Estimation and Quantization of Expected Persistence Diagrams

International audiencePersistence diagrams (PDs) are the most common descriptors used to encode the topology of structured data appearing in challenging learning tasks; think e.g. of graphs, time series or point clouds sampled close to a manifold. Given random objects and the corresponding distribution of PDs, one may want to build a statistical summary-such as a mean-of these random PDs, which is however not a trivial task as the natural geometry of the space of PDs is not linear. In this article, we study two such summaries, the Expected Persistence Diagram (EPD), and its quantization. The EPD is a measure supported on R 2 , which may be approximated by its empirical counterpart. We prove that this estimator is optimal from a minimax standpoint on a large class of models with a parametric rate of convergence. The empirical EPD is simple and efficient to compute, but possibly has a very large support, hindering its use in practice. To overcome this issue, we propose an algorithm to compute a quantization of the empirical EPD, a measure with small support which is shown to approximate with near-optimal rates a quantization of the theoretical EPD

Machine Learning Techniques To Mitigate Nonlinear Impairments In Optical Fiber System

The upcoming deployment of 5/6G networks, online services like 4k/8k HDTV (streamers and online games), the development of the Internet of Things concept, connecting billions of active devices, as well as the high-speed optical access networks, impose progressively higher and higher requirements on the underlying optical networks infrastructure. With current network infrastructures approaching almost unsustainable levels of bandwidth utilization/ data traffic rates, and the electrical power consumption of communications systems becoming a serious concern in view of our achieving the global carbon footprint targets, network operators and system suppliers are now looking for ways to respond to these demands while also maximizing the returns of their investments. The search for a solution to this predicted ªcapacity crunchº led to a renewed interest in alternative approaches to system design, including the usage of high-order modulation formats and high symbol rates, enabled by coherent detection, development of wideband transmission tools, new fiber types (such as multi-mode and ±core), and finally, the implementation of advanced digital signal processing (DSP) elements to mitigate optical channel nonlinearities and improve the received SNR. All aforementioned options are intended to boost the available optical systems’ capacity to fulfill the new traffic demands. This thesis focuses on the last of these possible solutions to the ªcapacity crunch," answering the question: ªHow can machine learning improve existing optical communications by minimizing quality penalties introduced by transceiver components and fiber media nonlinearity?". Ultimately, by identifying a proper machine learning solution (or a bevy of solutions) to act as a nonlinear channel equalizer for optical transmissions, we can improve the system’s throughput and even reduce the signal processing complexity, which means we can transmit more using the already built optical infrastructure. This problem was broken into four parts in this thesis: i) the development of new machine learning architectures to achieve appealing levels of performance; ii) the correct assessment of computational complexity and hardware realization; iii) the application of AI techniques to achieve fast reconfigurable solutions; iv) the creation of a theoretical foundation with studies demonstrating the caveats and pitfalls of machine learning methods used for optical channel equalization. Common measures such as bit error rate, quality factor, and mutual information are considered in scrutinizing the systems studied in this thesis. Based on simulation and experimental results, we conclude that neural network-based equalization can, in fact, improve the channel quality of transmission and at the same time have computational complexity close to other classic DSP algorithms

Sustainable scheduling policies for radio access networks based on LTE technology

A thesis submitted to the University of Bedfordshire in partial fulfilment of the requirements for the degree of Doctor of PhilosophyIn the LTE access networks, the Radio Resource Management (RRM) is one of the most important modules which is responsible for handling the overall management of radio resources. The packet scheduler is a particular sub-module which assigns the existing radio resources to each user in order to deliver the requested services in the most efficient manner. Data packets are scheduled dynamically at every Transmission Time Interval (TTI), a time window used to take the user’s requests and to respond them accordingly. The scheduling procedure is conducted by using scheduling rules which select different users to be scheduled at each TTI based on some priority metrics. Various scheduling rules exist and they behave differently by balancing the scheduler performance in the direction imposed by one of the following objectives: increasing the system throughput, maintaining the user fairness, respecting the Guaranteed Bit Rate (GBR), Head of Line (HoL) packet delay, packet loss rate and queue stability requirements. Most of the static scheduling rules follow the sequential multi-objective optimization in the sense that when the first targeted objective is satisfied, then other objectives can be prioritized. When the targeted scheduling objective(s) can be satisfied at each TTI, the LTE scheduler is considered to be optimal or feasible. So, the scheduling performance depends on the exploited rule being focused on particular objectives. This study aims to increase the percentage of feasible TTIs for a given downlink transmission by applying a mixture of scheduling rules instead of using one discipline adopted across the entire scheduling session. Two types of optimization problems are proposed in this sense: Dynamic Scheduling Rule based Sequential Multi-Objective Optimization (DSR-SMOO) when the applied scheduling rules address the same objective and Dynamic Scheduling Rule based Concurrent Multi-Objective Optimization (DSR-CMOO) if the pool of rules addresses different scheduling objectives. The best way of solving such complex optimization problems is to adapt and to refine scheduling policies which are able to call different rules at each TTI based on the best matching scheduler conditions (states). The idea is to develop a set of non-linear functions which maps the scheduler state at each TTI in optimal distribution probabilities of selecting the best scheduling rule. Due to the multi-dimensional and continuous characteristics of the scheduler state space, the scheduling functions should be approximated. Moreover, the function approximations are learned through the interaction with the RRM environment. The Reinforcement Learning (RL) algorithms are used in this sense in order to evaluate and to refine the scheduling policies for the considered DSR-SMOO/CMOO optimization problems. The neural networks are used to train the non-linear mapping functions based on the interaction among the intelligent controller, the LTE packet scheduler and the RRM environment. In order to enhance the convergence in the feasible state and to reduce the scheduler state space dimension, meta-heuristic approaches are used for the channel statement aggregation. Simulation results show that the proposed aggregation scheme is able to outperform other heuristic methods. When the aggregation scheme of the channel statements is exploited, the proposed DSR-SMOO/CMOO problems focusing on different objectives which are solved by using various RL approaches are able to: increase the mean percentage of feasible TTIs, minimize the number of TTIs when the RL approaches punish the actions taken TTI-by-TTI, and minimize the variation of the performance indicators when different simulations are launched in parallel. This way, the obtained scheduling policies being focused on the multi-objective criteria are sustainable. Keywords: LTE, packet scheduling, scheduling rules, multi-objective optimization, reinforcement learning, channel, aggregation, scheduling policies, sustainable

