Power series expansion and structural analysis for life cycle assessment

Goal, Scope and Background The usefulness of power series expansion for an LCA system has often been doubted, as those systems may not possess the unique properties that enable power series expansion and analyses based on the power series. This paper surveys the existing literature on power series expansion of monetary input-output system and discusses how the power series expansion can be utilized for more general systems including the LCA model. Methods The inherent properties of matrices that are capable of producing power series forms for their inverse and, further, can utilize structural path analysis are analyzed. Using these analyses, the way how a matrix that is not eligible for structural analyses is converted into an eligible form is investigated. A numerical example is presented to demonstrate the findings. Results The necessary and sufficient condition for an indecomposable, real square technology matrix can be expressed using power series was identified. Two additional conditions for a technology matrix to be utilized for structural analyses using power series expansion are discussed as well. It was also shown that an LCA system that fulfills the Hawkins-Simon condition can be easily converted into the form that is eligible for structural analysis by rescaling the columns and rows. Discussion As a numerical example, an application of accumulative structural path analysis for an LCA system is shown. The implications of the results are discussed in a more plain language as well. Conclusions The survey presented in this paper provides not only the conditions under which a linear system is expressed using a power series form but also the way to appropriately convert a system to utilize the rich analytical tools using power series expansion for structural analyses. Recommendations and Perspectives Widely used LCA databases and software tools have employed the linear systems approach as the basis. Much of these developments in the domain of LCA have been made, however, in isolation of the rich findings of IOA. There will be much to benefit LCA through an active dialogue between the two disciplines. There are rich analytical tools available through the use of power series expansion. The current survey will help software developers and LCA practitioners to apply such tools in LCA.     

Calculation of multicenter electric field gradient integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

The electric field induced within a molecule by its electrons determines a whole series of important physical properties of the molecule. In particular, the values of the gradient of this field at the nuclei determine the interaction of their quadrupole moments with the electrons. Using unsymmetrical one-range addition theorems introduced by one of the authors, the sets of series expansion relations for multicenter electric field gradient integrals over Slater-type orbitals in terms of multicenter charge density expansion coefficients and two-center basic integrals are presented. The convergence of the series is tested by calculating concrete cases for different values of quantum numbers, parameters and locations of orbitals.     

Discovery of a series of imidazopyrazine small molecule inhibitors of the kinase MAPKAPK5, that show activity using in vitro and in vivo models of rheumatoid arthritis

MAPKAPK5 has been proposed to play a role in regulation of matrix metalloprotease expression and so to be a potential target for intervention in rheumatoid arthritis. We present here the identification of a series of compounds against this target which are effective in both biochemical and cell assays. The expansion of the series is described, along with early SAR and pharmacokinetics for some representative compounds.     

Are there differences in the cell cycle of normal and malignant cells? An approach to the analysis of the clonal expansion of cells in malignant epithelial proliferations in situ

The Williams-Bjerknes model for clonal expansion of transformed cells in epithelia was used to examine a series of related questions about the growth of in situ proliferations in epidermis. Bowens disease, actinic keratosis and lentigo maligna lesions were reconstructed on a three-dimensional basis, and all were found to behave differently: the evidence supported the proposal that the 'carcinogenic advantage' enjoyed by transformed cells was proliferative in nature, and indeed varied between the three lesions. We conclude that the clonal expansion of a single cell, with different proliferative carcinogenic advantage, can explain the three-dimensional appearances of these in situ proliferations; furthermore, the well-known 'multifocality' of in situ epidermal proliferations can also be explained by the clonal expansion of a single transformed cell.     

