Cooperative Multi-robot Patrolling: A study of distributed approaches based on mathematical models of game theory to protect infrastructures

El principio de Teoría de Juegos permite desarrollar modelos estocásticos de patrullaje multi-robot para proteger infraestructuras criticas. La protección de infraestructuras criticas representa un gran reto para los países al rededor del mundo, principalmente después de los ataques terroristas llevados a cabo la década pasada. En este documento el termino infraestructura hace referencia a aeropuertos, plantas nucleares u otros instalaciones. El problema de patrullaje se define como la actividad de patrullar un entorno determinado para monitorear cualquier actividad o sensar algunas variables ambientales. En esta actividad, un grupo de robots debe visitar un conjunto de puntos de interés definidos en un entorno en intervalos de tiempo irregulares con propósitos de seguridad. Los modelos de partullaje multi-robot son utilizados para resolver este problema. Hasta el momento existen trabajos que resuelven este problema utilizando diversos principios matemáticos. Los modelos de patrullaje multi-robot desarrollados en esos trabajos representan un gran avance en este campo de investigación. Sin embargo, los modelos con los mejores resultados no son viables para aplicaciones de seguridad debido a su naturaleza centralizada y determinista. Esta tesis presenta cinco modelos de patrullaje multi-robot distribuidos e impredecibles basados en modelos matemáticos de aprendizaje de Teoría de Juegos. El objetivo del desarrollo de estos modelos está en resolver los inconvenientes presentes en trabajos preliminares. Con esta finalidad, el problema de patrullaje multi-robot se formuló utilizando conceptos de Teoría de Grafos, en la cual se definieron varios juegos en cada vértice de un grafo. Los modelos de patrullaje multi-robot desarrollados en este trabajo de investigación se han validado y comparado con los mejores modelos disponibles en la literatura. Para llevar a cabo tanto la validación como la comparación se ha utilizado un simulador de patrullaje y un grupo de robots reales. Los resultados experimentales muestran que los modelos de patrullaje desarrollados en este trabajo de investigación trabajan mejor que modelos de trabajos previos en el 80% de 150 casos de estudio. Además de esto, estos modelos cuentan con varias características importantes tales como distribución, robustez, escalabilidad y dinamismo. Los avances logrados con este trabajo de investigación dan evidencia del potencial de Teoría de Juegos para desarrollar modelos de patrullaje útiles para proteger infraestructuras. ABSTRACT Game theory principle allows to developing stochastic multi-robot patrolling models to protect critical infrastructures. Critical infrastructures protection is a great concern for countries around the world, mainly due to terrorist attacks in the last decade. In this document, the term infrastructures includes airports, nuclear power plants, and many other facilities. The patrolling problem is defined as the activity of traversing a given environment to monitoring any activity or sensing some environmental variables If this activity were performed by a fleet of robots, they would have to visit some places of interest of an environment at irregular intervals of time for security purposes. This problem is solved using multi-robot patrolling models. To date, literature works have been solved this problem applying various mathematical principles.The multi-robot patrolling models developed in those works represent great advances in this field. However, the models that obtain the best results are unfeasible for security applications due to their centralized and predictable nature. This thesis presents five distributed and unpredictable multi-robot patrolling models based on mathematical learning models derived from Game Theory. These multi-robot patrolling models aim at overcoming the disadvantages of previous work. To this end, the multi-robot patrolling problem was formulated using concepts of Graph Theory to represent the environment. Several normal-form games were defined at each vertex of a graph in this formulation. The multi-robot patrolling models developed in this research work have been validated and compared with best ranked multi-robot patrolling models in the literature. Both validation and comparison were preformed by using both a patrolling simulator and real robots. Experimental results show that the multirobot patrolling models developed in this research work improve previous ones in as many as 80% of 150 cases of study. Moreover, these multi-robot patrolling models rely on several features to highlight in security applications such as distribution, robustness, scalability, and dynamism. The achievements obtained in this research work validate the potential of Game Theory to develop patrolling models to protect infrastructures.

State space models for multi-setup operational modal analysis

Operational Modal Analysis consists on estimate the modal parameters of a structure (natural frequencies, damping ratios and modal vectors) from output-only vibration measurements. The modal vectors can be only estimated where a sensor is placed, so when the number of available sensors is lower than the number of tested points, it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors): some sensors stay at the same position from setup to setup, and the other sensors change the position until all the tested points are covered. The permanent sensors are then used to merge the mode shape estimated at each setup (or partial modal vectors) into global modal vectors. Traditionally, the partial modal vectors are estimated independently setup by setup, and the global modal vectors are obtained in a postprocess phase. In this work we present two state space models that can be used to process all the recorded setups at the same time, and we also present how these models can be estimated using the maximum likelihood method. The result is that the global mode shape of each mode is obtained automatically, and subsequently, a single value for the natural frequency and damping ratio of the mode is computed. Finally, both models are compared using real measured data.

