Cell fate specification during Caenorhabditis elegans male tail development

The cells of the specialized mating structures of the nematode Caenorhabditis elegans adult male tail develop from sex-specific divisions of postembryonic blast cells. One male-specific blast cell, B, is the precursor to all the cells of the copulatory spicules. Both cell interactions and autonomous fate specification mechanisms are utilized in the B lineage to specify fate.

During development the anterior daughter of B, B.a, generates four distinct pairs of cells. Cell ablation experiments indicate that the cells of each pair respond to positional cues provided by other male-specific blast cells. F and U promote anterior fates, Y.p promotes some posterior fates, and the B.a progeny promote posterior fates. The cells within each pair may also interact.

The lin-3/let-23 signalling pathway, identified for its function in C. elegans hermaphrodite vulval induction, mediates the signal from F and U. Reduction-of-function mutations in lin-3 (EGF-like signal), let-23 (receptor), sem-5 (adaptor), let-60 (ras), or lin-45 (raf) disrupt the fates of the anterior cells, and mimic F and U ablation. In addition, ectopically expressed lin-3 disrupts the fates of the posterior cells, and can promote anterior fates even in the absence of F and U.

A genetic screen of over 9000 mutagenized gametes recovered 22 mutations in 20 loci that disrupt fate specification in male tail lineages. Seven of these mutations may represent new genes that play a role in male tail development.

The first division of the B cell is asymmetric. The gene vab-3 is required for specification of B.a fates, and it may represent a factor whose activity is localized to the B.a cell via the gene lin-17. lin-17 acts both at the first division of the B cell and at specific other cell divisions in the lineage.

Design, specification, and synthesis of aircraft electric power systems control logic

Cyber-physical systems integrate computation, networking, and physical processes. Substantial research challenges exist in the design and verification of such large-scale, distributed sensing, ac- tuation, and control systems. Rapidly improving technology and recent advances in control theory, networked systems, and computer science give us the opportunity to drastically improve our approach to integrated flow of information and cooperative behavior. Current systems rely on text-based spec- ifications and manual design. Using new technology advances, we can create easier, more efficient, and cheaper ways of developing these control systems. This thesis will focus on design considera- tions for system topologies, ways to formally and automatically specify requirements, and methods to synthesize reactive control protocols, all within the context of an aircraft electric power system as a representative application area.

This thesis consists of three complementary parts: synthesis, specification, and design. The first section focuses on the synthesis of central and distributed reactive controllers for an aircraft elec- tric power system. This approach incorporates methodologies from computer science and control. The resulting controllers are correct by construction with respect to system requirements, which are formulated using the specification language of linear temporal logic (LTL). The second section addresses how to formally specify requirements and introduces a domain-specific language for electric power systems. A software tool automatically converts high-level requirements into LTL and synthesizes a controller.

The final sections focus on design space exploration. A design methodology is proposed that uses mixed-integer linear programming to obtain candidate topologies, which are then used to synthesize controllers. The discrete-time control logic is then verified in real-time by two methods: hardware and simulation. Finally, the problem of partial observability and dynamic state estimation is ex- plored. Given a set placement of sensors on an electric power system, measurements from these sensors can be used in conjunction with control logic to infer the state of the system.

Molecular genetics of the Drosophila eyes absent gene

The Drosophila compound eye has provided a genetic approach to understanding the specification of cell fates during differentiation. The eye is made up of some 750 repeated units or ommatidia, arranged in a lattice. The cellular composition of each ommatidium is identical. The arrangement of the lattice and the specification of cell fates in each ommatidium are thought to occur in development through cellular interactions with the local environment. Many mutations have been studied that disrupt the proper patterning and cell fating in the eye. The eyes absent (eya) mutation, the subject of this thesis, was chosen because of its eyeless phenotype. In eya mutants, eye progenitor cells undergo programmed cell death before the onset of patterning has occurred. The molecular genetic analysis of the gene is presented.

