Extrapolative Method Research Articles

X marks the spot: Accurate energies from intersecting extrapolations of continuum quantum Monte Carlo data.

We explore the application of an extrapolative method that yields very accurate total and relative energies from variational and diffusion quantum Monte Carlo (VMC and DMC) results. For a trial wave function consisting of a small configuration interaction (CI) wave function obtained from full CI quantum Monte Carlo and reoptimized in the presence of a Jastrow factor and an optional backflow transformation, we find that the VMC and DMC energies are smooth functions of the sum of the squared coefficients of the initial CI wave function and that quadratic extrapolations of the non-backflow VMC and backflow DMC energies intersect within uncertainty of the exact total energy. With adequate statistical treatment of quasi-random fluctuations, the extrapolate and intersect with polynomials of order two method is shown to yield results in agreement with benchmark-quality total and relative energies for the C2, N2, CO2, and H2O molecules, as well as for the C2 molecule in its first electronic singlet excited state, using only small CI expansion sizes.

Finding the Prior Leaf

Fragments of Latin-script medieval manuscript books evoke the whole to which they once belonged, encouraging us to build a mental model of the now-broken whole. Discussing fragments thus requires a way to describe not just the surviving objects and how they relate to their current context, but also how they related to the original. At the most basic level, relating individual pieces to an original codex requires identifying the fragment’s physical role and orientation in the codex. Then, if the text of the fragment is known, extrapolation can be used to reconstruct leaves, gatherings, and codicological units. An extrapolative method is documented and validated using experimental data and examples from the Fragmentarium web platform.

Role of NF-κB in Platelet Function.

Platelets are megakaryocyte-derived fragments lacking nuclei and prepped to maintain primary hemostasis by initiating blood clots on injured vascular endothelia. Pathologically, platelets undergo the same physiological processes of activation, secretion, and aggregation yet with such pronouncedness that they orchestrate and make headway the progression of atherothrombotic diseases not only through clot formation but also via forcing a pro-inflammatory state. Indeed, nuclear factor-κB (NF-κB) is largely implicated in atherosclerosis and its pathological complication in atherothrombotic diseases due to its transcriptional role in maintaining pro-survival and pro-inflammatory states in vascular and blood cells. On the other hand, we know little on the functions of platelet NF-κB, which seems to function in other non-genomic ways to modulate atherothrombosis. Therein, this review will resemble a rich portfolio for NF-κB in platelets, specifically showing its implications at the levels of platelet survival and function. We will also share the knowledge thus far on the effects of active ingredients on NF-κB in general, as an extrapolative method to highlight the potential therapeutic targeting of NF-κB in coronary diseases. Finally, we will unzip a new horizon on a possible extra-platelet role of platelet NF-κB, which will better expand our knowledge on the etiology and pathophysiology of atherothrombosis.

الانتهاكات الإسرائيلية بحق دور العبادة في قطاع غزة وموقف القانون الدولي الإنساني من ذلك

Places of worship in Gaza Strip have been subjected to many deliberate aggressions and destructions by the Israeli occupation forces, during the three wars against Gaza. This comes in clear violation of the rules of international humanitarian law, which emphasizes protection of these places from any aggression and excluding them from the cycle of conflict, between the States. Throughout this study, the researcher highlights the violations against places of worship during the aggression on Gaza Strip and the position of international humanitarian law. The methodology used in this research is the extrapolative method. It follows the international conventions and what these conventions have approved in relation to the subject of the study. The researcher also uses the analytical descriptive approach through reading and analysis of legal texts related to armed conflicts, which are mentioned in the international conventions; in the four Geneva Conventions of 1949, in the Additional Protocols I and II in 1977, and in the literature, books and publications related to this area. In addition to the practical approach, since the study is applied to Gaza Strip. The research concluded the following: The Israeli occupation forces destroyed many places of worship during its wars on the Gaza Strip in clear violation and a flagrant violation of international conventions, particularly the Hague Convention of 1954, which confirmed its protection of such places during any aggression. The violations of places of worship during the wars against Gaza Strip constitute war crimes as affirmed by the Rome Statute. This requires prosecution of the perpetrators, bringing them to justice, holding them accountable for their crimes.

