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This paper establishes a data-driven modeling framework for lean Hydrogen (H2)-air reaction rates for the Large Eddy Simulation (LES) of turbulent reactive flows. This is particularly challenging since H2 molecules diffuse much faster than heat, leading to large variations in burning rates, thermodiffusive instabilities at the subfilter scale, and complex turbulence-chemistry interactions. Our data-driven approach leverages a Convolutional Neural Network (CNN), trained to approximate filtered burning rates from emulated LES data. First, five different lean premixed turbulent H2-air flame Direct Numerical Simulations (DNSs) are computed each with a unique global equivalence ratio. Second, DNS snapshots are filtered and downsampled to emulate LES data. Third, a CNN is trained to approximate the filtered burning rates as a function of LES scalar quantities: progress variable, local equivalence ratio and flame thickening due to filtering. Finally, the performances of the CNN model are assessed on test solutions never seen during training. The model retrieves burning rates with very high accuracy. It is also tested on two filter and downsampling parameters and two global equivalence ratios between those used during training. For these interpolation cases, the model approximates burning rates with low error even though the cases were not included in the training dataset. This a priori study shows that the proposed data-driven machine learning framework is able to address the challenge of modeling lean premixed H2-air burning rates. It paves the way for a new modeling paradigm for the simulation of carbon-free hydrogen combustion systems.

Turbulent flows at the surface of the ocean deviate from geostrophic equilibrium on scales smaller than about 10 km. These scales are associated with important vertical transport of active and passive tracers, and should play a prominent role in the heat transport at climatic scales and for plankton dynamics. Measuring velocity fields on such small scales is notoriously difficult but new, high-resolution satellite altimetry is starting to reveal them. However, the satellite-derived velocities essentially represent the geostrophic flow component, and the impact of unresolved ageostrophic motions on particle dispersion needs to be understood to properly characterize transport properties. Here, we investigate ocean fine-scale turbulence using a model that represents some of the processes due to ageostrophic dynamics. We take a Lagrangian approach and focus on the predictability of the particle dynamics, comparing trajectories advected by either the full flow or by its geostrophic component only. Our results indicate that, over long times, relative dispersion is marginally affected by the filtering of the ageostrophic component. Nevertheless, advection by the filtered flow leads to an overestimation of the typical pair-separation rate, and to a bias on trajectories (in terms of displacement from the actual ones), whose importance grows with the Rossby number. We further explore the intensity of the transient particle clustering induced by ageostrophic motions and find that it can be significant, even for small flow compressibility. Indeed, we show that clustering is here due to the interplay between compressibility and persistent flow structures that trap particles, enhancing their aggregation., Comment: 19 pages, 10 figures

Variational data assimilation in ocean models depends on the ability to model general correlation operators in the presence of coastlines. Grid-point filters based on diffusion operators are widely used for this purpose, but come with a computational bottleneck - the costly estimation of normalization factors for every model grid point. In this paper, we show that a simple convolutional neural network can effectively learn these normalization factors with better accuracy than the current operational methods. Our network is tested with a two-dimensional diffusion operator from the NEMOVAR ocean data assimilation system, applied to a global ocean grid with approximately one degree horizontal resolution. The network is trained on exact normalization factors estimated by a brute-force method. Knowing that convolutional networks can only model translation-equivariant functions, we ensure that the normalization estimation problem is indeed translation-equivariant. Specifically, we show how the number of inputs of this problem can be reduced while preserving translation equivariance. Adding the distance to the coastline as an input channel is found to improve the performance of the network around coastlines. Extensions to three-dimensional diffusion and to higher horizontal resolutions are discussed. Removing the computational bottleneck associated with normalization opens the way to using adaptive correlation models for operational ocean data assimilation. The code for this work is publicly available at https://github.com/FolkeKS/DL-normalization/tree/core-features

