The Hodge--Poincar\'e polynomial of the moduli spaces of stable vector bundles over an algebraic curve

Let X be a nonsingular complex projective variety that is acted on by a reductive group $G$ and such that $X^{ss} \neq X_{(0)}^{s}\neq \emptyset$. We give formulae for the Hodge--Poincar\'e series of the quotient $X_{(0)}^s/G$. We use these computations to obtain the corresponding formulae for the Hodge--Poincar\'e polynomial of the moduli space of properly stable vector bundles when the rank and the degree are not coprime. We compute explicitly the case in which the rank equals 2 and the degree is even.Comment: Final published version. arXiv admin note: text overlap with arXiv:math/0305346, arXiv:math/0305347 by other author

Improved hydrogen gas production in microbial electrolysis cells using inexpensive recycled carbon fibre fabrics

Growing energy demands of wastewater treatment have made it vital for water companies to develop less energy intensive processes for treating wastewater if net zero emissions are to be achieved by 2050. Microbial electrolysis cells (MECs) have the potential to do this by treating water and producing renewable hydrogen gas as a product, but capital and operational costs have slowed their deployment. By using recycled carbon fibre mats, commercially viable MECs can brought closer to reality, where recycled carbon fibre anode MECs treating real wastewater (normalised ~3100 L d−1) were producing 66.77 L H2 d−1 while graphite felt anode MECs produced 3.65 L H2 d−1 per 1 m3 reactor, anodes costing £5.53 m−2 and £88.36 m−2 respectively, resulting in a total anode cost saving of 93%. This could incentivise the development of larger pilot systems, opening the door for generating greater value and a more sustainable wastewater treatment industry

On the Equivalence Problem for Toric Contact Structures on S^3-bundles over S^2$

We study the contact equivalence problem for toric contact structures on $S^3$-bundles over $S^2$. That is, given two toric contact structures, one can ask the question: when are they equivalent as contact structures while inequivalent as toric contact structures? In general this appears to be a difficult problem. To find inequivalent toric contact structures that are contact equivalent, we show that the corresponding 3-tori belong to distinct conjugacy classes in the contactomorphism group. To show that two toric contact structures with the same first Chern class are contact inequivalent, we use Morse-Bott contact homology. We treat a subclass of contact structures which include the Sasaki-Einstein contact structures $Y^{p,q}$ studied by physicists. In this subcase we give a complete solution to the contact equivalence problem by showing that $Y^{p,q}$ and $Y^{p'q'}$ are inequivalent as contact structures if and only if $p\neq p'$.Comment: 61 page

Hodge polynomials of some moduli spaces of Coherent Systems

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as complements of determinantal varieties and we prove that these are irreducible and smooth. These descriptions allow us to compute the Hodge polynomials of this moduli space in some cases. In particular, we give explicit computations for the cases in which $(n,d,k)=(3,d,1)$ and $d$ is even, obtaining from them the usual Poincar\'e polynomials.Comment: Formerly entitled: "A stratification of some moduli spaces of coherent systems on algebraic curves and their Hodge--Poincar\'e polynomials". The paper has been substantially shorten. Theorem 8.20 has been revised and corrected. Final version accepted for publication in International Journal of Mathematics. arXiv admin note: text overlap with arXiv:math/0407523 by other author

Metallochaperones Are Needed for Mycobacterium tuberculosis and Escherichia coli Nicotinamidase-Pyrazinamidase Activity.

Mycobacterium tuberculosis nicotinamidase-pyrazinamidase (PZAse) is a metalloenzyme that catalyzes conversion of nicotinamide-pyrazinamide to nicotinic acid-pyrazinoic acid. This study investigated whether a metallochaperone is required for optimal PZAse activity. M. tuberculosis and Escherichia coli PZAses (PZAse-MT and PZAse-EC, respectively) were inactivated by metal depletion (giving PZAse-MT-Apo and PZAse-EC-Apo). Reactivation with the E. coli metallochaperone ZnuA or Rv2059 (the M. tuberculosis analog) was measured. This was repeated following proteolytic and thermal treatment of ZnuA and Rv2059. The CDC1551 M. tuberculosis reference strain had the Rv2059 coding gene knocked out, and PZA susceptibility and the pyrazinoic acid (POA) efflux rate were measured. ZnuA (200 μM) achieved 65% PZAse-EC-Apo reactivation. Rv2059 (1 μM) and ZnuA (1 μM) achieved 69% and 34.3% PZAse-MT-Apo reactivation, respectively. Proteolytic treatment of ZnuA and Rv2059 and application of three (but not one) thermal shocks to ZnuA significantly reduced the capacity to reactivate PZAse-MT-Apo. An M. tuberculosis Rv2059 knockout strain was Wayne positive and susceptible to PZA and did not have a significantly different POA efflux rate than the reference strain, although a trend toward a lower efflux rate was observed after knockout. The metallochaperone Rv2059 restored the activity of metal-depleted PZAse in vitro Although Rv2059 is important in vitro, it seems to have a smaller effect on PZA susceptibility in vivo. It may be important to mechanisms of action and resistance to pyrazinamide in M. tuberculosis Further studies are needed for confirmation.IMPORTANCE Tuberculosis is an infectious disease caused by the bacterium Mycobacterium tuberculosis and remains one of the major causes of disease and death worldwide. Pyrazinamide is a key drug used in the treatment of tuberculosis, yet its mechanism of action is not fully understood, and testing strains of M. tuberculosis for pyrazinamide resistance is not easy with the tools that are presently available. The significance of the present research is that a metallochaperone-like protein may be crucial to pyrazinamide's mechanisms of action and of resistance. This may support the development of improved tools to detect pyrazinamide resistance, which would have significant implications for the clinical management of patients with tuberculosis: drug regimens that are appropriately tailored to the resistance profile of a patient's individual strain lead to better clinical outcomes, reduced onward transmission of infection, and reduction of the development of resistant strains that are more challenging and expensive to treat

