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.
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.
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.
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/.
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.
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.