A Generalized Framework for Virtual Substitution

We generalize the framework of virtual substitution for real quantifier elimination to arbitrary but bounded degrees. We make explicit the representation of test points in elimination sets using roots of parametric univariate polynomials described by Thom codes. Our approach follows an early suggestion by Weispfenning, which has never been carried out explicitly. Inspired by virtual substitution for linear formulas, we show how to systematically construct elimination sets containing only test points representing lower bounds

Better Answers to Real Questions

We consider existential problems over the reals. Extended quantifier elimination generalizes the concept of regular quantifier elimination by providing in addition answers, which are descriptions of possible assignments for the quantified variables. Implementations of extended quantifier elimination via virtual substitution have been successfully applied to various problems in science and engineering. So far, the answers produced by these implementations included infinitesimal and infinite numbers, which are hard to interpret in practice. We introduce here a post-processing procedure to convert, for fixed parameters, all answers into standard real numbers. The relevance of our procedure is demonstrated by application of our implementation to various examples from the literature, where it significantly improves the quality of the results

A Case Study on the Parametric Occurrence of Multiple Steady States

We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.Comment: Accepted into ISSAC 2017. This version has additional page showing all 11 CAD trees discussed in Section 2.1.

Evidence for an exotic S=-2, Q=-2 baryon resonance in proton-proton collisions at the CERN SPS

Results of resonance searches in the Xi - pi -, Xi - pi +, Xi -bar+ pi -, and Xi -bar+ pi + invariant mass spectra in proton-proton collisions at sqrt[s]=17.2 GeV are presented. Evidence is shown for the existence of a narrow Xi - pi - baryon resonance with mass of 1.862±0.002 GeV/c2 and width below the detector resolution of about 0.018 GeV/c2. The significance is estimated to be above 4.2 sigma . This state is a candidate for the hypothetical exotic Xi --3/2 baryon with S=-2, I=3 / 2, and a quark content of (dsdsu-bar). At the same mass, a peak is observed in the Xi - pi + spectrum which is a candidate for the Xi 03/2 member of this isospin quartet with a quark content of (dsusd-bar). The corresponding antibaryon spectra also show enhancements at the same invariant mass

Which simple types have a unique inhabitant?

International audienceWe study the question of whether a given type has a unique inhabitant modulo program equivalence. In the setting of simply-typed lambda-calculus with sums, equipped with the strong βη-equivalence, we show that uniqueness is decidable. We present a saturating focused logic that introduces irreducible cuts on positive types "as soon as possible". Backward search in this logic gives an effective algorithm that returns either zero, one or two distinct inhabitants for any given type. Preliminary application studies show that such a feature can be useful in strongly-typed programs, inferring the code of highly-polymorphic library functions, or "glue code" inside more complex terms

System size and centrality dependence of the balance function in A + A collisions at sqrt s NN = 17.2 GeV

Electric charge correlations were studied for p+p, C+C, Si+Si and centrality selected Pb+Pb collisions at sqrt s_NN = 17.2$ GeV with the NA49 large acceptance detector at the CERN-SPS. In particular, long range pseudo-rapidity correlations of oppositely charged particles were measured using the Balance Function method. The width of the Balance Function decreases with increasing system size and centrality of the reactions. This decrease could be related to an increasing delay of hadronization in central Pb+Pb collisions

Cabbage and fermented vegetables : From death rate heterogeneity in countries to candidates for mitigation strategies of severe COVID-19

Large differences in COVID-19 death rates exist between countries and between regions of the same country. Some very low death rate countries such as Eastern Asia, Central Europe, or the Balkans have a common feature of eating large quantities of fermented foods. Although biases exist when examining ecological studies, fermented vegetables or cabbage have been associated with low death rates in European countries. SARS-CoV-2 binds to its receptor, the angiotensin-converting enzyme 2 (ACE2). As a result of SARS-CoV-2 binding, ACE2 downregulation enhances the angiotensin II receptor type 1 (AT(1)R) axis associated with oxidative stress. This leads to insulin resistance as well as lung and endothelial damage, two severe outcomes of COVID-19. The nuclear factor (erythroid-derived 2)-like 2 (Nrf2) is the most potent antioxidant in humans and can block in particular the AT(1)R axis. Cabbage contains precursors of sulforaphane, the most active natural activator of Nrf2. Fermented vegetables contain many lactobacilli, which are also potent Nrf2 activators. Three examples are: kimchi in Korea, westernized foods, and the slum paradox. It is proposed that fermented cabbage is a proof-of-concept of dietary manipulations that may enhance Nrf2-associated antioxidant effects, helpful in mitigating COVID-19 severity.Peer reviewe

Nrf2-interacting nutrients and COVID-19 : time for research to develop adaptation strategies

There are large between- and within-country variations in COVID-19 death rates. Some very low death rate settings such as Eastern Asia, Central Europe, the Balkans and Africa have a common feature of eating large quantities of fermented foods whose intake is associated with the activation of the Nrf2 (Nuclear factor (erythroid-derived 2)-like 2) anti-oxidant transcription factor. There are many Nrf2-interacting nutrients (berberine, curcumin, epigallocatechin gallate, genistein, quercetin, resveratrol, sulforaphane) that all act similarly to reduce insulin resistance, endothelial damage, lung injury and cytokine storm. They also act on the same mechanisms (mTOR: Mammalian target of rapamycin, PPAR gamma:Peroxisome proliferator-activated receptor, NF kappa B: Nuclear factor kappa B, ERK: Extracellular signal-regulated kinases and eIF2 alpha:Elongation initiation factor 2 alpha). They may as a result be important in mitigating the severity of COVID-19, acting through the endoplasmic reticulum stress or ACE-Angiotensin-II-AT(1)R axis (AT(1)R) pathway. Many Nrf2-interacting nutrients are also interacting with TRPA1 and/or TRPV1. Interestingly, geographical areas with very low COVID-19 mortality are those with the lowest prevalence of obesity (Sub-Saharan Africa and Asia). It is tempting to propose that Nrf2-interacting foods and nutrients can re-balance insulin resistance and have a significant effect on COVID-19 severity. It is therefore possible that the intake of these foods may restore an optimal natural balance for the Nrf2 pathway and may be of interest in the mitigation of COVID-19 severity

Flip-Pushdown Automata with k Pushdown Reversals and E0L Systems are Incomparable

International audienc

Constructing a single cell in cylindrical algebraic decomposition

International audienc