The Martingale Approach to Financial Mathematics

In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In considering a slightly more complicated model over a finite probability space, we see that Q once again makes its appearance. Finally, in the context of continuous time, we build a framework of stochastic calculus to model the trajectories of asset prices on a finite time interval. Under the absence of arbitrage once more, we see that Q makes its return as a Radon-Nikodym derivative of our initial probability measure. Finally, we use the properties of Q and a stochastic differential equation that models the dynamics of the assets of our market, known as the Ito formula, in order to derive the classic Black-Scholes Equation

Long Non-Coding RNA in Controlling Chromatin Modification and Transcription.

Long non-coding RNAs (lncRNAs) are present in many eukaryotes and have an important function in controlling transcription. In the Transcriptional Gene Silencing (TGS) pathway lncRNAs can act as scaffolds for RNA binding proteins to target specific loci and affect chromatin structure. In many organisms genetic studies of TGS are limited because lncRNAs are produced by RNA Polymerase II (Pol II), the same polymerase responsible for transcribing protein coding genes. This limitation is overcome by using the model organism Arabidopsis thaliana in which lncRNA is produced by Pol V. Pol V is a specialized RNA polymerase which recently has evolutionarily diverged from Pol II in plants. Knockout mutants of Pol V allow the study of pathways involving lncRNA without disrupting the essential Pol II machinery. This tool has allowed discovery of many mechanistic principles of TGS. In this pathway, ARGONAUTE 4 binds to small interfering RNA (siRNA) and to lncRNA for chromatin targeting. Other proteins, SUPRESSOR OF TY INSERTION 5-LIKE (SPT5L) and INVOLVED IN DE NOVO 2 (IDN2) also bind to Pol V transcripts and are important for TGS. Components of TGS are essential for directing histone modification and de novo DNA methylation to affect Pol II transcription at specific loci. While this was thought to mainly occur to silence transposons, this work shows that TGS components localize to promoters and function in controlling gene expression. I also demonstrate that TGS is important for positioning nucleosomes, and that AGO4, IDN2, and SPT5L are all important for this function. This is in contrast to directing DNA methylation where AGO4 plays a large role, while the contribution of SPT5L and IDN2 is minor. I also find that TGS can control gene expression long-range by inhibiting long distance chromatin interactions. Overall this work revolutionizes how we think of TGS and is a major contribution to the mechanistic knowledge on the functions of lncRNA.PHDMolecular, Cellular and Developmental BiologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/110415/1/mjrowley_1.pd

RNA polymerase V targets transcriptional silencing components to promoters of protein‐coding genes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/1/tpj12034-sup-0010-TableS1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/2/tpj12034-sup-0006-FigureS4.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/3/tpj12034-sup-0007-FigureS5.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/4/tpj12034-sup-0003-FigureS1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/5/tpj12034-sup-0008-FigureS6.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/6/tpj12034-sup-0005-FigureS3.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/7/tpj12034-sup-0004-FigureS2.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/8/tpj12034-sup-0009-FigureS7.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/9/tpj12034.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96338/10/tpj12034-sup-0002-MethodsS1.pd

Rapid and highly variable warming of lake surface waters around the globe

In this first worldwide synthesis of in situ and satellite‐derived lake data, we find that lake summer surface water temperatures rose rapidly (global mean = 0.34°C decade−1) between 1985 and 2009. Our analyses show that surface water warming rates are dependent on combinations of climate and local characteristics, rather than just lake location, leading to the counterintuitive result that regional consistency in lake warming is the exception, rather than the rule. The most rapidly warming lakes are widely geographically distributed, and their warming is associated with interactions among different climatic factors—from seasonally ice‐covered lakes in areas where temperature and solar radiation are increasing while cloud cover is diminishing (0.72°C decade−1) to ice‐free lakes experiencing increases in air temperature and solar radiation (0.53°C decade−1). The pervasive and rapid warming observed here signals the urgent need to incorporate climate impacts into vulnerability assessments and adaptation efforts for lakes

ETV6 germline mutations cause HDAC3/NCOR2 mislocalization and upregulation of interferon response genes

