Reconstruction of networks from their betweenness centrality

In this paper we study the reconstruction of a network topology from the values of its betweenness centrality, a measure of the influence of each of its nodes in the dissemination of information over the network. We consider a simple metaheuristic, simulated annealing, as the combinatorial optimization method to generate the network from the values of the betweenness centrality. We compare the performance of this technique when reconstructing different categories of networks –random, regular, small-world, scale-free and clustered–. We show that the method allows an exact reconstruction of small networks and leads to good topological approximations in the case of networks with larger orders. The method can be used to generate a quasi-optimal topology fora communication network from a list with the values of the maximum allowable traffic for each node.

Reconstruction of the join time-delay Doppler-scale reflectivity density in the wide-band regime. A frame theory based approach

The inverse scattering problem concerning the determination of the joint time-delayDoppler-scale reflectivity density characterizing continuous target environments is addressed by recourse to the generalized frame theory. A reconstruction formula,involving the echoes of a frame of outgoing signals and its corresponding reciprocalframe, is developed. A ‘‘realistic’’ situation with respect to the transmission ofa finite number of signals is further considered. In such a case, our reconstruction formula is shown to yield the orthogonal projection of the reflectivity density onto a subspace generated by the transmitted signals.

Sparse image reconstruction on the sphere: implications of a new sampling theorem.

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.

The Application of 3D Reconstruction Techniques in the Analysis of Ancient Tarraco’s Urban Topography

The widespread implementation of GIS-based 3D topographical models has been a great aid in the development and testing of archaeological hypotheses. In this paper, a topographical reconstruction of the ancient city of Tarraco, the Roman capital of the Tarraconensis province, is presented. This model is based on topographical data obtained through archaeological excavations, old photographic documentation, georeferenced archive maps depicting the pre-modern city topography, modern detailed topographical maps and differential GPS measurements. The addition of the Roman urban architectural features to the model offers the possibility to test hypotheses concerning the ideological background manifested in the city shape. This is accomplished mainly through the use of 3D views from the main city accesses. These techniques ultimately demonstrate the ‘theatre-shaped’ layout of the city (to quote Vitrubius) as well as its southwest oriented architecture, whose monumental character was conceived to present a striking aspect to visitors, particularly those arriving from the sea.

Investigation of discrete imaging models and iterative image reconstruction in differential X-ray phase-contrast tomography.

Differential X-ray phase-contrast tomography (DPCT) refers to a class of promising methods for reconstructing the X-ray refractive index distribution of materials that present weak X-ray absorption contrast. The tomographic projection data in DPCT, from which an estimate of the refractive index distribution is reconstructed, correspond to one-dimensional (1D) derivatives of the two-dimensional (2D) Radon transform of the refractive index distribution. There is an important need for the development of iterative image reconstruction methods for DPCT that can yield useful images from few-view projection data, thereby mitigating the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods. In this work, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction in DPCT. We also investigate the use of one of the models with a modern image reconstruction algorithm for performing few-view image reconstruction of a tissue specimen.

Buccal mucosa graft for laryngotracheal reconstruction in severe laryngeal stenosis.

OBJECTIVE: An operative technique is described as a salvage treatment for severe subglottic and supraglottic laryngeal stenosis. In addition to expansion of the laryngeal framework with an anterior cartilage graft, as used in a classical laryngotracheal reconstruction, the scar tissue obliterating the airway lumen is excised and a mucosal graft is placed to reconstruct the inner lining of the airway. The graft is harvested from buccal mucosa. METHODS: The operative technique is outlined. Three cases, 2 paediatric and one adult, with complete or near complete laryngeal stenosis are presented where this operative technique was employed. In all patients several surgeries had been performed previously which were unsuccessful. RESULTS: In all 3 patients a patent airway was achieved with decannulation of the tracheostomy in the 2 paediatric patients. CONCLUSIONS: In patients with severe subglottic or supraglottic airway stenosis where other surgeries have failed, excision of endoluminal scar tissue and placement of a buccal mucosal graft, in addition to conventional laryngotracheal reconstruction, is a promising technique. In revision cases of subglottic stenosis cricotracheal resection might not be an option because of scarring from previous surgeries. This operation is an alternative, which allows an increase in the airway lumen by excising the scar tissue then re-lining the exposed internal lumen. The buccal mucosa reduces granulation formation and re-stenosis.