Extrapolative phase retrieval based on a hybrid of PhaseCut and alternating projection techniques

Phase retrieval is an important research topic in the optics field. It is aimed to reconstruct the wave-front from the intensity of the far-field diffracted field. To deal with the local stagnation of conventional iterative Fourier-based algorithms, an interesting recent approach formulates the phase retrieval problem as a tractable relaxation (called PhaseCut). Despite its powerful global capability, the operation of recasting a vector problem into a matrix problem leads to higher computational cost, which limits its use in far-field patterns with high resolution. In this paper, we develop an extrapolative alternating projection algorithm to cope with the reconstruction of high-resolution phase pattern. The algorithm starts with a low-resolution phase estimation solved by PhaseCut from the far-field amplitudes in the low frequency range, and then refines the initial estimation by an extrapolative iterative projection method, which has a low computational complexity. The iterative process is divided into various periods where the inputs of the algorithm (far-field amplitudes) are extrapolated to include more high frequency information. The main contribution is that the algorithm can quickly converge to the globally optimal and high-resolution solution with a high probability. We verified the validity of the algorithm with various numerical simulations.

Analysis of citrulline and metabolic related amino acids in plasma by derivatization and RPLC. Application of the extrapolative internal standard calibration method

We propose to apply the extrapolative internal standard calibration method (EISM) for quantitative analysis of citrulline and other metabolically related amino acids in plasma by pre-column derivatization, liquid chromatography and UV detection. Whenever derivatization is required and an amino acid-free matrix is nonexistent, the analytical challenge is to detect and correct matrix effects and, also to control the experimental conditions of the chemical reaction, mainly the concentration of the derivatizing reagents.Plasma samples contain free amino acids, non-peptidic amino acids and other amino compounds, such as biogenic amines, that would react with most derivatizing reagents and interfere in the analysis. In this particular work, and considering the scope of the intended application, chromatographic conditions were chosen for the analysis of citrulline, arginine, glutamine, glutamic acid, proline and ornithine by precolumn reaction with FMOC-Cl and RP-HPLC-UV analysis.Linear least square regression of analyte to internal standard (IS) signal ratio versus the amount of spiked standard amino acid were established and linear regression parameters for each curve were calculated. The information provides by an IS, which is also derivatized, can be used to detect matrix effects due to the chemical reaction. This calibration method was validated and the figures of merit were estimated.

ConReg-R: Extrapolative recalibration of the empirical distribution of p-values to improve false discovery rate estimates

BackgroundFalse discovery rate (FDR) control is commonly accepted as the most appropriate error control in multiple hypothesis testing problems. The accuracy of FDR estimation depends on the accuracy of the estimation of p-values from each test and validity of the underlying assumptions of the distribution. However, in many practical testing problems such as in genomics, the p-values could be under-estimated or over-estimated for many known or unknown reasons. Consequently, FDR estimation would then be influenced and lose its veracity.ResultsWe propose a new extrapolative method called Constrained Regression Recalibration (ConReg-R) to recalibrate the empirical p-values by modeling their distribution to improve the FDR estimates. Our ConReg-R method is based on the observation that accurately estimated p-values from true null hypotheses follow uniform distribution and the observed distribution of p-values is indeed a mixture of distributions of p-values from true null hypotheses and true alternative hypotheses. Hence, ConReg-R recalibrates the observed p-values so that they exhibit the properties of an ideal empirical p-value distribution. The proportion of true null hypotheses (π0) and FDR are estimated after the recalibration.ConclusionsConReg-R provides an efficient way to improve the FDR estimates. It only requires the p-values from the tests and avoids permutation of the original test data. We demonstrate that the proposed method significantly improves FDR estimation on several gene expression datasets obtained from microarray and RNA-seq experiments.ReviewersThe manuscript was reviewed by Prof. Vladimir Kuznetsov, Prof. Philippe Broet, and Prof. Hongfang Liu (nominated by Prof. Yuriy Gusev).

