Numerical Extrapolation Research Articles

Inferring True Species Richness and Complete Abundance Distribution in Six Reef-fish Communities from Red-sea, Using the Numerical Extrapolation of Incomplete Samplings

Even when ecological communities are incompletely sampled (which is most frequent in practice, at least for species-rich assemblages including many rare species), it remains possible to retrieve much more information than could be expected first, by applying numerical extrapolation to incomplete field data. Indeed, recently developed procedures of numerical extrapolation of partial samplings now allow to estimate, with fair accuracy, not only the number of the still unrecorded species but, moreover, the distribution of abundances of each of these unrecorded species, thereby making available the full range of the Species Abundance Distribution, despite dealing with incomplete data only. In turn, this allows to address a series of descriptive and functional aspects of the internal organization of species assemblages, which otherwise would have required disposing of truly exhaustive samplings.
 This approach is applied, here, to the previously reported partial samplings of six neighboring reef-fish communities from Tiran Island, Red Sea, with the goal of better understanding their internal organization in relation to their respective environments.
 In practice, the numerical completion contributes to avoid erroneous interpretations that would likely stem from considering only the incomplete field data. This point is especially relevant when studying reef-associated communities because accurate understanding of their organization will help guiding and refining at best the protective measures required by these particularly vulnerable communities.

Analytical Three-dimensional Magnetohydrostatic Equilibrium Solutions for Magnetic Field Extrapolation Allowing a Transition from Non-force-free to Force-free Magnetic Fields

For the extrapolation of magnetic fields into the solar corona from measurements taken in the photosphere (or chromosphere) force-free magnetic fields are typically used. This does not take into account that the lower layers of the solar atmosphere are not force-free. While some numerical extrapolation methods using magnetohydrostatic magnetic fields have been suggested, a complementary and numerically comparatively cheap method is to use analytical magnetohydrostatic equilibria to extrapolate the magnetic field. In this paper, we present a new family of solutions for a special class of analytical three-dimensional magnetohydrostatic equilibria, which can be of use for such magnetic field extrapolation. The new solutions allow for the more flexible modeling of a transition from non-force-free to (linear) force-free magnetic fields. In particular, the height and width of the region where this transition takes place can be specified by choosing appropriate model parameters.

Influence of Environmental Heterogeneity on the Species Composition, Species Richness and Species Abundances Unevenness in Reef-associated Conus Communities (Neogastropoda) from Papua New-Guinea

To what extent differences in species composition, species richness and species abundance unevenness between marine communities are attributable to heterogeneities of the surrounding environment and/or to inter-community distance is a fundamental issue to be addressed, in order to more deeply understand the functioning of marine ecosystems. A comparison between six reef-associated Conus communities, differing more or less in both their surrounding environment and their mutual geographical distance, offers a relevant opportunity to address these questions.
 As expected, environmental heterogeneities prove having a significant influence on the dissimilarity in species composition, whereas distance-decay in similarity reveals comparatively negligible, at least within the investigated range of distances, up to 60 km. Less expectedly, more homogeneous surrounding environments between communities tend, here, to increase the dissimilarity in species richness. At last, here, difference in species abundance unevenness between communities seems unrelated to either environmental heterogeneity or inter-community distance.
 From a methodological point of view, these results could not have been reliably established without the prior implementation of a least-biased procedure of numerical extrapolation applied to the available incomplete samplings. Also, the relevant assessment of dissimilarity in species composition required using a modified Jaccard index, rendered insensitive to bias-induced differences in communities species richness.

Procedures for handling computationally heavy cyclic load cases with application to a disc alloy material

ABSTRACTThe computational efficiency in analysing cyclically loaded structures is a highly prioritised issue for the gas turbine industry, as a cycle-by-cycle simulation of e.g. a turbine disc is far too time consuming. Hence, in this paper, the efficiency of two different procedures to handle computational expansive load cases, a numerical extrapolation and a parameter modification procedure, are evaluated and compared to a cycle-by-cycle simulation. For this, a local implementation approach was adopted, where a user-defined material subroutine is used for the cycle jumping procedures with good results. This in contrast to a global approach where the finite element simulation is restarted and mapping of the solution is performed at each cycle jump. From the comparison, it can be observed that the discrete parameter modification procedure is by margin the fastest one, but the accuracy depends on the material parameter optimisation routine. The extrapolation procedure can incorporate stability and/or termination criteria.

