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

Systematic Functional Analysis of Bicaudal-D Serine Phosphorylation and Intragenic Suppression of a Female Sterile Allele of BicD

Protein phosphorylation is involved in posttranslational control of essentially all biological processes. Using mass spectrometry, recent analyses of whole phosphoproteomes led to the identification of numerous new phosphorylation sites. However, the function of most of these sites remained unknown. We chose the Drosophila Bicaudal-D protein to estimate the importance of individual phosphorylation events. Being involved in different cellular processes, BicD is required for oocyte determination, for RNA transport during oogenesis and embryogenesis, and for photoreceptor nuclei migration in the developing eye. The numerous roles of BicD and the available evidence for functional importance of BicD phosphorylation led us to identify eight phosphorylation sites of BicD, and we tested a total of 14 identified and suspected phosphoserine residues for their functional importance in vivo in flies. Surprisingly, all these serines turned out to be dispensable for providing sufficient basal BicD activity for normal growth and development. However, in a genetically sensitized background where the BicDA40V protein variant provides only partial activity, serine 103 substitutions are not neutral anymore, but show surprising differences. The S103D substitution completely inactivates the protein, whereas S103A behaves neutral, and the S103F substitution, isolated in a genetic screen, restores BicDA40V function. Our results suggest that many BicD phosphorylation events may either be fortuitous or play a modulating function as shown for Ser103. Remarkably, amongst the Drosophila serines we found phosphorylated, Ser103 is the only one that is fully conserved in mammalian BicD

Numeric and Certified Isolation of the Singularities of the Projection of a Smooth Space Curve

International audienceLet CP ∩Q be a smooth real analytic curve embedded in R 3 , defined as the solutions of real analytic equations of the form P (x, y, z) = Q(x, y, z) = 0 or P (x, y, z) = ∂P ∂z = 0. Our main objective is to describe its projection C onto the (x, y)-plane. In general, the curve C is not a regular submanifold of R 2 and describing it requires to isolate the points of its singularity locus Σ. After describing the types of singularities that can arise under some assumptions on P and Q, we present a new method to isolate the points of Σ. We experimented our method on pairs of independent random polynomials (P, Q) and on pairs of random polynomials of the form (P, ∂P ∂z) and got promising results

Antifungal Activity of Resveratrol Derivatives against Candida Species

trans-Resveratrol (1a) is a phytoalexin produced by plants in response to infections by pathogens. Its potential activity against clinically relevant opportunistic fungal pathogens has previously been poorly investigated. Evaluated herein are the candidacidal activities of oligomers (2a, 3–5) of 1a purified from Vitis vinifera grape canes and several analogues (1b–1j) of 1a obtained through semisynthesis using methylation and acetylation. Moreover, trans-ε-viniferin (2a), a dimer of 1a, was also subjected to methylation (2b) and acetylation (2c) under nonselective conditions. Neither the natural oligomers of 1a (2a, 3–5) nor the derivatives of 2a were active against Candida albicans SC5314. However, the dimethoxy resveratrol derivatives 1d and 1e exhibited antifungal activity against C. albicans with minimum inhibitory concentration (MIC) values of 29–37 μg/mL and against 11 other Candida species. Compound 1e inhibited the yeast-to-hyphae morphogenetic transition of C. albicans at 14 μg/mL

A Set-Theoretic Method for Verifying Feasibility of a Fast Explicit Nonlinear Model Predictive Controller

In this chapter an algorithm for nonlinear explicit model predictive control is presented. A low complexity receding horizon control law is obtained by approximating the optimal control law using multiscale basis function approximation. Simultaneously, feasibility and stability of the approximate control law is ensured through the computation of a capture basin (region of attraction) for the closed-loop system. In a previous work, interval methods were used to construct the capture basin (feasible region), yet this approach suffered due to slow computation times and high grid complexity. In this chapter, we suggest an alternative to interval analysis based on zonotopes. The suggested method significantly reduces the complexity of the combined function approximation and verification procedure through the use of DC (difference of convex) programming, and recursive splitting. The result is a multiscale function approximation method with improved computational efficiency for fast nonlinear explicit model predictive control with guaranteed stability and constraint satisfaction

Identification of a Classical Bipartite Nuclear Localization Signal in the Drosophila TEA/ATTS Protein Scalloped

Drosophila melanogaster wing development has been shown to rely on the activity of a complex of two proteins, Scalloped (Sd) and Vestigial (Vg). Within this complex, Sd is known to provide DNA binding though its TEA/ATTS domain, while Vg modulates this binding and provides transcriptional activation through N- and C-terminal activation domains. There is also evidence that Sd is required for the nuclear translocation of Vg. Indeed, a candidate sequence which shows consensus to the bipartite family of nuclear localization signals (NLSs) has been identified within Sd previously, though it is not known if it is functional, or if additional unpredicted signals that mediate nuclear transport exist within the protein. By expressing various enhanced green fluorescent protein (eGFP) tagged constructs within Drosophila S2 cells, we demonstrate that this NLS is indeed functional and necessary for the proper nuclear localization of Sd. Additionally, the region containing the NLS is critical for the wildtype function of ectopically expressed Sd, in the context of wing development. Using site-directed mutagenesis, we have identified a group of five amino acids within this NLS which is critical for its function, as well as another group of two which is of lesser importance. Together with data that suggests that this sequence mediates interactions with Importin-α3, we conclude that the identified NLS is likely a classical bipartite signal. Further dissection of Sd has also revealed that a large portion of the C-terminal domain of the protein is required its proper nuclear localization. Finally, a Leptomycin B (LB) sensitive signal which appears to facilitate nuclear export is identified, raising the possibility that Sd also contains a nuclear export signal (NES)

Transient exposure to low levels of insecticide affects metabolic networks of honeybee larvae

The survival of a species depends on its capacity to adjust to changing environmental conditions, and new stressors. Such new, anthropogenic stressors include the neonicotinoid class of crop-protecting agents, which have been implicated in the population declines of pollinating insects, including honeybees (Apis mellifera). The low-dose effects of these compounds on larval development and physiological responses have remained largely unknown. Over a period of 15 days, we provided syrup tainted with low levels (2 µg/L−1) of the neonicotinoid insecticide imidacloprid to beehives located in the field. We measured transcript levels by RNA sequencing and established lipid profiles using liquid chromatography coupled with mass spectrometry from worker-bee larvae of imidacloprid-exposed (IE) and unexposed, control (C) hives. Within a catalogue of 300 differentially expressed transcripts in larvae from IE hives, we detect significant enrichment of genes functioning in lipid-carbohydrate-mitochondrial metabolic networks. Myc-involved transcriptional response to exposure of this neonicotinoid is indicated by overrepresentation of E-box elements in the promoter regions of genes with altered expression. RNA levels for a cluster of genes encoding detoxifying P450 enzymes are elevated, with coordinated downregulation of genes in glycolytic and sugar-metabolising pathways. Expression of the environmentally responsive Hsp90 gene is also reduced, suggesting diminished buffering and stability of the developmental program. The multifaceted, physiological response described here may be of importance to our general understanding of pollinator health. Muscles, for instance, work at high glycolytic rates and flight performance could be impacted should low levels of this evolutionarily novel stressor likewise induce downregulation of energy metabolising genes in adult pollinators

Counting the Number of Connected Components of a Set and Its Application to Robotics

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