Parameter Delta Research Articles

TH‐C‐220‐11: Interplay of Radiobiological Parameters in BED Calculations for a Linear‐Quadratic‐Linear Model

Purpose: In the framework of stereotactic body radiation therapy (SBRT), dose per fraction larger than 2Gy have become more common, challenging the applicability of the linear‐quadratic (LQ) model. Several authors have proposed ways to modify the LQ model to make it linear at large doses per fraction. Qualitatively, the modification implies a reduction of biological effect with respect of the standard LQ model for large doses. The purpose of this work is to quantitatively study the effect of the survival curve linearization at high doses for BED calculation relevant to prostate and lung SBRT. Method: We use a previously published linear‐quadratic‐linear model (LQL) to calculate BEDLQL and the equivalent dose in 2Gy fractions EQD2 for several clinically used fractionation schemes of prostate and lung cancer. The LQL model adds a parameter delta that makes the survival curve linear at high doses and is estimated to be 0.05–0.2Gy‐1. We compare BED and EQD2 for the LQ and LQL models. Results: For prostate cancer if alpha/beta=1.5–3Gy the difference in EQD2 between the LQ and LQL is 5 to 10% for cases with delta=0.2Gy‐1 and moderate dose per fraction d=3–4.3Gy. For extreme hypofractionation the effect is more pronounced with differences of up to 35% in EQD2. For the lung cancer SBRT, the BEDLQL for doses of 10‐12Gy is 3–25% smaller than BEDLQ with alpha/beta=10Gy while even bigger differences ranging from 10 to 40% are possible for normal tissues alpha/beta=3Gy. Conclusions: There is a clear interplay of the alpha/beta ratio and the parameter delta in terms of BED and EQD2 calculations for different fractionations. The impact of the parameter delta is significantly higher for low alpha/beta ratios. This is particularly important for the case of prostate cancer where a large value of delta (0.2Gy‐1 or so) could bring EQD2 below acceptable therapeutic.

Studies on pH and thermal stability of novel purified L-asparaginase from Pectobacterium carotovorum MTCC 1428

Glutaminase free L-asparaginase is known to be an excellent anticancer agent. In the present study, the combined effect of pH and temperature on the performance of purified novel L-asparaginase from Pectobacterium carotovorum MTCC 1428 was studied under assay conditions using response surface methodology (RSM). Deactivation studies and thermodynamic parameters of this therapeutically important enzyme were also investigated. The optimum pH and temperature of the purified L-asparaginase were found to be 8.49 and 39.3 degrees C, respectively. The minimum deactivation rate constant (k(d)) and maximum half life (t1/2) were found to be 0.041 min(-1) and 16.9 h, respectively at pH of 8.6 and 40 degreesC. Thermodynamic parameters (deltaG, deltaH, deltaS, and activation energies) were also evaluated for purified L-asparaginase. The probable mechanism of deactivation of purified L-asparaginase was explained to an extent on the basis of deactivation studies and thermodynamic parameters.

On a Simple Representation of the Kinnersley-Chitre Metric

A concise form of the Kinnersley-Chitre five-parameter metric for a spinning mass is obtained by exploiting a remarkable similarity between the metric's factor structure and the analogous structure of the Tomimatsu-Sato solutions with even distortion parameter delta. The corresponding general subfamily of asymptotically flat spacetimes containing four arbitrary real parameters is considered, and all configurations describing two extreme Kerr sources separated by a strut are identified and briefly discussed.

A model of photosystem II for the analysis of fast fluorescence rise in plant leaves

The polyphasic patterns of fluorescence induction rise in pea leaves in vivo and after the treatment with ionophores have been studied using a plant efficiency analyzer. To analyze in detail photosystem II (PS II) electron transfer processes, an extended PS II model was applied, which included the sums of exponential functions to specify explicitly the light-driven formation of the transmembrane electric potential (delta psi(t)) as well as pH in the lumen (pHL(t)) and stroma (pHs(t)). PS II model parameters and numerical coefficients in delta psi(t), and pHs(t) were evaluated to fit fluorescence induction data for different experimental conditions: leaf in vivo or after ionophore treatment at low or high light intensity. The model imitated changes in the pattern of fluorescence induction rise due to the elimination of transmembrane potential in the presence of ionophores, when delta psi = 0 and pHL(t), pHS(t) altered to small extent relative to control values in vivo, with maximum delta psi(t) approximately 90 MB and delta psi(t) approximately 40 MB, for the stationary state at deltapH aproximately equal to 1.8. As the light intensity was increased from 300 to 1200 micromol x m(-2) x s(-1), the heat dissipation rate constants increased threefold for nonradiative recombination of P680+Phe- and by approximately 30% for P680+Q(A)-. The parameters delta psi, pH(S) and pH(L) were analyzed as factors of PS II redox state populations and fluorescence yield. The kinetic mechanism of qE quenching is discussed, which is related with light induced pH(L) lumen acidification, when Q(A)- and P680+ recombination probability increases to regulate the QA reduction.

