Distributed Rate Allocation in Inter-Session Network Coding

In this work, we propose a distributed rate allocation algorithm that minimizes the average decoding delay for multimedia clients in inter-session network coding systems. We consider a scenario where the users are organized in a mesh network and each user requests the content of one of the available sources. We propose a novel distributed algorithm where network users determine the coding operations and the packet rates to be requested from the parent nodes, such that the decoding delay is minimized for all clients. A rate allocation problem is solved by every user, which seeks the rates that minimize the average decoding delay for its children and for itself. Since this optimization problem is a priori non-convex, we introduce the concept of equivalent packet flows, which permits to estimate the expected number of packets that every user needs to collect for decoding. We then decompose our original rate allocation problem into a set of convex subproblems, which are eventually combined to obtain an effective approximate solution to the delay minimization problem. The results demonstrate that the proposed scheme eliminates the bottlenecks and reduces the decoding delay experienced by users with limited bandwidth resources. We validate the performance of our distributed rate allocation algorithm in different video streaming scenarios using the NS-3 network simulator. We show that our system is able to take benefit of inter-session network coding for simultaneous delivery of video sessions in networks with path diversity.

Growth Codes: Intermediate Performance Analysis and Application to Video

Growth codes are a subclass of Rateless codes that have found interesting applications in data dissemination problems. Compared to other Rateless and conventional channel codes, Growth codes show improved intermediate performance which is particularly useful in applications where partial data presents some utility. In this paper, we investigate the asymptotic performance of Growth codes using the Wormald method, which was proposed for studying the Peeling Decoder of LDPC and LDGM codes. Compared to previous works, the Wormald differential equations are set on nodes' perspective which enables a numerical solution to the computation of the expected asymptotic decoding performance of Growth codes. Our framework is appropriate for any class of Rateless codes that does not include a precoding step. We further study the performance of Growth codes with moderate and large size codeblocks through simulations and we use the generalized logistic function to model the decoding probability. We then exploit the decoding probability model in an illustrative application of Growth codes to error resilient video transmission. The video transmission problem is cast as a joint source and channel rate allocation problem that is shown to be convex with respect to the channel rate. This illustrative application permits to highlight the main advantage of Growth codes, namely improved performance in the intermediate loss region.

Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

The rotation state of 67P/Churyumov-Gerasimenko from approach observations with the OSIRIS cameras on Rosetta

Aims. Approach observations with the Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS) experiment onboard Rosetta are used to determine the rotation period, the direction of the spin axis, and the state of rotation of comet 67P’s nucleus. Methods. Photometric time series of 67P have been acquired by OSIRIS since the post wake-up commissioning of the payload in March 2014. Fourier analysis and convex shape inversion methods have been applied to the Rosetta data as well to the available ground-based observations. Results. Evidence is found that the rotation rate of 67P has significantly changed near the time of its 2009 perihelion passage, probably due to sublimation-induced torque. We find that the sidereal rotation periods P1 = 12.76129 ± 0.00005 h and P2 = 12.4043 ± 0.0007 h for the apparitions before and after the 2009 perihelion, respectively, provide the best fit to the observations. No signs of multiple periodicity are found in the light curves down to the noise level, which implies that the comet is presently in a simple rotation state around its axis of largest moment of inertia. We derive a prograde rotation model with spin vector J2000 ecliptic coordinates λ = 65° ± 15°, β = + 59° ± 15°, corresponding to equatorial coordinates RA = 22°, Dec = + 76°. However, we find that the mirror solution, also prograde, at λ = 275° ± 15°, β = + 50° ± 15° (or RA = 274°, Dec = + 27°), is also possible at the same confidence level, due to the intrinsic ambiguity of the photometric problem for observations performed close to the ecliptic plane.

Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.

Automatic X-ray landmark detection and shape segmentation via data-driven joint estimation of image displacements

In this paper, we propose a new method for fully-automatic landmark detection and shape segmentation in X-ray images. To detect landmarks, we estimate the displacements from some randomly sampled image patches to the (unknown) landmark positions, and then we integrate these predictions via a voting scheme. Our key contribution is a new algorithm for estimating these displacements. Different from other methods where each image patch independently predicts its displacement, we jointly estimate the displacements from all patches together in a data driven way, by considering not only the training data but also geometric constraints on the test image. The displacements estimation is formulated as a convex optimization problem that can be solved efficiently. Finally, we use the sparse shape composition model as the a priori information to regularize the landmark positions and thus generate the segmented shape contour. We validate our method on X-ray image datasets of three different anatomical structures: complete femur, proximal femur and pelvis. Experiments show that our method is accurate and robust in landmark detection, and, combined with the shape model, gives a better or comparable performance in shape segmentation compared to state-of-the art methods. Finally, a preliminary study using CT data shows the extensibility of our method to 3D data.