Extrapolative Version of the Indirect Calibration Method

In this work, an idea is theoretically and experimentally developed the adaptation of the indirect method to calibration in the extrapolative mode. The proposed approach enables estimation of the analytical results through an extrapolative method in the case of both positive and negative slopes of calibration dependence. The principle of the method has been presented and its analytical usefulness has been experimentally tested, giving special attention to examination of the possibility of overcoming interferences. The experimental examples encompass the determination of phosphate and chlorite by flame atomic absorption spectrometry (FAAS) and UV/VIS spectrophotometry, respectively, in the presence of different strong interferents. It has been proven that the method can be an effective calibration tool provided the specific instrumental and chemical conditions are fulfilled.

Antinucleating action of polystyrene on the isothermal cold crystallization of poly(ethylene terephthalate)

AbstractThe effect of polystyrene (PS) on the kinetics of the cold crystallization of poly(ethylene terephthalate) (PET) was thoroughly investigated. The PET/PS blends were essentially immiscible, as observed by dynamic mechanical thermal analysis, which showed two distinct glass‐transition temperatures, and by scanning electron microscopy. The neat PET and its blends were isothermally cold‐crystallized at various temperatures, and the kinetic parameters were determined with the Avrami approach. PET and its blends presented values of the Avrami exponent close to 2, and the kinetic constant increased with the crystallization temperature increasing. For all the crystallization temperatures studied, the presence of only 1 wt % PS significantly reduced the rate of cold crystallization of PET. A further increase in the PS concentration did not show any significant influence. The blends presented higher values of the activation energy for cold crystallization, which was estimated from Arrhenius plots. The equilibrium melting temperature of neat PET was determined on the basis of the linear Hoffman–Weeks extrapolative method to be ∼ 255°C. This value decreased in the presence of PS, and this suggested limited solubility between PET and PS. From the spherulitic growth equation proposed by Hoffman and Lauritzen, the nucleation parameter was obtained, and it was shown to be higher for the neat PET than for the blends. Moreover, a transition of regimes (I → II) was observed in both PET and its blends. From the investigations conducted here, it is clear that PS in small amounts causes a reduction in the rate of PET crystallization, acting as an antinucleating agent. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Enthalpies of vaporization of N,N-dialkyl monamides at 298.15 K

Enthalpies of vaporization of several N,N-dialkyl monamides have been measured by correlation gas chromatography. The enthalpy values of the compounds are derived by an extrapolative method using the known enthalpy of vaporization values of basic amides at 298.15 K, used as standards. First order molecular connectivity valence indices of these amides ( 1 χ ν ) as described by Kier and Hall have been evaluated and are found to have an excellent correlation with measured enthalpies of vaporization in addition to several other indices, such as, solvent accessible surface area (SAS), molecular surface area (MSA) and solvent excluded volume (SEV). The quantitative structure–property relationship (QSPR) approach is used to predict the enthalpies of vaporization from molecular connectivity valence index.

