Linear relations between writhe and minimal crossing number in Conway families of ideal knots and links

We showed earlier how to predict the writhe of any rational knot or link in its ideal geometric configuration, or equivalently the average of the 3D writhe over statistical ensembles of random configurations of a given knot or link (Cerf and Stasiak 2000 Proc. Natl Acad. Sci. USA 97 3795). There is no general relation between the minimal crossing number of a knot and the writhe of its ideal geometric configuration. However, within individual families of knots linear relations between minimal crossing number and writhe were observed (Katritch et al 1996 Nature 384 142). Here we present a method that allows us to express the writhe as a linear function of the minimal crossing number within Conway families of knots and links in their ideal configuration. The slope of the lines and the shift between any two lines with the same

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Altered decision-making in multiple sclerosis: a sign of impaired emotional reactivity?

We assessed decision-making capacity and emotional reactivity in 20 patients with multiple sclerosis (MS) and in 16 healthy subjects using the Gambling Task (GT), a model of real-life decision making, and the skin conductance response (SCR). Demographic, neurological, affective, and cognitive parameters were analyzed in MS patients for their effect on decision-making performance. MS patients persisted longer (slope, -3.6%) than the comparison group (slope, -6.4%) in making disadvantageous choices as the GT progressed (p < 0.001), suggesting significant slower learning in MS. Patients with higher Expanded Disability Status Scale scores (EDSS >2.0) showed a different pattern of impairment in the learning process compared with patients with lower functional impairment (EDSS </=2.0). This slower learning was associated with impaired emotional reactivity (anticipatory SCR 3.9 vs 6.1 microSiemens [microS] for patients vs the comparison group, p < 0.0001; post-choice SCR 3.9 vs 6.2 microS, p < 0.0001), but not with executive dysfunction. Impaired emotional dimensions of behavior (assessed using the Dysexecutive Questionnaire, p < 0.002) also correlated with slower learning. Given the considerable consequences that impaired decision making can have on daily life, we suggest that this factor may contribute to handicap and altered quality of life secondary to MS and is dependent on emotional experience. Ann Neurol 2004.

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).

La construcció de la identitat europea: dimensions educatives

Construir una identitat europea es sentir-se membre d'una comunitat culturalment plural. Des d'Europa s'han establert diverses mesures per fomentar aquesta construcció d'una identitat europea. En aquest article s'analitzen de forma crítica alguns dels models proposats, els seus fonaments i les mesures educatives adoptades per fer-los realitat, fonamentalment des de la dimensió europea de l'educació. Es defensa un model de construcció de la identitat europea des de la ciutadaia múltiple, per la qual: "l'espai cívic comú europeu" implica la construcció conjunta d'una representació que té en compte les diferències i en el que els punts de vista diferents aconsegueixen complementar-se uns amb els altres. Per això es necessiten estratègies educatives que promoguin una noció de personalitat emancipadora i transcultural.

Which change talk dimensions are associated with subsequent drinking among young men receiving a brief motivational intervention in a non-clinical setting?

Background: Patient change talk (CT) during brief motivational interventions (BMI) has been linked with subsequent changes in drinking in clinical settings but this link has not been clearly established among young people in non-clinical populations. Objective: To determine which of several CT dimensions assessed during an effective BMI delivered in a non-clinical setting to 20-year old men are associated with drinking 6 months later. Methods: Of 125 individuals receiving a face-to-face BMI session (15.8 ± 5.4 minutes), we recorded and coded a subsample of 42 sessions using the Motivational Interviewing Skill Code 2.1. Each patient change talk utterance was categorized as `Reason´, `Ability´, `Desire´, `Need´, `Commitment´, `Taking steps´, or `Other´. Each utterance was graded according to its strength (absolute value from 1 to 3) and direction (i.e. towards (positive sign) or away (negative sign) from change/in favor of status quo). `Ability´, `Desire´, and `Need´ to change (`ADN´) were grouped together since these codes were too scarce to conduct analyses. Mean strength scores over the entire session were computed for each dimension and later dichotomized in towards change (i.e. mean core > 0) and away from change/in favor of status quo. Negative binomial regression models were used to assess the relationship between CT dimensions and drinking 6 months later, adjusting for drinking at baseline. Results: Compared to subjects with a `Taking steps´ score away from change/in favor of status quo, subjects with a positive `Taking steps´ score reported significantly less drinking 6 months later (Incidence Rate Ration [IRR] for drinks per week: 0.56, 95% Confidence Interval [CI] 0.31, 1.00). IRR (95%CI) for subjects with a positive `ADN´ score was 0.58, (0.32, 1.03). For subjects with a positive `Reason´, `Commitment´, and `Other´ scores, IRR (95%CI) were 1.28 (0.77; 2.12) 1.63 (0.85; 3.14) and 1.03 (0.61; 1.72), respectively. Conclusion: A change talk dimension reflecting steps taken towards change (`Taking steps´) is associated with less drinking 6 months later among young men receiving a BMI in a non-clinical setting. Encouraging patients to take steps towa change may be a worthy objective for clinicians and may explain BMI efficacy.

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.