Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic

In analogy with the Riemann zeta function at positive integers, for each finite field F_p^r with fixed characteristic p we consider Carlitz zeta values zeta_r(n) at positive integers n. Our theorem asserts that among the zeta values in {zeta_r(1), zeta_r(2), zeta_r(3), ... | r = 1, 2, 3, ...}, all the algebraic relations are those algebraic relations within each individual family {zeta_r(1), zeta_r(2), zeta_r(3), ...}. These are the algebraic relations coming from the Euler-Carlitz relations and the Frobenius relations. To prove this, a motivic method for extracting algebraic independence results from systems of Frobenius difference equations is developed.Comment: 14 page

Lossless convexification of optimal control problems

textThis dissertation begins with an introduction to finite-dimensional optimization and optimal control theory. It then proves lossless convexification for three problems: 1) a minimum time rendezvous using differential drag, 2) a maximum divert and landing, and 3) a general optimal control problem with linear state constraints and mixed convex and non-convex control constraints. Each is a unique contribution to the theory of lossless convexification. The first proves lossless convexification in the presence of singular controls and specifies a procedure for converting singular controls to the bang-bang type. The second is the first example of lossless convexification with state constraints. The third is the most general result to date. It says that lossless convexification holds when the state space is a strongly controllable subspace. This extends the controllability concepts used previously, and it recovers earlier results as a special case. Lastly, a few of the remaining research challenges are discussed.Aerospace Engineerin

Data Quality Assessment of Continuous Forest Inventory on State Forest Lands in Tennessee

The Tennessee Division of Forestry (TDF) implemented a Continuous Forest Inventory (CFI) system in 2009 for the 15 state forests, encompassing multiple physiographic land types and forest types. The initial design contained plans to measure the plots on five-year intervals. The objectives of the CFI system include: determining the growth by species and forest types for all state forest land, estimating growth models for individual trees in mixed hardwood stands, developing a harvest schedule, and assessing the impact of different silvicultural treatments over time. Following the implementation, the University of Tennessee Department of Forestry, Wildlife and Fisheries was asked to assess the study. The objectives for this assessment were to: assess the data quality of the initial plot measurements and identify inconsistencies; determine the usefulness of the Forest Vegetation Simulator (FVS) in producing accurate estimates of current volume per acre (VPA); and evaluate the current inventory design. In order to produce future growth estimates, an accurate estimate of the current inventory is needed. Known relationships in forestry were used to establish metrics for assessing the quality of the plot measurements. Two estimates of volume were used in this study: Lasher’s equation contained in FVS and the d2H (diameter and height) equation used by FIA. The FVS equation consistently over estimated volume at the acre level and individual tree level. The overall design was determined to be inadequate for providing information by forest type within each state forest. This can be remedied by utilizing stratified samples by delineating each forest by its forest type. The results of this investigation will provide a starting point for improving the work already conducted by the Division in regards to quantifying the current inventory of the Tennessee State Forest system

Thermodynamic modelling of synthetic communities predicts minimum free energy requirements for sulfate reduction and methanogenesis

Microbial communities are complex dynamical systems harbouring many species interacting together to implement higher-level functions. Among these higher-level functions, conversion of organic matter into simpler building blocks by microbial communities underpins biogeochemical cycles and animal and plant nutrition, and is exploited in biotechnology. A prerequisite to predicting the dynamics and stability of community-mediated metabolic conversions is the development and calibration of appropriate mathematical models. Here, we present a generic, extendable thermodynamic model for community dynamics and calibrate a key parameter of this thermodynamic model, the minimum energy requirement associated with growth-supporting metabolic pathways, using experimental population dynamics data from synthetic communities composed of a sulfate reducer and two methanogens. Our findings show that accounting for thermodynamics is necessary in capturing the experimental population dynamics of these synthetic communities that feature relevant species using low energy growth pathways. Furthermore, they provide the first estimates for minimum energy requirements of methanogenesis (in the range of −30 kJ mol−1) and elaborate on previous estimates of lactate fermentation by sulfate reducers (in the range of −30 to −17 kJ mol−1 depending on the culture conditions). The open-source nature of the developed model and demonstration of its use for estimating a key thermodynamic parameter should facilitate further thermodynamic modelling of microbial communities

Femtosecond Laser-Assisted In Situ Keratomileusis Treatment of Residual Refractive Error following Femtosecond Laser-Enabled Keratoplasty.

