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We analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another through dispersal or migration. We assume that the inter-patch migrations are detailed balanced and that the patches are identical with intra-patch dynamics governed by a mean-field ODE system with a coexistence equilibrium. By making use of an appropriate Lyapunov function coupled with LaSalle’s invariance principle, we are able to show that the coexistence equilibrium point within each patch is locally asymptotically stable if the inter-patch dispersal network is heterogeneous, whereas it is neutrally stable in the case of a homogeneous network. These results provide a mathematical proof confirming the existing numerical simulations and broaden the range of networks for which they are valid.

JPhys photonics 4, 034003 (2022). doi:10.1088/2515-7647/ac6ea5 special issue: "Focus on Nanophotonics and Biophotonics for Biomedical and Environmental Applications", The dynamics of biologically relevant molecules exposed to ionizing radiation contains many facets and spans several orders of magnitude in time and energy. In the extreme ultraviolet (XUV) spectral range, multi-electronic phenomena and bands of correlated states with inner-valence holes must be accounted for in addition to a plethora of vibrational modes and available dissociation channels. The ability to track changes in charge density and bond length during ultrafast reactions is an important endeavor toward more general abilities to simulate and control photochemical processes, possibly inspired by those that have evolved biologically. By using attosecond XUV pulses extending up to 35 eV and few-femtosecond near-infrared pulses, we have previously time-resolved correlated electronic dynamics and charge migration occurring in the biologically relevant molecule adenine after XUV-induced sudden ionization. Here, using additional experimental data, we comprehensively report on both electronic and vibrational dynamics of this nucleobase in an energy range little explored to date with high temporal resolution. The time-dependent yields of parent and fragment ions in the mass spectra are analyzed to extract exponential time constants and oscillation periods. Together with time-dependent density functional theory and ab-initio Green's function methods, we identify different vibrational and electronic processes. Beyond providing further insights into the XUV-induced dynamics of an important nucleobase, our work demonstrates that yields of specific dissociation outcomes can be influenced by sufficiently well-timed ultrashort pulses, therefore providing a new route for the control of the multi-electronic and dissociative dynamics of a DNA building block., Published by IOP Publishing, Bristol

Theoretical and experimental research studies have shown that ecosystems governed by non-transitive competition networks tend to maintain high levels of biodiversity. The theoretical body of work, however, has mainly focused on competition networks in which the outcomes of competition events are predetermined and hence deterministic, and where all species are identical up to their competitive relationships, an assumption that may limit the applicability of theoretical results to real-life situations. In this paper, we aim to probe the robustness of the link between biodiversity and non-transitive competition by introducing a three-dimensional winning probability parameter space, making the outcomes of competition events in a three-species in silico ecosystem uncertain. While two degenerate points in this parameter space have been the subject of previous studies, we investigate the remaining settings, which equip the species with distinct competitive abilities. We find that the impact of this modification depends on the spatial dimension of the system. When the system is well mixed, it collapses to monoculture, as is also the case in the non-transitive deterministic setting. In one dimension, chaotic patterns emerge, which tend to maintain biodiversity, and a power law relates the time that species manage to coexist to the degree of uncertainty regarding competition event outcomes. In two dimensions, the formation of spiral wave patterns ensures that biodiversity is maintained for moderate degrees of uncertainty, while considerable deviations from the non-transitive deterministic setting have strong negative effects on species coexistence. It can hence be concluded that non-transitive competition can still produce coexistence when the assumption of deterministic competition is abandoned. When the system collapses to monoculture, one observes a "survival of the strongest" law, as the species that has the highest probability of defeating its competitors has the best odds to become the sole survivor.