Événements et déformations tardi-métamorphiques dans le segment Ossola-Ticino (Val Vigezzo-Centovalli, Italie-Suisse)

RESUME: Une zone tectonique large et complexe, connue sous le nom de ligne des Centovalli, traverse le secteur des Alpes Centrales compris entre Domodossola et Locarno. Cette région, formée par le Val Vigezzo et la vallée des Centovalli, constitue la terminaison méridionale du dôme Lepontin et représente une portion de la zone des racines des nappes alpines. Elle fait partie d’une grande et complexe zone de cisaillement, en partie associée à des phénomènes hydrothermaux d’âge alpin (<20 Ma), qui comprend le système tectonique Insubrien et celui du Simplon. Le Val Vigezzo et les Centovalli constituent un vrai carrefour entre les principaux accidents tectoniques des Alpes ainsi qu'une zone de juxtaposition du socle Sudalpin avec la zone des racines de l’Austroalpin et du Pennique. Les phases de déformation et les structures géologiques qui peuvent être étudiées s'étalent sur une période comprise entre environ 35 Ma et l'actuel. L’étude détaillée de terrain a mis en évidence la présence de nombreuses roches et structures de déformation de type ductile et cassant tels que des mylonites, des cataclasites, des pseudotachylites, des kakirites, des failles minéralisées, des gouges de faille et des plis. Sur le terrain on a pu distinguer au moins quatre générations de plis liés aux différentes phases de déformation. Le nombre et la complexité de ces structures indiquent une histoire très compliquée, selon plusieurs étapes distinctes, parfois liées, voire même superposées. Une partie de ces structures de déformation affectent aussi les dépôts sédimentaires d’âge quaternaire, notamment des limons et des sables lacustres. Ces sédiments constituent les restes d'un bassin lacustre attribué à l'époque interglaciaire Riss/Würm (éemien, 67.000-120.000 ans) et ils affleurent dans la partie centrale de la zone étudiée, à l'Est de la plaine de Santa Maria Maggiore. Ces sédiments montrent en leur sein toute une série de structures de déformation tels que des plans de faille inverses, des structures conjuguées de raccourcissement et des véritables plis. Ces failles et ces plis représenteraient les évidences de surface d’une déformation probablement active en époque quaternaire. Une autre formation rocheuse a retenu tout notre attention; il s'agit d'un corps de brèches péridotitiques monogéniques qui affleure en discontinuité le long du versant méridional et le long du fond de la vallée Vigezzo sur environ 20 km. Ces brèches se posent indifféremment sur le socle (unités Finero, Orselina) ou sur les sédiments lacustres. Elles sont traversées par des plans de failles qui développent des véritables stries de faille et des gouges de faille; l’orientation de ces plans est la même que celle affectant les failles à gouges du socle. La genèse de cette brèche est liée à l'altération et au modelage glacier (rock-glaciers) d'une brèche tectonique originelle qui borde la partie externe du Corps de Finero. Les structures de déformation de cette brèche, pareillement à celles des sédiments lacustres, ont été considérées comme les évidences de surface d'une tectonique quaternaire active dans la région. La dernière phase de déformation cassante qui affecte cette région peut donc être considérée comme active en époque quaternaire. Une vue d’ensemble de la région étudiée nous permet de reconnaître à l’échelle régionale une zone de cisaillement complexe orientée E-W, parallèlement à l’axe de la vallée Centovalli-Val Vigezzo. Les données de terrain, indiquent que cette zone de cisaillement débute sous conditions ductiles et évolue en plusieurs étapes jusqu’à des conditions de failles cassantes de surface. La reconstruction de l'évolution géodynamique de la région a permis de définir trois étapes distinctes qui marquent le passage, de ce secteur de socle cristallin, de conditions P-T profondes à des conditions de surface. Dans ce contexte, on a reconnu trois phases principales de déformation à l’échelle régionale qui caractérisent ces trois étapes. La phase la plus ancienne est constituée par des mylonites en faciès amphibolite, associées à des mouvements de cisaillement dextre, qui sont ensuite remplacés par des mylonites en faciès schistes verts et des plis rétrovergentes liés au rétrocharriage des nappes alpines. Une deuxième étape est identifiée par le développement d’une phase hydrothermale liée à un système de failles extensives et décrochantes dextres à direction principale E-W, NE-SW et NW-SE. Leur caractérisation minéralogique a permis la mise en évidence des phases cristallines de néoformation liées à cet événement constituées par : K-feldspath (microcline), chlorites (Fe+Mg), épidotes, prehnite, zéolites (laumontite), sphène, calcite. Dans ce contexte, pour obtenir une meilleure caractérisation de cet événement hydrothermal on a utilisé des géothermomètres sur chlorites, sensible aussi à la pression et a la a(H2O), qui ont donné des valeurs descendantes comprises entre 450-200°C. Les