Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems

We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedness from the observation operators and preserves desired features of the unknown. Having studied the mechanism of the Tikhonov regularization, we propose a multi-scale generalization to the Tikhonov regularization method, so-called the Hierarchical Reconstruction (HR) method. First introduction of the HR method can be traced back to the Hierarchical Decomposition method in Image Processing. The HR method successively extracts information from the previous hierarchical residual to the current hierarchical term at a finer hierarchical scale. As the sum of all the hierarchical terms, the hierarchical sum from the HR method provides an reasonable approximate solution to the unknown, when the observation matrix satisfies certain conditions with specific stabilizing functions. When compared to the Tikhonov regularization method on solving the same inverse problems, the HR method is shown to be able to decrease the total number of iterations, reduce the approximation error, and offer self control of the approximation distance between the hierarchical sum and the unknown, thanks to using a ladder of finitely many hierarchical scales. We report numerical experiments supporting our claims on these advantages the HR method has over the Tikhonov regularization method.

Causal structure of the entanglement renormalization ansatz

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat space-like boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.

A model of macadamia with application to pruning in orchards

A self-organising model of macadamia, expressed using L-Systems, was used to explore aspects of canopy management. A small set of parameters control the basic architecture of the model, with a high degree of self-organisation occurring to determine the fate and growth of buds. Light was sensed at the leaf level and used to represent vigour and accumulated basipetally. Buds also sensed light so as to provide demand in the subsequent redistribution of the vigour. Empirical relationships were derived from a set of 24 completely digitised trees after conversion to multiscale tree graphs (MTG) and analysis with the OpenAlea software library. The ability to write MTG files was embedded within the model so that various tree statistics could be exported for each run of the model. To explore the parameter space a series of runs was completed using a high-throughput computing platform. When combined with MTG generation and analysis with OpenAlea it provided a convenient way in which thousands of simulations could be explored. We allowed the model trees to develop using self-organisation and simulated cultural practices such as hedging, topping, removal of the leader and limb removal within a small representation of an orchard. The model provides insight into the impact of these practices on potential for growth and the light distribution within the canopy and to the orchard floor by coupling the model with a path-tracing program to simulate the light environment. The lessons learnt from this will be applied to other evergreen, tropical fruit and nut trees.

Development of an historical landscape photography database to support landscape change analysis in the Northeast of Portugal

Repeat photography is an efficient, effective and useful method to identify trends of changes in the landscapes. It was used to illustrate long-term changes occurring in the landscapes. In the Northeast of Portugal, landscapes changes is currently driven mostly by agriculture abandonment and agriculture and energy policy. However, there is a need to monitoring changes in the region using a multitemporal and multiscale approach. This project aimed to establish an online repository of oblique digital photography from the region to be used to register the condition of the landscape as recorded in historical and contemporary photography over time as well as to support qualitative and quantitative assessment of change in the landscape using repeat photography techniques and methods. It involved the development of a relational database and a series of web-based services using PHP: Hypertext Preprocessor language, and the development of an interface, with Joomla, of pictures uploading and downloading by users. The repository will make possible to upload, store, search by location, theme, or date, display, and download pictures for Northeastern Portugal. The website service is devoted to help researchers to obtain quickly the photographs needed to apply RP through a developed search engine. It can be accessed at: http://esa.ipb.pt/digitalandscape/.

THERMAL VACUUM TEST CORRELATION OF A ZERO PROPELLANT LOAD CASE THERMAL CAPACITANCE PROPELLANT GAUGING ANALYTICAL MODEL

This thesis describes the development and correlation of a thermal model that forms the foundation of a thermal capacitance spacecraft propellant load estimator. Specific details of creating the thermal model for the diaphragm propellant tank used on NASA’s Magnetospheric Multiscale spacecraft using ANSYS and the correlation process implemented are presented. The thermal model was correlated to within +/- 3 Celsius of the thermal vacuum test data, and was determined sufficient to make future propellant predictions on MMS. The model was also found to be relatively sensitive to uncertainties in applied heat flux and mass knowledge of the tank. More work is needed to improve temperature predictions in the upper hemisphere of the propellant tank where predictions were found to be 2-2.5 Celsius lower than the test data. A road map for applying the model to predict propellant loads on the actual MMS spacecraft in 2017-2018 is also presented.

