Nested Sampling and its Applications in Stable Compressive Covariance Estimation and Phase Retrieval with Near-Minimal Measurements

Compressed covariance sensing using quadratic samplers is gaining increasing interest in recent literature. Covariance matrix often plays the role of a sufficient statistic in many signal and information processing tasks. However, owing to the large dimension of the data, it may become necessary to obtain a compressed sketch of the high dimensional covariance matrix to reduce the associated storage and communication costs. Nested sampling has been proposed in the past as an efficient sub-Nyquist sampling strategy that enables perfect reconstruction of the autocorrelation sequence of Wide-Sense Stationary (WSS) signals, as though it was sampled at the Nyquist rate. The key idea behind nested sampling is to exploit properties of the difference set that naturally arises in quadratic measurement model associated with covariance compression. In this thesis, we will focus on developing novel versions of nested sampling for low rank Toeplitz covariance estimation, and phase retrieval, where the latter problem finds many applications in high resolution optical imaging, X-ray crystallography and molecular imaging. The problem of low rank compressive Toeplitz covariance estimation is first shown to be fundamentally related to that of line spectrum recovery. In absence if noise, this connection can be exploited to develop a particular kind of sampler called the Generalized Nested Sampler (GNS), that can achieve optimal compression rates. In presence of bounded noise, we develop a regularization-free algorithm that provably leads to stable recovery of the high dimensional Toeplitz matrix from its order-wise minimal sketch acquired using a GNS. Contrary to existing TV-norm and nuclear norm based reconstruction algorithms, our technique does not use any tuning parameters, which can be of great practical value. The idea of nested sampling idea also finds a surprising use in the problem of phase retrieval, which has been of great interest in recent times for its convex formulation via PhaseLift, By using another modified version of nested sampling, namely the Partial Nested Fourier Sampler (PNFS), we show that with probability one, it is possible to achieve a certain conjectured lower bound on the necessary measurement size. Moreover, for sparse data, an l1 minimization based algorithm is proposed that can lead to stable phase retrieval using order-wise minimal number of measurements.

Use of acoustic telemetry techniques to understand the individual variability in movement ecology of juvenile lemon sharks, Negaprion brevirostris, in natural conditions, around Bimini Islands, Bahamas: a comparison study with preliminary personality traits observed in mesocosms

Dissertação de Mestrado, Biologia Marinha, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2016

On multimodality of obnoxious faclity location models

Obnoxious single facility location models are models that have the aim to find the best location for an undesired facility. Undesired is usually expressed in relation to the so-called demand points that represent locations hindered by the facility. Because obnoxious facility location models as a rule are multimodal, the standard techniques of convex analysis used for locating desirable facilities in the plane may be trapped in local optima instead of the desired global optimum. It is assumed that having more optima coincides with being harder to solve. In this thesis the multimodality of obnoxious single facility location models is investigated in order to know which models are challenging problems in facility location problems and which are suitable for site selection. Selected for this are the obnoxious facility models that appear to be most important in literature. These are the maximin model, that maximizes the minimum distance from demand point to the obnoxious facility, the maxisum model, that maximizes the sum of distance from the demand points to the facility and the minisum model, that minimizes the sum of damage of the facility to the demand points. All models are measured with the Euclidean distances and some models also with the rectilinear distance metric. Furthermore a suitable algorithm is selected for testing multimodality. Of the tested algorithms in this thesis, Multistart is most appropriate. A small numerical experiment shows that Maximin models have on average the most optima, of which the model locating an obnoxious linesegment has the most. Maximin models have few optima and are thus not very hard to solve. From the Minisum models, the models that have the most optima are models that take wind into account. In general can be said that the generic models have less optima than the weighted versions. Models that are measured with the rectilinear norm do have more solutions than the same models measured with the Euclidean norm. This can be explained for the maximin models in the numerical example because the shape of the norm coincides with a bound of the feasible area, so not all solutions are different optima. The difference found in number of optima of the Maxisum and Minisum can not be explained by this phenomenon.