Multisubstrate Michaëlis-Menten kinetics: Explicit dependence of substrate concentration on time for batch reactors

The problem of expressing the concentration of each of a set of substrates in a batch reactor as an explicit function of time in the case the multisubstrate system is described by Michaelis-Menten kinetics is tackled in dimensionless form via expansion as a Taylor series. The general analytical form for the coefficients of this expansion is obtained and estimates of the average quadratic error associated with increasing number of terms of the expansion is calculated. Considering the situation where the concentration of all substrates varies in a similar fashion, one concludes that use of four terms yields errors well within the range acceptable for predesign steps. In addition to other applications, the reasoning developed here finds applications in the statistical design and analysis of experiments aiming at the nonlinear fitting of kinetic parameters to actual data.     

Expansion microscopy: A chemical approach for super-resolution microscopy

Super-resolution microscopy is a series of imaging techniques that bypass the diffraction limit of resolution. Since the 1990s, optical approaches, such as single-molecular localization microscopy, have allowed us to visualize biological samples from the sub-organelle to the molecular level. Recently, a chemical approach called expansion microscopy emerged as a new trend in super-resolution microscopy. It physically enlarges cells and tissues, which leads to an increase in the effective resolution of any microscope by the length expansion factor. Compared with optical approaches, expansion microscopy has a lower cost and higher imaging depth but requires a more complex procedure. The integration of expansion microscopy and advanced microscopes significantly pushed forward the boundary of super-resolution microscopy. This review covers the current state of the art in expansion microscopy, including the latest methods and their applications, as well as challenges and opportunities for future research.     

Synthesis of C-6 substituted pyrazolo[1,5-a]pyridines with potent activity against herpesviruses

A novel series of potent C-6 substituted pyrazolo[1,5-a]pyridine inhibitors of herpes simplex viruses has been identified. A synthetic methodology was developed involving functionalization of a C-6 trifluoromethyl pyrazolo[1,5-a]pyridine to allow facile access to a diverse set of analogues from common late stage intermediates. The expansion of the SAR of this series at the 6 position allows for modifications to developability parameters such as clogP, while maintaining potency comparable to acyclovir.     

Benzodipyrazoles: a new class of potent CDK2 inhibitors

The synthesis and the preliminary expansion of this new class of CDK2 inhibitors are presented. The synthesis was accomplished using a solution-phase protocol amenable to rapid parallel expansion and suitable to be scaled-up in view of possible lead development. Following a medicinal chemistry program aimed at improving cell permeability and selectivity, a series of compounds with nanomolar activity in the biochemical assay and able to efficiently inhibit tumor cell proliferation has been obtained.     

Soft-tissue expansion: concepts and complications

Soft-tissue expansion complements existing reconstructive techniques and provides new vistas for the plastic surgeon. The technique finds use for overcoming a shortage of tissue, for obtaining skin with special desirable qualities, for creation of flaps otherwise not possible because of the resultant donor site or limited vascularity, for creation of flaps with functioning muscle and overlying soft tissue, and for minimizing flap donor-site problems. Careful planning should include patient counseling, optimum incision placement, and time for a leisurely, complete expansion. The surgery can often be performed under local anesthesia and expansion is tolerated well. Patients should be counseled that the incidence of major complications in an unselected series is 1 in 4 patients. Major complications, however, typically result in a delay in reconstruction and not tissue loss.     

Nonparametric Estimation of Population Density for Line Transect Sampling Using FOURIER Series

A nonparametric, robust density estimation method is explored for the analysis of right-angle distances from a transect line to the objects sighted. The method is based on the FOURIER series expansion of a probability density function over an interval. With only mild assumptions, a general population density estimator of wide applicability is obtained.     

Methods for short time series analysis of cell-based biosensor data.

This paper describes two approaches for sensing changes in spiking cells when only a limited amount of spike data is available, i.e., dynamically constructed local expansion rates and spike area distributions. The two methods were tested on time series from cultured neuron cells that exhibit spiking both autonomously and in the presence of periodic stimulation. Our tested hypothesis was that minute concentrations of toxins could affect the local statistics of the dynamics. Short data sets having relatively few spikes were generated from experiments on cells before and after being treated with a small concentration of channel blocker. In spontaneous spiking cells, local expansion rates show a sensitivity that correlates with channel concentration level, while stimulated cells show no such correlation. Spike area distributions on the other hand showed measurable differences between control and treated conditions for both types of spiking, and a much higher degree of sensitivity. Because these methods are based on analysis of short time series analysis, they might provide novel means for cell drug and toxin detection.     

