An NPZ Model with State-Dependent Delay due to Size-Structure in Juvenile Zooplankton

The study of planktonic ecosystems is important as they make up the bottom trophic levels of aquatic food webs. We study a closed Nutrient-Phytoplankton-Zooplankton (NPZ) model that includes size structure in the juvenile zooplankton. The closed nature of the system allows the formulation of a conservation law of biomass that governs the system. The model consists of a system of nonlinear ordinary differential equation coupled to a partial differential equation. We are able to transform this system into a system of delay differential equations where the delay is of threshold type and is state-dependent. The system of delay differential equations can be further transformed into one with fixed delay. Using the different forms of the model we perform a qualitative analysis of the solutions, which includes studying existence and uniqueness, positivity and boundedness, local and global stability, and conditions for extinction. Key parameters that are explored are the total biomass in the system and the maturity level at which the juvenile zooplankton reach maturity. Numerical simulations are also performed to verify our analytical results

Quantum Metropolis Sampling

The original motivation to build a quantum computer came from Feynman who envisaged a machine capable of simulating generic quantum mechanical systems, a task that is believed to be intractable for classical computers. Such a machine would have a wide range of applications in the simulation of many-body quantum physics, including condensed matter physics, chemistry, and high energy physics. Part of Feynman's challenge was met by Lloyd who showed how to approximately decompose the time-evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that basically acquired a monopoly for the simulation of interacting particles. Here, we demonstrate how to implement a quantum version of the Metropolis algorithm on a quantum computer. This algorithm permits to sample directly from the eigenstates of the Hamiltonian and thus evades the sign problem present in classical simulations. A small scale implementation of this algorithm can already be achieved with today's technologyComment: revised versio

Characterization of complex quantum dynamics with a scalable NMR information processor

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behaviour and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system, or measuring the decoherence rate from engineered environments.Comment: 4pages, 3 figures, revtex4, updated with version closer to that publishe

Practical learning method for multi-scale entangled states

We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of measurements is polynomial in the number of particles. Data post-processing for state reconstruction uses standard tools, namely matrix diagonalisation and conjugate gradient method, and scales polynomially with the number of particles. Our method prevents the build-up of errors from both numerical and experimental imperfections

Exponential speed-up with a single bit of quantum information: Testing the quantum butterfly effect

We present an efficient quantum algorithm to measure the average fidelity decay of a quantum map under perturbation using a single bit of quantum information. Our algorithm scales only as the complexity of the map under investigation, so for those maps admitting an efficient gate decomposition, it provides an exponential speed up over known classical procedures. Fidelity decay is important in the study of complex dynamical systems, where it is conjectured to be a signature of quantum chaos. Our result also illustrates the role of chaos in the process of decoherence.Comment: 4 pages, 2 eps figure

Size-structured planktonic ecosystems: constraints, controls and assembly instructions

Here we present a nutrient–phytoplankton–zooplankton (NPZ) model that has arbitrary size-resolution within the phytoplankton- and zooplankton-state variables. The model assumes allometric scaling of biological parameters. This particular version of the model (herbivorous zooplankton only) has analytical solutions that allow efficient exploration of the effects of allometric dependencies of various biological processes on the model's equilibrium solutions. The model shows that there are constraints on the possible combinations of allometric scalings of the biological rates that will allow ecosystems to be structured as we observe (larger organisms added as the total biomass increases). The diversity (number of size classes occupied) of the ecosystem is the result of simultaneous bottom-up and top-down control: resources determine which classes can exist; predation determines which classes do exist. Thus, the simultaneous actions of bottom-up and top-down controls are essential for maintaining and structuring planktonic ecosystems. One important conclusion from this model is that there are multiple, independent ways of obtaining any given biomass spectrum, and that the spectral slope is not, in and of itself, very informative concerning the underlying dynamics. There is a clear need for improved size-resolved field measurements of biological rates; these will both elucidate biological processes in the field, and allow strong testing of size-structured models of planktonic ecosystems

