Robust Control and Hot Spots in Dynamic Spatially Interconnected Systems

This paper develops linear quadratic robust control theory for a class of spatially invariant distributed control systems that appear in areas of economics such as New Economic Geography, management of ecological systems, optimal harvesting of spatially mobile species, and the like. Since this class of problems has an infinite dimensional state and control space it would appear analytically intractable. We show that by Fourier transforming the problem, the solution decomposes into a countable number of finite state space robust control problems each of which can be solved by standard methods. We use this convenient property to characterize “hot spots” which are points in the transformed space that correspond to “breakdown” points in conventional finite dimensional robust control, or where instabilities appear or where the value function loses concavity. We apply our methods to a spatial extension of a well known optimal fishing model.Distributed Parameter Systems, Robust Control, Spatial Invariance, Hot Spot, Agglomeration

Increasing the Power to Detect Causal Associations by Combining Genotypic and Expression Data in Segregating Populations

To dissect common human diseases such as obesity and diabetes, a systematic approach is needed to study how genes interact with one another, and with genetic and environmental factors, to determine clinical end points or disease phenotypes. Bayesian networks provide a convenient framework for extracting relationships from noisy data and are frequently applied to large-scale data to derive causal relationships among variables of interest. Given the complexity of molecular networks underlying common human disease traits, and the fact that biological networks can change depending on environmental conditions and genetic factors, large datasets, generally involving multiple perturbations (experiments), are required to reconstruct and reliably extract information from these networks. With limited resources, the balance of coverage of multiple perturbations and multiple subjects in a single perturbation needs to be considered in the experimental design. Increasing the number of experiments, or the number of subjects in an experiment, is an expensive and time-consuming way to improve network reconstruction. Integrating multiple types of data from existing subjects might be more efficient. For example, it has recently been demonstrated that combining genotypic and gene expression data in a segregating population leads to improved network reconstruction, which in turn may lead to better predictions of the effects of experimental perturbations on any given gene. Here we simulate data based on networks reconstructed from biological data collected in a segregating mouse population and quantify the improvement in network reconstruction achieved using genotypic and gene expression data, compared with reconstruction using gene expression data alone. We demonstrate that networks reconstructed using the combined genotypic and gene expression data achieve a level of reconstruction accuracy that exceeds networks reconstructed from expression data alone, and that fewer subjects may be required to achieve this superior reconstruction accuracy. We conclude that this integrative genomics approach to reconstructing networks not only leads to more predictive network models, but also may save time and money by decreasing the amount of data that must be generated under any given condition of interest to construct predictive network models

Import Tariffs Enforcement with Low Administrative Capacity

Import tariff receipts represent an important share of government revenues in many developing countries and there has recently been a surge in empirical studies showing how evasion in this field is a pervasive phenomenon. In the case of import tariffs, the tax base is the product of quantity and unit value, both of which have to be reported and need to be assessed by the custom authority during an audit. I show that when the fiscal authority has an imperfect detection technology, there is an additional incentive for the taxpayer to underdeclare, as a greater declaration in one dimension actually increases the fine when evasion in the other dimension is detected, and a tax base presenting this feature is subject to more evasion compared to a tax base that can be assessed directly. Also, when enforcement capacity is low, voluntary compliance is higher when the importer is required to declare only the total value of imports.tariff, tax evasion, multiplicative tax base, imperfect detection, low administrative capacity

A framework for clustering and adaptive topic tracking on evolving text and social media data streams.

