Two-dimensional random walk in a bounded domain

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.Comment: 4 pages, 7 eps figures, revtex

The statistical mechanics of complex signaling networks : nerve growth factor signaling

It is becoming increasingly appreciated that the signal transduction systems used by eukaryotic cells to achieve a variety of essential responses represent highly complex networks rather than simple linear pathways. While significant effort is being made to experimentally measure the rate constants for individual steps in these signaling networks, many of the parameters required to describe the behavior of these systems remain unknown, or at best, estimates. With these goals and caveats in mind, we use methods of statistical mechanics to extract useful predictions for complex cellular signaling networks. To establish the usefulness of our approach, we have applied our methods towards modeling the nerve growth factor (NGF)-induced differentiation of neuronal cells. Using our approach, we are able to extract predictions that are highly specific and accurate, thereby enabling us to predict the influence of specific signaling modules in determining the integrated cellular response to the two growth factors. We show that extracting biologically relevant predictions from complex signaling models appears to be possible even in the absence of measurements of all the individual rate constants. Our methods also raise some interesting insights into the design and possible evolution of cellular systems, highlighting an inherent property of these systems wherein particular ''soft'' combinations of parameters can be varied over wide ranges without impacting the final output and demonstrating that a few ''stiff'' parameter combinations center around the paramount regulatory steps of the network. We refer to this property -- which is distinct from robustness -- as ''sloppiness.''Comment: 24 pages, 10 EPS figures, 1 GIF (makes 5 multi-panel figs + caption for GIF), IOP style; supp. info/figs. included as brown_supp.pd

The sloppy model universality class and the Vandermonde matrix

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy; the system behavior depends only on a few `stiff' combinations of the parameters and is unchanged as other `sloppy' parameter combinations vary by orders of magnitude. We contrast examples of sloppy models (from systems biology, variational quantum Monte Carlo, and common data fitting) with systems which are not sloppy (multidimensional linear regression, random matrix ensembles). We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form, with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.Comment: New content adde

The longitudinal relationship between patient-reported outcomes and clinical characteristics among patients with focal segmental glomerulosclerosis in the nephrotic syndrome study network

Background. Understanding the relationship between clinical and patient-reported outcomes (PROs) will help support clinical care and future clinical trial design of novel therapies for focal segmental glomerulosclerosis (FSGS). Methods. FSGS patients ≥8 years of age enrolled in the Nephrotic Syndrome Study Network completed Patient-Reported Outcomes Measurement Information System PRO measures of health-related quality of life (HRQoL) (children: global health, mobility, fatigue, pain interference, depression, anxiety, stress and peer relationships; adults: physical functioning, fatigue, pain interference, sleep impairment, mental health, depression, anxiety and social satisfaction) at baseline and during longitudinal follow-up for a maximum of 5 years. Linear mixed-effects models were used to determine which demographic, clinical and laboratory features were associated with PROs for each of the eight children and eight adults studied. Results. There were 45 children and 114 adult FSGS patients enrolled that had at least one PRO assessment and 519 patient visits. Multivariable analyses among children found that edema was associated with global health (-7.6 points, P ¼ 0.02) and mobility (-4.2, P ¼ 0.02), the number of reported symptoms was associated with worse depression (-2.7 per symptom, P ¼ 0.009) and anxiety (-2.3, P ¼ 0.02) and the number of emergency room (ER) visits in the prior 6 months was associated with worse mobility (-2.8 per visit, P < 0.001) and fatigue (-2.4, P ¼ 0.03). Multivariable analyses among adults found the number of reported symptoms was associated with worse function in all eight PROMIS measures and the number of ER visits was associated with worse fatigue, pain interference, sleep impairment, depression, anxiety and social satisfaction. Laboratory markers of disease severity (i.e. proteinuria, estimated glomerular filtration rate and serum albumin) did not predict PRO in multivariable analyses, with the single exception of complete remission and better pain interference scores among children (þ9.3, P ¼ 0.03). Conclusions. PROs provide important information about HRQoL for persons with FSGS that is not captured solely by the examination of laboratory-based markers of disease. However, it is critical that instruments capture the patient experience and FSGS clinical trials may benefit from a disease-specific instrument more sensitive to within-patient changes

Optimal

experimental design in an epidermal growth factor receptor signalling and down-regulation mode

Stochastic formation of magnetic vortex structures in asymmetric disks triggered by chaotic dynamics

The non-trivial spin configuration in a magnetic vortex is a prototype for fundamental studies of nanoscale spin behaviour with potential applications in magnetic information technologies. Arrays of magnetic vortices interfacing with perpendicular thin films have recently been proposed as enabler for skyrmionic structures at room temperature, which has opened exciting perspectives on practical applications of skyrmions. An important milestone for achieving not only such skyrmion materials but also general applications of magnetic vortices is a reliable control of vortex structures. However, controlling magnetic processes is hampered by stochastic behaviour, which is associated with thermal fluctuations in general. Here we show that the dynamics in the initial stages of vortex formation on an ultrafast timescale plays a dominating role for the stochastic behaviour observed at steady state. Our results show that the intrinsic stochastic nature of vortex creation can be controlled by adjusting the interdisk distance in asymmetric disk arrays.close31