Inference in particle tracking experiments by passing messages between images

Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the trajectories of the particles. However, they become problematic as the motility and/or the density of the particles increases due to uncertainties on the trajectories that particles followed during the images' acquisition time. Here, we report an efficient method for learning parameters of the dynamics of the particles from their positions in time-consecutive images. Our algorithm belongs to the class of message-passing algorithms, known in computer science, information theory and statistical physics as Belief Propagation (BP). The algorithm is distributed, thus allowing parallel implementation suitable for computations on multiple machines without significant inter-machine overhead. We test our method on the model example of particle tracking in turbulent flows, which is particularly challenging due to the strong transport that those flows produce. Our numerical experiments show that the BP algorithm compares in quality with exact Markov Chain Monte-Carlo algorithms, yet BP is far superior in speed. We also suggest and analyze a random-distance model that provides theoretical justification for BP accuracy. Methods developed here systematically formulate the problem of particle tracking and provide fast and reliable tools for its extensive range of applications.Comment: 18 pages, 9 figure

Conservation Laws and the Philosophy of Mind: Opening the Black Box, Finding a Mirror

Since Leibniz's time, Cartesian mental causation has been criticized for violating the conservation of energy and momentum. (Non-epiphenomenalist property dualism is analogous.) Many dualist responses clearly fail. But conservation laws have important neglected features generally undermining the objection. Conservation is _local_, holding first not for the universe, but for everywhere separately. The energy (or momentum, etc.) in any volume changes only due to what flows through the boundaries (no teleportation). Constant total energy holds if the global summing-up of local conservation laws converges; it probably doesn't in reality. Energy (momentum) conservation holds if there is symmetry, the sameness of the laws over time (space). Thus, if there are time-places where symmetries fail due to nonphysical influence, conservation laws fail there and then, while holding elsewhere, such as refrigerators and stars. Noether's converse first theorem shows that conservation laws imply symmetries. Thus conservation trivially nearly entails the causal closure of the physical. But expecting conservation to hold in the brain (without looking) simply assumes the falsehood of Cartesianism. Hence Leibniz's objection begs the question. Empirical neuroscience is another matter. So is Einstein's General Relativity: far from providing a loophole, General Relativity makes mental causation _harder_

Conservation Laws and the Philosophy of Mind: Opening the Black Box, Finding a Mirror

Abstract: Since Leibniz’s time, Cartesian mental causation has been criticized for violating the conservation of energy and momentum. (Non-epiphenomenalist property dualism is analogous.) Many dualist responses clearly fail. But conservation laws have important neglected features generally undermining the objection. Conservation is local, holding first not for the universe, but for everywhere separately. The energy (or momentum, etc.) in any volume changes only due to what flows through the boundaries (no teleportation). Constant total energy holds if the global summing-up of local conservation laws converges; it probably doesn’t in reality. Energy (momentum) conservation holds if there is symmetry, the sameness of the laws over time (space). Thus, if there are time-places where symmetries fail due to nonphysical influence, conservation laws fail there and then, while holding elsewhere, such as refrigerators and stars. Noether’s converse first theorem shows that conservation laws imply symmetries. Thus conservation trivially nearly entails the causal closure of the physical. But expecting conservation to hold in the brain (without looking) simply assumes the falsehood of Cartesianism. Hence Leibniz’s objection begs the question. Empirical neuroscience is another matter. So is Einstein’s General Relativity: far from providing a loophole, General Relativity makes mental causation harder

On variational approximations for frequentist and bayesian inference

Variational approximations are approximate inference techniques for complex statisticalmodels providing fast, deterministic alternatives to conventional methods that,however accurate, take much longer to run. We extend recent work concerning variationalapproximations developing and assessing some variational tools for likelihoodbased and Bayesian inference. In particular, the first part of this thesis employs a Gaussian variational approximation strategy to handle frequentist generalized linear mixedmodels with general design random effects matrices such as those including spline basisfunctions. This method involves approximation to the distributions of random effectsvectors, conditional on the responses, via a Gaussian density. The second thread isconcerned with a particular class of variational approximations, known as mean fieldvariational Bayes, which is based upon a nonparametric product density restriction on the approximating density. Algorithms for inference and fitting for models with elaborateresponses and structures are developed adopting the variational message passingperspective. The modularity of variational message passing is such that extensions tomodels with more involved likelihood structures and scalability to big datasets are relatively simple. We also derive algorithms for models containing higher level randomeffects and non-normal responses, which are streamlined in support of computationalefficiency. Numerical studies and illustrations are provided, including comparisons witha Markov chain Monte Carlo benchmark