Recent advances and widespread usage of online web services and social media platforms, coupled with ubiquitous low cost devices, mobile technologies, and increasing capacity of lower cost storage, has led to a proliferation of Big data, ranging from, news, e-commerce clickstreams, and online business transactions to continuous event logs and social media expressions. These large amounts of online data, often referred to as data streams, because they get generated at extremely high throughputs or velocity, can make conventional and classical data analytics methodologies obsolete. For these reasons, the issues of management and analysis of data streams have been researched extensively in recent years. The special case of social media Big Data brings additional challenges, particularly because of the unstructured nature of the data, specifically free text. One classical approach to mine text data has been Topic Modeling. Topic Models are statistical models that can be used for discovering the abstract ``topics\u27\u27 that may occur in a corpus of documents. Topic models have emerged as a powerful technique in machine learning and data science, providing a great balance between simplicity and complexity. They also provide sophisticated insight without the need for real natural language understanding. However they have not been designed to cope with the type of text data that is abundant on social media platforms, but rather for traditional medium size corpora consisting of longer documents, adhering to a specific language and typically spanning a stable set of topics. Unlike traditional document corpora, social media messages tend to be very short, sparse, noisy, and do not adhere to a standard vocabulary, linguistic patterns, or stable topic distributions. They are also generated at high velocity that impose high demands on topic modeling; and their evolving or dynamic nature, makes any set of results from topic modeling quickly become stale in the face of changes in the textual content and topics discussed within social media streams. In this dissertation, we propose an integrated topic modeling framework built on top of an existing stream-clustering framework called Stream-Dashboard, which can extract, isolate, and track topics over any given time period. In this new framework, Stream Dashboard first clusters the data stream points into homogeneous groups. Then data from each group is ushered to the topic modeling framework which extracts finer topics from the group. The proposed framework tracks the evolution of the clusters over time to detect milestones corresponding to changes in topic evolution, and to trigger an adaptation of the learned groups and topics at each milestone. The proposed approach to topic modeling is different from a generic Topic Modeling approach because it works in a compartmentalized fashion, where the input document stream is split into distinct compartments, and Topic Modeling is applied on each compartment separately. Furthermore, we propose extensions to existing topic modeling and stream clustering methods, including: an adaptive query reformulation approach to help focus on the topic discovery with time; a topic modeling extension with adaptive hyper-parameter and with infinite vocabulary; an adaptive stream clustering algorithm incorporating the automated estimation of dynamic, cluster-specific temporal scales for adaptive forgetting to help facilitate clustering in a fast evolving data stream. Our experimental results show that the proposed adaptive forgetting clustering algorithm can mine better quality clusters; that our proposed compartmentalized framework is able to mine topics of better quality compared to competitive baselines; and that the proposed framework can automatically adapt to focus on changing topics using the proposed query reformulation strategy

Modeling, optimization, and sensitivity analysis of a continuous multi-segment crystallizer for production of active pharmaceutical ingredients

We have investigated the simulation-based, steady-state optimization of a new type of crystallizer for the production of pharmaceuticals. The multi-segment, multi-addition plug-flow crystallizer (MSMA-PFC) offers better control over supersaturation in one dimension compared to a batch or stirred-tank crystallizer. Through use of a population balance framework, we have written the governing model equations of population balance and mass balance on the crystallizer segments. The solution of these equations was accomplished through either the method of moments or the finite volume method. The goal was to optimize the performance of the crystallizer with respect to certain quantities, such as maximizing the mean crystal size, minimizing the coefficient of variation, or minimizing the sum of the squared errors when attempting to hit a target distribution. Such optimizations are all highly nonconvex, necessitating the use of the genetic algorithm. Our results for the optimization of a process for crystallizing flufenamic acid showed improvement in crystal size over prior literature results. Through the use of a novel simultaneous design and control (SDC) methodology, we have further optimized the flowrates and crystallizer geometry in tandem.^ We have further investigated the robustness of this process and observe significant sensitivity to error in antisolvent flowrate, as well as the kinetic parameters of crystallization. We have lastly performed a parametric study on the use of the MSMA-PFC for in-situ dissolution of fine crystals back into solution. Fine crystals are a known processing difficulty in drug manufacture, thus motivating the development of a process that can eliminate them efficiently. Prior results for cooling crystallization indicated this to be possible. However, our results show little to no dissolution is used after optimizing the crystallizer, indicating the negative impact of adding pure solvent to the process (reduced concentration via dilution, and decreased residence time) outweighs the positive benefits of dissolving fines. The prior results for cooling crystallization did not possess this coupling between flowrate, residence time, and concentration, thus making fines dissolution significantly more beneficial for that process. We conclude that the success observed in hitting the target distribution has more to do with using multiple segments and having finer control over supersaturation than with the ability to go below solubility. Our results showed that excessive nucleation still overwhelms the MSMA-PFC for in-situ fines dissolution when nucleation is too high

