Matching Items (14)

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Directional Sensor Control: Heuristic Approaches

Description

We study the problem of controlling multiple 2-D directional sensors while maximizing an objective function based on the information gain corresponding to multiple target locations. We assume a joint prior

We study the problem of controlling multiple 2-D directional sensors while maximizing an objective function based on the information gain corresponding to multiple target locations. We assume a joint prior Gaussian distribution for the target locations. A sensor generates a (noisy) measurement of a target only if the target lies within the field-of-view of the sensor, where the statistical properties of the measurement error depend on the location of the target with respect to the sensor and direction of the sensor. The measurements from the sensors are fused to form global estimates of target locations. This problem is combinatorial in nature-the computation time increases exponentially with the number of sensors. We develop heuristic methods to solve the problem approximately, and provide analytical results on performance guarantees. We then improve the performance of our heuristic approaches by applying an approximate dynamic programming approach called rollout. In addition, we address a variant of the above problem, where the goal is to map the sensors to the targets while maximizing the abovementioned objective function. This mapping problem also turns out to be combinatorial in nature, so we extend one of the above heuristics to solve this mapping problem approximately. We compare the performance of these heuristic approaches analytically and empirically.

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Created

Date Created
  • 2015-01-01

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Prediction of the binding affinities of peptides to class II MHC using a regularized thermodynamic model

Description

Background
The binding of peptide fragments of extracellular peptides to class II MHC is a crucial event in the adaptive immune response. Each MHC allotype generally binds a distinct subset

Background
The binding of peptide fragments of extracellular peptides to class II MHC is a crucial event in the adaptive immune response. Each MHC allotype generally binds a distinct subset of peptides and the enormous number of possible peptide epitopes prevents their complete experimental characterization. Computational methods can utilize the limited experimental data to predict the binding affinities of peptides to class II MHC.
Results
We have developed the Regularized Thermodynamic Average, or RTA, method for predicting the affinities of peptides binding to class II MHC. RTA accounts for all possible peptide binding conformations using a thermodynamic average and includes a parameter constraint for regularization to improve accuracy on novel data. RTA was shown to achieve higher accuracy, as measured by AUC, than SMM-align on the same data for all 17 MHC allotypes examined. RTA also gave the highest accuracy on all but three allotypes when compared with results from 9 different prediction methods applied to the same data. In addition, the method correctly predicted the peptide binding register of 17 out of 18 peptide-MHC complexes. Finally, we found that suboptimal peptide binding registers, which are often ignored in other prediction methods, made significant contributions of at least 50% of the total binding energy for approximately 20% of the peptides.
Conclusions
The RTA method accurately predicts peptide binding affinities to class II MHC and accounts for multiple peptide binding registers while reducing overfitting through regularization. The method has potential applications in vaccine design and in understanding autoimmune disorders. A web server implementing the RTA prediction method is available at http://bordnerlab.org/RTA/.

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Created

Date Created
  • 2010-01-20

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MultiRTA: A simple yet reliable method for predicting peptide binding affinities for multiple class II MHC allotypes

Description

Background
The binding of peptide fragments of antigens to class II MHC is a crucial step in initiating a helper T cell immune response. The identification of such peptide epitopes