The eye arises from the larval eye-antennal imaginal disc. During the third larval instar, a wave of differentiation progresses across the disc, marked by a furrow. Anterior to the furrow, proliferating cells are found in apparent disarray. Posterior to the furrow, clusters of differentiating cells can be discerned, that correspond to the ommatidia of the adult eye. Analysis of an allelic series of eya mutants in comparison to wild type revealed the presence of a selection point: a wave of programmed cell death that normally precedes the furrow. In eya mutants, an excessive number of eye progenitor cells die at this selection point, suggesting the eya gene influences the distribution of cells between fates of death and differentiation.

In addition to its role in the eye, the eya gene has an embryonic function. The eye function is autonomous to the eye progenitor cells. Molecular maps of the eye and embryonic phenotypes are different. Therefore, the function of eya in the eye can be treated independently of the embryonic function. Cloning of the gene reveals two cDNA's that are identical except for the use of an alternatively-spliced 5' exon. The predicted protein products differ only at the N-termini. Sequence analysis shows these two proteins to be the first of their kind to be isolated. Trangenic studies using the two cDNA's show that either gene product is able to rescue the eye phenotype of eya mutants.

The eya gene exhibits interallelic complementation. This interaction is an example of an "allelic position effect": an interaction that depends on the relative position in the genome of the two alleles, which is thought to be mediated by chromosomal pairing. The interaction at eya is essentially identical to a phenomenon known as transvection, which is an allelic position effect that is sensitive to certain kinds of chromosomal rearrangements. A current model for the mechanism of transvection is the trans action of gene regulatory regions. The eya locus is particularly well suited for the study of transvection because the mutant phenotypes can be quantified by scoring the size of the eye.

The molecular genetic analysis of eya provides a system for uncovering mechanisms underlying differentiation, developmentally regulated programmed cell death, and gene regulation.

Surface markers of regionalization in the vertebrate nervous system

In order to identify new molecules that might play a role in regional specification of the nervous system, we generated and characterized monoclonal antibodies (mAbs) that have positionally-restricted labeling patterns.

The FORSE-1 mAb was generated using a strategy designed to produce mAbs against neuronal cell surface antigens that might be regulated by regionally-restricted transcription factors in the developing central nervous system (CNS). FORSE-1 staining is enriched in the forebrain as compared to the rest of the CNS until E18. Between E11.5-E13.5, only certain areas of the forebrain are labeled. There is also a dorsoventrally-restricted region of labeling in the hindbrain and spinal cord. The mAb labels a large proteoglycan-like cell-surface antigen (>200 kD). The labeling pattern of FORSE-1 is conserved in various mammals and in chick.

To determine whether the FORSE-1 labeling pattern is similar to that of known transcription factors, the expression of BF-1 and Dlx-2 was compared with FORSE-1. There is a striking overlap between BF-1 and FORSE-1 in the telencephalon. In contrast, FORSE-1 and Dlx-2 have very different patterns of expression in the forebrain, suggesting that regulation by Dlx-2 alone cannot explain the distribution of FORSE-1. They do, however, share some sharp boundaries in the diencephalon. In addition, FORSE-1 identifies some previously unknown boundaries in the developing forebrain. Thus, FORSE-1 is a new cell surface marker that can be used to subdivide the embryonic forebrain into regions smaller than previously described, providing further complexity necessary for developmental patterning.

I also studied the expression of the cell surface protein CD9 in the developing and adult rat nervous system. CD9 is implicated in intercellular signaling and cell adhesion in the hematopoetic system. In the nervous system, CD9 may perform similar functions in early sympathetic ganglia, chromaffin cells, and motor neurons, all of which express the protein. The presence of CD9 on the surfaces of Schwann cells and axons at the appropriate time may allow the protein to participate in the cellular interactions involved in myelination.

Analysis-aware design of embedded systems software

In the past many different methodologies have been devised to support software development and different sets of methodologies have been developed to support the analysis of software artefacts. We have identified this mismatch as one of the causes of the poor reliability of embedded systems software. The issue with software development styles is that they are ``analysis-agnostic.'' They do not try to structure the code in a way that lends itself to analysis. The analysis is usually applied post-mortem after the software was developed and it requires a large amount of effort. The issue with software analysis methodologies is that they do not exploit available information about the system being analyzed.

