Applications of Convex Analysis to Signomial and Polynomial Nonnegativity Problems

Here is a question that is easy to state, but often hard to answer: Is this function nonnegative on this set? When faced with such a question, one often makes appeals to known inequalities. One crafts arguments that are sufficient to establish the nonnegativity of the function, rather than determining the function's precise range of values. This thesis studies sufficient conditions for nonnegativity of signomials and polynomials. Conceptually, signomials may be viewed as generalized polynomials that feature arbitrary real exponents, but with variables restricted to the positive orthant. Our methods leverage efficient algorithms for a type of convex optimization known as relative entropy programming (REP). By virtue of this integration with REP, our methods can help answer questions like the following: Is there some function, in this particular space of functions, that is nonnegative on this set? The ability to answer such questions is extremely useful in applied mathematics. Alternative approaches in this same vein (e.g., methods for polynomials based on semidefinite programming) have been used successfully as convex relaxation frameworks for nonconvex optimization, as mechanisms for analyzing dynamical systems, and even as tools for solving nonlinear partial differential equations. This thesis builds from the sums of arithmetic-geometric exponentials or SAGE approach to signomial nonnegativity. The term "exponential" appears in the SAGE acronym because SAGE parameterizes signomials in terms of exponential functions. Our first round of contributions concern the original SAGE approach. We employ basic techniques in convex analysis and convex geometry to derive structural results for spaces of SAGE signomials and exactness results for SAGE-based REP relaxations of nonconvex signomial optimization problems. We frame our analysis primarily in terms of the coefficients of a signomial's basis expansion rather than in terms of signomials themselves. The effect of this framing is that our results for signomials readily transfer to polynomials. In particular, we are led to define a new concept of SAGE polynomials. For sparse polynomials, this method offers an exponential efficiency improvement relative to certificates of nonnegativity obtained through semidefinite programming. We go on to create the conditional SAGE methodology for exploiting convex substructure in constrained signomial nonnegativity problems. The basic insight here is that since the standard relative entropy representation of SAGE signomials is obtained by a suitable application of convex duality, we are free to add additional convex constraints into the duality argument. In the course of explaining this idea we provide some illustrative examples in signomial optimization and analysis of chemical dynamics. The majority of this thesis is dedicated to exploring fundamental questions surrounding conditional SAGE signomials. We approach these questions through analysis frameworks of sublinear circuits and signomial rings. These sublinear circuits generalize simplicial circuits of affine-linear matroids, and lead to rich modes of analysis for sets that are simultaneously convex in the usual sense and convex under a logarithmic transformation. The concept of signomial rings lets us develop a powerful signomial Positivstellensatz and an elementary signomial moment theory. The Positivstellensatz provides for an effective hierarchy of REP relaxations for approaching the value of a nonconvex signomial minimization problem from below, as well as a first-of-its-kind hierarchy for approaching the same value from above. In parallel with our mathematical work, we have developed the sageopt python package. Sageopt drives all the examples and experiments used throughout this thesis, and has been used by engineers to solve high-degree polynomial optimization problems at scales unattainable by alternative methods. We conclude this thesis with an explanation of how our theoretical results affected sageopt's design.</p

Research and Practice in Voice Studies: Searching for a Methodology

As more and more actor training conservatoires become subsumed into university structures there is a growing pressure on practice based teachers of voice to become active researchers. At the same time there is a growing area of scholarly research within Voice Studies. This article examines the shifting patterns of research and practice within Voice Studies and uses, as a case study, the author’s experiences of teaching at the Royal Central School of Speech and Drama (RCSSD). The author examines tensions between practice and research within a conservatoire setting and explores potential research methodologies in relation to this. The author proposes Practice as Research (PaR) as a suitable methodology for research within practice based Voice Studies and draws on current discourses relating to PaR within Theatre and Performance. The author proposes a model for Voice Studies PaR, which is based on the work of Robin Nelson, and demonstrates how this is being applied within Voice Studies research at RCSSD. The author addresses issues of dissemination of PaR and briefly relates the work in the UK to growing research agendas internationally

Withstand Tests: More Than Meets the Eye

Presented at the Insulated Conductors Committee, San Antonio, Texas, October 26-29, 2008.This material is based upon work supported by the Department of Energy under Award No DE-FC02-04CH1237 and CDFI

Probing the Black Hole Engine with Measurements of the Relativistic X-ray Reflection Component

Over the last decades X-ray spectroscopy has proven to be a powerful tool for the estimation of black hole spin and several other key parameters in dozens of AGN and black hole X-ray binaries. In this White Paper, we discuss the observational and theoretical challenges expected in the exploration, discovery, and study of astrophysical black holes in the next decade. We focus on the case of accreting black holes and their electromagnetic signatures, with particular emphasis on the measurement of the relativistic reflection component in their X-ray spectra.Comment: Astro 2020 Decadal science White Pape

Resistance of Leishmania (Leishmania) amazonensis and Leishmania (Viannia) braziliensis to nitric oxide correlates with disease severity in Tegumentary Leishmaniasis

