Billiard-ball paradox for a quantum wave packet

Past studies of the billiard-ball paradox, a problem involving an object that travels back in time along a closed timelike curve (CTC), typically concern themselves with entirely classical histories, whereby any trajectorial effects associated with quantum mechanics cannot manifest. Here we develop a quantum version of the paradox, wherein a (semiclassical) wave packet evolves through a region containing a wormhole time machine. This is accomplished by mapping all relevant paths on to a quantum circuit, in which the distinction of the various paths is facilitated by representing the billiard particle with a clock state. For this model, we find that the Deutsch model (D-CTCs) provides self-consistent solutions in the form of a mixed state composed of terms which represent every possible configuration of the particle's evolution through the circuit. In the equivalent circuit picture (ECP), this reduces to a binomial distribution in the number of loops of time machine. The postselected teleportation (P-CTCs) prescription on the other hand predicts a pure-state solution in which the loop counts have binomial coefficient weights. We then discuss the model in the continuum limit, with a particular focus on the various methods one may employ in order to guarantee convergence in the average number of clock evolutions. Specifically, for D-CTCs, we find that it is necessary to regularise the theory's parameters, while P-CTCs alternatively require more contrived modification.Comment: 18 pages, 9 figure

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio

The genetic architecture of the human cerebral cortex

The cerebral cortex underlies our complex cognitive capabilities, yet little is known about the specific genetic loci that influence human cortical structure. To identify genetic variants that affect cortical structure, we conducted a genome-wide association meta-analysis of brain magnetic resonance imaging data from 51,665 individuals. We analyzed the surface area and average thickness of the whole cortex and 34 regions with known functional specializations. We identified 199 significant loci and found significant enrichment for loci influencing total surface area within regulatory elements that are active during prenatal cortical development, supporting the radial unit hypothesis. Loci that affect regional surface area cluster near genes in Wnt signaling pathways, which influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinson's disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder

Atmosphere-ocean-ice interactions in the Amundsen Sea Embayment, West Antarctica

Over recent decades outlet glaciers of the Amundsen Sea Embayment (ASE), West Antarctica, have accelerated, thinned and retreated, and are now contributing approximately 10% to global sea level rise. All the ASE glaciers flow into ice shelves, and it is the thinning of these since the 1970s, and their ungrounding from “pinning points” that is widely held to be responsible for triggering the glaciers’ decline. These changes have been linked to the inflow of warm Circumpolar Deep Water (CDW) onto the ASE's continental shelf. CDW delivery is highly variable, and is closely related to the regional atmospheric circulation. The ASE is south of the Amundsen Sea Low (ASL), which has a large variability and which has deepened in recent decades. The ASL is influenced by the phase of the Southern Annular Mode, along with tropical climate variability. It is not currently possible to simulate such complex atmosphere-ocean-ice interactions in models, hampering prediction of future change. The current retreat could mark the beginning of an unstable phase of the ASE glaciers that, if continued, will result in collapse of the West Antarctic Ice Sheet, but numerical ice-sheet models currently lack the predictive power to answer this question. It is equally possible that the recent retreat will be short-lived and that the ASE will find a new stable state. Progress is hindered by incomplete knowledge of bed topography in the vicinity of the grounding line. Furthermore, a number of key processes are still missing or poorly represented in models of ice-flow

Modular self-assembling and self-reconfiguring e-pucks

In this paper, we present the design of a new structural extension for the e-puck mobile robot. The extension may be used to transform what is traditionally a swarm robotics platform into a self-reconfigurable modular robotic system. We introduce a modified version of a previously developed collective locomotion algorithm and present new experimental results across three different themes. We begin by investigating how the performance of the collective locomotion algorithm is affected by the size and shape of the robotic structures involved, examining structures containing up to nine modules. Without alteration to the underlying algorithm, we then analyse the implicit self-assembling and self-reconfiguring capabilities of the system and show that the novel use of 'virtual sensors' can significantly improve performance. Finally, by examining a form of environment driven self-reconfiguration, we observe the behaviour of the system in a more complex environment. We conclude that the modular e-puck extension represents a viable platform for investigating collective locomotion, self-assembly and self-reconfiguration.</p