Surface velocity fields, digital elevation models and ice front positions derived from multi-mission SAR remote sensing data at Sjögren Inlet glaciers, Antarctic Peninsula

Substantial retreat or disintegration of numerous ice shelves have been observed on the Antarctic Peninsula. The ice shelf in the Prince Gustav Channel retreated gradually since the late 1980's and broke-up in 1995. Tributary glaciers reacted with speed-up, surface lowering and increased ice discharge, consequently contributing to sea level rise. We present a detailed long-term study (1993-2014) on the dynamic response of Sjögren Inlet glaciers to the disintegration of Prince Gustav Ice Shelf. We analyzed various remote sensing datasets to observe the reactions of the glaciers to the loss of the buttressing ice shelf. A strong increase in ice surface velocities was observed with maximum flow speeds reaching 2.82±0.48 m/d in 2007 and 1.50±0.32 m/d in 2004 at Sjögren and Boydell glaciers respectively. Subsequently, the flow velocities decelerated, however in late 2014, we still measured about two times the values of our first measurements in 1996. The tributary glaciers retreated 61.7±3.1 km² behind the former grounding line of the ice shelf. In regions below 1000 m a.s.l., a mean surface lowering of -68±10 m (-3.1 m/a) was observed in the period 1993-2014. The lowering rate decreased to -2.2 m/a in recent years. Based on the surface lowering rates, geodetic mass balances of the glaciers were derived for different time steps. High mass loss rate of -1.21±0.36 Gt/a was found in the earliest period (1993-2001). Due to the dynamic adjustments of the glaciers to the new boundary conditions the ice mass loss reduced to -0.59±0.11 Gt/a in the period 2012-2014, resulting in an average mass loss rate of -0.89±0.16 Gt/a (1993-2014). Including the retreat of the ice front and grounding line, a total mass change of -38.5±7.7 Gt and a contribution to sea level rise of 0.061±0.013 mm were computed. Analysis of the ice flux revealed that available bedrock elevation estimates at Sjögren Inlet are too shallow and are the major uncertainty in ice flux computations. This temporally dense time series analysis of Sjögren Inlet glaciers shows that the adjustments of tributary glaciers to ice shelf disintegration are still going on and provides detailed information of the changes in glacier dynamics.

Advantage of single-trial models for response to selection in wheat breeding multi-environment trials

An investigation was conducted to evaluate the impact of experimental designs and spatial analyses (single-trial models) of the response to selection for grain yield in the northern grains region of Australia (Queensland and northern New South Wales). Two sets of multi-environment experiments were considered. One set, based on 33 trials conducted from 1994 to 1996, was used to represent the testing system of the wheat breeding program and is referred to as the multi-environment trial (MET). The second set, based on 47 trials conducted from 1986 to 1993, sampled a more diverse set of years and management regimes and was used to represent the target population of environments (TPE). There were 18 genotypes in common between the MET and TPE sets of trials. From indirect selection theory, the phenotypic correlation coefficient between the MET and TPE single-trial adjusted genotype means [r(p(MT))] was used to determine the effect of the single-trial model on the expected indirect response to selection for grain yield in the TPE based on selection in the MET. Five single-trial models were considered: randomised complete block (RCB), incomplete block (IB), spatial analysis (SS), spatial analysis with a measurement error (SSM) and a combination of spatial analysis and experimental design information to identify the preferred (PF) model. Bootstrap-resampling methodology was used to construct multiple MET data sets, ranging in size from 2 to 20 environments per MET sample. The size and environmental composition of the MET and the single-trial model influenced the r(p(MT)). On average, the PF model resulted in a higher r(p(MT)) than the IB, SS and SSM models, which were in turn superior to the RCB model for MET sizes based on fewer than ten environments. For METs based on ten or more environments, the r(p(MT)) was similar for all single-trial models.

Improved multi-beam neural network scatterometer forward models

Current methods for retrieving near surface winds from scatterometer observations over the ocean surface require a foward sensor model which maps the wind vector to the measured backscatter. This paper develops a hybrid neural network forward model, which retains the physical understanding embodied in ¸mod, but incorporates greater flexibility, allowing a better fit to the observations. By introducing a separate model for the mid-beam and using a common model for the fore- and aft-beams, we show a significant improvement in local wind vector retrieval. The hybrid model also fits the scatterometer observations more closely. The model is trained in a Bayesian framework, accounting for the noise on the wind vector inputs. We show that adding more high wind speed observations in the training set improves wind vector retrieval at high wind speeds without compromising performance at medium or low wind speeds.

Multi-level visualisation using Gaussian process latent variable models

Projection of a high-dimensional dataset onto a two-dimensional space is a useful tool to visualise structures and relationships in the dataset. However, a single two-dimensional visualisation may not display all the intrinsic structure. Therefore, hierarchical/multi-level visualisation methods have been used to extract more detailed understanding of the data. Here we propose a multi-level Gaussian process latent variable model (MLGPLVM). MLGPLVM works by segmenting data (with e.g. K-means, Gaussian mixture model or interactive clustering) in the visualisation space and then fitting a visualisation model to each subset. To measure the quality of multi-level visualisation (with respect to parent and child models), metrics such as trustworthiness, continuity, mean relative rank errors, visualisation distance distortion and the negative log-likelihood per point are used. We evaluate the MLGPLVM approach on the ‘Oil Flow’ dataset and a dataset of protein electrostatic potentials for the ‘Major Histocompatibility Complex (MHC) class I’ of humans. In both cases, visual observation and the quantitative quality measures have shown better visualisation at lower levels.

