Convexification for a Coefficient Inverse Problem of Mean Field Games

The globally convergent convexification numerical method is constructed for a Coefficient Inverse Problem for the Mean Field Games System. A coefficient characterizing the global interaction term is recovered from the single measurement data. In particular, a new Carleman estimate for the Volterra integral operator is proven, and it stronger than the previously known one. Numerical results demonstrate accurate reconstructions from noisy data

Convexification Numerical Method for the Retrospective Problem of Mean Field Games

The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game of infinitely many rational players. In addition to traditional initial and terminal conditions, one extra terminal condition is assumed to be known. Carleman estimates and a Carleman Weight Function play the key role. Numerical experiments demonstrate a good performance for complicated functions. Various versions of the convexification have been actively used by this research team for a number of years to numerically solve coefficient inverse problems

Semantic Inference on Clinical Documents: Combining Machine Learning Algorithms With an Inference Engine for Effective Clinical Diagnosis and Treatment

Clinical practice calls for reliable diagnosis and optimized treatment. However, human errors in health care remain a severe issue even in industrialized countries. The application of clinical decision support systems (CDSS) casts light on this problem. However, given the great improvement in CDSS over the past several years, challenges to their wide-scale application are still present, including: 1) decision making of CDSS is complicated by the complexity of the data regarding human physiology and pathology, which could render the whole process more time-consuming by loading big data related to patients; and 2) information incompatibility among different health information systems (HIS) makes CDSS an information island, i.e., additional input work on patient information might be required, which would further increase the burden on clinicians. One popular strategy is the integration of CDSS in HIS to directly read electronic health records (EHRs) for analysis. However, gathering data from EHRs could constitute another problem, because EHR document standards are not unified. In addition, HIS could use different default clinical terminologies to define input data, which could cause additional misinterpretation. Several proposals have been published thus far to allow CDSS access to EHRs via the redefinition of data terminologies according to the standards used by the recipients of the data flow, but they mostly aim at specific versions of CDSS guidelines. This paper views these problems in a different way. Compared with conventional approaches, we suggest more fundamental changes; specifically, uniform and updatable clinical terminology and document syntax should be used by EHRs, HIS, and their integrated CDSS. Facilitated data exchange will increase the overall data loading efficacy, enabling CDSS to read more information for analysis at a given time. Furthermore, a proposed CDSS should be based on self-learning, which dynamically updates a knowledge model according to the data-stream-based upcoming data set. The experiment results show that our system increases the accuracy of the diagnosis and treatment strategy designs

Donor–Acceptor Fluorophores for Energy-Transfer-Mediated Photocatalysis

Triplet–triplet energy transfer (EnT) is a fundamental activation pathway in photocatalysis. In this work, we report the mechanistic origins of the triplet excited state of carbazole-cyanobenzene donor–acceptor (D–A) fluorophores in EnT-based photocatalytic reactions and demonstrate the key factors that control the accessibility of the 3LE (locally excited triplet state) and 3CT (charge-transfer triplet state) via a combined photochemical and transient absorption spectroscopic study. We found that the energy order between 1CT (charge transfer singlet state) and 3LE dictates the accessibility of 3LE/3CT for EnT, which can be effectively engineered by varying solvent polarity and D–A character to depopulate 3LE and facilitate EnT from the chemically more tunable 3CT state for photosensitization. Following the above design principle, a new D–A fluorophore with strong D–A character and weak redox potential is identified, which exhibits high efficiency for Ni(II)-catalyzed cross-coupling of carboxylic acids and aryl halides with a wide substrate scope and high selectivity. Our results not only provide key fundamental insight on the EnT mechanism of D–A fluorophores but also establish its wide utility in EnT-mediated photocatalytic reactions

Progress of In-stent Restenosis after Vertebral Artery Ostium Stenosis and Imaging Assessments

Stenting has become one of the primary procedure to treat vertebral artery ostium stenosis patients. Postoperative in­stent restenosis (ISR) of the stenting is still one of the unsolved issues and requires systematic and further investigation. Through imaging assessments, ISR could be identified and evaluated in clinical practice and researches

Machine Learning Enabled Prediction of Mechanical Properties of Tungsten Disulfide Monolayer

