Trapping in complex networks

We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $\rho(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show using theory and simulations that in ER networks, while for short times $\rho(t) \propto \exp(-Act)$, for longer times $\rho(t)$ exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the trap's location: $\rho(t)$ is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we find \rho(t)\propto\exp\left[-At/N^\frac{\gamma-2}{\gamma-1}\av{k}\right] for all $\gamma>2$, where $\gamma$ is the exponent of the degree distribution $P(k)\propto k^{-\gamma}$.Comment: Appendix adde

The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.Comment: Proceedings StatPhys 2

Phase transitions and configuration space topology

Equilibrium phase transitions may be defined as nonanalytic points of thermodynamic functions, e.g., of the canonical free energy. Given a certain physical system, it is of interest to understand which properties of the system account for the presence of a phase transition, and an understanding of these properties may lead to a deeper understanding of the physical phenomenon. One possible approach of this issue, reviewed and discussed in the present paper, is the study of topology changes in configuration space which, remarkably, are found to be related to equilibrium phase transitions in classical statistical mechanical systems. For the study of configuration space topology, one considers the subsets M_v, consisting of all points from configuration space with a potential energy per particle equal to or less than a given v. For finite systems, topology changes of M_v are intimately related to nonanalytic points of the microcanonical entropy (which, as a surprise to many, do exist). In the thermodynamic limit, a more complex relation between nonanalytic points of thermodynamic functions (i.e., phase transitions) and topology changes is observed. For some class of short-range systems, a topology change of the M_v at v=v_t was proved to be necessary for a phase transition to take place at a potential energy v_t. In contrast, phase transitions in systems with long-range interactions or in systems with non-confining potentials need not be accompanied by such a topology change. Instead, for such systems the nonanalytic point in a thermodynamic function is found to have some maximization procedure at its origin. These results may foster insight into the mechanisms which lead to the occurrence of a phase transition, and thus may help to explore the origin of this physical phenomenon.Comment: 22 pages, 6 figure

Distinguishing mechanisms underlying EMT tristability

Abstract Background The Epithelial-Mesenchymal Transition (EMT) endows epithelial-looking cells with enhanced migratory ability during embryonic development and tissue repair. EMT can also be co-opted by cancer cells to acquire metastatic potential and drug-resistance. Recent research has argued that epithelial (E) cells can undergo either a partial EMT to attain a hybrid epithelial/mesenchymal (E/M) phenotype that typically displays collective migration, or a complete EMT to adopt a mesenchymal (M) phenotype that shows individual migration. The core EMT regulatory network - miR-34/SNAIL/miR-200/ZEB1 - has been identified by various studies, but how this network regulates the transitions among the E, E/M, and M phenotypes remains controversial. Two major mathematical models – ternary chimera switch (TCS) and cascading bistable switches (CBS) - that both focus on the miR-34/SNAIL/miR-200/ZEB1 network, have been proposed to elucidate the EMT dynamics, but a detailed analysis of how well either or both of these two models can capture recent experimental observations about EMT dynamics remains to be done. Results Here, via an integrated experimental and theoretical approach, we first show that both these two models can be used to understand the two-step transition of EMT - E→E/M→M, the different responses of SNAIL and ZEB1 to exogenous TGF-β and the irreversibility of complete EMT. Next, we present new experimental results that tend to discriminate between these two models. We show that ZEB1 is present at intermediate levels in the hybrid E/M H1975 cells, and that in HMLE cells, overexpression of SNAIL is not sufficient to initiate EMT in the absence of ZEB1 and FOXC2. Conclusions These experimental results argue in favor of the TCS model proposing that miR-200/ZEB1 behaves as a three-way decision-making switch enabling transitions among the E, hybrid E/M and M phenotypes

Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1/{\epsilon}, and in the limit {\epsilon} -> 0, the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells. This convergence has been proved in Peletier, Savar\'e, and Veneroni, SIAM Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear structure of the equation. In this paper we re-prove the result by using solely the Wasserstein gradient-flow structure of the system. In particular we make no use of the linearity, nor of the fact that it is a second-order system. The first key step in this approach is a reformulation of the equation as the minimization of an action functional that captures the property of being a curve of maximal slope in an integrated form. The second important step is a rescaling of space. Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it represents. A consequence of these results is that solutions of the {\epsilon}-problem converge to a solution of the limiting problem.Comment: Added two sections, corrected minor typos, updated reference