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

The Status of Multi-Dimensional Core-Collapse Supernova Models

Models of neutrino-driven core-collapse supernova explosions have matured considerably in recent years. Explosions of low-mass progenitors can routinely be simulated in 1D, 2D, and 3D. Nucleosynthesis calculations indicate that these supernovae could be contributors of some lighter neutron-rich elements beyond iron. The explosion mechanism of more massive stars remains under investigation, although first 3D models of neutrino-driven explosions employing multi-group neutrino transport have become available. Together with earlier 2D models and more simplified 3D simulations, these have elucidated the interplay between neutrino heating and hydrodynamic instabilities in the post-shock region that is essential for shock revival. However, some physical ingredients may still need to be added/improved before simulations can robustly explain supernova explosions over a wide range of progenitors. Solutions recently suggested in the literature include uncertainties in the neutrino rates, rotation, and seed perturbations from convective shell burning. We review the implications of 3D simulations of shell burning in supernova progenitors for the ‘perturbations-aided neutrino-driven mechanism,’ whose efficacy is illustrated by the first successful multi-group neutrino hydrodynamics simulation of an 18 solar mass progenitor with 3D initial conditions. We conclude with speculations about the impact of 3D effects on the structure of massive stars through convective boundary mixing.

An identification procedure of multi-input Wiener models for the distortion analysis of nonlinear circuits

In this contribution, a system identification procedure of a two-input Wiener model suitable for the analysis of the disturbance behavior of integrated nonlinear circuits is presented. The identified block model is comprised of two linear dynamic and one static nonlinear block, which are determined using an parameterized approach. In order to characterize the linear blocks, an correlation analysis using a white noise input in combination with a model reduction scheme is adopted. After having characterized the linear blocks, from the output spectrum under single tone excitation at each input a linear set of equations will be set up, whose solution gives the coefficients of the nonlinear block. By this data based black box approach, the distortion behavior of a nonlinear circuit under the influence of an interfering signal at an arbitrary input port can be determined. Such an interfering signal can be, for example, an electromagnetic interference signal which conductively couples into the port of consideration. © 2011 Author(s).

Doubly charged Higgs through photon-photon collisions in 3-3-1 models

We study the production and signatures of doubly charged Higgs bosons (DCHBs) in the process gamma gamma <-> H(--)H(++) at the e(-)e(+) International Linear Collider and CERN Linear Collider, where the intermediate photons are given by the Weizsacker-Willians and laser backscattering distributions.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework.

MULTI-UNIT ACCIDENT CONTRIBUTIONS TO U.S. NUCLEAR REGULATORY COMMISSION QUANTITATIVE HEALTH OBJECTIVES: A SAFETY GOAL POLICY ANALYSIS USING MODELS FROM STATE-OF-THE-ART REACTOR CONSEQUENCE ANALYSES

The U.S. Nuclear Regulatory Commission implemented a safety goal policy in response to the 1979 Three Mile Island accident. This policy addresses the question “How safe is safe enough?” by specifying quantitative health objectives (QHOs) for comparison with results from nuclear power plant (NPP) probabilistic risk analyses (PRAs) to determine whether proposed regulatory actions are justified based on potential safety benefit. Lessons learned from recent operating experience—including the 2011 Fukushima accident—indicate that accidents involving multiple units at a shared site can occur with non-negligible frequency. Yet risk contributions from such scenarios are excluded by policy from safety goal evaluations—even for the nearly 60% of U.S. NPP sites that include multiple units. This research develops and applies methods for estimating risk metrics for comparison with safety goal QHOs using models from state-of-the-art consequence analyses to evaluate the effect of including multi-unit accident risk contributions in safety goal evaluations.

Dynamics of multi-articular coordination in neurobiological systems

Although previous work in nonlinear dynamics on neurobiological coordination and control has provided valuable insights from studies of single joint movements in humans, researchers have shown increasing interest in coordination of multi-articular actions. Multi-articular movement models have provided valuable insights on neurobiological systems conceptualised as degenerate, adaptive complex systems satisfying the constraints of dynamic environments. In this paper, we overview empirical evidence illustrating the dynamics of adaptive movement behavior in a range of multi-articular actions including kicking, throwing, hitting and balancing. We model the emergence of creativity and the diversity of neurobiological action in the meta-stable region of self organising criticality. We examine the influence on multi-articular actions of decaying and emerging constraints in the context of skill acquisition. We demonstrate how, in this context, transitions between preferred movement patterns exemplify the search for and adaptation of attractor states within the perceptual motor workspace as a function of practice. We conclude by showing how empirical analyses of neurobiological coordination and control have been used to establish a nonlinear pedagogical framework for enhancing acquisition of multi-articular actions.