On the flexibility of the design of Multiple Try Metropolis schemes

The Multiple Try Metropolis (MTM) method is a generalization of the classical Metropolis-Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities and show different numerical results

Multiplicative random walk Metropolis-Hastings on the real line

In this article we propose multiplication based random walk Metropolis Hastings (MH) algorithm on the real line. We call it the random dive MH (RDMH) algorithm. This algorithm, even if simple to apply, was not studied earlier in Markov chain Monte Carlo literature. The associated kernel is shown to have standard properties like irreducibility, aperiodicity and Harris recurrence under some mild assumptions. These ensure basic convergence (ergodicity) of the kernel. Further the kernel is shown to be geometric ergodic for a large class of target densities on $\mathbb{R}$. This class even contains realistic target densities for which random walk or Langevin MH are not geometrically ergodic. Three simulation studies are given to demonstrate the mixing property and superiority of RDMH to standard MH algorithms on real line. A share-price return data is also analyzed and the results are compared with those available in the literature

Coupled coarse graining and Markov Chain Monte Carlo for lattice systems

We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type algorithm with the proposal probability transition matrix based on the coarse-grained approximating measures introduced in a series of works of M. Katsoulakis, A. Majda, D. Vlachos and P. Plechac, L. Rey-Bellet and D.Tsagkarogiannis,. We prove that the proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.Comment: 20 pages, 4 figure

Competition-Colonization Trade-Offs, Competitive Uncertainty, and the Evolutionary Assembly of Species

We utilize a standard competition-colonization metapopulation model in order to study the evolutionary assembly of species. Based on earlier work showing how models assuming strict competitive hierarchies will likely lead to runaway evolution and self-extinction for all species, we adopt a continuous competition function that allows for levels of uncertainty in the outcome of competition. We then, by extending the standard patch-dynamic metapopulation model in order to include evolutionary dynamics, allow for the coevolution of species into stable communities composed of species with distinct limiting similarities. Runaway evolution towards stochastic extinction then becomes a limiting case controlled by the level of competitive uncertainty. We demonstrate how intermediate competitive uncertainty maximizes the equilibrium species richness as well as maximizes the adaptive radiation and self-assembly of species under adaptive dynamics with mutations of non-negligible size. By reconciling competition-colonization tradeoff theory with co-evolutionary dynamics, our results reveal the importance of intermediate levels of competitive uncertainty for the evolutionary assembly of species

Empowerment and Parent Gain as Mediators and Moderators of Distress in Mothers of Children with Autism Spectrum Disorders

Mothers of children with Autism Spectrum Disorders (ASD) experience considerable amounts of distress and experiences of crisis. The Family Adjustment and Adaptation Response model provides a theory for understanding the experience of distress and family crisis in families, and the purpose of the present study was to examine experiences of distress in mothers of individuals with ASD using this framework. We specifically investigated how parent empowerment and positive gain are related to their experiences of distress, whether as mediators or as moderators of child aggression. Participants included 156 mothers of children with ASD ranging in age from 4 – 21 years. Mothers completed an online survey of demographics, problem behaviors, family empowerment, positive gain, and distress. We conducted path analyses of multiple mediation and moderation. Results indicated that greater child problem behavior was related to less parent empowerment, which was related to greater maternal distress, supporting empowerment as a partial mediator. At the same time, greater child aggression was not related to maternal distress in mothers who report high rates of positive gain, suggesting that parent gain functions as a moderator. The implications for how and when clinicians intervene with families of children with ASD are discussed

Quantum spin liquid states in the two dimensional kagome antiferromagnets, ZnxCu4-x(OD)6Cl2

A three-dimensional system of interacting spins typically develops static long-range order when it is cooled. If the spins are quantum (S = 1/2), however, novel quantum paramagnetic states may appear. The most highly sought state among them is the resonating valence bond (RVB) state in which every pair of neighboring quantum spins form entangled spin singlets (valence bonds) and the singlets are quantum mechanically resonating amongst all the possible highly degenerate pairing states. Here we provide experimental evidence for such quantum paramagnetic states existing in frustrated antiferromagnets, ZnxCu4-x(OD)6Cl2, where the S = 1/2 magnetic Cu2+ moments form layers of a two-dimensional kagome lattice. We find that in Cu4(OD)6Cl2, where distorted kagome planes are weakly coupled to each other, a dispersionless excitation mode appears in the magnetic excitation spectrum below ~ 20 K, whose characteristics resemble those of quantum spin singlets in a solid state, known as a valence bond solid (VBS), that breaks translational symmetry. Doping nonmagnetic Zn2+ ions reduces the distortion of the kagome lattice, and weakens the interplane coupling but also dilutes the magnetic occupancy of the kagome lattice. The VBS state is suppressed and for ZnCu3(OD)6Cl2 where the kagome planes are undistorted and 90% occupied by the Cu2+ ions, the low energy spin fluctuations in the spin liquid phase become featureless

Pinwheel VBS state and triplet excitations in the two-dimensional deformed kagome lattice

