Browsing by Subject "CONVERGENCE"

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  • Leppanen, Juho; Stenlund, Mikko (2017)
    In this short note we consider the finite-dimensional distributions of sets of states generated by dispersing billiards with a random initial condition. We establish a functional correlation bound on the distance between the finite-dimensional distributions and corresponding product distributions. We demonstrate the usefulness of the bound by showing that it implies several limit theorems. The purpose of this note is to provide a tool facilitating the study of more general functionals of the billiard process.
  • Lehtola, Susi; Blockhuys, Frank; Van Alsenoy, Christian (2020)
    A uniform derivation of the self-consistent field equations in a finite basis set is presented. Both restricted and unrestricted Hartree-Fock (HF) theory as well as various density functional approximations are considered. The unitary invariance of the HF and density functional models is discussed, paving the way for the use of localized molecular orbitals. The self-consistent field equations are derived in a non-orthogonal basis set, and their solution is discussed also in the presence of linear dependencies in the basis. It is argued why iterative diagonalization of the Kohn-Sham-Fock matrix leads to the minimization of the total energy. Alternative methods for the solution of the self-consistent field equations via direct minimization as well as stability analysis are briefly discussed. Explicit expressions are given for the contributions to the Kohn-Sham-Fock matrix up to meta-GGA functionals. Range-separated hybrids and non-local correlation functionals are summarily reviewed.
  • Marjakangas, Emma-Liina; Ovaskainen, Otso; Abrego, Nerea; Grøtan, Vidar; de Oliveira, Alexandre A.; Prado, Paulo I.; de Lima, Renato A. F. (2021)
    Species co-occurrences in local communities can arise independent or dependent on species' niches. However, the role of niche-dependent processes has not been thoroughly deciphered when generalized to biogeographical scales, probably due to combined shortcomings of data and methodology. Here, we explored the influence of environmental filtering and limiting similarity, as well as biogeographical processes that relate to the assembly of species' communities and co-occurrences. We modelled jointly the occurrences and co-occurrences of 1016 tropical tree species with abundance data from inventories of 574 localities in eastern South America. We estimated species co-occurrences as raw and residual associations with models that excluded and included the environmental effects on the species' co-occurrences, respectively. Raw associations indicate co-occurrence of species, whereas residual associations indicate co-occurrence of species after accounting for shared responses to environment. Generally, the influence of environmental filtering exceeded that of limiting similarity in shaping species' co-occurrences. The number of raw associations was generally higher than that of the residual associations due to the shared responses of tree species to the environmental covariates. Contrary to what was expected from assuming limiting similarity, phylogenetic relatedness or functional similarity did not limit tree co-occurrences. The proportions of positive and negative residual associations varied greatly across the study area, and we found a significant tendency of some biogeographical regions having higher proportions of negative associations between them, suggesting that large-scale biogeographical processes limit the establishment of trees and consequently their co-occurrences.
  • Liu, Jie; Ilmarinen, Ville-Juhani (2020)
    This research investigated the moderation effects of core self-evaluation (CSE) on singles’ ideal partner preference, concerning distinctive similarity in personality. The data were collected from singles from three countries (i.e., China, Denmark, and US), and modelled in a multilevel profile analysis. The results show that CSE moderated distinctive profile similarity preference in that people high in CSE preferred higher distinctive profile similarity with their ideal partner. In addition, CSE moderated distinctive trait similarity preference in Emotionality, Extraversion, Agreeableness, and Conscientiousness in that people high in CSE preferred their ideal partner to share higher distinctive similarity on these four traits. Implications and limitations of the research and findings are also discussed.
  • Taylor, G.; Hillers, G. (2020)
    We present a new method for estimating time-series of relative seismic velocity changes (dv/v) within the Earth. Our approach is a Markov chain Monte Carlo (MCMC) technique that seeks to construct the full posterior probability distribution of the dv/v variations. Our method provides a robust, computationally efficient way to compute dv/v time-series that can incorporate information about measurement uncertainty, and any prior constraints that may be available. We demonstrate the method with a synthetic experiment, and then apply the MCMC algorithm to three data examples. In the first two examples we reproduce dv/v time-series associated with the response to the 2010 M 7.2 El Mayor-Cucapah earthquake at two sites in southern California, that have been studied in previous literature. In the San Jacinto fault zone environment we reproduce the dv/v signature of a deep creep slip sequence triggered by the El Mayor-Cucapah event, that is superimposed on a strong seasonal signal. At the Salton Sea Geothermal Field we corroborate the previously observed drop-and-recovery in seismic velocity caused by ground shaking related to the El Mayor-Cucapah event. In a third, new example we compute a month long velocity change time-series at hourly resolution at Pinion Flat, California. We observe a low amplitude variation in seismic velocity with a dominant frequency of 1 cycle per day, as well as a second transient signal with a frequency of 1.93 cycles per day. We attribute the 1-d periodicity in the dv/v variation to the combined effects of the diurnal tide and solar heating. The frequency of the signal at 1.93 cycles per day matches that of the lunar (semi-diurnal) tide. Analysis of the uncertainties in the Pinion Flat time-series shows that the error contains a signal with a frequency of 1 cycle per day. We attribute this variation to seismic noise produced by freight trains operating within the Coachella Valley. By demonstrating the applicability of the MCMC method in these examples, we show that it is well suited to tackle problems involving large data volumes that are typically associated with modern seismic experiments.