One of two-dimensional transition metal dichalcogenide materials, tungsten disulfide (WS2), has aroused much research interest, and its mechanical properties play an important role in a practical application. Here the mechanical properties of h-WS2 and t-WS2 monolayers in the armchair and zigzag directions are evaluated by utilizing the molecular dynamics (MD) simulations and machine learning (ML) technique. We mainly focus on the effects of chirality, system size, temperature, strain rate, and random vacancy defect on mechanical properties, including fracture strain, fracture strength, and Young’s modulus. We find that the mechanical properties of h-WS2 surpass those of t-WS2 due to the different coordination spheres of the transition metal atoms. It can also be observed that the fracture strain, fracture strength, and Young’s modulus decrease when temperature and vacancy defect ratio are enhanced. The random forest (RF) supervised ML algorithm is employed to model the correlations between different impact factors and target outputs. A total number of 3600 MD simulations are performed to generate the training and testing dataset for the ML model. The mechanical properties of WS2 (i.e., target outputs) can be predicted using the trained model with the knowledge of different input features, such as WS2 type, chirality, temperature, strain rate, and defect ratio. The mean square errors of ML predictions for the mechanical properties are orders of magnitude smaller than the actual values of each property, indicating good training results of the RF model

Plasma Cytokine and Growth Factor Profiling during Free Flap Transplantation

Ischemia and reperfusion (I/R) is an unavoidable condition during free flap transplantation. Restoration of blood flow is usually associated with a profound inflammatory response. Cytokines and growth factors are the functional proteins which exert their specific influence on injury or repair during the healing period. Plasma concentrations of 18 cytokines and growth factor proteins (IL6, IL8, IP10, TNFα, MCP1, Fractalkine, GRO, bFGF, GMCSF, IFNg, MIP1a, VEGF, sCD40L, IL10, TGFα, IL1β, IL12P40, and TNFβ) have been analyzed with respect to I/R status during microsurgery tissue transplantation in both, artery and vein, from patients by multiplexed immunoassay. Both technical feasibility and biostatistics data analysis approaches were thoroughly assessed. It has been found that, from all investigated proteins, the venous plasma levels of IL6 significantly increased during the ischemia period and mostly sustained their high levels during reperfusion, while venous plasma levels of IL8 showed in general a significant increase in the ischemia period followed by a rapid decrease in the reperfusion period. In conclusion, these findings direct toward an active involvement of tissue-resting leukocytes which may become therapeutic targets for concomitant medication in flap surgery to improve wound healing

Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation

The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of the so-called \textquotedblleft convexification" principle, which has been pursued by this research group for a number of years for some other CIPs for PDEs. Those PDEs are significantly different from RRTE. The presence of the Carleman Weight Function (CWF) in the numerical scheme is the key element of the convexification. CWF is the function, which is involved as the weight function in the Carleman estimate for the corresponding PDE operator. Convergence analysis is presented along with the results of numerical experiments, which confirm the theory. RRTE governs the propagation of photons in the diffuse medium in the case when they propagate along geodesic lines between their collisions. Geodesic lines are generated by the spatially variable dielectric constant of the medium

Postsynthetic Modification of the Nonanuclear Node in a Zirconium Metal−Organic Framework for Photocatalytic Oxidation of Hydrocarbons

Heterogeneous catalysis plays an indispensable role in chemical production and energy conversion. Incorporation of transition metals into metal oxides and zeolites is a common strategy to fine-tune the activity and selectivity of the resulting solid catalysts, as either the active center or promotor. Studying the underlying mechanism is however challenging. Decorating the metal-oxo clusters with transition metals in metal−organic frameworks (MOFs) via postsynthetic modification offers a rational approach to construct well-defined structural models for better understanding of the reaction mechanism. Therefore, it is important to expand the materials scope beyond the currently widely studied zirconium MOFs consisting of Zr6 nodes. In this work, we report the design and synthesis of a new (4,12)- connected Zr-MOF with ith topology that consists of rare Zr9 nodes. FeIII was further incorporated onto the Zr9 nodes of the framework, and the resulting MOF material exhibits significantly enhanced activity and selectivity toward the photocatalytic oxidation of toluene. This work demonstrates a delicate ligand design strategy to control the nuclearity of Zr-oxo clusters, which further dictates the number and binding sites of transition metals and the overall photocatalytic activity toward C−H activation. Our work paves the way for future exploration of the structure−activity study of catalysts using MOFs as the model system