Background
The binding of peptide fragments of antigens to class II MHC is a crucial step in initiating a helper T cell immune response. The identification of such peptide epitopes has potential applications in vaccine design and in better understanding autoimmune diseases and allergies. However, comprehensive experimental determination of peptide-MHC binding affinities is infeasible due to MHC diversity and the large number of possible peptide sequences. Computational methods trained on the limited experimental binding data can address this challenge. We present the MultiRTA method, an extension of our previous single-type RTA prediction method, which allows the prediction of peptide binding affinities for multiple MHC allotypes not used to train the model. Thus predictions can be made for many MHC allotypes for which experimental binding data is unavailable.
Results
We fit MultiRTA models for both HLA-DR and HLA-DP using large experimental binding data sets. The performance in predicting binding affinities for novel MHC allotypes, not in the training set, was tested in two different ways. First, we performed leave-one-allele-out cross-validation, in which predictions are made for one allotype using a model fit to binding data for the remaining MHC allotypes. Comparison of the HLA-DR results with those of two other prediction methods applied to the same data sets showed that MultiRTA achieved performance comparable to NetMHCIIpan and better than the earlier TEPITOPE method. We also directly tested model transferability by making leave-one-allele-out predictions for additional experimentally characterized sets of overlapping peptide epitopes binding to multiple MHC allotypes. In addition, we determined the applicability of prediction methods like MultiRTA to other MHC allotypes by examining the degree of MHC variation accounted for in the training set. An examination of predictions for the promiscuous binding CLIP peptide revealed variations in binding affinity among alleles as well as potentially distinct binding registers for HLA-DR and HLA-DP. Finally, we analyzed the optimal MultiRTA parameters to discover the most important peptide residues for promiscuous and allele-specific binding to HLA-DR and HLA-DP allotypes.
Conclusions
The MultiRTA method yields competitive performance but with a significantly simpler and physically interpretable model compared with previous prediction methods. A MultiRTA prediction webserver is available at http://bordnerlab.org/MultiRTA.

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Created

Date Created
  • 2010-09-24

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A fast algorithm for constructing efficient event-related functional magnetic resonance imaging designs

Description

We propose a novel, efficient approach for obtaining high-quality experimental designs for event-related functional magnetic resonance imaging (ER-fMRI), a popular brain mapping technique. Our proposed approach combines a greedy hill-climbing

We propose a novel, efficient approach for obtaining high-quality experimental designs for event-related functional magnetic resonance imaging (ER-fMRI), a popular brain mapping technique. Our proposed approach combines a greedy hill-climbing algorithm and a cyclic permutation method. When searching for optimal ER-fMRI designs, the proposed approach focuses only on a promising restricted class of designs with equal frequency of occurrence across stimulus types. The computational time is significantly reduced. We demonstrate that our proposed approach is very efficient compared with a recently proposed genetic algorithm approach. We also apply our approach in obtaining designs that are robust against misspecification of error correlations.

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Created

Date Created
  • 2013-11-30

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Control and Estimation Theory in Ranging Applications

Description

For the last 50 years, oscillator modeling in ranging systems has received considerable

attention. Many components in a navigation system, such as the master oscillator

driving the receiver system, as well the

For the last 50 years, oscillator modeling in ranging systems has received considerable

attention. Many components in a navigation system, such as the master oscillator

driving the receiver system, as well the master oscillator in the transmitting system

contribute significantly to timing errors. Algorithms in the navigation processor must

be able to predict and compensate such errors to achieve a specified accuracy. While

much work has been done on the fundamentals of these problems, the thinking on said

problems has not progressed. On the hardware end, the designers of local oscillators

focus on synthesized frequency and loop noise bandwidth. This does nothing to

mitigate, or reduce frequency stability degradation in band. Similarly, there are not

systematic methods to accommodate phase and frequency anomalies such as clock

jumps. Phase locked loops are fundamentally control systems, and while control

theory has had significant advancement over the last 30 years, the design of timekeeping

sources has not advanced beyond classical control. On the software end,

single or two state oscillator models are typically embedded in a Kalman Filter to

alleviate time errors between the transmitter and receiver clock. Such models are

appropriate for short term time accuracy, but insufficient for long term time accuracy.

Additionally, flicker frequency noise may be present in oscillators, and it presents

mathematical modeling complications. This work proposes novel H∞ control methods

to address the shortcomings in the standard design of time-keeping phase locked loops.

Such methods allow the designer to address frequency stability degradation as well

as high phase/frequency dynamics. Additionally, finite-dimensional approximants of

flicker frequency noise that are more representative of the truth system than the

tradition Gauss Markov approach are derived. Last, to maintain timing accuracy in

a wide variety of operating environments, novel Banks of Adaptive Extended Kalman

Filters are used to address both stochastic and dynamic uncertainty.

