Stationarity-conservation laws for certain linear fractional differential equations

The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for linear fractional differential equations. The examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1 dimensions are discussed in detail. The results are generalized to the mixed fractional-differential and mixed sequential fractional-differential systems for which the stationarity-conservation laws are obtained. The derived currents are used in construction of stationary nonlocal charges.Comment: 28 page

Principles of Discrete Time Mechanics: II. Classical field Theory

We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate the methodology. Stationary solutions to the discrete time Schrodinger wave equation are found to be identical to standard energy eigenvalue solutions except for a fundamental limit on the energy. Then we apply the formalism to the free neutral Klein Gordon system, deriving the equations of motion and conserved quantities such as the linear momentum and angular momentum. We show that there is an upper bound on the magnitude of linear momentum for physical particle-like solutions. We extend the formalism to the charged scalar field coupled to Maxwell's electrodynamics in a gauge invariant way. We apply the formalism to include the Maxwell and Dirac fields, setting the scene for second quantisation of discrete time mechanics and discrete time Quantum Electrodynamics.Comment: 23 pages, LateX, To be published in J.Phys.A: Math.Gen: contact email address: [email protected]

Effect of Gibberellic Acid (GA3) Inflorescence Application on Content of Bioactive Compounds and Antioxidant Potential of Grape (Vitis L.) ‘Einset Seedless’ Berries

Gibberellic acid (GA3) is a plant growth regulator widely used in the cultivation of seedless grape varieties to increase their yield. Hormonisation treatment has beneficial effects on yield size and quality, yet its influence on the level of biologically active compounds and grape antioxidant activity has not yet been studied extensively yet. Clusters of 11-year-old ‘Einset Seedless’ grapevines trained according to the singleGuyot pruning style were sprayed with GA3 at 100, 200 or 300 mg/L dose once, twice or three times.  Fruit harvested on 25 September were immediately examined for acidity, extract content, biologically active substances and antioxidant capacity using the DPPH test. In addition, correlations occurring between some parameters measured were calculated. Hormonisation had a negative effect on the content of extract, flavonoids and ascorbic acid, while it had no effect on the anthocyanin level. The antioxidant activity determined by the DPPH assay depended on dose and the number of treatments, and the analysed parameters were shown to decrease significantly with increasing application number. Gibberellic acid at 100 and 300 mg/L application rates had a significantly increased DPPH level compared to the control and 200 mg/L dose. The single GA3 treatment, and when applied three times, and application rates at 100 and 200 mg/L were shown to have a significant influence on phenolic acid content. The level of tannins after a single GA3 treatment and a 300 mg/L dose increased significantly

Extensions and degenerations of spectral triples

For a unital C*-algebra A, which is equipped with a spectral triple and an extension T of A by the compacts, we construct a family of spectral triples associated to T and depending on the two positive parameters (s,t). Using Rieffel's notation of quantum Gromov-Hausdorff distance between compact quantum metric spaces it is possible to define a metric on this family of spectral triples, and we show that the distance between a pair of spectral triples varies continuously with respect to the parameters. It turns out that a spectral triple associated to the unitarization of the algebra of compact operators is obtained under the limit - in this metric - for (s,1) -> (0, 1), while the basic spectral triple, associated to A, is obtained from this family under a sort of a dual limiting process for (1, t) -> (1, 0). We show that our constructions will provide families of spectral triples for the unitarized compacts and for the Podles sphere. In the case of the compacts we investigate to which extent our proposed spectral triple satisfies Connes' 7 axioms for noncommutative geometry.Comment: 40 pages. Addedd in ver. 2: Examples for the compacts and the Podle`s sphere plus comments on the relations to matricial quantum metrics. In ver.3 the word "deformations" in the original title has changed to "degenerations" and some illustrative remarks on this aspect are adde

Natural vs anthropogenic streams in Europe: History, ecology and implications for restoration, river-rewilding and riverine ecosystem services

