Faster Comparison of Stopping Times by Nested Conditional Monte Carlo

We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo. We derive the optimal number of nested simulations and prove that the algorithm is remarkably robust to misspecifications of this number. The method is applied to several problems related to Bermudan/American options. In these applications, our method allows to substantially increase the efficiency of other variance reduction techniques, namely, Quasi-Control Variates and Multilevel Monte Carlo

Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux-attachment to Z2 lattice gauge theories

Artificial magnetic fields and spin-orbit couplings have been recently generated in ultracold gases in view of realizing topological states of matter and frustrated magnetism in a highly-controllable environment. Despite being dynamically tunable, such artificial gauge fields are genuinely classical and exhibit no back-action from the neutral particles. Here we go beyond this paradigm, and demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices. Specifically, we propose a protocol by which atoms of one species carry a magnetic flux felt by another species, hence realizing an instance of flux-attachment. This is obtained by combining coherent lattice modulation techniques with strong Hubbard interactions. We demonstrate how this setting can be arranged so as to implement lattice models displaying a local Z2 gauge symmetry, both in one and two dimensions. We also provide a detailed analysis of a ladder toy model, which features a global Z2 symmetry, and reveal the phase transitions that occur both in the matter and gauge sectors. Mastering flux-attachment in optical lattices envisages a new route towards the realization of strongly-correlated systems with properties dictated by an interplay of dynamical matter and gauge fields.Comment: 11 pages, 6 figures, 11 pages supplement

Floquet approach to Z2\mathbb{Z}_{2} lattice gauge theories with ultracold atoms in optical lattices

Quantum simulation has the potential to investigate gauge theories in strongly-interacting regimes, which are up to now inaccessible through conventional numerical techniques. Here, we take a first step in this direction by implementing a Floquet-based method for studying $\mathbb{Z}_2$ lattice gauge theories using two-component ultracold atoms in a double-well potential. For resonant periodic driving at the on-site interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits $\mathbb{Z}_2$ symmetry. We study the dynamics of the system for different initial states and critically contrast the observed evolution with a theoretical analysis of the full time-dependent Hamiltonian of the periodically-driven lattice model. We reveal challenges that arise due to symmetry-breaking terms and outline potential pathways to overcome these limitations. Our results provide important insights for future studies of lattice gauge theories based on Floquet techniques

Chiral fermions and anomaly cancellation on orbifolds with Wilson lines and flux

We consider six-dimensional supergravity compactified on orbifolds with Wilson lines and bulk flux. Torus Wilson lines are decomposed into Wilson lines around the orbifold fixed points, and twisted boundary conditions of matter fields are related to fractional localized flux. Both, orbifold singularities and flux lead to chiral fermions in four dimensions. We show that in addition to the standard bulk and fixed point anomalies the Green-Schwarz term also cancels the four-dimensional anomaly induced by the flux background. The two axions contained in the antisymmetric tensor field both contribute to the cancellation of the four-dimensional anomaly and the generation of a vector boson mass via the Stueckelberg mechanism. An orthogonal linear combination of the axions remains massless and couples to the gauge field in the standard way. Furthermore, we construct convenient expressions for the wave functions of the zero modes and relate their multiplicity and behavior at the fixed points to the bulk flux quanta and the Wilson lines.Comment: 30 pages, 4 figures, 1 table, clarifying remarks adde

Stress‐ and pathway‐specific impacts of impaired jasmonoyl‐isoleucine (JA‐Ile) catabolism on defense signalling and biotic stress resistance

Jasmonate synthesis and signalling are essential for plant defense upregulation upon herbivore or microbial attacks. Stress-induced accumulation of jasmonoyl-isoleucine (JA-Ile), the bioactive hormonal form triggering transcriptional changes, is dynamic and transient because of the existence of potent removal mechanisms. Two JA-Ile turnover pathways operate in Arabidopsis, consisting in cytochrome P450 (CYP94)mediated oxidation and deconjugation by the amidohydrolases IAR3/ILL6. Understanding their impacts was previously blurred by gene redundancy and compensation mechanisms. Here we address the consequences of blocking these pathways on jasmonate homeostasis and defenses in double-2ah, triple-3cyp mutants, and a quintuple-5ko line deficient in all known JA-Ile-degrading activities. These lines reacted differently to either mechanical wounding/insect attack or fungal infection. Both pathways contributed additively to JA-Ile removal upon wounding, but their impairement had opposite impacts on insect larvae feeding. By contrast, only the ah pathway was essential for JA-Ile turnover upon infection by Botrytis, yet only 3cyp was more fungus-resistant. Despite building-up extreme JA-Ile levels, 5ko displayed near-wild-type resistance in both bioassays. Molecular analysis indicated that restrained JA-Ile catabolism resulted in enhanced defense/resistance only when genes encoding negative regulators were not simultaneously overstimulated. This occurred in discrete stress- and pathway-specific combinations, providing a framework for future defense-enhancing strategies