Purpose:To evaluate the safety and effectiveness of femtosecond laser-assisted in situ keratomileusis (LASIK) in the treatment of residual myopia and astigmatism following femtosecond laser-enabled keratoplasty (FLEK). Design:Retrospective case review. Methods:Chart review of all patients with prior FLEK who subsequently underwent femto-LASIK surgery after full suture removal was performed at the Gavin Herbert Eye Institute at the University of California, Irvine. A total of 14 eyes in 13 patients met this criterion, and their comprehensive examinations performed at standard intervals were reviewed. Main outcome measures include uncorrected distance visual acuity (UDVA) and corrected distance visual acuity (CDVA) expressed as the logarithm of the minimum angle of resolution (logMAR), manifest refractive astigmatism, and spherical equivalent. Results:From the preoperative visit to the 3 month visit, all 14 eyes significantly improved in UDVA (logMAR, 0.93 ± 0.23 to 0.44 ± 0.32, P = 0.002) with no loss of CDVA (logMAR, 0.26 ± 0.19 to 0.18 ± 0.23, P = 0.50). All 14 eyes showed significant improvement in manifest refractive astigmatism (4.71 ± 1.77 to 2.18 ± 1.45 diopters (D), P = 0.003) and spherical equivalent (-2.57 ± 2.45 to -0.48 ± 0.83 D, P = 0.0007). There were no flap or graft complications as a result of femto-LASIK. Conclusions:Our findings suggest that femto-LASIK on eyes with prior FLEK is safe and effective in improving visual acuity and reducing residual astigmatism

Assemblin Homolog of Herpes Simplex Virus Type 1 Retains Proteolytic Activity When Expressed as a Recombinant Two-Chain Enzyme

AbstractThe herpes simplex virus type 1 (HSV) maturational proteinase is synthesized as a precursor that undergoes two autoproteolytic cleavages; one at its (M)aturational site, which eliminates its carboxyl “tail,” and a second at its (R)elease site, which separates the amino proteolytic half of the precursor from its nonproteolytic carboxyl half. In cytomegalovirus (CMV) the proteolytic half of the precursor, called assemblin, undergoes a third cleavage at an (I)nternal site that converts it from a single-chain to a two-chain enzyme that retains activity. The HSV assemblin homolog has no I site and therefore does not form a counterpart two-chain enzyme. In the work reported here we have cloned and expressed HSV sequences that encode mimics of the Anand Acsubunits of two-chain CMV assemblin. We show that when these HSV sequences are coexpressed in eukaryotic cells, the resulting subunits associate spontaneously to form an active two-chain enzyme. We also show that the two-chain HSV enzyme, like the natural one-chain form, retains its marked preference for HSV over CMV substrates, and that intertypic recombinant two-chain assemblin (e.g., HSV An/CMV Ac) does not form because the cross-species subunits do not interact. We conclude from these results that (i) there are not intrinsic structural differences in the HSV assemblin homolog that preclude its functioning as a CMV-like two-chain enzyme, (ii) the substrate selectivity shown by the single-chain HSV enzyme was not noticeably relaxed in the HSV two-chain mimic, and (iii) the interactive domains, through which the Anand Acportions of the single-chain enzymes associate, differ between HSV and CMV

Student Support Services and the Behavioral Intervention Team | Brownbag Series

Bring your lunch and learn from your colleagues! Brownbag lunch presentations will be held four times this semester with different faculty members presenting topics that may be helpful to you