Optimal Confidence Bands for Shape-Restricted Curves

Let Y be a stochastic process on [0,1] satisfying dY(t)=n 1/2 f(t)dt+dW(t) , where n≥1 is a given scale parameter (`sample size'), W is standard Brownian motion and f is an unknown function. Utilizing suitable multiscale tests, we construct confidence bands for f with guaranteed given coverage probability, assuming that f is isotonic or convex. These confidence bands are computationally feasible and shown to be asymptotically sharp optimal in an appropriate sense.

A generalisation of the fractional Brownian field based on non-Euclidean norms

We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.

Risk measures with the CxLS property

In the present contribution, we characterise law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (Math. Finance 16:419–441, 2006), we show that these risk measures can be identified with a class of generalised shortfall risk measures. As a direct consequence, we are able to extend the results in Ziegel (Math. Finance, 2014, http://onlinelibrary.wiley.com/doi/10.1111/mafi.12080/abstract) and Bellini and Bignozzi (Quant. Finance 15:725–733, 2014) on convex elicitable risk measures and confirm that expectiles are the only elicitable coherent risk measures. Further, we provide a simple characterisation of robustness for convex risk measures in terms of a weak notion of mixture continuity.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Comparing Input- and Output-Oriented Measures of Technical Efficiency to Determine Local Returns to Scale in DEA Models

This paper shows how one can infer the nature of local returns to scale at the input- or output-oriented efficient projection of a technically inefficient input-output bundle, when the input- and output-oriented measures of efficiency differ.

Relative abundance and ranges of selected diatoms from Pliocene-Pleistocene sections of ODP Leg 177, Atlantic sector of the Southern Ocean

During Ocean Drilling Program (ODP) Leg 177, seven sites were drilled aligned on a transect across the Antarctic Circumpolar Current in the Atlantic sector of the Southern Ocean. The primary scientific objective of Leg 177 was the study of the Cenozoic paleoceanographic and paleoclimatic history of the southern high latitudes and its relationship with the Antarctic cryosphere development. Of special emphasis was the recovery of Pliocene-Pleistocene sections, allowing paleoceanographic studies at millennial or higher time resolution, and the establishment of refined biostratigraphic zonations tied to the geomagnetic polarity record and stable isotope records. At most sites, multiple holes were drilled to ensure complete recovery of the section. A description of the recovered sections and the construction of a multihole splice for the establishment of a continuous composite is presented in the Leg 177 Initial Reports volume for each of the sites (Gersonde, Hodell, Blum, et al., 1999). Here we present the relative abundance pattern and the stratigraphic ranges of diatom taxa encountered from shore-based light microscope studies completed on the Pliocene-Pleistocene sequences from six of the drilled sites (Sites 1089-1094). No shore-based diatom studies have been conducted on the Pliocene-Pleistocene sediments obtained at Site 1088, located on the northern crest of the Agulhas Ridge, because of the scattered occurrence and poor preservation of diatoms in these sections (Shipboard Scientific Party, 1999b). The data included in our report present the baseline of a diatom biostratigraphic study of Zielinski and Gersonde (2002), which (1) includes a refinement of the southern high-latitude Pliocene-Pleistocene diatom zonation, in particular for the middle and late Pleistocene, and (2) presents a biostratigraphic framework for the establishment of age models of the recovered sediment sections. Zielinski and Gersonde (2002) correlated the diatom ranges with the geomagnetic polarity record established shipboard (Sites 1090 and 1092) (Shipboard Scientific Party, 1999c, 1999d) and on shore (Sites 1089, 1091, 1093, and 1094) by Channell and Stoner (2002). The Pliocene-Pleistocene diatom zonation proposed by Zielinski and Gersonde (2002) relies on a diatom zonation from Gersonde and Bárcena (1998) for the northern belt of the Southern Ocean. Because of latitudinal differentiation of sea-surface temperature, nutrients, and salinity between Antarctic and Subantarctic/subtropical water masses, the Pliocene-Pleistocene stratigraphic marker diatoms are not uniformly distributed in the Southern Ocean (Fenner, 1991; Gersonde and Bárcena, 1998). As a consequence, Zielinski and Gersonde (2002) propose two diatom zonations for application in the Antarctic Zone south of the Polar Front (Southern Zonation, Sites 1094 and 1093) and the area encompassing the Polar Front Zone (PFZ) and the Subantarctic Zone (Northern Zonation, Sites 1089-1092). This accounts especially for the Pleistocene zonation where Hemidiscus karstenii, whose first abundant occurrence datum and last occurrence datum defines the subzonation of the northern Thalassiosira lentiginosa Zone, occurs only sporadically in the cold-water realm south of the PFZ and thus is not applicable in sections from this area. However, newly established marker species assigned to the genus Rouxia (Rouxia leventerae and Rouxia constricta) are more related to cold-water environments and allow a refinement of the Pleistocene stratigraphic zonation for the southern cold areas. A study relying on quantitative counts of both Rouxia species confirms the utility of these stratigraphic markers for the identification of sequences attributed to marine isotope Stages 6 and 8 in the southern Southern Ocean (Zielinski et al., 2002).

