The stochastic exit problem for dynamical systems

The problem of "exit against a flow" for dynamical systems subject to small Gaussian white noise excitation is studied. Here the word "flow" refers to the behavior in phase space of the unperturbed system's state variables. "Exit against a flow" occurs if a perturbation causes the phase point to leave a phase space region within which it would normally be confined. In particular, there are two components of the problem of exit against a flow:

i) the mean exit time

ii) the phase-space distribution of exit locations.

When the noise perturbing the dynamical systems is small, the solution of each component of the problem of exit against a flow is, in general, the solution of a singularly perturbed, degenerate elliptic-parabolic boundary value problem.

Singular perturbation techniques are used to express the asymptotic solution in terms of an unknown parameter. The unknown parameter is determined using the solution of the adjoint boundary value problem.

The problem of exit against a flow for several dynamical systems of physical interest is considered, and the mean exit times and distributions of exit positions are calculated. The systems are then simulated numerically, using Monte Carlo techniques, in order to determine the validity of the asymptotic solutions.

Robot navigation in dense crowds : statistical models and experimental studies of human robot cooperation

This thesis explores the problem of mobile robot navigation in dense human crowds. We begin by considering a fundamental impediment to classical motion planning algorithms called the freezing robot problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing predictive uncertainty by employing higher fidelity individual dynamics models or heuristically limiting the individual predictive covariance to prevent overcautious navigation. We demonstrate that both the individual prediction and the individual predictive uncertainty have little to do with this undesirable navigation behavior. Additionally, we provide evidence that dynamic agents are able to navigate in dense crowds by engaging in joint collision avoidance, cooperatively making room to create feasible trajectories. We accordingly develop interacting Gaussian processes, a prediction density that captures cooperative collision avoidance, and a "multiple goal" extension that models the goal driven nature of human decision making. Navigation naturally emerges as a statistic of this distribution.

Most importantly, we empirically validate our models in the Chandler dining hall at Caltech during peak hours, and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (collecting data on 488 runs). The multiple goal interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities nearing 1 person/m², while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as the multiple goal extension, and twice as often as the basic interacting Gaussian process approach. Furthermore, a reactive planner based on the widely used dynamic window approach proves insufficient for crowd densities above 0.55 people/m². We also show that our noncooperative planner or our reactive planner capture the salient characteristics of nearly any dynamic navigation algorithm. For inclusive validation purposes, we show that either our non-interacting planner or our reactive planner captures the salient characteristics of nearly any existing dynamic navigation algorithm. Based on these experimental results and theoretical observations, we conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.

Finally, we produce a large database of ground truth pedestrian crowd data. We make this ground truth database publicly available for further scientific study of crowd prediction models, learning from demonstration algorithms, and human robot interaction models in general.

Using climate extension to assist coastal decision-makers with climate adaptation

Coastal managers need accessible, trusted, tailored resources to help them interpret climate information, identify vulnerabilities, and apply climate information to decisions about adaptation on regional and local levels. For decades, climate scientists have studied the impacts that short term natural climate variability and long term climate change will have on coastal systems. For example, recent estimates based on Intergovernmental Panel on Climate Change (IPCC) warming scenarios suggest that global sea levels may rise 0.5 to 1.4 meters above 1990 levels by 2100 (Rahmstorf 2007; Grinsted, Moore, and Jevrejeva 2009). Many low-lying coastal ecosystems and communities will experience more frequent salt water intrusion events, more frequent coastal flooding, and accelerated erosion rates before they experience significant inundation. These changes will affect the ways coastal managers make decisions, such as timing surface and groundwater withdrawals, replacing infrastructure, and planning for changing land use on local and regional levels. Despite the advantages, managers’ use of scientific information about climate variability and change remains limited in environmental decision-making (Dow and Carbone 2007). Traditional methods scientists use to disseminate climate information, like peer-reviewed journal articles and presentations at conferences, are inappropriate to fill decision-makers’ needs for applying accessible, relevant climate information to decision-making. General guides that help managers scope out vulnerabilities and risks are becoming more common; for example, Snover et al. (2007) outlines a basic process for local and state governments to assess climate change vulnerability and preparedness. However, there are few tools available to support more specific decision-making needs. A recent survey of coastal managers in California suggests that boundary institutions can help to fill the gaps between climate science and coastal decision-making community (Tribbia and Moser 2008). The National Sea Grant College Program, the National Oceanic and Atmospheric Administration's (NOAA) university-based program for supporting research and outreach on coastal resource use and conservation, is one such institution working to bridge these gaps through outreach. Over 80% of Sea Grant’s 32 programs are addressing climate issues, and over 60% of programs increased their climate outreach programming between 2006 and 2008 (National Sea Grant Office 2008). One way that Sea Grant is working to assist coastal decision-makers with using climate information is by developing effective methods for coastal climate extension. The purpose of this paper is to discuss climate extension methodologies on regional scales, using the Carolinas Coastal Climate Outreach Initiative (CCCOI) as an example of Sea Grant’s growing capacities for climate outreach and extension. (PDF contains 3 pages)

