Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Modeling security and cooperation in wireless networks using game theory

This research involves the design, development, and theoretical demonstration of models resulting in integrated misbehavior resolution protocols for ad hoc networked devices. Game theory was used to analyze strategic interaction among independent devices with conflicting interests. Packet forwarding at the routing layer of autonomous ad hoc networks was investigated. Unlike existing reputation based or payment schemes, this model is based on repeated interactions. To enforce cooperation, a community enforcement mechanism was used, whereby selfish nodes that drop packets were punished not only by the victim, but also by all nodes in the network. Then, a stochastic packet forwarding game strategy was introduced. Our solution relaxed the uniform traffic demand that was pervasive in other works. To address the concerns of imperfect private monitoring in resource aware ad hoc networks, a belief-free equilibrium scheme was developed that reduces the impact of noise in cooperation. This scheme also eliminated the need to infer the private history of other nodes. Moreover, it simplified the computation of an optimal strategy. The belief-free approach reduced the node overhead and was easily tractable. Hence it made the system operation feasible. Motivated by the versatile nature of evolutionary game theory, the assumption of a rational node is relaxed, leading to the development of a framework for mitigating routing selfishness and misbehavior in Multi hop networks. This is accomplished by setting nodes to play a fixed strategy rather than independently choosing a rational strategy. A range of simulations was carried out that showed improved cooperation between selfish nodes when compared to older results. Cooperation among ad hoc nodes can also protect a network from malicious attacks. In the absence of a central trusted entity, many security mechanisms and privacy protections require cooperation among ad hoc nodes to protect a network from malicious attacks. Therefore, using game theory and evolutionary game theory, a mathematical framework has been developed that explores trust mechanisms to achieve security in the network. This framework is one of the first steps towards the synthesis of an integrated solution that demonstrates that security solely depends on the initial trust level that nodes have for each other.^

Modeling, simulation, and characterization of space debris in low-Earth orbit

Every space launch increases the overall amount of space debris. Satellites have limited awareness of nearby objects that might pose a collision hazard. Astrometric, radiometric, and thermal models for the study of space debris in low-Earth orbit have been developed. This modeled approach proposes analysis methods that provide increased Local Area Awareness for satellites in low-Earth and geostationary orbit. Local Area Awareness is defined as the ability to detect, characterize, and extract useful information regarding resident space objects as they move through the space environment surrounding a spacecraft. The study of space debris is of critical importance to all space-faring nations. Characterization efforts are proposed using long-wave infrared sensors for space-based observations of debris objects in low-Earth orbit. Long-wave infrared sensors are commercially available and do not require solar illumination to be observed, as their received signal is temperature dependent. The characterization of debris objects through means of passive imaging techniques allows for further studies into the origination, specifications, and future trajectory of debris objects. Conclusions are made regarding the aforementioned thermal analysis as a function of debris orbit, geometry, orientation with respect to time, and material properties. Development of a thermal model permits the characterization of debris objects based upon their received long-wave infrared signals. Information regarding the material type, size, and tumble-rate of the observed debris objects are extracted. This investigation proposes the utilization of long-wave infrared radiometric models of typical debris to develop techniques for the detection and characterization of debris objects via signal analysis of unresolved imagery. Knowledge regarding the orbital type and semi-major axis of the observed debris object are extracted via astrometric analysis. This knowledge may aid in the constraint of the admissible region for the initial orbit determination process. The resultant orbital information is then fused with the radiometric characterization analysis enabling further characterization efforts of the observed debris object. This fused analysis, yielding orbital, material, and thermal properties, significantly increases a satellite's Local Area Awareness via an intimate understanding of the debris environment surrounding the spacecraft.

Tracer-based assessment of flow paths, storage and runoff generation in northern catchments : a review

Peer reviewed

Visualisation of spatial patterns of connectivity and runoff ages derived from a traceraided model

We thank the European Research Council ERC (project GA 335910 VEWA) for funding the VeWa project.

Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis

The advances in three related areas of state-space modeling, sequential Bayesian learning, and decision analysis are addressed, with the statistical challenges of scalability and associated dynamic sparsity. The key theme that ties the three areas is Bayesian model emulation: solving challenging analysis/computational problems using creative model emulators. This idea defines theoretical and applied advances in non-linear, non-Gaussian state-space modeling, dynamic sparsity, decision analysis and statistical computation, across linked contexts of multivariate time series and dynamic networks studies. Examples and applications in financial time series and portfolio analysis, macroeconomics and internet studies from computational advertising demonstrate the utility of the core methodological innovations.

Chapter 1 summarizes the three areas/problems and the key idea of emulating in those areas. Chapter 2 discusses the sequential analysis of latent threshold models with use of emulating models that allows for analytical filtering to enhance the efficiency of posterior sampling. Chapter 3 examines the emulator model in decision analysis, or the synthetic model, that is equivalent to the loss function in the original minimization problem, and shows its performance in the context of sequential portfolio optimization. Chapter 4 describes the method for modeling the steaming data of counts observed on a large network that relies on emulating the whole, dependent network model by independent, conjugate sub-models customized to each set of flow. Chapter 5 reviews those advances and makes the concluding remarks.

Modeling, Analysis and Performance Comparison of Two Direct Sampling DCSK Receivers under Frequency Nonselective Fading Channels

Two direct sampling correlator-type receivers for differential chaos shift keying (DCSK) communication systems under frequency non-selective fading channels are proposed. These receivers operate based on the same hardware platform with different architectures. In the first scheme, namely sum-delay-sum (SDS) receiver, the sum of all samples in a chip period is correlated with its delayed version. The correlation value obtained in each bit period is then compared with a fixed threshold to decide the binary value of recovered bit at the output. On the other hand, the second scheme, namely delay-sum-sum (DSS) receiver, calculates the correlation value of all samples with its delayed version in a chip period. The sum of correlation values in each bit period is then compared with the threshold to recover the data. The conventional DCSK transmitter, frequency non-selective Rayleigh fading channel, and two proposed receivers are mathematically modelled in discrete-time domain. The authors evaluated the bit error rate performance of the receivers by means of both theoretical analysis and numerical simulation. The performance comparison shows that the two proposed receivers can perform well under the studied channel, where the performances get better when the number of paths increases and the DSS receiver outperforms the SDS one.

Passivity Framework for Modeling, Composing and Mitigating Cyber Attacks

Thesis (Ph.D.)--University of Washington, 2016-08

On T-Semisimplicity of Iwasawa Modules and Some Computations with Z3-Extensions

Thesis (Ph.D.)--University of Washington, 2016-08

Object-Oriented Modeling Simulation and Control of Activated Sludge Process

Object-oriented modeling is spreading in current simulation of wastewater treatments plants through the use of the individual components of the process and its relations to define the underlying dynamic equations. In this paper, we describe the use of the free-software OpenModelica simulation environment for the object-oriented modeling of an activated sludge process under feedback control. The performance of the controlled system was analyzed both under normal conditions and in the presence of disturbances. The object-oriented described approach represents a valuable tool in teaching provides a practical insight in wastewater process control field.