Influence of Coral Architecture on Species Richness and the Hierarchical Structuration of Species Abundances in Reef Fish Communities: A Case Study in the Eastern Tropical Pacific

The role of coral reef architecture on species richness and the internal structuration of the associated fish communities has already been addressed several times. The reported results, however, usually remain controversial, possibly because they are based upon incomplete field data issued from partial inventories. Indeed, incomplete samplings are almost unavoidable in practice with such species-rich communities having very uneven distribution of abundances. In this context, the numerical extrapolation of incompletely sampled communities may serve as a reliable surrogate. Accordingly, numerical extrapolations were implemented, here, to compare two fish-communities respectively associated to coral reefs that sharply differ from each-other by their topographic architectures. Both a higher total species richness and a sharper unevenness of species abundances were found to characterize the fish community associated to the more tormented reef habitat exhibiting the more complex architecture. Yet, paradoxically, the true intensity of the underlying process of hierarchical structuring of abundances proves being insensitive to the architecture of coral habitats. This apparent opposition between the unevenness pattern and the underlying structuring process results, in fact, from the additional negative dependence of abundance unevenness upon species richness.

Inferring Total Species Richness and the Exhaustive Hierarchical Structuring of Species Abundances in Tropical Sea-stars Communities (Asteroidea), Using Numerical Extrapolation of Partial Inventories

Inferring Total Species Richness and the Exhaustive Hierarchical Structuring of Species Abundances in Tropical Sea-stars Communities (Asteroidea), Using Numerical Extrapolation of Partial Inventories

Comparing the Complete Hierarchical Structuration of Species Abundances in Reef Fish Communities According to Coral Morphology, Using the Numerical Extrapolation of Only Incomplete Inventories

Comparing the Complete Hierarchical Structuration of Species Abundances in Reef Fish Communities According to Coral Morphology, Using the Numerical Extrapolation of Only Incomplete Inventories

Fast Far-Field Estimation Method by Compact Single Cut Near-Field Measurements for Electrically Long Antenna Array

This paper proposes a fast far-field estimation method of electrically long antenna in compact measurement space. The presented method estimates a far-field pattern on an orthogonal cut plane from the linear equivalent electric current and circular current distribution. The equivalent electric current data is measured in a reactive near-field region using a small loop probe. In the proposed method, the linear equivalent current distribution is extended by a simple numerical extrapolation formula for improving the accuracy of the estimated far field in the broadside direction. In the horizontal plane, the far-field pattern is calculated from both the circular equivalent electric and the magnetic distribution approximating equivalent magnetic current with equivalent electric current. We confirmed the validity of the proposed method from the numerical simulation and measurements results. The method allows accurate directivity measurement in a small space in about a few minutes.

The Full Hierarchical Structuration of Species Abundances Reliably Inferred from the Numerical Extrapolation of Still Partial Samplings: A Case Study with Marine Snail Communities in Mannar Gulf (India)

The detailed analysis of Species Abundance Distributions (S.A.D.s) can shed light on how member-species organize themselves within communities, provided that the complete distribution of species abundances is made available first. In this perspective, the numerical extrapolation applied to incomplete S.A.D. can effectively compensate for incompleteness, when having to deal with substantially incomplete samplings. Indeed, almost as much information can be released from extrapolated S.A.D.s as would be obtained from truly complete S.A.D.s, although the taxonomic identities of unrecorded species remain of course ignored by numerical extrapolation. To take full advantage of this new approach, a recently developed procedure allowing the least-biased numerical extrapolation of S.A.D.s has been applied to three partially sampled gastropods communities associated to coral-reef in Mannar Gulf (S-E India). The following main results were derived from the three numerically completed S.A.D.s: (i) once completed, all three numerically S.A.D.s fairly well comply with the log-normal model, suggesting that, in all three communities, the process of hierarchical structuration of species abundances likely involves the combined contributions of many independent factors; (ii) moreover, the same holds true for each of the two coexisting feeding guilds (primary and secondary consumers) considered separately; (iii) when compared to secondary consumers, the guild of primary consumers has a much lower species richness but, on the other hand, exhibits a more strongly structured distribution of species abundances, which materializes not only in term of the apparent unevenness of species abundances but also after having disentangled the genuine intensity of the underlying process driving the hierarchical structuration. All the preceding features are shared in common by the three communities studied, in line with the similarity of their environmental contexts. Only minor features can actually slightly distinguish between communities, reflecting the difference in distances between them.

