Theory of Lexicographic Differentiation in the Banach Space Setting

Derivative information is useful for many problems found in science and engineering that require equation solving or optimization. Driven by its utility and mathematical curiosity, researchers over the years have developed a variety of generalized derivatives. In this thesis, we will first take a look at Clarke’s generalized derivative for locally Lipschitz continuous functions between Euclidean spaces, which roughly is the smallest convex set containing all nearby derivatives of a domain point of interest. Clarke’s generalized derivative in this setting possesses a strong theoretical and numerical toolkit, which is analogous to that of the classical derivative. It includes nonsmooth versions of the chain rule, the mean value theorem, and the implicit function theorem, as well as nonsmooth equation-solving and optimization methods. However, it is generally difficult to obtain elements of Clarke’s generalized derivative in the Euclidean space setting. To address this issue, we use lexicographic differentiation by Nesterov and lexicographic directional differentiation by Khan and Barton. They are generalized derivatives theories for a subclass of locally Lipschitz continuous functions, called the class of lexicographically smooth functions, which help to find elements of Clarke\u27s generalized derivative in the Euclidean space setting systematically. Lexicographic derivatives are either elements of Clarke\u27s generalized derivative in the Euclidean space setting or at least indistinguishable from them as far as numerical tools are concerned. We outline a process by which we can find a lexicographic derivative once a lexicographic directional derivative is known. Lastly, we present lexicographic differentiation theory for a subclass of locally Lipschitz continuous functions mapping between Banach spaces that have Schauder bases, called, unsurprisingly, the class of lexicographically smooth functions. We provide a proof for Nesterov\u27s result that, as in the Euclidean space setting, lexicographic derivatives in this setting satisfy a sharp calculus rule

Extreme Environment Architecture.

D.Arch. Thesis. University of Hawaiʻi at Mānoa 2017

Kirchhoff's Circuit Law Applications to Graph Simplification in Search Problems

This paper proposes a new analysis of graph using the concept of electric potential, and also proposes a graph simplification method based on this analysis. Suppose that each node in the weighted-graph has its respective potential value. Furthermore, suppose that the start and terminal nodes in graphs have maximum and zero potentials, respectively. When we let the level of each node be defined as the minimum number of edges/hops from the start node to the node, the proper potential of each level can be estimated based on geometric proportionality relationship. Based on the estimated potential for each level, we can re-design the graph for path-finding problems to be the electrical circuits, thus Kirchhoff's Circuit Law can be directed applicable for simplifying the graph for path-finding problems

Single-Phase 13-Level Power Conditioning System for Peak Power Reduction of a High-Speed Railway Substation

The control and operation of a single-phase 13-level power conditioning system (PCS) for peak power reduction of a high-speed railway substation (HSRS) are proposed. This PCS is a single-phase 3100 V, 2 MVA 13-level H-bridge multi-level inverter structure. It has excellent power quality. It is easy to serialize by voltage. In addition, the DC bus power of each cell inverter is supplied by lithium-ion batteries. The generalized reduction gradient optimization algorithm based on past load pattern is applied to the power management system for peak power reduction of HSRS. The phase detector and power controller for the control of a single-phase PCS based on virtually coordinated axes using an all-pass filter are expected to be robust to external disturbances with fast response characteristics. This study also proposes an adapted select switch (ASS) method that can change the switching depending on the operation state of PCS and the state of charge (SOC) of the battery to minimize battery imbalance by controlling each cell inverter of the H-bridge. The validity of the proposed system was confirmed by PSiM simulation and experiments using a demonstration system of 6 MW PCS and 2.68 MWh batteries at one of Gyeongbu high-speed line substations in Korea. Document type: Articl

