A dynamical systems approach to the tilted Bianchi models of solvable type

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VI$_h$ and VII$_h$) with a perfect fluid and a linear barotropic $\gamma$-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi VII$_0$ models. We prove the important result that for non-inflationary Bianchi type VII$_h$ models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VII$_h$ invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exists closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VII$_h$ models there is a bifurcation in which a set of equilibrium points turn into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VII$_h$ models in this region the solution curves approach a compact surface which is topologically a torus.Comment: 29 page

The Futures of Bianchi type VII0 cosmologies with vorticity

We use expansion-normalised variables to investigate the Bianchi type VII$_0$ model with a tilted $\gamma$-law perfect fluid. We emphasize the late-time asymptotic dynamical behaviour of the models and determine their asymptotic states. Unlike the other Bianchi models of solvable type, the type VII$_0$ state space is unbounded. Consequently we show that, for a general non-inflationary perfect fluid, one of the curvature variables diverges at late times, which implies that the type VII$_0$ model is not asymptotically self-similar to the future. Regarding the tilt velocity, we show that for fluids with $\gamma<4/3$ (which includes the important case of dust, $\gamma=1$) the tilt velocity tends to zero at late times, while for a radiation fluid, $\gamma=4/3$, the fluid is tilted and its vorticity is dynamically significant at late times. For fluids stiffer than radiation ($\gamma>4/3$), the future asymptotic state is an extremely tilted spacetime with vorticity.Comment: 23 pages, v2:references and comments added, typos fixed, to appear in CQ

Generalised Hong-Ou-Mandel Experiments with Bosons and Fermions

The Hong-Ou-Mandel (HOM) dip plays an important role in recent linear optics experiments. It is crucial for quantum computing with photons and can be used to characterise the quality of single photon sources and linear optics setups. In this paper, we consider generalised HOM experiments with $N$ bosons or fermions passing simultaneously through a symmetric Bell multiport beam splitter. It is shown that for even numbers of bosons, the HOM dip occurs naturally in the coincidence detection in the output ports. In contrast, fermions always leave the setup separately exhibiting perfect coincidence detection. Our results can be used to verify or employ the quantum statistics of particles experimentally.Comment: 11 pages, 2 figures, more references adde

Fractional oscillator process with two indices

We introduce a new fractional oscillator process which can be obtained as solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short range dependence of the process are studied by considering the asymptotic properties of its covariance function. The fluctuation--dissipation relation of the process is investigated. The fractional oscillator process can be regarded as one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique.Comment: 32 page

The late-time behaviour of vortic Bianchi type VIII Universes

We use the dynamical systems approach to investigate the Bianchi type VIII models with a tilted $\gamma$-law perfect fluid. We introduce expansion-normalised variables and investigate the late-time asymptotic behaviour of the models and determine the late-time asymptotic states. For the Bianchi type VIII models the state space is unbounded and consequently, for all non-inflationary perfect fluids, one of the curvature variables grows without bound. Moreover, we show that for fluids stiffer than dust ($1<\gamma<2$), the fluid will in general tend towards a state of extreme tilt. For dust ($\gamma=1$), or for fluids less stiff than dust ($0<\gamma< 1$), we show that the fluid will in the future be asymptotically non-tilted. Furthermore, we show that for all $\gamma\geq 1$ the universe evolves towards a vacuum state but does so rather slowly, $\rho/H^2\propto 1/\ln t$.Comment: 19 pages, 3 ps figures, v2:typos fixed, refs and more discussion adde

Clinical translation of [18F]ICMT-11 for measuring chemotherapy-induced caspase 3/7 activation in breast and lung cancer

