The Continuous Skolem-Pisot Problem: On the Complexity of Reachability for Linear Ordinary Differential Equations

We study decidability and complexity questions related to a continuous analogue of the Skolem-Pisot problem concerning the zeros and nonnegativity of a linear recurrent sequence. In particular, we show that the continuous version of the nonnegativity problem is NP-hard in general and we show that the presence of a zero is decidable for several subcases, including instances of depth two or less, although the decidability in general is left open. The problems may also be stated as reachability problems related to real zeros of exponential polynomials or solutions to initial value problems of linear differential equations, which are interesting problems in their own right.Comment: 14 pages, no figur

Computational problems in matrix semigroups

This thesis deals with computational problems that are defined on matrix semigroups, which playa pivotal role in Mathematics and Computer Science in such areas as control theory, dynamical systems, hybrid systems, computational geometry and both classical and quantum computing to name but a few. Properties that researchers wish to study in such fields often turn out to be questions regarding the structure of the underlying matrix semigroup and thus the study of computational problems on such algebraic structures in linear algebra is of intrinsic importance. Many natural problems concerning matrix semigroups can be proven to be intractable or indeed even unsolvable in a formal mathematical sense. Thus, related problems concerning physical, chemical and biological systems modelled by such structures have properties which are not amenable to algorithmic procedures to determine their values. With such recalcitrant problems we often find that there exists a tight border between decidability and undecidability dependent upon particular parameters of the system. Examining this border allows us to determine which properties we can hope to derive algorithmically and those problems which will forever be out of our reach, regardless of any future advances in computational speed. There are a plethora of open problems in the field related to dynamical systems, control theory and number theory which we detail throughout this thesis. We examine undecidability in matrix semigroups for a variety of different problems such as membership and vector reachability problems, semigroup intersection emptiness testing and freeness, all of which are well known from the literature. We also formulate and survey decidability questions for several new problems such as vector ambiguity, recurrent matrix problems, the presence of any diagonal matrix and quaternion matrix semigroups, all of which we feel give a broader perspective to the underlying structure of matrix semigroups

Exploring the Moon's surface for remnants of the lunar mantle 1. Dunite xenoliths in mare basalts. A crustal or mantle origin?

Remotely sensed observations from recent missions (e.g., GRAIL, Kaguya, Chandrayaan-1) have been interpreted as indicating that the deep crust and upper mantle are close to or at the lunar surface in many large impact basins (e.g., Crisium, Apollo, Moscoviense). If this is correct, the capability of either impact or volcanic processes to transport mantle lithologies to the lunar surface should be enhanced in these regions. Somewhat problematic to these observations and interpretations is that examples of mantle lithologies in the lunar sample collection (Apollo Program, Luna Program, lunar meteorites) are at best ambiguous. Dunite xenoliths in high-Ti mare basalt 74275 are one of these ambiguous examples. In this high-Ti mare basalt, olivine occurs in three generations: olivine associated with dunite xenoliths, olivine megacrysts, and olivine microphenocrysts. The dunite xenoliths are anhedral in shape and are generally greater than 800 μm in diameter. The interior of the xenoliths are fairly homogeneous with regard to many divalent cations. For example, the Mg# (Mg/Mg + Fe × 100) ranges from 82 to 83 in their interiors and decreases from 82 to 68 over the 10–30 μm wide outer rim. Titanium and phosphorus X-ray maps of the xenolith illustrate that these slow diffusing elements preserve primary cumulate zoning textures. These textures indicate that the xenoliths consist of many individual olivine grains approximately 150–200 μm in diameter with low Ti, Al, and P cores. These highly incompatible elements are enriched in the outer Fe-rich rims of the xenoliths and slightly enriched in the rims of the individual olivine grains. Highly compatible elements in olivine such as Ni exhibit a decrease in the rim surrounding the xenolith, an increase in the incompatible element depleted cores of the individual olivine grains, and a slight decrease in the “interior rims” of the individual olivine grains. Inferred melt composition, liquid lines of descent, and zoning profiles enable the reconstruction of the petrogenesis of the dunite xenoliths. Preservation of primary magmatic zoning (Ti, P, Al) and lack of textures similar to high-pressure mineral assemblages exhibited by the Mg-suite (Shearer et al. 2015) indicate that these xenoliths do not represent deep crustal or shallow mantle lithologies. Further, they are chemically and mineralogically distinct from Mg-suite dunites identified from the Apollo 17 site. More likely, they represent olivine cumulates that crystallized from a low-Ti mare basalt at intermediate to shallow crustal levels. The parent basalt to the dunite xenolith lithology was more primitive than low-Ti basalts thus far returned from the Moon. Furthermore, this parental magma and its more evolved daughter magmas are not represented in the basalt sample suite returned from the Taurus-Littrow Valley by the Apollo 17 mission. The dunite xenolith records several episodes of crystallization and re-equilibration. During the last episode of re-equilibration, the dunite cumulate was sampled by the 74275 high-Ti basalt and transported over a period of 30–70 days to the lunar surface