Modeling, Simulation, and Characterization of Space Debris in low-Earth Orbit

Every space launch increases the overall amount of space debris. Satellites have limited awareness of nearby objects that might pose a collision hazard. Astrometric, radiometric, and thermal models for the study of space debris in low-Earth orbit have been developed. This modeled approach proposes analysis methods that provide increased Local Area Awareness for satellites in low-Earth and geostationary orbit. Local Area Awareness is defined as the ability to detect, characterize, and extract useful information regarding resident space objects as they move through the space environment surrounding a spacecraft. The study of space debris is of critical importance to all space-faring nations. Characterization efforts are proposed using long-wave infrared sensors for space-based observations of debris objects in low-Earth orbit. Long-wave infrared sensors are commercially available and do not require solar illumination to be observed, as their received signal is temperature dependent. The characterization of debris objects through means of passive imaging techniques allows for further studies into the origination, specifications, and future trajectory of debris objects. Conclusions are made regarding the aforementioned thermal analysis as a function of debris orbit, geometry, orientation with respect to time, and material properties. Development of a thermal model permits the characterization of debris objects based upon their received long-wave infrared signals. Information regarding the material type, size, and tumble-rate of the observed debris objects are extracted. This investigation proposes the utilization of long-wave infrared radiometric models of typical debris to develop techniques for the detection and characterization of debris objects via signal analysis of unresolved imagery. Knowledge regarding the orbital type and semi-major axis of the observed debris object are extracted via astrometric analysis. This knowledge may aid in the constraint of the admissible region for the initial orbit determination process. The resultant orbital information is then fused with the radiometric characterization analysis enabling further characterization efforts of the observed debris object. This fused analysis, yielding orbital, material, and thermal properties, significantly increases a satellite’s Local Area Awareness via an intimate understanding of the debris environment surrounding the spacecraft.

Modeling, control and field tests on an experimental irrigation canal

Irrigation canals are complex hydraulic systems difficult to control. Many models and control strategies have already been developed using linear control theory. In the present study, a PI controller is developed and implemented in a brand new prototype canal and its features evaluated experimentally. The base model relies on the linearized Saint-Venant equations which is compared with a reservoir model to check its accuracy. This technique will prove its capability and versatility in tuning properly a controller for this kind of systems.

Stochastic Assessment Of Environmental Flows In Semiarid Environments

The regimen of environmental flows (EF) must be included as terms of environmental demand in the management of water resources. Even though there are numerous methods for the computation of EF, the criteria applied at different steps in the calculation process are quite subjective whereas the results are fixed values that must be meet by water planners. This study presents a friendly-user tool for the assessment of the probability of compliance of a certain EF scenario with the natural regimen in a semiarid area in southern Spain. 250 replications of a 25-yr period of different hydrological variables (rainfall, minimum and maximum flows, ...) were obtained at the study site from the combination of Monte Carlo technique and local hydrological relationships. Several assumptions are made such as the independence of annual rainfall from year to year and the variability of occurrence of the meteorological agents, mainly precipitation as the main source of uncertainty. Inputs to the tool are easily selected from a first menu and comprise measured rainfall data, EF values and the hydrological relationships for at least a 20-yr period. The outputs are the probabilities of compliance of the different components of the EF for the study period. From this, local optimization can be applied to establish EF components with a certain level of compliance in the study period. Different options for graphic output and analysis of results are included in terms of graphs and tables in several formats. This methodology turned out to be a useful tool for the implementation of an uncertainty analysis within the scope of environmental flows in water management and allowed the simulation of the impacts of several water resource development scenarios in the study site.

The Potential Of Kohonen Method For Classifying Rivers Focused On Regional Environmental Flow Determination With ELOHA

This article highlights the potential benefits that the Kohonen method has for the classification of rivers with similar characteristics by determining regional ecological flows using the ELOHA (Ecological Limits of Hydrologic Alteration) methodology. Currently, there are many methodologies for the classification of rivers, however none of them include the characteristics found in Kohonen method such as (i) providing the number of groups that actually underlie the information presented, (ii) used to make variable importance analysis, (iii) which in any case can display two-dimensional classification process, and (iv) that regardless of the parameters used in the model the clustering structure remains. In order to evaluate the potential benefits of the Kohonen method, 174 flow stations distributed along the great river basin “Magdalena-Cauca” (Colombia) were analyzed. 73 variables were obtained for the classification process in each case. Six trials were done using different combinations of variables and the results were validated against reference classification obtained by Ingfocol in 2010, whose results were also framed using ELOHA guidelines. In the process of validation it was found that two of the tested models reproduced a level higher than 80% of the reference classification with the first trial, meaning that more than 80% of the flow stations analyzed in both models formed invariant groups of streams.