Singular kernels, multiscale decomposition of microstructure, and dislocation models

We consider a model for dislocations in crystals introduced by Koslowski, Cuiti\~no and Ortiz, which includes elastic interactions via a singular kernel behaving as the $H^{1/2}$ norm of the slip. We obtain a sharp-interface limit of the model within the framework of $\Gamma$-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitt\'e and Seppecher to which their rearrangement argument no longer applies. Instead we show that the microstructure must be approximately one-dimensional on most length scales and exploit this property to derive a sharp lower bound

Branching Structures in Elastic Shape Optimization

Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer. The paper discusses the optimization of such supporting structures in a specific class of domain patterns in 2D, which composes of periodic and branching period transitions on subdomain facets. These investigations can be considered as a case study to display examples of optimal branching domain patterns. In explicit, a rectangular domain is decomposed into rectangular subdomains, which share facets with neighbouring subdomains or with facets which split on one side into equally sized facets of two different subdomains. On each subdomain one considers an elastic material phase with stiff elasticity coefficients and an approximate void phase with orders of magnitude softer material. For given load on the outer domain boundary, which is distributed on a prescribed fine scale pattern representing the contact area of the shape, the interior elastic phase is optimized with respect to the compliance cost. The elastic stress is supposed to be continuous on the domain and a stress based finite volume discretization is used for the optimization. If in one direction equally sized subdomains with equal adjacent subdomain topology line up, these subdomains are consider as equal copies including the enforced boundary conditions for the stress and form a locally periodic substructure. An alternating descent algorithm is employed for a discrete characteristic function describing the stiff elastic subset on the subdomains and the solution of the elastic state equation. Numerical experiments are shown for compression and shear load on the boundary of a quadratic domain.Comment: 13 pages, 6 figure

Frontal brain asymmetries as effective parameters to assess the quality of audiovisual stimuli perception in adult and young cochlear implant users

How is music perceived by cochlear implant (CI) users? This question arises as "the next step" given the impressive performance obtained by these patients in language perception. Furthermore, how can music perception be evaluated beyond self-report rating, in order to obtain measurable data? To address this question, estimation of the frontal electroencephalographic (EEG) alpha activity imbalance, acquired through a 19-channel EEG cap, appears to be a suitable instrument to measure the approach/withdrawal (AW index) reaction to external stimuli. Specifically, a greater value of AW indicates an increased propensity to stimulus approach, and vice versa a lower one a tendency to withdraw from the stimulus. Additionally, due to prelingually and postlingually deafened pathology acquisition, children and adults, respectively, would probably differ in music perception. The aim of the present study was to investigate children and adult CI users, in unilateral (UCI) and bilateral (BCI) implantation conditions, during three experimental situations of music exposure (normal, distorted and mute). Additionally, a study of functional connectivity patterns within cerebral networks was performed to investigate functioning patterns in different experimental populations. As a general result, congruency among patterns between BCI patients and control (CTRL) subjects was seen, characterised by lowest values for the distorted condition (vs. normal and mute conditions) in the AW index and in the connectivity analysis. Additionally, the normal and distorted conditions were significantly different in CI and CTRL adults, and in CTRL children, but not in CI children. These results suggest a higher capacity of discrimination and approach motivation towards normal music in CTRL and BCI subjects, but not for UCI patients. Therefore, for perception of music CTRL and BCI participants appear more similar than UCI subjects, as estimated by measurable and not self-reported parameters

Tightness for a stochastic Allen--Cahn equation

We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds and prove tightness of of solutions in the sharp interface limit, and show convergence to phase-indicator functions.Comment: 27 pages, final Version to appear in "Stochastic Partial Differential Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new. It replaces and simplifies the old propositions 6.4-6.

The effect of body mass index on chest trauma severity and prognosis

AIM: Patients with thoracic trauma constitute one third of all the trauma cases, in west Sicily were recorded 941 thoracic trauma during the period between 2006 and 2009. Sicily is one of the Italian regions with the highest rate of obesity: some studies have demonstrated that obesity is an independent risk factor for mortality in high energy blunt traumas. MATERIAL OF STUDY: This study was conducted with trauma patients older than 20 years old who presented to our Department during the last five years. We only included thoracic injuries and politrauma with a thoracic involvement and a BMI > 25- Patients were divided into two groups: HET and LET patients. RESULTS: Thoracic trauma was more common in patients with a BMI > 25 than in normo-weight and clinic admission rate, length of hospital stay and ISS score increased in proportion with the increase of BMI. Both HET (high energy trauma) and LET (low energy trauma) revealed that overweight, obese and morbidly obese patients had greater admissions and length of hospital stay. DISCUSSION: The overweight and obese population has increased substantially over the last two decades and 61,5% of the Sicilian population is above normal weight. A large body mass with excess adiposity may contribute to HET injuries in several ways. Obesity has a number of comorbidities that reduce chances of recovery in overweight and obese patients experienced thoracic trauma both HET and LET. CONCLUSION: Obesity increases morbidity independently of injury severity in thoracic trauma patients. As BMI increased, length of hospital stay increased and prognosis deteriorates

Good news or bad news, which do you want first? The importance of the sequence and organization of Information for financial decision-making: a neuro-electrical imaging study

