Entanglement for any definition of two subsystems

The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a set of states. In this work we define the notion of an "absolutely entangled set" of quantum states: for any possible choice of global basis, at least one of the states in the set is entangled. Hence, for all bipartitions, i.e. any possible definition of the subsystems, the set features entanglement. We present a minimum example of this phenomenon, with a set of four states in $\mathbb{C}^4 = \mathbb{C}^2 \otimes \mathbb{C}^2$. Moreover, we propose a quantitative measure for absolute set entanglement. To lower-bound this quantity, we develop a method based on polynomial optimization to perform convex optimization over unitaries, which is of independent interest.Comment: Main: 5 pages, 2 figures; Appendix: 5 pages and 1 figur

Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints

We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decom- position approach into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. Both problems can be solved very efficiently with existing methods such as outer convexification with sum-up-rounding strategies and mixed-integer linear programming techniques. The coupling is handled using a penalty-approach. We provide an exactness result for the penalty which yields a solution approach that convergences to partial minima. We compare the quality of these dedicated points with those of other heuristics amongst an academic example and also for the optimization of electric transmission lines with switching of the network topology for flow reallocation in order to satisfy demands

Optimal configuration of digital communication network

As the costs for maintaining computer communication networks are rapidly rising, it is particularly important to design the network efficiently. The objective of this thesis is to model the minimum cost design of digital communications networks and propose a heuristical solution approach to the formulated model. The minimum cost design has been modeled as a zero-one integer programming problem. The Lagrangian relaxation method and subgradient optimization procedure have been used to find reasonably good feasible solutions. Although the reliability for computer communication networks is as important as the cost factor, only the cost factor is considered in the context of this thesis.http://archive.org/details/optimalconfigura1094527604Major, Republic of Korea ArmyApproved for public release; distribution is unlimited

Training issues and learning algorithms for feedforward and recurrent neural networks

Ph.DDOCTOR OF PHILOSOPH

Paints supply chain optimisation

Imperial Users onl

Power System Stability Analysis using Neural Network

This work focuses on the design of modern power system controllers for automatic voltage regulators (AVR) and the applications of machine learning (ML) algorithms to correctly classify the stability of the IEEE 14 bus system. The LQG controller performs the best time domain characteristics compared to PID and LQG, while the sensor and amplifier gain is changed in a dynamic passion. After that, the IEEE 14 bus system is modeled, and contingency scenarios are simulated in the System Modelica Dymola environment. Application of the Monte Carlo principle with modified Poissons probability distribution principle is reviewed from the literature that reduces the total contingency from 1000k to 20k. The damping ratio of the contingency is then extracted, pre-processed, and fed to ML algorithms, such as logistic regression, support vector machine, decision trees, random forests, Naive Bayes, and k-nearest neighbor. A neural network (NN) of one, two, three, five, seven, and ten hidden layers with 25%, 50%, 75%, and 100% data size is considered to observe and compare the prediction time, accuracy, precision, and recall value. At lower data size, 25%, in the neural network with two-hidden layers and a single hidden layer, the accuracy becomes 95.70% and 97.38%, respectively. Increasing the hidden layer of NN beyond a second does not increase the overall score and takes a much longer prediction time; thus could be discarded for similar analysis. Moreover, when five, seven, and ten hidden layers are used, the F1 score reduces. However, in practical scenarios, where the data set contains more features and a variety of classes, higher data size is required for NN for proper training. This research will provide more insight into the damping ratio-based system stability prediction with traditional ML algorithms and neural networks.Comment: Masters Thesis Dissertatio