A relation based measure of semantic similarity for Gene Ontology annotations

BackgroundVarious measures of semantic similarity of terms in bio-ontologies such as the Gene Ontology (GO) have been used to compare gene products. Such measures of similarity have been used to annotate uncharacterized gene products and group gene products into functional groups. There are various ways to measure semantic similarity, either using the topological structure of the ontology, the instances (gene products) associated with terms or a mixture of both. We focus on an instance level definition of semantic similarity while using the information contained in the ontology, both in the graphical structure of the ontology and the semantics of relations between terms, to provide constraints on our instance level description.Semantic similarity of terms is extended to annotations by various approaches, either though aggregation operations such as min, max and average or through an extrapolative method. These approaches introduce assumptions about how semantic similarity of terms relates to the semantic similarity of annotations that do not necessarily reflect how terms relate to each other.ResultsWe exploit the semantics of relations in the GO to construct an algorithm called SSA that provides the basis of a framework that naturally extends instance based methods of semantic similarity of terms, such as Resnik's measure, to describing annotations and not just terms. Our measure attempts to correctly interpret how terms combine via their relationships in the ontological hierarchy. SSA uses these relationships to identify the most specific common ancestors between terms. We outline the set of cases in which terms can combine and associate partial order constraints with each case that order the specificity of terms. These cases form the basis for the SSA algorithm. The set of associated constraints also provide a set of principles that any improvement on our method should seek to satisfy.ConclusionWe derive a measure of semantic similarity between annotations that exploits all available information without introducing assumptions about the nature of the ontology or data. We preserve the principles underlying instance based methods of semantic similarity of terms at the annotation level. As a result our measure better describes the information contained in annotations associated with gene products and as a result is better suited to characterizing and classifying gene products through their annotations.

Effect of small amount of poly(ethylene naphthalate) on isothermal crystallization and spherulitic morphology of poly(trimethylene terephthalate)

The effect of a small amount of poly(ethylene naphthalate) (PEN) in its blends with poly(trimethylene terephthalate) (PTT) on isothermal melt-crystallization kinetics and spherulitic morphology of the blends was thoroughly investigated. The maximum PEN content in the blends was 9 wt%. Due to the single composition-dependent glass transition temperature ( T g) that was observed for each blend, these blends appeared to be miscible in the amorphous state. After isothermal crystallization from the melt state, the neat PTT and its blends with PEN exhibited either double or triple melting endotherms. The triple endothermic peaks were observed in both the neat PTT and the blends when being crystallized at crystallization temperatures ( T c) of less than or equal to ∼195 °C. The equilibrium melting temperature ( T m 0 ) for the neat PTT was determined based on the linear Hoffman–Weeks extrapolative method to be ∼248 °C. Such values for the blends were found to decrease with the addition and increasing amount of PEN. Both the neat PTT and the blends were isothermally crystallized over the T c range of 190–205 °C. At a given T c, the 97PTT/3PEN blend exhibited a half-time of crystallization ( t 0.5) value that was lower, while it exhibited reciprocal half-time ( t 0.5 - 1 ), Avrami rate constant ( K A), and spherulitic growth rate ( G) values that were greater, than those of the neat PTT. With further increase in the PEN content, the t 0.5 value increased, while the t 0.5 - 1 , K A, and G values decreased. Analysis of the G values based on the Lauritzen–Hoffman's (LH) secondary nucleation theory showed that the neat PTT and the 91PTT/9PEN blend exhibited a regime II→III transition at ∼194 °C (∼467.2 K), while no regime transition was observed for the other two blends. The lateral and the fold surface free energies ( σ and σ e) and the work of chain folding ( q) for the neat PTT and the blends were 19.4, 30.2–46.3 erg cm −2, and 2.4–3.6 kcal mol −1, respectively. Lastly, the effect of both the T c and the PEN content on morphology and texture of the PTT spherulites was also investigated and the results showed that the texture of the spherulites became coarser with increasing T c and PEN content.