BACKGROUND: Nitric oxide (NO(•)) plays a pivotal role as a leishmanicidal agent in mouse macrophages. NO(• )resistant Escherichia coli and Mycobacterium tuberculosis have been associated with a severe outcome of these diseases. METHODS: In this study we evaluated the in vitro toxicity of nitric oxide for the promastigote stages of Leishmania (Viannia) braziliensis and Leishmania (Leishmania) amazonensis parasites, and the infectivity of the amastigote stage for human macrophages. Parasites were isolated from patients with cutaneous, mucosal or disseminated leishmaniasis, and NO(• )resistance was correlated with clinical presentation. RESULTS: Seventeen isolates of L. (L.) amazonensis or L. (V.) braziliensis promastigotes were killed by up to 8 mM of more of NaNO(2 )(pH 5.0) and therefore were defined as nitric oxide-susceptible. In contrast, eleven isolates that survived exposure to 16 mM NaNO(2 )were defined as nitric oxide-resistant. Patients infected with nitric oxide-resistant Leishmania had significantly larger lesions than patients infected with nitric oxide-susceptible isolates. Furthermore, nitric oxide-resistant L. (L.) amazonensis and L. (V.) braziliensis multiplied significantly better in human macrophages than nitric oxide-susceptible isolates. CONCLUSION: These data suggest that nitric oxide-resistance of Leishmania isolates confers a survival benefit for the parasites inside the macrophage, and possibly exacerbates the clinical course of human leishmaniasis

The structure of the KlcA and ArdB proteins reveals a novel fold and antirestriction activity against Type I DNA restriction systems in vivo but not in vitro

Plasmids, conjugative transposons and phage frequently encode anti-restriction proteins to enhance their chances of entering a new bacterial host that is highly likely to contain a Type I DNA restriction and modification (RM) system. The RM system usually destroys the invading DNA. Some of the anti-restriction proteins are DNA mimics and bind to the RM enzyme to prevent it binding to DNA. In this article, we characterize ArdB anti-restriction proteins and their close homologues, the KlcA proteins from a range of mobile genetic elements; including an ArdB encoded on a pathogenicity island from uropathogenic Escherichia coli and a KlcA from an IncP-1b plasmid, pBP136 isolated from Bordetella pertussis. We show that all the ArdB and KlcA act as anti-restriction proteins and inhibit the four main families of Type I RM systems in vivo, but fail to block the restriction endonuclease activity of the archetypal Type I RM enzyme, EcoKI, in vitro indicating that the action of ArdB is indirect and very different from that of the DNA mimics. We also present the structure determined by NMR spectroscopy of the pBP136 KlcA protein. The structure shows a novel protein fold and it is clearly not a DNA structural mimic

X-ray emission from the Sombrero galaxy: discrete sources

We present a study of discrete X-ray sources in and around the bulge-dominated, massive Sa galaxy, Sombrero (M104), based on new and archival Chandra observations with a total exposure of ~200 ks. With a detection limit of L_X = 1E37 erg/s and a field of view covering a galactocentric radius of ~30 kpc (11.5 arcminute), 383 sources are detected. Cross-correlation with Spitler et al.'s catalogue of Sombrero globular clusters (GCs) identified from HST/ACS observations reveals 41 X-rays sources in GCs, presumably low-mass X-ray binaries (LMXBs). We quantify the differential luminosity functions (LFs) for both the detected GC and field LMXBs, whose power-low indices (~1.1 for the GC-LF and ~1.6 for field-LF) are consistent with previous studies for elliptical galaxies. With precise sky positions of the GCs without a detected X-ray source, we further quantify, through a fluctuation analysis, the GC LF at fainter luminosities down to 1E35 erg/s. The derived index rules out a faint-end slope flatter than 1.1 at a 2 sigma significance, contrary to recent findings in several elliptical galaxies and the bulge of M31. On the other hand, the 2-6 keV unresolved emission places a tight constraint on the field LF, implying a flattened index of ~1.0 below 1E37 erg/s. We also detect 101 sources in the halo of Sombrero. The presence of these sources cannot be interpreted as galactic LMXBs whose spatial distribution empirically follows the starlight. Their number is also higher than the expected number of cosmic AGNs (52+/-11 [1 sigma]) whose surface density is constrained by deep X-ray surveys. We suggest that either the cosmic X-ray background is unusually high in the direction of Sombrero, or a distinct population of X-ray sources is present in the halo of Sombrero.Comment: 11 figures, 5 tables, ApJ in pres

Placentation defects are highly prevalent in embryonic lethal mouse mutants.

Large-scale phenotyping efforts have demonstrated that approximately 25-30% of mouse gene knockouts cause intrauterine lethality. Analysis of these mutants has largely focused on the embryo and not the placenta, despite the crucial role of this extraembryonic organ for developmental progression. Here we screened 103 embryonic lethal and sub-viable mouse knockout lines from the Deciphering the Mechanisms of Developmental Disorders program for placental phenotypes. We found that 68% of knockout lines that are lethal at or after mid-gestation exhibited placental dysmorphologies. Early lethality (embryonic days 9.5-14.5) is almost always associated with severe placental malformations. Placental defects correlate strongly with abnormal brain, heart and vascular development. Analysis of mutant trophoblast stem cells and conditional knockouts suggests that a considerable number of factors that cause embryonic lethality when ablated have primary gene function in trophoblast cells. Our data highlight the hugely under-appreciated importance of placental defects in contributing to abnormal embryo development and suggest key molecular nodes that govern placenta formation