Priorities and preferences of advanced soft tissue sarcoma patients starting palliative chemotherapy:baseline results from the HOLISTIC study

INTRODUCTION: Palliative chemotherapy is the principal treatment of patients with advanced soft tissue sarcomas (STS); however prognosis is limited (median overall survival 12-19 months). In this setting, patient values and priorities are central to personalised treatment decisions. PATIENTS AND METHODS: The prospective HOLISTIC study was conducted in the UK and the Netherlands assessing health-related quality of life in STS patients receiving palliative chemotherapy. Participants completed a questionnaire before starting chemotherapy, including attitudes towards quality of life (QoL) versus length of life (LoL), decisional control preferences, and decisional conflict. Chi-square and Fisher’s exact tests were used to evaluate associations between patient characteristics and preferences. RESULTS: One hundred and thirty-seven patients with advanced STS participated (UK: n = 72, the Netherlands: n = 65). Median age was 62 (27-79) years. Preference for extended LoL (n = 66, 48%) was slightly more common than preference for QoL (n = 56, 41%); 12 patients (9%) valued LoL and QoL equally (missing: n = 3). Younger patients (age <40 years) prioritised LoL, whereas two-thirds of older patients (aged ≥65 years) felt that QoL was equally or more important than LoL (P = 0.020). Decisional conflict was most common in patients who prioritised QoL (P = 0.024). Most patients preferred an active (n = 45, 33%) or collaborative (n = 59, 44%) role in treatment decisions. Gender, performance status, and country were significantly associated with preferred role. Concordance between preferred and actual role in chemotherapy decision was high (n = 104, 76%). CONCLUSIONS: Heterogeneous priorities and preferences among advanced STS patients support personalised decisions about palliative treatment. Considering individual differences during treatment discussions may enhance communication and optimise patient-centred care

Consensus on a video analysis framework of descriptors and definitions by the Rugby Union Video Analysis Consensus group

Using an expert consensus-based approach, a rugby union Video Analysis Consensus (RUVAC) group was formed to develop a framework for video analysis research in rugby union. The aim of the framework is to improve the consistency of video analysis work in rugby union and help enhance the overall quality of future research in the sport. To reach consensus, a systematic review and Delphi method study design was used. After a systematic search of the literature, 17 articles were used to develop the final framework that described and defined key actions and events in rugby union (rugby). Thereafter, a group of researchers and practitioners with experience and expertise in rugby video analysis formed the RUVAC group. Each member of the group examined the framework of descriptors and definitions and rated their level of agreement on a 5-point agreement Likert scale (1: strongly disagree; 2: disagree; 3: neitheragree or disagree; 4: agree; 5: strongly agree). The mean rating of agreement on the five-point scale (1: strongly disagree; 5: strongly agree) was 4.6 (4.3–4.9), 4.6 (4.4–4.9), 4.7 (4.5–4.9), 4.8 (4.6–5.0) and 4.8 (4.6–5.0) for the tackle, ruck, scrum, line-out and maul, respectively. The RUVAC group recommends using this consensus as the starting framework when conducting rugby video analysis research. Which variables to use (if not all) depends on the objectives of the study. Furthermore, the intention of this consensus is to help integrate video data with other data (eg, injury surveillance)

miR-132/212 knockout mice reveal roles for these miRNAs in regulating cortical synaptic transmission and plasticity

miR-132 and miR-212 are two closely related miRNAs encoded in the same intron of a small non-coding gene, which have been suggested to play roles in both immune and neuronal function. We describe here the generation and initial characterisation of a miR-132/212 double knockout mouse. These mice were viable and fertile with no overt adverse phenotype. Analysis of innate immune responses, including TLR-induced cytokine production and IFNβ induction in response to viral infection of primary fibroblasts did not reveal any phenotype in the knockouts. In contrast, the loss of miR-132 and miR-212, while not overtly affecting neuronal morphology, did affect synaptic function. In both hippocampal and neocortical slices miR-132/212 knockout reduced basal synaptic transmission, without affecting paired-pulse facilitation. Hippocampal long-term potentiation (LTP) induced by tetanic stimulation was not affected by miR-132/212 deletion, whilst theta burst LTP was enhanced. In contrast, neocortical theta burst-induced LTP was inhibited by loss of miR-132/212. Together these results indicate that miR-132 and/or miR-212 play a significant role in synaptic function, possibly by regulating the number of postsynaptic AMPA receptors under basal conditions and during activity-dependent synaptic plasticity