In the preceding paper of this series [Leontidis, E. Aroti, A. Belloni, L. J. Phys. Chem. B 2009, 113, 1447], we considered and modeled the increase of the surface pressure of dipalmitoyl phosphatidylcholine (DPPC) monolayers over electrolyte solutions of various monovalent sodium salts. The experimental results for salts with large, less hydrophilic anions can be successfully described by models treating ionic specificity either as specific partitioning in the interfacial lipid layer or as a result of ion-lipid dispersion interactions. However, the results for salts with more hydrophilic anions, such as chloride and fluoride, cannot be fitted by any of these models, while they clearly demonstrate the existence of a specific sodium-DPPC interaction. In the present paper, we first prove that the experimental results for sodium fluoride (NaF) can be fitted by a model that is based on simultaneous complexation of sodium ions with up to three lipid molecules, as suggested by recent molecular dynamics simulations. We then return to the experimental results of sodium salts with more hydrophobic anions, treated in the preceding paper, and prove that these can be fitted equally well with a complex model, which accounts for both sodium complexation with the lipid head groups and anion partitioning within the lipid monolayers. The partitioning parameters obtained from this more complete model correlate well with several measures of ion specificity, such as ionic volume, von Hippel chromatographic parameters, or viscosity B-coefficients. A model for these partitioning chemical potentials is created based on the competition of cavity and ion hydration terms. The model leads to an excellent correlation of the partitioning chemical potentials with a function of the ionic radius, suggesting that specific anion effects on this lipid model system are mostly a matter of ionic size. Two notable exceptions from this correlation are thiocyanate and acetate ions, the charge distribution of which is not spherically symmetric, so that they are expected to have orientational-dependent interactions with the water-lipid interface. The implications of the present results on ion specificity in general are discussed. © 2009 American Chemical Society. 113 5 1460 1467 Cited By :43

We study the effect of the sample thickness in planar crack front propagation in a disordered elastic medium using the random fuse model. We employ different loading conditions and we test their stability with respect to crack growth. We show that the thickness induces characteristic lengths in the stress enhancement factor in front of the crack and in the stress transfer function parallel to the crack. This is reflected by a thickness-dependent crossover scale in the crack front morphology that goes from from multi-scaling to self-affine with exponents in agreement with line depinning models and experiments. Finally, we compute the distribution of crack avalanches which is shown to depend on the thickness and the loading mode., Comment: 8 pages, 11 figures

The work in this licentiate thesis examines the adsorption of polyelectrolyte multilayers (PEM) onto wood fibres as a new way to influence the properties of the fibre surfaces and hence the fibres. Fundamental aspects of PEM formation on wood fibres have been studied, and discussed in terms of paper strength and wood fibre wettability. PEMs have been formed from three different polymer systems: 1) two strong polyelectrolytes (i.e., fully charged over a wide pH range), polydimethyldiallylammonium chloride (PDADMAC) and polystyrene sulphonate (PSS); 2) polyethylene oxide (PEO) and polyacrylic acid (PAA), formed at low pH and held together by hydrogen bonding; and 3) two weak polyelectrolytes, polyallylamine hydrochloride (PAH) and polyacrylic acid (PAA). The PEMs formed from PDADMAC/PSS and PEO/PAA were studied using Stagnation Point Adsorption Reflectometry (SPAR), with SiO2 as the substrate. This was done to establish the formation of PEMs and, using PDADMAC/PSS, also to predict the influence of salt concentration during PEM formation. The amount of PDADMAC/PSS adsorbed was found to increase with salt concentration up to approximately 0.1 M NaCl. The formation of PEMs from PAH/PAA has already been studied in terms of structure; amount adsorbed, and influence on paper strength. Sheets were formed from fibres treated with either PDADMAC/PSS or PEO/PAA PEMs and tested to determine paper tensile strength. Both PEM systems increased the tensile index and strain at break in the range of 100% when