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Created

Date Created
  • 2020

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Global Optimization Using Piecewise Linear Approximation

Description

Global optimization (programming) has been attracting the attention of researchers for almost a century. Since linear programming (LP) and mixed integer linear programming (MILP) had been well studied in early

Global optimization (programming) has been attracting the attention of researchers for almost a century. Since linear programming (LP) and mixed integer linear programming (MILP) had been well studied in early stages, MILP methods and software tools had improved in their efficiency in the past few years. They are now fast and robust even for problems with millions of variables. Therefore, it is desirable to use MILP software to solve mixed integer nonlinear programming (MINLP) problems. For an MINLP problem to be solved by an MILP solver, its nonlinear functions must be transformed to linear ones. The most common method to do the transformation is the piecewise linear approximation (PLA). This dissertation will summarize the types of optimization and the most important tools and methods, and will discuss in depth the PLA tool. PLA will be done using nonuniform partitioning of the domain of the variables involved in the function that will be approximated. Also partial PLA models that approximate only parts of a complicated optimization problem will be introduced. Computational experiments will be done and the results will show that nonuniform partitioning and partial PLA can be beneficial.

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Created

Date Created
  • 2020

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Critical coupling and synchronized clusters in arbitrary networks of Kuramoto oscillators

Description

The Kuramoto model is an archetypal model for studying synchronization in groups

of nonidentical oscillators where oscillators are imbued with their own frequency and

coupled with other oscillators though a network of

The Kuramoto model is an archetypal model for studying synchronization in groups

of nonidentical oscillators where oscillators are imbued with their own frequency and

coupled with other oscillators though a network of interactions. As the coupling

strength increases, there is a bifurcation to complete synchronization where all oscillators

move with the same frequency and show a collective rhythm. Kuramoto-like

dynamics are considered a relevant model for instabilities of the AC-power grid which

operates in synchrony under standard conditions but exhibits, in a state of failure,

segmentation of the grid into desynchronized clusters.

In this dissertation the minimum coupling strength required to ensure total frequency

synchronization in a Kuramoto system, called the critical coupling, is investigated.

For coupling strength below the critical coupling, clusters of oscillators form

where oscillators within a cluster are on average oscillating with the same long-term

frequency. A unified order parameter based approach is developed to create approximations

of the critical coupling. Some of the new approximations provide strict lower

bounds for the critical coupling. In addition, these approximations allow for predictions

of the partially synchronized clusters that emerge in the bifurcation from the

synchronized state.

Merging the order parameter approach with graph theoretical concepts leads to a

characterization of this bifurcation as a weighted graph partitioning problem on an

arbitrary networks which then leads to an optimization problem that can efficiently

estimate the partially synchronized clusters. Numerical experiments on random Kuramoto

systems show the high accuracy of these methods. An interpretation of the

methods in the context of power systems is provided.

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Created

Date Created
  • 2018

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Magnetic resonance parameter assessment from a second order time-dependent linear model

Description

This dissertation develops a second order accurate approximation to the magnetic resonance (MR) signal model used in the PARSE (Parameter Assessment by Retrieval from Single Encoding) method to recover information

This dissertation develops a second order accurate approximation to the magnetic resonance (MR) signal model used in the PARSE (Parameter Assessment by Retrieval from Single Encoding) method to recover information about the reciprocal of the spin-spin relaxation time function (R2*) and frequency offset function (w) in addition to the typical steady-state transverse magnetization (M) from single-shot magnetic resonance imaging (MRI) scans. Sparse regularization on an approximation to the edge map is used to solve the associated inverse problem. Several studies are carried out for both one- and two-dimensional test problems, including comparisons to the first order approximation method, as well as the first order approximation method with joint sparsity across multiple time windows enforced. The second order accurate model provides increased accuracy while reducing the amount of data required to reconstruct an image when compared to piecewise constant in time models. A key component of the proposed technique is the use of fast transforms for the forward evaluation. It is determined that the second order model is capable of providing accurate single-shot MRI reconstructions, but requires an adequate coverage of k-space to do so. Alternative data sampling schemes are investigated in an attempt to improve reconstruction with single-shot data, as current trajectories do not provide ideal k-space coverage for the proposed method.