Equations of State and the Phase Diagram of Dielectric and Metallic Helium-4

A new form of the semiempirical equation of state for the liquid phase of helium-4 is proposed that is based on the assumption that the structure of this phase consists of a mixture of dielectric and metallic components. It is postulated that solid dielectric helium with density higher than 5.3 g/cm3 becomes a metal. The values of the parameters of the equations of state for both solid phases and the liquid phase of helium are calculated. The unknown values of the initial data for helium are taken by analogy with the parameters for deuterium. The phase diagram, shock adiabat, isentropes, isotherms, and electrical conductivity in these processes are calculated with the use of the equations of state of solid and liquid phases of helium-4. The results of calculation are compared with experimental data in the range of pressures of up to 35 GPa for an isotherm, up to 150 GPa for a shock adiabat, up to 42 GPa for the melting curve, and up to 2000 GPa for isentropes, and showed quite satisfactory agreement. Numerical extrapolation of the melting curve is performed to a range of ultrahigh pressures of up to 8000 GPa.

Anomalous bulk behavior in the free parafermion Z(N) spin chain.

We demonstrate using direct numerical diagonalization and extrapolation methods that boundary conditions have a profound effect on the bulk properties of a simple Z(N) model for N≥3 for which the model Hamiltonian is non-Hermitian. For N=2 the model reduces to the well-known quantum Ising model in a transverse field. For open boundary conditions, the Z(N) model is known to be solved exactly in terms of free parafermions. Once the ends of the open chain are connected by considering the model on a ring, the bulk properties, including the ground-state energy per site, are seen to differ dramatically with increasing N. Other properties, such as the leading finite-size corrections to the ground-state energy, the mass gap exponent, and the specific-heat exponent, are also seen to be dependent on the boundary conditions. We speculate that this anomalous bulk behavior is a topological effect.

Estimating True Species Richness and the Degree of Hierarchical Structuring of Species Abundances in Eight Frog Communities from the North-Western Ghats of India

The Distribution of Species Abundances within natural communities – when properly analysed – can provide essential information regarding general aspects of the internal organisation of these communities. In particular, true species richness on the one hand and the intensity of the process of hierarchical structuring of species abundances on the other hand may be estimated independently and, thereby, can provide truly complementary information. In turn, specific issues may thereby be addressed. For example, whether one unique dominant factor or numerous combined factors are involved in the structuring process of a community can be tested contradictorily. Although these methods are not new conceptually, their implementation in common practice remains scarce. The reason is that the relevant implementation of these methods requires to be sure that virtually all member-species in the community have been sampled. As exhaustive samplings often reveal difficult to achieve in practice, an appropriate, least-biased procedure of numerical extrapolation of incomplete inventories is imperatively required.
 Considering the steadily increasing threats to the environment and biodiversity, especially facing the on-going climatic change, time has come now with ever greater urgency to go beyond the apparent limits of non-exhaustive sampling and make the most of what is available in terms of recorded field data, whatever the degree of incompleteness of species inventories.
 As a modest and limited attempt to concretise this wish at the local level, I try, hereafter, to highlight the importance of additional information that may be unveiled through adequate post-analysis of a set of eight frog communities, recently inventoried by Katwate, Apte & Raut in an amphibian hot-spot in the north-western Ghats of India. At last, the likely variations of both total species richness and the intensity of hierarchical structuring of species abundance are simulated as an answer to the steadily increasing influence of the ongoing climatic change.

