Mutual Extinction Research Articles

Observation of mutual extinction and transparency in light scattering

Interference of scattered waves is fundamental for modern light-scattering techniques, such as optical wavefront shaping. Recently, a new type of wavefront shaping was introduced where the extinction is manipulated instead of the scattered intensity. The underlying idea is that upon changing the phases or the amplitudes of incident beams, the total extinction will change due to interference described by the cross terms between different incident beams. Here, we experimentally demonstrate the mutual extinction and transparency effects in scattering media, in particular, a human hair and a silicon bar. To this end, we send two light beams with a variable mutual angle on the sample. Depending on the relative phase of the incident beams, we observe either nearly zero extinction, mutual transparency, or almost twice the single-beam extinction, mutual extinction, in agreement with theory. We use an analytical approximation for the scattering amplitude, starting from a completely opaque object, and we discuss the limitations of our approximation. We discuss the applications of the mutual extinction and transparency effects in various fields such as non-line-of-sight communications, microscopy, and biomedical imaging.

Towards policies that capture the expected value of biomolecular diversity for drug discovery, human health, and well-being

This paper aims to help policy makers with a characterization of the intrinsic value of biodiversity and its role as a critical foundation for sustainable development, human health, and well-being. Our objective is to highlight the urgent need to overcome economic, disciplinary, national, cultural, and regional barriers, in order to work out innovative measures to create a sustainable future and prevent the mutual extinction of humans and other species. We emphasize the pervasive neglect paid to the cross-dependency of planetary health, the health of individual human beings and other species. It is critical that social and natural sciences are taken into account as key contributors to forming policies related to biodiversity, conservation, and health management. We are reaching the target date of Nagoya treaty signatories to have accomplished measures to prevent biodiversity loss, providing a unique opportunity for policy makers to make necessary adjustments and refocus targets for the next decade. We propose recommendations for policy makers to explore novel avenues to halt the accelerated global loss of biodiversity. Beyond the critical ecological functions biodiversity performs, its enormous untapped the repertoire of natural molecular diversity is needed for solving accelerating global healthcare challenges.

Rich dynamics of a simple delay host-pathogen model of cell-to-cell infection for plant virus

Viral dynamics within plant hosts can be important for understanding plant disease prevalence and impacts. However, few mathematical modeling efforts aim to characterize within-plant viral dynamics. In this paper, we derive a simple system of delay differential equations that describes the spread of infection throughout the plant by barley and cereal yellow dwarf viruses via the cell-to-cell mechanism. By incorporating ratio-dependent incidence function and logistic growth of the healthy cells, the model can capture a wide range of biologically relevant phenomena via the disease-free, endemic, mutual extinction steady states, and a stable periodic orbit. We show that when the basic reproduction number is less than \begin{document}$ 1 $\end{document} ( \begin{document}$ R_0 ), the disease-free steady state is asymptotically stable. When \begin{document}$ R_0>1 $\end{document} , the dynamics either converge to the endemic equilibrium or enter a periodic orbit. Using a ratio-dependent transformation, we show that if the infection rate is very high relative to the growth rate of healthy cells, then the system collapses to the mutual extinction steady state. Numerical and bifurcation simulations are provided to demonstrate our theoretical results. Finally, we carry out parameter estimation using experimental data to characterize the effects of varying nutrients on the dynamics of the system. Our parameter estimates suggest that varying the nutrient supply of nitrogen and phosphorous can alter the dynamics of the infection in plants, specifically reducing the rate of viral production and the rate of infection in certain cases.

Mutual extinction and transparency of multiple incident light waves

When a wave is incident on a complex scattering medium, the transmitted intensity differs from the incident one due to extinction. In the absence of absorption, the extinguished power is equal to the total scattered power, a well-known conservation law termed the optical theorem. Here, we extend the case of a single incident wave to the situation of scattering and extinction by multiple incoming waves. The emerging generalized optical theorem has the exciting consequence that multiple incident waves show mutual extinction and mutual transparency, phenomena that do not exist in common forward scattering or self-extinction. Based on both exact calculations of realistic three-dimensional (3D) samples containing many (up to 104) scatterers and on approximate Fraunhofer diffraction theory we make the striking observation that the total extinction of two incident waves is greatly enhanced, called mutual extinction, or greatly reduced, mutual transparency, by up to 100% of the usual single-beam extinction. In view of the surprisingly strong mutual extinction and transparency, we propose new experiments to observe mutual extinction and transparency, namely in two-beam experiments with either elastic and absorbing scatterers, in optical wavefront shaping, in dynamic light scattering, and we discuss possible applications.

