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# Documents : Multi angle  Conférences Vidéo | enregistrements trouvés : 200

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## Multi angle  Interview at Cirm: Julia GOG Gog, julia (Personne interviewée) | CIRM (Editeur )

Professor Julia Gog is a British mathematician, David N. Moore Fellow and Director of Studies in Mathematics at Queens' College, Cambridge and Professor of mathematical biology in the University of Cambridge Department of Applied Mathematics and Theoretical Physics. She is also a member of the Cambridge Immunology Network and the Cambridge Infectious Diseases Interdisciplinary Research Centre.Her research specialises in using mathematical techniques to study infectious diseases, particularly influenza. Current projects include:

Models of influenza strain dynamics
Spatial spread of influenza
Within-host dynamics of influenza
In vitro dynamics of Salmonella
Bioinformatic methods to detect RNA signals in viruses

http://www.damtp.cam.ac.uk/research/dd/
Professor Julia Gog is a British mathematician, David N. Moore Fellow and Director of Studies in Mathematics at Queens' College, Cambridge and Professor of mathematical biology in the University of Cambridge Department of Applied Mathematics and Theoretical Physics. She is also a member of the Cambridge Immunology Network and the Cambridge Infectious Diseases Interdisciplinary Research Centre.Her research specialises in using mathematical ...

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## Multi angle  Interview at Cirm: Tom Britton Britton, Tom (Personne interviewée) | CIRM (Editeur )

Interview at Cirm: Tom Britton
Dean of Mathematics & Physics, Stockholm University
Research interests: applied probability models and statistical inference for such, in particular epidemic models, networks and applications towards genetics and molecular biology including phylogenetics.

Erdös number: 2

Associate editor for Journal of Mathematical Biology

The math departments of Stockholm University and The Royal Institute of Technology together form the Stockholm Mathematics Center (SMC)

Currently chairman of the Cramér Society (Swedish association for academic statisticians)
Interview at Cirm: Tom Britton
Dean of Mathematics & Physics, Stockholm University
Research interests: applied probability models and statistical inference for such, in particular epidemic models, networks and applications towards genetics and molecular biology including phylogenetics.

Erdös number: 2

Associate editor for Journal of Mathematical Biology

The math departments of Stockholm University and The Royal Institute of Technology ...

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## Multi angle  Matrix factorisation techniques for data integration Lê Cao, Kim-Anh (Auteur de la Conférence) | CIRM (Editeur )

Gene module detection methods aim to group genes with similar expression profiles to shed light into functional relationships and co-regulation, and infer gene regulatory networks. Methods proposed so far use clustering to group genes based on global similarity in their expression profiles (co-expression), bi-clustering to group genes and samples simultaneously, network inference to model regulatory relationships between genes. In this talk I will focus on multivariate matrix decomposition techniques that enable dimension reduction and the identification of molecular signatures.
We will consider two different types of assays: bulk and single cell assays. Bulk transcriptomics assays use RNA-sequencing techniques to monitor the average expression profile of all the constituent cells, but fail to identify the distinct transcriptional profiles from different cell types. Single cell assays use similar RNA-seq techniques (scRNA-seq) to those used for bulk cell populations, but provide unprecedented resolution at the cell level to understand cellular heterogeneity and uncover new biology. However, scRNA-seq present new computational and analytical challenges, because of their sheer size (100K - 500K of cells are sequenced) and their zero inflated distribution due to technical drop-outs.
I will illustrate how we can use matrix factorisation technique to mine these data and identify gene modules that underpin molecular mechanisms in cell identity in scRNA-seq. I will also give further perspective on how we could extend similar concepts to integrate different omics data types (e.g. bulk transcriptomics, proteomics, metabolomics) to identify tightly connected multi-omics signatures that holistically describe a biological system.
Gene module detection methods aim to group genes with similar expression profiles to shed light into functional relationships and co-regulation, and infer gene regulatory networks. Methods proposed so far use clustering to group genes based on global similarity in their expression profiles (co-expression), bi-clustering to group genes and samples simultaneously, network inference to model regulatory relationships between genes. In this talk I ...

