Adiabatic reduction near a bifurcation in stochastically modulated systems

We re-examine the procedure of adiabatic elimination of fast relaxing variables near a bifurcation point when some of the parameters of the system are stochastically modulated. Approximate stationary solutions of the Fokker-Planck equation are obtained near threshold for the pitchfork and transcritical bifurcations. Stochastic resonance between fast variables and random modulation may shift the effective bifurcation point by an amount proportional to the intensity of the fluctuations. We also find that fluctuations of the fast variables above threshold are not always Gaussian and centered around the (deterministic) center manifold as was previously believed. Numerical solutions obtained for a few illustrative examples support these conclusions.Comment: RevTeX, 19 pages and 16 figure

Lessons from history of socioeconomic improvements: a new approach to treating multi-drug-resistant tuberculosis

Summary This study investigated the trends in tuberculosis mortality through time in Switzerland. Information on the decline in mortality before chemotherapies were introduced may be useful in developing countries where drug-resistant tuberculosis is now becoming a major problem. Swiss data were collected from historical records and comparative data were obtained from the literature for England and Wales, New York, Japan, Brazil and Sierra Leone. Logistic curves were fitted to examine the rate of decline before introduction of pharmacotherapies and these show that the decline would have continued without the introduction of chemical therapies, including antibiotics. In Switzerland, England and Wales and New York, the decline had occurred long before the introduction of specific anti-tuberculosis agents. In Brazil and Japan, chemical therapy was co-incident with the decline in tuberculosis mortality rates. Overall, it is suggested that the effective control of tuberculosis can be achieved through a combination of chemical interventions, conservative therapy (rest, good nutrition, ventilation, etc.) as well as public health interventions addressing hygiene, nutrition, reducing exposure to infections and educating the population about tuberculosis

Potential population-level effectiveness of one-dose HPV vaccination in low-income and middle-income countries: a mathematical modelling analysis

BACKGROUND: Given the accumulating evidence that one-dose vaccination could provide high and sustained protection against human papillomavirus (HPV) infection and related diseases, we examined the population-level effectiveness and efficiency of one-dose HPV vaccination of girls compared with two-dose vaccination, using mathematical modelling. METHODS: In this mathematical modelling study, we used HPV-ADVISE LMIC, an individual-based transmission-dynamic model independently calibrated to four epidemiologically diverse low-income and middle-income countries (LMICs; India, Nigeria, Uganda, and Viet Nam). We parameterised and calibrated the model using sexual behaviour and epidemiological data identified from international population-based datasets and the literature. All base-case vaccination scenarios start in 2023 with the nonavalent vaccine and assumed 80% vaccination coverage with one or two doses. We assumed that two doses of vaccine provide 100% efficacy against vaccine-type infections and a lifelong duration of protection. We examined a non-inferior vaccination scenario for one dose compared with two doses, pessimistic scenarios of lower one-dose vaccine efficacy (85%) or a shorter duration of protection (ie, 20 or 30 years), and the effectiveness of a mitigation scenario in which schedules would switch from one dose to two doses. We also did sensitivity analyses by varying vaccination coverage. We used three outcomes: the relative reduction in cervical cancer incidence, the number of cervical cancers averted, and the number of vaccine doses needed to prevent one cervical cancer. FINDINGS: Assuming non-inferior vaccine characteristics for one dose compared with two doses, the model projections show that two-dose or one-dose routine vaccination of girls aged 9 years (with a multi-age cohort vaccination of girls aged 10-14 years) would avert 12·0 million (80% UI 9·5-14·5) cervical cancers in India, 4·7 million (3·4-5·8) in Nigeria, 2·3 million (1·9-2·6) in Uganda, and 0·4 million (0·2-0·5) in Viet Nam over 100 years. Under pessimistic assumptions of lower one-dose efficacy (85%) or a shorter duration of protection (ie, 30 years), one-dose routine vaccination would avert 69% (61-80) to 94% (92-96) of the cervical cancers averted with two-dose routine vaccination. However, when assuming a duration of protection of 20 years, one-dose routine vaccination would avert substantially fewer cervical cancers (ie, 35% [26-44] to 69% [65-71] of the cervical cancers averted with two-dose routine vaccination). A switch from one-dose to two-dose routine vaccination of girls aged 9 years, with a one-dose catch-up of girls aged 10-14 years, 5 years after the start of the vaccination programme, could mitigate potential losses in cervical cancer prevention from a short one-dose duration of protection (averting 92% [83-98] to 99% [97-100]) of the cervical cancers averted with two-dose routine vaccination). One-dose routine vaccination would result in fewer doses needed to prevent one cervical cancer than two-dose routine vaccination, even if the duration of protection is as low as 20 years. Finally, for countries with two-dose routine vaccination, adding one-dose multi-age cohort vaccination in the first year would provide similar benefits as a two-dose multi-age cohort vaccination, and would be more efficient even under the pessimistic assumptions of lower one-dose vaccine efficacy or duration of protection. INTERPRETATION: One-dose routine vaccination could avert most of the cervical cancers averted with two-dose vaccination while being more efficient, provided the duration of one-dose protection is greater than 20-30 years (depending on the LMIC). The doses saved by introducing one-dose routine vaccination could offer the opportunity to vaccinate girls before they age out of the vaccination window of 9-14 years and, potentially, to vaccinate boys or older age groups. FUNDING: Fonds de recherche du Québec-Santé, Digital Research Alliance of Canada, Bill & Melinda Gates Foundation

