On the Number of Synchronizing Colorings of Digraphs

We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have different colors. Such a coloring corresponds naturally to an automaton. The road coloring theorem states that every primitive digraph has a synchronizing coloring. In the present paper we study how many synchronizing colorings can exist for a digraph with $n$ vertices. We performed an extensive experimental investigation of digraphs with small number of vertices. This was done by using our dedicated algorithm exhaustively enumerating all small digraphs. We also present a series of digraphs whose fraction of synchronizing colorings is equal to $1-1/k^d$, for every $d \ge 1$ and the number of vertices large enough. On the basis of our results we state several conjectures and open problems. In particular, we conjecture that $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.Comment: CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1

A systematic review of the safety of lisdexamfetamine dimesylate

BACKGROUND: Here we review the safety and tolerability profile of lisdexamfetamine dimesylate (LDX), the first long-acting prodrug stimulant for the treatment of attention-deficit/hyperactivity disorder (ADHD). METHODS: A PubMed search was conducted for English-language articles published up to 16 September 2013 using the following search terms: (lisdexamfetamine OR lisdexamphetamine OR SPD489 OR Vyvanse OR Venvanse OR NRP104 NOT review [publication type]). RESULTS: In short-term, parallel-group, placebo-controlled, phase III trials, treatment-emergent adverse events (TEAEs) in children, adolescents, and adults receiving LDX were typical for those reported for stimulants in general. Decreased appetite was reported by 25-39 % of patients and insomnia by 11-19 %. The most frequently reported TEAEs in long-term studies were similar to those reported in the short-term trials. Most TEAEs were mild or moderate in severity. Literature relating to four specific safety concerns associated with stimulant medications was evaluated in detail in patients receiving LDX. Gains in weight, height, and body mass index were smaller in children and adolescents receiving LDX than in placebo controls or untreated norms. Insomnia was a frequently reported TEAE in patients with ADHD of all ages receiving LDX, although the available data indicated no overall worsening of sleep quality in adults. Post-marketing survey data suggest that the rate of non-medical use of LDX was lower than that for short-acting stimulants and lower than or equivalent to long-acting stimulant formulations. Small mean increases were seen in blood pressure and pulse rate in patients receiving LDX. CONCLUSIONS: The safety and tolerability profile of LDX in individuals with ADHD is similar to that of other stimulants

A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds

The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative method computing a coordinate independent property of a function (such as a zero or a local minimum). All possible Newton methods on manifolds are believed to come under this framework. Changes of coordinates, and not any Riemannian structure, are shown to play a natural role in lifting the Newton method to a manifold. The framework also gives new insight into the design of Newton methods in general.Comment: 36 page

Efficacy of lisdexamfetamine dimesylate throughout the day in children and adolescents with attention-deficit/hyperactivity disorder:results from a randomized, controlled trial

Lisdexamfetamine dimesylate (LDX) is a long-acting, prodrug stimulant therapy for patients with attention-deficit/hyperactivity disorder (ADHD). This randomized placebo-controlled trial of an optimized daily dose of LDX (30, 50 or 70 mg) was conducted in children and adolescents (aged 6–17 years) with ADHD. To evaluate the efficacy of LDX throughout the day, symptoms and behaviors of ADHD were evaluated using an abbreviated version of the Conners’ Parent Rating Scale-Revised (CPRS-R) at 1000, 1400 and 1800 hours following early morning dosing (0700 hours). Osmotic-release oral system methylphenidate (OROS-MPH) was included as a reference treatment, but the study was not designed to support a statistical comparison between LDX and OROS-MPH. The full analysis set comprised 317 patients (LDX, n = 104; placebo, n = 106; OROS-MPH, n = 107). At baseline, CPRS-R total scores were similar across treatment groups. At endpoint, differences (active treatment − placebo) in least squares (LS) mean change from baseline CPRS-R total scores were statistically significant (P < 0.001) throughout the day for LDX (effect sizes: 1000 hours, 1.42; 1400 hours, 1.41; 1800 hours, 1.30) and OROS-MPH (effect sizes: 1000 hours, 1.04; 1400 hours, 0.98; 1800 hours, 0.92). Differences in LS mean change from baseline to endpoint were statistically significant (P < 0.001) for both active treatments in all four subscales of the CPRS-R (ADHD index, oppositional, hyperactivity and cognitive). In conclusion, improvements relative to placebo in ADHD-related symptoms and behaviors in children and adolescents receiving a single morning dose of LDX or OROS-MPH were maintained throughout the day and were ongoing at the last measurement in the evening (1800 hours)

