Realistic calculations of carbon-based disordered systems

Carbon nanotubes rank amongst potential candidates for a new family of nanoscopic devices, in particular for sensing applications. At the same time that defects in carbon nanotubes act as binding sites for foreign species, our current level of control over the fabrication process does not allow one to specifically choose where these binding sites will actually be positioned. In this work we present a theoretical framework for accurately calculating the electronic and transport properties of long disordered carbon nanotubes containing a large number of binding sites randomly distributed along a sample. This method combines the accuracy and functionality of ab initio density functional theory to determine the electronic structure with a recursive Green`s functions method. We apply this methodology on the problem of nitrogen-rich carbon nanotubes, first considering different types of defects and then demonstrating how our simulations can help in the field of sensor design by allowing one to compute the transport properties of realistic nanotube devices containing a large number of randomly distributed binding sites.

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

On automorphisms of finite abelian p-groups

Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A(p). For a finite abelian p-group A of type (k(1),..., k(n)), simple necessary and sufficient conditions for an n x n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k(1), k(2)) is analyzed. (C) 2008 Mathematical Institute Slovak Academy of Sciences.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Integration of Ligand- and Target-Based Virtual Screening for the Discovery of Cruzain Inhibitors

A myriad of methods are available for virtual screening of small organic compound databases. In this study we have successfully applied a quantitative model of consensus measurements, using a combination of 3D similarity searches (ROCS and EON), Hologram Quantitative Structure Activity Relationships (HQSAR) and docking (FRED, FlexX, Glide and AutoDock Vina), to retrieve cruzain inhibitors from collected databases. All methods were assessed individually and then combined in a Ligand-Based Virtual Screening (LBVS) and Target-Based Virtual Screening (TBVS) consensus scoring, using Receiving Operating Characteristic (ROC) curves to evaluate their performance. Three consensus strategies were used: scaled-rank-by-number, rank-by-rank and rank-by-vote, with the most thriving the scaled-rank-by-number strategy, considering that the stiff ROC curve appeared to be satisfactory in every way to indicate a higher enrichment power at early retrieval of active compounds from the database. The ligand-based method provided access to a robust and predictive HQSAR model that was developed to show superior discrimination between active and inactive compounds, which was also better than ROCS and EON procedures. Overall, the integration of fast computational techniques based on ligand and target structures resulted in a more efficient retrieval of cruzain inhibitors with desired pharmacological profiles that may be useful to advance the discovery of new trypanocidal agents.

2D QSAR and similarity studies on cruzain inhibitors aimed at improving selectivity over cathepsin L

Hologram quantitative structure-activity relationships (HQSAR) were applied to a data set of 41 cruzain inhibitors. The best HQSAR model (Q(2) = 0.77; R-2 = 0.90) employing Surflex-Sim, as training and test sets generator, was obtained using atoms, bonds, and connections as fragment distinctions and 4-7 as fragment size. This model was then used to predict the potencies of 12 test set compounds, giving satisfactory predictive R-2 value of 0,88. The contribution maps obtained from the best HQSAR model are in agreement with the biological activities of the study compounds. The Trypanosoma cruzi cruzain shares high similarity with the mammalian homolog cathepsin L. The selectivity toward cruzam was checked by a database of 123 compounds, which corresponds to the 41 cruzain inhibitors used in the HQSAR model development plus 82 cathepsin L inhibitors. We screened these compounds by ROCS (Rapid Overlay of Chemical Structures), a Gaussian-shape volume overlap filter that can rapidly identify shapes that match the query molecule. Remarkably, ROCS was able to rank the first 37 hits as being only cruzain inhibitors. In addition, the area under the curve (AUC) obtained with ROCS was 0.96, indicating that the method was very efficient to distinguishing between cruzain and cathepsin L inhibitors. (c) 2007 Elsevier Ltd. All rights reserved.

