Moduli and periods of simply connected Enriques surfaces

We describe a period map for those simply connected Enriques surfaces in characteristic 2 whose canonical double cover is K3. The moduli stack for these surfaces has a Deligne-Mumford quotient that is an open substack of a $\mathbb P^1$-bundle over the period space. We also give some general results relating local and global moduli for algebraic varieties and describe the difference in their dimensions in terms of the failure of the automorphism group scheme to be reduced

Optimal Control and Differential Games with Measures

We consider control problems with trajectories which involve ordinary measureable control functions and controls which are measures. The payoff involves a running cost in time and a running cost against the control measures. In the optimal control problem we are trying to minimize this payoff with both controls. In the differential game problem we are trying to minimize the cost with the ordinary controls assuming that the measure controls are chosen to maximize the cost. We will characterize the value functions in both cases using viscosity solution theory by deriving the Bellman and Isaacs equations

Inverse optical tomography through PDE constrained optimisation in L∞

Fluorescent Optical Tomography (FOT) is a new bio-medical imaging method with wider industrial applications. It is currently intensely researched since it is very precise and with no side effects for humans, as it uses non-ionising red and infrared light. Mathematically, FOT can be modelled as an inverse parameter identification problem, associated with a coupled elliptic system with Robin boundary conditions. Herein we utilise novel methods of Calculus of Variations in L∞ to lay the mathematical foundations of FOT which we pose as a PDE-constrained minimisation problem in Lp and L∞

Established and Potential Physiological Roles of Bicarbonate-Sensing Soluble Adenylyl Cyclase (sAC) in Aquatic Animals

Soluble adenylyl cyclase (sAC) is a recently recognized source of the signaling molecule cyclic AMP (cAMP) that is genetically and biochemically distinct from the classic G-protein-regulated transmembrane adenylyl cyclases (tmACs). Mammalian sAC is distributed throughout the cytoplasm and it may be present in the nucleus and inside mitochondria. sAC activity is directly stimulated by HCO3-, and sAC has been confirmed to be a HCO3- sensor in a variety of mammalian cell types. In addition, sAC can functionally associate with carbonic anhydrases to act as a de facto sensor of pH and CO2. The two catalytic domains of sAC are related to HCO3--regilated adenylyl cyclases from cyanobacteria, suggesting the cAMP pathway is an evolutionarily conserved mechanism for sensing CO2 levels and/or acid/base conditions. Reports of sAC in aquatic animals are still limited but are rapidly accumulating. In shark gills, sAC senses blood alkalosis and triggers compensatory H+ absorption. And in sea urchin sperm, sAC may participate in the initiation of flagellar movement and in the acrosome reaction. Bioinformatics and RT-PCR results reveal that sAC orthologs are present in most animal phyla. This review summarizes the current knowledge on the physiological roles of sAC in aquatic animals and suggests additional functions in which sAC may be involved

The measurement and determinants of skill acquisition in young workers' first job

The article analyses participation in five types of training (formal on-site, formal off-site, informal co-worker training, learning by watching and learning by doing) and self-assessed skill acquisition in young Flemish workers' first job. A skill production function is estimated whereby the simultaneity of participation in the different types of training and skill acquisition is taken into account. The results clearly demonstrate the importance of informal training. Formal training participation is found to be only a fraction of total training participation. Moreover, the determinants of total training participation and skill acquisition differ from those of formal training participation. While some training types are complementary, others are clearly substitutes. Finally, most types of training generate additional skills. Nonetheless, learning by doing is found to be complementary to formal education in the production of both specific and general skills, whereas formal training serves as a substitute

The development and use of Actiphage® to detect viable mycobacteria from bovine tuberculosis and Johne’s disease-infected animals

Here, we describe the development of a method that exploits bacteriophage D29 as a lysis agent for efficient DNA extraction from low numbers of mycobacterial cells. This method (Actiphage®) used in combination with PCR achieved rapid and sensitive (LOD ≤ 10 cell ml−1) detection and identification of viable, pathogenic mycobacteria in blood samples within 6 h. We demonstrate that mycobacteriophage D29 can be used to detect a range of mycobacteria from clinical blood samples including both Mycobacterium tuberculosis complex and Mycobacterium avium subsp. paratuberculosis without the need for culture and confirms our earlier observations that a low‐level bacteraemia is associated with these infections in cattle. In a study of M. bovis‐infected cattle (n = 41), the sensitivity of the Actiphage® method was 95 % (95 % CI; 0.84–0.99) and specificity was 100 % (95% CI; 0.92–1). We further used Actiphage® to demonstrate viable Mycobacterium avium subsp. paratuberculosis is present in the blood of Johne’s infected cattle. This method provides a revolutionary new tool for the study of infections caused by these difficult to grow pathogens

Homogenization and enhancement for the G-equation

We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally we also consider advection depending on position at the integral scale

Potent antiviral activity against HSV-1 and SARS-CoV-2 by antimicrobial peptoids

Viral infections, such as those caused by Herpes Simplex Virus-1 (HSV-1) and SARS-CoV-2, affect millions of people each year. However, there are few antiviral drugs that can effectively treat these infections. The standard approach in the development of antiviral drugs involves the identification of a unique viral target, followed by the design of an agent that addresses that target. Antimicrobial peptides (AMPs) represent a novel source of potential antiviral drugs. AMPs have been shown to inactivate numerous different enveloped viruses through the disruption of their viral envelopes. However, the clinical development of AMPs as antimicrobial therapeutics has been hampered by a number of factors, especially their enzymatically labile structure as peptides. We have examined the antiviral potential of peptoid mimics of AMPs (sequence-specific N-substituted glycine oligomers). These peptoids have the distinct advantage of being insensitive to proteases, and also exhibit increased bioavailability and stability. Our results demonstrate that several peptoids exhibit potent in vitro antiviral activity against both HSV-1 and SARS-CoV-2 when incubated prior to infection. In other words, they have a direct effect on the viral structure, which appears to render the viral particles non-infective. Visualization by cryo-EM shows viral envelope disruption similar to what has been observed with AMP activity against other viruses. Furthermore, we observed no cytotoxicity against primary cultures of oral epithelial cells. These results suggest a common or biomimetic mechanism, possibly due to the differences between the phospholipid head group makeup of viral envelopes and host cell membranes, thus underscoring the potential of this class of molecules as safe and effective broad-spectrum antiviral agents. We discuss how and why differing molecular features between 10 peptoid candidates may affect both antiviral activity and selectivity