General Class Of Models Research Articles

Crowdsourcing Meets Ecology: Hemispherewide Spatiotemporal Species Distribution Models

Ecological systems are inherently complex. The processes that affect the distributions of animals and plants operate at multiple spatial and temporal scales, presenting a unique challenge for the development and coordination of effective conservation strategies, particularly for wide‐ranging species. In order to study ecological systems across scales, data must be collected at fine resolutions across broad spatial and temporal extents. Crowdsourcing has emerged as an efficient way to gather these data by engaging large numbers of people to record observations. However, data gathered by crowdsourced projects are often biased due to the opportunistic approach of data collection. In this article, we propose a general class of models called AdaSTEM (for adaptive spatiotemporal exploratory models) that are designed to meet these challenges by adapting to multiple scales while exploiting variation in data density common with crowdsourced data. To illustrate the use of AdaSTEM, we produce intraseasonal distribution estimates of long‐distance migrations across the Western Hemisphere using data from eBird, a citizen science project that utilizes volunteers to collect observations of birds. Subsequently, model diagnostics are used to quantify and visualize the scale and quality of distribution estimates. This analysis shows how AdaSTEM can automatically adapt to complex spatiotemporal processes across a range of scales, thus providing essential information for full‐life cycle conservation planning of broadly distributed species, communities, and ecosystems.

Composite-kink solutions of coupled nonlinear wave equations

We obtain exact traveling-wave solutions of the coupled nonlinear partial differential equations that describe the dynamics of two classical scalar fields in 1+1 dimensions. The solutions are kinks interpolating between neighboring vacua. We compute the classical kink mass and show that it saturates a Bogomol'nyi-type bound. We also present exact traveling-wave solutions of a more general class of models. Examples include coupled $\phi^4$ and sine-Gordon models.

Undecidability of Propositional Separation Logic and Its Neighbours

In this article, we investigate the logical structure of memory models of theoretical and practical interest. Our main interest is in “the logic behind a fixed memory model”, rather than in “a model of any kind behind a given logical system”. As an effective language for reasoning about such memory models, we use the formalism of separation logic. Our main result is that for any concrete choice of heap-like memory model, validity in that model is undecidable even for purely propositional formulas in this language. The main novelty of our approach to the problem is that we focus on validity in specific, concrete memory models, as opposed to validity in general classes of models. Besides its intrinsic technical interest, this result also provides new insights into the nature of their decidable fragments. In particular, we show that, in order to obtain such decidable fragments, either the formula language must be severely restricted or the valuations of propositional variables must be constrained. In addition, we show that a number of propositional systems that approximate separation logic are undecidable as well. In particular, this resolves the open problems of decidability for Boolean BI and Classical BI. Moreover, we provide one of the simplest undecidable propositional systems currently known in the literature, called “Minimal Boolean BI”, by combining the purely positive implication-conjunction fragment of Boolean logic with the laws of multiplicative *-conjunction, its unit and its adjoint implication, originally provided by intuitionistic multiplicative linear logic. Each of these two components is individually decidable: the implication-conjunction fragment of Boolean logic is co-NP-complete, and intuitionistic multiplicative linear logic is NP-complete. All of our undecidability results are obtained by means of a direct encoding of Minsky machines.

Predictions in multifield models of inflation

This paper presents a method for obtaining an analytic expression for the density function of observables in multifield models of inflation with sum-separable potentials. The most striking result is that the density function in general possesses a sharp peak and the location of this peak is only mildly sensitive to the distribution of initial conditions. A simple argument is given for why this result holds for a more general class of models than just those with sum-separable potentials and why for such models, it is possible to obtain robust predictions for observable quantities. As an example, the joint density function of the spectral index and running in double quadratic inflation is computed. For scales leaving the horizon 55 e-folds before the end of inflation, the density function peaks at ns = 0.967 and α = 0.0006 for the spectral index and running respectively.

Comment on “The paradox of the ‘paradox of the plankton’” by Record et al.