Upper-ocean turbulent flows at horizontal length scales smaller than the deformation radius depart from geostrophic equilibrium and develop important vertical velocities, which are key to marine ecology and climatic processes. Due to their small size and fast temporal evolution, these fine scales are difficult to measure during oceanographic campaigns. Instruments such as Lagrangian drifters have provided another way to characterize these scales through the analysis of pair-dispersion evolution, and have pointed out striking particle convergence events. By means of numerical simulations, we investigate such processes in a model of surface-ocean turbulence that includes ageostrophic motions. This model originates from a Rossby-number expansion of the primitive equations and reduces to the surface quasi-geostrophic model, a paradigm of submesoscale dynamics, in the limit of vanishing Rossby number. We focus on the effect of the ageostrophic dynamics on the pair-dispersion and clustering properties of Lagrangian tracer particles at the ocean surface. Our results indicate that while over long times the pair separation process is barely affected by the ageostrophic component of the velocity field, the latter is responsible for the formation of temporary particle aggregates, and the intensity of this phenomenon increases with the Rossby number. We further show that Lagrangian tracers preferentially accumulate in cyclonic frontal regions, which is in agreement with observations and other more realistic modeling studies. These findings appear interesting to improve the understanding of the turbulent transport by ocean fine scales, and in light of upcoming, new high-resolution satellite data of surface velocity fields., Comment: 12 pages, 10 figures

Quantum measurement is important to quantum computing as it extracts the outcome of the circuit at the end of the computation. Previously, all measurements have to be done at the end of the circuit. Otherwise, it will incur significant errors. But it is not the case now. Recently IBM started supporting dynamic circuits through hardware (instead of software by simulator). With mid-circuit hardware measurement, we can improve circuit efficacy and fidelity from three aspects: (a) reduced qubit usage, (b) reduced swap insertion, and (c) improved fidelity. We demonstrate this using real-world applications Bernstein Verizani on real hardware and show that circuit resource usage can be improved by 60\%, and circuit fidelity can be improved by 15\%. We design a compiler-assisted tool that can find and exploit the tradeoff between qubit reuse, fidelity, gate count, and circuit duration. We also developed a method for identifying whether qubit reuse will be beneficial for a given application. We evaluated our method on a representative set of essential applications. We can reduce resource usage by up to 80\% and circuit fidelity by up to 20\%.

The problem of computing the conditional expectation E[f (Y)|X] with least-square Monte-Carlo is of general importance and has been widely studied. To solve this problem, it is usually assumed that one has as many samples of Y as of X. However, when samples are generated by computer simulation and the conditional law of Y given X can be simulated, it may be relevant to sample K $\in$ N values of Y for each sample of X. The present work determines the optimal value of K for a given computational budget, as well as a way to estimate it. The main take away message is that the computational gain can be all the more important that the computational cost of sampling Y given X is small with respect to the computational cost of sampling X. Numerical illustrations on the optimal choice of K and on the computational gain are given on different examples including one inspired by risk management., Comment: Methodology and Computing in Applied Probability, In press

Starting from the radiative transfer equation and its usual boundary conditions, the objective of this work is to design Monte Carlo algorithms estimating the specific intensity spatial and angular derivatives as well as its geometric sensitivity. The present document is structured in three parts, each of them dedicated to a specific derivative of the intensity. Although they are all assembled here in one document each derivative is of interest independently whether it be for radiative transfers analysis or engineering conception. Therefore, they are thought to be written as three different papers and are presented here as such. Estimating derivatives of the specific intensity when solving radiative transfers using a Monte-Carlo algorithm is challenging. Finite differences are often not sufficiently accurate and directly estimating the derivative from a specific Monte-Carlo algorithm can lead to arduous formal or numerical developments. The proposition here is to work from the radiative transfer equation and its boundary conditions to design a physical model for each derivatives. Only then Monte-Carlo algorithms are built from the derivatives differential equations using the usual equivalent path integral. Since the same methodology is applied to the specific intensity spatial derivative, angular derivative and geometric sensitivity we chose to keep the same writing structure for all three parts so that all common ideas and developments appears exactly the same. We believe this choice to be coherent to facilitate the reader's understanding. Finally, these are preliminary versions of the final papers: for each parts the theory is fully described, but, although they have been implemented, the examples and algorithms sections are not always complete. This will be mentioned in the introductions of the concerned sections.