Governmental combat of migration between competing terrorist organisations

Each terrorist organisation is modelled with four coupled differential time equations for the evolution of ideologues, criminal mercenaries, captive participants, and capital sponsoring. Emigration of ideologues may cause unbounded growth of the organisation receiving ideologues. The organisation losing ideologues may reach a stationary state where ideologues are supported by capital sponsors and mercenaries. Emigration of mercenaries may cause the organisation losing mercenaries to experience growth. The organisation receiving mercenaries may lose capital sponsors permanently, allowing for the presence of mercenaries, or capital sponsors may rebound deterring mercenaries. Emigration of ideologues from one organisation to another requires more government intervention into the latter to ensure termination. Emigration of mercenaries from one organisation to another may require more government intervention into the latter, since mercenaries support ideologues. Competing terrorist organisations may facilitate their mutual extinction. Various intervention strategies are considered: the most threatening organisation is eliminated first, aided by competition from the least threatening, after which the remaining organisation is eliminated. The government’s instantaneous and accumulated utilities are analysed through time and compared, depending on emigration, competition, and government intervention strategies.

Global dynamics of a mutualism-competition model with one resource and multiple consumers.

Recent simulation modeling has shown that species can coevolve toward clusters of coexisting consumers exploiting the same limiting resource or resources, with nearly identical ratios of coefficients related to growth and mortality. This paper provides a mathematical basis for such as situation; a full analysis of the global dynamics of a new model for such a class of n-dimensional consumer-resource system, in which a set of consumers with identical growth to mortality ratios compete for the same resource and in which each consumer is mutualistic with the resource. First, we study the system of one resource and two consumers. By theoretical analysis, we demonstrate the expected result that competitive exclusion of one of the consumers can occur when the growth to mortality ratios differ. However, when these ratios are identical, the outcomes are complex. Either equilibrium coexistence or mutual extinction can occur, depending on initial conditions. When there is coexistence, interaction outcomes between the consumers can transition between effective mutualism, parasitism, competition, amensalism and neutralism. We generalize to the global dynamics of a system of one resource and multiple consumers. Changes in one factor, either a parameter or initial density, can determine whether all of the consumers either coexist or go to extinction together. New results are presented showing that multiple competing consumers can coexist on a single resource when they have coevolved toward identical growth to mortality ratios. This coexistence can occur because of feedbacks created by all of the consumers providing a mutualistic service to the resource. This is biologically relevant to the persistence of pollination-mutualisms.

Bifurcations and global dynamics in a predator–prey model with a strong Allee effect on the prey, and a ratio-dependent functional response

We extend a previous study of a predator–prey model with strong Allee effect on the prey in which the functional response is a function of the ratio of prey to predator. We prove that the solutions are always bounded and non-negative, and that the species can always tend to long-term extinction. By means of bifurcation analysis and advanced numerical techniques for the computation of invariant manifolds of equilibria, we explain the consequences of the (dis)appearance of limit cycles, homoclinic orbits, and heteroclinic connections in the global arrangement of the phase plane near a Bogdanov–Takens bifurcation. In particular, we find that the Allee threshold in the two-dimensional system is given as the boundary of the basin of attraction of an attracting positive equilibrium, and determine conditions for the mutual extinction or survival of the populations.