Road network maintenance and repair considering day-to-day traffic dynamics and transient congestion

Road maintenance and repair (M&R) are essential for keeping the performance of traffic infrastructure at a satisfactory level, and extending their lifetime to the fullest extent possible. For road networks, effective M&R plans should not be constructed in a myopic or ad-hoc fashion regardless of the subsequent benefits and costs associated with those projects considered. A hallmark of road M&R studies is the use of user equilibrium (UE) models to predict network traffic for a given set of road conditions with or without M&R. However, UE approaches ignore the traffic disequilibrium states and transient congestion as a result of M&R derived disruptions to network traffic on a day-to-day (DTD) time scale, which could produce additional substantial travel costs. As shown in the numerical studies on a M&R plan of the Sioux Falls network, the additional maintenance derived travel cost is about 4 billion, which is far exceed the actual M&R construction cost of 0.2 billion. Therefore, it is necessary to recognise the substantial social costs induced by maintenance-derived disruptions in the form of transient congestion when planning M&R. This realistic and pressing issue is not properly addressed by the road M&R planning problems with traffic equilibrium constraints. This thesis proposes a dual-time-scale road network M&R model aiming to simultaneously capture the long-term effects of M&R activities under traffic equilibria, and the maintenance-derived transient congestion using day-to-day (DTD) traffic evolutionary dynamics. The notion of ‘day’ is arbitrarily defined (e.g. weeks or months). The proposed M&R model consists of three sub-models: (1) a within-day dynamic network loading (DNL) model; (2) a day-to-day dynamic traffic assignment (DTD DTA) model; and (3) a day-to-day road quality model. The within-day traffic dynamics is captured by the Lighthill-Whitham-Richards (LWR) fluid dynamic network loading model. The day-to-day phase of the traffic dynamics specify travellers’ route and departure time choices in a stochastic manner based on a sequential mixed multinomial or nested Logit model. Travel information sharing behaviour is further integrated into this macroscopic doubly dynamic (both within-day and day-to-day dynamic) traffic assignment (DDTA) model to account for the impact of incomplete information on travel experiences. A deterministic day-to-day road quality model based on an exponential form of traffic flow is employed to govern the road deterioration process, where a quarter-car index (QI) is applied. All these dynamics are incorporated in a holistic dual-time-scale M&R model, which captures realistic phenomena associated with short-term and long-term effects of M&R, including physical queuing and spillback, road capacity reduction, temporal-spatial shift of congestion due to on-going M&R activities, and the tendency to converge to an equilibrium after M&R actions. Following the dual-time-scale road network M&R model, a bi-level road M&R optimisation model is proposed, where the aforementioned three sub-models are incorporated into the lower-level problem, while the upper-level is to minimise M&R expenditure and network travel costs while maintaining a satisfactory level of road quality. The M&R planning horizon is long yet finite (e.g. years or decades). A ‘quality-usage’ feedback mechanism is investigated in the proposed bi-level M&R model, namely, (1) the DTD road quality evolution as a result of DTD traffic loads and the M&R effectiveness; and (2) the evolution of DTD traffic in response to both DTD road deterioration and the improved road quality after M&R activities. The effectiveness of developed M&R optimisation model is demonstrated through case studies on the Sioux Falls network. A metaheuristic Genetic Algorithm (GA) approach is employed to solve the M&R problems given its highly nonlinear, nonconvex and non-differentiable nature. Explicit travellers’ choice behaviour dynamics and complex traffic phenomena such as network paradoxes arising from M&R activities are illustrated. Through a comparison with the results under the dynamic user equilibrium (DUE) method, the proposed DTD method achieves significant reduction in network travel cost of $ 25 million, approximately 20% of the total cost. This points to the benefit of using the DTD dynamics for capturing network’s responses to M&R in a more realistic way. The M&R model proposed in this thesis could provide valuable managerial insights for road M&R planning agencies.Open Acces

Supply Chain

Traditionally supply chain management has meant factories, assembly lines, warehouses, transportation vehicles, and time sheets. Modern supply chain management is a highly complex, multidimensional problem set with virtually endless number of variables for optimization. An Internet enabled supply chain may have just-in-time delivery, precise inventory visibility, and up-to-the-minute distribution-tracking capabilities. Technology advances have enabled supply chains to become strategic weapons that can help avoid disasters, lower costs, and make money. From internal enterprise processes to external business transactions with suppliers, transporters, channels and end-users marks the wide range of challenges researchers have to handle. The aim of this book is at revealing and illustrating this diversity in terms of scientific and theoretical fundamentals, prevailing concepts as well as current practical applications