  • Van Belleghem, Steven M.; Vangestel, Carl; De Wolf, Katrien; De Corte, Zoe; Most, Markus; Rastas, Pasi; De Meester, Luc; Hendrickx, Frederik (2018)
    When environments change, populations may adapt surprisingly fast, repeatedly and even at microgeographic scales. There is increasing evidence that such cases of rapid parallel evolution are fueled by standing genetic variation, but the source of this genetic variation remains poorly understood. In the salt-marsh beetle Pogonus chalceus, short-winged 'tidal' and long-winged 'seasonal' ecotypes have diverged in response to contrasting hydrological regimes and can be repeatedly found along the Atlantic European coast. By analyzing genomic variation across the beetles' distribution, we reveal that alleles selected in the tidal ecotype are spread across the genome and evolved during a singular and, likely, geographically isolated divergence event, within the last 190 Kya. Due to subsequent admixture, the ancient and differentially selected alleles are currently polymorphic in most populations across its range, which could potentially allow for the fast evolution of one ecotype from a small number of random individuals, as low as 5 to 15, from a population of the other ecotype. Our results suggest that cases of fast parallel ecological divergence can be the result of evolution at two different time frames: divergence in the past, followed by repeated selection on the same divergently evolved alleles after admixture. These findings highlight the importance of an ancient and, likely, allopatric divergence event for driving the rate and direction of contemporary fast evolution under gene flow. This mechanism is potentially driven by periods of geographic isolation imposed by large-scale environmental changes such as glacial cycles.
  • Leppänen, Juho (2017)
    In the setting of intermittent Pomeau-Manneville maps with time dependent parameters, we show a functional correlation bound widely useful for the analysis of the statistical properties of the model. We give two applications of this result, by showing that in a suitable range of parameters the bound implies the conditions of the normal approximation methods of Stein and Rio. For a single Pomeau-Manneville map belonging to this parameter range, both methods then yield a multivariate central limit theorem with a rate of convergence.
  • Abera, Temesgen; Heiskanen, Janne; Pellikka, Petri; Maeda, Eduardo (2020)
    Precipitation extremes have a strong influence on the exchange of energy and water between the land surface and the atmosphere. Although the Horn of Africa has faced recurrent drought and flood events in recent decades, it is still unclear how these events impact energy exchange and surface temperature across different ecosystems. Here, we analyzed the impact of precipitation extremes on spectral albedo (total shortwave, visible, and near-infrared (NIR) broadband albedos), energy balance, and surface temperature in four natural vegetation types: forest, savanna, grassland, and shrubland. We used remotely sensed observations of surface biophysical properties and climate from 2001 to 2016. Our results showed that, in forests and savannas, precipitation extremes led to divergent spectral changes in visible and NIR albedos, which cancelled each other limiting shortwave albedo changes. An exception to this pattern was observed in shrublands and grasslands, where both visible and NIR albedo increased during drought events. Given that shrublands and grasslands occupy a large fraction of the Horn of Africa (52%), our results unveil the importance of these ecosystems in driving the magnitude of shortwave radiative forcing in the region. The average regional shortwave radiative forcing during drought events (-0.64 W m(-2), SD 0.11) was around twice that of the extreme wet events (0.33 W m(-2), SD 0.09). Such shortwave forcing, however, was too small to influence the surface-atmosphere coupling. In contrast, the surface feedback through turbulent flux changes was strong across vegetation types and had a significant (P <0.05) impact on the surface temperature and net radiation anomalies, except in forests. The strongest energy exchange and surface temperature anomalies were observed over grassland and the smallest over forest, which was shown to be resilient to precipitation extremes. These results suggest that land management activities that support forest preservation, afforestation, and reforestation can help to mitigate the impact of drought through their role in modulating energy fluxes and surface temperature anomalies in the region.
  • Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther (2008)
  • Ercolano, Salvatore; Gaeta, Giuseppe Lucio; Ghinoi, Stefano; Silvestri, Francesco (2018)
    By using a novel database that observes 1,497 municipalities from the Lombardy region in Italy between 2005 and 2011, this paper provides an empirical test of the Waste Kuznets Curve (WKC) hypothesis. Fixed effects regression analyses, generalized method of moments models and a number of robustness checks strongly indicate that among the municipalities under scrutiny there is an inverted U-shaped relationship between economic development and waste generation. Nevertheless, only a few of the municipalities under scrutiny reach the turning point of the estimated curve. These findings contribute to the expanding empirical literature that tests WKC by using municipal data, considered the most appropriate for this kind of analysis.
  • Kaaronen, Roope Oskari; Manninen, Mikael A.; Roe, Emery Martin; Hukkinen, Janne; Eronen, Jussi T. (2021)
    Historical records are incomplete templates for preparing for an uncertain future. The global utility of past ecological knowledge for present/future purposes is questioned as we move from Holocene to Anthropocene. To increase the adaptive capacity of today’s societies, generalizable strategies must be identified for coping with uncertainty over a wide range of conditions and contingencies. We identify two key principles that increase adaptive capacities: diversification and precautionary heuristics. These sharply contrast with the present global state represented by the global production ecosystem characterized by: (1) homogenization and simplification of cultural practices and resource bases; (2) increased global connectivity and forced dissolution of cultural borders; and (3) centralization and intensification of modes of resource production and extraction. We highlight that responses of smaller-scale societies to risks and uncertainties are in many cases emulated by professionals in the high reliability management in today’s critical infrastructures. This provides a modern template for managing unpredictability in the Anthropocene.
  • Sasaki, Hiroaki; Kanamori, Takafumi; Hyvärinen, Aapo; Niu, Gang; Sugiyama, Masashi (2018)
    Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges enables us to find lower-dimensional structures hidden in data. A key technical challenge both in mode-seeking clustering and density ridge estimation is accurate estimation of the ratios of the first- and second-order density derivatives to the density. A naive approach takes a three-step approach of first estimating the data density, then computing its derivatives, and finally taking their ratios. However, this three-step approach can be unreliable because a good density estimator does not necessarily mean a good density derivative estimator, and division by the estimated density could significantly magnify the estimation error. To cope with these problems, we propose a novel estimator for the density-derivative-ratios. The proposed estimator does not involve density estimation, but rather directly approximates the ratios of density derivatives of any order. Moreover, we establish a convergence rate of the proposed estimator. Based on the proposed estimator, novel methods both for mode-seeking clustering and density ridge estimation are developed, and the respective convergence rates to the mode and ridge of the underlying density are also established. Finally, we experimentally demonstrate that the developed methods significantly outperform existing methods, particularly for relatively high-dimensional data.
  • Viitasaari, Lauri (2019)
    The quadratic variation of Gaussian processes plays an important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this article we study the convergence of quadratic sums of general Gaussian sequences. We provide necessary and sufficient conditions for different types of convergence including convergence in probability, almost sure convergence, L-p-convergence as well as weak convergence. We use a practical and simple approach which simplifies the existing methodology considerably. As an application, we show how convergence of the quadratic variation of a given process can be obtained by an appropriate choice of the underlying sequence.
  • Diekmann, Odo; Gyllenberg, Mats; Metz, Johan A. J. (2020)
    Considering the environmental condition as a given function of time, we formulate a physiologically structured population model as a linear non-autonomous integral equation for the, in general distributed, population level birth rate. We take this renewal equation as the starting point for addressing the following question: When does a physiologically structured population model allow reduction to an ODE without loss of relevant information? We formulate a precise condition for models in which the state of individuals changes deterministically, that is, according to an ODE. Specialising to a one-dimensional individual state, like size, we present various sufficient conditions in terms of individual growth-, death-, and reproduction rates, giving special attention to cell fission into two equal parts and to the catalogue derived in an other paper of ours (submitted). We also show how to derive an ODE system describing the asymptotic large time behaviour of the population when growth, death and reproduction all depend on the environmental condition through a common factor (so for a very strict form of physiological age).
  • Kemppainen, Antti; Smirnov, Stanislav (2017)
    In this paper, we provide a framework of estimates for describing 2D scaling limits by Schramm's SLE curves. In particular, we show that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical mechanics model will have scaling limits and those will be well described by Loewner evolutions with random driving forces. Interestingly, our proofs indicate that existence of a nondegenerate observable with a conformally- invariant scaling limit seems sufficient to deduce the required condition. Our paper serves as an important step in establishing the convergence of Ising and FK Ising interfaces to SLE curves; moreover, the setup is adapted to branching interface trees, conjecturally describing the full interface picture by a collection of branching SLEs.
