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.

Gait and behavior in an IL1β-mediated model of rat knee arthritis and effects of an IL1 antagonist.

Interleukin-1 beta (IL1β) is a proinflammatory cytokine that mediates arthritic pathologies. Our objectives were to evaluate pain and limb dysfunction resulting from IL1β over-expression in the rat knee and to investigate the ability of local IL1 receptor antagonist (IL1Ra) delivery to reverse-associated pathology. IL1β over-expression was induced in the right knees of 30 Wistar rats via intra-articular injection of rat fibroblasts retrovirally infected with human IL1β cDNA. A subset of animals received a 30 µl intra-articular injection of saline or human IL1Ra on day 1 after cell delivery (0.65 µg/µl hIL1Ra, n = 7 per group). Joint swelling, gait, and sensitivity were investigated over 1 week. On day 8, animals were sacrificed and joints were collected for histological evaluation. Joint inflammation and elevated levels of endogenous IL1β were observed in knees receiving IL1β-infected fibroblasts. Asymmetric gaits favoring the affected limb and heightened mechanical sensitivity (allodynia) reflected a unilateral pathology. Histopathology revealed cartilage loss on the femoral groove and condyle of affected joints. Intra-articular IL1Ra injection failed to restore gait and sensitivity to preoperative levels and did not reduce cartilage degeneration observed in histopathology. Joint swelling and degeneration subsequent to IL1β over-expression is associated limb hypersensitivity and gait compensation. Intra-articular IL1Ra delivery did not result in marked improvement for this model; this may be driven by rapid clearance of administered IL1Ra from the joint space. These results motivate work to further investigate the behavioral consequences of monoarticular arthritis and sustained release drug delivery strategies for the joint space.

A soft robust model for optimization under ambiguity

In this paper, we propose a framework for robust optimization that relaxes the standard notion of robustness by allowing the decision maker to vary the protection level in a smooth way across the uncertainty set. We apply our approach to the problem of maximizing the expected value of a payoff function when the underlying distribution is ambiguous and therefore robustness is relevant. Our primary objective is to develop this framework and relate it to the standard notion of robustness, which deals with only a single guarantee across one uncertainty set. First, we show that our approach connects closely to the theory of convex risk measures. We show that the complexity of this approach is equivalent to that of solving a small number of standard robust problems. We then investigate the conservatism benefits and downside probability guarantees implied by this approach and compare to the standard robust approach. Finally, we illustrate theme thodology on an asset allocation example consisting of historical market data over a 25-year investment horizon and find in every case we explore that relaxing standard robustness with soft robustness yields a seemingly favorable risk-return trade-off: each case results in a higher out-of-sample expected return for a relatively minor degradation of out-of-sample downside performance. © 2010 INFORMS.

Characterization of topographical effects on macrophage behavior in a foreign body response model.

Current strategies to limit macrophage adhesion, fusion and fibrous capsule formation in the foreign body response have focused on modulating material surface properties. We hypothesize that topography close to biological scale, in the micron and nanometric range, provides a passive approach without bioactive agents to modulate macrophage behavior. In our study, topography-induced changes in macrophage behavior was examined using parallel gratings (250 nm-2 mum line width) imprinted on poly(epsilon-caprolactone) (PCL), poly(lactic acid) (PLA) and poly(dimethyl siloxane) (PDMS). RAW 264.7 cell adhesion and elongation occurred maximally on 500 nm gratings compared to planar controls over 48 h. TNF-alpha and VEGF secretion levels by RAW 264.7 cells showed greatest sensitivity to topographical effects, with reduced levels observed on larger grating sizes at 48 h. In vivo studies at 21 days showed reduced macrophage adhesion density and degree of high cell fusion on 2 mum gratings compared to planar controls. It was concluded that topography affects macrophage behavior in the foreign body response on all polymer surfaces examined. Topography-induced changes, independent of surface chemistry, did not reveal distinctive patterns but do affect cell morphology and cytokine secretion in vitro, and cell adhesion in vivo particularly on larger size topography compared to planar controls.

