Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

Standardizing clinical trials workflow representation in UML for international site comparison.

BACKGROUND: With the globalization of clinical trials, a growing emphasis has been placed on the standardization of the workflow in order to ensure the reproducibility and reliability of the overall trial. Despite the importance of workflow evaluation, to our knowledge no previous studies have attempted to adapt existing modeling languages to standardize the representation of clinical trials. Unified Modeling Language (UML) is a computational language that can be used to model operational workflow, and a UML profile can be developed to standardize UML models within a given domain. This paper's objective is to develop a UML profile to extend the UML Activity Diagram schema into the clinical trials domain, defining a standard representation for clinical trial workflow diagrams in UML. METHODS: Two Brazilian clinical trial sites in rheumatology and oncology were examined to model their workflow and collect time-motion data. UML modeling was conducted in Eclipse, and a UML profile was developed to incorporate information used in discrete event simulation software. RESULTS: Ethnographic observation revealed bottlenecks in workflow: these included tasks requiring full commitment of CRCs, transferring notes from paper to computers, deviations from standard operating procedures, and conflicts between different IT systems. Time-motion analysis revealed that nurses' activities took up the most time in the workflow and contained a high frequency of shorter duration activities. Administrative assistants performed more activities near the beginning and end of the workflow. Overall, clinical trial tasks had a greater frequency than clinic routines or other general activities. CONCLUSIONS: This paper describes a method for modeling clinical trial workflow in UML and standardizing these workflow diagrams through a UML profile. In the increasingly global environment of clinical trials, the standardization of workflow modeling is a necessary precursor to conducting a comparative analysis of international clinical trials workflows.

High-fidelity, broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation.

We demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noisemodulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. In comparison with a previous slow-modulation method, eye-diagram and signal-to-noise ratio (SNR) analysis show that this broadband slow-light technique significantly increases the fidelity of a delayed data sequence, while maintaining the delay performance. A fractional delay of 0.81 with a SNR of 5.2 is achieved at the pump power of 350 mW using a 2-km-long highly nonlinear fiber with the fast noise-modulation method, demonstrating a 50% increase in eye-opening and a 36% increase in SNR in the comparison.

Probabilistic Fréchet means for time varying persistence diagrams

© 2015, Institute of Mathematical Statistics. All rights reserved.In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp, Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards. We fix this problem by altering the original definition of Fréchet mean so that it now becomes a probability measure on the set of persistence diagrams; in a nutshell, the mean of a set of diagrams will be a weighted sum of atomic measures, where each atom is itself a persistence diagram determined using a perturbation of the input diagrams. This definition gives for each N a map (Dp)^N→ℙ(Dp). We show that this map is Hölder continuous on finite diagrams and thus can be used to build a useful statistic on vineyards.

A Tissue-Engineered Microvascular System to Evaluate Vascular Progenitor Cells for Angiogenic Therapies

