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Nitrogen-Vacancy (NV) color centers in diamond have emerged as promising quantum solid-state systems, with applications ranging from quantum information processing to magnetic sensing. One of the most useful properties of NVs is the ability to read their ground-state spin projection optically at room temperature. This work provides a theoretical analysis of Purcell enhanced NV optical coupling, through which we find optimal parameters for maximal Signal to Noise Ratio (SNR) of the optical spin-state readout. We conclude that a combined increase in spontaneous emission (through Purcell enhancement) and in optical excitation could significantly increase the readout SNR.

Let $1\le mm$. We study the a.s. values of the $s-m$-dimensional Hausdorff and packing measures of $K\cap V$, where $V$ is a typical $n-m$-dimensional affine subspace. For $0<\rho<\frac{1}{2}$ let $C_{\rho}\subset[0,1]$ be the attractor of the IFS $\{f_{\rho,1},f_{\rho,2}\}$, where $f_{\rho,1}(t)=\rho\cdot t$ and $f_{\rho,2}(t)=\rho\cdot t+1-\rho$ for each $t\in\mathbb{R}$. We show that for certain numbers $0

We propose a simple model of landfill and study a minimal time control problem where the re-circulation leachate is the manipulated variable. We propose a scheme to construct the optimal strategy by dividing the state space into three subsets E0, Z1 and the complementary. On E0 and Z1, the optimal control is constant until reaching target, while it can exhibit a singular arc outside these two subsets. Moreover, the singular arc could have a barrier. In this case, we prove the existence of a switching curve that passes through a point of prior saturation under the assumption that the set E0 intersects the singular arc. Numerical computations allow then to determine the switching curve and depict the optimal synthesis.

This paper studies the bioremediation, in minimal time, of a water resource or reservoir using a single continuous bioreactor. The bioreactor is connected to two pumps, at different locations in the reservoir, that pump polluted water and inject back sufficiently clean water with the same flow rate. This leads to a minimal-time optimal control problem where the control variables are related to the inflow rates of both pumps. We obtain a non-convex problem for which it is not possible to directly prove the existence of its solutions. We overcome this difficulty and fully solve the studied problem by applying Pontryagin's principle to the associated generalized control problem. We also obtain explicit bounds on its value function via Hamilton-Jacobi-Bellman techniques.

Emergent phenomena share the fascinating property of not being obvious consequences of the design of the system in which they appear. This characteristic is no less relevant when attempting to simulate such phenomena, given that the outcome is not always a foregone conclusion. The present survey focuses on several simple model systems that exhibit surprisingly rich emergent behavior, all studied by MD simulation. The examples are taken from the disparate fields of fluid dynamics, granular matter and supramolecular self-assembly. In studies of fluids modeled at the detailed microscopic level using discrete particles, the simulations demonstrate that complex hydrodynamic phenomena in rotating and convecting fluids, the Taylor-Couette and Rayleigh-B\'enard instabilities, can not only be observed within the limited length and time scales accessible to MD, but even quantitative agreement can be achieved. Simulation of highly counterintuitive segregation phenomena in granular mixtures, again using MD methods, but now augmented by forces producing damping and friction, leads to results that resemble experimentally observed axial and radial segregation in the case of a rotating cylinder, and to a novel form of horizontal segregation in a vertically vibrated layer. Finally, when modeling self-assembly processes analogous to the formation of the polyhedral shells that package spherical viruses, simulation of suitably shaped particles reveals the ability to produce complete, error-free assembly, and leads to the important general observation that reversible growth steps contribute to the high yield. While there are limitations to the MD approach, both computational and conceptual, the results offer a tantalizing hint of the kinds of phenomena that can be explored, and what might be discovered when sufficient resources are brought to bear on a problem., Comment: 21 pages, 20 figures (v2 - minor text addition)