Spin Transport in a One-Dimensional Anisotropic Heisenberg Model

We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Δ is varied spin transport changes from ballistic for Δ<1 to anomalous at the isotropic point Δ=1, to diffusive for finite Δ>1, ending up as a perfect isolator in the Ising limit of infinite Δ. Using perturbation theory for large Δ a quantitative prediction is made for the dependence of diffusion constant on Δ.

OpenXXZSpin Chain: Nonequilibrium Steady State and a Strict Bound on Ballistic Transport

An explicit matrix product ansatz is presented, in the first two orders in the (weak) coupling parameter, for the nonequilibrium steady state of the homogeneous, nearest neighbor Heisenberg XXZ spin 1/2 chain driven by Lindblad operators which act only at the edges of the chain. The first order of the density operator becomes, in the thermodynamic limit, an exact pseudolocal conservation law and yields-via the Mazur inequality-a rigorous lower bound on the high-temperature spin Drude weight. Such a Mazur bound is a nonvanishing fractal function of the anisotropy parameter Δ for |Δ|<1.

A Fuzzy LP Approach to Option Portfolio

Abstract: Owing to the fluctuation of financial market from time to time,the volatility and stock price may occur imprecisely in the real world. Therefore, it is natural to consider the fuzzy volatility and fuzzy stock price in the financial market. Under these assumptions,the theoretical price deduced by Black–Scholes formula are will turn into the fuzzy numbers, and the derivatives, called the Greek parameters delta, gamma, of the BS model are also fuzzy numbers. An option portfolio considering these fuzzy numbers will be more accord with actual situations. In this paper, we propose a fuzzy programming model of option portfolio based a ranking criterion of fuzzy numbers, which the fuzzy option portfolio model is converted into a classical linear programming problem. Finally, a numerical example is given to illustrate the validity of the method. Key words: Ranking Criterion; Option portfolio; Fuzzy Linear Programming; Delta-Gamma Neutral

Measuring relevance between discrete and continuous features based on neighborhood mutual information

Measures of relevance between features play an important role in classification and regression analysis. Mutual information has been proved an effective measure for decision tree construction and feature selection. However, there is a limitation in computing relevance between numerical features with mutual information due to problems of estimating probability density functions in high-dimensional spaces. In this work, we generalize Shannon’s information entropy to neighborhood information entropy and propose a measure of neighborhood mutual information. It is shown that the new measure is a natural extension of classical mutual information which reduces to the classical one if features are discrete; thus the new measure can also be used to compute the relevance between discrete variables. In addition, the new measure introduces a parameter delta to control the granularity in analyzing data. With numeric experiments, we show that neighborhood mutual information produces the nearly same outputs as mutual information. However, unlike mutual information, no discretization is required in computing relevance when used the proposed algorithm. We combine the proposed measure with four classes of evaluating strategies used for feature selection. Finally, the proposed algorithms are tested on several benchmark data sets. The results show that neighborhood mutual information based algorithms yield better performance than some classical ones.