Quantum Approximation for Wireless Scheduling

This paper proposes a quantum approximate optimization algorithm (QAOA) method for wireless scheduling problems. The QAOA is one of the promising hybrid quantum-classical algorithms for many applications and it provides highly accurate optimization solutions in NP-hard problems. QAOA maps the given problems into Hilbert spaces, and then it generates Hamiltonian for the given objectives and constraints. Then, QAOA finds proper parameters from classical optimization approaches in order to optimize the expectation value of generated Hamiltonian. Based on the parameters, the optimal solution to the given problem can be obtained from the optimum of the expectation value of Hamiltonian. Inspired by QAOA, a quantum approximate optimization for scheduling (QAOS) algorithm is proposed. First of all, this paper formulates a wireless scheduling problem using maximum weight independent set (MWIS). Then, for the given MWIS, the proposed QAOS designs the Hamiltonian of the problem. After that, the iterative QAOS sequence solves the wireless scheduling problem. This paper verifies the novelty of the proposed QAOS via simulations implemented by Cirq and TensorFlow-Quantum

A Tutorial on Quantum Convolutional Neural Networks (QCNN)

Convolutional Neural Network (CNN) is a popular model in computer vision and has the advantage of making good use of the correlation information of data. However, CNN is challenging to learn efficiently if the given dimension of data or model becomes too large. Quantum Convolutional Neural Network (QCNN) provides a new solution to a problem to solve with CNN using a quantum computing environment, or a direction to improve the performance of an existing learning model. The first study to be introduced proposes a model to effectively solve the classification problem in quantum physics and chemistry by applying the structure of CNN to the quantum computing environment. The research also proposes the model that can be calculated with O(log(n)) depth using Multi-scale Entanglement Renormalization Ansatz (MERA). The second study introduces a method to improve the model's performance by adding a layer using quantum computing to the CNN learning model used in the existing computer vision. This model can also be used in small quantum computers, and a hybrid learning model can be designed by adding a quantum convolution layer to the CNN model or replacing it with a convolution layer. This paper also verifies whether the QCNN model is capable of efficient learning compared to CNN through training using the MNIST dataset through the TensorFlow Quantum platform

Three Factors to Improve Out-of-Distribution Detection

In the problem of out-of-distribution (OOD) detection, the usage of auxiliary data as outlier data for fine-tuning has demonstrated encouraging performance. However, previous methods have suffered from a trade-off between classification accuracy (ACC) and OOD detection performance (AUROC, FPR, AUPR). To improve this trade-off, we make three contributions: (i) Incorporating a self-knowledge distillation loss can enhance the accuracy of the network; (ii) Sampling semi-hard outlier data for training can improve OOD detection performance with minimal impact on accuracy; (iii) The introduction of our novel supervised contrastive learning can simultaneously improve OOD detection performance and the accuracy of the network. By incorporating all three factors, our approach enhances both accuracy and OOD detection performance by addressing the trade-off between classification and OOD detection. Our method achieves improvements over previous approaches in both performance metrics.Comment: Under revie

A New Cooperative MIMO Scheme Based on SM for Energy-Efficiency Improvement in Wireless Sensor Network

Improving the energy efficiency in wireless sensor networks (WSN) has attracted considerable attention nowadays. The multiple-input multiple-output (MIMO) technique has been proved as a good candidate for improving the energy efficiency, but it may not be feasible in WSN which is due to the size limitation of the sensor node. As a solution, the cooperative multiple-input multiple-output (CMIMO) technique overcomes this constraint and shows a dramatically good performance. In this paper, a new CMIMO scheme based on the spatial modulation (SM) technique named CMIMO-SM is proposed for energy-efficiency improvement. We first establish the system model of CMIMO-SM. Based on this model, the transmission approach is introduced graphically. In order to evaluate the performance of the proposed scheme, a detailed analysis in terms of energy consumption per bit of the proposed scheme compared with the conventional CMIMO is presented. Later, under the guide of this new scheme we extend our proposed CMIMO-SM to a multihop clustered WSN for further achieving energy efficiency by finding an optimal hop-length. Equidistant hop as the traditional scheme will be compared in this paper. Results from the simulations and numerical experiments indicate that by the use of the proposed scheme, significant savings in terms of total energy consumption can be achieved. Combining the proposed scheme with monitoring sensor node will provide a good performance in arbitrary deployed WSN such as forest fire detection system