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## Multi angle  Cell processes in space and time - exemplified with yeast mating Klipp, Edda (Auteur de la Conférence) | CIRM (Editeur )

Baker’s yeast (Saccharomyces cerevisiae) has a diploid life-style, but under stress conditions, it forms spores, which then release haploid cells of mating types MATa and MATα. MATa cells are a frequently used model organism for many cell biological studies of cell cycle, metabolism or signaling. MATa and MATα cells can also mate to form diploid cells again. To this end, they secrete the pheromones α-factor and a-factor, sense the opposite pheromone and form protrusions in the direction of a potential mating partner. Importantly, they cannot move towards their mating partner, thus, the formation of the mating shape called shmoo is a significant growth investment.
Combining experimental studies of the cellular responses to mating factor and the resulting shape changes with spatial mathematical modeling, we investigated three major steps in the mating process. Specifically, we asked the following questions: (i) How do yeast cells communicate to form sharp gradients of pheromones allowing for precise decisions about whether to engage in mating or to continue dividing instead ? (ii) How do the individual cells sense the resulting gradients and how do they implement this information in order to decide about the spatial location of the polarization spot and later mating project? (iii) How do they translate the sensed information into shape changes, i.e. directed growth?
While we here use data and further information on yeast cells, the investigated processes occur in many cells under different circumstances. The developed theoretical concepts are therefore of general importance.
Baker’s yeast (Saccharomyces cerevisiae) has a diploid life-style, but under stress conditions, it forms spores, which then release haploid cells of mating types MATa and MATα. MATa cells are a frequently used model organism for many cell biological studies of cell cycle, metabolism or signaling. MATa and MATα cells can also mate to form diploid cells again. To this end, they secrete the pheromones α-factor and a-factor, sense the opposite ...

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## Multi angle  Network approaches for personalized medicine Martinez-Rodriguez, Maria (Auteur de la Conférence) | CIRM (Editeur )

In this talk, I will present current activities of the Computational Systems Biology group at IBM Research, Zurich, focused on the inference and exploitation of networks of molecular interactions. Focusing first on the problem of network inference, a long-standing challenge for which many methods have been proposed, I will discuss how no single inference method performs optimally across all data sets.
However, a Wisdom of the Crowds approach based on the integration of multiple inference methods can increase the robustness and high performance of the inferred networks. To that aim, we have developed COSIFER, a web-based platform that enables the inference of molecular networks using different approaches and consensus strategies. Next, I will introduce INtERAcT, an approach to extract information about molecular interactions from a text corpus in a completely unsupervised manner. INtERAcT exploits word embeddings, a state-of-the-art technology for language modelling based on deep learning that does not require text labeling for training or domain-specific knowledge, and hence, can be easily applied to different scientific domains.
Moving into the applications, I will explain how prior information about the molecular interactions in a cell can be encoded in a network, which can be further used for gene prioritization. Such strategy is exploited by NetBiTE with the goal of identifying anti-cancer drug sensitivity biomarkers. Finally, I will discuss how a probabilistic application of network dynamics can enable the reconstruction of the cell-signaling dynamics using single-cell omics.
In this talk, I will present current activities of the Computational Systems Biology group at IBM Research, Zurich, focused on the inference and exploitation of networks of molecular interactions. Focusing first on the problem of network inference, a long-standing challenge for which many methods have been proposed, I will discuss how no single inference method performs optimally across all data sets.
However, a Wisdom of the Crowds approach ...

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## Multi angle  Learning interpretable networks from multivariate information in biological and clinical data Isambert, Hervé (Auteur de la Conférence) | CIRM (Editeur )

The reconstruction of graphical models (or networks) has become ubiquitous to analyze the rapidly expanding, information-rich data of biological or clinical interest. I will outline some network reconstruction methods and applications to large scale datasets. In particular, our group has developped information-theoretic methods and machine learning tools to infer and analyze interpretable graphical models from large scale genomics data (single cell transcriptomics, tumor expression and mutation data) as well as clinical data (analysis of medical records from breast cancer patients, Institut Curie, and from elderly patients with cognitive disorders, La Pitie-Salpetriere).
The reconstruction of graphical models (or networks) has become ubiquitous to analyze the rapidly expanding, information-rich data of biological or clinical interest. I will outline some network reconstruction methods and applications to large scale datasets. In particular, our group has developped information-theoretic methods and machine learning tools to infer and analyze interpretable graphical models from large scale genomics data (single ...

