On constrained multivariate splines and their approximations

Summary The variational formulation of multivariate spline functions is generalized to include cases where the function has to satisfy inequality constraints such as positivity and convexity. Condition for existence and uniqueness of a solution is given. Approximation to the solution can be obtained by solving the variational problem in a finite dimensional subspace. Conditions for convergence and error estimates of the approximations are presented, both for interpolation problems and smoothing problems. The general theory is illustrated by specific examples including the volume-matching problem and the one-sided thin plate spline.This research is partially supported by the U.S. Army Contract No. DAAG 29-77-G-0207, and by NSF Grant No. MCS-8101836Part of this paper is based on Chapters 2 and 3 of the author's Ph. D. thesis. The author would like to express his sincere thanks to Professor Grance Wahba and to two referees for many helpful comments     

Solving the Generalized Machine Assignment Problem in Group Technology

Many existing solution methodologies for machine assignment problems in group technology do not consider factors such as part demand, operation sequence and cost of intercellular moves. We formulate a 0-1 quadratic programming model that takes into account these factors in machine assignment. Two approaches are proposed to solve this problem. The first is an A*-based approach that generates optimal solutions. The second is a heuristic approach developed to solve problems with large number of machines and/or parts. The heuristic approach is shown to be efficient in producing good solutions in a computational study.     

Levitin–Polyak well-posedness for strong bilevel vector equilibrium problems and applications to traffic network problems with equilibrium constraints

In this paper we consider strong bilevel vector equilibrium problems and introduce the concepts of Levitin–Polyak well-posedness and Levitin–Polyak well-posedness in the generalized sense for such problems. The notions of upper/lower semicontinuity involving variable cones for vector-valued mappings and their properties are proposed and studied. Using these generalized semicontinuity notions, we investigate sufficient and/or necessary conditions of the Levitin–Polyak well-posedness for the reference problems. Some metric characterizations of these Levitin–Polyak well-posedness concepts in the behavior of approximate solution sets are also discussed. As an application, we consider the special case of traffic network problems with equilibrium constraints.     

Theranostic Iron@Gold Core–Shell Nanoparticles for Simultaneous Hyperthermia‐Chemotherapy upon Photo‐Stimulation

The challenges of nanoparticles, such as size‐dependent toxicity, nonbiocompatibility, or inability to undergo functionalization for drug conjugation, limit their biomedical application in more than one domain. Oval‐shaped iron@gold core–shell (oFe@Au) magnetic nanoparticles are engineered and their applications in magnetic resonance imaging (MRI), optical coherence tomography (OCT), and controlled drug release, are explored via photo stimulation‐generated hyperthermia. The oFe@Au nanoparticles have a size of 42.57 ± 5.99 nm and consist of 10.76 and 89.24 atomic % of Fe and Au, respectively. Upon photo‐stimulation for 10 and 15 minutes, the levels of cancer cell death induced by methotrexate‐conjugated oFe@Au nanoparticles are sixfold and fourfold higher, respectively, than oFe@Au nanoparticles alone. MRI and OCT confirm the application of these nanoparticles as a contrast agent. Finally, results of in vivo experiments reveal that the temperature is elevated by 13.2 °C, when oFe@Au nanoparticles are irradiated with a 167 mW cm^?2 808 nm laser, which results in a significant reduction in tumor volume and scab formation after 7 days, followed by complete disappearance after 14 days. The ability of these nanoparticles to generate heat upon photo‐stimulation also opens new doors for studying hyperthermia‐mediated controlled drug release for cancer therapy. Applications include biomedical engineering, cancer therapy, and theranostics fields.     

Planar Hall effect in biosensor with a tilted angle of the cross-junction

A typical planar Hall effect (PHE) sensor junction consists of two Hall bars that the bars appear normal to each other and the junction can have the required four terminals for current and voltage measurements. We are now introducing a tilted angle of the cross-junction and studying the role of the PHE therein. The results show that although there is a tilted angle of the cross-junction, the PHE voltage is remained constant. The result is interpreted by assuming the sensor material with the behavior of a basic single domain structure under the external magnetic field reversals. The calculations of the model are found to be in good concurrence with the experimental results.     