Sequence distribution and crystal structure of poly(ethylene/butylene terephthalate) copolyesters compared with poly(ethylene/trimethylene terephthalate) copolyesters

AbstractPoly(ethylene/butylene terephthalate) (EB) copolyesters were synthesized from ethylene glycol (EG), 1,4‐butanediol (BDO), and dimethyl terephthalate with different molar volume ratios. The constitutional units, characterized by 13C NMR, revealed a random distribution in the molecular chain. Nevertheless, crystallites formed across the full range of EG/BDO composition can be observed with the use of a differential scanning calorimeter and a wide angle X‐ray diffraction method. The reflection profile of the EB copolyesters was deconvoluted. Also, in the poly(ethylene/trimethylene terephthalate) (ET) copolyesters previously studied, the crystal structure was dominated by the sequence distribution of the copolyesters. The crystal structures of EB and ET copolyesters, in comparison with the different constitutional repeating units in the molecular chain, are discussed in this study. The glass transition temperature of EB and ET copolyesters were analyzed, considering the copolymer composition and the sequencing of the monomers, and their values were compared to the Johnston's equation. In addition, the analysis of the melting temperatures of both the EB and the ET copolyesters was carried out. The equilibrium melting temperatures of both copolyesters were calculated according to the Hoffman‐Weeks extrapolative method. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 405–419, 2007

Leading Indicators and Spatial Interactions: A Crime‐Forecasting Model for Proactive Police Deployment

We develop a leading indicator model for forecasting serious property and violent crimes based on the crime attractor and displacement theories of environmental criminology. The model, intended for support of tactical deployment of police resources, is at the microlevel scale; namely, 1‐month‐ahead forecasts over a grid system of 141 square grid cells 4000 feet on a side (with approximately 100 blocks per grid cell). The leading indicators are selected lesser crimes and incivilities entering the model in two ways: (1) as time lags within grid cells and (2) time and space lags averaged over grid cells contiguous to observation grid cells. Our validation case study uses 1.3 million police records from Pittsburgh, Pennsylvania, aggregated over the grid system for a 96‐month period ending in December 1998. The study uses the rolling‐horizon forecast experimental design with forecasts made over the 36‐month period ending in December 1998, yielding 5076 forecast errors per model. We estimated the leading indicator model using a robust linear regression model, a neural network, and a proven univariate, extrapolative forecast method for use as a benchmark in Granger causality testing. We find evidence of both the crime attractor and displacement theories. The results of comparative forecast experiments are that the leading indicator models provide acceptable forecasts that are significantly better than the extrapolative method in three out of four cases, and for the fourth there is a tie but poor forecast performance. The leading indicators find 41–53% of large crime volume changes in the three successful cases. The corresponding workload for police is quite acceptable, with on the average 5.2 potential large change cases per month to investigate and with 31% of such cases being positives.

Adaptive time stepping in biomolecular dynamics

We present an adaptive time stepping scheme based on the extrapolative method of Barth and Schlick [LN, J. Chem. Phys. 109, 1633 (1998)] to numerically integrate the Langevin equation with a molecular-dynamics potential. This approach allows us to use (on average) a time step for the strong nonbonded force integration corresponding to half the period of the fastest bond oscillation, without compromising the slow degrees of freedom in the problem. We show with simple examples how the dynamic step size stabilizes integration operators, and discuss some of the limitations of such stability. The method introduced uses a slightly more accurate inner integrator than LN to accommodate the larger steps. The adaptive time step approach reproduces temporal features of the bovine pancreatic trypsin inhibitor (BPTI) test system (similar to the one used in the original introduction of LN) compared to short-time integrators, but with energies that are shifted with respect to both LN, and traditional stochastic versions of Verlet. Although the introduction of longer steps has the effect of systematically heating the bonded components of the potential, the temporal fluctuations of the slow degrees of freedom are reproduced accurately. The purpose of this paper is to display a mechanism by which the resonance traditionally associated with using time steps corresponding to half the period of oscillations in molecular dynamics can be avoided. This has theoretical utility in terms of designing numerical integration schemes--the key point is that by factoring a propagator so that time steps are not constant one can recover stability with an overall (average) time step at a resonance frequency. There are, of course, limitations to this approach associated with the complicated, nonlinear nature of the molecular-dynamics (MD) potential (i.e., it is not as straightforward as the linear test problem we use to motivate the method). While the basic notion remains in the full Newtonian problem, it is easier to see the effects when damping is considered to be physical--that is, we do not view our method as a perturbation of Newtonian dynamics, we associate the damping with the environment, for example, a water bath (with gamma approximately 90 ps(-1)) [Zagrovic and Pande, J. Comp. Chem. 24, 1432 (2003)]. All stochastic approaches to MD are stabilized by large physical damping, but here, we are really using it only to show that the resonance frequency can be obtained. Another simplifying assumption used in this paper is "heavy" hydrogen (we take the hydrogen mass to be 10 amu)--the view here is that we are interested primarily in the slowest degrees of freedom, and this approach has effects similar to bond freezing and united atom treatments of hydrogen. So from the point of view of biomolecular applications, the method described here is best suited to studies in which water is not explicit (so that damping in the problem can really be viewed as environmental interaction), and the interest is in slow dynamics where the effects of hydrogen are neglectable. There are a number of parameters in the LN method and the one derived here, and we cannot in a short paper address all adjustments, so our primary goal as a first pass is to show that stability can be recovered for a set of numerically forced (and hence artificial) bond oscillations, and compare stability to fixed-step methods.