derniers mouvements sont mis en évidence par le développement d’une série de plans majeurs de failles à gouge, qui forment une structure en sigmoïdes d’épaisseur kilométrique reconnaissable à l’échelle de la vallée et caractérisée par des mouvements transpressifs avec une composante décrochante dextre toujours importante. Cette phase de déformation forme un système conjugué de failles avec direction moyenne E-W qui coupent la zone des racines des nappes alpines, la zone du Canavese et le corps ultramafique de Finero. Ce système se déroule de manière subparallèle à l'axe de la vallée le long de plusieurs dizaines de kilomètres. Une analyse complète et détaillée des gouges de faille par XRD a montré que la fraction argileuse (<2 µm) de ces gouges contient une partie de néoformation très importante constituée par, des illites, des chlorites et des interstratifiés de type illite/smectite ou chlorite/smectite. Des datations avec méthode K-Ar sur ces illites ont donné des valeurs comprises entre 12 et 4 Ma qui représentent l'âge de cette dernière déformation cassante. L'application de la méthode de la cristallinité de l'illite (C.I.) a permis d'évaluer les conditions thermiques qui caractérisent le déroulement de cette dernière phase tectonique qui se produit sous conditions de température caractéristiques de l'anchizone et de la diagenèse. L'ensemble des structures de déformation qu'on vient de décrire s'insère parfaitement dans le contexte de convergence oblique entre la plaque adriatique et celle européenne qui à produit l'orogène alpin. On peut considérer les structures tectoniques du Val Vigezzo-Centovalli comme l'expression d'une zone majeure de cisaillement "Simplo-Insubrienne". L'empilement structural et les structures tectoniques affleurantes dans la région sont le résultat de l'interaction entre un régime tectonique transpressif et un régime transtensif. Ces deux champs de tension sont antagonistes entre eux mais sont reliés, de toute façon, à une seule phase décrochante dextre principale, due à une convergence oblique entre deux plaques. À l'échelle de l'évolution géodynamique on peut distinguer différentes étapes au cours desquelles les structures de ces deux régimes tectoniques interagissent en manière différente. En accord avec les données géophysiques et les reconstructions paléodynamiques prises dans la littérature on considère que la ligne Rhône-Simplon-Centovalli représente l'évidence de surface de la suture majeure profonde entre la plaque Adriatique et celle Européenne. Les vitesses de soulèvement qui ont été calculées dans cette étude pour cette région des Alpes donnent une valeur moyenne de 0.8 mm/a qui est tout à fait comparable avec les données proposées par la littérature sur cette zone. La zone Val Vigezzo-Centovalli peut être donc considérée comme un carrefour géologique où se croisent différentes phases tectoniques qui représentent les évidences de surface d'une suture profonde majeure entre deux plaques dans un contexte de collision continentale. ABSTRACT: A wide and complex tectonic zone known as Centovalli line, crosses the Central Alps sector between Domodossola and Locarno. This area, formed by the Vigezzo Valley and Centovalli valley, constitutes the southernmost termination of the Lepontin dome and represents a portion of the alpine nappes root zone. It belongs to a large and complex shear-zone, partly associated with hydrothermal phenomena of alpine age (<20 My), which includes the Insubric Line and the Simplon fault zone. Vigezzo Valley and Centovalli constitute a real crossroads between the mains alpines tectonics lines as well as a zone of juxtaposition of the Southalpine basement with the Austroalpin and Pennique root zone. The deformation phases and the geological structures that can be studied between approximately 35 My and the present. The detailed field study showed the presence of many brittle and ductile deformation structures and fault rocks such as mylonites, cataclasites, pseudotachylites, kakirites, mineralized faults, fault gouges and folds. In the field we could distinguish at least four folds generations related to the various deformation phases. The number and the complexity of these structures indicate a very complicated history, comprising several different stages, that sometimes are related and even superimposed. Part of these deformation structures affect also the sedimentary deposits of quaternary age, in particular the silts and sands lake deposit. These sediments constitute the remainders of a lake basin ascribed to the interglacial Riss/Würm (Eemien, 67.000-120.000 years) and outcroping in the central part of the studied area, in the Eastern part of Santa Maria Maggiore plain. These sediments show a whole series of deformation structures such as inverse fault planes, combined shortening structures and true folds. These faults and folds would represent the surface evidence of a probably active tectonic deformation in quaternary time. Another rock formation attracted all our attention. It is a body of