AbstractCropp, R., and Norbury, J. 2014. Comment on “The paradox of the ‘paradox of the plankton’” by Record et al. – ICES Journal of Marine Science, 71: 293–295. The biodiversity of plankton ecosystems is no longer a paradox. The mathematical mechanisms that determine the coexistence of competitors in a general class of models, which includes almost all theoretical and applied mass conserving ecosystem models in present use, are clear. Knowledge of these mechanisms simplifies the identification and construction of models with the structural property that all species coexist for all time, irrespective of environmental forcings, spatial interactions, and further model complexities. Here, we discuss the “paradox of the ‘paradox of the plankton’” proposed by Record et al. (ICES Journal of Marine Science, 71: 236–240) and explain the mechanisms that underpin the solution.

Heterophilious Dynamics Enhances Consensus

We review a general class of models for self-organized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or “agents,” with the tendency to adjust to their “environmental averages.” This, in turn, leads to the formation of clusters, e.g., colonies of ants, flocks of birds, parties of people, rendezvous in mobile networks, etc. A natural question which arises in this context is to ask when and how clusters emerge through the self-alignment of agents, and what types of “rules of engagement” influence the formation of such clusters. Of particular interest to us are cases in which the self-organized behavior tends to concentrate into one cluster, reflecting a consensus of opinions, flocking of birds, fish, or cells, rendezvous of mobile agents, and, in general, concentration of other traits intrinsic to the dynamics. Many standard models for self-organized dynamics in social, biological, and physical sciences assume that the intensity of alignment increases as agents get closer, reflecting a common tendency to align with those who think or act alike. Moreover, “similarity breeds connection” reflects our intuition that increasing the intensity of alignment as the difference of positions decreases is more likely to lead to a consensus. We argue here that the converse is true: when the dynamics is driven by local interactions, it is more likely to approach a consensus when the interactions among agents increase as a function of their difference in position. Heterophily, the tendency to bond more with those who are different rather than with those who are similar, plays a decisive role in the process of clustering. We point out that the number of clusters in heterophilious dynamics decreases as the heterophily dependence among agents increases. In particular, sufficiently strong heterophilious interactions enhance consensus.

Generalized Residuals for General Models for Contingency Tables With Application to Item Response Theory

Generalized residuals are a tool employed in the analysis of contingency tables to examine possible sources of model error. They have typically been applied to log-linear models and to latent-class models. A general approach to generalized residuals is developed for a very general class of models for contingency tables. To illustrate their use, generalized residuals are applied to models based on item response theory (IRT) models. Such models are commonly applied to analysis of standardized achievement or aptitude tests. To obtain a realistic perspective on application of generalized residuals, actual testing data are employed.

The Demand for Youth: Explaining Age Differences in the Volatility of Hours

Over the business cycle young workers experience much greater volatility of hours worked than prime-aged workers. This can arise from age differences in labor supply or labor demand characteristics. To distinguish between these, we document that, for young workers, both the cyclical volatilities of hours and wages are greater than those of the prime-aged. We argue that a general class of models featuring only age-specific labor supply differences cannot reconcile these facts. We then show that a simple model featuring labor demand differences can. (JEL E32, J13, J22, J23, J31)

Effective equation of state for running vacuum: 'mirage' quintessence and phantom dark energy

Past analyses of the equation of state (EoS) of the Dark Energy (DE) were not incompatible with a phantom phase near our time. This has been the case in the years of WMAP observations, in combination with the remaining cosmological observables. Such situation did not completely disappear from the data collected from the Planck satellite mission. In it the EoS analysis may still be interpreted as suggesting w<-1, and so a mildly evolving DE cannot be discarded. In our opinion the usual ansatzs made on the structure of the EoS for dynamical DE models (e.g. quintessence and the like) are too simplified. In this work we examine in detail some of these issues and suggest that a general class of models with a dynamical vacuum energy density could explain the persistent phantom anomaly, despite there is no trace of real phantom behavior in them. The spurious or "mirage" effect is caused by an attempt to describe them as if the DE would be caused by fundamental phantom scalar fields. Remarkably, the effective DE behavior can also appear as quintessence in transit to phantom, or vice versa.

Semiparametric Bayesian information criterion for model selection in ultra-high dimensional additive models

For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little justification that the effects of the covariates are actually linear. Thus a semiparametric model, such as the additive model studied here, is a viable alternative. We demonstrate that theoretical results on the consistency of the BIC-type criterion can be extended to this more challenging situation, with dimension diverging exponentially fast with sample size. Besides, the assumptions on the distribution of the noises are relaxed in our theoretical studies. These efforts significantly enlarge the applicability of the criterion to a more general class of models.

