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A variational model for epitaxially strained films accounting for the presence of dislocations is considered. Existence, regularity and some qualitative properties of solutions are addressed. [ABSTRACT FROM AUTHOR]

Following some ideas of a recent paper by Ambrosio, Bourgain, Brezis and Figalli, we prove a formula for the total variation of certain SBV functions without making use of the distributional derivatives. [ABSTRACT FROM AUTHOR]

We obtain a sharp quantitative isoperimetric inequality for nonlocal s-perimeters, uniform with respect to s bounded away from 0. This allows us to address local and global minimality properties of balls with respect to the volume-constrained minimization of a free energy consisting of a nonlocal s-perimeter plus a non-local repulsive interaction term. In the particular case s = 1, the s-perimeter coincides with the classical perimeter, and our results improve the ones of Knuepfer and Muratov (Comm. Pure Appl. Math. 66(7):1129-1162, ; Comm. Pure Appl. Math., ) concerning minimality of balls of small volume in isoperimetric problems with a competition between perimeter and a nonlocal potential term. More precisely, their result is extended to its maximal range of validity concerning the type of nonlocal potentials considered, and is also generalized to the case where local perimeters are replaced by their nonlocal counterparts. [ABSTRACT FROM AUTHOR]

We discuss the local minimality of certain configurations for a nonlocal isoperimetric problem used to model microphase separation in diblock copolymer melts. We show that critical configurations with positive second variation are local minimizers of the nonlocal area functional and, in fact, satisfy a quantitative isoperimetric inequality with respect to sets that are L-close. The link with local minimizers for the diffuse-interface Ohta-Kawasaki energy is also discussed. As a byproduct of the quantitative estimate, we get new results concerning periodic local minimizers of the area functional and a proof, via second variation, of the sharp quantitative isoperimetric inequality in the standard Euclidean case. As a further application, we address the global and local minimality of certain lamellar configurations. [ABSTRACT FROM AUTHOR]

In this paper, we prove short time existence, uniqueness, and regularity for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained two-dimensional films. This is achieved by using the H-gradient flow structure of the evolution law, via De Giorgi's minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity. [ABSTRACT FROM AUTHOR]

We consider a variational model introduced in the physical literature to describe the epitaxial growth of an elastic film over a thick flat substrate when a lattice mismatch between the two materials is present. We study quantitative and qualitative properties of equilibrium configurations, that is, of local and global minimizers of the free-energy functional. More precisely, we determine analytically the critical threshold for the local minimality of the flat configuration and we also prove several results concerning its global minimality. The non-occurrence of singularities in non-flat global minimizers is also addressed. One of the main results of the paper is a new sufficient condition for local minimality, which provides the first extension of the classical criteria based on the positivity of the second variation to the context of functionals with bulk and surface energies. [ABSTRACT FROM AUTHOR]

In 1938 Herman Auerbach published a paper where he showed a deep connection between the solutions of the Ulam problem of floating bodies and a class of sets studied by Zindler, which are the planar sets whose bisecting chords all have the same length. In the same paper he conjectured that among Zindler sets the one with minimal area, as well as with maximal perimeter, is the so-called "Auerbach triangle". We prove this conjecture. [ABSTRACT FROM AUTHOR]

Abstract: The isoperimetric problem with respect to the product-type density on the Euclidean space is studied. In particular, existence, symmetry and regularity of minimizers is proved. In the special case , also the shape of all the minimizers is derived. Finally, a conjecture about the minimality of large cylinders in the case is formulated. [Copyright &y& Elsevier]

Abstract: Background: Treadmill is commonly used in routine evaluation of walking capacities, especially when dealing with energetic cost, as it allows to measure this motion on a long enough period. However, even when using powerful treadmills, it is impossible to avoid belt speed variations. The objective of this paper was to demonstrate that this instantaneous treadmill speed has to be taken into account in mechanical work calculation during treadmill walking. Methods: To do so, 11 healthy subjects participated in the study. They walked on treadmill at four different speeds: very slow , slow , normal and fast . To compute , the instantaneous mechanical work relatively to the instantaneous treadmill speed, we applied the work-energy theorem in a non-inertial reference frame induced by the treadmill speed variations. This value was then compared to , i.e. the instantaneous mechanical work computed with the usual approximation of a constant treadmill speed. Findings: The speed variations had an average value of 17% for the very slow speed and around 4.5% for the three other and more usual speeds. These variations have a strong influence on instantaneous mechanical work. Indeed, is nearly null when not considering speed variations whereas goes up to at higher speeds. Interpretation: To conclude, our work showed that the instantaneous treadmill speed has to be taken into account in mechanical work computation. This method may provide supplementary information in clinical assessments and analyses of gait. Indeed, when using the same methodology on formerly acquired data in a group of 13 hemiplegic patients, we found that if is not null in this impaired subjects group, is still 30% higher. [Copyright &y& Elsevier]

We prove a sharp quantitative version of the isoperimetric inequality in the space ℝn endowed with the Gaussian measure. [ABSTRACT FROM AUTHOR]

A quantitative version of the sharp Sobolev inequality in W1,p(Rn), 1 < p < n, is established with a remainder term involving the distance from the family of extremals. [ABSTRACT FROM AUTHOR]

