Financial market and pricing of emerging financial derivatives: A mathematical approach

Pricing has been one of the key problems of financial market theory. With the development of the modern financial market, various new financial derivatives have been created and need to be priced properly. In the thesis, we are going to use several mathematical tools to investigate the essential structure of the financial market and models for financial derivatives

A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and travelingwave solutions of the (2+1)-dimensional sine-Gordon equation are constructed. The traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a similar manner. Meanwhile, conservation laws are derived

Application of Artificial Intelligence Technologies in a Cloud-based Platform for ECG Analysis to Support the Diagnosis of a Critical Electrocardiography in Primary Care

BackgroundThe cloud-based platform for electrocardiography (ECG) analysis plays a supporting role in the prevention and treatment of cardiovascular diseases. During the construction of a cloud-based platform for ECG analysis, problems that should be focused and addressed are exploring ways to better use artificial intelligence (AI) technologies supporting ECG analysis, and improving the process and effectiveness of AI-aided diagnosis of a critical ECG.ObjectiveTo explore the use of AI technologies in a cloud-based platform for ECG analysis to support the diagnosis of a critical ECG in primary care.MethodsThe 12-lead resting ECGs (n=20 808) uploaded to Nalong Cloud-based ECG Analysis Platform by primary healthcare institutions were selected from June 2019 to June 2021. After being interpreted by AI-based algorithms and physicians, respectively, ECG findings were classified into critical group (critical ECGs) , normal group (normal ECGs) , and positive group (abnormal but not critical ECGs) . The results interpreted by the AI-based algorithm were compared with those interpreted by physicians (defined as the gold standard) to assess the diagnostic agreement and coincidence rate between AI-based and physician-based interpretations, and to assess the diagnostic sensitivity, and positive predictive value of AI-based interpretation. And the mean time for making diagnoses of three groups of ECGs was calculated.ResultsBy the AI-based interpretation, 619, 15 634 and 45 55 ECGs were included in the critical, positive, and normal groups, respectively. And by the physician-based interpretation, 619, 15 759 and 4 430 ECGs were included in the critical, positive, and normal groups, respectively. There was high agreement between AI-based and physician-based interpretation results of ECGs〔Kappa=0.984, 95%CI (0.982, 0.987) , P<0.001〕, with a diagnostic coincidence rate of 99.4%. The diagnostic sensitivity and positive predictive value of AI-based interpretation for ECGs was 99.4%, and 100.0%, respectively. The mean time for making diagnoses of critical ECGs, abnormal but not critical ECGs, and normal ECGs was statistically different (P<0.001) , the mean time of critical critical ECGs was shorter than normal ECGs and abnormal but not critical ECGs (P<0.001) .ConclusionAI technologies used in a cloud-based platform for ECG analysis could provide physicians with support for interpreting ECGs, which may contribute to improving the interpretation accuracy, optimizing the diagnostic process, shortening the time for diagnosing a critical ECG, and the treating of critical patients in primary care

Disorder induced multifractal superconductivity in monolayer niobium dichalcogenides

The interplay between disorder and superconductivity is a subtle and fascinating phenomenon in quantum many body physics. The conventional superconductors are insensitive to dilute nonmagnetic impurities, known as the Anderson's theorem. Destruction of superconductivity and even superconductor-insulator transitions occur in the regime of strong disorder. Hence disorder-enhanced superconductivity is rare and has only been observed in some alloys or granular states. Because of the entanglement of various effects, the mechanism of enhancement is still under debate. Here we report well-controlled disorder effect in the recently discovered monolayer NbSe$_2$ superconductor. The superconducting transition temperatures of NbSe$_2$ monolayers are substantially increased by disorder. Realistic theoretical modeling shows that the unusual enhancement possibly arises from the multifractality of electron wave functions. This work provides the first experimental evidence of the multifractal superconducting state

Neuromorphic Computing-Assisted Triboelectric Capacitive-Coupled Tactile Sensor Array for Wireless Mixed Reality Interaction.

Flexible tactile sensors show promise for artificial intelligence applications due to their biological adaptability and rapid signal perception. Triboelectric sensors enable active dynamic tactile sensing, while integrating static pressure sensing and real-time multichannel signal transmission is key for further development. Here, we propose an integrated structure combining a capacitive sensor for static spatiotemporal mapping and a triboelectric sensor for dynamic tactile recognition. A liquid metal-based flexible dual-mode triboelectric-capacitive-coupled tactile sensor (TCTS) array of 4 × 4 pixels achieves a spatial resolution of 7 mm, exhibiting a pressure detection limit of 0.8 Pa and a fast response of 6 ms. Furthermore, neuromorphic computing using the MXene-based synaptic transistor achieves 100% recognition accuracy of handwritten numbers/letters within 90 epochs based on dynamic triboelectric signals collected by the TCTS array, and cross-spatial information communication from the perceived multichannel tactile data is realized in the mixed reality space. The results illuminate considerable application possibilities of dual-mode tactile sensing technology in human-machine interfaces and advanced robotics

A closed‐loop representative day selection framework for generation and transmission expansion planning with demand response

Abstract In power systems with a high proportion of renewable energy resources (RES), the inherent stochasticity and volatility of RES necessitate careful consideration in power system planning. Scenario analysis is commonly employed to address the stochastic nature in power system planning. Existing studies generally adopt an open‐loop structure, where representative days are selected first and planning decisions are subsequently made. However, this method may not accurately represent the operating status of a system owing to changes in the power generation structure during the planning process. To address this limitation, this paper introduces a closed‐loop framework for representative day selection within the context of generation and transmission expansion planning (G&TEP), incorporating demand response (DR). The framework comprises three layers: representative day selection, planning decisions, and long‐term operational simulation. Initially, an approach for selecting representative days is proposed by combining the clustering and optimization‐based methods. Subsequently, a G&TEP model that incorporates DR is presented in the second layer. Lastly, the framework encompasses a three‐layer closed‐loop structure, enabling dynamic adjustments and enhancements to the representative day selection process to ensure optimality. Case studies on the reliability and operational test system of a power grid with large‐scale renewable integration (XJTU‐ROTS) demonstrate the effectiveness of our proposed framework