monogenic peridotite breccia which outcrops in discontinuity along the southernmost slope and the bottom of the Vigezzo valley on approximately 20 km. This breccia lies indifferently on the basement (Finero and Orselina units) or on the lake sediments. They are crossed by fault planes which developed slikenside and fault gouges whose orientation is the same of the faults gouges in the alpine basement. This breccia results from the weathering and the surface modelling of an original tectonic breccia which borders the external part of Finero peridotite body. This breccia deformation structures, like those of the lake sediments, were regarded as the surface interaction of active quaternary tectonics in the area. So the last brittle deformation phases which affects this area seems to be actives in quaternary time. Theoverall picture of the studied area on a regional scale enables us to point out a complex shear-zone directed E-W, parallel to the axis of the Centovalli and Vigezzo Valley. The field analysis indicates that this shear-zone began under ductile conditions and evolved in several stages to brittle faulting under surface conditions. The analysis of the geodynamic evolution of the area allows to define three different stages which mark the transition of this alpine basement root zone, from deep P-T conditions to P-T surface conditions. In this context on regional scale three principal deformation phases, which characterize these three stages can be distinguished. The oldest phase consisted of the amphibolitie facies mylonites, associated to dextral strikeslip movements. They are then replaced by green-schists facies mylonites and backfolds related to the backthrusting of the alpines nappes. A second episode is caracterized by the development of an hydrothermal phase bound to an extensive fault and dextral strike-slip fault system, with E-W, NW-SE and SE-NW principal directionsThe principal neoformed mineral phases related to this event are: K-feldspar (microcline), chlorites (Fe+Mg), epidotes prehnite, zéolites (laumontite), sphene and calcite. In this context, to obtain a better characterization of this hydrothermal event, we have used an chlorite geothermometer, sensitive also to the pressure and has the a(H2O), which gave downward values ranging between 450-200°C. The last movements are caracterized by the development of important gouge fault plans, which form a sigmoid structure of kilometric thickness which is recognizable at the valley scale, and is characterized by transpressive movements always with a significant dextral strike-slip component. This deformation phase forms a combined faults system with an average E-W direction, which cuts trough the alpine root zone, the Canavese zone and the Finero ultramafic body. This fault system takes place subparallel to the axis of the valley over several tens of kilometers. A complete and detailed XRD analysis of the gouges fault showed that the clay fraction (<2µm) contains a very significant neo-formation of illite, chlorites and mixed layered clays such as illite/smectite or chlorite/smectite. The K-Ar datings of the illite fraction <2µm gave values ranging between 12 and 4 My and the illite fraction <0.2µm gave more recents values until to 2,4-0 My.This values represent the age of this last brittle deformation. The application of the illite crystallinity method (C.I.) allowed evaluating the thermal conditions which characterize this tectonic phase that occured under temperature conditions of the anchizone and diagenesis. The whole set of deformation structures which we just described, perfectly fit the context of oblique convergence between the Adriatic and the European plate that produced the alpine orogen. We can regard the Vigezzo valley and Centovalli tectonic structures as the expression of a major "Simplo-Insubric" shear-zone. Structural stacking and tectonic structures that outcrop in the studied area, are the result of the interaction between a transpressive and a transtensve tectonic phases. These two tension fields are antagonistic but they are also connected, in any event, with only one principal dextral strike-slip movement, caused by an oblique convergence between two plates. On the geodynamic evolution scale we can distinguish various stages during which these two tectonic structures fields interact in various ways. In agreement with the geophysical data and the paleodynamic recostructions taken in the literature we considers that the Rhone-Simplon-Centovalli line are the surface feature of the major collision between the Adriatique and the European plate at depth. The uplift speeds we calculated in this study for this Alpine area give an average value of 0.8 mm/a, which is in good agreement with the data suggested by the literature on this zone. TheVigezzo Valley and Centovalli zone can therefore be regarded as a geological crossroad where various tectonic phases are superimposed. They represent the evidences of a major and deeper suture between two plates in a continental collision context.