Insect oral secretions suppress wound-induced responses in Arabidopsis

The induction of plant defences and their subsequent suppression by insects is thought to be an important factor in the evolutionary arms race between plants and herbivores. Although insect oral secretions (OS) contain elicitors that trigger plant immunity, little is known about the suppressors of plant defences. The Arabidopsis thaliana transcriptome was analysed in response to wounding and OS treatment. The expression of several wound-inducible genes was suppressed after the application of OS from two lepidopteran herbivores, Pieris brassicae and Spodoptera littoralis. This inhibition was correlated with enhanced S. littoralis larval growth, pointing to an effective role of insect OS in suppressing plant defences. Two genes, an ERF/AP2 transcription factor and a proteinase inhibitor, were then studied in more detail. OS-induced suppression lasted for at least 48 h, was independent of the jasmonate or salicylate pathways, and was not due to known elicitors. Interestingly, insect OS attenuated leaf water loss, suggesting that insects have evolved mechanisms to interfere with the induction of water-stress-related defence

X-ray Properties of Young Early Type Galaxies: II. Abundance Ratio in the Hot ISM

Using Chandra X-ray observations of young, post-merger elliptical galaxies, we present X-ray characteristics of age-related observational results, by comparing with typical old elliptical galaxies in terms of metal abundances in the hot interstellar matter (ISM). While the absolute element abundances may be uncertain because of unknown systematic errors and partly because of the smaller amount of hot gas in young ellipticals, the relative abundance ratios (e.g., the alpha-element to Fe ratio, most importantly Si/Fe ratio) can be relatively well constrained. We find that in two young elliptical galaxies (NGC 720 and NGC 3923) the Si to Fe abundance ratio is super-solar (at a 99% significance level), in contrast to typical old elliptical galaxies where the Si to Fe abundance ratio is close to solar. Also the O/Mg ratio is close to solar in the two young elliptical galaxies, as opposed to the sub-solar O/Mg ratio reported in old elliptical galaxies. Both features appear to be less significant outside the effective radius (roughly 30" for the galaxies under study), consistent with the observations that confine to the centermost regions the signatures of recent star formation in elliptical galaxies. Observed differences between young and old elliptical galaxies can be explained by the additional contribution from SNe II ejecta in the former. In young elliptical galaxies, the later star formation associated with recent mergers would have a dual effect, resulting both in galaxy scale winds - and therefore smaller observed amounts of hot ISM - because of the additional SNII heating, and in different metal abundances, because of the additional SNII yields.Comment: 21 pages, 4 color figures, ApJ in press, minor revisions for referee's comments, a new figure adde

X-ray observations of three young, early-type galaxies

Massive haloes of hot plasma exist around some, but not all elliptical galaxies. There is evidence that this is related to the age of the galaxy. In this paper, new X-ray observations are presented for three early-type galaxies that show evidence of youth, in order to investigate their X-ray components and properties. NGC 5363 and NGC 2865 were found to have X-ray emission dominated by purely discrete stellar sources. Limits are set on the mass distribution in one of the galaxies observed with XMM–Newton, NGC 4382, which contains significant hot gas. We detect the X-ray emission in NGC 4382 out to 4re. The mass-to-light ratio is consistent with a stellar origin in the inner regions but rises steadily to values indicative of some dark matter by 4re. These results are set in context with other data drawn from the literature, for galaxies with ages estimated from dynamical or spectroscopic indicators. Ages obtained from optical spectroscopy represent central luminosity-weighted stellar ages. We examine the X-ray evolution with age, normalized by B- and K-band luminosities. Low values of Log(LX/LB) and Log(LX/LK) are found for all galaxies with ages between 1 and 4 Gyr. Luminous X-ray emission only appears in older galaxies. This suggests that the interstellar medium is removed and then it takes several gigayears for hot gas haloes to build up, following a merger. A possible mechanism for gas expulsion might be associated with feedback from an active nucleus triggered during a merger