognized and documented in finite-dimensional variational analysis and optimization. Here we address general infinite-dimensional settings and derive comprehensive characterizations of both variational and strong variational convexity notions by developing novel techniques, which are essentially different from finite-dimensional counterparts. As a consequence of the obtained characterizations, we establish new quantitative and qualitative relationships between strong variational convexity and tilt stability of local minimizers in appropriate frameworks of Banach spaces

Local Minimizers of Nonconvex Functions in Banach Spaces via Moreau Envelopes

This paper investigates the preservation of local minimizers and strong minimizers of extended-real-valued lower semicontinuous functions under taking their Moreau envelopes. We address a general setting of Banach spaces, while all the obtained results are new even for functions in finite dimensions. Our main motivation came from applications to numerical methods in nonsmooth optimization dealing with broad classes of nondifferentiable and nonconvex functions. The paper also formulates and discusses some open questions stemming from this study

Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

A comprehensive evaluation of polygenic score and genotype imputation performances of human SNP arrays in diverse populations

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Synthesize and characterization of artificial human bone developed by using nanocomposite

The combination of biopolymers with bioceramics plays vital role in development of artificial bone. Hydroxyapatite is extensively used as a material in prosthetic bone repair and replacement. In this paper synthesis of Hydroxyapatite- Polymethyl methacrylate – Zirconia (Hap-PMMA-ZrO2) composite by using powder metallurgy technique. The mechanical, morphological, In-vitro biocompatibility and tribological properties were characterized by universal testing machine, micro-vickers hardness tester, high resolution transmission electron microscope (HR-TEM), MTT assay and pin-on-disc setup. In-vitro cytotoxicity test on HeLa cell lines shows cell viability constant when doses concentration increases so material found non-toxic. Results show that micro Vickers hardness i.e. 520 approximately matches with natural human bone i.e. 400. Compressive strength is less as compared to human bone because of powder metallurgy route used for fabrication and is 74 MPa. Density of proposed composite artificial human bone i.e. 1.52 g/cc is less as compared to natural bone i.e. 2.90 g/cc. The Hap-PMMA-ZrO2 composite will be good biomaterials for bone repair and replacement wor

Generalizability assessment of AI models across hospitals in a low-middle and high income country

The integration of artificial intelligence (AI) into healthcare systems within low-middle income countries (LMICs) has emerged as a central focus for various initiatives aiming to improve healthcare access and delivery quality. In contrast to high-income countries (HICs), which often possess the resources and infrastructure to adopt innovative healthcare technologies, LMICs confront resource limitations such as insufficient funding, outdated infrastructure, limited digital data, and a shortage of technical expertise. Consequently, many algorithms initially trained on data from non-LMIC settings are now being employed in LMIC contexts. However, the effectiveness of these systems in LMICs can be compromised when the unique local contexts and requirements are not adequately considered. In this study, we evaluate the feasibility of utilizing models developed in the United Kingdom (a HIC) within hospitals in Vietnam (a LMIC). Consequently, we present and discuss practical methodologies aimed at improving model performance, emphasizing the critical importance of tailoring solutions to the distinct healthcare systems found in LMICs. Our findings emphasize the necessity for collaborative initiatives and solutions that are sensitive to the local context in order to effectively tackle the healthcare challenges that are unique to these regions

Ultra-high field MRI for evaluation of rectal cancer stroma ex vivo : correlation with histopathology

Purpose or Objective: Current clinical MRI techniques in rectal cancer are unable to differentiate Stage T1 from T2 (invasion of muscularis propria) tumours, and the differentiation of tumour from desmoplastic reaction or fibrous tissue remains a challenge1. Diffusion tensor imaging (DTI) MRI has potential to assess collagen structure and organisation (anisotropy). To our knowledge, there have been no MRI studies assessing DTI MRI for rectal cancer ex vivo. The purpose of this study was to examine DTI MRI derived biomarkers of rectal cancer stromal heterogeneity at high field strength ex vivo

Chronic Stress Related to Cancer Incidence, including the Role of Metabolic Syndrome Components

Epidemiological results on the link between chronic stress and cancer initiation have been inconsistent. This study examined the relation between chronic biological stress, indicated as hair cortisol (HairF) and hair cortisone (HairE), and cancer incidence, adjusting for metabolic syndrome (MetS) components. We analyzed HairF and HairE samples from 6341 participants from the population-based cohort Lifelines in 2014. A linkage with the Dutch Nationwide Pathology Databank (Palga) provided the cancer incidence from 2015 to 2021. The association between dichotomized HairF and log-transformed HairE (LogHairE) and cancer incidence was estimated using Cox regression. MetS components were evaluated as confounders or moderators. Of the 2776 participants with known HairF levels and no cancer history, 238 developed cancer. The HairF level did not predict cancer incidence (HR: 0.993, 95%CI: 0.740–1.333). No confounders or moderators were identified. Among the 4699 participants with known HairE levels and no cancer history, 408 developed cancer. There was no association between LogHairE and cancer incidence (HR: 1.113, 95%CI: 0.738–1.678). When including age as a confounder and gender as a moderator, LogHairE was statistically significantly associated with cancer incidence (HR: 6.403, 95%CI: 1.110–36.92). In a population-based cohort, chronic biological stress, measured by HairE, was associated with cancer incidence, after controlling for age and gender.</p