Conduction electron scattering and spin flipping at sputtered Co/Ni interfaces

Current-perpendicular-to-plane magnetoresistance (CPP-MR) measurements let us quantify conduction electron scattering and spin flipping at a sputtered ferromagnetic/ferromagnetic $(\text{F}1/\text{F}2=\text{Co}/\text{Ni})$ interface, with important consequences for CPP-MR and spin-torque experiments with perpendicular anisotropy. We use ferromagnetically coupled ${[\text{Ni}/\text{Co}]}_{n}\text{Ni}$ multilayers, and Py-based, symmetric double exchange-biased spin valves containing inserts of ferromagnetically coupled ${[\text{Co}/\text{Ni}]}_{n}\text{Co}$ or ${[\text{Ni}/\text{Co}]}_{n}\text{Ni}$ multilayers, to derive Co/Ni interface specific resistances $A{R}_{\text{Co}/\text{Ni}}^{\ensuremath{\uparrow}}={0.03}_{\ensuremath{-}0.03}^{+0.02}\text{ }\text{f}\ensuremath{\Omega}\text{ }{\text{m}}^{2}$ and $A{R}_{\text{Co}/\text{Ni}}^{\ensuremath{\downarrow}}=1.00\ifmmode\pm\else\textpm\fi{}0.07\text{ }\text{f}\ensuremath{\Omega}\text{ }{\text{m}}^{2}$, and interface spin-flipping parameter ${\ensuremath{\delta}}_{\text{Co}/\text{Ni}}=0.35\ifmmode\pm\else\textpm\fi{}0.05$. The specific resistances are consistent with our no-free-parameter calculations for an interface thickness between 2 and 4 monolayers that is compatible with expectations.

Skewness in hedge funds returns: classical skewness coefficients vs Azzalini's skewness parameter

PurposeRecent literature discusses the persistence of skewness and tail risk in hedge fund returns. The aim of this paper is to suggest an alternative skewness measure, Azzalini's skewness parameter delta, which is derived as the normalized shape parameter from the skew‐normal distribution. The paper seeks to analyze the characteristics of this skewness measure compared with other indicators of skewness and to employ it in some typical risk and performance measurements.Design/methodology/approachThe paper first provides an overview of the skew‐normal distribution and its mathematical formulation. Then it presents some empirical estimations of the skew‐normal distribution for hedge fund returns and discusses the characteristics of using delta with respect to classical skewness coefficients. Finally, it illustrates how delta can be used in risk management and in a performance measurement context.FindingsThe results highlight the advantages of Azzalini's skewness parameter delta, especially with regard to its interpretation. Delta has a limpid financial interpretation as a skewness shock on normally distributed returns. The paper also derives some important characteristics of delta, including that it is more stable than other measures of skewness and inversely related to popular risk measures such as the value‐at‐risk (VaR) and the conditional value‐at‐risk (CVaR).Originality/valueThe contribution of the paper is to apply the skew‐normal distribution to a large sample of hedge fund returns. It also illustrates that using Azzalini's skewness parameter delta as a skewness measure has some advantages over classical skewness coefficients. The use of the skew‐normal and related distributions is a relatively new, but growing, field in finance and not much has been published on the topic. Skewness itself, however, has been the subject of a great deal of research. Therefore, the results contribute to three fields of research: skewed distributions, risk measurement, and hedge fund performance.

Short-baseline electron neutrino disappearance, tritium beta decay, and neutrinoless double-beta decay

We consider the interpretation of the MiniBooNE low-energy anomaly and the Gallium radioactive source experiments anomaly in terms of short-baseline electron neutrino disappearance in the framework of 3+1 four-neutrino mixing schemes. The separate fits of MiniBooNE and Gallium data are highly compatible, with close best-fit values of the effective oscillation parameters Delta m^2 and sin^2 2 theta. The combined fit gives Delta m^2 >~ 0.1 eV^2 and 0.11 < sin^2 2 theta < 0.48 at 2 sigma. We consider also the data of the Bugey and Chooz reactor antineutrino oscillation experiments and the limits on the effective electron antineutrino mass in beta-decay obtained in the Mainz and Troitsk Tritium experiments. The fit of the data of these experiments limits the value of sin^2 2 theta below 0.10 at 2 sigma. Considering the tension between the neutrino MiniBooNE and Gallium data and the antineutrino reactor and Tritium data as a statistical fluctuation, we perform a combined fit which gives Delta m^2 \simeq 2 eV and 0.01 < sin^2 2 theta < 0.13 at 2 sigma. Assuming a hierarchy of masses m_1, m_2, m_3 << m_4, the predicted contributions of m_4 to the effective neutrino masses in beta-decay and neutrinoless double-beta-decay are, respectively, between about 0.06 and 0.49 and between about 0.003 and 0.07 eV at 2 sigma. We also consider the possibility of reconciling the tension between the neutrino MiniBooNE and Gallium data and the antineutrino reactor and Tritium data with different mixings in the neutrino and antineutrino sectors. We find a 2.6 sigma indication of a mixing angle asymmetry.