12-month results from a novel test battery used in a duodenal levodopa infusion trial

A novel test battery consisting of self-assessments and motor tests (tapping and spiral drawing) for patients with Parkinson’s disease (PD) was developed for a hand computer with touch screen in a telemedicine setting. Tests are performed four times per day in the home environment during weeklong test periods. Results are processed into scores for different dimensions of the symptom state and an ‘overall score’ reflecting the global condition of a patient during a test period. The test battery was validated in a separate study recently submitted to Mov Disord. This test battery is currently being used in an open longitudinal trial (DAPHNE, EudraCT No. 2005- 002654-21) by sixty-five patients with advanced PD at nine clinics around Sweden. On inclusion, the patients were either receiving treatment with duodenal levodopa/carbidopa infusion (Duodopa®) (n=36), or they were candidates for receiving this treatment (n=29). We now present interim results for the first twelve months. Test periods were performed in three-month intervals. During most of the periods, UPDRS ratings were performed in afternoons at the start of the week. In twenty of the patients, scores were available during individually optimized oral polypharamacy, before receiving infusion and at least one test period after having started infusion treatment. Usability and compliance with performing tests, this far are good, both with patients and clinical staff. Correlations between test periods 2 and 3 during infusion treatment (three months apart) are stronger for overall test score than for total UPDRS, indicating good reliability. The correlation between overall test score and UPDRS for all test periods is adequate (r=-0.6). In an exact Wilcoxon signed rank test, where the endpoint is the change from the first to the twelve month test period (n=25), there was no change in test results in any of the test battery dimensions for the patients already receiving infusion when included. However, in the patients entering the study before receiving infusion, there was a significant change (improvement) from the baseline to the twelve month test period in dimensions; ‘off’, ‘dyskinesia’ and ‘satisfied’ and in the ‘overall score’ (n=15). The mean improvement in overall score after infusion was 29% (p=0.015). We conclude that the test battery is able to measure a functional improvement with infusion that is sustained over at least twelve months.

Computerized identification of motor complications in Parkinson's disease

Objective: To investigate whether spirography-based objective measures are able to effectively characterize the severity of unwanted symptom states (Off and dyskinesia) and discriminate them from motor state of healthy elderly subjects. Background: Sixty-five patients with advanced Parkinson’s disease (PD) and 10 healthy elderly (HE) subjects performed repeated assessments of spirography, using a touch screen telemetry device in their home environments. On inclusion, the patients were either treated with levodopa-carbidopa intestinal gel or were candidates for switching to this treatment. On each test occasion, the subjects were asked trace a pre-drawn Archimedes spiral shown on the screen, using an ergonomic pen stylus. The test was repeated three times and was performed using dominant hand. A clinician used a web interface which animated the spiral drawings, allowing him to observe different kinematic features, like accelerations and spatial changes, during the drawing process and to rate different motor impairments. Initially, the motor impairments of drawing speed, irregularity and hesitation were rated on a 0 (normal) to 4 (extremely severe) scales followed by marking the momentary motor state of the patient into 2 categories that is Off and Dyskinesia. A sample of spirals drawn by HE subjects was randomly selected and used in subsequent analysis. Methods: The raw spiral data, consisting of stylus position and timestamp, were processed using time series analysis techniques like discrete wavelet transform, approximate entropy and dynamic time warping in order to extract 13 quantitative measures for representing meaningful motor impairment information. A principal component analysis (PCA) was used to reduce the dimensions of the quantitative measures into 4 principal components (PC). In order to classify the motor states into 3 categories that is Off, HE and dyskinesia, a logistic regression model was used as a classifier to map the 4 PCs to the corresponding clinically assigned motor state categories. A stratified 10-fold cross-validation (also known as rotation estimation) was applied to assess the generalization ability of the logistic regression classifier to future independent data sets. To investigate mean differences of the 4 PCs across the three categories, a one-way ANOVA test followed by Tukey multiple comparisons was used. Results: The agreements between computed and clinician ratings were very good with a weighted area under the receiver operating characteristic curve (AUC) coefficient of 0.91. The mean PC scores were different across the three motor state categories, only at different levels. The first 2 PCs were good at discriminating between the motor states whereas the PC3 was good at discriminating between HE subjects and PD patients. The mean scores of PC4 showed a trend across the three states but without significant differences. The Spearman’s rank correlations between the first 2 PCs and clinically assessed motor impairments were as follows: drawing speed (PC1, 0.34; PC2, 0.83), irregularity (PC1, 0.17; PC2, 0.17), and hesitation (PC1, 0.27; PC2, 0.77). Conclusions: These findings suggest that spirography-based objective measures are valid measures of spatial- and time-dependent deficits and can be used to distinguish drug-related motor dysfunctions between Off and dyskinesia in PD. These measures can be potentially useful during clinical evaluation of individualized drug-related complications such as over- and under-medications thus maximizing the amount of time the patients spend in the On state.