Kinematics and Local Motion Planning for Quasi-static Whole-body Mobile Manipulation

This thesis studies mobile robotic manipulators, where one or more robot manipulator arms are integrated with a mobile robotic base. The base could be a wheeled or tracked vehicle, or it might be a multi-limbed locomotor. As robots are increasingly deployed in complex and unstructured environments, the need for mobile manipulation increases. Mobile robotic assistants have the potential to revolutionize human lives in a large variety of settings including home, industrial and outdoor environments.

Mobile Manipulation is the use or study of such mobile robots as they interact with physical objects in their environment. As compared to fixed base manipulators, mobile manipulators can take advantage of the base mechanism’s added degrees of freedom in the task planning and execution process. But their use also poses new problems in the analysis and control of base system stability, and the planning of coordinated base and arm motions. For mobile manipulators to be successfully and efficiently used, a thorough understanding of their kinematics, stability, and capabilities is required. Moreover, because mobile manipulators typically possess a large number of actuators, new and efficient methods to coordinate their large numbers of degrees of freedom are needed to make them practically deployable. This thesis develops new kinematic and stability analyses of mobile manipulation, and new algorithms to efficiently plan their motions.

I first develop detailed and novel descriptions of the kinematics governing the operation of multi- limbed legged robots working in the presence of gravity, and whose limbs may also be simultaneously used for manipulation. The fundamental stance constraint that arises from simple assumptions about friction and the ground contact and feasible motions is derived. Thereafter, a local relationship between joint motions and motions of the robot abdomen and reaching limbs is developed. Baseeon these relationships, one can define and analyze local kinematic qualities including limberness, wrench resistance and local dexterity. While previous researchers have noted the similarity between multi- fingered grasping and quasi-static manipulation, this thesis makes explicit connections between these two problems.

The kinematic expressions form the basis for a local motion planning problem that that determines the joint motions to achieve several simultaneous objectives while maintaining stance stability in the presence of gravity. This problem is translated into a convex quadratic program entitled the balanced priority solution, whose existence and uniqueness properties are developed. This problem is related in spirit to the classical redundancy resoxlution and task-priority approaches. With some simple modifications, this local planning and optimization problem can be extended to handle a large variety of goals and constraints that arise in mobile-manipulation. This local planning problem applies readily to other mobile bases including wheeled and articulated bases. This thesis describes the use of the local planning techniques to generate global plans, as well as for use within a feedback loop. The work in this thesis is motivated in part by many practical tasks involving the Surrogate and RoboSimian robots at NASA/JPL, and a large number of examples involving the two robots, both real and simulated, are provided.

Finally, this thesis provides an analysis of simultaneous force and motion control for multi- limbed legged robots. Starting with a classical linear stiffness relationship, an analysis of this problem for multiple point contacts is described. The local velocity planning problem is extended to include generation of forces, as well as to maintain stability using force-feedback. This thesis also provides a concise, novel definition of static stability, and proves some conditions under which it is satisfied.