In this thesis we address the above issues by developing a new methodology, called "analysis-aware" design, that links software development styles with the capabilities of analysis tools. This methodology forms the basis of a framework for interactive software development. The framework consists of an executable specification language and a set of analysis tools based on static analysis, testing, and model checking. The language enforces an analysis-friendly code structure and offers primitives that allow users to implement their own testers and model checkers directly in the language. We introduce a new approach to static analysis that takes advantage of the capabilities of a rule-based engine. We have applied the analysis-aware methodology to the development of a smart home application.

Experimental and theoretical studies of Notch signaling-mediated spatial pattern

Notch signaling acts in many diverse developmental spatial patterning processes. To better understand why this particular pathway is employed where it is and how downstream feedbacks interact with the signaling system to drive patterning, we have pursued three aims: (i) to quantitatively measure the Notch system's signal input/output (I/O) relationship in cell culture, (ii) to use the quantitative I/O relationship to computationally predict patterning outcomes of downstream feedbacks, and (iii) to reconstitute a Notch-mediated lateral induction feedback (in which Notch signaling upregulates the expression of Delta) in cell culture. The quantitative Notch I/O relationship revealed that in addition to the trans-activation between Notch and Delta on neighboring cells there is also a strong, mutual cis-inactivation between Notch and Delta on the same cell. This feature tends to amplify small differences between cells. Incorporating our improved understanding of the signaling system into simulations of different types of downstream feedbacks and boundary conditions lent us several insights into their function. The Notch system converts a shallow gradient of Delta expression into a sharp band of Notch signaling without any sort of feedback at all, in a system motivated by the Drosophila wing vein. It also improves the robustness of lateral inhibition patterning, where signal downregulates ligand expression, by removing the requirement for explicit cooperativity in the feedback and permitting an exceptionally simple mechanism for the pattern. When coupled to a downstream lateral induction feedback, the Notch system supports the propagation of a signaling front across a tissue to convert a large area from one state to another with only a local source of initial stimulation. It is also capable of converting a slowly-varying gradient in parameters into a sharp delineation between high- and low-ligand populations of cells, a pattern reminiscent of smooth muscle specification around artery walls. Finally, by implementing a version of the lateral induction feedback architecture modified with the addition of an autoregulatory positive feedback loop, we were able to generate cells that produce enough cis ligand when stimulated by trans ligand to themselves transmit signal to neighboring cells, which is the hallmark of lateral induction.

Control of dynamical systems with temporal logic specifications

This thesis is motivated by safety-critical applications involving autonomous air, ground, and space vehicles carrying out complex tasks in uncertain and adversarial environments. We use temporal logic as a language to formally specify complex tasks and system properties. Temporal logic specifications generalize the classical notions of stability and reachability that are studied in the control and hybrid systems communities. Given a system model and a formal task specification, the goal is to automatically synthesize a control policy for the system that ensures that the system satisfies the specification. This thesis presents novel control policy synthesis algorithms for optimal and robust control of dynamical systems with temporal logic specifications. Furthermore, it introduces algorithms that are efficient and extend to high-dimensional dynamical systems.

The first contribution of this thesis is the generalization of a classical linear temporal logic (LTL) control synthesis approach to optimal and robust control. We show how we can extend automata-based synthesis techniques for discrete abstractions of dynamical systems to create optimal and robust controllers that are guaranteed to satisfy an LTL specification. Such optimal and robust controllers can be computed at little extra computational cost compared to computing a feasible controller.

The second contribution of this thesis addresses the scalability of control synthesis with LTL specifications. A major limitation of the standard automaton-based approach for control with LTL specifications is that the automaton might be doubly-exponential in the size of the LTL specification. We introduce a fragment of LTL for which one can compute feasible control policies in time polynomial in the size of the system and specification. Additionally, we show how to compute optimal control policies for a variety of cost functions, and identify interesting cases when this can be done in polynomial time. These techniques are particularly relevant for online control, as one can guarantee that a feasible solution can be found quickly, and then iteratively improve on the quality as time permits.

The final contribution of this thesis is a set of algorithms for computing feasible trajectories for high-dimensional, nonlinear systems with LTL specifications. These algorithms avoid a potentially computationally-expensive process of computing a discrete abstraction, and instead compute directly on the system's continuous state space. The first method uses an automaton representing the specification to directly encode a series of constrained-reachability subproblems, which can be solved in a modular fashion by using standard techniques. The second method encodes an LTL formula as mixed-integer linear programming constraints on the dynamical system. We demonstrate these approaches with numerical experiments on temporal logic motion planning problems with high-dimensional (10+ states) continuous systems.