Given a periodic point $\omega$ in a $\psi$-mixing shift with countable alphabet, the sequence $\{S_{n}\}$ of random variables counting the number of multiple returns to shrinking cylindrical neighborhoods of $\omega$ is considered. Necessary and sufficient conditions for the convergence in distribution of $\{S_{n}\}$ are obtained, and it is shown that the limit is a Polya-Aeppli distribution. A global condition on the shift system, which guarantees the convergence in distribution of $\{S_{n}\}$ for every periodic point, is introduced. This condition is used to derive results for $f$-expansions and Gibbs measures. Results are also obtained concerning the possible limit distribution of sub-sequences $\{S_{n_{k}}\}$. A family of examples in which there is no convergence is presented. We exhibit also an example for which the limit distribution is pure Poissonian.

At low redshift, a handful of gamma-ray bursts (GRBs) have been discovered with peak luminosities ($L_{\rm iso} < 10^{48.5}~\rm{erg\,s}^{-1}$) substantially lower than the average of the more distant ones ($L_{\rm iso} > 10^{49.5}~\rm{erg\,s}^{-1}$). The properties of several low-luminosity (low-$L$) GRBs indicate that they can be due to shock break-out, as opposed to the emission from ultrarelativistic jets. Owing to this, it is highly debated how both populations are connected, and whether there is a continuum between them. The burst at redshift $z=0.283$ from 2012 April 22 is one of the very few examples of intermediate-$L$ GRBs with a $\gamma$-ray luminosity of $L\sim10^{48.9}~\rm{erg\,s}^{-1}$ that have been detected up to now. Together with the robust detection of its accompanying supernova SN 2012bz, it has the potential to answer important questions on the origin of low- and high-$L$ GRBs and the GRB-SN connection. We carried out a spectroscopy campaign using medium- and low-resolution spectrographs at 6--10-m class telescopes, covering the time span of 37.3 days, and a multi-wavelength imaging campaign from radio to X-ray energies over a duration of $\sim270$ days. Furthermore, we used a tuneable filter centred at H$\alpha$ to map star formation in the host galaxy and the surrounding galaxies. We used these data to extract and model the properties of different radiation components and incorporate spectral-energy-distribution fitting techniques to extract the properties of the host galaxy. Modelling the light curve and spectral energy distribution from the radio to the X-rays revealed the blast-wave to expand with an initial Lorentz factor of $\Gamma_0\sim60$, low for a high-$L$ GRB, and that the afterglow had an exceptional low peak luminosity-density of $\lesssim2\times10^{30}~\rm{erg\,s}^{-1}\,\rm{Hz}^{-1}$ in the sub-mm. [Abridged], Comment: 30 pages, 17 figures, 9 tables; abstract is abridged; images are shown at reduced resolution; comments are welcome

We report on the modulation of indirect excitons (IXs) as well as their transport by moving periodic potentials produced by surface acoustic waves (SAWs). The potential modulation induced by the SAW strain modifies both the band gap and the electrostatic field in the quantum wells confining the IX, leading to changes in their energy. In addition, this potential capture and transports IXs over several hundreds of {\mu}m. While the IX packets keep to a great extent their spatial shape during transport by the moving potential, the effective transport velocity is lower than the SAW group velocity and increases with the SAW amplitude. This behavior is attributed to the capture of IXs by traps along the transport path, thereby increasing the IX transit time. The experimental results are well-reproduced by an analytical model for the interaction between trapping centers and IXs during transport.

Excitons, quasi-particles consisting of electron-hole pairs bound by the Coulomb interaction, are a potential medium for processing of photonic information in the solid-state. Information processing via excitons requires efficient techniques for the transport and manipulation of these uncharged particles. We introduce here a novel concept for the interconnection of multiple remote exciton systems based on the long-range transport of dipolar excitons by a network of configurable interconnects driven by acoustic wave beams. By combining this network with electrostatic gates, we demonstrate an integrated exciton multiplexer capable of interconnecting, gating and routing exciton systems separated by millimeter distances. The multiplexer provides a scalable platform for the manipulation of exciton fluids with potential applications in information processing.