The Approximate Variance of a Function of Random Variables

In this communication we approximate the variance of a function of random variables by using a second degree Taylor series expansion, and demonstrate the increased accuracy this second degree approximation gives over the usual Delta method by using some examples from genetics.     

Tissue expansion in the reconstruction of Tessier craniofacial clefts: a series of 17 patients

Tessier craniofacial clefts are among the most surgically challenging examples of craniofacial dysmorphology. These clefts are characterized by hypoplasia of soft-tissue and skeletal elements throughout the three-dimensional extent of the cleft. Whereas bone grafting and craniofacial osteotomies have been successful toward correcting the underlying skeletal abnormalities, the ultimate success of these reconstructions has been limited by the deficiency of skin and soft tissue. This deficiency demands reconstruction ideally with tissue of like texture, consistency, and, especially in the face, color. Craniofacial tissue expansion was used toward reconstructing these facial clefts with like-quality tissue, allowing for tension-free reconstruction after osteotomy and bone grafting. Seventeen patients with Tessier craniofacial clefts underwent preoperative craniofacial soft-tissue expansion in the surgical management of their clefts. Tissue expansion was used in the primary correction of facial clefts in eight patients, with nine patients undergoing expansion before secondary surgery. In this series, tissue expansion has evolved as an important element in overcoming the skin and soft-tissue deficiency associated with these clefts, allowing for tension-free closure and improved aesthetic results in these surgically challenging patients.     

Analytical uncertainty propagation in life cycle inventory and impact assessment: application to an automobile front panel

Background, aim, and scope

Uncertainty information is essential for the proper use of life cycle assessment (LCA) and environmental assessments in decision making. So far, parameter uncertainty propagation has mainly been studied using Monte Carlo techniques that are relatively computationally heavy to conduct, especially for the comparison of multiple scenarios, often limiting its use to research or to inventory only. Furthermore, Monte Carlo simulations do not automatically assess the sensitivity and contribution to overall uncertainty of individual parameters. The present paper aims to develop and apply to both inventory and impact assessment an explicit and transparent analytical approach to uncertainty. This approach applies Taylor series expansions to the uncertainty propagation of lognormally distributed parameters.

Materials and methods

We first apply the Taylor series expansion method to analyze the uncertainty propagation of a single scenario, in which case the squared geometric standard deviation of the final output is determined as a function of the model sensitivity to each input parameter and the squared geometric standard deviation of each parameter. We then extend this approach to the comparison of two or more LCA scenarios. Since in LCA it is crucial to account for both common inventory processes and common impact assessment characterization factors among the different scenarios, we further develop the approach to address this dependency. We provide a method to easily determine a range and a best estimate of (a) the squared geometric standard deviation on the ratio of the two scenario scores, “A/B”, and (b) the degree of confidence in the prediction that the impact of scenario A is lower than B (i.e., the probability that A/B<1). The approach is tested on an automobile case study and resulting probability distributions of climate change impacts are compared to classical Monte Carlo distributions.

Results

The probability distributions obtained with the Taylor series expansion lead to results similar to the classical Monte Carlo distributions, while being substantially simpler; the Taylor series method tends to underestimate the 2.5% confidence limit by 1-11% and the 97.5% limit by less than 5%. The analytical Taylor series expansion easily provides the explicit contributions of each parameter to the overall uncertainty. For the steel front end panel, the factor contributing most to the climate change score uncertainty is the gasoline consumption (>75%). For the aluminum panel, the electricity and aluminum primary production, as well as the light oil consumption, are the dominant contributors to the uncertainty. The developed approach for scenario comparisons, differentiating between common and independent parameters, leads to results similar to those of a Monte Carlo analysis; for all tested cases, we obtained a good concordance between the Monte Carlo and the Taylor series expansion methods regarding the probability that one scenario is better than the other.