Adaptive Sampling with Mobile Sensor Networks

Mobile sensor networks have unique advantages compared with wireless sensor networks. The mobility enables mobile sensors to flexibly reconfigure themselves to meet sensing requirements. In this dissertation, an adaptive sampling method for mobile sensor networks is presented. Based on the consideration of sensing resource constraints, computing abilities, and onboard energy limitations, the adaptive sampling method follows a down sampling scheme, which could reduce the total number of measurements, and lower sampling cost. Compressive sensing is a recently developed down sampling method, using a small number of randomly distributed measurements for signal reconstruction. However, original signals cannot be reconstructed using condensed measurements, as addressed by Shannon Sampling Theory. Measurements have to be processed under a sparse domain, and convex optimization methods should be applied to reconstruct original signals. Restricted isometry property would guarantee signals can be recovered with little information loss. While compressive sensing could effectively lower sampling cost, signal reconstruction is still a great research challenge. Compressive sensing always collects random measurements, whose information amount cannot be determined in prior. If each measurement is optimized as the most informative measurement, the reconstruction performance can perform much better. Based on the above consideration, this dissertation is focusing on an adaptive sampling approach, which could find the most informative measurements in unknown environments and reconstruct original signals. With mobile sensors, measurements are collect sequentially, giving the chance to uniquely optimize each of them. When mobile sensors are about to collect a new measurement from the surrounding environments, existing information is shared among networked sensors so that each sensor would have a global view of the entire environment. Shared information is analyzed under Haar Wavelet domain, under which most nature signals appear sparse, to infer a model of the environments. The most informative measurements can be determined by optimizing model parameters. As a result, all the measurements collected by the mobile sensor network are the most informative measurements given existing information, and a perfect reconstruction would be expected. To present the adaptive sampling method, a series of research issues will be addressed, including measurement evaluation and collection, mobile network establishment, data fusion, sensor motion, signal reconstruction, etc. Two dimensional scalar field will be reconstructed using the method proposed. Both single mobile sensors and mobile sensor networks will be deployed in the environment, and reconstruction performance of both will be compared.In addition, a particular mobile sensor, a quadrotor UAV is developed, so that the adaptive sampling method can be used in three dimensional scenarios.

A functional representation of almost isometries

For each quasi-metric space X we consider the convex lattice SLip(1)(X) of all semi-Lipschitz functions on X with semi-Lipschitz constant not greater than 1. If X and Y are two complete quasi-metric spaces, we prove that every convex lattice isomorphism T from SLip(1)(Y) onto SLip(1)(X) can be written in the form Tf = c . (f o tau) + phi, where tau is an isometry, c > 0 and phi is an element of SLip(1)(X). As a consequence, we obtain that two complete quasi-metric spaces are almost isometric if, and only if, there exists an almost-unital convex lattice isomorphism between SLip(1)(X) and SLip(1) (Y).

Equilibrium existence in the circle model with linear quadratic transport cost

We treat the problem of existence of a location-then-price equilibrium in the circle model with a linear quadratic type of transportation cost function which can be either convex or concave. We show the existence of a unique perfect equilibrium for the concave case when the linear and quadratic terms are equal and of a unique perfect equilibrium for the convex case when the linear term is equal to zero. Aside from these two cases, there are feasible locations by the firms for which no equilibrium in the price subgame exists. Finally, we provide a full taxonomy of the price equilibrium regions in terms of weights of the linear and quadratic terms in the cost function.

Comparative Behavior of Wild and Hatchery Reared White Sea Bream (Diplodus sargus) Released on Artificial Reefs Off the Algarve (Southern Portugal)

Three hatchery produced and reared (HPR) and five wild white sea bream (Diplodus sargus) were double tagged with Vemco V8SC-2L acoustic transmitters and Floy Tag T-bar anchor tags, and released on artificial reefs located near a natural reef off the southern coast of Portugal. Passive telemetry was used to monitor movements of the white sea bream over a nine week period from April to June 2007. Differences in behavior at release, habitat association (artificial vs. natural reef), and in daily movements were registered. Wild fish moved from one habitat to the other with increased preference for the artificial habitat during the day, whereas HPR fish showed no site fidelity or consistent daily movement pattern and left the release site soon after release. Comparison of Minimum Convex Polygon (MCP) showed a higher area usage by wild fish. This experiment shows that these artificial reefs are used on a daily basis by wild white sea bream but apparently are not optimal release locations for hatchery produced white sea bream.

