Correcting curvature-density effects in the Hamilton-Jacobi skeleton

The Hainilton-Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton-Jacobi method

The fully connected N-dimensional skeleton: probing the evolution of the cosmic web

A method to compute the full hierarchy of the critical subsets of a density field is presented. It is based on a watershed technique and uses a probability propagation scheme to improve the quality of the segmentation by circumventing the discreteness of the sampling. It can be applied within spaces of arbitrary dimensions and geometry. This recursive segmentation of space yields, for a $d$-dimensional space, a $d-1$ succession of $n$-dimensional subspaces that fully characterize the topology of the density field. The final 1D manifold of the hierarchy is the fully connected network of the primary critical lines of the field : the skeleton. It corresponds to the subset of lines linking maxima to saddle points, and provides a definition of the filaments that compose the cosmic web as a precise physical object, which makes it possible to compute any of its properties such as its length, curvature, connectivity etc... When the skeleton extraction is applied to initial conditions of cosmological N-body simulations and their present day non linear counterparts, it is shown that the time evolution of the cosmic web, as traced by the skeleton, is well accounted for by the Zel'dovich approximation. Comparing this skeleton to the initial skeleton undergoing the Zel'dovich mapping shows that two effects are competing during the formation of the cosmic web: a general dilation of the larger filaments that is captured by a simple deformation of the skeleton of the initial conditions on the one hand, and the shrinking, fusion and disappearance of the more numerous smaller filaments on the other hand. Other applications of the N dimensional skeleton and its peak patch hierarchy are discussed.Comment: Accepted for publication in MNRA

CO2 multicyclic capture of pretreated/doped CaO in the Ca-looping process. Theory and experiments

We study in this paper the conversion of CaO-based CO2 sorbents when subjected to repeated carbonation/calcination cycles with a focus on thermally pretreated/doped sorbents. Analytical equations are derived to describe the evolution of conversion with the cycle number from a unifying model based on the balance between surface area loss due to sintering in the loopingcalcination stage and surface area regeneration as a consequence of solid-state diffusion during the looping-carbonation stage. Multicyclic CaO conversion is governed by the evolution of surface area loss/regeneration that strongly depends on the initial state of the pore skeleton. In the case of thermally pretreated sorbents, the initial pore skeleton is highly sintered and regeneration is relevant whereas, for nonpretreated sorbents, the initial pore skeleton is soft and regeneration is negligible. Experimental results are obtained for sorbents subjected to a preheating controlled rate thermal analysis (CRTA) program. By applying this preheating program in a CO2 enriched atmosphere, CaO can be subjected to a rapid carbonation followed by a slow rate controlled decarbonation, which yields a highly sintered skeleton displaying a small conversion in the first cycle and self-reactivation in the next ones. Conversely, carbonation of the sorbent at a slow controlled rate enhances CO2 solid-state diffusion, which gives rise, after a quick decarbonation, to a highly porous skeleton. In this case, CaO conversion in the first cycle is very large but it decays abruptly in subsequent cycles. Data on CaO conversion retrieved from the literature and from further experimental measurements performed in our work are analyzed as influenced by a variety of experimental variables such as preheating temperature program, preheating exposition time, atmosphere composition, presence of additives, and carbonation/calcination conditions. Conversion data are well fitted by the proposed model equations, which are of help for a quantitative interpretation on the effect of experimental conditions on the multicyclic sorbent performance as a function of sintering/ regeneration parameters inferred from the fittings and allow foreseeing the critical conditions to promote reactivation. The peculiar behavior of some pretreated sorbents, showing a maximum of conversion at a small number of cycles, is explained in the light of the mode

Lagrangian Volume Deformations around Simulated Galaxies

We present a detailed analysis of the local evolution of 206 Lagrangian Volumes (LVs) selected at high redshift around galaxy seeds, identified in a large-volume $\Lambda$ cold dark matter ($\Lambda$CDM) hydrodynamical simulation. The LVs have a mass range of $1 - 1500 \times 10^{10} M_\odot$. We follow the dynamical evolution of the density field inside these initially spherical LVs from $z=10$ up to $z_{\rm low} = 0.05$, witnessing highly non-linear, anisotropic mass rearrangements within them, leading to the emergence of the local cosmic web (CW). These mass arrangements have been analysed in terms of the reduced inertia tensor $I_{ij}^r$, focusing on the evolution of the principal axes of inertia and their corresponding eigendirections, and paying particular attention to the times when the evolution of these two structural elements declines. In addition, mass and component effects along this process have also been investigated. We have found that deformations are led by dark matter dynamics and they transform most of the initially spherical LVs into prolate shapes, i.e. filamentary structures. An analysis of the individual freezing-out time distributions for shapes and eigendirections shows that first most of the LVs fix their three axes of symmetry (like a skeleton) early on, while accretion flows towards them still continue. Very remarkably, we have found that more massive LVs fix their skeleton earlier on than less massive ones. We briefly discuss the astrophysical implications our findings could have, including the galaxy mass-morphology relation and the effects on the galaxy-galaxy merger parameter space, among others.Comment: 23 pages, 20 figures. Minor editorial improvement