Phase portraits of predator--prey systems with harvesting rates

We investigate positive equilibria and phase portraits of predator-prey systems with constant harvesting ratesarising in ecology. These systems are generalizations of the well--known predator--prey systemswith Beddington--DeAngelis functional responses. We seek the ranges of the five parameters involved for whichthe equilibria of the systems to be positive and obtainall the positive equilibria of the systems.We prove that these positive equilibria are saddles, topological saddles, nodes, saddle-nodes, foci, centers, or cusps by providing suitable ranges of the five parameters. These results show how the harvesting rate and another parameter used in the Beddington--DeAngelis functional responses affect the dynamical behaviors of these systems. In particular, if the harvesting rate is larger than $1/4$ or the parameter just mentioned is too large, then the mutual extinction occurs.

Modelling Foot-and-Mouth Disease Virus Dynamics in Oral Epithelium to Help Identify the Determinants of Lysis

Foot-and-mouth disease virus (FMDV) causes an economically important disease of cloven-hoofed livestock; of interest here is the difference in lytic behaviour that is observed in bovine epithelium. On the skin around the feet and tongue, the virus rapidly replicates, killing cells, and resulting in growing lesions, before eventually being cleared by the immune response. In contrast, there is usually minimal lysis in the soft palate, but virus may persist in tissue long after the animal has recovered from the disease. Persistence of virus has important implications for disease control, while identifying the determinant of lysis in epithelium is potentially important for the development of prophylactics. To help identify which of the differences between oral and pharyngeal epithelium are responsible for such dramatically divergent FMDV dynamics, a simple model has been developed, in which virus concentration is made explicit to allow the lytic behaviour of cells to be fully considered. Results suggest that localised structuring of what are fundamentally similar cells can induce a bifurcation in the behaviour of the system, explicitly whether infection can be sustained or results in mutual extinction, although parameter estimates indicate that more complex factors may be involved in maintaining viral persistence, or that there are as yet unquantified differences between the intrinsic properties of cells in these regions.

The Set-off Paradox in International Arbitration

Set-off is a defence to the whole or a portion of a claim based on a defendant’s claim to money which entails the mutual extinction of both claims, in full or in part. Set-off can be substantial in nature or procedural. When the defendant’s counterclaim or cross-claim does not fall within the scope of the arbitration agreement, the arbitral tribunal might be faced with a serious difficulty. Arbitral practice has so far resolved this problem in favour of party autonomy, as reflected in article 19-3 of the UNCITRAL Rules. This entails that arbitral proceedings may have to be stayed when the counterclaim or cross-claim does not fall within the arbitral tribunal’s jurisdiction, as provided by article 29 of the Swiss Concordat intercantonal. Yet this approach is not satisfactory when the law applicable to set-off provides for ipso iure retroactive extinction of the claims. Applicable arbitration rules may allow for this problem to be addressed, as in article 21-5 of the Swiss Rules of International Arbitration, which provides that ‘the arbitral tribunal shall have jurisdiction to hear a set-off defence even when the relationship out of which this defence is said to arise is not within the scope of the arbitration clause or is the object of another arbitration agreement or forum-selection clause’. Some authors, such as Prof. Poudret, suggested that, set-off being a defence attached to the main claim, the arbitral tribunal’s jurisdiction thereto should by nature be extended to the related counterclaim or cross-claim. Whether such an approach is appropriate is discussed in this article. The author submits that arbitral tribunals should abstain from extending their jurisdiction to a cross-claim or counterclaim falling outside their jurisdiction.

Solving ratio-dependent predator–prey system with constant effort harvesting using Adomian decomposition method

In this paper, an algorithm based on Adomian’s decomposition method is developed to approximate the solution of the ratio-dependent predator–prey system with constant effort harvesting. The convergence of the decomposition series is enhanced using Padé approximation technique. The qualitative analysis of the model reveals that constant effort prey harvesting may contribute to mutual extinction as a possible outcome of predator–prey interaction. Some plots of the population of predator and prey versus time are presented to illustrate the performance and the accuracy of the algorithm. The decomposition method has the advantage of being more concise for numerical purposes.