approximately 10 layers had been adsorbed. After several PEM layers had been adsorbed, the sheets made of fibres treated with PDADMAC/PSS differed in tensile strength depending on the polymer adsorbed in the outermost layer. A higher tensile strength was detected when PDADMAC rather than PSS was adsorbed in the outermost layer. Sheets made of fibres treated with PEO/PAA displayed a linear increase in strength, independent of which polymer that was adsorbed in the outermost layer. The amount of adsorbed PDADMAC/PSS, as analysed using nitrogen and sulphur analysis, respectively, increased linearly, but with a higher amount adsorbed in the first layer. A comparison of the adsorption onto the SiO2-surfaces (SPAR-measurements) and fibres shows some differences. This is apparent both regarding the adsorption in the first layer and in the change in adsorbed amount with salt concentration. Despite this, one can conclude that SiO2 and wood fibres show very similar trends, and that SiO2 can be used as a convenient model surface in predicting PEM formation on wood fibres. Individual fibres were also partially treated using a Dynamic Contact Angle Analyser, and the treated and untreated parts were analysed in terms of wettability and surface structure. The differences in wettability are significant, depending on the polymer system used and, with PAH/PAA PEMs, the pH strategy show a large influence in wettability. PDADMAC/PSS and PAH/PAA PEMs both had a large influence on wettability, depending on the polymer adsorbed in the outermost layer, wettability being lower when the cationic polymer was adsorbed in the outermost layer. With the PEO/PAA system, however, the polymer adsorbed in the outermost layer caused no detectable difference. These results, when compared against the paper strength results, indicate that the strongest sheets are formed of the fibres with the lowest wettability. This may be explained in terms of wet adhesion: since the fibre networks are formed in water, lower wettability would give a stronger force between the fibres during consolidation, resulting in a greater contact area and thus probably a stronger dry adhesion between the fibres in the formed sheet. This is furthermore also supported by wet adhesion measurements using Atomic Force Microscopy where PEMs formed from PAH/PAA, show that the pull-off force is increased when PAH is adsorbed in the outermost layer, compared to when PAA is adsorbed in the outermost layer. Denna licentiatavhandling behandlar adsorption av polyelektrolytmultiskikt (multiskikt) på cellulosafibrer som ett nytt sätt att påverka en fibers ytegenskaper. Grundläggande förutsättningar för bildandet av multiskikt på fibrer diskuteras i termer av pappersstyrka och fibervätning. Multiskikt har bildats med hjälp av tre olika polymerkombinationer; 1.) två starka polyelektrolyter, polydiallyldimetylammoniumklorid (PDADMAC) och polystyrensulfanat (PSS), 2.) polyetylenoxid (PEO) och polyakrylsyra (PAA), adsorberade vid lågt pH och sammanhållna av icke elektrostatiska vätebindningar, och 3.) två svaga polyelektrolyter, polyallylaminhydroklorid (PAH) och PAA. Uppbyggnaden av multiskikt bestående av PDADMAC/PSS och PEO/PAA på kiseloxid studerades med Stagnationspunktsreflektometri (SPAR) för att undersöka att uppbyggnad av PEM skett, samt att studera hur uppbyggnaden påverkas av koncentrationen NaCl i polymerlösningen. Försöken visade att den adsorberade mängden PDADMAC/PSS ökade med saltkoncentrationen upp till 0,05-0,1 M NaCl. Uppbyggnaden av multiskikt bestående av PAH/PAA är sedan tidigare studerad undersöks därför inte specifikt i detta arbete. Laboratorieark tillverkades av fibrer som behandlats med multiskikt bestående av PDADMAC/PSS, respektive PAH/PAA. Fysikalisk pappersprovning av arken visade för båda systemen en ökning med cirka 100 % i dragindex för ark som tillverkats av fibrer som behandlats med cirka tio lager, jämfört med ark som tillverkats av icke-behandlade fibrer. Ark tillverkade från PDADMAC/PSS-behandlade fibrer visade att när 5-7 lager adsorberats, ett högre dragindex då PDADMAC adsorberats i det yttersta lagret, jämfört med då PSS adsorberats i det yttersta lagret. Ark tillverkade från fibrer behandlade med PEO/PAA visade ingen skillnad i dragindex beroende av vilken polymer som adsorberats i det yttersta lagret. Den adsorberade mängden PDADMAC/PSS på fibrerna bestämdes med hjälp av kväve- respektive svavelanalys. Den adsorberade mängden polymer ökad linjärt som en funktion av antalet adsorberade lager, men med en högre adsorberad mängd i det första