Unification in Abelian Semigroups

Unification in equational theories, i.e. solving of equations in varieties, is a basic operation in Computational Logic, in Artificial Intelligence (AI) and in many applications of Computer Science. In particular the unification of terms in the presence of an associative and commutative f unction, i.e. solving of equations in Abelian Semigroups, turned out to be of practical relevance for Term Rewriting Systems, Automated Theorem Provers and many AI-programming languages. The observation that unification under associativity and commutativity reduces to the solution of certain linear diophantine equations is the basis for a complete and minimal unification algorithm. The set of most general unifiers is closely related to the notion of a basis for the linear solution space of these equations. These results are extended to unification in free term algebras combined with Abelian Semigroups

Coexistence of competitors mediated by nonlinear noise

Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative models such as Fokker- Planck diffusion is not less convincing, movement of populations is most commonly modelled using the diffusion law due to Fick. An interesting feature of Fokker-Planck diffusion is the fact that for spatially varying diffusion coefficients the stationary solution is not a homogeneous distribution – in contrast to Fick’s law of diffusion. Instead, concentration accumulates in regions of low diffusivity and tends to lower levels for areas of high diffusivity. Thus, we may interpret the stationary distribution of the Fokker-Planck diffusion as a reflection of different levels of habitat quality. Moreover, the most common model for environmental fluctuations, linear multiplicative noise, is based on the assumption that individuals respond independently to stochastic environmental fluctuations. For large population densities the assumption of independence is debatable and the model further implies that noise intensities can increase to arbitrarily high levels. Therefore, instead of the commonly used linear multiplicative noise model, we implement environmental variability by an alternative nonlinear noise term which never exceeds a certain maximum noise intensity. With Fokker-Planck diffusion and the nonlinear noise model replacing the classical approaches we investigate a simple invasive system based on the Lotka-Volterra competition model. We observe that the heterogeneous stationary distribution generated by Fokker-Planck diffusion generally facilitates the formation of segregated habitats of resident and invader. However, this segregation can be broken by nonlinear noise leading to coexistence of resident and invader across the whole spatial domain, an effect that would not be possible in the non-spatial version of the competition model for the parameters considered here

Identification of a Hemolysis Threshold That Increases Plasma and Serum Zinc Concentration.

Background: Plasma or serum zinc concentration (PZC or SZC) is the primary measure of zinc status, but accurate sampling requires controlling for hemolysis to prevent leakage of zinc from erythrocytes. It is not established how much hemolysis can occur without changing PZC/SZC concentrations.Objective: This study determines a guideline for the level of hemolysis that can significantly elevate PZC/SZC.Methods: The effect of hemolysis on PZC/SZC was estimated by using standard hematologic variables and mineral content. The calculated hemolysis threshold was then compared with results from an in vitro study and a population survey. Hemolysis was assessed by hemoglobin and iron concentrations, direct spectrophotometry, and visual assessment of the plasma or serum. Zinc and iron concentrations were determined by inductively coupled plasma spectrometry.Results: A 5% increase in PZC/SZC was calculated to result from the lysis of 1.15% of the erythrocytes in whole blood, corresponding to ∼1 g hemoglobin/L added into the plasma or serum. Similarly, the addition of simulated hemolysate to control plasma in vitro caused a 5% increase in PZC when hemoglobin concentrations reached 1.18 ± 0.10 g/L. In addition, serum samples from a population nutritional survey were scored for hemolysis and analyzed for changes in SZC; samples with hemolysis in the range of 1-2.5 g hemoglobin/L showed an estimated increase in SZC of 6% compared with nonhemolyzed samples. Each approach indicated that a 5% increase in PZC/SZC occurs at ∼1 g hemoglobin/L in plasma or serum. This concentration of hemoglobin can be readily identified directly by chemical hemoglobin assays or indirectly by direct spectrophotometry or matching to a color scale.Conclusions: A threshold of 1 g hemoglobin/L is recommended for PZC/SZC measurements to avoid increases in zinc caused by hemolysis. The use of this threshold may improve zinc assessment for monitoring zinc status and nutritional interventions