Turbulence in the upper ocean in the submesoscale range (scales smaller than the deformation radius) plays an important role for the heat exchange with the atmosphere and for oceanic biogeochemistry. Its dynamics should strongly depend on the seasonal cycle and the associated mixed-layer instabilities. The latter are particularly relevant in winter and are responsible for the formation of energetic small scales that extend over the whole depth of the mixed layer. The knowledge of the transport properties of oceanic flows at depth, which is essential to understand the coupling between surface and interior dynamics, however, is still limited. By means of numerical simulations, we explore the Lagrangian dispersion properties of turbulent flows in a quasi-geostrophic model system allowing for both thermocline and mixed-layer instabilities. The results indicate that, when mixed-layer instabilities are present, the dispersion regime is local from the surface down to depths comparable with that of the interface with the thermocline, while in their absence dispersion quickly becomes nonlocal versus depth. We then identify the origin of such behavior in the existence of fine-scale energetic structures due to mixed-layer instabilities. We further discuss the effect of vertical shear on the Lagrangian particle spreading and address the correlation between the dispersion properties at the surface and at depth, which is relevant to assess the possibility of inferring the dynamical features of deeper flows from the more accessible surface ones., Comment: 13 pages, 11 figures

We demonstrate swept-source optical coherence tomography in real-time by high throughput digital Fresnel hologram rendering from optically-acquired interferograms with a high-speed camera. The interferogram stream is spatially rescaled with respect to wavelength to compensate for field-of-view dilation inherent to discrete Fresnel transformation. Holograms are calculated from an input stream of 16-bit, 1024-by-1024-pixel interferograms recorded at up to 512 frames per second with a digital camera. All calculations are performed by a NVIDIA TITAN Xp graphics card on single-precision floating-point complex-valued arrays (32-bit per quadrature). It allows sustained computation of 1024-by-1024-by-256-voxel volumes at 10 billion voxel/s, from which three perpendicular cuts are displayed in real-time at user-selected locations, up to 38 frames per second., Comment: 5 pages, 5 figs

The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value. These conditional expectations are classically computed by regression techniques on a finite dimensional vector space. In this work, we study neural networks approximations of conditional expectations. We prove the convergence of the well-known Longstaff and Schwartz algorithm when the standard least-square regression is replaced by a neural network approximation. We illustrate the numerical efficiency of neural networks as an alternative to standard regression methods for approximating conditional expectations on several numerical examples.

We present a unified approach to those observables of stochastic processes under reset that take the form of averages of functionals depending on the most recent renewal period. We derive solutions for the observables, and determine the conditions for existence and equality of their stationary values with and without reset. For intermittent reset times, we derive exact asymptotic expressions for observables that vary asymptotically as a power of time. We illustrate the general approach with general and particular results for the power spectral density, and moments of subdiffusive processes. We focus on coupling of the process and reset via a diffusion-decay process with microscopic dependence between transport and decay. In contrast to the uncoupled case, we find that restarting the particle upon decay does not produce a probability current equal to the decay rate, but instead drastically alters the time dependence of the decay rate and the resulting current., Comment: 15 pages, 2 figures, corrected copying error in (S42), homogenize terminology, v3 add references, improve title

When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each problem-parameter $\varsigma$. The principle is the following: Monte Carlo considers A as the expectation of a random variable, this expectation is an integral, this integral can be derivated as function of the problem-parameter to give a new integral, and this new integral can in turn be evaluated using Monte Carlo. The two Monte Carlo computations (of A and $\partial$ $\varsigma$ A) are simultaneous when they make use of the same random samples, i.e. when the two integrals have the exact same structure. It was proven theoretically that this was always possible, but nothing insures that the two estimators have the same convergence properties: even when a large enough sample-size is used so that A is evaluated very accurately, the evaluation of $\partial$ $\varsigma$ A using the same sample can remain inaccurate. We discuss here such a pathological example: null-collision algorithms are very successful when dealing with radiative transfer in heterogeneous media, but they are sources of convergence difficulties as soon as sensitivity-evaluations are considered. We analyse theoretically these convergence difficulties and propose an alternative solution.