lagret. Dessa resultat har jämförts med den adsorberade mängden för multiskikt uppbyggda med SPAR på kiseloxid. Jämförelsen visade att det finns skillnader i uppbyggnaden mellan skikt byggda på kiseloxid och fibrer, men att kiseloxid med god tillförlitlighet kan användas som modellyta för att förutsäga generella trender för adsorptionen av samma polymersystem på cellulosafibrer. Multiskikt har också bildats på enskilda fibrer med hjälp av en dynamisk kontaktvinkelmätare (DCA). Genom att behandla en del av en fiber, och jämföra den behandlade delen med den obehandlade delen på samma, kan ett multiskikts inverkan på fiberns ytstruktur och vätningsegenskaper studeras. De olika polymersystemen visade en avsevärd skillnad i förmågan att påverka en fibers vätningsegenskaper. För fibrer behandlade med PAH/PAA är också pH av stor betydelse för graden inverkan på fiberns vätningsegenskaper. Fibrer behandlade med PDADMAC/PSS och PAH/PAA, visade en sämre vätningsförmåga då den katjoniska polymeren adsorberats i det yttersta lagret, och vice versa. För enskilda fibrer behandlade med PEO/PAA, kunde inte konstateras någon skillnad beroende av vilken polymer som adsorberats i det yttersta lagret. Vid en jämförelse mellan vätningsförmåga och pappersstyrka kan konstateras att de ark som visade den högsta styrkan tillverkats av fibrer där den lägsta vätningsförmågan har kunnat konstateras. Denna skillnad kan diskuteras med utgångspunkten i att en lägre vätningsförmåga resulterar i en högre våt adhesion och därmed en starkare interaktion mellan de polymerbehandlade ytorna i vått tillstånd. Det föreslås i avhandlingen att den ökade kraft som detta resulterar i vid bildandet av en fiber-fiberfog ger upphov till en högre kontaktarea och därmed, förmodligen, också en högre torr adhesion. Kraftmätningar i vått tillstånd för behandlade kiselmodellytor med hjälp av atomkraftsmikroskopi (AFM) har för PAH/PAA visat att den våta adhesionen är högre då PAH är adsorberats i det yttersta lagret, jämfört med då PAA adsorberats i det yttersta lagret. Detta stödjer hypotesen att en lägre vätning gynnar uppkomsten av en stark fiber-fiberfog. QC 20101118

This paper presents a biologically inspired, hardware-realisable spiking neuron model, which we call the Temporal Noisy-Leaky Integrator (TNLI). The dynamic applications of the model as well as its applications in Computational Neuroscience are demonstrated and a learning algorithm based on postsynaptic delays is proposed. The TNLI incorporates temporal dynamics at the neuron level by modelling both the temporal summation of dendritic postsynaptic currents which have controlled delay and duration and the decay of the somatic potential due to its membrane leak. Moreover, the TNLI models the stochastic neurotransmitter release by real neuron synapses (with probabilistic RAMs at each input) and the firing times including the refractory period and action potential repolarisation. The temporal features of the TNLI make it suitable for use in dynamic time-dependent tasks like its application as a motion and velocity detector system presented in this paper. This is done by modelling the experimental velocity selectivity curve of the motion sensitive H1 neuron of the visual system of the fly. This application of the TNLI indicates its potential applications in artificial vision systems for robots. It is also demonstrated that Hebbian-based learning can be applied in the TNLI for postsynaptic delay training based on coincidence detection, in such a way that an arbitrary temporal pattern can be detected and recognised. The paper also demonstrates that the TNLI can be used to control the firing variability through inhibition with 80% inhibition to concurrent excitation, firing at high rates is nearly consistent with a Poisson-type firing variability observed in cortical neurons. It is also shown with the TNLI, that the gain of the neuron (slope of its transfer function) can be controlled by the balance between inhibition and excitation, the gain being a decreasing function of the proportion of inhibitory inputs. Finally, in the case of perfect balance between inhibition and excitation, i.e. where the average input current is zero, the neuron can still fire as a result of membrane potential fluctuations. The firing rate is then determined by the average input firing rate. Overall this work illustrates how a hardware-realisable neuron model can capitalise on the unique computational capabilities of biological neurons. © 2002 Elsevier Science Ltd. All rights reserved. 15 7 891 908 Cited By :27