Changes in midbrain pain receptor expression, gait and behavioral sensitivity in a rat model of radiculopathy.

Intervertebral disc herniation may contribute to inflammatory processes that associate with radicular pain and motor deficits. Molecular changes at the affected dorsal root ganglion (DRG), spinal cord, and even midbrain, have been documented in rat models of radiculopathy or nerve injury. The objective of this study was to evaluate gait and the expression of key pain receptors in the midbrain in a rodent model of radiculopathy. Radiculopathy was induced by harvesting tail nucleus pulposus (NP) and placing upon the right L5 DRG in rats (NP-treated, n=12). Tail NP was discarded in sham-operated animals (n=12). Mechanical allodynia, weight-bearing, and gait were evaluated in all animals over time. At 1 and 4 weeks after surgery, astrocyte and microglial activation was tested in DRG sections. Midbrain sections were similarly evaluated for immunoreactivity to serotonin (5HT(2B)), mu-opioid (µ-OR), and metabotropic glutamate (mGluR4 and 5) receptor antibodies. NP-treated animals placed less weight on the affected limb 1 week after surgery and experienced mechanical hypersensitivity over the duration of the study. Astroctye activation was observed at DRGs only at 4 weeks after surgery. Findings for pain receptors in the midbrain of NP-treated rats included an increased expression of 5HT(2B) at 1, but not 4 weeks; increased expression of µ-OR and mGluR5 at 1 and 4 weeks (periaqueductal gray region only); and no changes in expression of mGluR4 at any point in this study. These observations provide support for the hypothesis that the midbrain responds to DRG injury with a transient change in receptors regulating pain responses.

Discharge competence and pattern formation in peatlands: a meta-ecosystem model of the Everglades ridge-slough landscape.

Regular landscape patterning arises from spatially-dependent feedbacks, and can undergo catastrophic loss in response to changing landscape drivers. The central Everglades (Florida, USA) historically exhibited regular, linear, flow-parallel orientation of high-elevation sawgrass ridges and low-elevation sloughs that has degraded due to hydrologic modification. In this study, we use a meta-ecosystem approach to model a mechanism for the establishment, persistence, and loss of this landscape. The discharge competence (or self-organizing canal) hypothesis assumes non-linear relationships between peat accretion and water depth, and describes flow-dependent feedbacks of microtopography on water depth. Closed-form model solutions demonstrate that 1) this mechanism can produce spontaneous divergence of local elevation; 2) divergent and homogenous states can exhibit global bi-stability; and 3) feedbacks that produce divergence act anisotropically. Thus, discharge competence and non-linear peat accretion dynamics may explain the establishment, persistence, and loss of landscape pattern, even in the absence of other spatial feedbacks. Our model provides specific, testable predictions that may allow discrimination between the self-organizing canal hypotheses and competing explanations. The potential for global bi-stability suggested by our model suggests that hydrologic restoration may not re-initiate spontaneous pattern establishment, particularly where distinct soil elevation modes have been lost. As a result, we recommend that management efforts should prioritize maintenance of historic hydroperiods in areas of conserved pattern over restoration of hydrologic regimes in degraded regions. This study illustrates the value of simple meta-ecosystem models for investigation of spatial processes.

BAYESIAN MODEL SEARCH AND MULTILEVEL INFERENCE FOR SNP ASSOCIATION STUDIES.

Technological advances in genotyping have given rise to hypothesis-based association studies of increasing scope. As a result, the scientific hypotheses addressed by these studies have become more complex and more difficult to address using existing analytic methodologies. Obstacles to analysis include inference in the face of multiple comparisons, complications arising from correlations among the SNPs (single nucleotide polymorphisms), choice of their genetic parametrization and missing data. In this paper we present an efficient Bayesian model search strategy that searches over the space of genetic markers and their genetic parametrization. The resulting method for Multilevel Inference of SNP Associations, MISA, allows computation of multilevel posterior probabilities and Bayes factors at the global, gene and SNP level, with the prior distribution on SNP inclusion in the model providing an intrinsic multiplicity correction. We use simulated data sets to characterize MISA's statistical power, and show that MISA has higher power to detect association than standard procedures. Using data from the North Carolina Ovarian Cancer Study (NCOCS), MISA identifies variants that were not identified by standard methods and have been externally "validated" in independent studies. We examine sensitivity of the NCOCS results to prior choice and method for imputing missing data. MISA is available in an R package on CRAN.

