Homological tree-based strategies for image analysis

Homological characteristics of digital objects can be obtained in a straightforward manner computing an algebraic map φ over a finite cell complex K (with coefficients in the finite field F2={0,1}) which represents the digital object [9]. Computable homological information includes the Euler characteristic, homology generators and representative cycles, higher (co)homology operations, etc. This algebraic map φ is described in combinatorial terms using a mixed three-level forest. Different strategies changing only two parameters of this algorithm for computing φ are presented. Each one of those strategies gives rise to different maps, although all of them provides the same homological information for K. For example, tree-based structures useful in image analysis like topological skeletons and pyramids can be obtained as subgraphs of this forest

Facies de abanico fluvial en los afloramientos orientales de Formación Peraltilla

La Formación Peraltilla está constituida por una sucesión estratigráfica heterolitica, del Oligoceno inferior. El análisis de facies indica una asociación de ambientes de abanicos fluviales húmedos, formados por canales múltiples de baja sinuosidad, y una tendencia vertical a la progradación de los sistemas fluviales

Connectivity forests for homological analysis of digital volumes

In this paper, we provide a graph-based representation of the homology (information related to the different “holes” the object has) of a binary digital volume. We analyze the digital volume AT-model representation [8] from this point of view and the cellular version of the AT-model [5] is precisely described here as three forests (connectivity forests), from which, for instance, we can straightforwardly determine representative curves of “tunnels” and “holes”, classify cycles in the complex, computing higher (co)homology operations,... Depending of the order in which we gradually construct these trees, tools so important in Computer Vision and Digital Image Processing as Reeb graphs and topological skeletons appear as results of pruning these graphs

Using membrane computing for obtaining homology groups of binary 2D digital images

Membrane Computing is a new paradigm inspired from cellular communication. Until now, P systems have been used in research areas like modeling chemical process, several ecosystems, etc. In this paper, we apply P systems to Computational Topology within the context of the Digital Image. We work with a variant of P systems called tissue-like P systems to calculate in a general maximally parallel manner the homology groups of 2D images. In fact, homology computation for binary pixel-based 2D digital images can be reduced to connected component labeling of white and black regions. Finally, we use a software called Tissue Simulator to show with some examples how these systems wor

Effect of preparation conditions on the polymorphism and transport properties of lanthanum molybdates

In this work, La6MoO12-based compounds were investigated as part of a new family of materials very competitive as hydrogen separation membranes [1,2]. La5.4MoO11.1 was synthesized by the freeze-drying precursor method and the calcination conditions were optimized in order to obtain single phases. Several cooling rates were applied and different polymorphs were obtained: a simple cubic fluorite symmetry (Fm-3m) for the sample cooled by quenching, and two different rhombohedral (R-3) space groups for the samples cooled at 50 ºC•min-1 and 0.5 ºC•min-1 (see Figure below). For the quenched sample, the Rietveld refinement was satisfactory in a Fm-3m space group. For the other two compositions no structural model was available and were indexed in a R-3 space group, however some small reflections were not given any intensity by the model used. Transmission electron microscopy confirmed the presence of superstructures for those samples. All ceramic materials were obtained with relative densities close to 100% after sintering at 1500 ºC. Stability studies demonstrated that all three polymorphs were stable in oxidizing and reducing conditions at 800 ºC for 48 hours. The three samples present a significant proton contribution to the conductivity at temperatures lower than 800 ºC. These results were confirmed by thermogravimetric analysis. The highest conductivity values were observed for the samples prepared by quenching. The three polymorphs display a small p-type electronic contribution to the overall conductivity in oxidizing conditions and n-type electronic one in very reducing conditions, much more significant for the samples cooled by quenching and at 50 ºC•min-1.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Homological computation using spanning trees

We introduce here a new F2 homology computation algorithm based on a generalization of the spanning tree technique on a finite 3-dimensional cell complex K embedded in ℝ3. We demonstrate that the complexity of this algorithm is linear in the number of cells. In fact, this process computes an algebraic map φ over K, called homology gradient vector field (HGVF), from which it is possible to infer in a straightforward manner homological information like Euler characteristic, relative homology groups, representative cycles for homology generators, topological skeletons, Reeb graphs, cohomology algebra, higher (co)homology operations, etc. This process can be generalized to others coefficients, including the integers, and to higher dimension

The Cadiz Contourite Channel: Sandy contourites, bedforms and dynamic current interaction

The Cadiz Contourite Channel is the largest and most prominent contourite channel in the middle slope of the Gulf of Cadiz, and is known to channelise the southern branch of the Lower Core of Mediterranean Outflow Water (MOW) as it flows westwards from the Gibraltar Gateway. The channel lies in water depth between 650 and 1500 m, is 150 km long, 2–12 km wide, up to 120 m deep, and broadly s-shaped in plan view. It has several associated subparallel marginal channels and shorter spillover channel segments. Its geometry is controlled by the interaction of a strong bottom current with the seafloor morphology, affected by neotectonic deformation and diapiric intrusion. Bottom photographs and dredge hauls reveal a channel floor shaped by high-energy flow, in places with bare rock, boulders and gravel, and elsewhere covered with sandy contourites. The rocky substrate and derived clasts are formed of authigenic iron-rich carbonates, testifying the high degree of fluid escape from adjacent diapiric ridges and mud volcanoes. The sandy substrate shows a wide range of current-induced bedforms including small, straight-crested ripples, large sinuous sand waves and dunes (wavelength 3.5–5 m, height 0.3–0.9 m), weak surface lineation on sands, and aligned gravel stringers and deep erosive scours around large boulders. Bedform orientation indicates flows directed to the south/south-west (main channel) and west (spillover channel), which can be related to MOW bottom currents, and current velocities that vary between about 0.2 and 0.8 m s− 1, even in the same channel location. However, current vane orientation was clearly responding, at least in part, to tidal effects and periodicity in the Gulf of Cadiz at the time the photographs were taken. Maximum current velocities are achieved by a combination of barotropic and internal tides (probably generated at the continental slope) that reinforce the normal MOW flow. In addition, meteorologically-induced internal waves with periods shorter than tidal ones may exert an even greater influence on current intensity, especially when they occur at times of sudden changes of meteorological forcing. This effect further influences MOW variability. In all cases, the funnelling effect of the Cadiz Channel amplifies tidal or meteorologically-induced bottom currents

Quantum numbers of the X (3872 ) state and orbital angular momentum in its ρ0J /ψ decay

Angular correlations in B+ → X(3872)K+ decays, with X(3872) → ρ 0J/ψ, ρ 0 → π +π − and J/ψ → µ +µ −, are used to measure orbital angular momentum contributions and to determine the J P C value of the X(3872) meson. The data correspond to an integrated luminosity of 3.0 fb−1 of proton-proton collisions collected with the LHCb detector. This determination, for the first time performed without assuming a value for the orbital angular momentum, confirms the quantum numbers to be J P C = 1++. The X(3872) is found to decay predominantly through S wave and an upper limit of 4% at 95% C.L. is set on the D-wave contribution