Graph Theoretic Algorithms Adaptable to Quantum Computing

Computational methods are rapidly emerging as an essential tool for understanding and solving complex engineering problems, which complement the traditional tools of experimentation and theory. When considered in a discrete computational setting, many engineering problems can be reduced to a graph coloring problem. Examples range from systems design, airline scheduling, image segmentation to pattern recognition, where energy cost functions with discrete variables are extremized. However, using discrete variables over continuous variables introduces some complications when defining differential quantities, such as gradients and Hessians involved in scientific computations within solid and fluid mechanics. Consequently, graph techniques are under-utilized in this important domain. However, we have recently witnessed great developments in quantum computing where physical devices can solve discrete optimization problems faster than most well-known classical algorithms. This warrants further investigation into the re-formulation of scientific computation problems into graph-theoretic problems, thus enabling rapid engineering simulations in a soon-to-be quantum computing world. The computational techniques developed in this thesis allow the representation of surface scalars, such as perimeter and area, using discrete variables in a graph. Results from integral geometry, specifically Cauchy-Crofton relations, are used to estimate these scalars via submodular functions. With this framework, several quantities important to engineering applications can be represented in graph-based algorithms. These include the surface energy of cracks for fracture prediction, grain boundary energy to model microstructure evolution, and surface area estimates (of grains and fibers) for generating conformal meshes. Combinatorial optimization problems for these applications are presented first. The last two chapters describe two new graph coloring algorithms implemented on a physical quantum computing device: the D-wave quantum annealer. The first algorithm describes a functional minimization approach to solve differential equations. The second algorithm describes a realization of the Boltzmann machine learning algorithm on a quantum annealer. The latter allows generative and discriminative learning of data, which has vast applications in many fields. Theoretical aspects and the implementation of these problems are outlined with a focus on engineering applications.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168116/1/sidsriva_1.pd

Earthquake damage assessment in urban area from Very High Resolution satellite data

The use of remote sensing within the domain of natural hazards and disaster management has become increasingly popular, due in part to increased awareness of environmental issues, including climate change, but also to the improvement of geospatial technologies and the ability to provide high quality imagery to the public through the media and internet. As technology is enhanced, demand and expectations increase for near-real-time monitoring and images to be relayed to emergency services in the event of a natural disaster. During a seismic event, in particular, it is fundamental to obtain a fast and reliable map of the damage of urban areas to manage civil protection interventions. Moreover, the identification of the destruction caused by an earthquake provides seismology and earthquake engineers with informative and valuable data, experiences and lessons in the long term. An accurate survey of damage is also important to assess the economic losses, and to manage and share the resources to be allocated during the reconstruction phase. Satellite remote sensing can provide valuable pieces of information on this regard, thanks to the capability of an instantaneous synoptic view of the scene, especially if the seismic event is located in remote regions, or if the main communication systems are damaged. Many works exist in the literature on this topic, considering both optical data and radar data, which however put in evidence some limitations of the nadir looking view, of the achievable level of details and response time, and the criticality of image radiometric and geometric corrections. The visual interpretation of optical images collected before and after a seismic event is the approach followed in many cases, especially for an operational and rapid release of the damage extension map. Many papers, have evaluated change detection approaches to estimate damage within large areas (e.g., city blocks), trying to quantify not only the extension of the affected area but also the level of damage, for instance correlating the collapse ratio (percentage of collapsed buildings in an area) measured on ground with some change parameters derived from two images, taken before and after the earthquake. Nowadays, remotely sensed images at Very High Resolution (VHR) may in principle enable production of earthquake damage maps at single-building scale. The complexity of the image forming mechanisms within urban settlements, especially of radar images, makes the interpretation and analysis of VHR images still a challenging task. Discrimination of lower grade of damage is particularly difficult using nadir looking sensors. Automatic algorithms to detect the damage are being developed, although as matter of fact, these works focus very often on specific test cases and sort of canonical situations. In order to make the delivered product suitable for the user community, such for example Civil Protection Departments, it is important to assess its reliability on a large area and in different and challenging situations. Moreover, the assessment shall be directly compared to those data the final user adopts when carrying out its operational tasks. This kind of assessment can be hardly found in the literature, especially when the main focus is on the development of sophisticated and advanced algorithms. In this work, the feasibility of earthquake damage products at the scale of individual buildings, which relies on a damage scale recognized as a standard, is investigated. To this aim, damage maps derived from VHR satellite images collected by Synthetic Aperture Radar (SAR) and optical sensors, were systematically compared to ground surveys carried out by different teams and with different purposes and protocols. Moreover, the inclusion of a priori information, such as vulnerability models for buildings and soil geophysical properties, to improve the reliability of the resulting damage products, was considered in this study. The research activity presented in this thesis was carried out in the framework of the APhoRISM (Advanced PRocedures for volcanIc Seismic Monitoring) project, funded by the European Union under the EC-FP7 call. APhoRISM was aimed at demonstrating that an appropriate management and integration of satellite and ground data can provide new improved products useful for seismic and volcanic crisis management

Assembly Line

An assembly line is a manufacturing process in which parts are added to a product in a sequential manner using optimally planned logistics to create a finished product in the fastest possible way. It is a flow-oriented production system where the productive units performing the operations, referred to as stations, are aligned in a serial manner. The present edited book is a collection of 12 chapters written by experts and well-known professionals of the field. The volume is organized in three parts according to the last research works in assembly line subject. The first part of the book is devoted to the assembly line balancing problem. It includes chapters dealing with different problems of ALBP. In the second part of the book some optimization problems in assembly line structure are considered. In many situations there are several contradictory goals that have to be satisfied simultaneously. The third part of the book deals with testing problems in assembly line. This section gives an overview on new trends, techniques and methodologies for testing the quality of a product at the end of the assembling line

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set