Discussion

The Taylor series expansion method addresses the crucial need of accounting for dependencies in LCA, both for common LCI processes and common LCIA characterization factors. The developed approach in Eq. 8, which differentiates between common and independent parameters, estimates the degree of confidence in the prediction that scenario A is better than B, yielding results similar to those found with Monte Carlo simulations.

Conclusions

The probability distributions obtained with the Taylor series expansion are virtually equivalent to those from a classical Monte Carlo simulation, while being significantly easier to obtain. An automobile case study on an aluminum front end panel demonstrated the feasibility of this method and illustrated its simultaneous and consistent application to both inventory and impact assessment. The explicit and innovative analytical approach, based on Taylor series expansions of lognormal distributions, provides the contribution to the uncertainty from each parameter and strongly reduces calculation time.     

Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences

In this paper methods from differential algebra are used to study the structural identifiability of biological and pharmacokinetics models expressed in state-space form and with a structure given by rational functions. The focus is on the examples presented and on the application of efficient, automatic methods to test for structural identifiability for various input-output experiments. Differential algebra methods are coupled with Gr?bner bases, Lie derivatives and the Taylor series expansion in order to obtain efficient algorithms. In particular, an upper bound on the number of derivatives needed for the Taylor series approach for a structural identifiability analysis of rational function models is given.     

Characterization of Demographic Expansions From Pairwise Comparisons of Linked Microsatellite Haplotypes

This work extends the methods of demographic inference based on the distribution of pairwise genetic differences between individuals (mismatch distribution) to the case of linked microsatellite data. Population genetics theory describes the distribution of mutations among a sample of genes under different demographic scenarios. However, the actual number of mutations can rarely be deduced from DNA polymorphisms. The inclusion of mutation models in theoretical predictions can improve the performance of statistical methods. We have developed a maximum-pseudolikelihood estimator for the parameters that characterize a demographic expansion for a series of linked loci evolving under a stepwise mutation model. Those loci would correspond to DNA polymorphisms of linked microsatellites (such as those found on the Y chromosome or the chloroplast genome). The proposed method was evaluated with simulated data sets and with a data set of chloroplast microsatellites that showed signal for demographic expansion in a previous study. The results show that inclusion of a mutational model in the analysis improves the estimates of the age of expansion in the case of older expansions.     

Geometrical comparison of two protein structures using Wigner‐D functions

In this article, we develop a quantitative comparison method for two arbitrary protein structures. This method uses a root‐mean‐square deviation characterization and employs a series expansion of the protein's shape function in terms of the Wigner‐D functions to define a new criterion, which is called a “similarity value.” We further demonstrate that the expansion coefficients for the shape function obtained with the help of the Wigner‐D functions correspond to structure factors. Our method addresses the common problem of comparing two proteins with different numbers of atoms. We illustrate it with a worked example. Proteins 2014; 82:2756–2769. © 2014 Wiley Periodicals, Inc.     

Chlorophyll a fluorescence and carbon assimilation in developing leaves of light-grown cucumber

The development of photochemical activity and carbon assimilation in light-grown cucumber (Cucumis sativus L. cv Natsusairaku) leaves was studied to determine the pattern of acquisition and its relationship to leaf growth and expansion. Measurements of chlorophyll a fluorescence showed that leaves acquire photochemical function over a period of 6 or more days, and gas exchange studies showed increases in carbon assimilation over a parallel time period. As leaves expand and mature, they undergo a sequential, three-step series of changes in fluorescence response. The initial kinetics show the absence of wholly functional quenching mechanisms. Dynamic imaging of fluorescence kinetics showed that a temporal series of changes occurred within defined areas of individual developing leaves. The spatial acquisition of photochemical activity in leaves was basipetal as is their directional expansion, development of air spaces and stomata, and the cessation of imported carbon.