Abstract: The treadmill is frequently used in research and clinical assessments for gait analysis. To evaluate mechanical energy and dynamics of walking, the fluctuations of the treadmill speed have to be taken into account. A new algorithm is presented in this study to determine instantaneous treadmill speed using solely the kinematic data of subjects. The algorithm uses an automatic detection of heel contact (HC) and toe off (TO) during treadmill walking. Kinematic data were collected from two groups (healthy adult, ; hemiplegic adult, ). The gait events determination is validated by comparison with two visual inspection methods. Our algorithm is able to determine instantaneous treadmill speed with accuracy. In fact, the root mean square error between the computed speed (CS) and the measure speed (MS) was weak with an average value of ms−1. So, the computed speed reflects the variations of the belt speed and could be an important contribution to energetic and dynamic gait analysis on a treadmill. [Copyright &y& Elsevier]

Strained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavorable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup in which the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume-constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero-contact-angle condition between islands and wetting layers. [ABSTRACT FROM AUTHOR]

Abstract: The classical Sobolev embedding theorem of the space of functions of bounded variation into is proved in a sharp quantitative form. [Copyright &y& Elsevier]

Anti-vascular endothelial growth factor (anti-VEGF) agents are the standard treatment for neovascular age-related macular degeneration (nAMD); however, previous studies have suggested possible adverse events. Conclusions Ischemic colitis is uncommon in patients treated with anti-VEGF agents, occurring in approximately 1.1 to 1.4 per 1,000 patients, and, in crude analysis, it does not appear to differ meaningfully between different medications. [Extracted from the article]

A quantitative version of Pólya–Szegő inequality is proven for log-concave functions in the case of Steiner and Schwarz rearrangements. [ABSTRACT FROM AUTHOR]

The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets. [ABSTRACT FROM AUTHOR]

We establish new lower semicontinuity results for energy functionals containing a very general volume term of polyconvex type and a surface term depending on the spatial variable in a discontinuous way. [ABSTRACT FROM AUTHOR]

cAMP pathway plays a major role in the pathogenesis of cortisol-producing adrenocortical adenomas (CPA). cAMP-induced steroidogenesis is preceded by actin cytoskeleton reorganization, a process regulated by cofilin activity. In this study we investigated cofilin role in mediating cAMP effects on cell morphology and steroidogenesis in adrenocortical tumor cells. We demonstrated that forskolin induced cell rounding and strongly reduced phosphorylated (P)-cofilin/total cofilin ratio in Y1 (-52 ± 16%, p < 0.001) and human CPA cells (-53 ± 18%, p < 0.05). Cofilin silencing significantly reduced both forskolin-induced morphological changes and progesterone production (1.3-fold vs 1.8-fold in controls, p < 0.05), whereas transfection of wild-type or S3A (active), but not S3D (inactive) cofilin, potentiated forskolin effects on cell rounding and increased 3-fold progesterone synthesis with respect to control (p < 0.05). Furthermore, cofilin dephosphorylation by a ROCK inhibitor potentiated forskolin-induced cell rounding and steroidogenesis (2-fold increase vs forskolin alone). Finally, we found a reduced P-cofilin/total cofilin ratio and increased cofilin expression in CPA vs endocrine inactive adenomas by western blot and immunohistochemistry. Overall, these results identified cofilin as a mediator of cAMP effects on both morphological changes and steroidogenesis in mouse and human adrenocortical tumor cells. [ABSTRACT FROM AUTHOR]

Introduction/Background Upper limb volume assessment is the first step in lymphedema diagnosis and rehabilitative management. Circumferential method (CM), the most commonly used limb volumetric method, showed several limitations in common clinical rehabilitation practice and recently a new method using three-dimensional laser scanning (LS3D) has been proposed for limb volume measurement and validated by our group in healthy subjects. Aim of this study was to verify the reproducibility and reliability of LS3D compared to CM in upper limb volume measurement in women affected by breast cancer related lymphedema (BCRL). Material and method We included young women (aged > 18 and < 45 years) affected by BCRL, with normal weight (BMI > 18 and < 25 kg/m 2 ). Two raters randomly performed both LS3D and CM upper limb volume evaluation twice in each subject (the mean value of the two CM and LS3D evaluations was used) at baseline and at the end of the rehabilitative lymphedema treatment. CM assessments were performed by two expert lymphotherapists with more than 20 years of experience in lymphedema treatment and blinded to other rater's assessments. Results Ten BCRL patients, mean aged 54.3 ± 10.2 years have been enrolled. Both LS3D and CM showed a significant inter and intra-operator correlation in upper limb volume measurement ( r 2 = 0.99; P < 0.0001). LS3D showed a strong correlation with CM ( r 2 = 0.99; P < 0.0001); moreover LS3D was significantly quicker in upper limb volume measurement than CM (195 ± 24 s vs 258 ± 19 s; P < 0.0001). Conclusion Results of this small pilot study suggest that LS3D seems to be a highly reproducible, reliable and easy to use method to evaluate upper limb volume in BCRL patients, as previously evidenced in healthy subjects. Our results suggest a potential implementation of LS3D as a useful tool in lymphedema common clinical rehabilitation practice. Future investigations should address its reliability and reproducibility in different stages of lymphedema. [ABSTRACT FROM AUTHOR]