Enumerating Minimal Connected Dominating Sets

The question to enumerate all (inclusion-wise) minimal connected dominating sets in a graph of order n in time significantly less than 2? is an open question that was asked in many places. We answer this question affirmatively, by providing an enumeration algorithm that runs in time ?(1.9896?), using polynomial space only. The key to this result is the consideration of this enumeration problem on 2-degenerate graphs, which is proven to be possible in time ?(1.9767?). Apart from solving this old open question, we also show new lower bound results. More precisely, we construct a family of graphs of order n with ?(1.4890?) many minimal connected dominating sets, while previous examples achieved ?(1.4422?). Our example happens to yield 4-degenerate graphs. Additionally, we give lower bounds for the previously not considered classes of 2-degenerate and of 3-degenerate graphs, which are ?(1.3195?) and ?(1.4723?), respectively. We also address essential questions concerning output-sensitive enumeration. Namely, we give reasons why our algorithm cannot be turned into an enumeration algorithm that guarantees polynomial delay without much efforts. More precisely, we prove that it is NP-complete to decide, given a graph G and a vertex set U, if there exists a minimal connected dominating set D with U ? D, even if G is known to be 2-degenerate. Our reduction also shows that even any subexponential delay is not easy to achieve for enumerating minimal connected dominating sets. Another reduction shows that no FPT-algorithms can be expected for this extension problem concerning minimal connected dominating sets, parameterized by |U|. This also adds one more problem to the still rather few natural parameterized problems that are complete for the class W[3]. We also relate our enumeration problem to the famous open Hitting Set Transversal problem, which can be phrased in our context as the question to enumerate all minimal dominating sets of a graph with polynomial delay by showing that a polynomial-delay enumeration algorithm for minimal connected dominating sets implies an affirmative algorithmic solution to the Hitting Set Transversal problem

VARIABILITY OF STRIDE FREQUENCY AND PRONATION VELOCITY DURING A 16 DAY RELAY-RUN AROUND GERMANY – A CASE STUDY

This case study analyzed stride frequency, represented by time of gait cycle (TGC), and maximum pronation velocity (MPV) for one subject running 350 km over 16 consecutive days. Data collection took place during a day-and-night team relay-race around Germany in 2008. TGC and MPV measurements were performed by a gyrometer incorporated in the subject’s running shoe and recorded by a portable data logger. For data analysis TGC and MPV velocity were determined in 25 runs for altogether 112,532 steps of the right foot. Means and standard deviations of both parameters for complete runs and for all consecutive five-minute segments within each run were calculated. Results showed an increase of TGC and a decrease of MPV within single runs. Between run comparisons across all 25 runs showed no systematic change in TGC and MPV during the relay-race. Interestingly, during the unfamiliar night-runs TGC and MPV were increased compared to day-runs, potentially caused by altered biorhythm or limited vision at night

Plants and mental disorders: the case of Catalan linguistic area

Introduction: Mental disorders are among the leading causes of ill-health and disability worldwide. Despite the disease burden they cause, including significant direct and indirect impacts on individual’s health and major social and economic consequences in all countries of the world, it is still one of the most neglected areas of public health. In such a context, the medicinal plants traditionally used to pale these pathologies are presented as a promising tool for future drug development for the management of mental health disorders. The aim of the present study is to analyze the information about plant species used to treat mental disorders in the Catalan linguistic area (CLA) and compare these traditional uses with pharmacological literature in order to evaluate the most quoted taxa and their uses and to provide a basis for further research. Methods: Data have been recovered from the “Etnobotànica dels Països Catalans” webpage (https://etnobotanica.iec.cat/) and the meta-analytic work carried out in the present study covers 27 prospections performed in different territories between 1990 and 2019. Descriptive statistics and quantitative ethnobotany were carried out and some ethnobotanical indices were calculated. Results and Discussion: The number of use reports analysed to treat mental disorders in CLA is 2,544 spread over 183 taxa belonging to 64 families, being the most cited the Malvaceae (29.36% of use reports), Lamiaceae (16.71%), Caprifoliaceae (7.94%), Rutaceae (7.47%) and Papaveraceae (6.01%). The most used taxa to treat or alleviate the mental disorders have been Tilia platyphyllos Scop. (24.53%), Valeriana officinalis L. (7.47%), Salvia officinalis L. (5.07%), Sambucus nigra L. (4.28%), and Ruta chalepensis L. (3.89%). The flowers or inflorescences (47.68%), followed by aerial part (23.49%), have been the most used plant parts, and tisane the most commonly used pharmaceutical form (78.03%). The most reported use is as sedative with 40.92%, followed by anticephalalgic (21. 19%) and tranquilizer (20.01%). The informant consensus factor (FIC) was 0.93, and 3.72% was the ethnobotanicity index (EI) value. The information is coincidental with at least one of the comprehensive pharmacological literature sources checked for 73.68% of ethnobotanical uses

Stratigraphy and petrology of the Miocene Montjuïc delta (Barcelona, Spain)

The Neogene rift in the Catalan Coastal Ranges, which is located in the NE part of the Eastern Iberian Margin, corresponds to a system of grabens formed at the north-western edge of the Valencia Trough. In the central part of the Catalan Coastal Ranges are the Vallès - Penedès half-graben in the onshore and the Barcelona half-graben in the offshore, which are separated by the Garraf and the Collserola-Montnegre horsts. Montjuïc hill is a tilted block, which is located to the S of the Barcelona city, between the Collserola-Montnegre horst and the Barcelona half-graben . The Middle Miocene section of Montjuïc is constituted by an alternation of conglomerate, sandstone, mudstone and marlstone beds. The Montjuïc section was divided into four lithostratigraphic units from base to top: (1) The Morrot conglomerate and sandstone Unit, interpreted as delta plain deposits; (2) the Castell conglomerate, sandstone and mudstone Unit considered as proximal delta front deposits; (3) the Miramar marlstone Unit attributed to prodelta deposits; and (4) the Mirador conglomerate, sandstone and mudstone Unit interpreted as delta front deposits. As regards the foraminifera association, the Miocene of Montjuïc may be attributed to the N9-N10 zones of Blow, indicating a Serravallian age. The palaeobotanical record suggests that the climate during the deposition of the Miocene of Montjuïc was temperate-warm and humid. The sandstones and conglomerates are litharenites and lithorudites; they show variable amounts of matrix and are well cemented. The main framework components are quartz, rock fragments and K-feldspar. The Collserola mountain, where Palaeozoic materials crop out is the deduced source area. Montjuïc sandstones are characterized by an early silicic cementation consisting of K-feldspar overgrowths, quartz overgrowths, mesoquartz intergranular cement and a microquartz transformation of a former detrital matrix. A surface cementation is considered for these cements in the absence of compaction and the geological setting