Self-reported symptoms and motor tests via telemetry in a 36-month levodopa-carbidopa intestinal gel infusion trial

Objective To investigate if a home environment test battery can be used to measure effects of Parkinson’s disease (PD) treatment intervention and disease progression. Background Seventy-seven patients diagnosed with advanced PD were recruited in an open longitudinal 36-month study at 10 clinics in Sweden and Norway; 40 of them were treated with levodopa-carbidopa intestinal gel (LCIG) and 37 patients were candidates for switching from oral PD treatment to LCIG. They utilized a mobile device test battery, consisting of self-assessments of symptoms and objective measures of motor function through a set of fine motor tests (tapping and spiral drawings), in their homes. Both the LCIG-naïve and LCIG-non-naïve patients used the test battery four times per day during week-long test periods. Methods Assessments The LCIG-naïve patients used the test battery at baseline (before LCIG), month 0 (first visit; at least 3 months after intraduodenal LCIG), and thereafter quarterly for the first year and biannually for the second and third years. The LCIG-non-naïve patients used the test battery from the first visit, i.e. month 0. Out of the 77 patients, only 65 utilized the test battery; 35 were LCIG-non-naïve and 30 LCIG-naïve. In 20 of the LCIG-naïve patients, assessments with the test battery were available during oral treatment and at least one test period after having started infusion treatment. Three LCIG-naïve patients did not use the test battery at baseline but had at least one test period of assessments thereafter. Hence, n=23 in the LCIG-naïve group. In total, symptom assessments in the full sample (including both patient groups) were collected during 379 test periods and 10079 test occasions. For 369 of these test periods, clinical assessments including UPDRS and PDQ-39 were performed in afternoons at the start of the test periods. The repeated measurements of the test battery were processed and summarized into scores representing patients’ symptom severities over a test period, using statistical methods. Six conceptual dimensions were defined; four subjectively-reported: ‘walking’, ‘satisfied’, ‘dyskinesia’, and ‘off’ and two objectively-measured: ‘tapping’ and ‘spiral’. In addition, an ‘overall test score’ (OTS) was defined to represent the global health condition of the patient during a test period. Statistical methods Change in the test battery scores over time, that is at baseline and follow-up test periods, was assessed with linear mixed-effects models with patient ID as a random effect and test period as a fixed effect of interest. The within-patient variability of OTS was assessed using intra-class correlation coefficient (ICC), for the two patient groups. Correlations between clinical rating scores and test battery scores were assessed using Spearman’s rank correlations (rho). Results In LCIG-naïve patients, mean OTS compared to baseline was significantly improved from the first test period on LCIG treatment until month 24. However, there were no significant changes in mean OTS scores of LCIG-non-naïve patients, except for worse mean OTS at month 36 (p<0.01, n=16). The mean scores of all subjectively-reported dimensions improved significantly throughout the course of the study, except ‘walking’ at month 36 (p=0.41, n=4). However, there were no significant differences in mean scores of objectively-measured dimensions between baseline and other test periods, except improved ‘tapping’ at month 6 and month 36, and ‘spiral’ at month 3 (p<0.05). The LCIG-naïve patients had a higher within-subject variability in their OTS scores (ICC=0.67) compared to LCIG-non-naïve patients (ICC=0.71). The OTS correlated adequately with total UPDRS (rho=0.59) and total PDQ-39 (rho=0.59). Conclusions In this 3-year follow-up study of advanced PD patients treated with LCIG we found that it is possible to monitor PD progression over time using a home environment test battery. The significant improvements in the mean OTS scores indicate that the test battery is able to measure functional improvement with LCIG sustained over at least 24 months.