Surface Flow Structure of the Gulf Stream From Composite Imagery and Satellite-Tracked Drifters

A unique set of coutemporaneous satellite-tracked drifters and five-day composite Advanced Very High Resolution Radionmeter (AVHRR) satellite imagery of the North Atlantic has been analyzed to examine the surface flow structure of the Gulf Stream. The study region was divided into two sections, greater than 37 degrees N and less than 37 degrees N, in order to answer the question of geographic variability. Fractal and spectral analyses methods were applied to the data. Fractal analysis of the Lagrangian trajectories showed a fractal dimension of 1.21 +/- 0.02 with a scaling range of 83 - 343 km. The fractal dimension of the temperature fronts of the composite imagery is similar for the two regions with D = 1.11 +/- 0.01 over a scaling range of 4 - 44 km. Spectral analysis also reports a fairly consistent value for the spectral slope and its scaling range. Therefore, we conclude there is no geographic variability in the data set. A suitable scaling range for this contemporaneous data set is 80 - 200 km which is consistent with the expected physical conditions in the region. Finally, we address the idea of using five-day composite imagery to infer the surface flow of the Gulf Stream. Close analyses of the composite thermal fronts and the Lagrangian drifter trajectories show that the former is not a good indicator of the latter

Surface contamination of cars : a review

This review surveys the problem of surface contamination for cars, which poses a growing engineering challenge to vehicle manufacturers, operators and users. Both drivers’ vision and vehicle visibility need to be maintained under a wide range of environmental conditions. This requires managing the flow of surface water on wind screens and side glazing. The rate of deposition of solid contaminants on glazing, lights, license plates and external mirrors also needs to be minimised. Maintaining vehicle aesthetics and limiting the transfer of contaminants to the hands and clothes of users from soiled surfaces are also significant issues. Recently, keeping camera lenses clean has emerged as a key concern, as these systems transition from occasional manoeuvring aids to sensors for safety systems. The deposition of water and solid contaminants onto car surfaces is strongly influenced by unsteady vehicle aerodynamic effects. Airborne water droplets falling as rain or lifted as spray by tyres interact with wakes, vortices and shear flows and accumulate on vehicle surfaces as a consequence. The same aerodynamic effects also control the movement of surface water droplets, rivulets and films; hence, particular attention is paid to surface water management over the front side-glass and the deposition of contaminants on the rear surfaces. The test methods used in the automotive industry are reviewed, as are numerical simulation techniques

Assessing Human Error Against a Benchmark of Perfection

An increasing number of domains are providing us with detailed trace data on human decisions in settings where we can evaluate the quality of these decisions via an algorithm. Motivated by this development, an emerging line of work has begun to consider whether we can characterize and predict the kinds of decisions where people are likely to make errors. To investigate what a general framework for human error prediction might look like, we focus on a model system with a rich history in the behavioral sciences: the decisions made by chess players as they select moves in a game. We carry out our analysis at a large scale, employing datasets with several million recorded games, and using chess tablebases to acquire a form of ground truth for a subset of chess positions that have been completely solved by computers but remain challenging even for the best players in the world. We organize our analysis around three categories of features that we argue are present in most settings where the analysis of human error is applicable: the skill of the decision-maker, the time available to make the decision, and the inherent difficulty of the decision. We identify rich structure in all three of these categories of features, and find strong evidence that in our domain, features describing the inherent difficulty of an instance are significantly more powerful than features based on skill or time.Comment: KDD 2016; 10 page

Forgetful maps between Deligne-Mostow ball quotients

We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P^1, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livn\'e fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also include a retraction of a 3-dimensional ball quotient onto one of its 1-dimensional totally geodesic complex submanifolds