Transfer entropy reconstruction and labeling of neuronal connections from simulated calcium imaging

Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exceeds a small minimum frequency. Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter-burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network. By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.

In silico pathway reconstruction: Iron-sulfur cluster biogenesis in Saccharomyces cerevisiae

Background: Current advances in genomics, proteomics and other areas of molecular biology make the identification and reconstruction of novel pathways an emerging area of great interest. One such class of pathways is involved in the biogenesis of Iron-Sulfur Clusters (ISC). Results: Our goal is the development of a new approach based on the use and combination of mathematical, theoretical and computational methods to identify the topology of a target network. In this approach, mathematical models play a central role for the evaluation of the alternative network structures that arise from literature data-mining, phylogenetic profiling, structural methods, and human curation. As a test case, we reconstruct the topology of the reaction and regulatory network for the mitochondrial ISC biogenesis pathway in S. cerevisiae. Predictions regarding how proteins act in ISC biogenesis are validated by comparison with published experimental results. For example, the predicted role of Arh1 and Yah1 and some of the interactions we predict for Grx5 both matches experimental evidence. A putative role for frataxin in directly regulating mitochondrial iron import is discarded from our analysis, which agrees with also published experimental results. Additionally, we propose a number of experiments for testing other predictions and further improve the identification of the network structure. Conclusion: We propose and apply an iterative in silico procedure for predictive reconstruction of the network topology of metabolic pathways. The procedure combines structural bioinformatics tools and mathematical modeling techniques that allow the reconstruction of biochemical networks. Using the Iron Sulfur cluster biogenesis in S. cerevisiae as a test case we indicate how this procedure can be used to analyze and validate the network model against experimental results. Critical evaluation of the obtained results through this procedure allows devising new wet lab experiments to confirm its predictions or provide alternative explanations for further improving the models.

Biblio-MetReS: A bibliometric network reconstruction application and server

Background: Reconstruction of genes and/or protein networks from automated analysis of the literature is one of the current targets of text mining in biomedical research. Some user-friendly tools already perform this analysis on precompiled databases of abstracts of scientific papers. Other tools allow expert users to elaborate and analyze the full content of a corpus of scientific documents. However, to our knowledge, no user friendly tool that simultaneously analyzes the latest set of scientific documents available on line and reconstructs the set of genes referenced in those documents is available. Results: This article presents such a tool, Biblio-MetReS, and compares its functioning and results to those of other user-friendly applications (iHOP, STRING) that are widely used. Under similar conditions, Biblio-MetReS creates networks that are comparable to those of other user friendly tools. Furthermore, analysis of full text documents provides more complete reconstructions than those that result from using only the abstract of the document. Conclusions: Literature-based automated network reconstruction is still far from providing complete reconstructions of molecular networks. However, its value as an auxiliary tool is high and it will increase as standards for reporting biological entities and relationships become more widely accepted and enforced. Biblio- MetReS is an application that can be downloaded from http://metres.udl.cat/. It provides an easy to use environment for researchers to reconstruct their networks of interest from an always up to date set of scientific documents.

