Green's function retrieval and fluctuations of cross density of states in multiple scattering media

In this article we derive the average and the variance of the cross-correlation of a noise wavefield. The noise cross-correlation function (NCF) is widely used to passively estimate the Green's function between two probes and is proportional to the cross density of states (CDOS) in photonic and plasmonic systems. We first explain from the ladder approximation how the diffusion halo plays the role of secondary sources to reconstruct the mean Green's function. We then show that fluctuations of NCF are governed by several non-Gaussian correlations. An infinite-range NCF correlation dominates CDOS fluctuations and proves that NCF is not a self averaging quantity with respect to the plurality of noise sources. The link between these correlations and the intensity ones is highlighted. These results are supported by numerical simulations and are of importance for passive imaging applications and material science.Comment: 5 pages, 4 figures, 1 supplemental materia

Assessing the conservation value of waterbodies: the example of the Loire floodplain (France)

In recent decades, two of the main management tools used to stem biodiversity erosion have been biodiversity monitoring and the conservation of natural areas. However, socio-economic pressure means that it is not usually possible to preserve the entire landscape, and so the rational prioritisation of sites has become a crucial issue. In this context, and because floodplains are one of the most threatened ecosystems, we propose a statistical strategy for evaluating conservation value, and used it to prioritise 46 waterbodies in the Loire floodplain (France). We began by determining a synthetic conservation index of fish communities (Q) for each waterbody. This synthetic index includes a conservation status index, an origin index, a rarity index and a richness index. We divided the waterbodies into 6 clusters with distinct structures of the basic indices. One of these clusters, with high Q median value, indicated that 4 waterbodies are important for fish biodiversity conservation. Conversely, two clusters with low Q median values included 11 waterbodies where restoration is called for. The results picked out high connectivity levels and low abundance of aquatic vegetation as the two main environmental characteristics of waterbodies with high conservation value. In addition, assessing the biodiversity and conservation value of territories using our multi-index approach plus an a posteriori hierarchical classification methodology reveals two major interests: (i) a possible geographical extension and (ii) a multi-taxa adaptation

Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fourier–Mellin Transform

In this paper we focus on extended Euclidean registration of a set of noisy images. We provide an appropriate statistical model for this kind of registration problems, and a new criterion based on Fourier-type transforms is proposed to estimate the translation, rotation and scaling parameters to align a set of images. This criterion is a two step procedure which does not require the use of a reference template onto which aligning all the images. Our approach is based on M-estimation and we prove the consistency of the resulting estimators. A small scale simulation study and real examples are used to illustrate the numerical performances of our procedure

A very short proof of Forester's rigidity result

The deformation space of a simplicial G-tree T is the set of G-trees which can be obtained from T by some collapse and expansion moves, or equivalently, which have the same elliptic subgroups as T. We give a short proof of a rigidity result by Forester which gives a sufficient condition for a deformation space to contain an Aut(G)-invariant G-tree. This gives a sufficient condition for a JSJ splitting to be invariant under automorphisms of G. More precisely, the theorem claims that a deformation space contains at most one strongly slide-free G-tree, where strongly slide-free means the following: whenever two edges e_1, e_2 incident on a same vertex v are such that G_{e_1} is a subset of G_{e_2}, then e_1 and e_2 are in the same orbit under G_v.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper10.abs.htm

Isotropic realizability of current fields in R^3

This paper deals with the isotropic realizability of a given regular divergence free field j in R^3 as a current field, namely to know when j can be written as sigma Du for some isotropic conductivity sigma, and some gradient field Du. The local isotropic realizability in R^3 is obtained by Frobenius' theorem provided that j and curl j are orthogonal in R^3. A counter-example shows that Frobenius' condition is not sufficient to derive the global isotropic realizability in R^3. However, assuming that (j, curl j, j x curl j) is an orthogonal basis of R^3, an admissible conductivity sigma is constructed from a combination of the three dynamical flows along the directions j/|j|, curl j/|curl j| and (j/|j|^2) x curl j. When the field j is periodic, the isotropic realizability in the torus needs in addition a boundedness assumption satisfied by the flow along the third direction (j/|j|^2) x \curl j. Several examples illustrate the sharpness of the realizability conditions.Comment: 22 page