Grain boundary pinning and glassy dynamics in stripe phases

We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the non-adiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value $R_g \sim \lambda_0\ \epsilon^{-1/2}\exp(|a|/\sqrt{\epsilon})$, where$\epsilon\ll 1$is the dimensionless distance away from threshold,$\lambda_0$the stripe wavelength, and$a$ a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.Comment: 17 pages, 8 figures. Corrected version with one new figur

Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow

We develop a theory to describe the reorientation phenomena in the lamellar phase of block copolymer melt under reciprocating shear flow. We show that similar to the steady-shear, the oscillating flow anisotropically suppresses fluctuations and gives rise to the parallel-perpendicular orientation transition. The experimentally observed high-frequency reverse transition is explained in terms of interaction between the melt and the shear-cell walls.Comment: RevTex, 3 pages, 1 figure, submitted to PR

Ordering of the lamellar phase under a shear flow

The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free-energy and the evolution follows a convection-diffusion equation. Lamellae order preferentially with the normal along the vorticity direction. Typical lengths grow as $\gamma t^{5/4}$ (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D=3

Treatment decisions and employment of breast cancer patients: Results of a population‐based survey

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142258/1/cncr30959.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142258/2/cncr30959_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142258/3/cncr30959-sup-0001-suppinfo1.pd

On the well-posedness of the stochastic Allen-Cahn equation in two dimensions

White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d \geq 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen-Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that a series of published numerical studies are problematic: shrinking the mesh size in these simulations does not lead to the recovery of a physically meaningful limit.Comment: 21 pages, 4 figures; accepted by Journal of Computational Physics (Dec 2011

New Method for Phase transitions in diblock copolymers: The Lamellar case

A new mean-field type theory is proposed to study order-disorder transitions (ODT) in block copolymers. The theory applies to both the weak segregation (WS) and the strong segregation (SS) regimes. A new energy functional is proposed without appealing to the random phase approximation (RPA). We find new terms unaccounted for within RPA. We work out in detail transitions to the lamellar state and compare the method to other existing theories of ODT and numerical simulations. We find good agreements with recent experimental results and predict that the intermediate segregation regime may have more than one scaling behavior.Comment: 23 pages, 8 figure

Phase diagram for diblock copolymer melts under cylindrical confinement

We extensively study the phase diagram of a diblock copolymer melt confined in a cylindrical nanopore using real-space self-consistent mean-field theory. We discover a rich variety of new two-dimensional equilibrium structures that have no analog in the unconfined system. These include non-hexagonally coordinated cylinder phases and structures intermediate between lamellae and cylinders. We map the stability regions and phase boundaries for all the structures we find. As the pore radius is decreased, the pore accommodates fewer cylindrical domains and structural transitions occur as cylinders are eliminated. Our results are consistent with experiments, but we also predict phases yet to be observed.Comment: 12 pages, 3 figures. submitted to Physical Review Letter