The Cr Redox Record of fO2 Variation in Angrites. Evidence for Redox Conditions of Angrite Petrogenesis and Parent Body

Angrites represent some of the earliest stages of planetesimal differentiation. Not surprisingly, there is no simple petrogenetic model for their origin. Petrogenesis has been linked to both magmatic and impact processes. Studies demonstrated that melting of chondritic material (e.g. CM, CV) at redox conditions where pure iron metal is unstable (e.g., IW+1 to IW+2) produced angrite-like melts. Alternatively, angrites were produced at more reducing conditions (<IW) with their exotic melt compositions resulting from carbonates in the source or from nebular condensation. Clearly, understanding what role fO2 plays in producing angrite magmas is critical for deciphering their petrogenesis and extending our understanding of primordial melting of asteroids. Calculations for the fO2 conditions of angrite crystallization are limited, and only preliminary attempts been made to understand the changes in fO2 that occurred during petrogenesis. Many of the angrites have phase assemblages which provide conflicting signals about redox conditions during crystallization (e.g., Fe metal and a Fe-Ti oxide with potential Fe3+. There have been several estimates of fO2 for angrites. Most notably, experiments examined the variation of DEu/DGd with fO2, between plagioclase and fassaitic pyroxene in equilibrium with an angrite melt composition. They used their observations to estimate the fO2 of crystallization to be approximately IW+0.6 for angrite LEW 86010. This estimate is only a "snapshot" of fO2 conditions during co-crystallization of plagioclase and pyroxene. Preliminary XANES analyses of V redox state in pyroxenes from D'Orbigny reported changes in fO2 from IW-0.7 during early pyroxene crystallization to IW+0.5 during latter episodes of pyroxene crystallization [15]. As this was a preliminary report, it presented limited information concerning the effects of pyroxene orientation and composition on the V valence measurements, and the effect of melt composition on valence and partitioning behavior of V. A closer examination of fO2 as recorded by Cr valence state in olivine will allow us to test models for primordial melting of chondritic material to produce the angrite parent melts. Here, we report the our initial stages of examining the origin and conditions of primordial melting on the angrite parent body and test some of the above models by integrating an experimental study of Cr and V valence partitioning between olivine [OL] and an angrite melt, with micro-scale determinations of Cr and V oxidation state in OL in selected "volcanic" angrites

A Serpin shapes the extracellular environment to prevent influenza A virus maturation

Interferon-stimulated genes (ISGs) act in concert to provide a tight barrier against viruses. Recent studies have shed light on the contribution of individual ISG effectors to the antiviral state, but most have examined those acting on early, intracellular stages of the viral life cycle. Here, we applied an image-based screen to identify ISGs inhibiting late stages of influenza A virus (IAV) infection. We unraveled a directly antiviral function for the gene SERPINE1, encoding plasminogen activator inhibitor 1 (PAI-1). By targeting extracellular airway proteases, PAI-1 inhibits IAV glycoprotein cleavage, thereby reducing infectivity of progeny viruses. This was biologically relevant for IAV restriction in vivo. Further, partial PAI-1 deficiency, attributable to a polymorphism in human SERPINE1, conferred increased susceptibility to IAV in vitro. Together, our findings reveal that manipulating the extracellular environment to inhibit the last step in a virus life cycle is an important mechanism of the antiviral response

The Mineralogical Record of Oxygen Fugacity Variation and Alteration in Northwest Africa 8159: Evidence for Interaction Between a Mantle Derived Martian Basalt and a Crustal Component(s)

