Rigorous mean-field dynamics of lattice bosons: Quenches from the Mott insulator

We provide a rigorous derivation of Gutzwiller mean-field dynamics for lattice bosons, showing that it is exact on fully connected lattices. We apply this formalism to quenches in the interaction parameter from the Mott insulator to the superfluid state. Although within mean-field the Mott insulator is a steady state, we show that a dynamical critical interaction $U_d$ exists, such that for final interaction parameter $U_f>U_d$ the Mott insulator is exponentially unstable towards emerging long-range superfluid order, whereas for $U_f<U_d$ the Mott insulating state is stable. We discuss the implications of this prediction for finite-dimensional systems.Comment: 6 pages, 3 figures, published versio

What's hot in conservation biogeography in a changing climate? Going beyond species range dynamics

International audienceIn recent decades Earth's rapidly changing climate, driven by anthropogenic greenhouse gas emissions, has affected species distributions and phenology, ecological communities and ecosystem processes, effects that are increasingly being observed globally (Allen et al., 2010; Doney et al., 2012; Franklin, Serra‐Diaz, Syphard, & Regan, 2016; Parmesan, 2006; Walther et al., 2002). Pleistocene shifts in species ranges during glacial–interglacial transitions reveal large‐scale biome shifts and no‐analog species assemblages (MacDonald et al., 2008; Nolan et al., 2018; Williams & Jackson, 2007); the pace of current anthropogenic warming outstrips past changes in the Earth system and climate, however, leading to new climate novelties and ecological communities (Ordonez, Williams, & Svenning, 2016). Global scientific consensus now emphasizes that global warming should be kept to 1.5°C to avoid catastrophic changes in ecosystems and the services they provide to people (IPCC, 2018), and climate change threats to biodiversity are being prioritized in international policy response (Ferrier et al., 2016)

Subgame maxmin strategies in zero-sum stochastic games with tolerance levels

We study subgame φ-maxmin strategies in two-player zero-sum stochastic games with finite action spaces and a countable state space. Here φ denotes the tolerance function, a function which assigns a non-negative tolerated error level to every subgame. Subgame φ-maxmin strategies are strategies of the maximizing player that guarantee the lower value in every subgame within the subgame-dependent tolerance level as given by φ. First, we provide necessary and sufficient conditions for a strategy to be a subgame φ-maxmin strategy. As a special case we obtain a characterization for subgame maxmin strategies, i.e. strategies that exactly guarantee the lower value at every subgame. Secondly, we present sufficient conditions for the existence of a subgame φ-maxmin strategy. Finally, we show the possibly surprising result that the existence of subgame φ-maxmin strategies for every positive tolerance function φ is equivalent to the existence of a subgame maxmin strategy

Applicability of the generalized Gibbs ensemble after a quench in the quantum Ising chain

We investigate the out-of-equilibrium dynamics of the one-dimensional quantum Ising model after a sudden quench in the transverse magnetic field. While for a translationally invariant system the statistical description of the asymptotic order parameter correlations after the quench can be performed in terms of the generalized Gibbs ensemble, we show that a breaking of translational invariance, e.g. by perturbing the boundary conditions, disrupts its validity. This effect, which of course vanishes in the thermodynamic limit, is shown to be very important in the presence of disorder

Out of equilibrium dynamics with Matrix Product States

Theoretical understanding of strongly correlated systems in one spatial dimension (1D) has been greatly advanced by the density-matrix renormalization group (DMRG) algorithm, which is a variational approach using a class of entanglement-restricted states called Matrix Product States (MPSs). However, DRMG suffers from inherent accuracy restrictions when multiple states are involved due to multi-state targeting and also the approximate representation of the Hamiltonian and other operators. By formulating the variational approach of DMRG explicitly for MPSs one can avoid errors inherent in the multi-state targeting approach. Furthermore, by using the Matrix Product Operator (MPO) formalism, one can exactly represent the Hamiltonian and other operators. The MPO approach allows 1D Hamiltonians to be templated using a small set of finite state automaton rules without reference to the particular microscopic degrees of freedom. We present two algorithms which take advantage of these properties: eMPS to find excited states of 1D Hamiltonians and tMPS for the time evolution of a generic time-dependent 1D Hamiltonian. We properly account for time-ordering of the propagator such that the error does not depend on the rate of change of the Hamiltonian. Our algorithms use only the MPO form of the Hamiltonian, and so are applicable to microscopic degrees of freedom of any variety, and do not require Hamiltonian-specialized implementation. We benchmark our algorithms with a case study of the Ising model, where the critical point is located using entanglement measures. We then study the dynamics of this model under a time-dependent quench of the transverse field through the critical point. Finally, we present studies of a dipolar, or long-range Ising model, again using entanglement measures to find the critical point and study the dynamics of a time-dependent quench through the critical point.Comment: 35 pages, 10 figures, submitted to NJP for the focus issue "Out of equilibrium dynamics in strongly interacting 1D systems

