Blow-up dynamics of self-attracting diffusive particles driven by competing convexities

In this paper, we analyze the dynamics of an $N$ particles system evolving according the gradient flow of an energy functional. The particle system is a consistent approximation of the Lagrangian formulation of a one parameter family of non-local drift-diffusion equations in one spatial dimension. We shall prove the global in time existence of the trajectories of the particles (under a sufficient condition on the initial distribution) and give two blow-up criteria. All these results are consequences of the competition between the discrete entropy and the discrete interaction energy. They are also consistent with the continuous setting, that in turn is a one dimension reformulation of the parabolic-elliptic Keller-Segel in high dimensions

Optically-pumped saturable absorber for fast switching between continuous-wave and passively mode-locked regimes of a Nd:YVO4 laser

We report on the fast (~50 μs) remote-controlled switching between continuous-wave (cw), cw mode-locked (ML) and Q-switched ML modes of operation of a Nd:YVO4 laser using an optically-pumped saturable absorber (SA). Pulses as short as 40 ps with an average output power of 0.5 W are obtained in cw ML regime

Uniqueness of stationary states for singular Keller–Segel type models

We consider a generalised Keller–Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are more singular than Newtonian interaction. We show uniqueness of stationary states (if they exist) in any dimension both in the diffusion-dominated regime and in the fair-competition regime when attraction and repulsion are in balance. As stationary states are radially symmetric decreasing, the question of uniqueness reduces to the radial setting. Our key result is a sharp generalised Hardy–Littlewood–Sobolev type functional inequality in the radial setting

Resistance to novel drug classes

Understanding the mechanisms that underlie resistance development to novel drugs is essential to a better clinical management of resistant viruses and to prevent further resistance development and spread. RECENT FINDINGS: Integrase inhibitors and CCR5 antagonists are the more recent antiretroviral classes developed. The HIV-1 integrase, responsible for the chromosomal integration of the newly synthesized double-stranded viral DNA into the host genomic DNA, represents a new and important target; and two integrase inhibitors (INIs), raltegravir and elvitegravir, have been shown promising results in clinical trials. Viral entry is also an attractive step for the development of new drugs against HIV variants resistant to current antiretroviral drugs, and two CCR5 antagonists have been designed to inhibit HIV-1 binding to R5 co-receptor and are under clinical investigation. SUMMARY: Drug resistance to INIs occurs through the selection of mutations within HIV integrase. The kinetic of selection seems rapid and one mutation alone is able to confer resistance to integrase inhibitor, suggesting that this class of drug has a low genetic barrier. Two ways could explain the failure of the CCR5 antagonist class: a rapid outgrowth of pre-existing archived X4 virus or the selection of a resistance to CCR5 antagonists through amino acid changes in V

Eigenelements of a General Aggregation-Fragmentation Model

We consider a linear integro-differential equation which arises to describe both aggregation-fragmentation processes and cell division. We prove the existence of a solution (\lb,\U,\phi) to the related eigenproblem. Such eigenelements are useful to study the long time asymptotic behaviour of solutions as well as the steady states when the equation is coupled with an ODE. Our study concerns a non-constant transport term that can vanish at $x=0,$ since it seems to be relevant to describe some biological processes like proteins aggregation. Non lower-bounded transport terms bring difficulties to find $a\ priori$ estimates. All the work of this paper is to solve this problem using weighted-norms

Efficient Parallel Simulation of Atherosclerotic Plaque Formation Using Higher Order Discontinuous Galerkin Schemes

Abstract The compact Discontinuous Galerkin 2 (CDG2) method was successfully tested for elliptic problems, scalar convection-diffusion equations and compressible Navier-Stokes equations. In this paper we use the newly developed DG method to solve a mathematical model for early stages of atherosclerotic plaque formation. Atherosclerotic plaque is mainly formed by accumulation of lipid-laden cells in the arterial walls which leads to a heart attack in case the artery is occluded or a thrombus is built through a rupture of the plaque. After describing a mathematical model and the discretization scheme, we present some benchmark tests comparing the CDG2 method to other commonly used DG methods. Furthermore, we take parallelization and higher order discretization schemes into account.

The multifactorial pathways towards resistance to the cytosine analogues emtricitabine and lamivudine: Evidences from literature

The article by Bulteel et al.,1 published in the September issue of the journal, has investigated the rate of M184V emergence in patients receiving HAART combinations containing efavirenz (EFV), tenofovir (TDF) and lamivudine (3 TC) or emtricitabine (FTC) within the UK Collaborative HIV Cohort. By analyzing 304 genotypic resistance tests, the authors asserted that, although patients receiving 3 TC-based regimens were more likely to develop M184V than those receiving FTC-based regimens (event rate: 0.55 [95%CI: 0.28–0.96] for 3 TC versus 0.34 [95%CI: 0.21–0.46] for FTC), this association was not statistically significant in both univariable and multivariable models. These results are different from those reported in previous studies from our and other groups2, 3 and 4 showing a significant decrease in M184V emergence in patients failing FTC + TDF-based compared to 3 TC + TDF-based HAART (Table 1). The lower prevalence of M184V in FTC-containing regimen was also supported by a recently published letter showing a strong trend (P = 0.051) towards higher rates of resistance to the 3 TC containing regimen 5.5 (1.8–12.8) per 1000 patient years when compared with the FTC containing regimens 1.7 (0.8–3.2) per 1000 patient year

A mathematical model for mechanotransduction at the early steps of suture formation

Growth and patterning of craniofacial sutures are subjected to the effects of mechanical stress. Mechanotransduction processes occurring at the margins of the sutures are not precisely understood. Here, we propose a simple theoretical model based on the orientation of collagen fibres within the suture in response to local stress. We demonstrate that fibre alignment generates an instability leading to the emergence of interdigitations. We confirm the appearance of this instability both analytically and numerically. To support our model, we use histology and synchrotron x-ray microtomography and reveal the fine structure of fibres within the sutural mesenchyme and their insertion into the bone. Furthermore, using a mouse model with impaired mechanotransduction, we show that the architecture of sutures is disturbed when forces are not interpreted properly. Finally, by studying the structure of sutures in the mouse, the rat, an actinopterygian (\emph{Polypterus bichir}) and a placoderm (\emph{Compagopiscis croucheri}), we show that bone deposition patterns during dermal bone growth are conserved within jawed vertebrates. In total, these results support the role of mechanical constraints in the growth and patterning of craniofacial sutures, a process that was probably effective at the emergence of gnathostomes, and provide new directions for the understanding of normal and pathological suture fusion

Passive mode locking of a Tm,Ho:KY(WO4)(2) laser around 2 μm

We report the first demonstration, to our knowledge, of passive mode locking in a Tm3+, Ho3+-codoped KYWO42 laser operating in the 2000-2060 nm spectral region. An InGaAsSb-based quantum well semiconductor saturable absorber mirror is used for the initiation and stabilization of the ultrashort pulse generation. Pulses as short as 3.3 ps were generated at 2057 nm with average output powers up to 315 mW at a pulse repetition frequency of 132 MHz for 1.15 W of absorbed pump power at 802 nm from a Ti:sapphire laser