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## Multi angle  From data to biological processes: interactions, networks and analyses, to understand cellular functions Brun, Christine (Auteur de la Conférence) | CIRM (Editeur )

Basics on the biology of molecular interactions and interaction data will be given all along the presentation of some of our research projects.

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## Multi angle  Part 1 - Networks of prior knowledge as frames to understand complex biological data Saez-Rodriguez, Julio (Auteur de la Conférence) | CIRM (Editeur )

Modern technologies allow us to profile in high detail biomedical samples at fast decreasing costs. New technologies are opening new data modalities, in particular to measure at the single cell level. Prior knowledge, and biological networks in particular, are useful to integrate this data and distill mechanistic insight. This can help to interpret the result of machine learning or statistical analysis, as well as generate input features for these methods. In addition, they can be converted in dynamic mechanistic models to gain more specific insight. I will give an overview of these approaches showcasing some examples and approaches used in the field.
Modern technologies allow us to profile in high detail biomedical samples at fast decreasing costs. New technologies are opening new data modalities, in particular to measure at the single cell level. Prior knowledge, and biological networks in particular, are useful to integrate this data and distill mechanistic insight. This can help to interpret the result of machine learning or statistical analysis, as well as generate input features for ...

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## Multi angle  Rank optimality for the Burer-Monteiro factorization Waldspurger, Irène (Auteur de la Conférence) | CIRM (Editeur )

The Burer-Monteiro factorization is a classical heuristic used to speed up the solving of large scale semidefinite programs when the solution is expected to be low rank: One writes the solution as the product of thinner matrices, and optimizes over the (low-dimensional) factors instead of over the full matrix. Even though the factorized problem is non-convex, one observes that standard first-order algorithms can often solve it to global optimality. This has been rigorously proved by Boumal, Voroninski and Bandeira, but only under the assumption that the factorization rank is large enough, larger than what numerical experiments suggest. We will describe this result, and investigate its optimality. More specifically, we will show that, up to a minor improvement, it is optimal: without additional hypotheses on the semidefinite problem at hand, first-order algorithms can fail if the factorization rank is smaller than predicted by current theory.
The Burer-Monteiro factorization is a classical heuristic used to speed up the solving of large scale semidefinite programs when the solution is expected to be low rank: One writes the solution as the product of thinner matrices, and optimizes over the (low-dimensional) factors instead of over the full matrix. Even though the factorized problem is non-convex, one observes that standard first-order algorithms can often solve it to global ...

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## Multi angle  Part 2 - Dynamic logic models complement machine learning for personalized medicine Saez-Rodriguez, Julio (Auteur de la Conférence) | CIRM (Editeur )

In the second talk, I will present some of our work on this area. Our work on this area, where we have focused on transcriptomics and (phospho)proteomics to study signaling networks. Our tools range from a meta-resource of biological knowledge (Omnipath) to methods to infer pathway and transcription factor activities (PROGENy and DoRothEA, respectively) from gene expression and subsequently infer causal paths among them (CARNIVAL), to tools to infer logic models from phosphoproteomic and phenotypic data (CellNOpt and PHONEMeS). We have recently adapted these tools to single-cell data. I will illustrate their utility in cases of biomedical relevance, in particular to improve our understanding of cancer and to develop novel therapeutic opportunities. As main application I will discuss our work analysing, as a model for personalized medicine, large pharmaco-genomic screenings in cell lines. These screenings provide rich information about alterations in tumours that confer drug sensitivity or resistance. Integration of this data with prior knowledge provides biomarkers and offer hypotheses for novel combination therapies. Our own analysis as well as the results of a crowdsourcing effort (as part of a DREAM
challenge) reveals that prediction of drug efficacy from basal omics data is that discussed above is far from accurate, implying important limitations for personalised medicine. An important aspect that deserves detailed attention is the dynamics of signaling networks and how they response to perturbations such as drug treatment.
I will present how cell-specific logic models, trained with measurements upon perturbations, can provides new biomarkers and treatment opportunities not noticeable by static molecular characterisation.
In the second talk, I will present some of our work on this area. Our work on this area, where we have focused on transcriptomics and (phospho)proteomics to study signaling networks. Our tools range from a meta-resource of biological knowledge (Omnipath) to methods to infer pathway and transcription factor activities (PROGENy and DoRothEA, respectively) from gene expression and subsequently infer causal paths among them (CARNIVAL), to tools to ...

