Soft cells and the geometry of seashells.

A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces. However, many tilings in Nature are characterized by shapes with curved edges, nonflat faces, and few, if any, sharp corners.

Polygonal tessellations as predictive models of molecular monolayers.

Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by covalent, hydrogen or van der Waals interactions-self-assembly of alike molecules results in a large variety of complex patterns even in two dimensions (2D). Prediction of pattern formation for 2D molecular networks is extremely important, though very challenging, and so far, relied on computationally involved approaches such as density functional theory, classical molecular dynamics, Monte Carlo, or machine learning.

Curvature flows, scaling laws and the geometry of attrition under impacts.

Impact induced attrition processes are, beyond being essential models of industrial ore processing, broadly regarded as the key to decipher the provenance of sedimentary particles. Here we establish the first link between microscopic, particle-based models and the mean field theory for these processes. Based on realistic computer simulations of particle-wall collision sequences we first identify the well-known damage and fragmentation energy phases, then we show that the former is split into the abrasion phase with infinite sample lifetime (analogous to Sternberg's Law) at finite asymptotic mass and the cleavage phase with finite sample lifetime, decreasing as a power law of the impact velocity (analogous to Basquin's Law).

Plato's cube and the natural geometry of fragmentation.

Plato envisioned Earth's building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra-shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural two-dimensional (2D) fragments, from mud cracks to Earth's tectonic plates, has two attractors: "Platonic" quadrangles and "Voronoi" hexagons.

Universal characteristics of particle shape evolution by bed-load chipping.

River currents, wind, and waves drive bed-load transport, in which sediment particles collide with each other and Earth's surface. A generic consequence is impact attrition and rounding of particles as a result of chipping, often referred to in geological literature as abrasion. Recent studies have shown that the rounding of river pebbles can be modeled as diffusion of surface curvature, indicating that geometric aspects of impact attrition are insensitive to details of collisions and material properties.

Author Correction: Shape evolution of ooids: a geometric model.

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Shape evolution of ooids: a geometric model.

Striking shapes in nature have been documented to result from chemical precipitation - such as terraced hot springs and stromatolites - which often proceeds via surface-normal growth. Another studied class of objects is those whose shape evolves by physical abrasion - the primary example being river and beach pebbles - which results in shape-dependent surface erosion. While shapes may evolve in a self-similar manner, in neither growth nor erosion can a surface remain invariant.

Reconstructing the transport history of pebbles on Mars.

The discovery of remarkably rounded pebbles by the rover Curiosity, within an exhumed alluvial fan complex in Gale Crater, presents some of the most compelling evidence yet for sustained fluvial activity on Mars. While rounding is known to result from abrasion by inter-particle collisions, geologic interpretations of sediment shape have been qualitative. Here we show how quantitative information on the transport distance of river pebbles can be extracted from their shape alone, using a combination of theory, laboratory experiments and terrestrial field data.

Universality of fragment shapes.

The shape of fragments generated by the breakup of solids is central to a wide variety of problems ranging from the geomorphic evolution of boulders to the accumulation of space debris orbiting Earth. Although the statistics of the mass of fragments has been found to show a universal scaling behavior, the comprehensive characterization of fragment shapes still remained a fundamental challenge. We performed a thorough experimental study of the problem fragmenting various types of materials by slowly proceeding weathering and by rapid breakup due to explosion and hammering.

How river rocks round: resolving the shape-size paradox.

River-bed sediments display two universal downstream trends: fining, in which particle size decreases; and rounding, where pebble shapes evolve toward ellipsoids. Rounding is known to result from transport-induced abrasion; however many researchers argue that the contribution of abrasion to downstream fining is negligible. This presents a paradox: downstream shape change indicates substantial abrasion, while size change apparently rules it out.

Geographical variations in current clinical practice on transfusions and iron chelation therapy across various transfusion-dependent anaemias.

Background And Objectives: Many patients with chronic anaemia require blood transfusions as part of their treatment regimen. As a result, iron overload will inevitably develop if not adequately managed by iron chelation therapy. There are many guidelines relating to transfusion and chelation practices for patients with transfusion-dependent anaemia; however, there is a lack of information on how treatment practices differ around the world.

Deferasirox for up to 3 years leads to continued improvement of myocardial T2* in patients with β-thalassemia major.

Background: Prospective data on cardiac iron removal are limited beyond one year and longer-term studies are, therefore, important.

Design And Methods: Seventy-one patients in the EPIC cardiac substudy elected to continue into the 3(rd) year, allowing cardiac iron removal to be analyzed over three years.

Results: Mean deferasirox dose during year 3 was 33.

Response of iron overload to deferasirox in rare transfusion-dependent anaemias: equivalent effects on serum ferritin and labile plasma iron for haemolytic or production anaemias.