Cryptic complexity in felid vertebral evolution: shape differentiation and allometry of the axial skeleton

Members of the mammalian family Felidae (extant and extinct cats) are grossly phenotypically similar, but display a 300-fold range in body size, from less than 1 kg to more than 300 kg. In addition to differences in body mass, felid species show dietary and locomotory specializations that correlate to skull and limb osteological measurements, such as shape or cross-sectional area. However, ecological correlates to the axial skeleton are yet untested. Here, we build on previous studies of the biomechanical and morphological evolution of the felid appendicular skeleton by conducting a quantitative analysis of morphology and allometry in the presacral vertebral column across extant cats. Our results demonstrate that vertebral columns of arboreal, scansorial and terrestrial felids significantly differ in morphology, specifically in the lumbar region, while no distinction based on dietary specialization was found. Body size significantly influences vertebral morphology, with clear regionalization of allometry along the vertebral column, suggesting that anterior (cervicals and thoracics) and posterior (lumbar) vertebrae may be independently subjected to distinct selection pressures

Recent origin of low trabecular bone density in modern humans

Humans are unique, compared with our closest living relatives (chimpanzees) and early fossil hominins, in having an enlarged body size and lower limb joint surfaces in combination with a relatively gracile skeleton (i.e., lower bone mass for our body size). Some analyses have observed that in at least a few anatomical regions modern humans today appear to have relatively low trabecular density, but little is known about how that density varies throughout the human skeleton and across species or how and when the present trabecular patterns emerged over the course of human evolution. Here, we test the hypotheses that (i) recent modern humans have low trabecular density throughout the upper and lower limbs compared with other primate taxa and (ii) the reduction in trabecular density first occurred in early Homo erectus, consistent with the shift toward a modern human locomotor anatomy, or more recently in concert with diaphyseal gracilization in Holocene humans. We used peripheral quantitative CT and microtomography to measure trabecular bone of limb epiphyses (long bone articular ends) in modern humans and chimpanzees and in fossil hominins attributed to Australopithecus africanus, Paranthropus robustus/early Homo from Swartkrans, Homo neanderthalensis, and early Homo sapiens. Results show that only recent modern humans have low trabecular density throughout the limb joints. Extinct hominins, including pre-Holocene Homo sapiens, retain the high levels seen in nonhuman primates. Thus, the low trabecular density of the recent modern human skeleton evolved late in our evolutionary history, potentially resulting from increased sedentism and reliance on technological and cultural innovations

Binary black hole evolutions of approximate puncture initial data

Approximate solutions to the Einstein field equations are a valuable tool to investigate gravitational phenomena. An important aspect of any approximation is to investigate and quantify its regime of validity. We present a study that evaluates the effects that approximate puncture initial data, based on "skeleton" solutions to the Einstein constraints as proposed by Faye et al. [PRD 69, 124029 (2004)], have on numerical evolutions. Using data analysis tools, we assess the effectiveness of these constraint-violating initial data and show that the matches of waveforms from skeleton data with the corresponding waveforms from constraint-satisfying initial data are > 0.97 when the total mass of the binary is > 40M(solar). In addition, we demonstrate that the differences between the skeleton and the constraint-satisfying initial data evolutions, and thus waveforms, are due to negative Hamiltonian constraint violations present in the skeleton initial data located in the vicinity of the punctures. During the evolution, the skeleton data develops both Hamiltonian and momentum constraint violations that decay with time, with the binary system relaxing to a constraint-satisfying solution with black holes of smaller mass and thus different dynamics

Aesthetic restoration in maxillo-mandibular malformations: the role of genioplasty

Aim: The aim of this study was to determinate how orthognatic surgery aids to cure many skull and face abnormalities and to help re-establishing the correct occlusive relation thanks to the repositioning of the maxillo-mandibular skeleton basis. Methods: The study included 183 male patients and 338 female patients, with an average age of 23 years. The sample series was divided according to specific pathologies. All patients underwent surgical procedures and the therapeutic strategy was determined based on the anomalies presented. Results: 113 patients had a II class dental skeletal occlusion, 180 patients had a III class dental-skeletal occlusion and 222 patients had skull-facial abnormalities. 5 patients underwent only a genioplasty, 82 patients underwent a genioplasty associated with BSSO, 175 patients underwent a genioplasty associated with Le Fort I osteotomy and the remaining 253 patients underwent a genioplasty associated with BSSO and Le Fort I osteotomy. Conclusion: The experience shows that genioplasty has been successfully introduced in orthognathic surgical therapeutic procedures, for dental-skeleton abnormalities and mandibular asymmetries treatment. In recent years, the evolution of computer systems has allowed an accurate assessment and programming, by means of the three-dimensional display, which are of great help in the course of diagnosis and evaluation of the displacements to be carried out, in order to obtain optimal aesthetic results