Dynamics in a ratio-dependent predator–prey model with predator harvesting

The objective of this paper is to study systematically the dynamical properties of a ratio-dependent predator–prey model with nonzero constant rate predator harvesting. It is shown that the model has at most two equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena, including the bifurcation of cusp type of codimension 2 (i.e., Bogdanov–Takens bifurcation), the subcritical and supercritical Hopf bifurcations. These results reveal far richer dynamics compared to the model with no harvesting and different dynamics compared to the model with nonzero constant rate prey harvesting in [D. Xiao, L. Jennings, Bifurcations of a ratio-dependent predator–prey system with constant rate harvesting, SIAM Appl. Math. 65 (2005) 737–753]. Biologically, it is shown that nonzero constant rate predator harvesting can prevent mutual extinction as a possible outcome of the predator prey interaction, and remove the singularity of the origin, which was regarded as “pathological behavior” for a ratio-dependent predator prey model in [P. Yodzis, Predator–prey theory and management of multispecies fisheries, Ecological Applications 4 (2004) 51–58].

Temporally explicit habitat ecology and the coexistence of species.

Habitats may have dynamics that exist independently of the population densities of species occupying the habitat. For example, ephemeral habitat patches may disappear regardless of whether a particular species is present or not. Such habitat dynamics are frequently modelled by ignoring age-related variation in patch turnover rates. This can be thought of as a temporally implicit approach. An alternative, temporally explicit approach involves using age-structured models in order to describe variations in habitat dynamics. Simple models of coexistence between competing species show that temporally implicit models may be misleading where there is age-related variation in patch dynamics. Changing the shape of the patch survivorship function but not the average patch survivorship can result in mutual extinction, monocultures or coexistence of an inferior and a superior competitor. An explicit treatment of habitat demography may therefore offer improved predictive models and alternative landscape management strategies.

A Variation on a Basic Theme: The Transition to Farming in Southern Central Europe

This paper attempts to summarize the past years of research on the Mesolithic–Neolithic transition in Central Europe and to review recent discussions about the origin and spread of the Early Neolithic. Particular emphasis is given to the debate about migration or diffusion. A combined migrationist/diffusionist model is presented, arguing for an emergence of a farming economy among hunter-gatherer populations in Transdanubia and the subsequent spread of this economy through migration. The new settlers interacted with local Mesolithic groups and adopted and incorporated local material culture and sometimes even aspects of local Mesolithic economy, a process which continued throughout the Early Neolithic. With time, population increase, subsequent competition for resources, and climatic instability led to a destabilization of traditional Early Neolithic society and finally to the outbreak of severe intercommunity violence. The only escape from mutual extinction was a rearrangement of subsistence and social and political structures, possibly with contributions from surviving Terminal Mesolithic groups.

Optical pumping-induced spatio-temporal modifications to propagation, polarization and intensity of laser beams in sodium vapour

Circularly polarized laser beams propagating through sodium vapour and tuned to the buffer-gas-broadened atomic transition can optically pump sodium atoms into a non-absorbing ground state. This causes an intensity-dependent refractive index gradient along as well as transverse to the laser beam propagation direction, giving rise to a number of nonlinear spatio-temporal intensity and polarization pattern creating processes. In the case of a single circularly polarized laser beam we have observed self-focusing and defocusing, the transformation of the incident Gaussian beam intensity profiles into ring profiles, a large shift of about 5 GHz of the maximum of the absorption profile when suitable magnetic fields are applied and the deflection of a beam by the inhomogeneous transverse magnetic field of a current-carrying wire. When two beams of opposite circular polarization are superimposed, astonishing effects such as the mutual deflection of both beams (beam bouncing), the mutual extinction of both beams (beam switching), the separation of initially overlapping beams (beam splitting) and the mutual attraction of both beams (beam attraction) can be observed. While most of the effects can be well described for the stationary state by a to atomic transition model, the correct description of the dynamics requires the consideration of all hyperfine states.

Dynamics of laser beam switching in sodium vapor

The interaction of left- and right-hand circularly polarized narrow-band cw laser beams that copropagate through sodium vapor and are tuned to the homogeneously broadened D1 transition can lead to the mutual extinction of both beams. Such beam switching is caused by an intensity- and polarization-dependent refractive index due to optical pumping even at low intensities. The dynamics of beam switching is investigated experimentally and explained qualitatively by the conventional J = 1/2 to J = 1/2 transition model. The accurate quantitative description, however, is only achieved by an extended model comprising hyperfine ground states in spite of homogeneous line broadening by argon buffer gas, which is larger than the hyperfine splitting.

