On the Absence of Cross-Confinement for Dynamically Generated Multi-Chern-Simons Theories

We show that when the induced parity breaking part of the effective action for the low-momentum region of U(1) x ... x U(1) Maxwell gauge field theory with massive fermions in 3 dimensions is coupled to a \phi^4 scalar field theory, it is not possible to eliminate the screening of the long-range Coulomb interactions and get external charges confined in the broken Higgs phase. This result is valid for non-zero temperature as well.Comment: 7 pages, LaTe

Error analysis for deep neural network approximations of parametric hyperbolic conservation laws

We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that the approximation error can be made as small as desired with ReLU neural networks that overcome the curse of dimensionality. In addition, we provide an explicit upper bound on the generalization error in terms of the training error, number of training samples and the neural network size. The theoretical results are illustrated by numerical experiments

Generic bounds on the approximation error for physics-informed (and) operator learning

We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator learning. These bounds guarantee that PINNs and (physics-informed) DeepONets or FNOs will efficiently approximate the underlying solution or solution operator of generic partial differential equations (PDEs). Our framework utilizes existing neural network approximation results to obtain bounds on more involved learning architectures for PDEs. We illustrate the general framework by deriving the first rigorous bounds on the approximation error of physics-informed operator learning and by showing that PINNs (and physics-informed DeepONets and FNOs) mitigate the curse of dimensionality in approximating nonlinear parabolic PDEs

TLK1B promotes repair of UV-damaged DNA through chromatin remodeling by Asf1

BACKGROUND: The mammalian protein kinase TLK1 is a homologue of Tousled, a gene involved in flower development in Arabidopsis thaliana. The function of TLK1 is not well known, although knockout of the gene in Drosophila, or expression of a dominant negative mutant in mouse mammary cells causes loss of nuclear divisions and chromosome mis-segregation. TLK1B is a splice variant of TLK1 and it confers radioresistance in a normal mammary mouse cell line possibly due to increased chromatin remodeling capacity, but the mechanism of resistance remains to be fully elucidated. RESULTS: We now show that TLK1B also affords protection against UV radiation. We find that nuclear extracts isolated from TLK1B-containing mouse cells promote more efficient chromatin assembly than comparable extracts lacking TLK1B. TLK1B-containing extracts are also more efficient in repair of UV-damaged plasmid DNA assembled into nucleosomes. One of the two known substrates of TLK1 (or TLK1B) is the histone chaperone Asf1, and immuno-inactivation experiments suggest that TLK1B increases UV-repair through the action of Asf1 on chromatin assembly/disassembly. CONCLUSION: Our studies provide evidence for TLK1B-mediated phosphorylation of Asf1 triggering DNA repair. We suggest that this occurs via Asf1-mediated chromatin assembly at the sites of UV damage

Bulk Kalb-Ramond field in Randall Sundrum scenario

We have considered the most general gauge invariant five-dimensional action of a second rank antisymmetric Kalb-Ramond tensor gauge theory, including a topological term of the form $\epsilon^{ABLMN}B_{AB}H_{LMN}$ in a Randall-Sundrum scenario. Such a tensor field $B_{AB}$ (whose rank-3 field strength tensor is $H_{LMN}$), which appears in the massless sector of a heterotic string theory, is assumed to coexist with the gravity in the bulk. The third rank field strength corresponding to the Kalb-Ramond field has a well-known geometric interpretation as the spacetime torsion. The only non-trivial classical solutions corresponding to the effective four-dimensional action are found to be self-dual or anti-selfdual Kalb-Ramond fields. This ensures that the four-dimensional effective action on the brane is parity-conserving. The massive modes for both cases, lying in the TeV range, are related to the fundamental parameters of the theory. These modes can be within the kinematic reach of forthcoming TeV scale experiments. However, the couplings of the massless as well as massive Kalb-Ramond modes with matter on the visible brane are found to be suppressed vis-a-vis that of the graviton by the warp factor, whence the conclusion is that both the massless and the massive torsion modes appear much weaker than curvature to an observer on the visible brane.Comment: 15 Pages,2 figures,Late

Contact angles on a soft solid: from Young's law to Neumann's law

The contact angle that a liquid drop makes on a soft substrate does not obey the classical Young's relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact angles different from that predicted by Neumann's law, which applies when the drop is floating on another liquid. Here we derive an elasto-capillary model for contact angles on a soft solid, by coupling a mean-field model for the molecular interactions to elasticity. We demonstrate that the limit of vanishing elastic modulus yields Neumann's law or a slight variation thereof, depending on the force transmission in the solid surface layer. The change in contact angle from the rigid limit (Young) to the soft limit (Neumann) appears when the length scale defined by the ratio of surface tension to elastic modulus $\gamma/E$ reaches a few molecular sizes

Elastic deformation due to tangential capillary forces \ud

A sessile liquid drop can deform the substrate on which it rests if the solid is sufficiently “soft.” In this paper we compute the detailed spatial structure of the capillary forces exerted by the drop on the solid substrate using a model based on Density Functional Theory. We show that, in addition to the normal forces, the drop exerts a previously unaccounted tangential force. The resultant effect on the solid is a pulling force near the contact line directed towards the interior of the drop, i.e., not along the interface. The resulting elastic deformations of the solid are worked out and illustrate the importance of the tangential force

Leishmania Donovani Cell Surface Sialoglycans Regulate Susceptibility for Siglec Mediated Macrophage Invasion and Parasite Survival

Glycoconjugates play a pivotal role in the survival of Leishmania parasites in destructive surroundings. An important constituent present on many glycoconjugates is sialic acid. By virtue of their peripheral position on oligosaccharide chains of glycoconjugates, sialic acids are well suited as molecular determinants of specific biological processes, including the interaction of pathogenic microorganisms with sialylated cellular receptors. Differences in a2,3- and a2,6-sialoglycan patterns detected in clonal virulent Leishmania donovani promastigotes, correlated with the level of a2,3- and a2,6-sialyltransferase activity present in these parasites. The role of macrophage sialic acid-receptors in uptake and survival of L.donovani was studied in the murine macrophage cell line raw 264.7. Macrophage invasion was dependent on the binding to Siglec-1, while suppression of MAPK signaling was mediated through Siglec-5. Sialic acid removal by neuraminidase treatment reduced parasite infectivity. The presence of trypsin resistant sialic acid residues in the neuraminidase treated parasites grown in a serum free medium in presence of sialoglycoconjugates indicated that the parasites could salvage sialic acid from exogenous sialoglycans and reutilize it for de novo glycoprotein sialylation in L.donovani parasites. Thus, our results demonstrate the involvement of sialoglycans in the invasion as well as the survival process of L.donovani parasites