Taxis-driven pattern formation in a predator-prey model with group defense

We consider a reaction-diffusion(-taxis) predator-prey system with group defense in the prey. Taxis-driven instability can occur if the group defense influences the taxis rate (Wang et al., 2017). We elaborate that this mechanism is indeed possible but biologically unlikely to be responsible for pattern formation in such a system. Conversely, we show that patterns in excitable media such as spatiotemporal Sierpinski gasket patterns occur in the reaction-diffusion model as well as in the reaction-diffusion-taxis model. If group defense leads to a dome-shaped functional response, these patterns can have a rescue effect on the predator population in an invasion scenario. Preytaxis with prey repulsion at high prey densities can intensify this mechanism leading to taxis-induced persistence. In particular, taxis can increase parameter regimes of successful invasions and decrease minimum introduction areas necessary for a successful invasion. Last, we consider the mean period of the irregular oscillations. As a result of the underlying mechanism of the patterns, this period is two orders of magnitude smaller than the period in the nonspatial system. Counter-intuitively, faster-moving predators lead to lower oscillation periods and eventually to extinction of the predator population. The study does not only provide valuable insights on theoretical spatially explicit predator-prey models with group defense but also comparisons of ecological data with model simulations. © 2020 Elsevier B.V

A type IV functional response with different shapes in a predator-prey model.

Group defense is a phenomenon that occurs in many predator-prey systems. Different functional responses with substantially different properties representing such a mechanism exist. Here, we develop a functional response using timescale separation. A prey-dependent catch rate represents the group defense. The resulting functional response contains a single parameter that controls whether the group defense functional response is saturating or dome-shaped. Based on that, we show that the catch rate must not increase monotonically with increasing prey density to lead to a dome-shaped functional response. We apply bifurcation analysis to show that non-monotonic group defense is usually more successful. However, we also find parameter regions in which a paradox occurs. In this case, higher group defense can give rise to a stable limit cycle, while for lower values, the predator would go extinct. The study does not only provide valuable insight on how to include functional responses representing group defense in mathematical models, but it also clarifies under which circumstances the usage of different functional responses is appropriate

Concept logics

Concept languages (as used in BACK, KL-ONE, KRYPTON, LOOM) are employed as knowledge representation formalisms in Artificial Intelligence. Their main purpose is to represent the generic concepts and the taxonomical hierarchies of the domain to be modeled. This paper addresses the combination of the fast taxonomical reasoning algorithms (e.g. subsumption, the classifier etc.) that come with these languages and reasoning in first order predicate logic. The interface between these two different modes of reasoning is accomplished by a new rule of inference, called constrained resolution. Correctness, completeness as well as the decidability of the constraints (in a restricted constraint language) are shown

Opening the AC-Unification Race

This note reports about the implementation of AC-unification algorithms, based on the variable-abstraction method of Stickel and on the constant-abstraction method of Livesey, Siekmann, and Herold. We give a set of 105 benchmark examples and compare execution times for implementations of the two approaches. This documents for other researchers what we consider to be the state-of-the-art performance for elementary AC-unification problems

High Deposition Rate Aluminium Doped Zinc Oxide Films with Highly Efficient Light Trapping for Silicon Thin Film Solar Cells

Abstract Aluminium doped zinc oxide films were deposited on glass substrates at high rates by reactive mid frequency sputtering. The in-line sputter system allows oxygen influx along the middle and sides of a dual cathode system. The effect of varying the oxygen flow from the sides on the electrical and optical properties together with the surface morphology after wet chemical etching was investigated. Increasing the amount of oxygen flow from the sides improved the resistivity profile of static prints and gave highly conductive and transparent films in dynamic deposition mode. The etched films developed rough surface textures with effective light scattering which could be controlled by the oxygen balance between the middle and sides. Optimally textured films were used as front contacts in 1cm2 single junction µc-Si:H solar cells yielding an initial efficiency of 8.4 %. The improvement in light trapping lead to short circuit densities higher than that of the reference solar cells

Fighting Enemies and Noise: Competition of Residents and Invaders in a Stochastically Fluctuating Environment

The possible control of competitive invasion by infection of the invader and multiplicative noise is studied. The basic model is the Lotka-Volterra competition system with emergent carrying capacities. Several stationary solutions of the non-infected and infected system are identified as well as parameter ranges of bistability. The latter are used for the numerical study of invasion phenomena. The diffusivities, the infection but in particular the white and coloured multiplicative noise are the control parameters. It is shown that not only competition, possible infection and mobilities are important drivers of the invasive dynamics but also the noise and especially its color and the functional response of populations to the emergence of noise