Guaranteeing the homotopy type of a set defined by non-linear inequalities

This paper provides an effective method to create an abstract simplicial complex homotopy equivalent to a given set S described by non-linear inequalities (polynomial or not). To our knowledge, no other numerical algorithm is able to deal with this type of problem. The proposed approach divides S into subsets that have been proven to be contractible using interval arithmetic. The method is close to Čech cohomology and uses the nerve theorem. Some examples illustrate the principle of the approach. This algorithm has been implemented

On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis

This paper presents a new numerical algorithm based on interval analysis able to verify that a continuously differentiable function is injective. The efficiency of the method is demonstrated by illustrative examples. These examples have been treated by a C++ solver which is made available

State estimation of a dehydration process by interval analysis

This article presents a general methodology of state estimation by interval analysis in a dynamic system modeled by difference equations. The methodology is applied to a pineapple osmotic dehydration process, in order to predict the behavior of the process within a range of allowed perturbation. The paper presents simulations and validations

Borders Start With Numbers: How Migration Data Create “Fake Illegals”

Sudden rises in migration across the borders of the Global North have persistently attracted substantial media attention and fueled hostility toward “irregular migrants” and “bogus refugees.” While existing qualitative studies have extensively criticized the migrant-refugee distinction, we offer unique quantitative evidence of how migration numbers and labels construct impressions of increased irregular migration while in fact creating “fake illegals.” We conduct a two-stage mixed-method analysis, demonstrating first that data on “irregular/illegal border crossings” (IBCs) published by Frontex have become an authoritative source of information on migration flows cited in a corpus of mainstream news media articles. We then posit that, while persecutions and violence in countries of origin may trigger migration, it is policies in destination states that determine who “is” and “isn’t” a refugee. In turn, we develop a novel method to divide IBCs into those who would likely obtain asylum in 31 European destination states (“likely refugees”) and those who would not (“likely irregular migrants”) across time given asylum acceptance rates by nationality. We estimate that between 2009 and 2021 most border crossers labeled as “irregular/illegal” (55.4%) were actually “likely refugees,” a proportion we estimate to be 75.5% at the peak of arrivals in 2015. Thus, we find that sudden and large increases in border crossings concentrated in space likely concern forced rather than irregular migrants. Altogether, our constructivist approach reveals how migration data and categories both influence and are influenced by securitized border policies and that, in this respect, borders start with numbers

Determination of set-membership identifiability sets

International audienceThis paper concerns the concept of set-membership identifiability introduced in \cite{jauberthie}. Given a model, a set-membership identifiable set is a connected set in the parameter domain of the model such that its corresponding trajectories are distinct to trajectories arising from its complementary. For obtaining the so-called set-membership identifiable sets, we propose an algorithm based on interval analysis tools. The proposed algorithm is decomposed into three parts namely {\it mincing}, {\it evaluating} and {\it regularization} (\cite{jaulin2}). The latter step has been modified in order to obtain guaranteed set-membership identifiable sets. Our algorithm will be tested on two examples

Efficient importance sampling in low dimensions using affine arithmetic

Despite the development of sophisticated techniques such as sequential Monte Carlo, importance sampling (IS) remains an important Monte Carlo method for low dimensional target distributions. This paper describes a new technique for constructing proposal distributions for IS, using affine arithmetic. This work builds on the Moore rejection sampler to which we provide a comparison

Mind the Gap: Computing Finance-Neutral Output Gaps in Latin-American Economies

We compute a measure of the finance-neutral potential output for Colombia, Chile and Mexico. Our methodology is based on Borio et al (2013, 2014) and incorporates the cycle of credit, house prices and the real exchange rate on the computation of the output gap. The literature on business cycles in emerging market economies, particularly papers focusing on Latin American economies, has highlighted the importance of including shocks to the interest rate in world capital markets together with financial frictions; terms of trade fluctuations; and a procyclical government spending process. Our results show that around the financial crises of the 1990s the finance-neutral output gap behaved differently than the traditional measures observed by policymakers. In particular, gaps are higher before crises and lower after them

Long Astral Microtubules and RACK-1 Stabilize Polarity Domains during Maintenance Phase in Caenorhabditis elegans Embryos

Cell polarity is a very well conserved process important for cell differentiation, cell migration, and embryonic development. After the establishment of distinct cortical domains, polarity cues have to be stabilized and maintained within a fluid and dynamic membrane to achieve proper cell asymmetry. Microtubules have long been thought to deliver the signals required to polarize a cell. While previous studies suggest that microtubules play a key role in the establishment of polarity, the requirement of microtubules during maintenance phase remains unclear. In this study, we show that depletion of Caenorhabditis elegans RACK-1, which leads to short astral microtubules during prometaphase, specifically affects maintenance of cortical PAR domains and Dynamin localization. We then investigated the consequence of knocking down other factors that also abolish astral microtubule elongation during polarity maintenance phase. We found a correlation between short astral microtubules and the instability of PAR-6 and PAR-2 domains during maintenance phase. Our data support a necessary role for astral microtubules in the maintenance phase of cell polarity