Determining ground states of correlated electron systems is fundamental to understanding novel phenomena in condensed matter physics. A difficulty, however, arises in a geometrically frustrated system in which the incompatibility between the global topology of an underlying lattice and local spin interactions gives rise to macroscopically degenerate ground states, potentially prompting the emergence of quantum spin states, such as resonating valence bond (RVB) and valence bond solid (VBS). Although theoretically proposed to exist in a kagome lattice -- one of the most highly frustrated lattices in two dimensions (2D) being comprised of corner-sharing triangles -- such quantum-fluctuation-induced states have not been observed experimentally. Here we report the first realization of the "pinwheel" VBS ground state in the S=1/2 deformed kagome lattice antiferromagnet Rb2Cu3SnF12. In this system, a lattice distortion breaks the translational symmetry of the ideal kagome lattice and stabilizes the VBS state.Comment: 10 pages, 4 figures and Supplemental Informatio

Evidence from Individual Inference for High-Dimensional Coexistence: Long-Term Experiments on Recruitment Response

Background: For competing species to coexist, individuals must compete more with others of the same species than with those of other species. Ecologists search for tradeoffs in how species might partition the environment. The negative correlations among competing species that would be indicative of tradeoffs are rarely observed. A recent analysis showed that evidence for partitioning the environment is available when responses are disaggregated to the individual scale, in terms of the covariance structure of responses to environmental variation. That study did not relate that variation to the variables to which individuals were responding. To understand how this pattern of variation is related to niche variables, we analyzed responses to canopy gaps, long viewed as a key variable responsible for species coexistence. Methodology/Principal Findings: A longitudinal intervention analysis of individual responses to experimental canopy gaps with 12 yr of pre-treatment and 8 yr post-treatment responses showed that species-level responses are positively correlated – species that grow fast on average in the understory also grow fast on average in response to gap formation. In other words, there is no tradeoff. However, the joint distribution of individual responses to understory and gap showed a negative correlation – species having individuals that respond most to gaps when previously growing slowly also have individuals that respond least to gaps when previously growing rapidly (e.g., Morus rubra), and vice versa (e.g., Quercus prinus). Conclusions/Significance: Because competition occurs at the individual scale, not the species scale, aggregated speciesleve

Five fathers' experience of an adult son sustaining a cervical spinal cord injury: an Interpretative Phenomenological Analysis

The paper presents an in-depth idiographic study exploring the experience of fathers who have an adult son with a cervical spinal cord injury (SCI). Five participants were recruited and individual semi-structured interviews were conducted. The interviews were transcribed verbatim and analysed using Interpretative Phenomenological Analysis (IPA). Two super-ordinate themes are presented highlighting. Firstly, the ongoing negative impact of their sons’ injury on the participants’ role as fathers’. This comprises the negative impact on emotions with guilt common for failing in their perceived role as a father. The dissonance experienced between wanting to help encourage their sons’ independence. Concern experienced due to their sons altered life trajectory and anxiety because they won’t be alive to protect their son in the future. Secondly, how participants cope and adjust to their son’s SCI are presented. Comprising of how positive thinking, such as focusing on their son surviving the trauma; and the influence of seeing their son cope well affects how participants cope. Also, reflecting on how the injury has changed their life helps participants, to an extent, make sense of the trauma. The results are discussed in relation to the relevant extant literature to give a unique perspective about how SCI impacts their perceived role as fathers and the struggle to cope and adjust to the trauma. Future research investigating the impact of SCI on the family is warranted to better understand the wider implications

Global parameter search reveals design principles of the mammalian circadian clock

Background: Virtually all living organisms have evolved a circadian (~24 hour) clock that controls physiological and behavioural processes with exquisite precision throughout the day/night cycle. The suprachiasmatic nucleus (SCN), which generates these ~24 h rhythms in mammals, consists of several thousand neurons. Each neuron contains a gene-regulatory network generating molecular oscillations, and the individual neuron oscillations are synchronised by intercellular coupling, presumably via neurotransmitters. Although this basic mechanism is currently accepted and has been recapitulated in mathematical models, several fundamental questions about the design principles of the SCN remain little understood. For example, a remarkable property of the SCN is that the phase of the SCN rhythm resets rapidly after a 'jet lag' type experiment, i.e. when the light/ dark (LD) cycle is abruptly advanced or delayed by several hours. Results: Here, we describe an extensive parameter optimization of a previously constructed simplified model of the SCN in order to further understand its design principles. By examining the top 50 solutions from the parameter optimization, we show that the neurotransmitters' role in generating the molecular circadian rhythms is extremely important. In addition, we show that when a neurotransmitter drives the rhythm of a system of coupled damped oscillators, it exhibits very robust synchronization and is much more easily entrained to light/dark cycles. We were also able to recreate in our simulations the fast rhythm resetting seen after a 'jet lag' type experiment. Conclusion: Our work shows that a careful exploration of parameter space for even an extremely simplified model of the mammalian clock can reveal unexpected behaviours and non-trivial predictions. Our results suggest that the neurotransmitter feedback loop plays a crucial role in the robustness and phase resetting properties of the mammalian clock, even at the single neuron level