Centred approach to the period of anharmonic oscillators

We present a simple method for obtaining a concise series expression for the period of one-dimensional classical oscillators. The series converges well for typical potentials and is of a form that is often suitable for obtaining approximate expressions for the period valid to any order in the amplitude desired. The method is most easily applied to even potentials. However, by employing the lower turning point expansion discussed in the appendices it may readily be applied even to those potentials where the lower turning point may not be solved for explicitly in terms of the upper turning point. We demonstrate the method by obtaining expressions for the periods of both the simple pendulum and tadpole orbits

Studies of the aetiopathogenesis of pouchitis

The ileal pouch offers a unique opportunity to study the inter-relationships between the gut microbiota, barrier function and host immune responses. Intestinal dendritic cells (DC) are pivotal in the maintenance of gut immune homeostasis. Impaired barrier function due to altered cell to cell junctions, enables interactions between the microbiota and host immune responses prior to the onset of inflammation and epithelial damage. The role of innate immune factors in pouchitis remains unclear. We performed cross sectional and longitudinal studies of patients following restorative proctocolectomy and assessed DC and tight junction protein (TJP) characteristics in the ileal pouch. Increased expression of the “pore-forming” claudin 2 was an early event in the development of pouch inflammation and aberrant DC expression of gut homing markers was characterised in the ileum and ileal pouch of ulcerative colitis patients without inflammation. DC phenotype in pouchitis suggested an activated innate immune response to microbial signals. Intestinal immune responses may be manipulated by modification of the gut microbiota. An emerging approach is transplantation of the entire “organ” of the gut microbiota. Effects of faecal microbiota transplantation (FMT) on recipient microbiota and immune responses in inflammatory bowel diseases are unknown. A single nasogastrically delivered FMT from a healthy donor to patients with chronic pouchitis, resulted in some shift in the composition of the microbiota, with specific changes in the abundance of species suggestive of a “healthier” pouch microbiota. However, microbiota engraftment success varied greatly between recipients and regardless of engraftment success, FMT did not result in immunological response or clinical efficacy. In conclusion, aberrant DC and TJP characteristics are associated with inflammation of the ileal pouch. Manipulation of the microbiota by FMT may be one means of modifying DC and TJP expression in the ileal pouch. However, these factors were not influenced by a single nasogastrically delivered FMT.Open Acces

Shape-dependent bounds on cell growth rates

I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like \textit{E.\ coli}. Simple modeling immediately implies that it is the elongated profiles of such cells that allows for them to grow -- as observed -- at exponential rates in nutrient-rich media. Growth is strongly suppressed when nutrient capture is diffusion-limited: In three dimensions, the length is bounded by $\log L \lesssim t^{1/2}$, and in lower dimensions growth is algebraic. Similar bounds are easily obtained for other cell geometries, groups of cells, \textit{etc}. Fits of experimental growth curves to such bounds can be used to estimate various quantities of interest, including generalized metabolic rates.Comment: Third version now includes a section on typical experimental conditions. Title has been changed. To be published in Europhysics Letter

Electrostatic interactions between discrete helices of charge

We analytically examine the pair interaction for parallel, discrete helices of charge. Symmetry arguments allow for the energy to be decomposed into a sum of terms, each of which has an intuitive geometric interpretation. Truncated Fourier expansions for these terms allow for accurate modeling of both the axial and azimuthal terms in the interaction energy and these expressions are shown to be insensitive to the form of the interaction. The energy is evaluated numerically through application of an Ewald-like summation technique for the particular case of unscreened Coulomb interactions between the charges of the two helices. The mode structures and electrostatic energies of flexible helices are also studied. Consequences of the resulting energy expressions are considered for both F-actin and A-DNA aggregates

Renormalization Group-Motivated Learning

We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space RG in a lattice while considers the overall information loss in momentum-space RG. Here we compromise the two measures for the non-spatial data set. For weakly correlated data close to Gaussian, we use the correlation of data as a metric for the proximity of data points, but minimize an overall projection error for optimal coarse-graining steps. It compresses the data to maximize the correlation between the two data points to be compressed while minimizing the correlation between the paired data and other data points. We show that this approach can effectively reduce the dimensionality of the data while preserving the essential features. We extend our method to incorporate non-linear features by replacing correlation measures with mutual information. This results in an information-bottleneck-like trade-off: maximally compress the data while preserving the information among the compressed data and the rest. Indeed, our approach can be interpreted as an exact form of information-bottleneck-like trade off near linear data. We examine our method with random Gaussian data and the Ising model to demonstrate its validity and apply glass systems. Our approach has potential applications in various fields, including machine learning and statistical physics

Thiopurine monotherapy is effective in ulcerative colitis but significantly less so in Crohn’s disease: long-term outcomes for 11 928 patients in the UK inflammatory bowel disease bioresource

Objective: Thiopurines are widely used as maintenance therapy in inflammatory bowel disease (IBD) but the evidence base for their use is sparse and their role increasingly questioned. Using the largest series reported to date, we assessed the long-term effectiveness of thiopurines in ulcerative colitis (UC) and Crohn’s disease (CD), including their impact on need for surgery. Design: Outcomes were assessed in 11 928 patients (4968 UC, 6960 CD) in the UK IBD BioResource initiated on thiopurine monotherapy with the intention of maintaining medically induced remission. Effectiveness was assessed retrospectively using patient-level data and a definition that required avoidance of escalation to biological therapy or surgery while on thiopurines. Analyses included overall effectiveness, time-to-event analysis for treatment escalation and comparison of surgery rates in patients tolerant or intolerant of thiopurines. Results: Using 68 132 patient-years of exposure, thiopurine monotherapy appeared effective for the duration of treatment in 2617/4968 (52.7%) patients with UC compared with 2378/6960 (34.2%) patients with CD (p<0.0001). This difference was corroborated in a multivariable analysis: after adjusting for variables including treatment era, thiopurine monotherapy was less effective in CD than UC (OR 0.47, 95% CI 0.43 to 0.51, p<0.0001). Thiopurine intolerance was associated with increased risk of surgery in UC (HR 2.44, p<0.0001); with a more modest impact on need for surgery in CD (HR=1.23, p=0.0015). Conclusion: Thiopurine monotherapy is an effective long-term treatment for UC but significantly less effective in CD