Occupational practices and problems of rural artisanal fisherfolks in Oyan Dam area of Ogun State

Artisanal Fish Societies constitutes one of the poorest societies in the developing world. Attempts to harness the potentials of the societies have often failed due to the enormity of the problem of poverty. This study was conducted in four major fishing villages namely; Abule titun, Apojola, Imama Odo and Ibaro in order to investigate the occupational practices and the problems of rural artisanal fisherfolks in Oyam's Dam, area of Ogun State. Eighty respondents were randomly selected among the artisanal fisher folks for interview using interview guide. The findings revealed that 43.8% of the fisherfolks are within active range of 31-40 years while 30% are within 21-30 years range. Also 31% had no formal education indicating a relatively high level of illiteracy among the fisherfolks while majority of the respondents practice fishing activities using paddle and canoe. It was similarly discovered from the study that the most pressing problems of the fisherfolks is the lack of basic social amenities like electricity, potable water, access roads, hospitals and markets. It is therefore recommended that basic social infrastructures be provided for the artisanal fishing communities in order to improve their social welfare, standard of living and the capacity to have a sustainable fishing occupation in the interest of food security and poverty alleviation

Poverty alleviation among fishermen within the floodplains of Kaduna River: implication for introducing commercial fish farming at village level in Doko local government area of Niger State, Nigeria

A diagnostic survey was conducted among the fishermen in six selected villages in Doko Local Government Area of Niger State. One hundred and fifty fishermen were randomly selected and interviewed to find out whether or not they had interest in commercial fish farming aimed at improving their livelihood. The dwindling fish catches in the natural flood plain ponds and Ex-bow Lakes continue to have a serious negative effect on the socio-economic well being of the village communities in question. A break on natural regular annual flooding of the plains had resulted into very low natural fish recruitment. Data analysis using simple descriptive statistics revealed that land tenure system, educational status, inadequate infrastructural facilities, religious taboos, existing fish species among others were found to be favourable indices for commercial fish farming. However, serious conflicts among the fishermen concerning the ownership status of these natural fish ponds are found to be major obstacles to commercial fish farming despite that the traditional ownership of the ponds were vested in the lands of individuals and village communities. Extensive fish farming and small-scale fish farming in the ponds and Ex-bow Lake with improved management practices are considered to be profitable venture. Despite the fact that fish seeds supply and extension effort are still inadequate, the fish farmers have indicated willingness to adopt commercial fish farming in the Ex-bow Lakes and flood plains in order to restore abundant fish production thereby providing for their food security and also increasing the daily income

Impact assessment of Niger State fisheries legislation on fisheries conservation in Edozhigi local government area (L.G.A.) of Niger State

A preliminary survey was conducted among the fishermen in five selected villages in Edozhigi L.G.A. of Niger State. One hundred and fifty fishermen were randomly selected and interviewed to find out the impact of Niger State fisheries legislation on fisheries conservation resources in the area. The analysis of data collected using descriptive statistics indicated that undersized mesh of gill nets, beach seines and traps are being used unabated. Also, fenced barriers across the entrance of flood plain ponds and Ex-bow lakes from the main stream are in the area. The fisheries rules and regulations implementers are rarely seen or not seen at all in the area. The decreasing nature of fish catches was detected. It is observed that government policy on fish conversation is neglected due to inadequate or lack of funding for meaningful extension and implementation of the fisheries rules and regulations