Utformningen hos toppuniversitets logotyper : en visuell innehållsanalys

Föreliggande studie syftar till att genom en visuell innehållsanalys kartlägga gemensamma drag i 120 universitetslogotypers visuella utformning, samt undersöka samband mellan dessa karaktärsdrag och universitetens internationella rankningsposition.Med utgångspunkt från topprankningslistan Times Higher Education World University Rankings med 400 internationella universitet, indelade i fyra grupper i intervaller om 100 (d.v.s. rankningsposition 1–100, 101–200 etc.), valdes 30 universitet ut per grupp genom ett obundet slumpmässigt urval. Logotyperna för universiteten inhämtades främst från deras grafiska manualer.I studien presenteras förekomsten av generella drag med avseende på färg, typografi, typologi, detaljrikedom samt innehåll och form. Resultatet visade på tydliga gemensamma drag med i regel en till två dominerande karaktärsdrag per kategori. Resultaten tyder dock inte på att universitetens rakningsposition påverkar den visuella utformningen.

Digital spiral analysis for objective assessment of fine motor timing variability in Parkinson's disease

OBJECTIVES: To develop a method for objective assessment of fine motor timing variability in Parkinson’s disease (PD) patients, using digital spiral data gathered by a touch screen device. BACKGROUND: A retrospective analysis was conducted on data from 105 subjects including65 patients with advanced PD (group A), 15 intermediate patients experiencing motor fluctuations (group I), 15 early stage patients (group S), and 10 healthy elderly subjects (HE) were examined. The subjects were asked to perform repeated upper limb motor tasks by tracing a pre-drawn Archimedes spiral as shown on the screen of the device. The spiral tracing test was performed using an ergonomic pen stylus, using dominant hand. The test was repeated three times per test occasion and the subjects were instructed to complete it within 10 seconds. Digital spiral data including stylus position (x-ycoordinates) and timestamps (milliseconds) were collected and used in subsequent analysis. The total number of observations with the test battery were as follows: Swedish group (n=10079), Italian I group (n=822), Italian S group (n = 811), and HE (n=299). METHODS: The raw spiral data were processed with three data processing methods. To quantify motor timing variability during spiral drawing tasks Approximate Entropy (APEN) method was applied on digitized spiral data. APEN is designed to capture the amount of irregularity or complexity in time series. APEN requires determination of two parameters, namely, the window size and similarity measure. In our work and after experimentation, window size was set to 4 and similarity measure to 0.2 (20% of the standard deviation of the time series). The final score obtained by APEN was normalized by total drawing completion time and used in subsequent analysis. The score generated by this method is hence on denoted APEN. In addition, two more methods were applied on digital spiral data and their scores were used in subsequent analysis. The first method was based on Digital Wavelet Transform and Principal Component Analysis and generated a score representing spiral drawing impairment. The score generated by this method is hence on denoted WAV. The second method was based on standard deviation of frequency filtered drawing velocity. The score generated by this method is hence on denoted SDDV. Linear mixed-effects (LME) models were used to evaluate mean differences of the spiral scores of the three methods across the four subject groups. Test-retest reliability of the three scores was assessed after taking mean of the three possible correlations (Spearman’s rank coefficients) between the three test trials. Internal consistency of the methods was assessed by calculating correlations between their scores. RESULTS: When comparing mean spiral scores between the four subject groups, the APEN scores were different between HE subjects and three patient groups (P=0.626 for S group with 9.9% mean value difference, P=0.089 for I group with 30.2%, and P=0.0019 for A group with 44.1%). However, there were no significant differences in mean scores of the other two methods, except for the WAV between the HE and A groups (P<0.001). WAV and SDDV were highly and significantly correlated to each other with a coefficient of 0.69. However, APEN was not correlated to neither WAV nor SDDV with coefficients of 0.11 and 0.12, respectively. Test-retest reliability coefficients of the three scores were as follows: APEN (0.9), WAV(0.83) and SD-DV (0.55). CONCLUSIONS: The results show that the digital spiral analysis-based objective APEN measure is able to significantly differentiate the healthy subjects from patients at advanced level. In contrast to the other two methods (WAV and SDDV) that are designed to quantify dyskinesias (over-medications), this method can be useful for characterizing Off symptoms in PD. The APEN was not correlated to none of the other two methods indicating that it measures a different construct of upper limb motor function in PD patients than WAV and SDDV. The APEN also had a better test-retest reliability indicating that it is more stable and consistent over time than WAV and SDDV.