Functional Groups Assisted Tunable Dielectric Permittivity of Guest-Free Zn-Based Coordination Polymers for Gate Dielectrics

The dielectric properties of coordination polymers has been a topic of recent interest, but the role of different functional groups on the dielectric properties of these polymers has not yet been fully addressed. Herein, the effects of electron-donating (R=NH₂) and electron-withdrawing (R=NO₂) groups on the dielectric behavior of such materials were investigated for two thermally stable and guest-free Zn-based coordination polymers, [Zn(L₁)(L₂)]_n ( 1 ) and [Zn(L₁)(L₃)]_n ( 2 ) [L₁=2-(2-pyridyl) benzimidazole (Pbim), L₂=5-aminoisophthalate (Aip), and L₃=5-nitroisophthalate (Nip)]. The results of dielectric studies of 1 revealed that it possesses a high dielectric constant (κ=65.5 at 1 kHz), while compound 2 displayed an even higher dielectric constant (κ=110.3 at 1 kHz). The electron donating and withdrawing effects of the NH₂ and NO₂ substituents induce changes in the polarity of the polymers, which is due to the inductive effect from the aryl ring for both NO₂ and NH₂. Theoretical results from density functional theory (DFT) calculations, which also support the experimental findings, show that both compounds have a distinct electronic behavior with diverse wide bandgaps. The significance of the current work is to provide information about the structure-dielectric property relationships. So, this study promises to pave the way for further research on the effects of different functional groups on coordination polymers on their dielectric properties.     

C3′‐Deoxygenation of Paromamine Catalyzed by a Radical S‐Adenosylmethionine Enzyme: Characterization of the Enzyme AprD4 and Its Reductase Partner AprD3

C3′‐deoxygenation of aminoglycosides results in their decreased susceptibility to phosphorylation thereby increasing their efficacy as antibiotics. However, the biosynthetic mechanism of C3′‐deoxygenation is unknown. To address this issue, aprD4 and aprD3 genes from the apramycin gene cluster in Streptomyces tenebrarius were expressed in E. coli and the resulting gene products were characterized in vitro. AprD4 is shown to be a radical S‐adenosylmethionine (SAM) enzyme, catalyzing homolysis of SAM to 5′‐deoxyadenosine (5′‐dAdo) in the presence of paromamine. [4′‐²H]‐Paromamine was prepared and used to show that its C4′‐H is transferred to 5′‐dAdo by AprD4, during which the substrate is dehydrated to a product consistent with 4′‐oxolividamine. In contrast, paromamine is reduced to a deoxy product when incubated with AprD4/AprD3/NADPH. These results show that AprD4 is the first radical SAM diol‐dehydratase and, along with AprD3, is responsible for 3′‐deoxygenation in aminoglycoside biosynthesis.     

Positively charged liposomes consisting of the KTTKS pentapeptide conjugated with rhodamine increase rhodamine toxicity in E. coli and zebrafish embryo

Liposomes composed of cell‐penetrating peptide derivatives increased transport across the cell membrane. Conjugating rhodamine to a cell‐penetrating peptide increased the toxicity of rhodamine in E. coli and zebrafish embryos. A similar total protein inhibition pattern with different intensities, indicating that the interaction pathways of the rho‐KTTKS‐CONH₂ monomer and liposomes were the same. It suggests that the rho‐KTTKS‐CONH₂ liposomes showed higher toxicity because better transport across the cell membrane increased the effective concentration inside cells. The staining of zebrafish embryos using rho‐KTTKS‐CONH₂ liposomes showed a longer retention time, suggesting that it can penetrate deeper tissues or organs in zebrafish.     

Multiplex metal-detection based assay (MMDA) for COVID-19 diagnosis and identification of disease severity biomarkers

The ongoing COVID-19 pandemic caused by SARS-CoV-2 highlights the urgent need to develop sensitive methods for diagnosis and prognosis. To achieve this, multidimensional detection of SARS-CoV-2 related parameters including virus loads, immune response, and inflammation factors is crucial. Herein, by using metal-tagged antibodies as reporting probes, we developed a multiplex metal-detection based assay (MMDA) method as a general multiplex assay strategy for biofluids. This strategy provides extremely high multiplexing capability (theoretically over 100) compared with other reported biofluid assay methods. As a proof-of-concept, MMDA was used for serologic profiling of anti-SARS-CoV-2 antibodies. The MMDA exhibits significantly higher sensitivity and specificity than ELISA for the detection of anti-SARS-CoV-2 antibodies. By integrating the high dimensional data exploration/visualization tool (tSNE) and machine learning algorithms with in-depth analysis of multiplex data, we classified COVID-19 patients into different subgroups based on their distinct antibody landscape. We unbiasedly identified anti-SARS-CoV-2-nucleocapsid IgG and IgA as the most potently induced types of antibodies for COVID-19 diagnosis, and anti-SARS-CoV-2-spike IgA as a biomarker for disease severity stratification. MMDA represents a more accurate method for the diagnosis and disease severity stratification of the ongoing COVID-19 pandemic, as well as for biomarker discovery of other diseases.

A MMDA platform is developed by using metal-tagged antibodies as reporting probes combined with machine learning algorithms, as a general strategy for highly multiplexed biofluid assay.