Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

Polydispersity index from linear viscoelastic data: Unimodal and bimodal linear polymer melts

This article describes a method for determining the polydispersity index Ip2=Mz/Mw of the molecular weight distribution (MWD) of linear polymeric materials from linear viscoelastic data. The method uses the Mellin transform of the relaxation modulus of a simple molecular rheological model. One of the main features of this technique is that it enables interesting MWD information to be obtained directly from dynamic shear experiments. It is not necessary to achieve the relaxation spectrum, so the ill-posed problem is avoided. Furthermore, a determinate shape of the continuous MWD does not have to be assumed in order to obtain the polydispersity index. The technique has been developed to deal with entangled linear polymers, whatever the form of the MWD is. The rheological information required to obtain the polydispersity index is the storage G′(ω) and loss G″(ω) moduli, extending from the terminal zone to the plateau region. The method provides a good agreement between the proposed theoretical approach and the experimental polydispersity indices of several linear polymers for a wide range of average molecular weights and polydispersity indices. It is also applicable to binary blends.

Comparison between a linear ion trap and a triple quadruple MS in the sensitive detection of large peptides at femtomole amounts on column.

In addition to the importance of sample preparation and extract separation, MS detection is a key factor in the sensitive quantification of large undigested peptides. In this article, a linear ion trap MS (LIT-MS) and a triple quadrupole MS (TQ-MS) have been compared in the detection of large peptides at subnanomolar concentrations. Natural brain natriuretic peptide, C-peptide, substance P and D-Junk-inhibitor peptide, a full D-amino acid therapeutic peptide, were chosen. They were detected by ESI and simultaneous MS(1) and MS(2) acquisitions. With direct peptide infusion, MS(2) spectra revealed that fragmentation was peptide dependent, milder on the LIT-MS and required high collision energies on the TQ-MS to obtain high-intensity product ions. Peptide adsorption on surfaces was overcome and peptide dilutions ranging from 0.1 to 25 nM were injected onto an ultra high-pressure LC system with a 1 mm id analytical column and coupled with the MS instruments. No difference was observed between the two instruments when recording in LC-MS(1) acquisitions. However, in LC-MS(2) acquisitions, a better sensitivity in the detection of large peptides was observed with the LIT-MS. Indeed, with the three longer peptides, the typical fragmentation in the TQ-MS resulted in a dramatic loss of sensitivity (> or = 10x).

Peroxisome Proliferator-Activated Receptor beta/delta in the Brain: Facts and Hypothesis.

peroxisome proliferator-activated receptors (PPARs) are nuclear receptors acting as lipid sensors. Besides its metabolic activity in peripheral organs, the PPAR beta/delta isotype is highly expressed in the brain and its deletion in mice induces a brain developmental defect. Nevertheless, exploration of PPARbeta action in the central nervous system remains sketchy. The lipid content alteration observed in PPARbeta null brains and the positive action of PPARbeta agonists on oligodendrocyte differentiation, a process characterized by lipid accumulation, suggest that PPARbeta acts on the fatty acids and/or cholesterol metabolisms in the brain. PPARbeta could also regulate central inflammation and antioxidant mechanisms in the damaged brain. Even if not fully understood, the neuroprotective effect of PPARbeta agonists highlights their potential benefit to treat various acute or chronic neurological disorders. In this perspective, we need to better understand the basic function of PPARbeta in the brain. This review proposes different leads for future researches.

Lag-one autocorrelation in short series: Estimation and hypothesis testing

In the first part of the study, nine estimators of the first-order autoregressive parameter are reviewed and a new estimator is proposed. The relationships and discrepancies between the estimators are discussed in order to achieve a clear differentiation. In the second part of the study, the precision in the estimation of autocorrelation is studied. The performance of the ten lag-one autocorrelation estimators is compared in terms of Mean Square Error (combining bias and variance) using data series generated by Monte Carlo simulation. The results show that there is not a single optimal estimator for all conditions, suggesting that the estimator ought to be chosen according to sample size and to the information available of the possible direction of the serial dependence. Additionally, the probability of labelling an actually existing autocorrelation as statistically significant is explored using Monte Carlo sampling. The power estimates obtained are quite similar among the tests associated with the different estimators. These estimates evidence the small probability of detecting autocorrelation in series with less than 20 measurement times.

Micro-Computer Based Linear Scheduling Application for Highway Construction Project Control, HR-339A, 1995

This report describes a new approach to the problem of scheduling highway construction type projects. The technique can accurately model linear activities and identify the controlling activity path on a linear schedule. Current scheduling practices are unable to accomplish these two tasks with any accuracy for linear activities, leaving planners and manager suspicious of the information they provide. Basic linear scheduling is not a new technique, and many attempts have been made to apply it to various types of work in the past. However, the technique has never been widely used because of the lack of an analytical approach to activity relationships and development of an analytical approach to determining controlling activities. The Linear Scheduling Model (LSM) developed in this report, completes the linear scheduling technique by adding to linear scheduling all of the analytical capabilities, including computer applications, present in CPM scheduling today. The LSM has tremendous potential, and will likely have a significant impact on the way linear construction is scheduled in the future.