Comparative studies of Vulva development in C. briggsae

As evolution progresses, developmental changes occur. Genes lose and gain molecular partners, regulatory sequences, and new functions. As a consequence, tissues evolve alternative methods to develop similar structures, more or less robust. How this occurs is a major question in biology. One method of addressing this question is by examining the developmental and genetic differences between similar species. Several studies of nematodes Pristionchus pacificus and Oscheius CEW1 have revealed various differences in vulval development from the well-studied C. elegans (e.g. gonad induction, competence group specification, and gene function.)

I approached the question of developmental change in a similar manner by using Caenorhabditis briggsae, a close relative of C. elegans. C. briggsae allows the use of transgenic approaches to determine developmental changes between species. We determined subtle changes in the competence group, in 1° cell specification, and vulval lineage.

We also analyzed the let-60 gene in four nematode species. We found conservation in the codon identity and exon-intron boundaries, but lack of an extended 3' untranslated region in Caenorhabditis briggsae.

Neural network design for switching network control

A neural network is a highly interconnected set of simple processors. The many connections allow information to travel rapidly through the network, and due to their simplicity, many processors in one network are feasible. Together these properties imply that we can build efficient massively parallel machines using neural networks. The primary problem is how do we specify the interconnections in a neural network. The various approaches developed so far such as outer product, learning algorithm, or energy function suffer from the following deficiencies: long training/ specification times; not guaranteed to work on all inputs; requires full connectivity.

Alternatively we discuss methods of using the topology and constraints of the problems themselves to design the topology and connections of the neural solution. We define several useful circuits-generalizations of the Winner-Take-All circuitthat allows us to incorporate constraints using feedback in a controlled manner. These circuits are proven to be stable, and to only converge on valid states. We use the Hopfield electronic model since this is close to an actual implementation. We also discuss methods for incorporating these circuits into larger systems, neural and nonneural. By exploiting regularities in our definition, we can construct efficient networks. To demonstrate the methods, we look to three problems from communications. We first discuss two applications to problems from circuit switching; finding routes in large multistage switches, and the call rearrangement problem. These show both, how we can use many neurons to build massively parallel machines, and how the Winner-Take-All circuits can simplify our designs.

Next we develop a solution to the contention arbitration problem of high-speed packet switches. We define a useful class of switching networks and then design a neural network to solve the contention arbitration problem for this class. Various aspects of the neural network/switch system are analyzed to measure the queueing performance of this method. Using the basic design, a feasible architecture for a large (1024-input) ATM packet switch is presented. Using the massive parallelism of neural networks, we can consider algorithms that were previously computationally unattainable. These now viable algorithms lead us to new perspectives on switch design.

Efficient methods for stochastic optimal control

The Hamilton Jacobi Bellman (HJB) equation is central to stochastic optimal control (SOC) theory, yielding the optimal solution to general problems specified by known dynamics and a specified cost functional. Given the assumption of quadratic cost on the control input, it is well known that the HJB reduces to a particular partial differential equation (PDE). While powerful, this reduction is not commonly used as the PDE is of second order, is nonlinear, and examples exist where the problem may not have a solution in a classical sense. Furthermore, each state of the system appears as another dimension of the PDE, giving rise to the curse of dimensionality. Since the number of degrees of freedom required to solve the optimal control problem grows exponentially with dimension, the problem becomes intractable for systems with all but modest dimension.

In the last decade researchers have found that under certain, fairly non-restrictive structural assumptions, the HJB may be transformed into a linear PDE, with an interesting analogue in the discretized domain of Markov Decision Processes (MDP). The work presented in this thesis uses the linearity of this particular form of the HJB PDE to push the computational boundaries of stochastic optimal control.