Polymorphisms in the gene regions of the adaptor complex LAMTOR2/LAMTOR3 and their association with breast cancer risk.

Background: The late endosomal LAMTOR complex serves as a convergence point for both the RAF/MEK/ERK and the PI3K/AKT/mTOR pathways. Interestingly, both of these signalling cascades play a significant role in the aetiology of breast cancer. Our aim was to address the possible role of genetic polymorphisms in LAMTOR2 and LAMTOR3 as genetic risk factors for breast cancer. Methodology/Results: We sequenced the exons and exon-intron boundaries of LAMTOR2 (p14) and LAMTOR3 (MP1) in 50 prospectively collected pairs of cancerous tissue and blood samples from breast cancer patients and compared their genetic variability. We found one single nucleotide polymorphism (SNP) in LAMTOR2 (rs7541) and two SNPs in LAMTOR3 (rs2298735 and rs148972953) in both tumour and blood samples, but no somatic mutations in cancerous tissues. In addition, we genotyped all three SNPs in 296 samples from the Risk Prediction of Breast Cancer Metastasis Study and found evidence of a genetic association between rs148972953 and oestrogen (ER) and progesterone receptor negative status (PR) (ER: OR = 3.60 (1.15-11.28); PR: OR = 4.27 (1.43-12.72)). However, when we additionally genotyped rs148972953 in the MARIE study including 2,715 breast cancer cases and 5,216 controls, we observed neither a difference in genotype frequencies between patients and controls nor was the SNP associated with ER or PR. Finally, all three SNPs were equally frequent in breast cancer samples and female participants (n = 640) of the population-based SAPHIR Study. Conclusions: The identified polymorphisms in LAMTOR2 and LAMTOR3 do not seem to play a relevant role in breast cancer. Our work does not exclude a role of other not yet identified SNPs or that the here annotated polymorphism may in fact play a relevant role in other diseases. Our results underscore the importance of replication in association studies

In situ δ7Li, Li/Ca, and Mg/Ca analyses of synthetic aragonites

Author Posting. © American Geophysical Union, 2011. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 12 (2011): Q03001, doi:10.1029/2010GC003322.In situ secondary ion mass spectrometry (SIMS) analyses of δ7Li, Li/Ca, and Mg/Ca were performed on five synthetic aragonite samples precipitated from seawater at 25°C at different rates. The compositions of δ7Li in bulk aragonites and experimental fluids were measured by multicollector inductively coupled plasma–mass spectrometry (MC-ICP-MS). Both techniques yielded similar δ7Li in aragonite when SIMS analyses were corrected to calcium carbonate reference materials. Fractionation factors α7Li/6Li range from 0.9895 to 0.9923, which translates to a fractionation between aragonite and fluid from −10.5‰ to −7.7‰. The within-sample δ7Li range determined by SIMS is up to 27‰, exceeding the difference between bulk δ7Li analyses of different aragonite precipitates. Moreover, the centers of aragonite hemispherical bundles (spherulites) are enriched in Li/Ca and Mg/Ca relative to spherulite fibers by up to factors of 2 and 8, respectively. The Li/Ca and Mg/Ca ratios of spherulite fibers increase with aragonite precipitation rate. These results suggest that precipitation rate is a potentially important consideration when using Li isotopes and elemental ratios in natural carbonates as a proxy for seawater composition and temperature.SIMS analyses were supported by U.S. NSF, EAR, Instrumentation and Facilities Program. The development of the method for bulk d7Li analysis and the MC‐ICP‐MS measurements were covered by NSF grant EAR/IF‐0318137. Precipitation experiments were supported by NSF through grants OCE‐0402728, OCE‐0527350, and OCE‐0823527 to Glenn Gaetani and Anne Cohen and through grant EAR‐0337481 to Bruce Watson

Functional diversity of chemokines and chemokine receptors in response to viral infection of the central nervous system.

