Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes

Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error correcting codes into larger fault-tolerant networks. Here we present an efficient heuristic decoding scheme for foliated quantum codes, based on message passing between primal and dual code 'sheets'. We test this decoder on two different families of sparse quantum error correcting code: turbo codes and bicycle codes, and show reasonably high numerical performance thresholds. We also present a construction schedule for building such code states.Comment: 23 pages, 15 figures, accepted for publication in Phys. Rev.

Allee Effects May Slow the Spread of Parasites in a Coastal Marine Ecosystem

Allee effects are thought to mediate the dynamics of population colonization, particularly for invasive species. However, Allee effects acting on parasites have rarely been considered in the analogous process of infectious disease establishment and spread. We studied the colonization of uninfected wild juvenile Pacific salmon populations by ectoparasitic salmon lice (Lepeophtheirus salmonis) over a 4-year period. In a data set of 68,376 fish, we observed 85 occurrences of precopular pair formation among 1,259 preadult female and 613 adult male lice. The probability of pair formation was dependent on the local abundance of lice, but this mate limitation is likely offset somewhat by mate-searching dispersal of males among host fish. A mathematical model of macroparasite population dynamics that incorporates the empirical results suggests a high likelihood of a demographic Allee effect, which can cause the colonizing parasite populations to die out. These results may provide the first empirical evidence for Allee effects in a macroparasite. Furthermore, the data give a rare detailed view of Allee effects in colonization dynamics and suggest that Allee effects may dampen the spread of parasites in a coastal marine ecosystem

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

Modélisation numérique des échanges hydrauliques et thermiques entre rivière et nappe alluviale

Dans les régions de plaine, la présence d'un cours d'eau s'accompagne généralement de celle d'une nappe alluviale. Des échanges entre nappe et rivière ont lieu à travers le fond du lit et les berges. Ces écoulements ont une influence sur leur régime thermique respectif. Dans un premier temps, afin de préciser ce terme souvent négligé du bilan thermique des cours d'eau, nous avons calculé, à l'aide d'un modèle numérique, le débit et les apports thermiques correspondants en provenance de la nappe lorsque la nappe alimente la rivière. Les résultats sont fonction de paramètres décrivant la forme du système, de la perméabilité de la couche aquifère et de la pente de la surface piézométrique. A l'inverse, lorsque le cours d'eau alimente la nappe de façon permanente, le régime thermique du cours d'eau, dont les fluctuations annuelles sont plus marquées que celles de la nappe, est susceptible d'influencer celui de la nappe. Nous avons également simulé cette influence. De plus, on a envisagé l'effet sur la nappe d'un échauffement du cours d'eau au-dessus de sa température naturelle. Des abaques ont été tracés pour regrouper les résultats. Ils permettent de connaître pour un grand nombre de situations, la distance depuis la rive à laquelle subsiste un échauffement dans l'aquifère égal à la moitié de l'échauffement de la rivière.In the plain, rivers are generally connected to an aquifer, with water exchanges occurring between the two in both directions. In order to quantify the water and heat exchanges a model based on a cross-section of the alluvial aquifer was designed. A parameter study was conducted with this model to draw nomograms pointing to a broad range of application of the results. These results are expressed in terms of the following parameters :- hydraulic conductivity of the aquifer,- slope of the hydraulic head in the aquifer,- geometric ratios describing the river-aquifer contact and thicknesses of the saturated and unsaturated parts of the aquifer.First the water discharges and corresponding heat transfers from the aquifer toward the river are estimated. This factor of the thermal balance of the river, usually neglected, is important in order to avoid systematic errors when modeling the thermal. behaviour of the river. Restricting the energy balance of a river to the exchanges through the water-atmosphere interface, thus neglecting the inputs of water from the aquifer which is colder than the river in summer and warmer in winter, lead to a biased calibration of the river thermal modes.On the other hand, the river affects the thermal behaviour of the aquifer, since the annual fluctuations of this temperature are greater important than the temperature fluctuations in the aquifer. When river and aquifer only exchange heat by conduction, the river influences the aquifer in a very restricted zone, only a few metres away from the bank. As soon as the river water enters the aquifer however, the thermal influence of the river may extend to several hundreds metres from the bank.The effect on the aquifer of an artificial increase in the river temperature was then simulated to produce situation at steady state for one or two years. The resulting increase in the aquifer temperature is calculated for a cross section. Results are gathered on monograms giving the distance between the river bank and the site where the temperature increase in the aquifer equals 50 % of the temperature increase of the river. This distance depends on the following main variables : water velocity in the aquifer, thickness of the saturated and unsaturated parts of the aquifer.Finally we have shown that the thermal balance of a river shoutd include heat exchanges with the alluvial aquifer, when noticeable inputs from the aquifer exist. Thermal modifications in the alluvial aquifer, due to water advection from the river are also reported.The search for wide applications of the results led us to simplify the actual configurations of the shape of the system and its hydraulic and thermal boundary conditions. At a given site the direction of the water fluxes between river and aquifer may change several times a year and transient hydraulic conditions will have to be considered in some real cases.Applications of these findings may be made, for example, in the fields of water supply or for a heat pump using water from this type of river-aquifer system