Microbial predation in coupled chemostats: A global study of two coupled nonlinear oscillators

Predator-prey systems in continuously operated chemostats exhibit sustained oscillations over a wide range of operating conditions. When two such chemostats interact through flow exchange, the interplay of the oscillation frequencies gives rise to a wealth of dynamic behavior patterns. Using numerical bifurcation techniques, we perform a detailed computational study of these patterns and the transitions between them as the coupling strength and relative frequencies of the two chemostats vary. We concentrate on certain strong resonance phenomena between the two frequencies as well as their mutual extinction and provide a representative sampling of possible phase portraits for our model system. Our observations corroborate recent mathematical results and case studies of coupled nonlinear chemical oscillators in which regions of mutual extinction as well as the Arnol'd structure for two-parameter families of maps of the plane have been observed. We highlight certain unexpected features of the operating diagram discovered through our computational study and discuss their implication for the dynamic response of the chemostat system.

Evolutionary Instability in Predator-prey Systems

The dynamical stability properties of Lotka-Volterra equations have been used frequently to predict the persistence of predator-prey assemblages and trophic webs, yet they do not take into account evolutionary change. The incorporation of genetic variation into a stable food web will make it less stable in many cases. Since populations containing genetic variation do persist in nature, such theoretical results appear paradoxical. In order to attempt to resolve this paradox, we develop a model based on phenotypic change in investment in predatory or anti-predator traits, in coevolving species. The model is akin to previous models of arms-race coevolution using evolutionarily stable strategy (ESS) theory, but we seek to understand the evolutionary dynamics in phenotype space, as well as to identify any evolutionarily stable states that may occur. The relationship between investment and the Lotka-Volterra interaction terms is defined in a very general form, so as to cover a wide range of cases in nature. From the general case and more specific examples based on hypotheses about the factors affecting predator-prey interactions, we derive conditions for the occurrence of coevolutionarily stable states, where both species are playing evolutionarily stable strategies with respect to their interaction with the other species. Coevolutionarily stable states are found to be unusual outcomes of predator-prey coevolution. However, lack of evolutionary stability is not seen to imply ecological impermanence, as natural selection is found to prevent mutual extinction of predator and prey under certain conditions.

The structure of K3C60 and the mechanism of superconductivity.

Analysis of the interatomic distances in the superconducting substance K3C60 indicates that each of the K atoms in tetrahedral interstices between C60 spheres accepts three electrons from C60, thus becoming quadricovalent; its four bonds resonate among the 24 adjacent carbon atoms to give a strong framework in which the negative charges are localized on these K atoms. The electric current is carried by the motion of positive charges (holes) through the network of C60 spheres and the K atoms in octahedral holes. Superconductivity is favored by the localization of the negative charges on the tetrahedral K atoms and their noninvolvement in valence-bond resonance, decreasing the rate of mutual extinction of electrons and holes.

Some common dynamic features of coupled reacting systems

A computational study of the dynamic behavior of several models describing coupled oscillatory chemical reactors is presented. Special emphasis is placed on the identification of bifurcations and dynamic features that are qualitatively common in large classes of such systems. We investigate the effects of systematically varying two parameters: (a) the strength of the coupling between the two reactors, and (b) the difference between the “natural’ states of the systems when they are uncoupled. For reactors which naturally oscillate, an interesting scenario involving quasiperiodicity and resonance is observed. This resembles the behavior observed in periodically forced oscillators. Indeed, the entire structure of resonance regions, and the breaking of quasiperiodic solutions as the coupling strength increases, appears to be a common feature of coupled reacting systems and coupled oscillators in general. A two-parameter computational study of the phenomenon of mutual extinction of the oscillations, which has been theoretically predicted, is also presented. The examples studied include chemical reactions in both isothermal and nonisothermal coupled CSTRs as well as a microbial predator-prey interaction in coupled isothermal chemostats.