Conservative Signal Processing Architectures For Asynchronous, Distributed Optimization Part II: Example Systems

This paper provides examples of various synchronous and asynchronous signal processing systems for performing optimization, utilizing the framework and elements developed in a preceding paper. The general strategy in that paper was to perform a linear transformation of stationarity conditions applicable to a class of convex and nonconvex optimization problems, resulting in algorithms that operate on a linear superposition of the associated primal and dual decision variables. The examples in this paper address various specific optimization problems including the LASSO problem, minimax-optimal filter design, the decentralized training of a support vector machine classifier, and sparse filter design for acoustic equalization. Where appropriate, multiple algorithms for solving the same optimization problem are presented, illustrating the use of the underlying framework in designing a variety of distinct classes of algorithms. The examples are accompanied by numerical simulation and a discussion of convergence

Unveiling The Tree: A Convex Framework for Sparse Problems

This paper presents a general framework for generating greedy algorithms for solving convex constraint satisfaction problems for sparse solutions by mapping the satisfaction problem into one of graph traversal on a rooted tree of unknown topology. For every pre-walk of the tree an initial set of generally dense feasible solutions is processed in such a way that the sparsity of each solution increases with each generation unveiled. The specific computation performed at any particular child node is shown to correspond to an embedding of a polytope into the polytope received from that nodes parent. Several issues related to pre-walk order selection, computational complexity and tractability, and the use of heuristic and/or side information is discussed. An example of a single-path, depth-first algorithm on a tree with randomized vertex reduction and a run-time path selection algorithm is presented in the context of sparse lowpass filter design

Parameter recovery for transient signals

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 115-118).Transient signals naturally arise in numerous disciplines for which the decay rates and amplitudes carry some informational significance. Even when the decay rates are known, solving for the amplitudes results in an ill-conditioned formulation. Transient signals in the presence of noise are further complicated as the signal-to-noise ratio asymptotically decreases in time. In this thesis the Discrete-Time Transient Transform and the Discrete Transient Transform are defined in order to represent a general signal using a linear combination of decaying exponential signals. A common approach to computing a change of basis is to make use of the dual basis. Two algorithms are proposed for generating a dual basis: the first algorithm is specific to a general exponential basis, e.g., real exponential or harmonically related complex exponential bases are special cases of the general exponential basis, while the second algorithm is usable for any general basis. Several properties of a transient domain representation are discussed. Algorithms for computing numerically stable approximate transient spectra are additionally proposed. The inherent infinite bandwidth of a continuous-time transient signal motivates in part the development of a framework for recovering the decay rates and amplitudes of a discrete-time lowpass filtered transient signal. This framework takes advantage of existing parameter modeling, identification, and recovery techniques to determine the decay rates while an alternating projection method utilizing the Discrete Transient Transform determines the amplitudes.by Tarek A. Lahlou.S.M

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

Decentralized signal processing systems with conservation principles

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 271-277).In this thesis, a framework for designing fixed-point and optimization algorithms realized as asynchronous, distributed signal processing systems is developed with an emphasis on the system's stability, robustness, and variational properties. These systems are formed by connecting basic modules together via interconnecting networks. Several classes of systems are constructed using interconnecting networks that obey certain conservation principles where these principles specifically allow steady-state system variables to be interpreted as solutions to optimization problems in a generally non-convex class and provide local conditions on the individual modules to ensure that the variables tend to such solutions, including when the communication between modules is asynchronous and uncoordinated. A particular class of signal processing systems, referred to as scattering systems, is designed that can solve convex and non-convex optimization problems, and where convex problems do not require problem-specific tuning parameters. Connections between scattering systems and their gradient-based and proximal counterparts are also established. The primary contributions of this thesis broadly serve to assist with designing and implementing scattering systems, both by leveraging existing signal processing paradigms and by developing new results in signal processing theory. To demonstrate the utility of the framework, scattering algorithms implemented as web-services and decentralized processor networks are presented and used to solve problems related to optimum filter design, sparse signal recovery, supervised learning, and non-convex regression.by Tarek Aziz Lahlou.Ph. D

Focal Adhesion Kinase-Related Proline-Rich Tyrosine Kinase 2 and Focal Adhesion Kinase Are Co-Overexpressed in Early-Stage and Invasive ErbB-2-Positive Breast Cancer and Cooperate for Breast Cancer Cell Tumorigenesis and Invasiveness

Early cancer cell migration and invasion of neighboring tissues are mediated by multiple events, including activation of focal adhesion signaling. Key regulators include the focal adhesion kinase (FAK) and FAK-related proline-rich tyrosine kinase 2 (Pyk2), whose distinct functions in cancer progression remain unclear. Here, we compared Pyk2 and FAK expression in breast cancer and their effects on ErbB-2-induced tumorigenesis and the potential therapeutic utility of targeting Pyk2 compared with FAK in preclinical models of breast cancer. Pyk2 is overexpressed in tissues from early and advanced breast cancers and overexpressed with both FAK and epidermal growth factor receptor-2 (ErbB-2) in a subset of breast cancer cases. Down-regulation of Pyk2 in ErbB-2-positive, FAK-proficient, and FAK-deficient cells reduced cell proliferation, which correlated with reduced mitogen-activated protein kinase (MAPK) activity. In contrast, Pyk2 silencing had little impact on cell migration and invasion. In vivo, Pyk2 down-regulation reduced primary tumor growth induced by a metastatic variant of ErbB-2-positive MDA 231 breast cancer cells but had little effect on lung metastases in contrast to FAK down-regulation. Dual reduction of Pyk2 and FAK expression resulted in strong inhibition of both primary tumor growth and lung metastases. Together, these data support the cooperative function of Pyk2 and FAK in breast cancer progression and suggest that dual inhibition of FAK and Pyk2 is an efficient therapeutic approach for targeting invasive breast cancer