A prominent geochemical feature of basaltic magmatism on Mars is the large range in initial Sr isotopic ratios (approx. 0.702 - 0.724) and initial epsilon-Nd values (approx. -10 to greater than +50). Within this range, the shergottites fall into three discreet subgroups. These subgroups have distinct bulk rock REE patterns, mineral chemistries (i.e. phosphate REE patterns, Ni, Co, V in olivine), oxygen fugacity of crystallization, and stable isotopes, such as O. In contrast, nakhlites and chassignites have depleted epsilon-Nd values (greater than or equal to +15), have REE patterns that are light REE enriched, and appear to have crystallized near the FMQ buffer. The characteristics of these various martian basalts have been linked to different reservoirs in the martian crust and mantle, and their interactions during the petrogenesis of these magmas. These observations pose interesting interpretive challenges to our understanding of the conditions of the martian mantle (e.g. oxygen fugacity) and the interaction of mantle derived magmas with the martian crust and surface. Martian meteorite NWA 8159 is a unique fine-grained augite basalt derived from a highly depleted mantle source as reflected in its initial epsilon-Nd value, contains a pronounced light REE depleted pattern, and crystallized presumably under very oxidizing conditions. Although considerably older than both shergottites and nahklites, it has been petrogenetically linked to both styles of martian magmatism. These unique characteristics of NWA 8159 may provide an additional perspective for deciphering the petrogenesis of martian basalts and the nature of the crust of Mars

Progress and challenges in incorporating climate change information into transportation research and design

The vulnerability of our nation\u27s transportation infrastructure to climate change and extreme weather is now well documented and the transportation community has identified numerous strategies to potentially mitigate these vulnerabilities. The challenges to the infrastructure sector presented by climate change can only be met through collaboration between the climate science community, who evaluate what the future will likely look like, and the engineering community, who implement our societal response. To facilitate this process, the authors asked: what progress has been made and what needs to be done now in order to allow for the graceful convergence of these two disciplines? In late 2012, the Infrastructure and Climate Network (ICNet), a National Science Foundation-supported research collaboration network, was established to answer that question. This article presents examples of how the ICNet experience has shown the way toward a new generation of innovation and cross-disciplinary research, challenges that can be address by such collaboration, and specific guidance for partnerships and methods to effectively address complex questions requiring a cogeneration of knowledge

“What if There's Something Wrong with Her?”‐How Biomedical Technologies Contribute to Epistemic Injustice in Healthcare

While there is a steadily growing literature on epistemic injustice in healthcare, there are few discussions of the role that biomedical technologies play in harming patients in their capacity as knowers. Through an analysis of newborn and pediatric genetic and genomic sequencing technologies (GSTs), I argue that biomedical technologies can lead to epistemic injustice through two primary pathways: epistemic capture and value partitioning. I close by discussing the larger ethical and political context of critical analyses of GSTs and their broader implications for just and equitable healthcare delivery

1946: Abilene Christian College Bible Lectures - Full Text

Abilene Christian College Lectures - 1946 INTRODUCTION It has been our purpose at Abilene Christian College down through the years to provide in the Annual Bible Lectureship programs that which would be appropriate for the time and most useful to the students and to the Lectureship visitors. The general subject for the 1946 lectures is “Things That Cannot Be Shaken.” This subject was selected because one of the battles, if not the battle, which the church faces today is against those forces which would undermine the bases of gospel truth. Many denominational leaders, in one way or another, are denying even the fundamentals of fundamentals— God is, the Bible is God\u27s Revelation, Jesus Christ is the Son of God and The Kingdom Cannot Be Shaken. Many others, some without knowing what they do, are accepting false teachings and ideologies which, if allowed to run their course, will destroy all true religion. It is believed that the 1946 lectures and this edition of the lectures will help toward establishing in the hearts of men the truth of the important theses discussed. It was the purpose of those who arranged the program that the Lectureship should, also, hold up Christianity as a working, practical religion; hence, the meetings on “Work in New Fields” and “The Church at Work.” The attendance of this Lectureship was the largest in the history of these yearly meetings. On Wednesday evening Brother Nichol spoke to a crowd of approximately 1700 persons. Other evening lectures were attended by crowds almost as large. Visitors came from more than a score of States and, also, from Canada and Mexico. It is the hope of all of us at the College that the fellowship of the 1946 Lectureship and the instruction given by the various speakers will continue to do good for years without end. DON H. MORRIS