Sub-Planckian black holes and the Generalized Uncertainty Principle

The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution under $M \leftrightarrow M^{-1}$ naturally implies a Generalized Uncertainty Principle with the linear form $\Delta x \sim \frac{1}{\Delta p} + \Delta p$. We also demonstrate a natural dimensional reduction feature, in that the gravitational radius and thermodynamics of sub-Planckian objects resemble that of $(1+1)$-D gravity. The temperature of sub-Planckian black holes scales as $M$ rather than $M^{-1}$ but the evaporation of those smaller than $10^{-36}$g is suppressed by the cosmic background radiation. This suggests that relics of this mass could provide the dark matter.Comment: 12 pages, 9 figures, version published in J. High En. Phy

Treatment response and remission in a double-blind, randomized, head-to-head study of lisdexamfetamine dimesylate and atomoxetine in children and adolescents with attention-deficit hyperactivity disorder

The Author(s) 2014. This article is published with open access at Springerlink.com Objectives A secondary objective of this head-to-head study of lisdexamfetamine dimesylate (LDX) and ato-moxetine (ATX) was to assess treatment response rates in children and adolescents with attention-deficit hyperactiv-ity disorder (ADHD) and an inadequate response to methylphenidate (MPH). The primary efficacy and safety outcomes of the study, SPD489-317 (ClinicalTrials.gov NCT01106430), have been published previously. Methods In this 9-week, double-blind, active-controlled study, patients aged 6–17 years with a previous inadequate response to MPH were randomized (1:1) to dose-optimized LDX (30, 50 or 70 mg/day) or ATX (patients \70 kg: 0.5–1.2 mg/kg/day, not to exceed 1.4 mg/kg/day; patients C70 kg: 40, 80 or 100 mg/day). Treatment response was a secondary efficacy outcome and was predefined as a reduction from baseline in ADHD Rating Scale IV (ADHD-RS-IV) total score of at least 25, 30 or 50 %. Sustained response was predefined as a reduction from baseline in ADHD-RS-IV total score (C25, C30 or C50 %) or a Clinical Global Impressions (CGI)–Improvement (CGI–I) score of 1 or 2 throughout weeks 4–9. CGI– Severity (CGI–S) scores were also assessed, as an indicator of remission. Results A total of 267 patients were enrolled (LDX, n = 133; ATX, n = 134) and 200 completed the study (LDX, n = 99; ATX, n = 101). By week 9, significantly (p \ 0.01) greater proportions of patients receiving LDX than ATX met the response criteria of a reduction from baseline in ADHD-RS-IV total score of at least 25 % (90.5 vs. 76.7 %), 30 % (88.1 vs. 73.7 %) or 50 % (73.0 vs. 50.4 %). Sustained response rates were also signifi-cantly (p \ 0.05) higher among LDX-treated patient

Genetic, serological and biochemical characterization of Leishmania tropica from foci in northern Palestine and discovery of zymodeme MON-307