The ability of tissue engineered constructs to replace diseased or damaged organs is limited without the incorporation of a functional vascular system. To design microvasculature that recapitulates the vascular niche functions for each tissue in the body, we investigated the following hypotheses: (1) cocultures of human umbilical cord blood-derived endothelial progenitor cells (hCB-EPCs) with mural cells can produce the microenvironmental cues necessary to support physiological microvessel formation in vitro; (2) poly(ethylene glycol) (PEG) hydrogel systems can support 3D microvessel formation by hCB-EPCs in coculture with mural cells; (3) mesenchymal cells, derived from either umbilical cord blood (MPCs) or bone marrow (MSCs), can serve as mural cells upon coculture with hCB-EPCs. Coculture ratios between 0.2 (16,000 cells/cm2) and 0.6 (48,000 cells/cm2) of hCB-EPCs plated upon 3.3 µg/ml of fibronectin-coated tissue culture plastic with (80,000 cells/cm2) of human aortic smooth muscle cells (SMCs), results in robust microvessel structures observable for several weeks in vitro. Endothelial basal media (EBM-2, Lonza) with 9% v/v fetal bovine serum (FBS) could support viability of both hCB-EPCs and SMCs. Coculture spatial arrangement of hCB-EPCs and SMCs significantly affected network formation with mixed systems showing greater connectivity and increased solution levels of angiogenic cytokines than lamellar systems. We extended this model into a 3D system by encapsulation of a 1 to 1 ratio of hCB-EPC and SMCs (30,000 cells/µl) within hydrogels of PEG-conjugated RGDS adhesive peptide (3.5 mM) and PEG-conjugated protease sensitive peptide (6 mM). Robust hCB-EPC microvessels formed within the gel with invasion up to 150 µm depths and parameters of total tubule length (12 mm/mm2), branch points (127/mm2), and average tubule thickness (27 µm). 3D hCB-EPC microvessels showed quiescence of hCB-EPCs (<1% proliferating cells), lumen formation, expression of EC proteins connexin 32 and VE-cadherin, eNOS, basement membrane formation by collagen IV and laminin, and perivascular investment of PDGFR-β+/α-SMA+ cells. MPCs present in <15% of isolations displayed >98% expression for mural markers PDGFR-β, α-SMA, NG2 and supported hCB-EPC by day 14 of coculture with total tubule lengths near 12 mm/mm2. hCB-EPCs cocultured with MSCs underwent cell loss by day 10 with a 4-fold reduction in CD31/PECAM+ cells, in comparison to controls of hCB-EPCs in SMC coculture. Changing the coculture media to endothelial growth media (EBM-2 + 2% v/v FBS + EGM-2 supplement containing VEGF, FGF-2, EGF, hydrocortisone, IGF-1, ascorbic acid, and heparin), promoted stable hCB-EPC network formation in MSC cocultures over 2 weeks in vitro, with total segment length per image area of 9 mm/mm2. Taken together, these findings demonstrate a tissue engineered system that can be utilized to evaluate vascular progenitor cells for angiogenic therapies.

CD45+ Cells Present Within Mesenchymal Stem Cell Populations Affect Network Formation of Blood-Derived Endothelial Outgrowth Cells.

Mesenchymal stem cells (MSCs) and endothelial progenitor cells (EPCs) represent promising cell sources for angiogenic therapies. There are, however, conflicting reports regarding the ability of MSCs to support network formation of endothelial cells. The goal of this study was to assess the ability of human bone marrow-derived MSCs to support network formation of endothelial outgrowth cells (EOCs) derived from umbilical cord blood EPCs. We hypothesized that upon in vitro coculture, MSCs and EOCs promote a microenvironment conducive for EOC network formation without the addition of angiogenic growth supplements. EOC networks formed by coculture with MSCs underwent regression and cell loss by day 10 with a near 4-fold and 2-fold reduction in branch points and mean segment length, respectively, in comparison with networks formed by coculture vascular smooth muscle cell (SMC) cocultures. EOC network regression in MSC cocultures was not caused by lack of vascular endothelial growth factor (VEGF)-A or changes in TGF-β1 or Ang-2 supernatant concentrations in comparison with SMC cocultures. Removal of CD45+ cells from MSCs improved EOC network formation through a 2-fold increase in total segment length and number of branch points in comparison to unsorted MSCs by day 6. These improvements, however, were not sustained by day 10. CD45 expression in MSC cocultures correlated with EOC network regression with a 5-fold increase between day 6 and day 10 of culture. The addition of supplemental growth factors VEGF, fibroblastic growth factor-2, EGF, hydrocortisone, insulin growth factor-1, ascorbic acid, and heparin to MSC cocultures promoted stable EOC network formation over 2 weeks in vitro, without affecting CD45 expression, as evidenced by a lack of significant differences in total segment length (p=0.96). These findings demonstrate the ability of MSCs to support EOC network formation correlates with removal of CD45+ cells and improves upon the addition of soluble growth factors.