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## Multi angle  Gradient descent for wide two-layer neural networks Bach, Francis (Auteur de la Conférence) | CIRM (Editeur )

Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training and generalization behavior of infinitely wide two-layer neural networks with homogeneous activations. We show that the limits of the gradient flow on exponentially tailed losses can be fully characterized as a max-margin classifier in a certain non-Hilbertian space of functions.
Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training and generalization behavior of infinitely wide two-layer neural networks with homogeneous activations. We show that the limits of the gradient flow on exponentially tailed losses can be fully characterized as a ...

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## Multi angle  Bridging the gap between optimal transport and MMD Sinkhorn divergences Genevay, Aude (Auteur de la Conférence) | CIRM (Editeur )

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## Multi angle  What does back propagation compute? Pauwels, Edouard (Auteur de la Conférence) | CIRM (Editeur )

We are interested in nonsmooth analysis of backpropagation as implemented in modern machine learning librairies, such as Tensorflow or Pytorch. First I will illustrate how blind application of
differential calculus to nonsmooth objects can be problematic, requiring a proper mathematical model.
Then I will introduce a weak notion of generalized derivative, named conservativity, and illustrate how it complies with calculus and optimization for well structured objects. We provide stability results for empirical risk minimization similar as in the smooth setting for the combination of nonsmooth automatic differentiation, minibatch stochastic approximation and first order optimization. This is joint work with Jérôme Bolte.
We are interested in nonsmooth analysis of backpropagation as implemented in modern machine learning librairies, such as Tensorflow or Pytorch. First I will illustrate how blind application of
differential calculus to nonsmooth objects can be problematic, requiring a proper mathematical model.
Then I will introduce a weak notion of generalized derivative, named conservativity, and illustrate how it complies with calculus and optimization for ...

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## Multi angle  Mathematical modelling and investigation of macrophages heterogeneity and their impact on the evolution of the cancer Eftimie, Raluca (Auteur de la Conférence) | CIRM (Editeur )

Macrophages are a type of immune cells that can be present in high numbers in some solid tumours. The heterogeneity of macrophage populations (with the anti-tumour M1 cells and thepro-tumour M2 cells being the two extreme phenotypes) has led to difficulties in understanding the innate immune responses to tumours. Here we introduce a class of mathematical models for the interactions between a population of tumour-associated macrophages (structured by their phenotype) and a population of cancer cells (that could be structured by their mutation status). We then use this class of models to confirm that the M1 cells kill tumours, while the M2 cells can lead to tumour growth. In addition, we show that macrophages with mixed phenotypes can contribute to either tumour growth or tumour decay. We also show that tumour dormancy is associated not only with an increased heterogeneity of cancer population, but also with an increased heterogeneity of macrophage population.
Macrophages are a type of immune cells that can be present in high numbers in some solid tumours. The heterogeneity of macrophage populations (with the anti-tumour M1 cells and thepro-tumour M2 cells being the two extreme phenotypes) has led to difficulties in understanding the innate immune responses to tumours. Here we introduce a class of mathematical models for the interactions between a population of tumour-associated macrophages (...

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## Multi angle  Mathematical models and their applications in hypertension and autism Layton, Anita T. (Auteur de la Conférence) | CIRM (Editeur )

Computational modeling can be used to reveal insights into the mechanisms and potential side effects of a new drug. Here we will focus on two major diseases: diabetes, which affects 1 in 10 people in North America, and hypertension, which affects 1 in 3 adults. For diabetes, we are interested in a class of relatively novel drug treatment, the SGLT2 inhibitors (sodium-glucose co-transporter 2 inhibitors). E.g., Dapagliflozin, Canagliflozin, and Empagliflozin. We conduct simulations to better understand any side effect these drugs may have on our kidneys (which are the targets of SGLT2 inhibitors). Interestingly, these drugs may have both positive and negative side effects. For hypertension, we want to better understand the sex differences in the efficacy of some of the drug treatments. Women generally respond better to ARBs (angiotensin receptor blockers) than ACE inhibitors (angiontensin converting enzyme inhibitors), whereas the opposite is true for men. We have developed the first sex-specific computational model of blood pressure regulation, and applied that model to assess whether the ”one-size-fits-all” approach to blood pressure control is appropriate with regards to sex.
Computational modeling can be used to reveal insights into the mechanisms and potential side effects of a new drug. Here we will focus on two major diseases: diabetes, which affects 1 in 10 people in North America, and hypertension, which affects 1 in 3 adults. For diabetes, we are interested in a class of relatively novel drug treatment, the SGLT2 inhibitors (sodium-glucose co-transporter 2 inhibitors). E.g., Dapagliflozin, Canagliflozin, and ...