Home range, residency and movements of Diplodus sargus and Diplodus vulgaris in a coastal lagoon: Connectivity between nursery and adult habitats

Acoustic telemetry and standard tag-recapture were used to determine the home range and residency of juveniles and sub-adults of Diplodus sargus and Diplodus vulgaris in the Ria Formosa (Portugal) coastal lagoon. Maximum time between recaptures for the standard tag-recapture method was 128 days for D. sargus and 30 days for D. vulgaris. The majority of the fish were recaptured in the vicinity of the tagging location. Fish tagged with acoustic transmitters had a maximum period of time between first and last detections of 62 days for D. sargus and 260 days for D. vulgaris. Minimum convex polygons areas ranged between 148 024 m(2) and 525 930 m(2) for D. sargus and between 23 786 m(2) and 42134 m(2) for D. vulgaris. Both species presented a high residency index between first and last detections. Two D. sargus tagged with acoustic tags were recaptured by fishermen outside the coastal lagoon at distances of 12 km and 90 km from the tagging position, providing evidence that this species leaves the Ria Formosa during the winter time for the adjacent coastal waters. The results of this study reinforce the importance of Ria Formosa as a nursery for D. sargus and D. vulgaris in the south coast of Portugal. (C) 2009 Elsevier Ltd. All rights reserved.

Site fidelity and movements of gilthead sea bream (Sparus aurata) in a coastal lagoon (Ria Formosa, Portugal)

Short-time site fidelity and movements of gilthead sea bream (Sparus aurata) in a coastal lagoon were determined using passive acoustic telemetry. Nine fish, ranging from 20.1 to 32.5 cm total length, were surgically implanted with acoustic transmitters and monitored for up to 179 days. Minimum convex polygon areas ranged from 18,698.6 m(2) to 352,711.9 m(2). Home range sizes were small, with individuals using core areas on a daily basis. However, these core areas shifted within the study site over time towards the opening to the sea. Two different diel behaviors were recorded, with some individuals more active at night and others during day time. Some individuals also demonstrated homing abilities, returning to the capture site after being released more than 4 km away. (C) 2008 Elsevier Ltd. All rights reserved.

Cálculo de constantes ópticas de películas delgadas de Cu3BiS3 a través del método de Wolfe

Se calculó la obtención de las constantes ópticas usando el método de Wolfe. Dichas contantes: coeficiente de absorción (α), índice de refracción (n) y espesor de una película delgada (d ), son de importancia en el proceso de caracterización óptica del material. Se realizó una comparación del método del Wolfe con el método empleado por R. Swanepoel. Se desarrolló un modelo de programación no lineal con restricciones, de manera que fue posible estimar las constantes ópticas de películas delgadas semiconductoras, a partir únicamente, de datos de transmisión conocidos. Se presentó una solución al modelo de programación no lineal para programación cuadrática. Se demostró la confiabilidad del método propuesto, obteniendo valores de α = 10378.34 cm−1, n = 2.4595, d =989.71 nm y Eg = 1.39 Ev, a través de experimentos numéricos con datos de medidas de transmitancia espectral en películas delgadas de Cu3BiS3.

TECTONIC CONTROLS ON FLUVIAL LANDSCAPE DEVELOPMENT IN CENTRAL-EASTERN PORTUGAL: INSIGHTS FROM LONG PROFILE TRIBUTARY STREAM ANALYSES