CMIP5 climate model analyses: Climate extremes in the United States

Given the increases in spatial resolution and other improvements in climate modeling capabilities over the last decade since the CMIP3 simulations were completed, CMIP5 provides a unique opportunity to assess scientific understanding of climate variability and change over a range of historical and future conditions. With participation from over 20 modeling groups and more than 40 global models, CMIP5 represents the latest and most ambitious coordinated international climate model intercomparison exercise to date. Observations dating back to 1900 show that the temperatures in the twenty-first century have the largest spatial extent of record breaking and much above normal mean monthly maximum and minimum temperatures. The 20-yr return value of the annual maximum or minimum daily temperature is one measure of changes in rare temperature extremes.

Contribution of the North Atlantic subtropical high to regional climate model (RCM) skill in simulating southeastern United States summer precipitation

© 2014, Springer-Verlag Berlin Heidelberg.This study assesses the skill of advanced regional climate models (RCMs) in simulating southeastern United States (SE US) summer precipitation and explores the physical mechanisms responsible for the simulation skill at a process level. Analysis of the RCM output for the North American Regional Climate Change Assessment Program indicates that the RCM simulations of summer precipitation show the largest biases and a remarkable spread over the SE US compared to other regions in the contiguous US. The causes of such a spread are investigated by performing simulations using the Weather Research and Forecasting (WRF) model, a next-generation RCM developed by the US National Center for Atmospheric Research. The results show that the simulated biases in SE US summer precipitation are due mainly to the misrepresentation of the modeled North Atlantic subtropical high (NASH) western ridge. In the WRF simulations, the NASH western ridge shifts 7° northwestward when compared to that in the reanalysis ensemble, leading to a dry bias in the simulated summer precipitation according to the relationship between the NASH western ridge and summer precipitation over the southeast. Experiments utilizing the four dimensional data assimilation technique further suggest that the improved representation of the circulation patterns (i.e., wind fields) associated with the NASH western ridge substantially reduces the bias in the simulated SE US summer precipitation. Our analysis of circulation dynamics indicates that the NASH western ridge in the WRF simulations is significantly influenced by the simulated planetary boundary layer (PBL) processes over the Gulf of Mexico. Specifically, a decrease (increase) in the simulated PBL height tends to stabilize (destabilize) the lower troposphere over the Gulf of Mexico, and thus inhibits (favors) the onset and/or development of convection. Such changes in tropical convection induce a tropical–extratropical teleconnection pattern, which modulates the circulation along the NASH western ridge in the WRF simulations and contributes to the modeled precipitation biases over the SE US. In conclusion, our study demonstrates that the NASH western ridge is an important factor responsible for the RCM skill in simulating SE US summer precipitation. Furthermore, the improvements in the PBL parameterizations for the Gulf of Mexico might help advance RCM skill in representing the NASH western ridge circulation and summer precipitation over the SE US.

Comparing the model-simulated global warming signal to observations using empirical estimates of unforced noise.

The comparison of observed global mean surface air temperature (GMT) change to the mean change simulated by climate models has received much public and scientific attention. For a given global warming signal produced by a climate model ensemble, there exists an envelope of GMT values representing the range of possible unforced states of the climate system (the Envelope of Unforced Noise; EUN). Typically, the EUN is derived from climate models themselves, but climate models might not accurately simulate the correct characteristics of unforced GMT variability. Here, we simulate a new, empirical, EUN that is based on instrumental and reconstructed surface temperature records. We compare the forced GMT signal produced by climate models to observations while noting the range of GMT values provided by the empirical EUN. We find that the empirical EUN is wide enough so that the interdecadal variability in the rate of global warming over the 20(th) century does not necessarily require corresponding variability in the rate-of-increase of the forced signal. The empirical EUN also indicates that the reduced GMT warming over the past decade or so is still consistent with a middle emission scenario's forced signal, but is likely inconsistent with the steepest emission scenario's forced signal.

