On deflation and multiplicity structure

This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction uses a single linear differential form defined from the Jacobian matrix of the input, and defines the deflated system by applying this differential form to the original system. The advantages of this new deflation is that it does not introduce new variables and the increase in the number of equations is linear in each iteration instead of the quadratic increase of previous methods. The second construction gives the coefficients of the so-called inverse system or dual basis, which defines the multiplicity structure at the singular root. We present a system of equations in the original variables plus a relatively small number of new variables that completely deflates the root in one step. We show that the isolated simple solutions of this new system correspond to roots of the original system with given multiplicity structure up to a given order. Both constructions are "exact" in that they permit one to treat all conjugate roots simultaneously and can be used in certification procedures for singular roots and their multiplicity structure with respect to an exact rational polynomial system.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0508

Closed-state inactivation involving an internal gate in Kv4.1 channels modulates pore blockade by intracellular quaternary ammonium ions.

Voltage-gated K(+) (Kv) channel activation depends on interactions between voltage sensors and an intracellular activation gate that controls access to a central pore cavity. Here, we hypothesize that this gate is additionally responsible for closed-state inactivation (CSI) in Kv4.x channels. These Kv channels undergo CSI by a mechanism that is still poorly understood. To test the hypothesis, we deduced the state of the Kv4.1 channel intracellular gate by exploiting the trap-door paradigm of pore blockade by internally applied quaternary ammonium (QA) ions exhibiting slow blocking kinetics and high-affinity for a blocking site. We found that inactivation gating seemingly traps benzyl-tributylammonium (bTBuA) when it enters the central pore cavity in the open state. However, bTBuA fails to block inactivated Kv4.1 channels, suggesting gated access involving an internal gate. In contrast, bTBuA blockade of a Shaker Kv channel that undergoes open-state P/C-type inactivation exhibits fast onset and recovery inconsistent with bTBuA trapping. Furthermore, the inactivated Shaker Kv channel is readily blocked by bTBuA. We conclude that Kv4.1 closed-state inactivation modulates pore blockade by QA ions in a manner that depends on the state of the internal activation gate

Dissipative collisions in 16^{16}O + 27^{27}Al at Elab_{lab}=116 MeV

The inclusive energy distributions of fragments (3$\leq$Z$\leq$7) emitted in the reaction $^{16}$O + $^{27}$Al at $E_{lab} =$116 MeV have been measured in the angular range $\theta_{lab}$= 15$^\circ$ - 115$^\circ$. A non-linear optimisation procedure using multiple Gaussian distribution functions has been proposed to extract the fusion-fission and deep inelastic components of the fragment emission from the experimental data. The angular distributions of the fragments, thus obtained, from the deep inelastic component are found to fall off faster than those from the fusion-fission component, indicating shorter life times of the emitting di-nuclear systems. The life times of the intermediate di-nuclear configurations have been estimated using a diffractive Regge-pole model. The life times thus extracted ($\sim 1 - 5\times 10^{-22}$ Sec.) are found to decrease with the increase in the fragment charge. Optimum Q-values are also found to increase with increasing charge transfer i.e. with the decrease in fragment charge.Comment: 9 pages, 4 figures, 1 tabl

8Be cluster emission versus alpha evaporation in 28Si + 12C

The possible occurence of highly deformed configurations in the $^{40}$Ca di-nuclear system formed in the $^{28}$Si + $^{12}$C reaction is investigated by analyzing the spectra of emitted light charged particles. Both inclusive and exclusive measurements of the heavy fragments (A $\geq$ 10) and their associated light charged particles (protons and $\alpha$ particles) have been made at the IReS Strasbourg {\sc VIVITRON} Tandem facility at bombarding energies of $E_{lab}$ ($^{28}$Si) = 112 MeV and 180 MeV by using the {\sc ICARE} charged particle multidetector array. The energy spectra, velocity distributions, in-plane and out-of-plane angular correlations of light charged particles are compared to statistical-model calculations using a consistent set of parameters with spin-dependent level densities. This spin dependence approach suggests the onset of large nuclear deformation in $^{40}$Ca at high spin. This conclusion might be connected with the recent observation of superdeformed bands in the $^{40}$Ca nucleus. The analysis of $\alpha$ particles in coincidence with $^{32}$S fragments suggests a surprisingly strong $^{8}$Be cluster emission of a binary nature.Comment: 39 pages 15 figure

Search for emission of unstable 8^8Be clusters from hot 40^40Ca and 56^56Ni nuclei

The possible occurence of highly deformed configurations is investigated in the $^{40}$Ca and $^{56}$Ni di-nuclear systems as formed in the $^{28}$Si + $^{12}$C and $^{28}$Si + $^{28}$Si reactions, respectively, by using the properties of emitted light charged particles. Inclusive as well as exclusive data of the heavy fragments (A $\geq$ 6) and their associated light charged particles (p, d, t, and $\alpha$-particles) have been collected at the IReS Strasbourg VIVITRON Tandem facility with two bombarding energies $E_{lab}(^{28}$Si) = 112 and 180 MeV by using the ICARE charged particle multidetector array, which consists of nearly 40 telescopes. The measured energy spectra, velocity distributions, in-plane and out-of-plane angular correlations are analysed by Monte Carlo CASCADE statistical-model calculations using a consistent set of parameters with spin-dependent level densities. Although significant deformation effects at high spin are needed, the remaining disagreement observed in the $^{28}$Si + $^{12}$C reaction for the S evaporation residue suggests an unexpected large unstable $^{8}$Be cluster emission of a binary nature.Comment: 13 pages latex, 9 eps figures. Paper presented at the XXXIX International Winter Meeting on Nuclear Physics, Bormio(Italy) January 22-27, 2001 (to be published at Ricerca Scientifica ed Educazione Permanente

Down syndrome and postoperative complications after paediatric cardiac surgery: a propensity-matched analysis

OBJECTIVESThe incidence of congenital heart disease is approximately 50%, mostly related to endocardial cushion defects. The aim of our study was to investigate the postoperative complications that occur after paediatric cardiac surgery.METHODSOur perioperative data were analysed in paediatric patients with Down syndrome undergoing cardiac surgery. We retrospectively analysed the data from 2063 consecutive paediatric patients between January 2003 and December 2008. After excluding the patients who died or had missing data, the analysed database (before propensity matching) contained 129 Down patients and 1667 non-Down patients. After propensity matching, the study population comprised 222 patients and 111 patients had Down syndrome.RESULTSBefore propensity matching, the occurrences of low output syndrome (21.2 vs 32.6%, P = 0.003), pulmonary complication (14 vs 28.7%, P < 0.001) and severe infection (11.9 vs 22.5%, P = 0.001) were higher in the Down group. Down patients were more likely to have prolonged mechanical ventilation [median (interquartile range) 22 (9-72) h vs 49 (24-117) h, P = 0.007]. The total intensive care unit length of stay [6.9 (4.2-12.4) days vs 8.3 (5.3-13.2) days, P = 0.04] and the total hospital length of stay [17.3 (13.3-23.2) days vs 18.3 (15.1-23.6) days, P = 0.05] of the Down patients were also longer. Mortality was similar in the two groups before (3.58 vs 3.88%, P = 0.86) and after (5.4 vs 4.5%, P = 1.00) propensity matching. After propensity matching, there was no difference in the occurrence of adverse events.CONCLUSIONSAfter propensity matching Down syndrome was not associated with increased mortality or complication rate following congenital cardiac surgery