Polynomial Time corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length

We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential equations with polynomial right-hand side. This result gives a purely continuous (time and space) elegant and simple characterization of $\operatorname{PTIME}$. This is the first time such classes are characterized using only ordinary differential equations. Our characterization extends to functions computable in polynomial time over the reals in the sense of computable analysis. This extends to deterministic complexity classes above polynomial time. This may provide a new perspective on classical complexity, by giving a way to define complexity classes, like $\operatorname{PTIME}$, in a very simple way, without any reference to a notion of (discrete) machine. This may also provide ways to state classical questions about computational complexity via ordinary differential equations, i.e.~by using the framework of analysis

high myopic photorefractive keratectomy outcomes with the alcon Wavelight® eX500 excimer laser

Purpose: To present refractive outcomes from consecutive cases with the Alcon Wavelight® EX500 excimer laser using photorefractive keratectomy (PRK) in patients with high myopia. Methods: A retrospective chart review of consecutive cases of high myopic eyes ($6.0 Diopters [D]) undergoing PRK with the Alcon Wavelight EX500 excimer laser (Alcon Labo- ratories, Fort Worth, TX, USA) was done. Moderately high myopic eyes (6.0 to ,8.0 D [6 D]) were compared with high myopic eyes (8.0 D or greater [8 D]). Outcomes measured included pre- and postoperative refractive error, uncorrected distance visual acuity (UDVA), corrected distance visual acuity, spherical equivalent correction (SEQ), haze incidence, and intraocular pressure (IOP). Results: One hundred eighteen eyes of 63 patients were evaluated, with 59 eyes having 12 months of follow-up. Thirty-one eyes of 19 patients had 8.0 D or more of myopia. Twelve- month average LogMAR UDVA was −0.06 (20/17) for the 6 D group and −0.08 (20/16) for the 8 D group. Average 12-month SEQ was −0.18 D and preoperatively was −7.52 D for the 6 D group and −0.09 and −9.02 in the 8 D group. Sixty-five eyes (86%) and 24 eyes (96%) had an SEQ within 0.50 D of emmetropia at 3 months in the 6 and 8 D groups, respectively. One eye had visually significant haze developed at 8 months. Three eyes had IOP elevation that resolved with addition of short-term topical IOP-lowering medication. Conclusion: High myopic PRK with the Alcon Wavelight EX500 excimer laser yields excel- lent refractive outcomes with a low incidence of complications

USP2-45 Is a Circadian Clock Output Effector Regulating Calcium Absorption at the Post-Translational Level.

The mammalian circadian clock influences most aspects of physiology and behavior through the transcriptional control of a wide variety of genes, mostly in a tissue-specific manner. About 20 clock-controlled genes (CCGs) oscillate in virtually all mammalian tissues and are generally considered as core clock components. One of them is Ubiquitin-Specific Protease 2 (Usp2), whose status remains controversial, as it may be a cogwheel regulating the stability or activity of core cogwheels or an output effector. We report here that Usp2 is a clock output effector related to bodily Ca2+ homeostasis, a feature that is conserved across evolution. Drosophila with a whole-body knockdown of the orthologue of Usp2, CG14619 (dUsp2-kd), predominantly die during pupation but are rescued by dietary Ca2+ supplementation. Usp2-KO mice show hyperabsorption of dietary Ca2+ in small intestine, likely due to strong overexpression of the membrane scaffold protein NHERF4, a regulator of the Ca2+ channel TRPV6 mediating dietary Ca2+ uptake. In this tissue, USP2-45 is found in membrane fractions and negatively regulates NHERF4 protein abundance in a rhythmic manner at the protein level. In clock mutant animals (Cry1/Cry2-dKO), rhythmic USP2-45 expression is lost, as well as the one of NHERF4, confirming the inverse relationship between USP2-45 and NHERF4 protein levels. Finally, USP2-45 interacts in vitro with NHERF4 and endogenous Clathrin Heavy Chain. Taken together these data prompt us to define USP2-45 as the first clock output effector acting at the post-translational level at cell membranes and possibly regulating membrane permeability of Ca2+

A Probabilistic Framework for Security Scenarios with Dependent Actions

This work addresses the growing need of performing meaningful probabilistic analysis of security. We propose a framework that integrates the graphical security modeling technique of attack–defense trees with probabilistic information expressed in terms of Bayesian networks. This allows us to perform probabilistic evaluation of attack–defense scenarios involving dependent actions. To improve the efficiency of our computations, we make use of inference algorithms from Bayesian networks and encoding techniques from constraint reasoning. We discuss the algebraic theory underlying our framework and point out several generalizations which are possible thanks to the use of semiring theory

Computability of ordinary differential equations

In this paper we provide a brief review of several results about the computability of initial-value problems (IVPs) defined with ordinary differential equations (ODEs). We will consider a variety of settings and analyze how the computability of the IVP will be affected. Computational complexity results will also be presented, as well as computable versions of some classical theorems about the asymptotic behavior of ODEs.info:eu-repo/semantics/publishedVersio

Stratégie de réduction des micropolluants à l'échelle d'une agglomération : comparaison entre les effluents d’exutoires pluviaux et d’une station d'épuration

Colloque avec actes et comité de lecture. Internationale.International audienc

CXCR2 Signaling Protects Oligodendrocytes and Restricts Demyelination in a Mouse Model of Viral-Induced Demyelination