Associations between step duration variability and inertial measurement unit derived gait characteristics

Inertial measurement units (IMU) provide a convenient tool for gait stability assessment. However, it is unclear how various gait characteristics relate to each other and whether gait characteristics can be obtained from resultant acceleration. Therefore, step duration variability was measured in treadmill walking from 39 young ambulant volunteers (age 24.2 [± 2.5] y; height 1.79 [± 0.09] m; mass 71.6 [± 12.0] kg) using motion capture. Accelerations and gyrations were simultaneously recorded with an IMU. Harmonic ratio, maximum Lyapunov exponents, and multiscale sample entropy (MSE) were calculated. Step duration variability was positively associated with MSE with coarseness levels = 3-6 (r = -.33 to -.42, P ≤ .045). Harmonic ratio and MSE with all coarseness levels were negatively associated (r = -.45 to -.57, P ≤ .004). The MSE with coarseness level = 2 was negatively associated with short-term maximum Lyapunov exponents (r = -.32, P = .047). The agreement between resultant and vertical acceleration derived gait characteristics was excellent (ICC = 0.97-0.99). In conclusion, MSE with varying coarseness levels was associated with the other gait characteristics evaluated in the study. Resultant and vertical acceleration derived results had excellent agreement, which suggests that resultant acceleration is a viable alternative to considering the acceleration dimensions independently.

Optimization of Pattern Matching Algorithms for Multi- and Many-Core Platforms

Image and video compression play a major role in the world today, allowing the storage and transmission of large multimedia content volumes. However, the processing of this information requires high computational resources, hence the improvement of the computational performance of these compression algorithms is very important. The Multidimensional Multiscale Parser (MMP) is a pattern-matching-based compression algorithm for multimedia contents, namely images, achieving high compression ratios, maintaining good image quality, Rodrigues et al. [2008]. However, in comparison with other existing algorithms, this algorithm takes some time to execute. Therefore, two parallel implementations for GPUs were proposed by Ribeiro [2016] and Silva [2015] in CUDA and OpenCL-GPU, respectively. In this dissertation, to complement the referred work, we propose two parallel versions that run the MMP algorithm in CPU: one resorting to OpenMP and another that converts the existing OpenCL-GPU into OpenCL-CPU. The proposed solutions are able to improve the computational performance of MMP by 3 and 2:7 , respectively. The High Efficiency Video Coding (HEVC/H.265) is the most recent standard for compression of image and video. Its impressive compression performance, makes it a target for many adaptations, particularly for holoscopic image/video processing (or light field). Some of the proposed modifications to encode this new multimedia content are based on geometry-based disparity compensations (SS), developed by Conti et al. [2014], and a Geometric Transformations (GT) module, proposed by Monteiro et al. [2015]. These compression algorithms for holoscopic images based on HEVC present an implementation of specific search for similar micro-images that is more efficient than the one performed by HEVC, but its implementation is considerably slower than HEVC. In order to enable better execution times, we choose to use the OpenCL API as the GPU enabling language in order to increase the module performance. With its most costly setting, we are able to reduce the GT module execution time from 6.9 days to less then 4 hours, effectively attaining a speedup of 45 .

Challenges in imaging and predictive modeling of rhizosphere processes

Background Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions. Scope In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding. Conclusions We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes.

Singularity and multifractal characterization of signals with wavelets. Application to clay soil images

In the field of multiscale analysis of signals, including images, the wavelet transform is one of the most attractive and powerful tool due to its ability to focus on signals structures at different scales. Wavelet Transform at different scales is successfully applied to image characterization (which can be applied to a watermarking scheme) and multiscale singularity detection and processing. In this work we show further research of computation of multifractals properties such as the multifractal spectrum (D(alpha)) applied to dye stained images of natural terrain. This can be useful for statically describing preferential flow path geometry.

Assessing the ability of rural agrarian areas to provide cultural ecosystem services (CES): A multi scale social indicator framework (MSIF)

Assessing the ways in which rural agrarian areas provide Cultural Ecosystem Services (CES) is proving difficult to achieve. This research has developed an innovative methodological approach named as Multi Scale Indicator Framework (MSIF) for capturing the CES embedded into the rural agrarian areas. This framework reconciles a literature review with a transdisciplinary participatory workshop. Both of these sources reveal that societal preferences diverge upon judgemental criteria which in turn relate to different visual concepts that can be drawn from analyzing attributes, elements, features and characteristics of rural areas. We contend that it is now possible to list a group of possible multi scale indicators for stewardship, diversity and aesthetics. These results might also be of use for improving any existing European indicators frameworks by also including CES. This research carries major implications for policy at different levels of governance, as it makes possible to target and monitor policy instruments to the physical rural settings so that cultural dimensions are adequately considered. There is still work to be developed on regional specific values and thresholds for each criteria and its indicator set. In practical terms, by developing the conceptual design within a common framework as described in this paper, a considerable step forward toward the inclusion of the cultural dimension in European wide assessments can be made