In this paper we study the strict majority bootstrap percolation process on graphs. Vertices may be active or passive. Initially, active vertices are chosen independently with probability p. Each passive vertex becomes active if at least half of its neighbors are active (and thereafter never changes its state). If at the end of the process all vertices become active then we say that the initial set of active vertices percolates on the graph. We address the problem of finding graphs for which percolation is likely to occur for small values of p. Specifically, we study a graph that we call r-wheel: a ring of n vertices augmented with a universal vertex where each vertex in the ring is connected to its r closest neighbors to the left and to its r closest neighbors to the right. We prove that the critical probability is 1/4. In other words, if p>1/4 then for large values of r percolation occurs with probability arbitrarily close to 1 as n goes to infinity. On the other hand, if p<1/4 then the probability of percolation is bounded away from 1., Comment: 10 pages

In this paper we show experimental evidence of a few correlation regimes of a cold dipolar exciton fluid, created optically in a semiconductor bilayer heterostructure. In the higher temperature regime, the average interaction energy between the particles shows a surprising temperature dependence which is an evidence for correlations beyond the mean field model. At a lower temperature, there is a sharp increase in the interaction energy of optically active excitons, accompanied by a strong reduction in their apparent population. This is an evidence for a sharp macroscopic transition to a dark state as was suggested theoretically.

We consider the chemostat model with the substrate concentration as the single measurement. We propose a control strategy that drives the system at a steady state maximizing the gas production without the knowledge of the specific growth rate. Our approach separates the extremum seeking problem from the feedback control problem such that each of the two subproblems can be solved with relatively simple algorithms. We are then free to choose any numerical optimization algorithm. We give a demonstration for two choices: one is based on slow-fast dynamics and numerical continuation, the other is a combination of golden-section and Newton iteration. The method copes with non-monotonic growth functions.

High-throughput sequencing of RNA transcripts (RNA-seq) has become the method of choice for detection of differential expression (DE). Concurrent with the growing popularity of this technology there has been a significant research effort devoted towards understanding the statistical properties of this data and the development of analysis methods. We report on a comprehensive evaluation of the commonly used DE methods using the SEQC benchmark data set. We evaluate a number of key features including: assessment of normalization, accuracy of DE detection, modeling of genes expressed in only one condition, and the impact of sequencing depth and number of replications on identifying DE genes. We find significant differences among the methods with no single method consistently outperforming the others. Furthermore, the performance of array-based approach is comparable to methods customized for RNA-seq data. Perhaps most importantly, our results demonstrate that increasing the number of replicate samples provides significantly more detection power than increased sequencing depth., Comment: Manuscript includes supplementary figures

We study how a particular spatial structure with a buffer impacts the number of equilibria and their stability in the chemostat model. We show that the occurrence of a buffer can allow a species to persist or on the opposite to go extinct, depending on the characteristics of the buffer. For non-monotonic response functions, we characterize the buffered configurations that make the chemostat dynamics globally asymptotically stable, while this is not possible with single, serial or parallel vessels of the same total volume and input flow. These results are illustrated with the Haldane kinetic function., Comment: 9th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2013), Toulouse : France (2013)

We show that for all $\psi$-mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to compound Poisson distributions. We also describe completely the asymptotic behavior of these distributions., Comment: slightly revised version

We show that for certain configurations of two chemostats fed in parallel, the presence of two different species in each tank can improve the yield of the whole process, compared to the same configuration having the same species in each volume. This leads to a (so-called) "transgressive over-yielding" due to spatialization., Comment: MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, Vienna : Austria (2012)

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate., Comment: expansion of ideas from proceedings paper (17 pages, 8 figures), proceedings paper is version v1

Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random Boolean networks (RBNs). We start this paper by proving that, if we fix the values of the source nodes (nodes with in-degree 0), the expected number of fixed points of any RBN is one (independently of the topology we choose). For finding such fixed points we use the {\alpha}-asynchronous dynamics (where every node is updated independently with probability 0 < {\alpha} < 1). In fact, it is well-known that asynchrony avoids the cycle attractors into which parallel dynamics tends to fall. We perform simulations and we show the remarkable property that, if for a given RBN with scale-free topology and {\alpha}-asynchronous dynamics an initial configuration reaches a fixed point, then every configuration also reaches a fixed point. By contrast, in the parallel regime, the percentage of initial configurations reaching a fixed point (for the same networks) is dramatically smaller. We contrast the results of the simulations on scale-free networks with the classical Erdos-Renyi model of random networks. Everything indicates that scale-free networks are extremely robust. Finally, we study the mean and maximum time/work needed to reach a fixed point when starting from randomly chosen initial configurations., Comment: 13 pages

The self-assembly of polyhedral shells, each constructed from 60 trapezoidal particles, is simulated using molecular dynamics. The spatial organization of the component particles in this shell is similar to the capsomer proteins forming the capsid of a T=1 virus. Growth occurs in the presence of an atomistic solvent and, under suitable conditions, achieves a high yield of complete shells. The simulations provide details of the structure and lifetime of the particle clusters that appear as intermediate states along the growth pathway, and the nature of the transitions between them. In certain respects the growth of size-60 shells from trapezoidal particles resembles the growth of icosahedral shells from triangular particles studied previously, with reversible bonding playing a major role in avoiding incorrect assembly, although the details differ due to particle shape and bond organization. The strong preference for maximal bonding exhibited by the triangular particle clusters is also apparent for trapezoidal particles, but this is now confined to early growth, and is less pronounced as shells approach completion along a variety of pathways., Comment: 8 pages, 12 figures (revised shorter version)

In this work we study the computational power of graph-based models of distributed computing in which each node additionally has access to a global whiteboard. A node can read the contents of the whiteboard and, when activated, can write one message of O(log n) bits on it. When the protocol terminates, each node computes the output based on the final contents of the whiteboard. We consider several scheduling schemes for nodes, providing a strict ordering of their power in terms of the problems which can be solved with exactly one activation per node. The problems used to separate the models are related to Maximal Independent Set, detection of cycles of length 4, and BFS spanning tree constructions.

The objective of the paper is to evaluate the ability of reactive transport models and their numerical implementations (such as MIN3P) to simulate simple microbial transformations in conditions of chemostat or gradostat models, that are popular in microbial ecology and waste treatment ecosystems. To make this comparison, we first consider an abstract ecosystem composed of a single limiting resource and a single microbial species that are carried by advection. In a second stage, we consider another microbial species in competition for the same limiting resource. Comparing the numerical solutions of the two models, we found that the numerical accuracy of simulations of advective transport models performed with MIN3P depends on the evolution of the concentrations of the microbial species: when the state of the system is close to a non-hyperbolic equilibrium, we observe a numerical inaccuracy that may be due to the discretization method used in numerical approximations of reactive transport equations. Therefore, one has to be cautious about the predictions given by the models.

In this work, we study a model of the chemostat where the species are present in two forms, isolated bacteria and under an aggregated form like attached bacteria or bacteria in flocks. We show that our general model contains a lot of models which were previously considered in the literature. Assuming that flocculation and deflocculation dynamics are fast with respect to the growth of the species, we construct a reduced chemostat-like model in which both the growth functions and the apparent dilution rate depend on the density of the species. We also show that such a model involving monotonic growth rates may exhibit bistability, while it may only occur in the classical chemostat model when the growth rate in non monotonic.

