Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks

The combination of adaptive network algorithms and stochastic geometric dynamics has the potential to make a large impact in distributed control and signal processing applications. However, both literatures contain fundamental unsolved problems. The thesis is thus in two main parts. In part I, we consider stochastic differential equations (SDEs) evolving in a matrix Lie group. To undertake any kind of statistical signal processing or control task in this setting requires the simulation of such geometric SDEs. This foundational issue has barely been addressed previously. Chapter 1 contains background and motivation. Chapter 2 develops numerical schemes for simulating SDEs that evolve in SO(n) and SE(n). We propose novel, reliable, efficient schemes based on diagonal Padé approximants, where each trajectory lies in the respective manifold. We prove first order convergence in mean uniform squared error using a new proof technique. Simulations for SDEs in SO(50) are provided. In part II, we study adaptive networks. These are collections of individual agents (nodes) that cooperate to solve estimation, detection, learning and adaptation problems in real time from streaming data, without a fusion center. We study general diffusion LMS algorithms - including real time consensus - for distributed MMSE parameter estimation. This choice is motivated by two major flaws in the literature. First, all analyses assume the regressors are white noise, whereas in practice serial correlation is pervasive. Dealing with it however is much harder than the white noise case. Secondly, since the algorithms operate in real time, we must consider realization-wise behavior. There are no such results. To remedy these flaws, we uncover the mixed time scale structure of the algorithms. We then perform a novel mixed time scale stochastic averaging analysis. Chapter 3 contains background and motivation. Realization-wise stability (chapter 4) and performance including network MSD, EMSE and realization-wise fluctuations (chapter 5) are then studied. We develop results in the difficult but realistic case of serial correlation. We observe that the popular ATC, CTA and real time consensus algorithms are remarkably similar in terms of stability and performance for small constant step sizes. Parts III and IV contain conclusions and future work

"Nested" cryptic diversity in a widespread marine ecosystem engineer: a challenge for detecting biological invasions

<p>Abstract</p> <p>Background</p> <p>Ecosystem engineers facilitate habitat formation and enhance biodiversity, but when they become invasive, they present a critical threat to native communities because they can drastically alter the receiving habitat. Management of such species thus needs to be a priority, but the poorly resolved taxonomy of many ecosystem engineers represents a major obstacle to correctly identifying them as being either native or introduced. We address this dilemma by studying the sea squirt <it>Pyura stolonifera</it>, an important ecosystem engineer that dominates coastal communities particularly in the southern hemisphere. Using DNA sequence data from four independently evolving loci, we aimed to determine levels of cryptic diversity, the invasive or native status of each regional population, and the most appropriate sampling design for identifying the geographic ranges of each evolutionary unit.</p> <p>Results</p> <p>Extensive sampling in Africa, Australasia and South America revealed the existence of "nested" levels of cryptic diversity, in which at least five distinct species can be further subdivided into smaller-scale genetic lineages. The ranges of several evolutionary units are limited by well-documented biogeographic disjunctions. Evidence for both cryptic native diversity and the existence of invasive populations allows us to considerably refine our view of the native versus introduced status of the evolutionary units within <it>Pyura stolonifera </it>in the different coastal communities they dominate.</p> <p>Conclusions</p> <p>This study illustrates the degree of taxonomic complexity that can exist within widespread species for which there is little taxonomic expertise, and it highlights the challenges involved in distinguishing between indigenous and introduced populations. The fact that multiple genetic lineages can be native to a single geographic region indicates that it is imperative to obtain samples from as many different habitat types and biotic zones as possible when attempting to identify the source region of a putative invader. "Nested" cryptic diversity, and the difficulties in correctly identifying invasive species that arise from it, represent a major challenge for managing biodiversity.</p

Guidelines for the use and interpretation of assays for monitoring autophagy (3rd edition)

In 2008 we published the first set of guidelines for standardizing research in autophagy. Since then, research on this topic has continued to accelerate, and many new scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Accordingly, it is important to update these guidelines for monitoring autophagy in different organisms. Various reviews have described the range of assays that have been used for this purpose. Nevertheless, there continues to be confusion regarding acceptable methods to measure autophagy, especially in multicellular eukaryotes. For example, a key point that needs to be emphasized is that there is a difference between measurements that monitor the numbers or volume of autophagic elements (e.g., autophagosomes or autolysosomes) at any stage of the autophagic process versus those that measure fl ux through the autophagy pathway (i.e., the complete process including the amount and rate of cargo sequestered and degraded). In particular, a block in macroautophagy that results in autophagosome accumulation must be differentiated from stimuli that increase autophagic activity, defi ned as increased autophagy induction coupled with increased delivery to, and degradation within, lysosomes (inmost higher eukaryotes and some protists such as Dictyostelium ) or the vacuole (in plants and fungi). In other words, it is especially important that investigators new to the fi eld understand that the appearance of more autophagosomes does not necessarily equate with more autophagy. In fact, in many cases, autophagosomes accumulate because of a block in trafficking to lysosomes without a concomitant change in autophagosome biogenesis, whereas an increase in autolysosomes may reflect a reduction in degradative activity. It is worth emphasizing here that lysosomal digestion is a stage of autophagy and evaluating its competence is a crucial part of the evaluation of autophagic flux, or complete autophagy. Here, we present a set of guidelines for the selection and interpretation of methods for use by investigators who aim to examine macroautophagy and related processes, as well as for reviewers who need to provide realistic and reasonable critiques of papers that are focused on these processes. These guidelines are not meant to be a formulaic set of rules, because the appropriate assays depend in part on the question being asked and the system being used. In addition, we emphasize that no individual assay is guaranteed to be the most appropriate one in every situation, and we strongly recommend the use of multiple assays to monitor autophagy. Along these lines, because of the potential for pleiotropic effects due to blocking autophagy through genetic manipulation it is imperative to delete or knock down more than one autophagy-related gene. In addition, some individual Atg proteins, or groups of proteins, are involved in other cellular pathways so not all Atg proteins can be used as a specific marker for an autophagic process. In these guidelines, we consider these various methods of assessing autophagy and what information can, or cannot, be obtained from them. Finally, by discussing the merits and limits of particular autophagy assays, we hope to encourage technical innovation in the field

Design and Synthesis of Peptidyl-Sulfoxides and Peptidyl-Sulfinamides as Enzyme Inhibitors

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