A general linear relaxometry model of R1 using imaging data.

PURPOSE: The longitudinal relaxation rate (R1 ) measured in vivo depends on the local microstructural properties of the tissue, such as macromolecular, iron, and water content. Here, we use whole brain multiparametric in vivo data and a general linear relaxometry model to describe the dependence of R1 on these components. We explore a) the validity of having a single fixed set of model coefficients for the whole brain and b) the stability of the model coefficients in a large cohort. METHODS: Maps of magnetization transfer (MT) and effective transverse relaxation rate (R2 *) were used as surrogates for macromolecular and iron content, respectively. Spatial variations in these parameters reflected variations in underlying tissue microstructure. A linear model was applied to the whole brain, including gray/white matter and deep brain structures, to determine the global model coefficients. Synthetic R1 values were then calculated using these coefficients and compared with the measured R1 maps. RESULTS: The model's validity was demonstrated by correspondence between the synthetic and measured R1 values and by high stability of the model coefficients across a large cohort. CONCLUSION: A single set of global coefficients can be used to relate R1 , MT, and R2 * across the whole brain. Our population study demonstrates the robustness and stability of the model. Magn Reson Med, 2014. © 2014 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. Magn Reson Med 73:1309-1314, 2015. © 2014 Wiley Periodicals, Inc.

Potential yield, return, and tree diversity of managed, uneven-aged Douglas-fir stands

Abstract

Fecundity versus offspring size in the greater white-toothed shrew Crocidura russula

1. The relationships between female body mass (WWal)i, tter size (m), juvenile growth rate (G) and mass at weaning (W20) were examined by monitoring natural litters in 29 greater white-toothed shrews, Crocidura russula (Hermann 1780). The trade-offs between m and G or W20 were further investigated by manipulating litter sizes: each of seven females reared four litters of 2, 4, 6 and 8 offspring. 2. Offspring mass at weaning (W20) exhibited a large variance, most of which could be attributed (ANCOVA on manipulated litters) to two effects: a litter-size effect, and a female individual effect, referred to as 'female quality'. 3. Litter size explained 68% of the variance in W20 among manipulated litters (linear regression). The limited milk supply was probably responsible for this effect, because litter size depressed growth rate during the first half of the lactation period (G1), but not during the weaning stage (G2). 4. Among non-manipulated litters, litter size correlated positively with maternal body mass (Wa), so that large females tended to produce small juveniles. This correlation between m and Wa is seen as the result of a body-mass dependence in the cost of raising a litter of a given size, during either pregnancy or lactation. 5. Differences in 'female quality' explained 16% of the variance in W20 among manipulated litters. This factor did not affect GI and may thus relate to differences among offspring of different females in their rates of processing milk and/or external food during late lactation. 6. 'Female quality' was independent of both body mass and litter size: larger females did not produce larger offspring when controlled for litter size, while higher-quality females did not produce larger litters. 7. Our results support the hypothesis that most variance in adult and juvenile body masses is non-genetic, and stems from the trade-off between litter size and offspring size.

Residence time, expansion toward the equator in the invaded range and native range size matter to climatic niche shifts in non-native species

Aim Identifying climatic niche shifts and their drivers is important to accurately predict the risk of biological invasions. The niches of non-native plants and birds have recently been assessed in large-scale multi-species studies, but such large-scale tests are lacking for non-native reptiles and amphibians (herpetofauna). Furthermore, little is known about the factors contributing to niche shifts when they occur. Based on the occurrence of 71 reptile and amphibian species, we compared native and non-native realized niches in 101 invaded ranges at a worldwide scale and identified the factors that affect niche shifts. Location The world except the Antarctic. Methods We assessed climatic niche dynamics in a gridded environmental space allowing the quantification of niche overlap and expansion into climatic conditions not colonized by the species in their native range. We analyzed the factors affecting niche shifts using a model averaging approach based on generalized linear mixed-effects models. Results Approximately 57% of the invaded ranges (51% for amphibians and 61% for reptiles) showed niche shifts (≥10% expansion in the realized climatic niche). Island endemics, species introduced to Oceania and invaded ranges outside the native biogeographic realm showed a higher proportion of niche shifts. Niche shifts were more likely for species that had smaller native range sizes, were introduced earlier into a new range or invaded areas located at lower latitudes than the native range. Main conclusions The proportion of niche shifts for non-native herpetofauna was higher than those for Holarctic non-native plants and European non-native birds. The 'climate matching hypothesis' should be used with caution for species shifting their niche because it could underestimate the risk of their establishment.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

SAT Modulo Linear Arithmetic for Solving Polynomial

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world.