Telescoping is not time compression: a model of the dating of autobiographical events.

A model of telescoping is proposed that assumes no systematic errors in dating. Rather, the overestimation of recent occurrences of events is based on the combination of three factors: (1) Retention is greater for recent events; (2) errors in dating, though unbiased, increase linearly with the time since the dated event; and (3) intrusions often occur from events outside the period being asked about, but such intrusions do not come from events that have not yet occurred. In Experiment 1, we found that recall for colloquia fell markedly over a 2-year interval, the magnitude of errors in psychologists' dating of the colloquia increased at a rate of .4 days per day of delay, and the direction of the dating error was toward the middle of the interval. In Experiment 2, the model used the retention function and dating errors from the first study to predict the distribution of the actual dates of colloquia recalled as being within a 5-month period. In Experiment 3, the findings of the first study were replicated with colloquia given by, instead of for, the subjects.

An evaluation of remifentanil-sevoflurane response surface models in patients emerging from anesthesia: model improvement using effect-site sevoflurane concentrations.

INTRODUCTION: We previously reported models that characterized the synergistic interaction between remifentanil and sevoflurane in blunting responses to verbal and painful stimuli. This preliminary study evaluated the ability of these models to predict a return of responsiveness during emergence from anesthesia and a response to tibial pressure when patients required analgesics in the recovery room. We hypothesized that model predictions would be consistent with observed responses. We also hypothesized that under non-steady-state conditions, accounting for the lag time between sevoflurane effect-site concentration (Ce) and end-tidal (ET) concentration would improve predictions. METHODS: Twenty patients received a sevoflurane, remifentanil, and fentanyl anesthetic. Two model predictions of responsiveness were recorded at emergence: an ET-based and a Ce-based prediction. Similarly, 2 predictions of a response to noxious stimuli were recorded when patients first required analgesics in the recovery room. Model predictions were compared with observations with graphical and temporal analyses. RESULTS: While patients were anesthetized, model predictions indicated a high likelihood that patients would be unresponsive (> or = 99%). However, after termination of the anesthetic, models exhibited a wide range of predictions at emergence (1%-97%). Although wide, the Ce-based predictions of responsiveness were better distributed over a percentage ranking of observations than the ET-based predictions. For the ET-based model, 45% of the patients awoke within 2 min of the 50% model predicted probability of unresponsiveness and 65% awoke within 4 min. For the Ce-based model, 45% of the patients awoke within 1 min of the 50% model predicted probability of unresponsiveness and 85% awoke within 3.2 min. Predictions of a response to a painful stimulus in the recovery room were similar for the Ce- and ET-based models. DISCUSSION: Results confirmed, in part, our study hypothesis; accounting for the lag time between Ce and ET sevoflurane concentrations improved model predictions of responsiveness but had no effect on predicting a response to a noxious stimulus in the recovery room. These models may be useful in predicting events of clinical interest but large-scale evaluations with numerous patients are needed to better characterize model performance.

Snap-shot multispectral imaging of vascular dynamics in a mouse window-chamber model.

Understanding tumor vascular dynamics through parameters such as blood flow and oxygenation can yield insight into tumor biology and therapeutic response. Hyperspectral microscopy enables optical detection of hemoglobin saturation or blood velocity by either acquiring multiple images that are spectrally distinct or by rapid acquisition at a single wavelength over time. However, the serial acquisition of spectral images over time prevents the ability to monitor rapid changes in vascular dynamics and cannot monitor concurrent changes in oxygenation and flow rate. Here, we introduce snap shot-multispectral imaging (SS-MSI) for use in imaging the microvasculature in mouse dorsal-window chambers. By spatially multiplexing spectral information into a single-image capture, simultaneous acquisition of dynamic hemoglobin saturation and blood flow over time is achieved down to the capillary level and provides an improved optical tool for monitoring rapid in vivo vascular dynamics.