Genomic donor cassette sharing during VLRA and VLRC assembly in jawless vertebrates

Lampreys possess two T-like lymphocyte lineages that express either variable lymphocyte receptor (VLR) A or VLRC antigen receptors. VLRA+ and VLRC+ lymphocytes share many similarities with the two principal T-cell lineages of jawed vertebrates expressing the αβ and γδ T-cell receptors (TCRs). During the assembly of VLR genes, several types of genomic cassettes are inserted, in step-wise fashion, into incomplete germ-line genes to generate the mature forms of antigen receptor genes. Unexpectedly, the structurally variable components of VLRA and VLRC receptors often possess partially identical sequences; this phenomenon of module sharing between these two VLR isotypes occurs in both lampreys and hagfishes. By contrast, VLRA and VLRC molecules typically do not share their building blocks with the structurally analogous VLRB receptors that are expressed by B-like lymphocytes. Our studies reveal that VLRA and VLRC germ-line genes are situated in close proximity to each other in the lamprey genome and indicate the interspersed arrangement of isotype-specific and shared genomic donor cassettes; these features may facilitate the shared cassette use. The genomic structure of the VLRA/VLRC locus in lampreys is reminiscent of the interspersed nature of the TCRA/TCRD locus in jawed vertebrates that also allows the sharing of some variable gene segments during the recombinatorial assembly of TCR genes

Head-on infall of two compact objects: Third post-Newtonian Energy Flux

Head-on infall of two compact objects with arbitrary mass ratio is investigated using the multipolar post-Minkowskian approximation method. At the third post-Newtonian order the energy flux, in addition to the instantaneous contributions, also includes hereditary contributions consisting of the gravitational-wave tails, tails-of-tails and the tail-squared terms. The results are given both for infall from infinity and also for infall from a finite distance. These analytical expressions should be useful for the comparison with the high accuracy numerical relativity results within the limit in which post-Newtonian approximations are valid.Comment: 25 pages, 2 figures, This version includes the changes appearing in the Erratum published in Phys. Rev.

Zero-Reachability in Probabilistic Multi-Counter Automata

We study the qualitative and quantitative zero-reachability problem in probabilistic multi-counter systems. We identify the undecidable variants of the problems, and then we concentrate on the remaining two cases. In the first case, when we are interested in the probability of all runs that visit zero in some counter, we show that the qualitative zero-reachability is decidable in time which is polynomial in the size of a given pMC and doubly exponential in the number of counters. Further, we show that the probability of all zero-reaching runs can be effectively approximated up to an arbitrarily small given error epsilon > 0 in time which is polynomial in log(epsilon), exponential in the size of a given pMC, and doubly exponential in the number of counters. In the second case, we are interested in the probability of all runs that visit zero in some counter different from the last counter. Here we show that the qualitative zero-reachability is decidable and SquareRootSum-hard, and the probability of all zero-reaching runs can be effectively approximated up to an arbitrarily small given error epsilon > 0 (these result applies to pMC satisfying a suitable technical condition that can be verified in polynomial time). The proof techniques invented in the second case allow to construct counterexamples for some classical results about ergodicity in stochastic Petri nets.Comment: 20 page

Testing post-Newtonian theory with gravitational wave observations

The Laser Interferometric Space Antenna (LISA) will observe supermassive black hole binary mergers with amplitude signal-to-noise ratio of several thousands. We investigate the extent to which such observations afford high-precision tests of Einstein's gravity. We show that LISA provides a unique opportunity to probe the non-linear structure of post-Newtonian theory both in the context of general relativity and its alternatives.Comment: 9 pages, 2 figure

Selection of the lamprey VLRC antigen receptor repertoire

The alternative adaptive immune system of jawless vertebrates is based on different isotypes of variable lymphocyte receptors (VLRs) that are composed of leucine-rich repeats (LRRs) and expressed by distinct B- and T-like lymphocyte lineages. VLRB is expressed by B-like cells, whereas VLRA and VLRC are expressed by two T-like lineages that develop in the thymoid, a thymus-like structure in lamprey larvae. In each case, stepwise combinatorial insertions of different types of short donor LRR cassettes into incomplete germ-line genes are required to generate functional VLR gene assemblies. It is unknown, however, whether the diverse repertoires of VLRs that are expressed by peripheral blood lymphocytes are shaped by selection after their assembly. Here, we identify signatures of selection in the peripheral repertoire of VLRC antigen receptors that are clonally expressed by one of the T-like cell types in lampreys. Selection strongly favors VLRC molecules containing four internal variable leucine-rich repeat (LRRV) modules, although VLRC assemblies encoding five internal modules are initially equally frequent. In addition to the length selection, VLRC molecules in VLRC+ peripheral lymphocytes exhibit a distinct pattern of high entropy sites in the N-terminal LRR1 module, which is inserted next to the germ-line–encoded LRRNT module. This is evident in comparisons to VLRC gene assemblies found in the thymoid and to VLRC gene assemblies found in some VLRA+ cells. Our findings are the first indication to our knowledge that selection operates on a VLR repertoire and provide a framework to establish the mechanism by which this selection occurs during development of the VLRC+ lymphocyte lineage

Culture and Colonial Legacy: Evidence from Public Goods Games

We conduct a public goods game in three small towns in the Indian state of Rajasthan. Due to historical military conquest, until 1947 these towns were on opposite sides of a colonial border separating British India from the Princely States. Our research design offers a treatment comparison between the towns of (British) Kekri and (Princely) Sarwar, and a control comparison between Princely Sarwar and Shahpura. We find that participants from (British) Kekri are more co-operative in mixed-town groups. The differences are driven by individuals with family ties to the towns, highlighting the enduring effects of colonial rule on co-operation norms

Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux

The instantaneous contributions to the 3PN gravitational wave luminosity from the inspiral phase of a binary system of compact objects moving in a quasi elliptical orbit is computed using the multipolar post-Minkowskian wave generation formalism. The necessary inputs for this calculation include the 3PN accurate mass quadrupole moment for general orbits and the mass octupole and current quadrupole moments at 2PN. Using the recently obtained 3PN quasi-Keplerian representation of elliptical orbits the flux is averaged over the binary's orbit. Supplementing this by the important hereditary contributions arising from tails, tails-of-tails and tails squared terms calculated in a previous paper, the complete 3PN energy flux is obtained. The final result presented in this paper would be needed for the construction of ready-to-use templates for binaries moving on non-circular orbits, a plausible class of sources not only for the space based detectors like LISA but also for the ground based ones.Comment: 40 pages. Minor changes in text throughout. Minor typos in Eqs. (3.3b), (7.7f), (8.19d) and (8.20) corrected. Matches the published versio

Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame

The equations of motion of compact binary systems and their associated Lagrangian formulation have been derived in previous works at the third post-Newtonian (3PN) approximation of general relativity in harmonic coordinates. In the present work we investigate the binary's relative dynamics in the center-of-mass frame (center of mass located at the origin of the coordinates). We obtain the 3PN-accurate expressions of the center-of-mass positions and equations of the relative binary motion. We show that the equations derive from a Lagrangian (neglecting the radiation reaction), from which we deduce the conserved center-of-mass energy and angular momentum at the 3PN order. The harmonic-coordinates center-of-mass Lagrangian is equivalent, {\it via} a contact transformation of the particles' variables, to the center-of-mass Hamiltonian in ADM coordinates that is known from the post-Newtonian ADM-Hamiltonian formalism. As an application we investigate the dynamical stability of circular binary orbits at the 3PN order.Comment: 31 pages, to appear in Classical and Quantum Gravit