Vortex-Lattice Utilization

The many novel, innovative, and unique implementations and applications of the vortex-lattice method to aerodynamic design and analysis which have been performed by Industry, Government, and Universities were presented. Although this analytical tool is not new, it continues to be utilized and refined in the aeronautical community

Mono- and Dinuclear Nonheme Iron Model Complexes: O-O Bond Activation, Structural Characterization and Reactivity Study

University of Minnesota Ph.D. dissertation. May 2015. Major: Chemistry. Advisor: Lawrence Que. 1 computer file (PDF); xxvi, 190 pages.The structures and reactivities of mono- and dinuclear nonheme iron model complexes were investigated. In Chapters 2 and 3, O-O bond activation of H2O2 by the dinuclear complexes [(FeIII2(μ-O)(μ-OH)L2]3+ (1A) and [(FeIII2(μ-OH)2L2]4+ (2A), L = tris(3,5-di-methyl-4-methoxypyridyl-2-methyl)amine, to form the high-valent [(FeIV2(μ-O)(OH)(O)L2]3+ (3A) and [(FeIV2(μ-O)2L2]4+ (4A) was studied. H2O2 and H2O competed for binding to the Fe centers of 1A and 2A, and [H2O2] was rate limiting under the concentrations studied. The presence of base increased the H2O2 activation rate for 2A, but not for 1A. The H2O2 activation rates by 1A and 2A were comparable to that of the mononuclear nonheme iron complex [FeII(TMC)]2+ (TMC = tetramethylcyclam) (J. Am. Chem. Soc. 2010, 2134-2135) after accounting for water inhibition. A crystal structure of [(FeIV2(μ-O)2L2]4+ (4A), or diamond core, was solved and described the Fe2O2 core in more detail than the original EXAFS structural assignment. In addition, structures of other complexes with Fe2O2L2 cores in different oxidation and protonation states were also studied and compared to the Fe2O2 cores of the high-valent enzymes intermediates RNR-X and sMMO-Q. In Chapter 4, iron complexes supported by the TMC ligand were studied by X-ray crystallography. A second isomer of the [FeIV(O)(TMC)]2+ complex was found, and the mechanism of conversion to the original isomer was explored. Additionally, the crystal structure of (TMC)FeIII(μ-O)Sc(NCCH3)(OTf)4 complex was obtained and used to reassign the Fe oxidation state of the originally reported (TMC)FeIV(μ-O)Sc(OH)(OTf)4 complex.(Nat. Chem. 2010, 756-759) In Chapter 5, the hydrogen atom transfer (HAT) rates of a series of S = 2 mononuclear nonheme iron complexes, [FeIV(O)TMG2dien(X)]2+,+ (X = CH3CN, Cl-, Br-, N3-, CH3CO2- and CF3CO2-; TMG2dien = 1,1-bis{2-[N2-(1,1,3,3- tetramethylguanidino)]ethyl}amine), were reported. Substitution of CH3CN with carboxylate and halide anions cis to the oxo ligand increased the HAT oxidation rate by as much as 15 times. A series of S = 1 nonheme iron complexes, [FeIV(O)TPA(Y)]2+,+ (Y = CH3CN, Cl-, CH3CO2- and CF3CO2-; TPA = tris(pyridyl-2-methyl)amine), was also investigated to explore what effect spin state has on reactivity. The HAT rates were similar for the [FeIV(O)TPA(Y)]2+,+ series, while OAT rates were much faster for the [FeIV(O)TPA(CH3CN)]2+ species