  • Fefferman, Charles; Ivanov, Sergei; Kurylev, Yaroslav; Lassas, Matti; Narayanan, Hariharan (2020)
    We study the geometric Whitney problem on how a Riemannian manifold (M, g) can be constructed to approximate a metric space (X, d(X)). This problem is closely related to manifold interpolation (or manifold reconstruction) where a smooth n-dimensional submanifold S subset of R-m, m > n needs to be constructed to approximate a point cloud in Rm. These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian manifold includes the construction of its topology, differentiable structure, and metric. We give constructive solutions to the above problems. Moreover, we characterize the metric spaces that can be approximated, by Riemannian manifolds with bounded geometry: We give sufficient conditions to ensure that a metric space can be approximated, in the Gromov-Hausdorff or quasi-isometric sense, by a Riemannian manifold of a fixed dimension and with bounded diameter, sectional curvature, and injectivity radius. Also, we show that similar conditions, with modified values of parameters, are necessary. As an application of the main results, we give a new characterization of Alexandrov spaces with two-sided curvature bounds. Moreover, we characterize the subsets of Euclidean spaces that can be approximated in the Hausdorff metric by submanifolds of a fixed dimension and with bounded principal curvatures and normal injectivity radius. We develop algorithmic procedures that solve the geometric Whitney problem for a metric space and the manifold reconstruction problem in Euclidean space, and estimate the computational complexity of these procedures. The above interpolation problems are also studied for unbounded metric sets and manifolds. The results for Riemannian manifolds are based on a generalization of the Whitney embedding construction where approximative coordinate charts are embedded in R-m and interpolated to a smooth submanifold.
  • Kuusi, Tuomo; Misawa, Masashi; Nakamura, Kenta (2020)
    We study doubly nonlinear parabolic equation arising from the gradient flow for p-Sobolev type inequality, referred as p-Sobolev flow from now on, which includes the classical Yamabe flow on a bounded domain in Euclidean space in the special case . In this article we establish a priori estimates and regularity results for the p-Sobolev type flow, which are necessary for further analysis and classification of limits as time tends to infinity.
  • Leikas, Sointu; Ilmarinen, Ville; Verkasalo, Markku; Vartiainen, Hanna-Leena; Lönnqvist, Jan-Erik (2018)
    Spousal similarity and its consequences are widely studied, but methodologically challenging topics. We employed Response Surface Analysis to examine similarity along political attitudes, personal values, and personality traits. Opposite-sex couples (624 individuals) expecting a child were recruited. Spouses were highly similar regarding their political attitudes and moderately similar regarding trait Openness and the personal values Universalism and Tradition. Similarity for other traits and values was weak (e.g. Conscientiousness, Power values) or non-existent (e.g. Neuroticism, Benevolence values). Similarity in conservative vs. liberal attitudes was non-linear: a conservative-conservative union was most common. Women's relationship satisfaction was related to similarity in left-right and liberal-conservative political attitudes, and both partners' satisfaction was related to similarity in Self-Direction values. Similarity in personality traits was unrelated to relationship satisfaction.
  • Stevanovic, Melisa; Himberg, Tommi; Niinisalo, Maija; Kahri, Mikko; Peräkylä, Anssi; Sams, Mikko; Hari, Riitta (2017)
    We studied behavioral matching during joint decision making. Drawing on motion-capture and voice data from 12 dyads, we analyzed body-sway and pitch-register matching during sequential transitions and continuations, with and without mutual visibility. Body sway was matched most strongly during sequential transitions in the conditions of mutual visibility. Pitch-register matching was higher during sequential transitions than continuations only when the participants could not see each other. These results suggest that both body sway and pitch register are used to manage sequential transitions, while mutual visibility influences the relative weights of these two resources. The conversational data are in Finnish with English translation.
  • Piras, Simone; Wesz Jr., Valdemar João; Ghinoi, Stefano (2021)
    In the last decades, Brazil has become one of the largest soybean producers and exporters in the world. Although dedicated policies have been implemented since the 1960s, the recent rapid transition towards an agricultural system largely based on soy has had a strong impact on the country’s socio-economic structure—not only in terms of land and labour markets but also on its diverse ecosystems. According to the extant literature, soy has had a beneficial impact on local human development, measured by the human development index (HDI) of the municipalities. However, there is a lack of empirical studies assessing the impact of soy expansion on the single dimensions of the HDI (longevity, education, and income) to disentangle the indirect effects of socio-environmental change while controlling for other local dynamics. To fill this gap, we applied econometric methods to a novel dataset combining municipal-level data on soy production with socio-economic and environmental data for the period 1991–2010. Our findings confirm the positive relation between soy expansion and the HDI at local level, but this relation differs between different HDI dimensions. The marginal benefits of soy expansion are increasing for the income dimension but decreasing for education and longevity. On the other hand, changes in soy productivity (a proxy for agricultural intensification) have a more complex impact on the HDI and its dimensions, but in general its marginal benefits are decreasing over time. Further research could expand the time series once more up-to-date information becomes available.