An Eulerian Approach to the Analysis of Krause's Consensus Models

Abstract. In this paper we analyze a class of multi-agent consensus dynamical systems inspired by Krause’s original model. As in Krause’s, the basic assumption is the so-called bounded confidence: two agents can influence each other only when their state values are below a given distance threshold R. We study the system under an Eulerian point of view considering (possibly continuous) probability distributions of agents and we present original convergence results. The limit distribution is always necessarily a convex combination of delta functions at least R far apart from each other: in other terms these models are locally aggregating. The Eulerian perspective provides the natural framework for designing a numerical algorithm, by which we obtain several simulations in 1 and 2 dimensions

NLS ground states on metric trees: existence results and open questions

We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric graphs, several new features appear, such as the existence of minimizers with positive energy, and the emergence of unexpected threshold phenomena. We also study the problem with a radial symmetry constraint that is in principle different from the free problem due to the failure of the Pólya–Szegő inequality for radial rearrangements. A key role is played by a new Poincaré inequality with remainder

Uniqueness and non–uniqueness of prescribed mass NLS ground states on metric graphs

We consider the problem of uniqueness of ground states of prescribed mass for the Nonlinear Schrödinger Energy with power nonlinearity on noncompact metric graphs. We first establish that the Lagrange multiplier appearing in the NLS equation is constant on the set of ground states of mass μ, up to an at most countable set of masses. Then we apply this result to obtain uniqueness of ground states on two specific noncompact graphs. Finally we construct a graph that admits at least two ground states with the same mass having different Lagrange multipliers. Our proofs are based on careful variational arguments and rearrangement techniques, and hold both for the subcritical range p∈(2,6) and in the critical case p=6

Changes in the transcriptional profile in response to overexpression of the osteopontin-c splice isoform in ovarian (OvCar-3) and prostate (PC-3) cancer cell lines.

BACKGROUND: Especially in human tumor cells, the osteopontin (OPN) primary transcript is subject to alternative splicing, generating three isoforms termed OPNa, OPNb and OPNc. We previously demonstrated that the OPNc splice variant activates several aspects of the progression of ovarian and prostate cancers. The goal of the present study was to develop cell line models to determine the impact of OPNc overexpression on main cancer signaling pathways and thus obtain insights into the mechanisms of OPNc pro-tumorigenic roles. METHODS: Human ovarian and prostate cancer cell lines, OvCar-3 and PC-3 cells, respectively, were stably transfected to overexpress OPNc. Transcriptomic profiling was performed on these cells and compared to controls, to identify OPNc overexpression-dependent changes in gene expression levels and pathways by qRT-PCR analyses. RESULTS: Among 84 genes tested by using a multiplex real-time PCR Cancer Pathway Array approach, 34 and 16, respectively, were differentially expressed between OvCar-3 and PC-3 OPNc-overexpressing cells in relation to control clones. Differentially expressed genes are included in all main hallmarks of cancer, and several interacting proteins have been identified using an interactome network analysis. Based on marked up-regulation of Vegfa transcript in response to OPNc overexpression, we partially validated the array data by demonstrating that conditioned medium (CM) secreted from OvCar-3 and PC-3 OPNc-overexpressing cells significantly induced endothelial cell adhesion, proliferation and migration, compared to CM secreted from control cells. CONCLUSIONS: Overall, the present study elucidated transcriptional changes of OvCar-3 and PC-3 cancer cell lines in response to OPNc overexpression, which provides an assessment for predicting the molecular mechanisms by which this splice variant promotes tumor progression features

Stability of the Faber-Krahn inequality for the Short-time Fourier Transform

We prove a sharp quantitative version of the Faber--Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit $\delta(f;\Omega)$ which measures by how much the STFT of a function $f\in L^2(\mathbb R)$ fails to be optimally concentrated on an arbitrary set $\Omega\subset \mathbb R^2$ of positive, finite measure. We then show that an optimal power of the deficit $\delta(f;\Omega)$ controls both the $L^2$-distance of $f$ to an appropriate class of Gaussians and the distance of $\Omega$ to a ball, through the Fraenkel asymmetry of $\Omega$. Our proof is completely quantitative and hence all constants are explicit. We also establish suitable generalizations of this result in the higher-dimensional context.Comment: 46 page

The "Crossed Leg Sign" in the Emergency Department (or Tilli's Sign): A New Semiotic Sign for the Early Evaluation of Patients Accessing the Emergency Setting.

