Temporal Gillespie algorithm: Fast simulation of contagion processes on time-varying networks

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling.Comment: Minor changes and updates to reference

How memory generates heterogeneous dynamics in temporal networks

Empirical temporal networks display strong heterogeneities in their dynamics, which profoundly affect processes taking place on these networks, such as rumor and epidemic spreading. Despite the recent wealth of data on temporal networks, little work has been devoted to the understanding of how such heterogeneities can emerge from microscopic mechanisms at the level of nodes and links. Here we show that long-term memory effects are present in the creation and disappearance of links in empirical networks. We thus consider a simple generative modeling framework for temporal networks able to incorporate these memory mechanisms. This allows us to study separately the role of each of these mechanisms in the emergence of heterogeneous network dynamics. In particular, we show analytically and numerically how heterogeneous distributions of contact durations, of inter-contact durations and of numbers of contacts per link emerge. We also study the individual effect of heterogeneities on dynamical processes, such as the paradigmatic Susceptible-Infected epidemic spreading model. Our results confirm in particular the crucial role of the distributions of inter-contact durations and of the numbers of contacts per link

Role of Positron Emission Tomography in Imaging of Non-neurologic Disorders of the Head, Neck, and Teeth in Veterinary Medicine.

Positron Emission Tomography (PET) is an imaging technique that provides functional information, in addition to structural information obtained with computed tomography (CT). The most common application is cancer staging, using 18F-Fluorodeoxyglucose (18F-FDG), a radioactive analog of glucose. Although limited data are available in the veterinary literature, human studies have demonstrated benefit with the addition of PET both for assessment of the primary tumor and for detection of metastatic disease. 18F-FDG PET appears to be more accurate at detecting the margin of oral neoplasia, in particular for tumors arising from highly vascularized tissue, such as the lingual and laryngeal areas. 18F-FDG PET has a high sensitivity for the detection of lymph node metastasis, however the specificity is variable between studies. Tracers beyond 18F-FDG can also be used for oncology imaging. 18F-Fluoride (18F-NaF) is an excellent osseous tracer, useful in assessing bone involvement of primary tumors or osseous metastasis. Other specific tracers can be used to assess cell proliferation or hypoxia for tumor characterization. 18F-FDG is also an excellent tracer for detection of inflammation. Human studies have demonstrated its value for the assessment of periodontitis and dental implant infection. 18F-NaF has been used to assess disorders of the temporomandibular joint in the human literature, demonstrating good correlation with arthralgia and therapeutic outcome. Both 18F-NaF and 18F-FDG had good concordance with localization of cervical pain in people. PET will likely have a growing role in veterinary medicine not only for oncologic imaging but also for assessment of inflammation and pain