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordIn Europe and North America the prevailing model of “natural” lowland streams is incised-meandering channels with silt-clay floodplains, and this is the typical template for stream restoration. Using both published and new unpublished geological and historical data from Europe we critically review this model, show how it is inappropriate for the European context, and examine the implications for carbon sequestration and Riverine Ecosystem Services (RES) including river rewilding. This paper brings together for the first time, all the pertinent strands of evidence we now have on the long-term trajectories of floodplain system from sediment-based dating to sedaDNA. Floodplain chronostratigraphy shows that early Holocene streams were predominantly multi-channel (anabranching) systems, often choked with vegetation and relatively rarely single-channel actively meandering systems. Floodplains were either non-existent or limited to adjacent organic-filled palaeochannels, spring/valley mires and flushes. This applied to many, if not most, small to medium rivers but also major sections of the larger rivers such as the Thames, Seine, Rhône, Lower Rhine, Vistula and Danube. As shown by radiocarbon and optically stimulated luminescence (OSL) dating during the mid-late Holocene c. 4–2 ka BP, overbank silt-clay deposition transformed European floodplains, covering former wetlands and silting-up secondary channels. This was followed by direct intervention in the Medieval period incorporating weir and mill-based systems – part of a deep engagement with rivers and floodplains which is even reflected in river and floodplain settlement place names. The final transformation was the “industrialisation of channels” through hard-engineering – part of the Anthropocene great acceleration. The primary causative factor in transforming pristine floodplains was accelerated soil erosion caused by deforestation and arable farming, but with effective sediment delivery also reflecting climatic fluctuations. Later floodplain modifications built on these transformed floodplain topographies. So, unlike North America where channel-floodplain transformation was rapid, the transformation of European streams occurred over a much longer time-period with considerable spatial diversity regarding timing and kind of modification. This has had implications for the evolution of RES including reduced carbon sequestration over the past millennia. Due to the multi-faceted combination of catchment controls, ecological change and cultural legacy, it is impractical, if not impossible, to identify an originally natural condition and thus restore European rivers to their pre-transformation state (naturalisation). Nevertheless, attempts to restore to historical (pre-industrial) states allowing for natural floodplain processes can have both ecological and carbon offset benefits, as well as additional abiotic benefits such as flood attenuation and water quality improvements. This includes rewilding using beaver reintroduction which has overall positive benefits on river corridor ecology. New developments, particularly biomolecular methods offer the potential of unifying modern ecological monitoring with the reconstruction of past ecosystems and their trajectories. The sustainable restoration of rivers and floodplains designed to maximise desirable RES and natural capital must be predicated on the awareness that Anthropocene rivers are still largely imprisoned in the banks of their history and this requires acceptance of an increased complexity for the achievement and maintenance of desirable restoration goals.OSL dating from the Severn-Wye Basin was undertaken at the Geochronology Laboratories, University of Gloucestershire under grants from the EU Leader+ Programme (administered by English Heritage) and the Leverhulme Flood and Flow Project (RPG-2016-004)

Lack of consensus in social systems

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let

Challenges for the representation of morphology in ontology lexicons

Recent years have experienced a growing trend in the publication of language resources as Linguistic Linked Data (LLD) to enhance their discovery, reuse and the interoperability of tools that consume language data. To this aim, the OntoLex-lemon model has emerged as a de facto standard to represent lexical data on the Web. However, traditional dictionaries contain a considerable amount of morphological information which is not straightforwardly representable as LLD within the current model. In order to fill this gap a new Morphology Module of OntoLex-lemon is currently being developed. This paper presents the results of this model as on-going work as well as the underlying challenges that emerged during the module development. Based on the MMoOn Core ontology, it aims to account for a wide range of morphological information, ranging from endings to derive whole paradigms to the decomposition and generation of lexical entries which is in compliance to other OntoLex-lemon modules and facilitates the encoding of complex morphological data in ontology lexicons

Configurations of the circle of Willis: a computed tomography angiography based study on a Polish population

The aim of the study was to investigate the distribution of the circle of Willis variants in Polish population by means of computed tomography angiography (CTA). The results were then analysed and compared with another study that used similar methods but that was carried out on an ethnically distinct population. Patients presenting with intracranial pathology were excluded from the initial study population. In total, 250 CTA belonging to 129 female and 121 male patients were reviewed. A modified classification system of the circle was proposed, which took into consideration the anterior and the posterior aspects of the circle individually. The typical variant of Willis’s circle occurred in 16.80% of cases. The anterior and the posterior portions of the circle were normal in 47.20% and 26.80% of the patients respectively. As forthe anterior part, lack of the anterior communicating artery was the most frequent abnormality (22.80%). Bilateral absence of posterior communicating arteries was the most common anomaly in the posterior part of the circle (29.20%). This type of anomaly was also the most common, when taking into consideration the entire circle (12.00%). There were statistically significant differences between the age groupsand genders when considering the occurrence of an incomplete circle. Overall, a substantial proportion of patients manifested clinically important variants that were incapable of providing collateral circulation. Comparison with other imaging-based and cadaveric studies revealed noticeable differences, that may have resulted from the variable technical features of other studies or other factors such as the ethnical origins of the studied populations

Irreducibility of multilayer network dynamics: the case of the voter model

10 pages, 6 figuresThis work has been supported by the Spanish MINECO and FEDER under projects INTENSE@COSYP (FIS2012-30634), and by the EU Commission through the project LASAGNE (FP7-ICT-318132). VL also acknowledges support from EPSRC project GALE (EP/K020633/1