A Fast Algorithm for Computing the p-Curvature

We design an algorithm for computing the $p$-curvature of a differential system in positive characteristic $p$. For a system of dimension $r$ with coefficients of degree at most $d$, its complexity is \softO (p d r^\omega) operations in the ground field (where $\omega$ denotes the exponent of matrix multiplication), whereas the size of the output is about $p d r^2$. Our algorithm is then quasi-optimal assuming that matrix multiplication is (\emph{i.e.} $\omega = 2$). The main theoretical input we are using is the existence of a well-suited ring of series with divided powers for which an analogue of the Cauchy--Lipschitz Theorem holds.Comment: ISSAC 2015, Jul 2015, Bath, United Kingdo

A Fast Decodable Full-Rate STBC with High Coding Gain for 4x2 MIMO Systems

In this work, a new fast-decodable space-time block code (STBC) is proposed. The code is full-rate and full-diversity for 4x2 multiple-input multiple-output (MIMO) transmission. Due to the unique structure of the codeword, the proposed code requires a much lower computational complexity to provide maximum-likelihood (ML) decoding performance. It is shown that the ML decoding complexity is only O(M^{4.5}) when M-ary square QAM constellation is used. Finally, the proposed code has highest minimum determinant among the fast-decodable STBCs known in the literature. Simulation results prove that the proposed code provides the best bit error rate (BER) performance among the state-of-the-art STBCs.Comment: 2013 IEEE 24th International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), London : United Kingdom (2013

Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time

We present families of (hyper)elliptic curve which admit an efficient deterministic encoding function

The Theorem of Jentzsch--Szeg\H{o} on an analytic curve. Application to the irreducibility of truncations of power series

The theorem of Jentzsch--Szeg\H{o} describes the limit measure of a sequence of discrete measures associated to the zeroes of a sequence of polynomials in one variable. Following the presentation of this result by Andrievskii and Blatt in their book, we extend this theorem to compact Riemann surfaces, then to analytic curves over an ultrametric field. The particular case of the projective line over an ultrametric field gives as corollaries information about the irreducibility of the truncations of a power series in one variable.Comment: 16 pages; the application to irreducibility and the final example have been correcte

Kinetic approaches to lactose operon induction and bimodality

The quasi-equilibrium approximation is acceptable when molecular interactions are fast enough compared to circuit dynamics, but is no longer allowed when cellular activities are governed by rare events. A typical example is the lactose operon (lac), one of the most famous paradigms of transcription regulation, for which several theories still coexist to describe its behaviors. The lac system is generally analyzed by using equilibrium constants, contradicting single-event hypotheses long suggested by Novick and Weiner (1957). Enzyme induction as an all-or-none phenomenon. Proc. Natl. Acad. Sci. USA 43, 553-566) and recently refined in the study of (Choi et al., 2008. A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science 322, 442-446). In the present report, a lac repressor (LacI)-mediated DNA immunoprecipitation experiment reveals that the natural LacI-lac DNA complex built in vivo is extremely tight and long-lived compared to the time scale of lac expression dynamics, which could functionally disconnect the abortive expression bursts and forbid using the standard modes of lac bistability. As alternatives, purely kinetic mechanisms are examined for their capacity to restrict induction through: (i) widely scattered derepression related to the arrival time variance of a predominantly backward asymmetric random walk and (ii) an induction threshold arising in a single window of derepression without recourse to nonlinear multimeric binding and Hill functions. Considering the complete disengagement of the lac repressor from the lac promoter as the probabilistic consequence of a transient stepwise mechanism, is sufficient to explain the sigmoidal lac responses as functions of time and of inducer concentration. This sigmoidal shape can be misleadingly interpreted as a phenomenon of equilibrium cooperativity classically used to explain bistability, but which has been reported to be weak in this system