Blockwise SVD with error in the operator and application to blind deconvolution

We consider linear inverse problems in a nonparametric statistical framework. Both the signal and the operator are unknown and subject to error measurements. We establish minimax rates of convergence under squared error loss when the operator admits a blockwise singular value decomposition (blockwise SVD) and the smoothness of the signal is measured in a Sobolev sense. We construct a nonlinear procedure adapting simultaneously to the unknown smoothness of both the signal and the operator and achieving the optimal rate of convergence to within logarithmic terms. When the noise level in the operator is dominant, by taking full advantage of the blockwise SVD property, we demonstrate that the block SVD procedure overperforms classical methods based on Galerkin projection or nonlinear wavelet thresholding. We subsequently apply our abstract framework to the specific case of blind deconvolution on the torus and on the sphere

Estimating the number of change-points in a two-dimensional segmentation model without penalization

In computational biology, numerous recent studies have been dedicated to the analysis of the chromatin structure within the cell by two-dimensional segmentation methods. Motivated by this application, we consider the problem of retrieving the diagonal blocks in a matrix of observations. The theoretical properties of the least-squares estimators of both the boundaries and the number of blocks proposed by L\'evy-Leduc et al. [2014] are investigated. More precisely, the contribution of the paper is to establish the consistency of these estimators. A surprising consequence of our results is that, contrary to the onedimensional case, a penalty is not needed for retrieving the true number of diagonal blocks. Finally, the results are illustrated on synthetic data.Comment: 30 pages, 8 figure

Shot noise in carbon nanotube based Fabry-Perot interferometers

We report on shot noise measurements in carbon nanotube based Fabry-Perot electronic interferometers. As a consequence of quantum interferences, the noise power spectral density oscillates as a function of the voltage applied to the gate electrode. The quantum shot noise theory accounts for the data quantitatively. It allows to confirm the existence of two nearly degenerate orbitals. At resonance, the transmission of the nanotube approaches unity, and the nanotube becomes noiseless, as observed in quantum point contacts. In this weak backscattering regime, the dependence of the noise on the backscattering current is found weaker than expected, pointing either to electron-electron interactions or to weak decoherence

Conserved spin and orbital phase along carbon nanotubes connected with multiple ferromagnetic contacts

We report on spin dependent transport measurements in carbon nanotubes based multi-terminal circuits. We observe a gate-controlled spin signal in non-local voltages and an anomalous conductance spin signal, which reveal that both the spin and the orbital phase can be conserved along carbon nanotubes with multiple ferromagnetic contacts. This paves the way for spintronics devices exploiting both these quantum mechanical degrees of freedom on the same footing.Comment: 8 pages - minor differences with published versio

The Iliad’s big swoon: a case of innovation within the epic tradition

In book 5 of the Iliad Sarpedon suffers so greatly from a wound that his ‘‘ψυχή leaves him’. Rather than dying, however, Sarpedon lives to fight another day. This paper investigates the phrase τὸν δὲ λίπε ψυχή in extant archaic Greek poetry to gain a sense of its traditional referentiality and better assess the meaning of Sarpedon’s swoon. Finding that all other instances of the ψυχή leaving the body signify death, it suggests that the Iliad exploits a traditional unit of utterance to flag up the importance of Sarpedon to this version of the Troy story

Chemical and vibratory signals used in alarm communication in the termite Reticulitermes flavipes (Rhinotermitidae)

Termites have evolved diverse defence strategies to protect themselves against predators, including a complex alarm communication system based on vibroacoustic and/or chemical signals. In reaction to alarm signals, workers and other vulnerable castes flee away while soldiers, the specialized colony defenders, actively move toward the alarm source. In this study, we investigated the nature of alarm communication in the pest Reticulitermes flavipes. We found that workers and soldiers of R. flavipes respond to various danger stimuli using both vibroacoustic and chemical alarm signals. Among the danger stimuli, the blow of air triggered the strongest response, followed by crushed soldier head and light flash. The crushed soldier heads, which implied the alarm pheromone release, had the longest-lasting effect on the group behaviour, while the responses to other stimuli decreased quickly. We also found evidence of a positive feedback, as the release of alarm pheromones increased the vibratory communication among workers and soldiers. Our study demonstrates that alarm modalities are differentially expressed between castes, and that the response varies according to the nature of stimuli

Strong quantum memory at resonant Fermi edges revealed by shot noise

Studies of non-equilibrium current fluctuations enable assessing correlations involved in quantum transport through nanoscale conductors. They provide additional information to the mean current on charge statistics and the presence of coherence, dissipation, disorder, or entanglement. Shot noise, being a temporal integral of the current autocorrelation function, reveals dynamical information. In particular, it detects presence of non-Markovian dynamics, i.e., memory, within open systems, which has been subject of many current theoretical studies. We report on low-temperature shot noise measurements of electronic transport through InAs quantum dots in the Fermi-edge singularity regime and show that it exhibits strong memory effects caused by quantum correlations between the dot and fermionic reservoirs. Our work, apart from addressing noise in archetypical strongly correlated system of prime interest, discloses generic quantum dynamical mechanism occurring at interacting resonant Fermi edges.Comment: 6 pages, 3 figure

Age structure, dispersion and diet of a population of stoats (Mustela erminea) in southern Fiordland during the decline phase of the beechmast cycle

The dispersion, age structure and diet of stoats (Mustela erminea) in beech forest in the Borland and Grebe Valleys, Fiordland National Park, were examined during December and January 2000/01, 20 months after a heavy seed-fall in 1999. Thirty trap stations were set along a 38-km transect through almost continuous beech forest, at least 1 km apart. Mice were very scarce (nights, C/100TN) along two standard index lines placed at either end of the transect, compared with November 1999 (>60/100TN), but mice were detected (from footprints in stoat tunnels) along an 8 km central section of the transect (stations 14-22). Live trapping with one trap per station (total 317.5 trap nights) in December 2000 caught 2 female and 23 male stoats, of which 10 (including both females) were radio collared. The minimum range lengths of the two females along the transect represented by the trap line were 2.2 and 6.0 km; those of eight radio-tracked males averaged 2.9 ± 1.7 km. Stations 14-22 tended to be visited more often, by more marked individual stoats, than the other 21 stations. Fenn trapping at the same 30 sites, but with multiple traps per station (1333.5 trap nights), in late January 2001 collected carcasses of 35 males and 28 females (including 12 of the marked live-trapped ones). Another two marked males were recovered dead. The stoat population showed no sign of chronic nutritional stress (average fat reserve index = 2.8 on a scale of 1-4 where 4 = highest fat content); and only one of 63 guts analysed was empty. Nevertheless, all 76 stoats handled were adults with 1-3 cementum annuli in their teeth, showing that reproduction had failed that season. Prey categories recorded in descending frequency of occurrence were birds, carabid beetle (ground beetle), weta, possum, rat, and mouse. The frequencies of occurrence of mice and birds in the diet of these stoats (10% and 48%, respectively) were quite different from those in stoats collected in Pig Creek, a tributary of the Borland River (87%, 5%), 12 months previously when mice were still abundant. Five of the six stoat guts containing mice were collected within 1 km of stations 14-22

Quadratic optimal functional quantization of stochastic processes and numerical applications

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a Hilbert-valued random variable, using a nearest neighbour projection on a finite codebook. A special emphasis is made on the computational aspects and the numerical applications, in particular the pricing of some path-dependent European options.Comment: 41 page