Reduction of respiratory motion artifacts for free-breathing whole-heart coronary MRA by weighted iterative reconstruction.

PURPOSE: To combine weighted iterative reconstruction with self-navigated free-breathing coronary magnetic resonance angiography for retrospective reduction of respiratory motion artifacts. METHODS: One-dimensional self-navigation was improved for robust respiratory motion detection and the consistency of the acquired data was estimated on the detected motion. Based on the data consistency, the data fidelity term of iterative reconstruction was weighted to reduce the effects of respiratory motion. In vivo experiments were performed in 14 healthy volunteers and the resulting image quality of the proposed method was compared to a navigator-gated reference in terms of acquisition time, vessel length, and sharpness. RESULT: Although the sampling pattern of the proposed method contained 60% more samples with respect to the reference, the scan efficiency was improved from 39.5 ± 10.1% to 55.1 ± 9.1%. The improved self-navigation showed a high correlation to the standard navigator signal and the described weighting efficiently reduced respiratory motion artifacts. Overall, the average image quality of the proposed method was comparable to the navigator-gated reference. CONCLUSION: Self-navigated coronary magnetic resonance angiography was successfully combined with weighted iterative reconstruction to reduce the total acquisition time and efficiently suppress respiratory motion artifacts. The simplicity of the experimental setup and the promising image quality are encouraging toward future clinical evaluation. Magn Reson Med 73:1885-1895, 2015. © 2014 Wiley Periodicals, Inc.

Surgical reconstruction of TMJ

Certain situations and pathological processes that arise with temporomandibular joint destruction can only be resolved with surgical reconstructive procedures in order to attempt a functional and anatomical rehabilitation of this joint. Many of these situations can be surgically treated with the patient's own autologous tissues. However, in some patients reconstruction is complex and the use of autologous tissues is unadvisable whereas reconstruction utilizing alloplastic materials may be an appropriate alternative. The following report describes 4 clinical cases in which autologous grafts or Christensen joint prosthesis are employed in temporomandibular joint reconstruction

Lake-level and salinity reconstruction from diatom analyses in Quillagua Formation (Late Neogene, Central Andean Forearc, Northern Chile)

A sedimentary and micropaleontological study of the Quillagua Formation provides a detailed paleohydrological reconstruction of the lacustrine system which occupied the present-day hyperarid Quillagua-Llamara fore-arc Basin (Northern Chile) from lattermost Miocene to Early Pliocene times.

The measurement of ice velocity, mass balance and thinning-rate on Johnsons Glacier, Livingston Island, South Shetland Islands, Antarctica

A network of twenty stakes was set up on Johnsons Glacier in order to determine its dynamics. During the austral summers from 1994-95 to 1997-98, we estimated surface velocities, mass balances and ice thickness variations. Horizontal velocity increased dow nstream from 1 m a- 1 near the ice divides to 40 m a- 1 near the ice terminus. The accumulation zone showed low accumulation rates (maximum of 0,6 m a- 1 (ice)), whereas in the lower part of the glacier, ablation rates were 4,3 m a- 1 (ice). Over the 3-year study period, both in the accumulation and ablation zones, we detected a reduction in the ice surface level ranging from 2 to 10 m from the annual ve rt ical velocities and ice-thinning data, the mass balance was obtained and compared with the mass balance field values, resulting in similar estimates. Flux values were calculated using cross-section data and horizontal velocities, and compared with the results obtained by means of mass balance and ice thinning data using the continuity equation. The two methods gave similar results.