An Automated Images-to-Graphs Framework for High Resolution Connectomics

Reconstructing a map of neuronal connectivity is a critical challenge in contemporary neuroscience. Recent advances in high-throughput serial section electron microscopy (EM) have produced massive 3D image volumes of nanoscale brain tissue for the first time. The resolution of EM allows for individual neurons and their synaptic connections to be directly observed. Recovering neuronal networks by manually tracing each neuronal process at this scale is unmanageable, and therefore researchers are developing automated image processing modules. Thus far, state-of-the-art algorithms focus only on the solution to a particular task (e.g., neuron segmentation or synapse identification). In this manuscript we present the first fully automated images-to-graphs pipeline (i.e., a pipeline that begins with an imaged volume of neural tissue and produces a brain graph without any human interaction). To evaluate overall performance and select the best parameters and methods, we also develop a metric to assess the quality of the output graphs. We evaluate a set of algorithms and parameters, searching possible operating points to identify the best available brain graph for our assessment metric. Finally, we deploy a reference end-to-end version of the pipeline on a large, publicly available data set. This provides a baseline result and framework for community analysis and future algorithm development and testing. All code and data derivatives have been made publicly available toward eventually unlocking new biofidelic computational primitives and understanding of neuropathologies.Comment: 13 pages, first two authors contributed equally V2: Added additional experiments and clarifications; added information on infrastructure and pipeline environmen

Application of First Principle Modeling in Combination with Empirical Design of Experiments and Real-Time Data Management for the Automated Control of Pharmaceutical Unit Operations

The U.S. Food and Drug Administration has accepted the guidelines put forth by the International Conference on Harmonization (ICH-Q8) that allow for operational flexibility within a validated design space. These Quality by Design initiatives have allowed drug manufacturers to incorporate more rigorous scientific controls into their production streams. Fully automated control systems can incorporate information about a process back into the system to adjust process variables to consistently hit product quality targets (feedback control), or monitor variability in raw materials or intermediate products to adjust downstream manufacturing operations (feedforward control). These controls enable increased process understanding, continuous process and product improvement, assurance of product quality, and the possibility of real-time release. Control systems require significant planning and an initial investment, but the improved product quality and manufacturing efficiency provide ample incentive for the expense. The fluid bed granulation and drying unit operation was an excellent case study for control systems implementation because it is a complex unit operation with dynamic powder movement, high energy input, solid-liquid-gas interactions, and difficulty with scale-up development. Traditionally, fluid bed control systems have either used first principle calculations to control the internal process environment or purely empirical methods that incorporate online process measurements with process models. This dissertation was predicated on the development of a novel hybrid control system that combines the two traditional approaches. The hybrid controls reduced the number of input factors for the creation of efficient experimental designs, reduced the variability between batches, enabled control of the drying process for a sensitive active pharmaceutical ingredient, rendered preconditioned air systems unnecessary, and facilitated the collection of data for the development of process models and the rigorous calculation of design spaces. Significant variably in the inlet airstream was able to be mitigated using feedforward controls, while process analytical technology provided immediate feedback about the process for strict control of process inputs. Tolerance surfaces provided the ideal tool for determining design spaces that assured the reduction of manufacturing risk among all future batches, and the information gained using small scale experimentation was leveraged to provide efficient scale-up, making these control systems feasible for consistent use