Background Many cases of cutaneous leishmaniasis (CL) have been recorded in the Jenin District based on their clinical appearance. Here, their parasites have been characterized in depth. Methods Leishmanial parasites isolated from 12 human cases of CL from the Jenin District were cultured as promastigotes, whose DNA was extracted. The ITS1 sequence and the 7SL RNA gene were analysed as was the kinetoplast minicircle DNA (kDNA) sequence. Excreted factor (EF) serotyping and multilocus enzyme electrophoresis (MLEE) were also applied. Results This extensive characterization identified the strains as Leishmania tropica of two very distinct sub-types that parallel the two sub-groups discerned by multilocus microsatellite typing (MLMT) done previously. A high degree of congruity was displayed among the results generated by the different analytical methods that had examined various cellular components and exposed intra-specific heterogeneity among the 12 strains. Three of the ten strains subjected to MLEE constituted a new zymodeme, zymodeme MON-307, and seven belonged to the known zymodeme MON-137. Ten of the 15 enzymes in the profile of zymodeme MON-307 displayed different electrophoretic mobilities compared with the enzyme profile of the zymodeme MON-137. The closest profile to that of zymodeme MON-307 was that of the zymodeme MON-76 known from Syria. Strains of the zymodeme MON-307 were EF sub-serotype A2 and those of the zymodeme MON-137 were either A9 or A9B4. The sub-serotype B4 component appears, so far, to be unique to some strains of L. tropica of zymodeme MON-137. Strains of the zymodeme MON-137 displayed a distinctive fragment of 417 bp that was absent in those of zymodeme MON-307 when their kDNA was digested with the endonuclease RsaI. kDNA-RFLP after digestion with the endonuclease MboI facilitated a further level of differentiation that partially coincided with the geographical distribution of the human cases from which the strains came. Conclusions The Palestinian strains that were assigned to different genetic groups differed in their MLEE profiles and their EF types. A new zymodeme, zymodeme MON-307 was discovered that seems to be unique to the northern part of the Palestinian West Bank. What seemed to be a straight forward classical situation of L. tropica causing anthroponotic CL in the Jenin District might be a more complex situation, owing to the presence of two separate sub-types of L. tropica that, possibly, indicates two separate transmission cycles involving two separate types of phlebotomine sand fly vector

Standard decomposition of expansive ergodically supported dynamics

In this work we introduce the notion of weak quasigroups, that are quasigroup operations defined almost everywhere on some set. Then we prove that the topological entropy and the ergodic period of an invertible expansive ergodically supported dynamical system $(X,T)$ with the shadowing property establishes a sufficient criterion for the existence of quasigroup operations defined almost everywhere outside of universally null sets and for which $T$ is an automorphism. Furthermore, we find a decomposition of the dynamics of $T$ in terms of $T$-invariant weak topological subquasigroups.Comment: 18 pages, the conditions on the entropy in Theorem 3.5 was improved. Some small changes in the text, by adding more explanation

Dynamics of conflicts in Wikipedia

In this work we study the dynamical features of editorial wars in Wikipedia (WP). Based on our previously established algorithm, we build up samples of controversial and peaceful articles and analyze the temporal characteristics of the activity in these samples. On short time scales, we show that there is a clear correspondence between conflict and burstiness of activity patterns, and that memory effects play an important role in controversies. On long time scales, we identify three distinct developmental patterns for the overall behavior of the articles. We are able to distinguish cases eventually leading to consensus from those cases where a compromise is far from achievable. Finally, we analyze discussion networks and conclude that edit wars are mainly fought by few editors only.Comment: Supporting information adde

An observational study of once-daily modified-release methylphenidate in ADHD: effectiveness on symptoms and impairment, and safety

ADHD affects over 5% of children worldwide. It is typically treated with stimulant medications, and methylphenidate (MPH) is the most commonly prescribed. This study investigated the effectiveness, on symptoms and impairment, and safety of Equasym XL®, a combination of 30% immediate-release and 70% modified-release MPH, in the treatment of ADHD in daily clinical practice. This open-label, observational, post-marketing surveillance study was conducted in 169 centres in Germany. Eligible patients, aged 6–17 years, were diagnosed with ADHD and about to begin treatment with Equasym XL®. Effectiveness was assessed by physicians using the clinical global impression (CGI) severity and improvement scales; teachers and parents completed questionnaires evaluating ADHD symptoms and behavioural problems (DAYAS, FBB-ADHD and SDQ-P). Assessments were carried out at baseline, after 1–3 and 6–12 weeks of treatment. Of 852 enrolled patients, 822 were evaluable; 25.30% were treatment naïve, 69.84% had previously received different MPH formulations, and 4.87% had received other medications. ADHD symptoms improved from baseline to last visit for the majority of patients for all outcome measures. According to physician ratings of core ADHD symptoms, 75.73% of patients showed improvements on the CGI-Improvement scale, 17.77% had no change, and 6.50% worsened. In teacher and parent ratings, the effectiveness of Equasym XL® was rated better than prior therapy at all measured time points across the day, particularly late morning (teachers) and early afternoon (parents). Equasym XL® was generally well tolerated; only 3.16% of patients permanently discontinued treatment due to adverse events. Equasym XL® is effective and well tolerated in daily clinical practice