Encounters with neurotropic viruses result in varied outcomes ranging from encephalitis, paralytic poliomyelitis or other serious consequences to relatively benign infection. One of the principal factors that control the outcome of infection is the localized tissue response and subsequent immune response directed against the invading toxic agent. It is the role of the immune system to contain and control the spread of virus infection in the central nervous system (CNS), and paradoxically, this response may also be pathologic. Chemokines are potent proinflammatory molecules whose expression within virally infected tissues is often associated with protection and/or pathology which correlates with migration and accumulation of immune cells. Indeed, studies with a neurotropic murine coronavirus, mouse hepatitis virus (MHV), have provided important insight into the functional roles of chemokines and chemokine receptors in participating in various aspects of host defense as well as disease development within the CNS. This chapter will highlight recent discoveries that have provided insight into the diverse biologic roles of chemokines and their receptors in coordinating immune responses following viral infection of the CNS

Parent-of-origin-specific allelic associations among 106 genomic loci for age at menarche.

Age at menarche is a marker of timing of puberty in females. It varies widely between individuals, is a heritable trait and is associated with risks for obesity, type 2 diabetes, cardiovascular disease, breast cancer and all-cause mortality. Studies of rare human disorders of puberty and animal models point to a complex hypothalamic-pituitary-hormonal regulation, but the mechanisms that determine pubertal timing and underlie its links to disease risk remain unclear. Here, using genome-wide and custom-genotyping arrays in up to 182,416 women of European descent from 57 studies, we found robust evidence (P < 5 × 10(-8)) for 123 signals at 106 genomic loci associated with age at menarche. Many loci were associated with other pubertal traits in both sexes, and there was substantial overlap with genes implicated in body mass index and various diseases, including rare disorders of puberty. Menarche signals were enriched in imprinted regions, with three loci (DLK1-WDR25, MKRN3-MAGEL2 and KCNK9) demonstrating parent-of-origin-specific associations concordant with known parental expression patterns. Pathway analyses implicated nuclear hormone receptors, particularly retinoic acid and γ-aminobutyric acid-B2 receptor signalling, among novel mechanisms that regulate pubertal timing in humans. Our findings suggest a genetic architecture involving at least hundreds of common variants in the coordinated timing of the pubertal transition

FGF receptor genes and breast cancer susceptibility: results from the Breast Cancer Association Consortium

Background:Breast cancer is one of the most common malignancies in women. Genome-wide association studies have identified FGFR2 as a breast cancer susceptibility gene. Common variation in other fibroblast growth factor (FGF) receptors might also modify risk. We tested this hypothesis by studying genotyped single-nucleotide polymorphisms (SNPs) and imputed SNPs in FGFR1, FGFR3, FGFR4 and FGFRL1 in the Breast Cancer Association Consortium. Methods:Data were combined from 49 studies, including 53 835 cases and 50 156 controls, of which 89 050 (46 450 cases and 42 600 controls) were of European ancestry, 12 893 (6269 cases and 6624 controls) of Asian and 2048 (1116 cases and 932 controls) of African ancestry. Associations with risk of breast cancer, overall and by disease sub-type, were assessed using unconditional logistic regression. Results:Little evidence of association with breast cancer risk was observed for SNPs in the FGF receptor genes. The strongest evidence in European women was for rs743682 in FGFR3; the estimated per-allele odds ratio was 1.05 (95 confidence interval=1.02-1.09, P=0.0020), which is substantially lower than that observed for SNPs in FGFR2. Conclusion:Our results suggest that common variants in the other FGF receptors are not associated with risk of breast cancer to the degree observed for FGFR2. © 2014 Cancer Research UK