Factorization of Spanning Trees on Feynman Graphs

In order to use the Gaussian representation for propagators in Feynman amplitudes, a representation which is useful to relate string theory and field theory, one has to prove first that each $\alpha$- parameter (where $\alpha$ is the parameter associated to each propagator in the $\alpha$-representation of the Feynman amplitudes) can be replaced by a constant instead of being integrated over and second, prove that this constant can be taken equal for all propagators of a given graph. The first proposition has been proven in one recent letter when the number of propagators is infinite. Here we prove the second one. In order to achieve this, we demonstrate that the sum over the weighted spanning trees of a Feynman graph $G$ can be factorized for disjoint parts of $G$. The same can also be done for cuts on $G$, resulting in a rigorous derivation of the Gaussian representation for super-renormalizable scalar field theories. As a by-product spanning trees on Feynman graphs can be used to define a discretized functional space.Comment: 47 pages, Plain Tex, 3 PostScript figure

Fighting covid-19 outbreaks in prisons

Improving prison health services is critical for fighting epidemics such as covid-19. Prisoners are at much higher risk of infectious diseases than communities outside. Eruption of covid-19 in prisons emphasises the need to improve prison healthcare. Health education for inmates and prison staff must be intensified, and better treatment and prevention measures require increased funding. More non-custodial sentences would decongest prisons, reducing the potential for the outbreaks. Links between prison and national health services should be strengthened

tRNA splicing

Introns interrupt the continuity of many eukaryal genes, and therefore their removal by splicing is a crucial step in gene expression. Interestingly, even within Eukarya there are at least four splicing mechanisms. mRNA splicing in the nucleus takes place in two phosphotransfer reactions on a complex and dynamic machine, the spliceosome. This reaction is related in mechanism to the two self-splicing mechanisms for Group 1 and Group 2 introns. In fact the Group 2 introns are spliced by an identical mechanism to mRNA splicing, although there is no general requirement for either proteins or co-factors. Thus it seems likely that the Group 2 and nuclear mRNA splicing reactions have diverged from a common ancestor. tRNA genes are also interrupted by introns, but here the splicing mechanism is quite different because it is catalyzed by three enzymes, all proteins and with an intrinsic requirement for ATP hydrolysis. tRNA splicing occurs in all three major lines of descent, the Bacteria, the Archaea, and the Eukarya. In bacteria the introns are self-splicing (1-3). Until recently it was thought that the mechanisms of tRNA splicing in Eukarya and Archaea were unrelated as well. In the past year, however, it has been found that the first enzyme in the tRNA splicing pathway, the tRNA endonuclease, has been conserved in evolution since the divergence of the Eukarya and the Archaea. Surprising insights have been obtained by comparison of the structures and mechanisms of tRNA endonuclease from these two divergent lines

Radiation generated by accelerating and rotating charged black holes in (anti-)de Sitter space

Asymptotic behaviour of gravitational and electromagnetic fields of exact type D solutions from the large Plebanski-Demianski family of black hole spacetimes is analyzed. The amplitude and directional structure of radiation is evaluated in cases when the cosmological constant is non-vanishing, so that the conformal infinities have either de Sitter-like or anti-de Sitter-like character. In particular, explicit relations between the parameters that characterize the sources (that is their mass, electric and magnetic charges, NUT parameter, rotational parameter, and acceleration) and properties of the radiation generated by them are presented. The results further elucidate the physical interpretation of these solutions and may help to understand radiative characteristics of more general spacetimes than those that are asymptotically flat.Comment: 24 pages, 18 figures. To appear in Classical and Quantum Gravit

Pathwise Performance of Debt Based Policies for Wireless Networks with Hard Delay Constraints

Hou et al have introduced a framework to serve clients over wireless channels when there are hard deadline constraints along with a minimum delivery ratio for each client's flow. Policies based on "debt," called maximum debt first policies (MDF) were introduced, and shown to be throughput optimal. By "throughput optimality" it is meant that if there exists a policy that fulfils a set of clients with a given vector of delivery ratios and a vector of channel reliabilities, then the MDF policy will also fulfill them. The debt of a user is the difference between the number of packets that should have been delivered so as to meet the delivery ratio and the number of packets that have been delivered for that client. The maximum debt first (MDF) prioritizes the clients in decreasing order of debts at the beginning of every period. Note that a throughput optimal policy only guarantees that \begin{small} \liminf_{T \to \infty} \frac{1}{T}\sum_{t=1}^{T} \mathbbm{1}\{\{client n$'s packet is delivered in frame$t} \} \geq q_{i} \end{small}, where the right hand side is the required delivery ratio for client $i$. Thus, it only guarantees that the debts of each user are $o(T)$, and can be otherwise arbitrarily large. This raises the interesting question about what is the growth rate of the debts under the MDF policy. We show the optimality of MDF policy in the case when the channel reliabilities of all users are same, and obtain performance bounds for the general case. For the performance bound we obtain the almost sure bounds on $\limsup_{t\to\infty}\frac{d_{i}(t)}{\phi(t)}$ for all $i$, where $\phi(t) = \sqrt{2t\log\log t}$

Influence of aggregate size and fraction on shrinkage induced micro-cracking of mortar and concrete

In this paper, the influence of aggregate size and volume fraction on shrinkage induced micro-cracking and permeability of concrete and mortar was investigated. Nonlinear finite element analyses of model concrete and mortar specimens were performed. The aggregate diameter was varied between 2 and 16 mm. Furthermore, a range of volume fractions between 0.1 and 0.5 was studied. The nonlinear analyses were based on a 2D lattice approach in which aggregates were simplified as monosized cylindrical inclusions. The analysis results were interpreted by means of crack width and change of permeability. The results show that increasing aggregate diameter (at equal volume fraction) and decreasing volume fraction (at equal aggregate diameter) greatly increases permeability.Comment: 12th International Conference on Fracture (ICF 12