This study examines the long profiles of tributaries of the Tejo (Tagus) and Zêzere rivers in central eastern Portugal (West Iberia) in order to provide new insights into the patterns, timing and controls on drainage development during the Pleistocene to Holocene incision stage. The long profiles were extracted from lower order tributary streams associated with the trunk drainage of the Tejo River and one main tributary, the Zêzere River (Fig. 1). These streams flow through a landscape strongly influenced by variations in bedrock lithology (mainly granites and metasediments), fault structures delimiting crustal blocks with distinct uplift rates, and a base-level lowering history (tectonic uplift / eustatic). The long profiles of the tributaries of the Tejo and Zêzere rivers record a series of transient and permanent knickpoints. The permanent knickpoints have direct correlation with the bedrock strength, corresponding to the outcropping of very hard quartzites or to the transition from softer (slates/metagreywaques) to harder (granite) basement. The analyzed streams/rivers record also an older transient knickpoint/knickzone separating: a) an upstream relict graded profile, with lower steepness and higher concavity, that reflects a long period of quasi-equilibrium conditions reached after the beginning of the incision stage; and b) a downstream reach displaying a rejuvenated long profile, with steeper gradient and lower concavity, particularly for the final segment, which is often convex (Fig. 2). The rejuvenated reaches testify the upstream propagation of several incision waves that are the response of each stream to continuous or increasing crustal uplift and dominant periods of base-level lowering by the trunk drainages, coeval of low sea level conditions. The long profiles and their morphological configurations enabled spatial and relative temporal patterns of incision to be quantified for each individual tributary stream. The incision values of streams flowing in uplifted blocks of the Portuguese Central Range (PCR) (ca.380-280 m) indicate differential uplift and are higher than the incision values of streams flowing on the adjacent South Portugal planation surface – the Meseta (ca. 200 m). The normalized steepness index, calculated using the method of Wobus et al. (2006), proved to be sensitive to active tectonics, as lower ksn values were found in relict graded profiles of streams located in less uplifted blocks, (e.g. Sertã stream in the PCR), or in those flowing through tectonic depressions. Fig. 1 – Geological map of the study area. 1 – fluvial terraces (Pleistocene); 2 – sedimentary cover (Paleogene and Neogene); 3 – slates and metasandstones (Devonian); 4 – slates and quartzites (Silurian); 5 – quartzites (Ordovician); 6 – slates and metagreywackes (Precambrian to Cambrian); 7 – slates, metagreywackes and limestones (Precambrian); 8 – granites and ortogneisses; 9 – diorites and gabros; 10 - fault. SFf – Sobreira Formosa fault; Sf – Sertã fault; Pf – Ponsul fault; Gf – Grade fault. The differential uplift indicated by the distribution of the ksn values and by the fluvial incision was likely accumulated on a few major faults, as the Sobreira Formosa fault (SFf), thus corroborating the tectonic activity of these faults. Due to the fact that the relict graded profiles can be correlated with other geomorphic references documented in the study area, namely the T1 terrace of the Tagus River (with an age of ca. 1 Myr), the following incision rates can be estimated: a) for the studied streams located in uplifted blocks of the PCR, 0.38 m/kyr to 0.28 m/kyr; b) for the streams flowing on the South Portugal planation surface, 0.20 m/kyr. The differential uplift inferred between crustal blocks in the study area corroborates the neotectonic activity of the bordering faults, which has been proposed in previous studies based upon less robust data. Fig. 2 – Longitudinal profile of the Nisa stream a tributary of the Tejo River. Note the equilibrium relict profile upstream the older transient knickpoint (hatched line) and the downstream rejuvenated profile (continuous line). Legend: tKP – transient knickpoint; rKp – resistant knickpoint; Mt – schist and phyllite; Gr – granite; Hf – hornfels; Og – orthogneisse. In the inset Distance – Slope plots, fill circles correspond to the relict graded profile, crosses correspond to the rejuvenated profile located downstream the older transient knickpoint (tKP).

Tectonic and lithological controls on fluvial landscape development in central-eastern Portugal: Insights from long profile tributary stream analyses

This study examines the long profiles of tributaries of the Tagus and Zêzere rivers in Portugal (West Iberia) in order to provide new insights into patterns, timing, and controls on drainage development during the Quaternary incision stage. The studied streams are incised into a relict culminant fluvial surface, abandoned at the beginning of the incision stage. The streams flow through a landscape with bedrock variations in lithology (mainly granites and metasediments) and faulted blocks with distinct uplift rates. The long profiles of the analyzed streams record an older transitory knickpoint/knickzone separating (1) an upstream relict graded profile, with lower steepness and higher concavity, that reflects a long period of quasi-equilibrium conditions reached after the beginning of the incision stage, and (2) a downstream rejuvenated long profile, with steeper gradient and lower concavity, particularly for the final reach, which is often convex. The rejuvenated reaches testify to the upstream propagation of several incision waves, interpreted as the response of each stream to increasing crustal uplift and prolonged periods of base-level lowering by the trunk drainages, coeval with low sea level conditions. The morphological configurations of the long profiles enabled spatial and relative temporal patterns of incisions to be quantified. The incision values of streams flowing on the Portuguese Central Range (PCR; ca. 380–150 m) are variable but generally higher than the incision values of streams flowing on the adjacent South Portugal Planation Surface (SPPS; ca. 220–110 m), corroborating differential uplift of the PCR relative to the SPPS. Owing to the fact that the relict graded profiles can be correlated with the Tagus River T1 terrace (1.1–0.9 My) present in the study area, incision rates can be estimated (1) for the streams located in the PCR, 0.38–0.15 m/ky and (2) for the streams flowing on the SPPS, 0.22–0.12 m/ky. The differential uplift inferred in the study area supports the neotectonic activity of the bordering faults, as proposed in previous studies based upon other geological evidence.