Zigzag edge modes in aZ2topological insulator: Reentrance and completely flat spectrum

The spectrum and wave function of helical edge modes in Z_2 topological insulator are derived on a square lattice using Bernevig-Hughes-Zhang (BHZ) model. The BHZ model is characterized by a "mass" term M (k) that is parameterized as M (k) = Delta - B k^2. A topological insulator realizes when the parameters Delta and B fall on the regime, either 0 < Delta /B < 4 or 4 < Delta /B < 8. At Delta /B = 4, which separates the cases of positive and negative (quantized) spin Hall conductivities, the edge modes show a corresponding change that depends on the edge geometry. In the (1,0)-edge, the spectrum of edge mode remains the same against change of Delta /B, although the main location of the mode moves from the zone center for Delta /B < 4, to the zone boundary for Delta /B > 4 of the 1D Brillouin zone. In the (1,1)-edge geometry, the group velocity at the zone center changes sign at Delta /B = 4 where the spectrum becomes independent of the momentum, i.e. flat, over the whole 1D Brillouin zone. Furthermore, for Delta/B < 1.354..., the edge mode starting from the zone center vanishes in an intermediate region of the 1D Brillouin zone, but reenters near the zone boundary, where the energy of the edge mode is marginally below the lowest bulk excitations. On the other hand, the behavior of reentrant mode in real space is indistinguishable from an ordinary edge mode.

Coordination‐Induced Spin Crossover (CISCO) through Axial Bonding of Substituted Pyridines to Nickel–Porphyrins: σ‐Donor versus π‐Acceptor Effects

Nickel-porphyrins, with their rigid quadratic planar coordination framework, provide an excellent model to study the coordination-induced spin crossover (CISCO) effect because bonding of one or two axial ligands to the metal center leads to a spin transition from S=0 to S=1. Herein, both equilibrium constants K(1S) and K(2), and for the first time also the corresponding thermodynamic parameters DeltaH(1S), DeltaH(2), DeltaS(1S), and DeltaS(2), are determined for the reaction of a nickel-porphyrin (Ni-tetrakis(pentafluorophenyl)porphyrin) with different 4-substituted pyridines by temperature-dependent NMR spectroscopy. The association constants K(1S) and K(2) are correlated with the basicity of the 4-substituted pyridines (R: OMe>H>CO(2)Et>NO(2)) whereas the DeltaH(1S) values exhibit a completely different order (OMe<H>CO(2)Et>NO(2)). 4-Nitropyridine exhibits the largest binding enthalpy, which, however, is overcompensated by a large negative binding entropy. We attribute the large association enthalpy of nitropyridine with porphyrin to the back donation of electrons from the Ni d(xz) and d(yz) orbitals into the pi orbitals of pyridine, and the negative association entropy to a decrease in vibrational and internal rotation entropy of the more rigid porphyrin-pyridine complex. Back donation for the nitro- and cyanopyridine complexes is also confirmed by IR spectroscopy, and shows a shift of the N-O and C-N vibrations, respectively, to lower wave numbers. X-ray structures of 2:1 complexes with nitro-, cyano-, and dimethylaminopyridine provide further indication of a back donation. A further trend has been observed: the more basic the pyridine the larger is K(1S) relative to K(2). For nitropyridine K(2) is 17 times larger than K(1S) and in the case of methoxypyridine K(2) and K(1S) are almost equal.

Bistable or Oscillating State Depending on Station and Temperature in Three‐Station Glycorotaxane Molecular Machines