On compatibility and improvement of different quantum state assignments

When Alice and Bob have different quantum knowledges or state assignments (density operators) for one and the same specific individual system, then the problems of compatibility and pooling arise. The so-called first Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in terms of possessed or sharp (i. e., probability one) properties. The second BFM condition is shown to be generally invalid in an infinite-dimensional state space. An argument leading to a procedure of improvement of one state assifnment on account of the other and vice versa is presented.Comment: 8 page

A niche perspective on the range expansion of symbionts

Range expansion results from complex eco-evolutionary processes where range dynamics and niche shifts interact in a novel physical space and/or environment, with scale playing a major role. Obligate symbionts (i.e. organisms permanently living on hosts) differ from free-living organisms in that they depend on strong biotic interactions with their hosts which alter their niche and spatial dynamics. A symbiotic lifestyle modifies organism–environment relationships across levels of organisation, from individuals to geographical ranges. These changes influence how symbionts experience colonisation and, by extension, range expansion. Here, we investigate the potential implications of a symbiotic lifestyle on range expansion capacity. We present a unified conceptual overview on range expansion of symbionts that integrates concepts grounded in niche and metapopulation theories. Overall, we explain how niche-driven and dispersal-driven processes govern symbiont range dynamics through their interaction across scales, from host switching to geographical range shifts. First, we describe a background framework for range dynamics based on metapopulation concepts applied to symbiont organisation levels. Then, we integrate metapopulation processes operating in the physical space with niche dynamics grounded in the environmental arena. For this purpose, we provide a definition of the biotope (i.e. living place) specific to symbionts as a hinge concept to link the physical and environmental spaces, wherein the biotope unit is a metapopulation patch (either a host individual or a land fragment). Further, we highlight the dual nature of the symbionts' niche, which is characterised by both host traits and the external environment, and define proper conceptual variants to provide a meaningful unification of niche, biotope and symbiont organisation levels. We also explore variation across systems in the relative relevance of both external environment and host traits to the symbiont's niche and their potential implications on range expansion. We describe in detail the potential mechanisms by which hosts, through their function as biotopes, could influence how some symbionts expand their range – depending on the life history and traits of both associates. From the spatial point of view, hosts can extend symbiont dispersal range via host-mediated dispersal, although the requirement for among-host dispersal can challenge symbiont range expansion. From the niche point of view, homeostatic properties of host bodies may allow symbiont populations to become insensitive to off-host environmental gradients during host-mediated dispersal. These two potential benefits of the symbiont–host interaction can enhance symbiont range expansion capacity. On the other hand, the central role of hosts governing the symbiont niche makes symbionts strongly dependent on the availability of suitable hosts. Thus, environmental, dispersal and biotic barriers faced by suitable hosts apply also to the symbiont, unless eventual opportunities for host switching allow the symbiont to expand its repertoire of suitable hosts (thus expanding its fundamental niche). Finally, symbionts can also improve their range expansion capacity through their impacts on hosts, via protecting their affiliated hosts from environmental harshness through biotic facilitation.info:eu-repo/semantics/publishedVersio

The effect of stochastic perturbations on plankton transport by internal solitary waves

Internal solitary and solitary-like waves are a commonly observed feature of density stratified natural waters, including lakes and the coastal ocean. Since such waves induce significant currents throughout the water column they can be responsible for significant transport of both passive and swimming biota. We consider simple models of moving zooplankton based on the Langevin equation. The small amplitude randomness significantly alters the nature of particle motion. In particular, passage through the wave leads to strongly non Gaussian particle distributions. When the plankton swims to return to its equilibrium photic level, a steady state that balances randomness, swimming and wave-induced motions is possible. We discuss possible implications of this steady state for organisms that feed on plankton

Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10^-5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wavefunctions than classical computers.Comment: 11 pages, 13 figure