Tectonic and lithological controls on fluvial landscape development in central-eastern Portugal: Insights from long profile tributary stream analyses

This study examines the long profiles of tributaries of the Tagus and Zêzere rivers in Portugal (West Iberia) in order to provide new insights into patterns, timing, and controls on drainage development during the Quaternary incision stage. The studied streams are incised into a relict culminant fluvial surface, abandoned at the beginning of the incision stage. The streams flow through a landscape with bedrock variations in lithology (mainly granites and metasediments) and faulted blocks with distinct uplift rates. The long profiles of the analyzed streams record an older transitory knickpoint/knickzone separating (1) an upstream relict graded profile, with lower steepness and higher concavity, that reflects a long period of quasi-equilibrium conditions reached after the beginning of the incision stage, and (2) a downstream rejuvenated long profile, with steeper gradient and lower concavity, particularly for the final reach, which is often convex. The rejuvenated reaches testify to the upstream propagation of several incision waves, interpreted as the response of each stream to increasing crustal uplift and prolonged periods of base-level lowering by the trunk drainages, coeval with low sea level conditions. The morphological configurations of the long profiles enabled spatial and relative temporal patterns of incisions to be quantified. The incision values of streams flowing on the Portuguese Central Range (PCR; ca. 380–150 m) are variable but generally higher than the incision values of streams flowing on the adjacent South Portugal Planation Surface (SPPS; ca. 220–110 m), corroborating differential uplift of the PCR relative to the SPPS. Owing to the fact that the relict graded profiles can be correlated with the Tagus River T1 terrace (1.1–0.9 My) present in the study area, incision rates can be estimated (1) for the streams located in the PCR, 0.38–0.15 m/ky and (2) for the streams flowing on the SPPS, 0.22–0.12 m/ky. The differential uplift inferred in the study area supports the neotectonic activity of the bordering faults, as proposed in previous studies based upon other geological evidence.

Análise Exploratória da Métrica de Superfície Topográfica para Previsão do Nível Freático - Aplicação a um Sistema Cársico e Rochas Fracturadas

Partindo da premissa de que não só o nível freático acompanha a linha topográfica do terreno, mas também a direcção de escorrência das bacias subterrâneas tende a coincidir com a direcção predominante de escorrência das bacias hidrográficas à superfície, principalmente em aquíferos fracturados, foi realizado um estudo com o objectivo de definir um modelo explicativo do nível freático no sistema aquífero Estremoz-Cano e no sector pouco produtivo das rochas ígneas e metamórficas da Zona de Ossa Morena (ZOM), em função das característica métricas do terreno, aferidas a partir da uma análise espacial raster, com multi-resolução, gradativa e interpolativa. Diferentes modelos foram criados e testados a partir dos dados do nível hidroestático, da elevação do terreno e de indíces métricos do terreno computados a partir de uma superfície digital de terreno hidrologicamente funcional. A análise estatística das variáveis independentes computadas permitiu concluir que o nível hidrostático (NHE) é extremamente correlacionável com o índice de convexidade calculado (Convex) e a elevação do terreno numa Regressão Linear do Tipo Piecewise.