Heat flow measurements in the Weddell Sea

From January to March 1987, heat flow measurements were tried at four sites (Sites 689, 690, 695, and 696) during ODP Leg 113, in the Weddell Sea, Antarctica. At Site 690 (Maud Rise), a convex upward shaped temperature vs. depth profile was observed. This profile cannot be explained by steady-state conduction through solid materials only. We conclude that the minimum heat flow value at Site 690 is 45 mW/m2. A prominent bottom simulating reflector (BSR) was observed at 600 mbsf at Site 695. However, the observed temperature is too high to explain the BSR as a gas hydrate. The origin of the BSR remains unknown, although it is probably of biogenic origin as observed in the Bering Sea during DSDP Leg 19. After correcting for the effects of sedimentation, heat flow values at Sites 695 and 696 are 69 and 63 mW/m2, respectively. Furthermore, we compiled heat flow data south of 50°S. In the Weddell Sea region, the eastern part shows relatively low heat flow in comparison with the western part, with the boundary between them at about 15°W longitude.

Mineral composition and major element oxides of gabbros from ODP Hole 179-1105A, southwest Indian Ridge

Hole 1105A penetrated 158 m of gabbros at a site offset 1.3 km east-northeast from Hole 735B on the Atlantis Bank near the Atlantis II Fracture Zone. A total of 118 m of dominantly medium- to coarse-grained intercalated Fe-Ti oxide gabbro and olivine gabbro was recovered from Hole 1105A that shows many petrographic features similar to those recovered from the upper part of Hole 735B. The main rock types are distinguished based on the constituent cumulus phases, with the most primitive gabbros consisting of olivine, plagioclase, and clinopyroxene. The inferred crystallization order is subsequently Fe-Ti oxides (ilmenite and titanomagnetite), followed by orthopyroxene, then apatite, and finally biotite. Orthopyroxene appears to replace olivine in a narrow middle interval. The magmatic evolution is likewise reflected in the mineral compositions. Plagioclase varies from An66 to An28. Olivine varies from Fo78 to Fo35. The gap in olivine crystallization occurs between Fo46 and Fo40 and coincides approximately with the appearance of orthopyroxene (~En50). The clinopyroxenes show large compositional variation in Mg/(Mg + Fe total) from 0.84 to 0.51. The nonquadrilateral cations of clinopyroxene similarly show large variations with Ti increasing for the olivine gabbros and decreasing for the Fe-Ti oxide gabbros with the decrease in Mg/(Mg + Fe total). The apatites are mainly flourapatites. The compositional variation in the gabbros is interpreted as a comagmatic suite resulting from fractional crystallization. Pyroxene geothermometry suggests equilibration temperatures from 1100°C and below. The coexisting Fe-Ti oxide minerals indicate subsolidus equilibration temperatures from 900°C for olivine gabbros to 700°C for the most evolved apatite-bearing gabbros. The cryptic variation in the olivine gabbros defines two or three lenses, 40 to 60 m thick, each characterized by a distinct convex zoning with a lower segment indicating upward reverse fractionation, a central maximum, and an upper segment showing normal fractionation. The Fe-Ti oxide gabbros show cryptic variations independent of the host olivine gabbros and reveal a systematic upward normal fractionation trend transgressing host olivine gabbro boundaries. Forward fractional crystallization modeling, using a likely parental magma composition from the Atlantis II Fracture Zone (MgO = 7.2 wt%; Mg/[Mg + Fe2+] = 0.62), closely matches the compositions of coexisting olivine, plagioclase, and clinopyroxene. This modeling suggests cosaturation of olivine, plagioclase, and clinopyroxene from 1155°C and the addition of Fe-Ti oxides from 1100°C. The liquid line of descent initially shows increasing FeO with moderately increasing SiO2. After saturation of Fe-Ti oxides, the liquid strongly decreases in FeO and TiO2 and increases in SiO2, reaching dacitic compositions at ~10% liquid remaining. The calculations indicate that formation of olivine gabbros can be accounted for by <65% fractionation and that only the residual 35% liquid was saturated in Fe-Ti oxides. The modeling of the solid fractionation products shows that both the olivine gabbro and the Fe-Ti oxide gabbros contain very small amounts of trapped liquid (<5%). The implications are that the gabbros represent crystal mush that originated in a recharging and tapping subaxial chamber. Compaction and upward melt migration in the crystal mush appear to have been terminated with relatively large amounts of interstitial liquid remaining in the upper parts of the cumulate mush. This termination may have been caused by tectonic disturbances, uplift, and associated withdrawal of magma into the subaxial dike and sill system. Prolonged compaction and cooling of the trapped melt in the mush formed small differentiated bodies and lenses by pressure release migration and crystallization along syntectonic channels. This resulted in differentiation products along lateral and vertical channelways in the host gabbro that vary from olivine gabbro, to Fe-Ti oxide gabbro, gabbronorite, and apatite gabbros and show large compositional variations independent of the host olivine gabbros.