Background: Effective anticancer therapy is thought to involve induction of tumour cell death through apoptosis and/or necrosis. [18F]ICMT-11, an isatin sulfonamide caspase-3/7-specific radiotracer, has been developed for PET imaging and shown to have favourable dosimetry, safety, and biodistribution. We report the translation of [18F]ICMT-11 PET to measure chemotherapy-induced caspase-3/7 activation in breast and lung cancer patients receiving first-line therapy. Results: Breast tumour SUVmax of [18F]ICMT-11 was low at baseline and unchanged following therapy. Measurement of M30/M60 cytokeratin-18 cleavage products showed that therapy was predominantly not apoptosis in nature. While increases in caspase-3 staining on breast histology were seen, post-treatment caspase-3 positivity values were only approximately 1%; this low level of caspase-3 could have limited sensitive detection by [18F]ICMT-11-PET. Fourteen out of 15 breast cancer patients responded to first–line chemotherapy (complete or partial response); one patient had stable disease. Four patients showed increases in regions of high tumour [18F]ICMT-11 intensity on voxel-wise analysis of tumour data (classed as PADS); response was not exclusive to patients with this phenotype. In patients with lung cancer, multi-parametric [18F]ICMT-11 PET and MRI (diffusion-weighted- and dynamic contrast enhanced-MRI) showed that PET changes were concordant with cell death in the absence of significant perfusion changes. Conclusion: This study highlights the potential use of [18F]ICMT-11 PET as a promising candidate for non-invasive imaging of caspase3/7 activation, and the difficulties encountered in assessing early-treatment responses. We summarize that tumour response could occur in the absence of predominant chemotherapy-induced caspase-3/7 activation measured non-invasively across entire tumour lesions in patients with breast and lung cancer

The Child Brain Computes and Utilizes Internalized Maternal Choices

As children grow, they gradually learn how to make decisions independently. However, decisions like choosing healthy but less-tasty foods can be challenging for children whose self-regulation and executive cognitive functions are still maturing. We propose a computational decision-making process in which children estimate their mother's choices for them as well as their individual food preferences. By employing functional magnetic resonance imaging during real food choices, we find that the ventromedial prefrontal cortex (vmPFC) encodes children's own preferences and the left dorsolateral prefrontal cortex (dlPFC) encodes the projected mom's choices for them at the time of children's choice. Also, the left dlPFC region shows an inhibitory functional connectivity with the vmPFC at the time of children's own choice. Our study suggests that in part, children utilize their perceived caregiver's choices when making choices for themselves, which may serve as an external regulator of decision-making, leading to optimal healthy decisions

Optically Thick Radio Cores of Narrow-Waist Bipolar Nebulae

We report our search for optically thick radio cores in sixteen narrow-waist bipolar nebulae. Optically thick cores are a characteristic signature of collimated ionized winds. Eleven northern nebulae were observed with the Very Large Array (VLA) at 1.3 cm and 0.7 cm, and five southern nebulae were observed with the Australia Telescope Compact Array (ATCA) at 6 cm and 3.6 cm. Two northern objects, 19W32 and M 1-91, and three southern objects, He 2-25, He 2-84 and Mz 3, were found to exhibit a compact radio core with a rising spectrum consistent with an ionized jet. Such jets have been seen in M 2-9 and may be responsible for shaping bipolar structure in planetary nebulae.Comment: 29 pages, accepted for publication in Ap

Surface-reconstructed Icosahedral Structures for Lead Clusters

We describe a new family of icosahedral structures for lead clusters. In general, structures in this family contain a Mackay icosahedral core with a reconstructed two-shell outer-layer. This family includes the anti-Mackay icosahedra, which have have a Mackay icosahedral core but with most of the surface atoms in hexagonal close-packed positions. Using a many-body glue potential for lead, we identify two icosahedral structures in this family which have the lowest energies of any known structure in the size range from 900 to 15000 lead atoms. We show that these structures are stabilized by a feature of the many-body glue part of the interatomic potential.Comment: 9 pages, 8 figure

Synthesis and characterization of nickel ferrite magnetic nanoparticles by co-precipitation method

Magnetic nickel ferrite (NiFe2O4) nanoparticles have been synthesized via co-precipitation method by varying the metal precursors ratio. Four different precursors ratio (Fe:Ni) are varied at 40:60, 50:50, 60:40 and 80:20. The size of the nanoparticles is found to increase with increasing iron (Fe) content. In addition, the morphology of the particles are observed to change from spherical to a shape similar to a nanooctahedral particle when the Fe content in the initial precursors ratio increases. The X-ray Diffraction (XRD) patterns have proved the presence of nickel ferrite nanoparticles. The magnetic properties characterized by Vibrating Sample Magnetometer (VSM) at room temperature proved that the assynthesized nickel ferrite nanoparticles are ferromagnetic and the saturation magnetization (Ms) increases with the content of Fe in the sample