Analysis of trophic networks: an optimisation approach.

We introduce a methodology to study the possible matter flows of an ecosystem defined by observational biomass data and realistic biological constraints. The flows belong to a polyhedron in a multi dimensional space that may make statistical exploration difficult in practice; instead, we propose to solve a convex optimization problem. Seven criteria based on ecological network indices have been selected to be used as convex goal functions. Numerical results show that the method is fast and can be used for large systems. Minimum flow solutions are analyzed using flow decomposition in paths and circuits. Their consistency is also tested by introducing a system of differential equations for the biomasses and examining the stability of the biomass fixed point. The method is illustrated and explained throughout the text on an ecosystem toy model. It is also applied to realistic food models.

DISPERSION OF A NEW CORONAVIRUS SARS-COV-2 BY AIRLINES IN 2020: TEMPORAL ESTIMATES OF THE OUTBREAK IN MEXICO.

BACKGROUND: On January 23, 2020, China imposed a quarantine on the city of Wuhan to contain the SARS-CoV-2 outbreak. Regardless of this measure, the new infection has spread to several countries around the world. OBJECTIVE: We developed a method to study the dissemination of this infection by airline routes and provide estimations of the time of arrival of the outbreak to different cities. METHODS: Using the Kermack and McKendrick model complemented with diffusion on a graph composed of nodes and edges, we made an analysis of COVID-19 dispersion to other cities by air travel. RESULTS: The estimation was accurate in that it was possible to predict in the middle of February 2020 the arrival of the first outbreak in Mexico, which eventually occurred between March 20 and 30. This estimation was robust with respect to small changes in epidemiological parameters at the other nodes. CONCLUSIONS: The estimation of the time of arrival of the outbreak from its epicenter, allows for a time period to implement and strengthen preventive measures aimed at the general population as well as to strengthen hospital infrastructure and training of human resources. In the present study, this estimation was accurate, as observed from the real data of the beginning of the outbreak in Mexico City up to April 6, 2020.

Stopping a reaction-diffusion front.

We revisit the problem of pinning a reaction-diffusion front by a defect, in particular by a reaction-free region. Using collective variables for the front and numerical simulations, we compare the behaviors of a bistable and monostable front. A bistable front can be pinned as confirmed by a pinning criterion, the analysis of the time independent problem, and simulations. Conversely, a monostable front can never be pinned, it gives rise to a secondary pulse past the defect and we calculate the time this pulse takes to appear. These radically different behaviors of bistable and monostable fronts raise issues for modelers in particular areas of biology, as for example, the study of tumor growth in the presence of different tissues.

Reduced Maxwell-Duffing description of extremely short pulses in nonresonant media.

The propagation of extremely short pulses of an electromagnetic field (electromagnetic spikes) is considered in the framework of a model wherein the material medium is represented by anharmonic oscillators with cubic nonlinearities (Duffing model) and waves can propagate only in the right direction. The system of reduced Maxwell-Duffing equations admits two families of exact analytical solutions in the form of solitary waves. These are bright spikes propagating on a zero background, and bright and dark spikes propagating on a nonzero background. We find that these steady-state pulses are stable in terms of boundedness of the Hamiltonian. Direct simulations demonstrate that these pulses are very robust against perturbations. We find that a high-frequency modulated electromagnetic pulse evolves into a breather-like one. Conversely, a low frequency pulse transforms into a quasiharmonic wave.

Dispersion of a new coronavirus SARS-COV-2 by airlines in 2020: temporal estimates of the outbreak in Mexico

ABSTRACT Background: On January 23, 2020, China imposed a quarantine on the city of Wuhan to contain the SARS-CoV-2 outbreak. Regardless of this measure, the new infection has spread to several countries around the world. Objective: We developed a method to study the dissemination of this infection by airline routes and provide estimations of the time of arrival of the outbreak to different cities. Methods: Using the Kermack and McKendrick model complemented with diffusion on a graph composed of nodes and edges, we made an analysis of COVID-19 dispersion to other cities by air travel. Results: The estimation was accurate in that it was possible to predict in the middle of February 2020 the arrival of the first outbreak in Mexico, which eventually occurred between March 20 and 30. This estimation was robust with respect to small changes in epidemiological parameters at the other nodes. Conclusions: The estimation of the time of arrival of the outbreak from its epicenter, allows for a time period to implement and strengthen preventive measures aimed at the general population as well as to strengthen hospital infrastructure and training of human resources. In the present study, this estimation was accurate, as observed from the real data of the beginning of the outbreak in Mexico City up to April 6, 2020.

Nonlinear waves in networks: model reduction for the sine-Gordon equation.

To study how nonlinear waves propagate across Y- and T-type junctions, we consider the two-dimensional (2D) sine-Gordon equation as a model and examine the crossing of kinks and breathers. Comparing energies for different geometries reveals that, for small widths, the angle of the fork plays no role. Motivated by this, we introduce a one-dimensional effective model whose solutions agree well with the 2D simulations for kink and breather solutions. These exhibit two different behaviors: a kink crosses if it has sufficient energy; conversely a breather crosses when v>1-ω, where v and ω are, respectively, its velocity and frequency. This methodology can be generalized to more complex nonlinear wave models.