High-yield, straightforward synthesis of two- and three-station [2]rotaxane molecular machines based on an anilinium, a triazolium, and a mono- or disubstituted pyridinium amide station is reported. In the case of the pH-sensitive two-station molecular machines, large-amplitude movement of the macrocycle occurred. However, the presence of an intermediate third station led, after deprotonation of the anilinium station, and depending on the substitution of the pyridinium amide, either to exclusive localization of the macrocycle around the triazolium station or to oscillatory shuttling of the macrocycle between the triazolium and monosubstituted pyridinium amide station. Variable-temperature (1)H NMR investigation of the oscillating system was performed in CD(2)Cl(2). The exchange between the two stations proved to be fast on the NMR timescale for all considered temperatures (298-193 K). Interestingly, decreasing the temperature displaced the equilibrium between the two translational isomers until a unique location of the macrocycle around the monosubstituted pyridinium amide station was reached. Thermodynamic constants K were evaluated at each temperature: the thermodynamic parameters DeltaH and DeltaS were extracted from a Van't Hoff plot, and provided the Gibbs energy DeltaG. Arrhenius and Eyring plots afforded kinetic parameters, namely, energies of activation E(a), enthalpies of activation DeltaH( not equal), and entropies of activation DeltaS( not equal). The DeltaG values deduced from kinetic parameters match very well with the DeltaG values determined from thermodynamic parameters. In addition, whereas signal coalescence of pyridinium hydrogen atoms located next to the amide bond was observed at 205 K in the oscillating rotaxane and at 203 K in the two-station rotaxane with a unique location of the macrocycle around the pyridinium amide, no separation of (1)H NMR signals of the considered hydrogen atoms was seen in the corresponding nonencapsulated thread. It is suggested that the macrocycle acts as a molecular brake for the rotation of the pyridinium-amide bond when it interacts by hydrogen bonding with both the amide NH and the pyridinium hydrogen atoms at the same time.

Influence of pocket‐size on misaligned hole‐entry journal bearing

PurposeHole‐entry hybrid journal bearings are widely used in many applications owing to their favourable characteristics. Ever increasing technological developments demand much improved performance from these class of bearings operating under the most stringent, exact and precise conditions. Therefore, it becomes imperative that the hole‐entry journal bearings be designed on the basis of more accurately predicted bearing characteristics data. The purpose of this paper is to describe a theoretical study to demonstrate the combined influence of the effect of pocket size at the outlet of supply holes and the journal misalignment on the performance of an orifice compensated hole‐entry hybrid journal bearing system.Design/methodology/approachFinite element method is used to solve the Reynolds equation governing the flow of an incompressible lubricant in the clearance space between the journal and bearing together with equation of flow through an orifice. The journal misalignment has been accounted for by defining a pair of misalignment parameters sigma and delta. The effect of pocket size at the outlet of supply holes has been accounted by defining a non‐dimensional parameter which is function of diameter of pocket and journal diameter.FindingsThe results presented in this paper indicate that the effect of journal misalignment is, in general, to cause a reduction in bearing dynamic characteristics parameters whereas the effect of pocket size is to slightly compensate this loss. Performance of a two lobe four recessed journal bearing, a proper selection of bearing offset factor along with type of restrictor (capillary or orifice) is essential.Originality/valueThis paper presents valuable data relating to hole‐entry hybrid journal bearings useful for bearing designers.

Characterization of the surface tension and solubility parameter of epoxy resin by using inverse gas chromatography

Inverse gas chromatography (IGC) was used to measure the surface tension and solubility parameter of E51 epoxy resin in this work. By using the Schultz method, decane, nonane, octane and heptane were chosen as the neutral probes to calculate the dispersive surface tensions (gamma(D)). Based on the Good-van Oss equation, the specific surface tension (gamma(SP)) of E51 epoxy resin was calculated with the acidic probe of dichloromethane and the basic probe of toluene. The results showed that the gamma(D) and gamma(SP) of the E51 resin decreased linearly with the increase of temperature. According to the Flory-Huggins parameters (chi) between the resin and a series of probes, the solubility parameters (delta) of E51 resin at different temperatures were estimated using the method developed by DiPaola-Baranyi and Guillet. It was found that the values of delta of the E51 resin were 11.78, 11.57, 11.48 and 11.14 MPa1/2 at 30, 40, 50 and 60 degrees C, respectively. The dispersive component (delta(D)) and the specific component (delta(SP)) of solubility parameter at different temperatures of the E51 resin were investigated according to the relationships between surface tension, cohesion energy and solubility parameter. The results showed that the values of delta(D) were higher than those of delta(SP) for the epoxy resin, and both of them decreased with the increase of temperature.