ARIMA Models are Clicks Away

It is often the case that managers and social scientists are called to deal with time series. Time series analysis usually involves a study of the components of the time series and finding models that permit statistical inferences and predictions. ARIMA models are, in theory, the most general class of models for forecasting a time series. The commonly known Box-Jenkins approach to ARIMA model building is an iterative process. To facilitate the iterative process and to relieve the boredom of computational errands, we have developed an assistor for building ARIMA models. The assistor is implemented in Java with embedded R for statistical functions. With the help of the assistor ARIMA models for time series are few clicks away, thus enabling users to focus their efforts on the decision problems at hand.

Adaptive Spatio-Temporal Exploratory Models: Hemisphere-wide species distributions from massively crowdsourced eBird data

Broad-scale spatiotemporal processes in conservation and sustainability science, such as continent-wide animal movement, occur across a range of spatial and temporal scales. Understanding these processes at multiple scales is crucial for developing and coordinating conservation strategies across national boundaries. In this paper we propose a general class of models we call AdaSTEM, for Adaptive Spatio-Temporal Exploratory Models, that are able to exploit variation in the density of observations while adapting to multiple scales in space and time. We show that this framework is able to efficiently discover multiscale structure when it is present, while retaining predictive performance when absent. We provide an empirical comparison and analysis, offer theoretical insights from the ensemble loss decomposition, and deploy AdaSTEM to estimate the spatiotemporal distribution of Barn Swallow (Hirundo rustica) across the Western Hemisphere using massively crowdsourced eBird data.

Bulk renormalization and particle spectrum in codimension-two brane worlds

We study the Casimir energy due to bulk loops of matter fields in codimension-two brane worlds and discuss how effective field theory methods allow us to use this result to renormalize the bulk and brane operators. In the calculation we explicitly sum over the Kaluza-Klein (KK) states with a new convenient method, which is based on a combined use of zeta function and dimensional regularization. Among the general class of models we consider we include a supersymmetric example, 6D gauged chiral supergravity. Although much of our discussion is more general, we treat in some detail a class of compactifications, where the extra dimensions parametrize a rugby ball shaped space with size stabilized by a bulk magnetic flux. The rugby ball geometry requires two branes, which can host the Standard Model fields and carry both tension and magnetic flux (of the bulk gauge field), the leading terms in a derivative expansion. The brane properties have an impact on the KK spectrum and therefore on the Casimir energy as well as on the renormalization of the brane operators. A very interesting feature is that when the two branes carry exactly the same amount of flux, one half of the bulk supersymmetries survives after the compactification, even if the brane tensions are large. We also discuss the implications of these calculations for the natural value of the cosmological constant when the bulk has two large extra dimensions and the bulk supersymmetry is partially preserved (or completely broken).

Optimal advertising and pricing in a class of general new-product adoption models

In [21], Sethi et al. introduced a particular new-product adoption model. They determine optimal advertising and pricing policies of an associated deterministic infinite horizon discounted control problem. Their analysis is based on the fact that the corresponding Hamilton–Jacobi–Bellman (HJB) equation is an ordinary non-linear differential equation which has an analytical solution. In this paper, generalizations of their model are considered. We take arbitrary adoption and saturation effects into account, and solve finite and infinite horizon discounted variations of associated control problems. If the horizon is finite, the HJB-equation is a 1st order non-linear partial differential equation with specific boundary conditions. For a fairly general class of models we show that these partial differential equations have analytical solutions. Explicit formulas of the value function and the optimal policies are derived. The controlled Bass model with isoelastic demand is a special example of the class of controlled adoption models to be examined and will be analyzed in some detail.