We study cellular automata with respect to a new communication complexity problem: each of two players know half of some finite word, and must be able to tell whether the state of the central cell will follow a given evolution, by communicating as little as possible between each other. We present some links with classical dynamical concepts, especially equicontinuity, expansiveness, entropy and give the asymptotic communication complexity of most elementary cellular automata., Comment: submitted to TCS

This paper has been withdrawn by the authors., Comment: This paper has been withdrawn by the authors

The problem of determining total distance ascended during a mountain bike trip is addressed. Altitude measurements are obtained from GPS receivers utilizing both GPS-based and barometric altitude data, with data averaging used to reduce fluctuations. The estimation process is sensitive to the degree of averaging, and is related to the well-known question of determining coastline length. Barometric-based measurements prove more reliable, due to their insensitivity to GPS altitude fluctuations., Comment: 10 pages, 9 figures (v.2: minor revisions)

We show a large enhancement of two-photon absorption processes in nanocrystal quantum dots and of light upconversion efficiency from the IR to the near-IR spectral regime, using a hybrid optical device in which near-IR emitting InAs quantum dots were embedded on top a metallic nanoslit array. The resonant enhancement of these nonlinear optical processes is due to the strong local electromagnetic field enhancements inside the nanoslit array structure at the extraordinary transmission resonances. A maximal two-photon absorption enhancement of more than 20 was inferred. Different high field regions were identified for different polarizations, which can be used for designing and optimizing efficient nonlinear processes in such hybrid structures. Combining nanocrystal quantum dots with subwavelength metallic nanostructures is therfore a promising way for a range of possible nonlinear optical devices., Comment: 14 pages, 7 figures

Given hydric capacity and nutrient flow of a chemostat-like system, we analyse the influence of a spatial structure on the output concentrations at steady-state. Three configurations are compared: perfectly-mixed, serial and parallel with diffusion rate. We show the existence of a threshold on the input concentration of nutrient for which the benefits of the serial and parallel configurations over the perfectly-mixed one are reversed. In addition, we show that the dependency of the output concentrations on the diffusion rate can be non-monotonic, and give precise conditions for the diffusion effect to be advantageous. The study encompasses dead-zone models

We present an intuitive analytical model for extraordinary optical transmission (EOT) through corrugated metallic films. In the framework of this model, EOT emerges from standing wave resonances of the different diffraction orders, and is an inherent property of periodic structures, which does not require specific polarization dependent properties such as surface plasmons. The model correctly predicts the conditions for the EOT resonances in various geometrical configurations, in both TE and TM polarizations,and in the subwavelength and non-subwavelength spectral regimes, using the same underlying mechanism., Comment: 7 pages, 6 figures

We address the issue of minimal time optimal control of fedbatch reactor in presence of complex non monotonic kinetics, that can be typically characterized by the combination of two Haldane models. The optimal synthesis may present several singular arcs. Global optimal trajectory results are provided on the basis of a numerical approach that considers an approximation method with smooth control inputs.

We study minimal time strategies for the treatment of pollution of large volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists in feeding the bioreactor from the resource, the clean output returning to the resource with the same flow rate. We first characterize the optimal policies among constant and feedback controls, under the assumption of a uniform concentration in the resource. In a second part, we study the influence of an inhomogeneity in the resource, considering two measurements points. With the help of the Maximum Principle, we show that the optimal control law is non-monotonic and terminates with a constant phase, contrary to the homogeneous case for which the optimal flow rate is decreasing with time. This study allows the decision makers to identify situations for which the benefit of using non-constant flow rates is significant.

In this paper we ask which properties of a distributed network can be computed from a little amount of local information provided by its nodes. The distributed model we consider is a restriction of the classical CONGEST (distributed) model and it is close to the simultaneous messages (communication complexity) model defined by Babai, Kimmel and Lokam. More precisely, each of these n nodes -which only knows its own ID and the IDs of its neighbors- is allowed to send a message of O(log n) bits to some central entity, called the referee. Is it possible for the referee to decide some basic structural properties of the network topology G? We show that simple questions like, "does G contain a square?", "does G contain a triangle?" or "Is the diameter of G at most 3? cannot be solved in general. On the other hand, the referee can decode the messages in order to have full knowledge of G when G belongs to many graph classes such as planar graphs, bounded treewidth graphs and, more generally, bounded degeneracy graphs. We leave open questions related to the connectivity of arbitrary graphs.