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## Multi angle  Cell-like membranes are shaped by actin dynamics:a biometric approach to study cell functions Sykes, Cécile (Auteur de la Conférence) | CIRM (Editeur )

The detailed mechanisms of many cell functions such as motility, traffic, division or filopodia formation is difficult to address due to cell complexity. In all these functions, a common observation is that cytoskeleton assembly correlates with membrane deformation based on active forces. The exact role, in particular, of the actin cytoskeleton in cell membrane deformation, with pushing or pulling forces is what we address here experimentally. We conceive stripped-down experimental systems that reproduce cellular behaviours in simplified conditions: cytoskeleton dynamics are reproduced on liposome membranes. Inspired by how actin forces can exert forces on membranes and organelles, we address now how the nucleus, which is the most rigid cell organelle, is deformed by the actin cytoskeleton during cell translocation.
Actin polymerization through the growth of a branched actin network is able to initiate membrane tubules and spikes by pushing or pulling, which mimics the formation of endocytic vesicles and filopodia. By changing experimentally membrane tension and cytoskeleton structure, we displace the system within a phase diagram where inward or outward deformations are favoured. Moreover, shells of branched actin networks grown around liposomes display buckling and wrinkling under an osmotic deflation, thereby confirming their elastic properties. The time during which we let the network grow around liposomes allows us to vary the shell thickness, and to unveil the transition at which buckling or wrinkling occurs. Our results are in excellent agreement with the general mechanisms of buckling and wrinkling found in various systems spanning from pollen grains to the development of the gut or the brain.
The role of actin on membrane trafficking is unveiled by using preformed membrane tubes and growing an actin network around them in a form of a sleeve. We show that actin is able to modulate the thickness of tubes maintained under force. In a cell, where membrane tubes are constantly pulled by motors walking on microtubules, we predict that actin provides a way of maintaining a variety of tube thicknesses.
We study the translocation of the nucleus when cells move through narrow spaces that are smaller than their nuclei. We find that proteins of the nuclear membrane, such as nesprins, accumulate at the nucleus front during nucleus deformation and pull the nucleus forward.
The detailed mechanisms of many cell functions such as motility, traffic, division or filopodia formation is difficult to address due to cell complexity. In all these functions, a common observation is that cytoskeleton assembly correlates with membrane deformation based on active forces. The exact role, in particular, of the actin cytoskeleton in cell membrane deformation, with pushing or pulling forces is what we address here experimentally. ...

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## Multi angle  Near-criticality in mathematical models of epidemics Luczak, Malwina (Auteur de la Conférence) | CIRM (Editeur )

In an epidemic model, the basic reproduction number $R_{0}$ is a function of the parameters (such as infection rate) measuring disease infectivity. In a large population, if $R_{0}> 1$, then the disease can spread and infect much of the population (supercritical epidemic); if $R_{0}< 1$, then the disease will die out quickly (subcritical epidemic), with only few individuals infected.
For many epidemics, the dynamics are such that $R_{0}$ can cross the threshold from supercritical to subcritical (for instance, due to control measures such as vaccination) or from subcritical to supercritical (for instance, due to a virus mutation making it easier for it to infect hosts). Therefore, near-criticality can be thought of as a paradigm for disease emergence and eradication, and understanding near-critical phenomena is a key epidemiological challenge.
In this talk, we explore near-criticality in the context of some simple models of SIS (susceptible-infective-susceptible) epidemics in large homogeneous populations.
In an epidemic model, the basic reproduction number $R_{0}$ is a function of the parameters (such as infection rate) measuring disease infectivity. In a large population, if $R_{0}> 1$, then the disease can spread and infect much of the population (supercritical epidemic); if $R_{0}< 1$, then the disease will die out quickly (subcritical epidemic), with only few individuals infected.
For many epidemics, the dynamics are such that $R_{0}$ can ...