Numerical simulation models associated with hydraulic engineering take a wide array of data into account to produce predictions: rainfall contribution to the drainage basin (characterized by soil nature, infiltration capacity and moisture), current water height in the river, topography, nature and geometry of the river bed, etc. This data is tainted with uncertainties related to an imperfect knowledge of the field, measurement errors on the physical parameters calibrating the equations of physics, an approximation of the latter, etc. These uncertainties can lead the model to overestimate or underestimate the flow and height of the river. Moreover, complex assimilation models often require numerous evaluations of physical solvers to evaluate these uncertainties, limiting their use for some real-time operational applications. In this study, we explore the possibility of building a predictor for river height at an observation point based on drainage basin time series data. An array of data-driven techniques is assessed for this task, including statistical models, machine learning techniques and deep neural network approaches. These are assessed on several metrics, offering an overview of the possibilities related to hydraulic time-series. An important finding is that for the same hydraulic quantity, the best predictors vary depending on whether the data is produced using a physical model or real observations., Comment: Submitted to SimHydro 2019

This work presents a new approach for premixed turbulent combustion modeling based on convolutional neural networks (CNN). We first propose a framework to reformulate the problem of subgrid flame surface density estimation as a machine learning task. Data needed to train the CNN is produced by direct numerical simulations (DNS) of a premixed turbulent flame stabilized in a slot-burner configuration. A CNN inspired from a U-Net architecture is designed and trained on the DNS fields to estimate sub-grid scale wrinkling. It is then tested on an unsteady turbulent flame where the mean inlet velocity is increased for a short time and the flame must react to a varying turbulent incoming flow. The CNN is found to efficiently extract the topological nature of the flame and predict subgrid scale wrinkling, outperforming classical algebraic models. This method can be seen as a data-driven extension of dynamic formulations, where topological information was extracted in a hand-designed fashion.

Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by fluctuations in both transitions times and decay rates. We introduce and analyze a model framework that explicitly connects microscopic fluctuations with the mescoscopic description. For broad distributions of transport and reaction time scales we compute the particle density and derive the equations governing its evolution, finding power-law decay of the survival probability, and spatially heterogeneous decay that leads to subdiffusion and an asymptotically stationary surviving-particle density. These anomalies are clearly attributable to non-Markovian effects that couple transport and chemical properties in both reaction and diffusion terms., Comment: Explain model and applications in more detail. 19 pages, 6 figures

We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing effective computation of both universal and modelspecific percolation quantities in the case when both random processes are Poisson processes. The algorithm extends percolation algorithm by Newman and Ziff (M.E.J. Newman and R.M. Ziff, Phys Rev E, 64(1):016706, 2001) to handle inhomogeneous lattices. In particular, we use the proposed method to compute critical exponents and cluster density distribution in two and three dimensions for the model of parallel random tubes connected randomly by bonds, which models the connectivity properties of activated carbon., Comment: 10 pages, 8 figures

Flows of suspensions are often affected by wall slip, that is the fluid velocity $v_{f}$ in the vicinity of a boundary differs from the wall velocity $v_{w}$ due to the presence of a lubrication layer. While the slip velocity $v_s=\vert v_{f}-v_{w}\vert$ robustly scales linearly with the stress $\sigma$ at the wall in dilute suspensions, there is no consensus regarding denser suspensions that are sheared in the bulk, for which slip velocities have been reported to scale as a $v_s\propto\sigma^p$ with exponents $p$ inconsistently ranging between 0 and 2. Here we focus on a suspension of soft thermoresponsive particles and show that $v_s$ actually scales as a power law of the viscous stress $\sigma-\sigma_c$, where $\sigma_c$ denotes the yield stress of the bulk material. By tuning the temperature across the jamming transition, we further demonstrate that this scaling holds true over a large range of packing fractions $\phi$ on both sides of the jamming point and that the exponent $p$ increases continuously with $\phi$, from $p=1$ in the case of dilute suspensions to $p=2$ for jammed assemblies. These results allow us to successfully revisit inconsistent data from the literature and paves the way for a continuous description of wall slip above and below jamming., Comment: 6 pages, 4 figures - accepted for publication as a Rapid Communication in Phys. Rev. E

We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we calculate exact and asymptotic values of the ensemble averaged mean squared displacement and find that it increases subdiffusively, as either a power or the logarithm of time. Numerical simulations show that the probability density function of the displacement is non-Gaussian. We discuss the relevance of the model for the analysis of single-particle tracking experiments and its relation to other sources of subdiffusion. In particular we discuss an intimate connection with diffusion on percolation processes., Comment: 5 pages, 2 figures; Added reference. Change figure color for accessibility