Determination of propane chloroderivatives in environmental samples

Studies on determination of the semi-volatile halogenoorganic compounds (SVHCs) in the sewage samples have been carried out and a new method has been developed. Both the static (headspace) and dynamic (stripping with adsorption on solid phase) method of extraction into gaseous phase turned out to be the most efficient ones for determination of SVHCs in the rich environmental matrixes. In order to determine the low concentrations of SVHCs in the presence of high amounts of inorganic compounds and hardly volatile organic compounds (nitro compounds, dyes, fats and so on), the selective extraction and selection of the adequate parameters of the final analysis (GC-ECD) are required. The developed methods (headspace and stripping) of the semi-volatile compounds determination were subjected to a statistical evaluation by determining the precision of measurement (max. R.S.D. = 6.02) and interval of uncertainty (max. ±6.31%). Application of the conventional extrapolative method for quantitative determination of analytes in the complex environmental matrixes gives the satisfying results.

Miscibility, thermal properties and polymorphism of syndiotactic polystyrene/poly(styrene- co-α-methyl styrene) blends

This work examined the miscibility, crystallization kinetics, melting behavior and crystal structure of syndiotactic polystyrene (sPS)/poly(styrene- co-α-methyl styrene) blends. Differential scanning calorimetry, polarized light microscopy and wide angle X-ray diffraction technique were used to approach the goals. The single composition-dependent T gs of the blends and the melting temperature ( T m) depression of sPS in the blends indicated the miscible characteristic of the blend system at all compositions. Furthermore, the T gs of the blends could be predicted by either of the Gordon–Taylor equation (with K=0.99) or the Fox equation with a slightly higher deviation. The dynamic and isothermal crystallization abilities of sPS were hindered with the incorporation of the miscible copolymer. Complex melting behavior was observed for melt-crystallized pure sPS and its blends as well. Nevertheless, the blends showed relatively simpler melting curves. Comparing with melt-crystallized samples, the cold-crystallized samples exhibited simpler melting behavior. The equilibrium melting temperature ( T m 0) of β form sPS crystal determined from the conventional extrapolative method is 295.2 °C. The Flory–Huggins interaction parameter, χ, of the blends was estimated to be −0.27. The crystal morphology of sPS was disturbed in the blends. Only underdeveloped granular-like crystalline superstructure of sPS exhibited in cold-crystallized blends. Moreover, the existence of the copolymer in the blends apparently reduced the possibility of forming the less stable α form sPS crystals.