Objectives: It is widely assumed that, at matched transfusional iron-loading rates, responses to chelation therapy are similar, irrespective of the underlying condition. However, data are limited for rare transfusion-dependent anaemias, and it remains to be elucidated if response differs, depending on whether the anaemia has a primary haemolytic or production mechanism.

Methods: The efficacy and safety of deferasirox (Exjade®) in rare transfusion-dependent anaemias were evaluated over 1 yr, with change in serum ferritin as the primary efficacy endpoint.

Clinical efficacy and safety evaluation of tailoring iron chelation practice in thalassaemia patients from Asia-Pacific: a subanalysis of the EPIC study of deferasirox.

Although thalassaemia is highly prevalent in the Asia-Pacific region, clinical data on efficacy and safety profiles of deferasirox in patients from this region are rather limited. Recently, data from the multicentre Evaluation of Patients' Iron Chelation with Exjade (EPIC) study in 1744 patients with different anaemias has provided an opportunity to analyse 1115 thalassaemia patients, of whom 444 patients were from five countries in the Asia-Pacific region (AP) for whom thalassaemia management and choice of iron chelators were similar. Compared to the rest of the world (ROW), baseline clinical data showed that the AP group appeared to be more loaded with iron (3745.

Continued improvement in myocardial T2* over two years of deferasirox therapy in β-thalassemia major patients with cardiac iron overload.

Background: The efficacy of cardiac iron chelation in transfusion-dependent patients has been demonstrated in one-year prospective trials. Since normalization of cardiac T2* takes several years, the efficacy and safety of deferasirox was assessed for two years in patients with β-thalassemia major in the cardiac sub-study of the EPIC trial.

Design And Methods: Eligible patients with myocardial T2* greater than 5 to less than 20 ms received deferasirox, with the primary endpoint being the change in T2* from baseline to two years.

Iron chelation therapy with deferasirox in patients with aplastic anemia: a subgroup analysis of 116 patients from the EPIC trial.

The prospective 1-year Evaluation of Patients' Iron Chelation with Exjade (EPIC) study enrolled a large cohort of 116 patients with aplastic anemia; the present analyses evaluated the efficacy and safety of deferasirox in this patient population. After 1 year, median serum ferritin decreased significantly from 3254 ng/mL at baseline to 1854 ng/mL (P < .001).

Deferasirox in iron-overloaded patients with transfusion-dependent myelodysplastic syndromes: Results from the large 1-year EPIC study.

The prospective 1-year EPIC study enrolled 341 patients with myelodysplastic syndromes (MDS); although baseline iron burden was >2500ng/mL, approximately 50% were chelation-naïve. Overall median serum ferritin decreased significantly at 1 year (p=0.002).

Efficacy of deferasirox in reducing and preventing cardiac iron overload in beta-thalassemia.

Cardiac iron overload causes most deaths in beta-thalassemia major. The efficacy of deferasirox in reducing or preventing cardiac iron overload was assessed in 192 patients with beta-thalassemia in a 1-year prospective, multicenter study. The cardiac iron reduction arm (n = 114) included patients with magnetic resonance myocardial T2* from 5 to 20 ms (indicating cardiac siderosis), left ventricular ejection fraction (LVEF) of 56% or more, serum ferritin more than 2500 ng/mL, liver iron concentration more than 10 mg Fe/g dry weight, and more than 50 transfused blood units.

Tailoring iron chelation by iron intake and serum ferritin: the prospective EPIC study of deferasirox in 1744 patients with transfusion-dependent anemias.

Unlabelled: Background Following a clinical evaluation of deferasirox (Exjade) it was concluded that, in addition to baseline body iron burden, ongoing transfusional iron intake should be considered when selecting doses. The 1-year EPIC study, the largest ever investigation conducted for an iron chelator, is the first to evaluate whether fixed starting doses of deferasirox, based on transfusional iron intake, with dose titration guided by serum ferritin trends and safety markers, provides clinically acceptable chelation in patients (aged >or=2 years) with transfusional hemosiderosis from various types of anemia.

Design And Methods: The recommended initial dose was 20 mg/kg/day for patients receiving 2-4 packed red blood cell units/month and 10 or 30 mg/kg/day was recommended for patients receiving less or more frequent transfusions, respectively.

Geometry and self-righting of turtles.

Terrestrial animals with rigid shells face imminent danger when turned upside down. A rich variety of righting strategies of beetle and turtle species have been described, but the exact role of the shell's geometry in righting is so far unknown. These strategies are often based on active mechanisms, e.

Sturdy cycles in the chaotic Tribolium castaneum data series.

Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting of discrete individuals and demographic noise has been analyzed in laboratory population data Henson et al.

Discrete and continuous state population models in a noisy world.

Simple ecological models operate mostly with population densities using continuous variables. However, in reality densities could not change continuously, since the population itself consists of integer numbers of individuals. At first sight this discrepancy appears to be irrelevant, nevertheless, it can cause large deviations between the actual statistical behaviour of biological populations and that predicted by the corresponding models.