Molecular transport in living systems regulates numerous processes underlying biological function. Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive motion been associated with nonergodic behavior. These findings have stimulated new questions for their implications in statistical mechanics and cell biology. Is nonergodicity a common strategy shared by living systems? Which physical mechanisms generate it? What are its implications for biological function? Here, we use single particle tracking to demonstrate that the motion of DC-SIGN, a receptor with unique pathogen recognition capabilities, reveals nonergodic subdiffusion on living cell membranes. In contrast to previous studies, this behavior is incompatible with transient immobilization and therefore it can not be interpreted according to continuous time random walk theory. We show that the receptor undergoes changes of diffusivity, consistent with the current view of the cell membrane as a highly dynamic and diverse environment. Simulations based on a model of ordinary random walk in complex media quantitatively reproduce all our observations, pointing toward diffusion heterogeneity as the cause of DC-SIGN behavior. By studying different receptor mutants, we further correlate receptor motion to its molecular structure, thus establishing a strong link between nonergodicity and biological function. These results underscore the role of disorder in cell membranes and its connection with function regulation. Due to its generality, our approach offers a framework to interpret anomalous transport in other complex media where dynamic heterogeneity might play a major role, such as those found, e.g., in soft condensed matter, geology and ecology., Comment: 27 pages, 5 figures

Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random diffusivities. The particle is never trapped, but rather performs continuous Brownian motion with the local diffusion constant. Under simple assumptions on the distribution of the sizes and diffusivities, we find that the mean squared displacement displays subdiffusion due to non-ergodicity for both annealed and quenched disorder. The model is formulated as a walk continuous in both time and space, similar to the L\'{e}vy walk., Comment: 6 pages, 2 figures; removed spurious pi from (13), and k from inline eqn preceding (11). Fixed other typos

We prove that enhanced entanglement percolation via lattice transformation is possible even if the new lattice is more poorly connected in that: i) the coordination number (a local property) decreases, or ii) the classical percolation threshold (a global property) increases. In searching for protocols to transport entanglement across a network, it seems reasonable to try transformations that increase connectivity. In fact, all examples that we are aware of violate both conditions i and ii. One might therefore conjecture that all good transformations must violate them. Here we provide a counter-example that satisfies both conditions by introducing a new method, partial entanglement swapping. This result shows that a transformation may not be rejected on the basis of satisfying conditions i or ii. Both the result and the new method constitute steps toward answering basic questions, such as whether there is a minimum amount of local entanglement required to achieve long-range entanglement., Comment: 6 pages, 4 figures, Fixed omitted word in previous version

Using the exact $N$-particle ground state wave function for a one-dimensional gas of hard-core bosons in a harmonic trap we develop an algorithm to compute the reduced single-particle density matrix and corresponding momentum distribution. Accurate numerical results are presented for up to N=8 particles, and the momentum distributions are compared to a recent analytic approximation., Comment: 6 pages, 5 figures. This paper was published in 2002, but has not been arXived until now

The concentration and distribution of quantum entanglement is an essential ingredient in emerging quantum information technologies. Much theoretical and experimental effort has been expended in understanding how to distribute entanglement in one-dimensional networks. However, as experimental techniques in quantum communication develop, protocols for multi-dimensional systems become essential. Here, we focus on recent theoretical developments in protocols for distributing entanglement in regular and complex networks, with particular attention to percolation theory and network-based error correction., Comment: 60 pages, 24 figures; updated references; clarified text; typographical corrections

We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest method consists of performing entanglement swappings along the shortest chain of links connecting the two nodes. However, we show that this method may be improved upon by choosing a protocol with a specific ordering of swappings and purifications. A priori, the design that produces optimal improvement is not clear. However, we parametrize the choices and find that the optimal values depend strongly on the desired measure of improvement. As an initial application, we apply the new improved protocols to the Erd\"os--R\'enyi network and obtain results including low density limits and an exact calculation of the average entanglement gained at the critical point., Comment: 15 pages, 19 figures. New version includes improvements suggested in referee report

This paper is devoted to pricing American options using Monte Carlo and the Malliavin calculus. Unlike the majority of articles related to this topic, in this work we will not use localization fonctions to reduce the variance. Our method is based on expressing the conditional expectation E[f(St)/Ss] using the Malliavin calculus without localization. Then the variance of the estimator of E[f(St)/Ss] is reduced using closed formulas, techniques based on a conditioning and a judicious choice of the number of simulated paths. Finally, we perform the stopping times version of the dynamic programming algorithm to decrease the bias. On the one hand, we will develop the Malliavin calculus tools for exponential multi-dimensional diffusions that have deterministic and no constant coefficients. On the other hand, we will detail various nonparametric technics to reduce the variance. Moreover, we will test the numerical efficiency of our method on a heterogeneous CPU/GPU multi-core machine.