This is done by crafting together previously disjoint lines of research in computation. The first of these is the use of Sum of Squares (SOS) techniques for synthesis of control policies. A candidate polynomial with variable coefficients is proposed as the solution to the stochastic optimal control problem. An SOS relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving sub-optimality gap. The resulting approximate solutions are shown to be guaranteed over- and under-approximations for the optimal value function. It is shown that these results extend to arbitrary parabolic and elliptic PDEs, yielding a novel method for Uncertainty Quantification (UQ) of systems governed by partial differential constraints. Domain decomposition techniques are also made available, allowing for such problems to be solved via parallelization and low-order polynomials.

The optimization-based SOS technique is then contrasted with the Separated Representation (SR) approach from the applied mathematics community. The technique allows for systems of equations to be solved through a low-rank decomposition that results in algorithms that scale linearly with dimensionality. Its application in stochastic optimal control allows for previously uncomputable problems to be solved quickly, scaling to such complex systems as the Quadcopter and VTOL aircraft. This technique may be combined with the SOS approach, yielding not only a numerical technique, but also an analytical one that allows for entirely new classes of systems to be studied and for stability properties to be guaranteed.

The analysis of the linear HJB is completed by the study of its implications in application. It is shown that the HJB and a popular technique in robotics, the use of navigation functions, sit on opposite ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. Analytical solutions to the HJB in these settings are available in simplified domains, yielding guidance towards optimality for approximation schemes. Finally, the use of HJB equations in temporal multi-task planning problems is investigated. It is demonstrated that such problems are reducible to a sequence of SOC problems linked via boundary conditions. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification.

Incremental Control Synthesis for Robotics in the Presence of Temporal Logic Specifications

This thesis presents methods for incrementally constructing controllers in the presence of uncertainty and nonlinear dynamics. The basic setting is motion planning subject to temporal logic specifications. Broadly, two categories of problems are treated. The first is reactive formal synthesis when so-called discrete abstractions are available. The fragment of linear-time temporal logic (LTL) known as GR(1) is used to express assumptions about an adversarial environment and requirements of the controller. Two problems of changes to a specification are posed that concern the two major aspects of GR(1): safety and liveness. Algorithms providing incremental updates to strategies are presented as solutions. In support of these, an annotation of strategies is developed that facilitates repeated modifications. A variety of properties are proven about it, including necessity of existence and sufficiency for a strategy to be winning. The second category of problems considered is non-reactive (open-loop) synthesis in the absence of a discrete abstraction. Instead, the presented stochastic optimization methods directly construct a control input sequence that achieves low cost and satisfies a LTL formula. Several relaxations are considered as heuristics to address the rarity of sampling trajectories that satisfy an LTL formula and demonstrated to improve convergence rates for Dubins car and single-integrators subject to a recurrence task.

Structural Design under Seismic Risk Using Multiple Performance Objectives

Structural design is a decision-making process in which a wide spectrum of requirements, expectations, and concerns needs to be properly addressed. Engineering design criteria are considered together with societal and client preferences, and most of these design objectives are affected by the uncertainties surrounding a design. Therefore, realistic design frameworks must be able to handle multiple performance objectives and incorporate uncertainties from numerous sources into the process.

In this study, a multi-criteria based design framework for structural design under seismic risk is explored. The emphasis is on reliability-based performance objectives and their interaction with economic objectives. The framework has analysis, evaluation, and revision stages. In the probabilistic response analysis, seismic loading uncertainties as well as modeling uncertainties are incorporated. For evaluation, two approaches are suggested: one based on preference aggregation and the other based on socio-economics. Both implementations of the general framework are illustrated with simple but informative design examples to explore the basic features of the framework.

The first approach uses concepts similar to those found in multi-criteria decision theory, and directly combines reliability-based objectives with others. This approach is implemented in a single-stage design procedure. In the socio-economics based approach, a two-stage design procedure is recommended in which societal preferences are treated through reliability-based engineering performance measures, but emphasis is also given to economic objectives because these are especially important to the structural designer's client. A rational net asset value formulation including losses from uncertain future earthquakes is used to assess the economic performance of a design. A recently developed assembly-based vulnerability analysis is incorporated into the loss estimation.

The presented performance-based design framework allows investigation of various design issues and their impact on a structural design. It is a flexible one that readily allows incorporation of new methods and concepts in seismic hazard specification, structural analysis, and loss estimation.