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## Multi angle  Evolutionary ecology of antibiotic resistance Lehtinen, Sonja (Auteur de la Conférence) | CIRM (Editeur )

Antibiotic resistance is a serious public health concern. Responding to this problem effectively requires characterising the factors (i.e. evolutionary and ecological processes) that determine resistance frequencies. At present, we do not have ecologically plausible models of resistance that are able to replicate observed trends - we are therefore unable to make credible predictions about resistance dynamics. In this talk, I will present work motivated by three tends observed in Streptococcus pneumoniae resistance data: the stable coexistence of antibiotic sensitivity and resistance, variation between resistance frequencies between pneumococcal lineages and correlation in resistance to different antibiotics. I will propose that variation in the fitness benefit gained from resistance arising from variation in the duration of carriage of pneumococcal lineages is a parsimonious explanation for all three trends. This eco-evolutionary framework could allow more accurate prediction of future resistance levels and play a role in informing strategies to prevent the spread of resistance.
Antibiotic resistance is a serious public health concern. Responding to this problem effectively requires characterising the factors (i.e. evolutionary and ecological processes) that determine resistance frequencies. At present, we do not have ecologically plausible models of resistance that are able to replicate observed trends - we are therefore unable to make credible predictions about resistance dynamics. In this talk, I will present work ...

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## Multi angle  Island filters for inference on metapopulation dynamics Ionides, Edward (Auteur de la Conférence) | CIRM (Editeur )

Low-dimensional compartment models for biological systems can be fitted to time series data using Monte Carlo particle filter methods. As dimension increases, for example when analyzing a collection of spatially coupled populations, particle filter methods rapidly degenerate. We show that many independent Monte Carlo calculations, each of which does not attempt to solve the filtering problem, can be combined to give a global filtering solution with favorable theoretical scaling properties under a weak coupling condition. The independent Monte Carlo calculations are called islands, and the operation carried out on each island is called adapted simulation, so the complete algorithm is called an adapted simulation island filter. We demonstrate this methodology and some related algorithms on a model for measles transmission within and between cities.
Low-dimensional compartment models for biological systems can be fitted to time series data using Monte Carlo particle filter methods. As dimension increases, for example when analyzing a collection of spatially coupled populations, particle filter methods rapidly degenerate. We show that many independent Monte Carlo calculations, each of which does not attempt to solve the filtering problem, can be combined to give a global filtering solution ...

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## Multi angle  Towards reproducibility and transparency in mathematical and computational epidemiology Frost, Simon (Auteur de la Conférence) | CIRM (Editeur )

Mathematical models of infectious disease transmission are increasingly used to guide public health and policy decisions. Hence, it is important that every effort is made to ensure that models are ‘correct’, made difficult by the frequent need to simulate a model numerically. The best we can do in most cases is to be able to replicate a model i.e. generate the same results from the same inputs (model plus parameters), or failing that, reproduce results that are similar. This can be achieved by sharing the computer code, and/or providing a sufficiently detailed description of the model. I will illustrate that it is often difficult to replicate or reproduce results of modeling publications, using case studies that highlight some of the many causes of this failure. I will argue that the FAIR principles proposed for data - that they should be Findable, Accessible, Interoperable and Reusable - are equally valid for modeling studies, and go a long way towards ensuring reproducibility. I will present Epirecipes (http://epirecip.es) a FAIR platform that both allows models to be replicated exactly, while fostering the idea that a wide variety of approaches are needed to ensure the robustness of model results. The added value from this platform includes resources for teaching, acting as a ‘Rosetta Stone’ - allowing models from one computer language to be ported to another, and as a repository of best practices, potential pitfalls, and technical tricks that are all too often tucked away in papers or textbooks. As quoted from ‘The Turing Way’ (https://the-turing-way.netlify.com), a handbook for reproducible science, reproducing models of infectious disease should be ‘too easy not to do’.
Mathematical models of infectious disease transmission are increasingly used to guide public health and policy decisions. Hence, it is important that every effort is made to ensure that models are ‘correct’, made difficult by the frequent need to simulate a model numerically. The best we can do in most cases is to be able to replicate a model i.e. generate the same results from the same inputs (model plus parameters), or failing that, reproduce ...

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