This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice of the directions of stratification and the allocation rule within each strata. Several choices have been proposed but, even if they provide variance reduction, their implementation is computationally intensive and not applicable to realistic payoffs, in particular not to Asian options with barrier. Moreover, all these previously published methods employ orthogonal directions for multiple stratification. In this work we investigate the use of algorithms producing convenient directions, generally non-orthogonal, combining a lower computational cost with a comparable variance reduction. In addition, we study the accuracy of optimal allocation in terms of variance reduction compared to the Latin Hypercube Sampling. We consider the directions obtained by the Linear Transformation and the Principal Component Analysis. We introduce a new procedure based on the Linear Approximation of the explained variance of the payoff using the law of total variance. In addition, we exhibit a novel algorithm that permits to correctly generate normal vectors stratified along non-orthogonal directions. Finally, we illustrate the efficiency of these algorithms in the computation of the price of different path-dependent options with and without barriers in the Black-Scholes and in the Cox-Ingersoll-Ross markets., Comment: 21 pages, 11 tables

Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad and Dufresne, Fu and Su, and Arouna. We establish the convergence and asymptotic normality of the adaptive Monte Carlo estimator under local assumptions which are easily verifiable in practice. We present one way of approximating the optimal importance sampling parameter using a randomly truncated stochastic algorithm. Finally, we apply this technique to some examples of valuation of financial derivatives.

Financial institutions have massive computations to carry out overnight which are very demanding in terms of the consumed CPU. The challenge is to price many different products on a cluster-like architecture. We have used the Premia software to valuate the financial derivatives. In this work, we explain how Premia can be embedded into Nsp, a scientific software like Matlab, to provide a powerful tool to valuate a whole portfolio. Finally, we have integrated an MPI toolbox into Nsp to enable to use Premia to solve a bunch of pricing problems on a cluster. This unified framework can then be used to test different parallel architectures.

We present percolation strategies based on multipartite measurements to propagate entanglement in quantum networks. We consider networks spanned on regular lattices whose bonds correspond to pure but non-maximally entangled pairs of qubits, with any quantum operation allowed at the nodes. Despite significant effort in the past, improvements over naive (classical) percolation strategies have been found for only few lattices, often with restrictions on the initial amount of entanglement in the bonds. In contrast, multipartite entanglement percolation outperform the classical percolation protocols, as well as all previously known quantum ones, over the entire range of initial entanglement and for every lattice that we considered., Comment: revtex4, 4 pages

We study strategies for establishing long-distance entanglement in quantum networks. Specifically, we consider networks consisting of regular lattices of nodes, in which the nearest neighbors share a pure, but non-maximally entangled pair of qubits. We look for strategies that use local operations and classical communication. We compare the classical entanglement percolation protocol, in which every network connection is converted with a certain probability to a singlet, with protocols in which classical entanglement percolation is preceded by measurements designed to transform the lattice structure in a way that enhances entanglement percolation. We analyze five examples of such comparisons between protocols and point out certain rules and regularities in their performance as a function of degree of entanglement and choice of operations., Comment: 12 pages, 17 figures, revtex4. changes from v3: minor stylistic changes for journal reviewer, minor changes to figures for journal editor

We report on the frequency performance of a low cost (~500$) radio-frequency sine wave generator, using direct digital synthesis (DDS) and a field-programmable gate array (FPGA). The output frequency of the device may be changed dynamically to any arbitrary value ranging from DC to 10 MHz without any phase slip. Sampling effects are substantially reduced by a high sample rate, up to 1 MHz, and by a large memory length, more than 2.10^5 samples. By using a low noise external oscillator to clock the DDS, we demonstrate a phase noise as low as that of the master clock, that is at the level of -113 dB.rad^2/Hz at 1 Hz from the carrier for an output frequency of 3.75 MHz. The device is successfully used to confine an ultracold atomic cloud of rubidium 87 in a RF-based trap, and there is no extra heating from the RF source., Comment: 10 pages, 6 figures