Occupational practice and problems of artisanal fisherfolk in Oyan dam area of Ogun State

Artisanal Fish Societies constitutes one of the poorest societies in the developing world. Attempts to harness the potentials of such societies have often failed due to the enormity of the problem of poverty. This study was conducted in four major fishing villages namely: Abule Titun, Apojola, Imala Odo and Ibaro in order to investigate the occupational practices and the problems of rural artisanal fisherfolks in Oyam's Dam, area of Ogun State. Eighty respondents were randomly selected among the artisanal fisher folks for interview using interview guide. The findings revealed that 43.8% of the fisherfolks are within active age range of 31-40 years while 30% are within 21-30 years range. Also 31% had no formal education indicating a relatively high level of illiteracy among the fisherfolks while majority of the respondents practice fishing activities using paddle and canoe. It was similarly discovered from the study that the most pressing problems of the fishfolks is the lack of basic social amenities like electricity, potable water, access roads, hospital and markets. It is therefore recommended that basic social infrastructures be provided for the artisanal fishing communities in order to improve their social welfare, standard of living and the capacity to have a sustainable fishing occupation in the interest of food security and poverty alleviation

Strategies for the Stereoselective Synthesis of Carbon Quaternary Centers via Transition Metal-Catalyzed Alkylation of Enolate Compounds

Notwithstanding advances in modern chemical methods, the selective installation of sterically encumbered carbon stereocenters, in particular all-carbon quaternary centers, remains an unsolved problem in organic chemistry. The prevalence of all-carbon quaternary centers in biologically active natural products and pharmaceutical compounds provides a strong impetus to address current limitations in the state of the art of their generation. This thesis presents four related projects, all of which share in the goal of constructing highly-congested carbon centers in a stereoselective manner, and in the use of transition-metal catalyzed alkylation as a means to address that goal.

The first research described is an extension of allylic alkylation methodology previously developed in the Stoltz group to small, strained rings. This research constitutes the first transition metal-catalyzed enantioselective α-alkylation of cyclobutanones. Under Pd-catalysis, this chemistry affords all–carbon α-quaternary cyclobutanones in good to excellent yields and enantioselectivities.

Next is described our development of a (trimethylsilyl)ethyl β-ketoester class of enolate precursors, and their application in palladium–catalyzed asymmetric allylic alkylation to yield a variety of α-quaternary ketones and lactams. Independent coupling partner synthesis engenders enhanced allyl substrate scope relative to allyl β-ketoester substrates; highly functionalized α-quaternary ketones generated by the union of our fluoride-triggered β-ketoesters and sensitive allylic alkylation coupling partners serve to demonstrate the utility of this method for complex fragment coupling.

Lastly, our development of an Ir-catalyzed asymmetric allylic alkylation of cyclic β-ketoesters to afford highly congested, vicinal stereocenters comprised of tertiary and all-carbon quaternary centers with outstanding regio-, diastereo-, and enantiocontrol is detailed. Implementation of a subsequent Pd-catalyzed alkylation affords dialkylated products with pinpoint stereochemical control of both chiral centers. The chemistry is then extended to include acyclic β-ketoesters and similar levels of selective and functional group tolerance are observed. Critical to the successful development of this method was the employment of iridium catalysis in concert with N-aryl-phosphoramidite ligands.

Some experiments on solving multistage stochastic mixed 0-1 programs with time stochastic dominance constraints

In this work we extend to the multistage case two recent risk averse measures for two-stage stochastic programs based on first- and second-order stochastic dominance constraints induced by mixed-integer linear recourse. Additionally, we consider Time Stochastic Dominance (TSD) along a given horizon. Given the dimensions of medium-sized problems augmented by the new variables and constraints required by those risk measures, it is unrealistic to solve the problem up to optimality by plain use of MIP solvers in a reasonable computing time, at least. Instead of it, decomposition algorithms of some type should be used. We present an extension of our Branch-and-Fix Coordination algorithm, so named BFC-TSD, where a special treatment is given to cross scenario group constraints that link variables from different scenario groups. A broad computational experience is presented by comparing the risk neutral approach and the tested risk averse strategies. The performance of the new version of the BFC algorithm versus the plain use of a state-of-the-artMIP solver is also reported.