BACKGROUND: The functional role of ELR-positive CXC chemokines during viral-induced demyelination was assessed. Inoculation of the neuroattenuated JHM strain of mouse hepatitis virus (JHMV) into the CNS of susceptible mice results in an acute encephalomyelitis that evolves into a chronic demyelinating disease, modeling white matter pathology observed in the human demyelinating disease Multiple Sclerosis. METHODOLOGY/PRINCIPAL FINDINGS: JHMV infection induced the rapid and sustained expression of transcripts specific for the ELR+ chemokine ligands CXCL1 and CXCL2, as well as their binding receptor CXCR2, which was enriched within the spinal cord during chronic infection. Inhibiting CXCR2 signaling with neutralizing antiserum significantly (p<0.03) delayed clinical recovery. Moreover, CXCR2 neutralization was associated with an increase in the severity of demyelination that was independent of viral recrudescence or modulation of neuroinflammation. Rather, blocking CXCR2 was associated with increased numbers of apoptotic cells primarily within white matter tracts, suggesting that oligodendrocytes were affected. JHMV infection of enriched oligodendrocyte progenitor cell (OPC) cultures revealed that apoptosis was associated with elevated expression of cleaved caspase 3 and muted Bcl-2 expression. Inclusion of CXCL1 within JHMV infected cultures restricted caspase 3 cleavage and increased Bcl-2 expression that was associated with a significant (p<0.001) decrease in apoptosis. CXCR2 deficient oligodendrocytes were refractory to CXCL1 mediated protection from JHMV-induced apoptosis, readily activating caspase 3 and down regulating Bcl-2. CONCLUSION/SIGNIFICANCE: These findings highlight a previously unappreciated role for CXCR2 signaling in protecting oligodendrocyte lineage cells from apoptosis during inflammatory demyelination initiated by viral infection of the CNS

In Situ Dividing and Phagocytosing Retinal Microglia Express Nestin, Vimentin, and NG2 In Vivo

BACKGROUND: Following injury, microglia become activated with subsets expressing nestin as well as other neural markers. Moreover, cerebral microglia can give rise to neurons in vitro. In a previous study, we analysed the proliferation potential and nestin re-expression of retinal macroglial cells such as astrocytes and Müller cells after optic nerve (ON) lesion. However, we were unable to identify the majority of proliferative nestin(+) cells. Thus, the present study evaluates expression of nestin and other neural markers in quiescent and proliferating microglia in naïve retina and following ON transection in adult rats in vivo. METHODOLOGY/PRINCIPAL FINDINGS: For analysis of cell proliferation and cells fates, rats received BrdU injections. Microglia in retinal sections or isolated cells were characterized using immunofluorescence labeling with markers for microglia (e.g., Iba1, CD11b), cell proliferation, and neural cells (e.g., nestin, vimentin, NG2, GFAP, Doublecortin etc.). Cellular analyses were performed using confocal laser scanning microscopy. In the naïve adult rat retina, about 60% of resting ramified microglia expressed nestin. After ON transection, numbers of nestin(+) microglia peaked to a maximum at 7 days, primarily due to in situ cell proliferation of exclusively nestin(+) microglia. After 8 weeks, microglia numbers re-attained control levels, but 20% were still BrdU(+) and nestin(+), although no further local cell proliferation occurred. In addition, nestin(+) microglia co-expressed vimentin and NG2, but not GFAP or neuronal markers. Fourteen days after injury and following retrograde labeling of retinal ganglion cells (RGCs) with Fluorogold (FG), nestin(+)NG2(+) microglia were positive for the dye indicating an active involvement of a proliferating cell population in phagocytosing apoptotic retinal neurons. CONCLUSIONS/SIGNIFICANCE: The current study provides evidence that in adult rat retina, a specific resident population of microglia expresses proteins of immature neural cells that are involved in injury-induced cell proliferation and phagocytosis while transdifferentiation was not observed

Ischemia-Reperfusion Injury and Pregnancy Initiate Time-Dependent and Robust Signs of Up-Regulation of Cardiac Progenitor Cells

To explore how cardiac regeneration and cell turnover adapts to disease, different forms of stress were studied for their effects on the cardiac progenitor cell markers c-Kit and Isl1, the early cardiomyocyte marker Nkx2.5, and mast cells. Adult female rats were examined during pregnancy, after myocardial infarction and ischemia-reperfusion injury with/out insulin like growth factor-1(IGF-1) and hepatocyte growth factor (HGF). Different cardiac sub-domains were analyzed at one and two weeks post-intervention, both at the mRNA and protein levels. While pregnancy and myocardial infarction up-regulated Nkx2.5 and c-Kit (adjusted for mast cell activation), ischemia-reperfusion injury induced the strongest up-regulation which occurred globally throughout the entire heart and not just around the site of injury. This response seems to be partly mediated by increased endogenous production of IGF-1 and HGF. Contrary to c-Kit, Isl1 was not up-regulated by pregnancy or myocardial infarction while ischemia-reperfusion injury induced not a global but a focal up-regulation in the outflow tract and also in the peri-ischemic region, correlating with the up-regulation of endogenous IGF-1. The addition of IGF-1 and HGF did boost the endogenous expression of IGF and HGF correlating to focal up-regulation of Isl1. c-Kit expression was not further influenced by the exogenous growth factors. This indicates that there is a spatial mismatch between on one hand c-Kit and Nkx2.5 expression and on the other hand Isl1 expression. In conclusion, ischemia-reperfusion injury was the strongest stimulus with both global and focal cardiomyocyte progenitor cell marker up-regulations, correlating to the endogenous up-regulation of the growth factors IGF-1 and HGF. Also pregnancy induced a general up-regulation of c-Kit and early Nkx2.5+ cardiomyocytes throughout the heart. Utilization of these pathways could provide new strategies for the treatment of cardiac disease