Reaction-diffusion front crossing a local defect.

The interaction of a Zeldovich-Frank-Kamenetsky reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple, collective variable, ordinary differential equations for the front position and width. Their solutions are in good agreement with the solutions of the full problem. Finally, using this reduced model, we explain the pinning of the front on a large defect and obtain a quantitative criterion.

High-dose chemotherapy with autologous hematopoietic stem-cell transplantation in metastatic breast cancer: overview of six randomized trials.

PURPOSE: High doses of effective chemotherapy are compelling if they can be delivered safely. Substantial interest in supporting high-dose chemotherapy with bone marrow or autologous hematopoietic stem-cell transplantation in the 1980s and 1990s led to the initiation of randomized trials to evaluate its effect in the treatment of metastatic breast cancer. METHODS: We identified six randomized trials in metastatic breast cancer that evaluated high doses of chemotherapy with transplant support versus a control regimen without stem-cell support. We assembled a single database containing individual patient information from these trials. The primary analysis of overall survival was a log-rank test comparing high dose versus control. We also used Cox proportional hazards regression, adjusting for known covariates. We addressed potential treatment differences within subsets of patients. RESULTS: The effect of high-dose chemotherapy on overall survival was not statistically different (median, 2.16 v 2.02 years; P = .08). A statistically significant advantage in progression-free survival (median, 0.91 v 0.69 years) did not translate into survival benefit. Subset analyses found little evidence that there are groups of patients who might benefit from high-dose chemotherapy with hematopoietic support. CONCLUSION: Overall survival of patients with metastatic breast cancer in the six randomized trials was not significantly improved by high-dose chemotherapy; any benefit from high doses was small. No identifiable subset of patients seems to benefit from high-dose chemotherapy.

High-dose chemotherapy with autologous stem-cell support as adjuvant therapy in breast cancer: overview of 15 randomized trials.

PURPOSE: Adjuvant high-dose chemotherapy (HDC) with autologous hematopoietic stem-cell transplantation (AHST) for high-risk primary breast cancer has not been shown to prolong survival. Individual trials have had limited power to show overall benefit or benefits within subsets. METHODS: We assembled individual patient data from 15 randomized trials that compared HDC versus control therapy without stem-cell support. Prospectively defined primary end points were relapse-free survival (RFS) and overall survival (OS). We compared the effect of HDC versus control by using log-rank tests and proportional hazards regression, and we adjusted for clinically relevant covariates. Subset analyses were by age, number of positive lymph nodes, tumor size, histology, hormone receptor (HmR) status, and human epidermal growth factor receptor 2 (HER2) status. RESULTS: Of 6,210 total patients (n = 3,118, HDC; n = 3,092 control), the median age was 46 years; 69% were premenopausal, 29% were postmenopausal, and 2% were unknown menopausal status; 49.5% were HmR positive; 33.5% were HmR negative, and 17% were unknown HmR status. The median follow-up was 6 years. After analysis was adjusted for covariates, HDC was found to prolong relapse-free survival (RFS; hazard ratio [HR], 0.87; 95% CI, 0.81 to 0.93; P < .001) but not overall survival (OS; HR, 0.94; 95% CI, 0.87 to 1.02; P = .13). For OS, no covariates had statistically significant interactions with treatment effect, and no subsets evinced a significant effect of HDC. Younger patients had a significantly better RFS on HDC than did older patients. CONCLUSION: Adjuvant HDC with AHST prolonged RFS in high-risk primary breast cancer compared with control, but this did not translate into a significant OS benefit. Whether HDC benefits patients in the context of targeted therapies is unknown.

Vortex polarity switching by a spin-polarized current.

The spin-transfer effect is investigated for the vortex state of a magnetic nanodot. A spin current is shown to act similarly to an effective magnetic field perpendicular to the nanodot. Then a vortex with magnetization (polarity) parallel to the current polarization is energetically favorable. Following a simple energy analysis and using direct spin-lattice simulations, we predict the polarity switching of a vortex. For magnetic storage devices, an electric current is more effective to switch the polarity of a vortex in a nanodot than the magnetic field.

Importance of the internal shape mode in magnetic vortex dynamics.

We investigate the motion of a nonplanar vortex in a circular easy-plane magnet with a rotating in-plane magnetic field. Our numerical simulations of the Landau-Lifshitz equations show that the vortex tends to a circular limit trajectory, with an orbit frequency which is lower than the driving field frequency. To describe this we develop a new collective variable theory by introducing additional variables which account for the internal degrees of freedom of the vortex core, strongly coupled to the translational motion. We derive the evolution equations for these collective variables and find limit-cycle solutions whose characteristics are in qualitative agreement with the simulations of the many-spin system.