Carbon Sequestration in Relation to Topographic Aspects and Land Use in Northeast of Thailand

The Distribution of Species Abundances within natural communities – when properly analysed – can provide essential information regarding general aspects of the internal organisation of these communities. In particular, true species richness on the one hand and the intensity of the process of hierarchical structuring of species abundances on the other hand may be estimated independently and, thereby, can provide truly complementary information. In turn, specific issues may thereby be addressed. For example, whether one unique dominant factor or numerous combined factors are involved in the structuring process of a community can be tested contradictorily. Although these methods are not new conceptually, their implementation in common practice remains scarce. The reason is that the relevant implementation of these methods requires to be sure that virtually all member-species in the community have been sampled. As exhaustive samplings often reveal difficult to achieve in practice, an appropriate, least-biased procedure of numerical extrapolation of incomplete inventories is imperatively required.
 Considering the steadily increasing threats to the environment and biodiversity, especially facing the on-going climatic change, time has come now with ever greater urgency to go beyond the apparent limits of non-exhaustive sampling and make the most of what is available in terms of recorded field data, whatever the degree of incompleteness of species inventories.
 As a modest and limited attempt to concretise this wish at the local level, I try, hereafter, to highlight the importance of additional information that may be unveiled through adequate post-analysis of a set of eight frog communities, recently inventoried by Katwate, Apte & Raut in an amphibian hot-spot in the north-western Ghats of India. At last, the likely variations of both total species richness and the intensity of hierarchical structuring of species abundance are simulated as an answer to the steadily increasing influence of the ongoing climatic change.

Numerical Extrapolation of the Species Abundance Distribution Unveils the True Species Richness and the Hierarchical Structuring of a Partially Sampled Marine Gastropod Community in the Andaman Islands (India)

Even when it remains substantially incomplete, the partial inventory of a species assemblage can provide much more information than could be expected at first. This can be achieved by applying a rigorous numerical extrapolation procedure that fully extends the incomplete sampling in numerical terms and, thereby, provides reliable estimates regarding not only the number but also the distribution of abundances for the whole set of the undetected species. As a result, this makes available the full range of the Species Abundance Distribution of the yet partially sampled assemblage and, thus, allows to address a series of interesting issues regarding the process and pattern of the hierarchical structuring of species abundances within the studied assemblage of species. Moreover, the same kind of numerical extrapolation may be applied separately to each subset of species, within the whole assemblage, that may have relevant interest (taxonomic subgroups, feeding guilds, etc…). Thus, deconstructing the Species Abundance Distribution can provide further detailed insights into the functional organisation of the studied assemblage. The mathematical and algorithmic basis for this extrapolating procedure has been developed recently, to be applied to the numerical extension of both the Species Accumulation Curve and the Species Abundance Distribution. The wide potential interest of this new methodological approach, when having to deal with substantially incomplete inventories of species (which is doomed to become inevitable with increasingly species-rich assemblages), is illustrated by a detailed case study of a marine gastropod assemblage on rocky shore under tropical climate.

Regularization with numerical extrapolation for finite and UV-divergent multi-loop integrals

We give numerical integration results for Feynman loop diagrams such as those covered by Laporta (2000) and by Baikov and Chetyrkin (2010), and which may give rise to loop integrals with UV singularities. We explore automatic adaptive integration using multivariate techniques from the ParInt package for multivariate integration, as well as iterated integration with programs from the Quadpack package, and a trapezoidal method based on a double exponential transformation. ParInt is layered over MPI (Message Passing Interface), and incorporates advanced parallel/distributed techniques including load balancing among processes that may be distributed over a cluster or a network/grid of nodes. Results are included for 2-loop vertex and box diagrams and for sets of 2-, 3- and 4-loop self-energy diagrams with or without UV terms. Numerical regularization of integrals with singular terms is achieved by linear and non-linear extrapolation methods.

Hybrid model testing using pre-offset and asymmetric truncation design for deepwater semi-submersible with highly compliant mooring system

The hybrid model testing technique has been widely used for evaluating the safety of deepwater floating systems. In this technique, a full-depth mooring system is equivalently substituted with a truncated model by employing truncation design. However, for a deepwater platform with a highly compliant mooring system, the large offset resulting from harsh environments makes it difficult to realize truncation design. The conventional symmetrically truncated mooring system starts to lose its accuracy. To achieve sufficient equivalence and enlarge the offset limit of the truncated model, a pre-offset and asymmetric truncation design is proposed in this paper for a deepwater semi-submersible system. The feasibility of the technique was first validated by numerical calculations. Thereafter, hybrid model testing was performed successfully for a semi-submersible with a highly compliant mooring system operating in harsh environments. Numerical reconstruction and extrapolation were performed, and the numerical results showed good agreement with experimental results. However, some remarkable discrepancies were observed in vertical motions because of nonlinear effects such as wave impact and the influence of bracings.