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Created

Date Created
  • 2019

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A variational approach to planning, allocation and mapping in robot swarms using infinite dimensional models

Description

This thesis considers two problems in the control of robotic swarms. Firstly, it addresses a trajectory planning and task allocation problem for a swarm of resource-constrained robots that cannot localize

This thesis considers two problems in the control of robotic swarms. Firstly, it addresses a trajectory planning and task allocation problem for a swarm of resource-constrained robots that cannot localize or communicate with each other and that exhibit stochasticity in their motion and task switching policies. We model the population dynamics of the robotic swarm as a set of advection-diffusion- reaction (ADR) partial differential equations (PDEs).

Specifically, we consider a linear parabolic PDE model that is bilinear in the robots' velocity and task-switching rates. These parameters constitute a set of time-dependent control variables that can be optimized and transmitted to the robots prior to their deployment or broadcasted in real time. The planning and allocation problem can then be formulated as a PDE-constrained optimization problem, which we solve using techniques from optimal control. Simulations of a commercial pollination scenario validate the ability of our control approach to drive a robotic swarm to achieve predefined spatial distributions of activity over a closed domain, which may contain obstacles. Secondly, we consider a mapping problem wherein a robotic swarm is deployed over a closed domain and it is necessary to reconstruct the unknown spatial distribution of a feature of interest. The ADR-based primitives result in a coefficient identification problem for the corresponding system of PDEs. To deal with the inherent ill-posedness of the problem, we frame it as an optimization problem. We validate our approach through simulations and show that reconstruction of the spatially-dependent coefficient can be achieved with considerable accuracy using temporal information alone.

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Created

Date Created
  • 2014

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Test-based falsification and conformance testing for cyber-physical systems

Description

In this dissertation, two problems are addressed in the verification and control of Cyber-Physical Systems (CPS):

1) Falsification: given a CPS, and a property of interest that the CPS must satisfy

In this dissertation, two problems are addressed in the verification and control of Cyber-Physical Systems (CPS):

1) Falsification: given a CPS, and a property of interest that the CPS must satisfy under all allowed operating conditions, does the CPS violate, i.e. falsify, the property?

2) Conformance testing: given a model of a CPS, and an implementation of that CPS on an embedded platform, how can we characterize the properties satisfied by the implementation, given the properties satisfied by the model?

Both problems arise in the context of Model-Based Design (MBD) of CPS: in MBD, the designers start from a set of formal requirements that the system-to-be-designed must satisfy.

A first model of the system is created.

Because it may not be possible to formally verify the CPS model against the requirements, falsification tries to verify whether the model satisfies the requirements by searching for behavior that violates them.

In the first part of this dissertation, I present improved methods for finding falsifying behaviors of CPS when properties are expressed in Metric Temporal Logic (MTL).

These methods leverage the notion of robust semantics of MTL formulae: if a falsifier exists, it is in the neighborhood of local minimizers of the robustness function.

The proposed algorithms compute descent directions of the robustness function in the space of initial conditions and input signals, and provably converge to local minima of the robustness function.

The initial model of the CPS is then iteratively refined by modeling previously ignored phenomena, adding more functionality, etc., with each refinement resulting in a new model.

Many of the refinements in the MBD process described above do not provide an a priori guaranteed relation between the successive models.

Thus, the second problem above arises: how to quantify the distance between two successive models M_n and M_{n+1}?

If M_n has been verified to satisfy the specification, can it be guaranteed that M_{n+1} also satisfies the same, or some closely related, specification?

This dissertation answers both questions for a general class of CPS, and properties expressed in MTL.

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Created

Date Created
  • 2015