Investment decisions are largely based on the information investors received from the target firm. Thaler introduced the hedonic editing framework, in which suggests that integration/segregation of information influence individual's perceived value. Meanwhile, when evaluating the evidence and information in a sequence, order effect and biases have been found to have an impact in various areas. In this research, the influence of the Organization of Information (Integration vs. Segregation) and the Sequence of Information (Negative-Positive order vs. Positive-Negative order) on individual's investment decision-making both at the behavioral level (decision) and neurometrix level (measured by an individual's emotion and Approach Withdraw tendency) was assessed for the three groups of information: a piece of Big Positive Information and a piece of Small Negative Information, a piece of Big Negative Information and a piece of Small Positive Information, and a piece of Small Negative information. The behavioral results, which are an individual's final investment decision, were consistent for all three scenarios. In general, individuals will invest more/retire less when receiving two pieces of information in a Negative-Positive order. However, the neurometric results (Emotional Index, Approach Withdraw Index and results from LORETA) show differences among information groups. An effect of the Sequence of Information and the Organization of Information was found for the different scenarios. The results suggest that in the scenarios that involve large-scale information, the organization of information (Integration vs. Segregation) influences the emotion and Approach Withdraw tendency. The results of this investigation should provide insight for effective communication of information, especially when large-scale information is involved

Therapeutic sequences in patients with grade 1−2 neuroendocrine tumors (NET): an observational multicenter study from the ELIOS group

Purpose: Many different treatments are suggested by guidelines to treat grade 1−2 (G1−G2) neuroendocrine tumors (NET). However, a precise therapeutic algorithm has not yet been established. This study aims at identifying and comparing the main therapeutic sequences in G1−G2 NET. Methods: A retrospective observational Italian multicenter study was designed to collect data on therapeutic sequences in NET. Median progression-free survival (PFS) was compared between therapeutic sequences, as well as the number and grade of side effects and the rate of dose reduction/treatment discontinuation. Results: Among 1182 patients with neuroendocrine neoplasia included in the ELIOS database, 131 G1–G2 gastroenteropancreatic, lung and unknown primary NET, unresectable or persistent/relapsing after surgery, treated with ≥2 systemic treatments, were included. Four main therapeutic sequences were identified in 99 patients: (A) somatostatin analogs (SSA) standard dose to SSA high dose (n = 36), (B) SSA to everolimus (n = 31), (C) SSA to chemotherapy (n = 17), (D) SSA to peptide receptor radionuclide therapy (PRRT) (n = 15). Median PFS of the second-line treatment was not reached in sequence A, 33 months in sequence B, 20 months in sequence C, 30 months in sequence D (p = 0.16). Both total number and severity of side effects were significantly higher in sequences B and C than A and D (p = 0.04), as well as the rate of dose reduction/discontinuation (p = 0.03). Conclusions: SSA followed by SSA high dose, everolimus, chemotherapy or PRRT represent the main therapeutic sequences in G1−G2 NET. Median PFS was not significantly different between sequences. However, the sequences with SSA high dose or PRRT seem to be better tolerated than sequences with everolimus or chemotherapy

Nutrition and neuroendocrine tumors: An update of the literature.

Neuroendocrine tumors (NETs) are a heterogeneous group of neoplasms with worldwide increasing incidence, high prevalence and survival. Both the tumor itself and the systemic therapy may have an impact on patients' nutrition. Malnutrition negatively impacts on outcome in NETs patients. Moreover, it has been demonstrated that body mass index was a risk factor for NET development and that metabolic syndrome was associated with worse prognosis in these patients. Of note, food could also interact with the metabolism of oral target therapy and antineoplastic agents used for the treatment of progressive NETs. Therefore, the nutritional assessment, based on body composition, and lifestyle modifications should be an integral component of management of the NET patients. The nutrition care plans are an integral part of the multidisciplinary management team for patients with NETs. Nutritionists with expertise in NETs can provide dietary approaches to improve the quality of life and nutritional status during various therapeutic modalities used in patients with NETs. The aim of this review is to critically discuss the importance of nutrition and body composition in patients with NETs

Motion of a droplet for the Stochastic mass conserving Allen-Cahn equation

We study the stochastic mass-conserving Allen-Cahn equation posed on a smoothly bounded domain of R2 with additive, spatially smooth, space-time noise. This equation describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It^o calculus to derive the stochastic dynamics of the center of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco [2] for the deterministic problem. In the stochastic case depending on the scaling, the motion is driven by the change in the curvature of the boundary and the stochastic forcing. Moreover, under the assumption of a su ciently small noise strength, we establish stochastic stability of a neighborhood of the manifold of boundary droplet states in the L2- and H1-norms, which means that with overwhelming probability the solution stays close to the manifold for very long time-scales

Massive Star Cluster Formation and Destruction in Luminous Infrared Galaxies in GOALS

We present the results of a {\it Hubble Space Telescope} ACS/HRC FUV, ACS/WFC optical study into the cluster populations of a sample of 22 Luminous Infrared Galaxies in the Great Observatories All-Sky LIRG Survey. Through integrated broadband photometry we have derived ages and masses for a total of 484 star clusters contained within these systems. This allows us to examine the properties of star clusters found in the extreme environments of LIRGs relative to lower luminosity star-forming galaxies in the local Universe. We find that by adopting a Bruzual \& Charlot simple stellar population (SSP) model and Salpeter initial mass function, the age distribution of clusters declines as $dN/d\tau = \tau^{-0.9 +/- 0.3}$, consistent with the age distribution derived for the Antennae Galaxies, and interpreted as evidence for rapid cluster disruption occuring in the strong tidal fields of merging galaxies. The large number of $10^{6} M_{\odot}$ young clusters identified in the sample also suggests that LIRGs are capable of producing more high-mass clusters than what is observed to date in any lower luminosity star-forming galaxy in the local Universe. The observed cluster mass distribution of $dN/dM = M^{-1.95 +/- 0.11}$ is consistent with the canonical -2 power law used to describe the underlying initial cluster mass function (ICMF) for a wide range of galactic environments. We interpret this as evidence against mass-dependent cluster disruption, which would flatten the observed CMF relative to the underlying ICMF distribution.Comment: 63 pages, 58 Figures, 56 Tables, Accepted for publication in Ap