Cosmological Implications Of Ultralight Axionlike Fields

Cosmological observations are used to test for imprints of an ultralight axionlike field (ULA), with a range of potentials V(ϕ)∝[1−cos(ϕ/f)]ⁿ set by the axion-field value ϕ and decay constant f. Scalar field dynamics dictate that the field is initially frozen and then begins to oscillate around its minimum when the Hubble parameter drops below some critical value. For n=1, once dynamical, the axion energy density dilutes as matter; for n=2 it dilutes as radiation and for n=3 it dilutes faster than radiation. Both the homogeneous evolution of the ULA and the dynamics of its linear perturbations are included, using an effective fluid approximation generalized from the usual n=1 case. ULA models are parametrized by the redshift z(c) when the field becomes dynamical, the fractional energy density f(z(c))≡Ωₐ(z(c))/Ωₜₒₜ(z(c)) in the axion field at zc, and the effective sound speed c²ₛ. Using Planck, BAO and JLA data, constraints on fzc are obtained. ULAs are degenerate with dark energy for all three potentials if 1+z(c)≲10. When 3×10⁴≳1+z(c)≳10, f(z(c)) is constrained to be ≲0.004 for n=1 and f(z(c))≲0.02 for the other two potentials. The constraints then relax with increasing zc. These results have implications for ULAs as a resolution to cosmological tensions, such as discrepant measurements of the Hubble constant, or the EDGES measurement of the global 21 cm signal

Interaction and flocculation of spherical colloids wetted by a surface-induced corona of paranematic order

Particles dispersed in a liquid crystal above the nematic-isotropic phase transition are wetted by a surface-induced corona of paranematic order. Such coronas give rise to pronounced two-particle interactions. In this article, we report details on the analytical and numerical study of these interactions published recently [Phys. Rev. Lett. 86, 3915 (2001)]. We especially demonstrate how for large particle separations the asymptotic form of a Yukawa potential arises. We show that the Yukawa potential is a surprisingly good description for the two-particle interactions down to distances of the order of the nematic coherence length. Based on this fact, we extend earlier studies on a temperature induced flocculation transition in electrostatically stabilized colloidal dispersions [Phys. Rev. E 61, 2831 (2000)]. We employ the Yukawa potential to establish a flocculation diagram for a much larger range of the electrostatic parameters, namely the surface charge density and the Debye screening length. As a new feature, a kinetically stabilized dispersion close to the nematic-isotropic phase transition is found.Comment: Revtex v4.0, 16 pages, 12 Postscript figures. Accepted for publication in Phys. Rev.

Development of Analytical Models of T- and U-shaped Cantilever-based MEMS Devices for Sensing and Energy Harvesting Applications

Dynamic-mode cantilever-based structures supporting end masses are frequently used as MEMS/NEMS devices in application areas as diverse as chemical/biosensing, atomic force microscopy, and energy harvesting. This paper presents a new analytical solution for the free vibration of a cantilever with a rigid end mass of finite size. The effects of both translational and rotational inertia as well as horizontal eccentricity of the end mass are incorporated into the model. This model is general regarding the end-mass distribution/geometry and is validated here for the commonly encountered geometries of T- and U-shaped cantilevers. Comparisons with 3D FEA simulations and experiments on silicon and organic MEMS are quite encouraging. The new solution gives insight into device behavior, provides an efficient tool for preliminary design, and may be extended in a straightforward manner to account for inherent energy dissipation in the case of organic-based cantilevers

A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid Kernel

The Trotter-Suzuki approximation leads to an efficient algorithm for solving the time-dependent Schr\"odinger equation. Using existing highly optimized CPU and GPU kernels, we developed a distributed version of the algorithm that runs efficiently on a cluster. Our implementation also improves single node performance, and is able to use multiple GPUs within a node. The scaling is close to linear using the CPU kernels, whereas the efficiency of GPU kernels improve with larger matrices. We also introduce a hybrid kernel that simultaneously uses multicore CPUs and GPUs in a distributed system. This kernel is shown to be efficient when the matrix size would not fit in the GPU memory. Larger quantum systems scale especially well with a high number nodes. The code is available under an open source license.Comment: 11 pages, 10 figure

Sexual and marital trajectories and HIV infection among ever-married women in rural Malawi.

OBJECTIVE: To explore how sexual and marital trajectories are associated with HIV infection among ever-married women in rural Malawi. METHODS: Retrospective survey data and HIV biomarker data for 926 ever-married women interviewed in the Malawi Diffusion and Ideational Change Project were used. The associations between HIV infection and four key life course transitions considered individually (age at sexual debut, premarital sexual activity, entry into marriage and marital disruption by divorce or death) were examined. These transitions were then sequenced to construct trajectories that represent the variety of patterns in the data. The association between different trajectories and HIV prevalence was examined, controlling for potentially confounding factors such as age and region. RESULTS: Although each life course transition taken in isolation may be associated with HIV infection, their combined effect appeared to be conditional on the sequence in which they occurred. Although early sexual debut, not marrying one's first sexual partner and having a disrupted marriage each increased the likelihood of HIV infection, their risk was not additive. Women who both delayed sexual debut and did not marry their first partner are, once married, more likely to experience marital disruption and to be HIV-positive. Women who marry their first partner but who have sex at a young age, however, are also at considerable risk. CONCLUSIONS: These findings identify the potential of a life course perspective for understanding why some women become infected with HIV and others do not, as well as the differentials in HIV prevalence that originate from the sequence of sexual and marital transitions in one's life. The analysis suggests, however, the need for further data collection to permit a better examination of the mechanisms that account for variations in life course trajectories and thus in lifetime probabilities of HIV infection