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Subcutaneously administered dexmedetomidine is efficiently absorbed and is associated with attenuated cardiovascular effects in healthy volunteers

Purpose: Palliative care patients often need sedation to alleviate intractable anxiety, stress, and pain. Dexmedetomidine is used for sedation of intensive care patients, but there is no prior information on its subcutaneous (SC) administration, a route that would be favored in palliative care. We compared the pharmacokinetics and cardiovascular, sympatholytic, and sedative effects of SC and intravenously (IV) administered dexmedetomidine in healthy volunteers.Methods: An open two-period, cross-over design with balanced randomization was used. Ten male subjects were randomized to receive 1 μg/kg dexmedetomidine both IV and SC. Concentrations of dexmedetomidine and catecholamines in plasma were measured. Pharmacokinetic variables were calculated with non-compartmental methods. In addition, cardiovascular and sedative drug effects were monitored.Results: Eight subjects completed both treatment periods. Peak concentrations of dexmedetomidine were observed 15 min after SC administration (median; range 15–240). The mean bioavailability of SC dexmedetomidine was 81% (AUC0-∞ ratio × 100%, range 49–97%). The mean (SD) peak concentration of dexmedetomidine in plasma was 0.3 (0.1) ng/ml, and plasma concentrations associated with sedative effects (i.e., > 0.2 ng/ml) were maintained for 4 h after SC dosing. Plasma noradrenaline concentrations were significantly lower (P Conclusions: Dexmedetomidine is relatively rapidly and efficiently absorbed after SC administration. Subcutaneous dexmedetomidine may be a feasible alternative in palliative sedation, and causes attenuated cardiovascular effects compared to IV administration.</p

A Comparison of Eight Optimization Methods Applied to a Wind Farm Layout Optimization Problem

Selecting a wind farm layout optimization method is difficult. Comparisons between optimization methods in different papers can be uncertain due to the difficulty of exactly reproducing the objective function. Comparisons by just a few authors in one paper can be uncertain if the authors do not have experience using each algorithm. In this work we provide an algorithm comparison for a wind farm layout optimization case study between eight optimization methods applied, or directed, by researchers who developed those algorithms or who had other experience using them. We provided the objective function to each researcher to avoid ambiguity about relative performance due to a difference in objective function. While these comparisons are not perfect, we try to treat each algorithm more fairly by having researchers with experience using each algorithm apply each algorithm and by having a common objective function provided for analysis. The case study is from the IEA Wind Task 37, based on the Borssele III and IV wind farms with 81 turbines. Of particular interest in this case study is the presence of disconnected boundary regions and concave boundary features. The optimization methods studied represent a wide range of approaches, including gradient-free, gradient-based, and hybrid methods; discrete and continuous problem formulations; single-run and multi-start approaches; and mathematical and heuristic algorithms. We provide descriptions and references (where applicable) for each optimization method as well as lists of pros and cons to help readers determine an appropriate method for their use case. All the optimization methods perform similarly, with optimized wake loss values between 15.48 % and 15.70 % as compared to 17.28 % for the unoptimized provided layout. Each of the layouts found were different, but all layouts exhibited similar characteristics. Strong similarities across all the layouts include tightly packing wind turbines along the outer borders, loosely spacing turbines in the internal regions, and allocating similar numbers of turbines to each discrete boundary region. The best layout by AEP was found using a new sequential allocation method, discreet exploration-based optimization (DEBO). Based on the results in this study, it appears that using an optimization algorithm can significantly improve wind farm performance, but there are many optimization methods that can perform well on the wind farm layout optimization problem given that they are applied correctly.</p

Exploring possible selves in a first-year physics foundation class: Engaging students by establishing relevance

Students often complain that they cannot see the relevance of what they are being taught in foundation physics classes. While revising and adjusting the curriculum and teaching are important, this study suggests it might also be useful to help students view their learning in relation to their future career aspirations. This paper reports on a study conducted with first-year students enrolled in a compulsory foundation physics unit with a history of low pass rates.Working within a “possible selves” framework, activities were designed to help students position their learning in relation to possible future lives and careers. Two cohorts of students (N ¼ 93) engaged in an intensive workshop comprising multiple activities relating to self and career. Self-reflection worksheets were analyzed using content analysis. The results indicate that students experience immediate benefits from these activities through self-reflection on the current self, future possible professional selves, and the role of current studies in narrowing the gap between the two

Comparison of mouse mammary gland imaging techniques and applications: Reflectance confocal microscopy, GFP Imaging, and ultrasound

<p>Abstract</p> <p>Background</p> <p>Genetically engineered mouse models of mammary gland cancer enable the <it>in vivo </it>study of molecular mechanisms and signaling during development and cancer pathophysiology. However, traditional whole mount and histological imaging modalities are only applicable to non-viable tissue.</p> <p>Methods</p> <p>We evaluated three techniques that can be quickly applied to living tissue for imaging normal and cancerous mammary gland: reflectance confocal microscopy, green fluorescent protein imaging, and ultrasound imaging.</p> <p>Results</p> <p>In the current study, reflectance confocal imaging offered the highest resolution and was used to optically section mammary ductal structures in the whole mammary gland. Glands remained viable in mammary gland whole organ culture when 1% acetic acid was used as a contrast agent. Our application of using green fluorescent protein expressing transgenic mice in our study allowed for whole mammary gland ductal structures imaging and enabled straightforward serial imaging of mammary gland ducts in whole organ culture to visualize the growth and differentiation process. Ultrasound imaging showed the lowest resolution. However, ultrasound was able to detect mammary preneoplastic lesions 0.2 mm in size and was used to follow cancer growth with serial imaging in living mice.</p> <p>Conclusion</p> <p>In conclusion, each technique enabled serial imaging of living mammary tissue and visualization of growth and development, quickly and with minimal tissue preparation. The use of the higher resolution reflectance confocal and green fluorescent protein imaging techniques and lower resolution ultrasound were complementary.</p