Influence of chemical activation of a 35% hydrogen peroxide bleaching gel on its penetration and efficacy—In vitro study

Objectives The aim of this study was to evaluate the effects of chemical activation of hydrogen peroxide (HP) gel on colour changes and penetration through the tooth structure. Methods One hundred and four bovine incisors were used. One dentine (CD) disc and one enamel–dentine (ED) disc were prepared from each tooth. They were positioned over artificial pulpal chambers and the bleaching was performed with an experimental 35% HP gel. Two control and six experimental groups were prepared. In the positive control group (PC) no chemical activator was used. In the negative control group (NC) the specimens did not receive any bleaching. Each experimental group received a different chemical activator (manganese gluconate—MG; manganese chlorite—MC; ferrous sulphate—FS; ferrous chlorite—FC; and mulberries root extract—MRE). After the bleaching procedure a sample of solution was collected from the artificial pulpal chamber and the HP concentration was measured. The data were analysed using ANOVA, Tukey's, and Dunnett's tests. Results The groups MG and FS showed a significantly lower penetration of HP than the PC group. For the parameter Delta E, all the groups, with the exception of the group MRE, showed a significantly higher means in relation to the PC group in ED colour. For dentine colour, just the groups MG and FS had significant differences in relation to PC. Conclusions The addition of MG and FS decreases the penetration of HP. The chemical activation using metal salts tested was effective in increasing the bleaching effect.

New interpretation of the Haasen plot for solute-strengthened alloys

The Haasen plot (inverse activation area 1/Delta alpha vs. offset flow stress sigma-sigma(s)) for solute-strengthened alloys is usually assumed additive, 1/Delta alpha = 1/Delta alpha(s) + 1/Delta alpha(f), with 1/Delta alpha(f) similar to beta(sigma-sigma(s)) due to forest interactions. Experiments often show a slope textlessbeta. Here, a model for the dislocation activation enthalpy is proposed that predicts a slope 1/(Delta alpha(s)sigma(s)) determined only by solute parameters Delta alpha(s) and sigma(s) and not directly connected to forest hardening. This parameter-free prediction agrees well with a wide range of experiments on Al-X alloys at T = 78 K. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Relations between the Fractional Stokes−Einstein and Nernst−Einstein Equations and Velocity Correlation Coefficients in Ionic Liquids and Molten Salts

It is often asserted that deviation from the Nernst-Einstein relation (NE) between the molar conductivity (Lambda) and ion self-diffusion coefficients (D(i)) in ionic liquids (ILs) and molten salts is evidence for ion pairing. The NE was originally derived for noninteracting ions, as in an infinitely dilute electrolyte solution. In reality, mass, charge, momentum, and energy transport processes in ILs and molten salts involve correlated interionic collisions, caging, and vortex motions, as in any other dense liquid. Phenomenological theory using nonequilibrium thermodynamics and literature molecular dynamics simulations shows that deviations from the simple NE expression occur due to differences in cross-correlations of ionic velocities. ILs have also been shown, like molecular liquids generally, and model fluids such as the Lennard-Jones, to fit the fractional form of the Stokes-Einstein relation, D(i)/T proportional to (1/eta)(t) and Lambda proportional to (1/eta)(t), where eta is the shear viscosity. Here, it is shown that when this is the case, the NE deviation parameter Delta is then a constant, independent of temperature and pressure (consistent with experiment) and the value of the parameter t; it is a function of the ionic charges and volumes, but not the masses. Therefore, Delta is not a measure of "ionicity": it is necessary to seek other independent evidence to determine whether ion pairing is present in a given ionic liquid or molten salt. The use of "apparent" transport numbers derived from self-diffusion coefficients to describe charge transport in pure salts is argued to be unnecessary.

Triaxial collapse and virialisation of dark-matter haloes

We reconsider the ellipsoidal-collapse model and extend it in two ways: We modify the treatment of the external gravitational shear field, introducing a hybrid model in between linear and non-linear evolution, and we introduce a virialisation criterion derived from the tensor virial theorem to replace the ad-hoc criterion employed so far. We compute the collapse parameters delta_c and Delta_v and find that they increase with ellipticity e and decrease with prolaticity p. We marginalise them over the appropriate distribution of e and p and show the marginalised results as functions of halo mass and virialisation redshift. While the hybrid model for the external shear gives results very similar to those obtained from the non-linear model, ellipsoidal collapse changes the collapse parameters typically by (20...50)%, in a way increasing with decreasing halo mass and decreasing virialisation redshift. We qualitatively confirm the dependence on mass and virialisation redshift of a fitting formula for delta_c, but find noticeable quantitative differences in particular at low mass and high redshift. The derived mass function is in good agreement with mass functions recently proposed in the literature.