Miscibility and thermal properties of melt‐mixed poly(trimethylene terephthalate)/amorphous copolyester blends

AbstractThis work examined the miscibility, crystallization kinetics, and melting behavior of melt‐mixed poly(trimethylene terephthalate) (PTT)/poly(ethylene‐co‐cyclohexane 1,4‐dimethanol terephthalate) (PETG) blends. Differential scanning calorimetry (DSC) and wide‐angle X‐ray diffraction techniques were used to approach the goals. The single composition‐dependent glass‐transition temperatures of the blends and the equilibrium melting temperature (T) depression of PTT in the blends indicated the miscible characteristic of the blend system at all compositions. T of pure PTT, determined with a conventional extrapolative method, was 525.8 K. Furthermore, the Flory–Huggins interaction parameter was estimated to be −0.38. The dynamic and isothermal crystallization abilities of PTT were hindered by the incorporation of PETG. A complex melting behavior was observed for pure PTT and its blends. The observed complex melting behavior resulted mainly from the recrystallization and/or reorganization of the originally formed crystals during the heating scans. For the samples crystallized under the same conditions, the degree of recrystallization and/or reorganization declined with increasing PETG contents in the blends. The preliminary results obtained from the DSC experiments suggested that untraceable interchange reactions occurred in the studied blends. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2264–2274, 2003

The Melting Line, the Crystallization Line, and the Equilibrium Melting Temperature of Isotactic Polystyrene

It is known that the determination of the equilibrium melting temperatures of polymers which show recrystallization during heating is a difficult problem. This is mainly due to the difficulty encountered in determining the melting temperature of the initial lamellae which exist before recrystallization takes place. We are reporting here the results of a study investigating this problem for a representative polymer, namely isotactic polystyrene. Both the crystallization line and the Gibbs−Thomson melting line were constructed on the basis of time- and temperature-dependent SAXS measurements, respectively. When the two lines are plotted on the same graph, they intersect each other at a finite crystal thickness and at temperature of about 243 °C. This temperature is very close to the commonly reported values of the equilibrium melting temperature of isotactic polystyrene obtained using the Hoffman−Weeks extrapolative method, namely 242 °C. However, the value obtained from the intercept of the Gibbs−Thomson melting line is found to lie in the range of 289 ± 5 °C. This new, higher value of the equilibrium melting temperature of isotactic polystyrene might justify the high melting temperatures found for some isotactic polystyrene samples, which were as high as 255 °C for samples with a shish kebab morphology. Finally, DSC curves were recorded for samples crystallized at different crystallization temperatures in order to compare the Gibbs−Thomson melting line obtained by the SAXS measurements and that obtained by the DSC curves. The result of such comparison showed a good agreement.

Langevin stabilization of molecular dynamics

In this paper we show the possibility of using very mild stochastic damping to stabilize long time step integrators for Newtonian molecular dynamics. More specifically, stable and accurate integrations are obtained for damping coefficients that are only a few percent of the natural decay rate of processes of interest, such as the velocity autocorrelation function. Two new multiple time stepping integrators, Langevin Molly (LM) and Brünger–Brooks–Karplus–Molly (BBK–M), are introduced in this paper. Both use the mollified impulse method for the Newtonian term. LM uses a discretization of the Langevin equation that is exact for the constant force, and BBK–M uses the popular Brünger–Brooks–Karplus integrator (BBK). These integrators, along with an extrapolative method called LN, are evaluated across a wide range of damping coefficient values. When large damping coefficients are used, as one would for the implicit modeling of solvent molecules, the method LN is superior, with LM closely following. However, with mild damping of 0.2 ps−1, LM produces the best results, allowing long time steps of 14 fs in simulations containing explicitly modeled flexible water. With BBK–M and the same damping coefficient, time steps of 12 fs are possible for the same system. Similar results are obtained for a solvated protein–DNA simulation of estrogen receptor ER with estrogen response element ERE. A parallel version of BBK–M runs nearly three times faster than the Verlet-I/r-RESPA (reversible reference system propagator algorithm) when using the largest stable time step on each one, and it also parallelizes well. The computation of diffusion coefficients for flexible water and ER/ERE shows that when mild damping of up to 0.2 ps−1 is used the dynamics are not significantly distorted.