Numerical integration and extrapolation for finite and UV-divergent 3-loop Feynman integrals

Automatic numerical integration attempts to alleviate the detailed application of solution methods to the problem. We use automatic multivariate integration with PARINT combined with numerical extrapolation for classes of 3-loop UV-divergent self-energy diagrams with massive internal lines, and finite or UV-divergent massless vertex diagrams. The extrapolation is performed with respect to the dimensional regularization parameter. It is shown that the PARINT software handles the integrations accurately and efficiently.

Feynman loop numerical integral expansions for 3-loop vertex diagrams

The inclusion of higher order corrections by multi-loop diagrams is required in perturbation methods for precise theoretical calculations of high energy interactions. We address 3-loop vertex Feynman diagrams with massless internal lines, and which may exhibit ultra-violet (UV) singularities. The computational methods target automatic numerical integration and extrapolation to approximate the leading coefficients of the integral expansion with respect to the dimensional regularization parameter. Convergence acceleration is achieved by applying linear extrapolation on the integral expansion. Multivariate integration is performed with the ParInt software package, layered over MPI (Message Passing Interface) to speed up the computations. Integrand transformations result in diminishing the effect of singular behavior in the integrand.

Nowcasting of deep convective clouds and heavy precipitation: Comparison study between NWP model simulation and extrapolation

An evaluation of convective cloud forecasts performed with the numerical weather prediction (NWP) model COSMO and extrapolation of cloud fields is presented using observed data derived from the geostationary satellite Meteosat Second Generation (MSG). The present study focuses on the nowcasting range (1–5h) for five severe convective storms in their developing stage that occurred during the warm season in the years 2012–2013. Radar reflectivity and extrapolated radar reflectivity data were assimilated for at least 6h depending on the time of occurrence of convection. Synthetic satellite imageries were calculated using radiative transfer model RTTOV v10.2, which was implemented into the COSMO model. NWP model simulations of IR10.8μm and WV06.2μm brightness temperatures (BTs) with a horizontal resolution of 2.8km were interpolated into the satellite projection and objectively verified against observations using Root Mean Square Error (RMSE), correlation coefficient (CORR) and Fractions Skill Score (FSS) values. Naturally, the extrapolation of cloud fields yielded an approximately 25% lower RMSE, 20% higher CORR and 15% higher FSS at the beginning of the second forecasted hour compared to the NWP model forecasts. On the other hand, comparable scores were observed for the third hour, whereas the NWP forecasts outperformed the extrapolation by 10% for RMSE, 15% for CORR and up to 15% for FSS during the fourth forecasted hour and 15% for RMSE, 27% for CORR and up to 15% for FSS during the fifth forecasted hour. The analysis was completed by a verification of the precipitation forecasts yielding approximately 8% higher RMSE, 15% higher CORR and up to 45% higher FSS when the NWP model simulation is used compared to the extrapolation for the first hour. Both the methods yielded unsatisfactory level of precipitation forecast accuracy from the fourth forecasted hour onward.

High Performance and Increased Precision Techniques for Feynman Loop Integrals

For the investigation of physics within and beyond the Standard Model, a precise evaluation of higher order corrections in perturbative quantum field theory is required. We have worked on the development of a computational method for Feynman loop integrals with a fully numerical approach. It is based on numerical integration and extrapolation techniques. In this paper, we describe the status and new developments in our techniques for the numerical computation of Feynman loop integrals.Separation of ultra-violet divergences is important for the renormalization procedure. In our analyses, the separation can be done numerically. For 2-loop integrals we have performed the calculations for up to 4-point functions, and for 2-point functions we can handle up to 4- loop integrals. We report the status and accuracy of the computations with detailed numerical comparisons to results in the literature, in order to demonstrate that our method will evolve into an important component of automated systems for the study of higher-order radiative corrections.