ETV6 is an ETS family transcription factor that plays a key role in hematopoiesis and megakaryocyte development. Our group and others have identified germline mutations in ETV6 resulting in autosomal dominant thrombocytopenia and predisposition to malignancy; however, molecular mechanisms defining the role of ETV6 in megakaryocyte development have not been well established. Using a combination of molecular, biochemical, and sequencing approaches in patient-derived PBMCs, we demonstrate abnormal cytoplasmic localization of ETV6 and the HDAC3/NCOR2 repressor complex that led to overexpression of HDAC3-regulated interferon response genes. This transcriptional dysregulation was also reflected in patient-derived platelet transcripts and drove aberrant proplatelet formation in megakaryocytes. Our results suggest that aberrant transcription may predispose patients with ETV6 mutations to bone marrow inflammation, dysplasia, and megakaryocyte dysfunction

Recent experimental results in sub- and near-barrier heavy ion fusion reactions

Recent advances obtained in the field of near and sub-barrier heavy-ion fusion reactions are reviewed. Emphasis is given to the results obtained in the last decade, and focus will be mainly on the experimental work performed concerning the influence of transfer channels on fusion cross sections and the hindrance phenomenon far below the barrier. Indeed, early data of sub-barrier fusion taught us that cross sections may strongly depend on the low-energy collective modes of the colliding nuclei, and, possibly, on couplings to transfer channels. The coupled-channels (CC) model has been quite successful in the interpretation of the experimental evidences. Fusion barrier distributions often yield the fingerprint of the relevant coupled channels. Recent results obtained by using radioactive beams are reported. At deep sub-barrier energies, the slope of the excitation function in a semi-logarithmic plot keeps increasing in many cases and standard CC calculations over-predict the cross sections. This was named a hindrance phenomenon, and its physical origin is still a matter of debate. Recent theoretical developments suggest that this effect, at least partially, may be a consequence of the Pauli exclusion principle. The hindrance may have far-reaching consequences in astrophysics where fusion of light systems determines stellar evolution during the carbon and oxygen burning stages, and yields important information for exotic reactions that take place in the inner crust of accreting neutron stars.Comment: 40 pages, 63 figures, review paper accepted for EPJ

Post-depositional fracturing and subsidence of pumice flow deposits: Lascar Volcano, Chile

Unconsolidated pyroclastic flow deposits of the 1993 eruption of Lascar Volcano, Chile, have, with time, become increasingly dissected by a network of deeply penetrating fractures. The fracture network comprises orthogonal sets of decimeter-wide linear voids that form a pseudo-polygonal grid visible on the deposit surface. In this work, we combine shallow surface geophysical imaging tools with remote sensing observations and direct field measurements of the deposit to investigate these fractures and their underlying causal mechanisms. Based on ground penetrating radar images, the fractures are observed to have propagated to depths of up to 10 m. In addition, orbiting radar interferometry shows that deposit subsidence of up to 1 cm/year occurred between 1993 and 1996 with continued subsidence occurring at a slower rate thereafter. In situ measurements show that 1 m below the surface, the 1993 deposits remain 5°C to 15°C hotter, 18 years after emplacement, than adjacent deposits. Based on the observed subsidence as well as estimated cooling rates, the fractures are inferred to be the combined result of deaeration, thermal contraction, and sedimentary compaction in the months to years following deposition. Significant environmental factors, including regional earthquakes in 1995 and 2007, accelerated settling at punctuated moments in time. The spatially variable fracture pattern relates to surface slope and lithofacies variations as well as substrate lithology. Similar fractures have been reported in other ignimbrites but are generally exposed only in cross section and are often attributed to formation by external forces. Here we suggest that such interpretations should be invoked with caution, and deformation including post-emplacement subsidence and fracturing of loosely packed ash-rich deposits in the months to years postemplacement is a process inherent in the settling of pyroclastic material

Three-dimensional genome architecture persists in a 52,000-year-old woolly mammoth skin sample

Analyses of ancient DNA typically involve sequencing the surviving short oligonucleotides and aligning to genome assemblies from related, modern species. Here, we report that skin from a female woolly mammoth (†Mammuthus primigenius) that died 52,000 years ago retained its ancient genome architecture. We use PaleoHi-C to map chromatin contacts and assemble its genome, yielding 28 chromosome-length scaffolds. Chromosome territories, compartments, loops, Barr bodies, and inactive X chromosome (Xi) superdomains persist. The active and inactive genome compartments in mammoth skin more closely resemble Asian elephant skin than other elephant tissues. Our analyses uncover new biology. Differences in compartmentalization reveal genes whose transcription was potentially altered in mammoths vs. elephants. Mammoth Xi has a tetradic architecture, not bipartite like human and mouse. We hypothesize that, shortly after this mammoth's death, the sample spontaneously freeze-dried in the Siberian cold, leading to a glass transition that preserved subfossils of ancient chromosomes at nanometer scale