Flexible marginalized models for bivariate longitudinal ordinal data

Random effects models are commonly used to analyze longitudinal categorical data. Marginalized random effects models are a class of models that permit direct estimation of marginal mean parameters and characterize serial correlation for longitudinal categorical data via random effects (Heagerty, 1999). Marginally specified logistic-normal models for longitudinal binary data. Biometrics 55, 688-698; Lee and Daniels, 2008. Marginalized models for longitudinal ordinal data with application to quality of life studies. Statistics in Medicine 27, 4359-4380). In this paper, we propose a Kronecker product (KP) covariance structure to capture the correlation between processes at a given time and the correlation within a process over time (serial correlation) for bivariate longitudinal ordinal data. For the latter, we consider a more general class of models than standard (first-order) autoregressive correlation models, by re-parameterizing the correlation matrix using partial autocorrelations (Daniels and Pourahmadi, 2009). Modeling covariance matrices via partial autocorrelations. Journal of Multivariate Analysis 100, 2352-2363). We assess the reasonableness of the KP structure with a score test. A maximum marginal likelihood estimation method is proposed utilizing a quasi-Newton algorithm with quasi-Monte Carlo integration of the random effects. We examine the effects of demographic factors on metabolic syndrome and C-reactive protein using the proposed models.

On Existence analysis of steady flows of generalized Newtonian fluids with concentration dependent power-law index

We study a system of partial differential equations describing a steady flow of an incompressible generalized Newtonian fluid, wherein the Cauchy stress is concentration dependent. Namely, we consider a coupled system of the generalized Navier–Stokes equations and convection–diffusion equation with non-linear diffusivity. We prove the existence of a weak solution for certain class of models by using a generalization of the monotone operator theory which fits into the framework of generalized Sobolev spaces with variable exponent. Such a framework is involved since the function spaces, where we look for the weak solution, are “dependent” of the solution itself, and thus, we a priori do not know them. This leads us to the principal a priori assumptions on the model parameters that ensure the Hölder continuity of the variable exponent. We present here a constructive proof based on the Galerkin method that allows us to obtain the result for very general class of models.

Phenomenology of WIMPy baryogenesis models

A possible connection between the abundances of baryonic and dark matter (DM) has been explored so far mostly in the context of the so-called asymmetric DM. Recently, a very different mechanism, dubbed ``WIMPy baryogenesis'', has been proposed to relate the baryon asymmetry to DM annihilation. The DM candidate is a weakly interacting massive particle (WIMP), and the usual WIMP scenario is slightly extended to accommodate baryogenesis, which is accomplished around the time of DM freeze-out. We construct an effective field theory that encompasses a quite general class of models which implement the WIMPy baryogenesis. Under some reasonable, simplifying assumptions, we show that a good portion of the parameter space is allowed for these models, after experimental constraints are taken into account. Bounds from the LHC require that the WIMP be heavier than 400 GeV.

Qubit models of black hole evaporation

Recently, several simple quantum mechanical toy models of black hole evaporation have appeared in the literature attempting to illuminate the black hole information paradox. We present a general class of models that is large enough to describe both unitary and nonunitary evaporation, and study a few specific examples to clarify some potential confusions regarding recent results. We also generalize Mathur’s bound on small corrections to black hole dynamics. Conclusions are then drawn about the requirements for unitary evaporation of black holes in this class of models. We present a one-parameter family of models that continuously deforms nonunitary Hawking evaporation into a unitary process. The required deformation is large.

Fuzzy Set Based Models and Methods of Decision Making and Power Engineering Problems

The results of research into the use of fuzzy set based models and methods of multicriteria decision making for solving power engineering problems are presented. Two general classes of models related to multiobjective (X，M> models) and multiattribute (X，R> models) problems are considered. The analysisX，M> of models is based on the use of the Bellman-Zadeh approach to decision making in a fuzzy environment. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. Several techniques based on fuzzy preference modeling are considered for the analysis of X，R> models. A review of the authors’ results associated with the application of these models and methods for solving diverse types of problems of power system and subsystems planning and operation is presented. The recent results on the use ofX，M> andX，R> models and methods of their analysis for the allocation of reactive power sources in distribution systems and for the prioritization in maintenance planning in distribution systems, respectively, are considered.

Modelling random effect variance with double hierarchical generalized linear models

Random-effect models are becoming increasingly popular in the analysis of data. Lee and Nelder (2006) introduced double hierarchical generalized linear models (DHGLMs) in which not only the mean but also the residual variance (overdispersion) can be further modelled as random-effect models. In this article, we introduce DHGLMs that allow random-effect models for both the variances of random effects and the residual variance. We show how to use this general model class for the analysis of data and discuss how to select the best fitting model using the likelihood and various model-checking plots.