Role of fisheries extension officers in FFDA at Balasore

The first FFDA in Orissa state was established in the year 1976. The study was conducted in Balasore district of the State. The findings revealed that all of the FEOs were not well qualified but trained and experienced. The duration of training obtained varied from 3 to 10 months. An FEO has a large area under his jurisdiction. Cycle was used by most of the FEOs to visit the fish farmers which resulted in infrequent visits. The FEOs were not satisfied with the working conditions, promotion avenues and conveyance facilities. There was interference of political bodies in leasing out ponds. The amount of loan sanctioned was not adequate to start fish farming. They also revealed that marketing aspects were totally neglected by the FFDA.

Past trends, present stocks and possible future state of the fisheries of the Tanzania part of the Lake Victoria

The Tanzania part of Lake Victoria is the most important single fishery resource for the country. Past fishing practice caused disparity between the relative abundance in the catches and in the available stocks by overfishing some species while under-fishing others. Preliminary studies of distribution pattern, biomass estimates, etc, as derived from bollom trawl exploratory data, and the trend of the commercial catch statistics from 1958 to 1970, suggest that many of the commercially preferred species may not have the biotic potential 10 sustain higher yields under present ecological and fishing regimes. Haplochromis and a few other fish might be the only hope. Geographic extension of fishing to deeper waters may not be very promising as species diversificarion and fish density decline with depth. To develop and manage the fisheries, make full use of the resource and ensure economic and biological perpetuation of thc fishery, the appropriate fishing strategy cannot be properly developcd overnight.

Global state synchronization in networks of cyclic feedback systems

This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory. The method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling. The method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system. The result is illustrated for a network of biochemical oscillators. © 2011 IEEE.

State-space inference and learning with Gaussian processes

State-space inference and learning with Gaussian processes (GPs) is an unsolved problem. We propose a new, general methodology for inference and learning in nonlinear state-space models that are described probabilistically by non-parametric GP models. We apply the expectation maximization algorithm to iterate between inference in the latent state-space and learning the parameters of the underlying GP dynamics model. Copyright 2010 by the authors.

State estimation over a communication network: Measurement or estimate communication?

In this paper we consider the problem of state estimation over a communication network. Using estimation quality as a metric, two communication schemes are studied and compared. In scheme one, each sensor node communicates its measurement data to the remote estimator, while in scheme two, each sensor node communicates its local state estimate to the remote estimator. We show that with perfect communication link, if the sensor has unlimited computation capability, the two schemes produce the same estimate at the estimator, and if the sensor has limited computation capability, scheme one is always better than scheme two. On the other hand, when data packet drops occur over the communication link, we show that if the sensor has unlimited computation capability, scheme two always outperforms scheme one, and if the sensor has limited computation capability, we show that in general there exists a critical packet arrival rate, above which scheme one outperforms scheme two. Simulations are provided to demonstrate the two schemes under various circumstances. © South China University of Technology and Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2010.

Development of realistic liquid equations of state for multi-phase CFD modelling

Several equations of state (EOS) have been incorporated into a novel algorithm to solve a system of multi-phase equations in which all phases are assumed to be compressible to varying degrees. The EOSs are used to both supply functional relationships to couple the conservative variables to the primitive variables and to calculate accurately thermodynamic quantities of interest, such as the speed of sound. Each EOS has a defined balance of accuracy, robustness and computational speed; selection of an appropriate EOS is generally problem-dependent. This work employs an AUSM+-up method for accurate discretisation of the convective flux terms with modified low-Mach number dissipation for added robustness of the solver. In this paper we show a newly-developed time-marching formulation for temporal discretisation of the governing equations with incorporated time-dependent source terms, as well as considering the system of eigenvalues that render the governing equations hyperbolic.