This paper investigates when it is possible for a partial ordering P to force Pκ(λ) \ V to be stationary in VP. It follows from a result of Gitik that whenever P adds a new real, then Pκ(λ) \ V is stationary in VP for each regular uncountable cardinal κ in VP and all cardinals λ > κ in VP [4]. However, a covering theorem of Magidor implies that when no new ω-sequences are added, large cardinals become necessary [7]. The (...) following is equiconsistent with a proper class of ω₁-Erdős cardinals: If P is N₁-Cohen forcing, then Pκ(λ) \ V is stationary in VP, for all regular κ ≥ N₂ and all λ > κ. The following is equiconsistent with an ω₁-Erdős cardinal: If P is N₁-Cohen forcing, then PN₂ (N₃) \ V is stationary in VP. The following is equiconsistent with κ measurable cardinals: If P is κ-Cohen forcing, then Pκ + (Nκ \ V is stationary in VP. (shrink)

We investigate stationarity of types over models in simple theories. In particular, we show that in simple theories with finite SU-rank, any complete type over a model having Cantor-Bendixson rank is stationary.

I analyze various natural assumptions which imply that the set {ω1L[x]∣x⊆ω}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\{\omega_1^{L[x]} \mid x \subseteq \omega\}}$$\end{document} is stationary in ω1. The focal questions are which implications hold between them, what their consistency strengths are, and which large cardinal assumptions outright imply them.

We give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order ) equal to κ++, and use it to prove the following theorem on mutual stationarity at n.Let ω1 denote the first uncountable cardinal of V and set to be the class of ordinals of cofinality ω1.TheoremIf every sequence n m. In particular, there is such a model in which (...) for all sufficiently large m<ω, the class of measurables λ with oM≥ωm is, in V, stationary below m+2. (shrink)

We discuss some of the relationships between the notion of "mutual stationarity" of Foreman and Magidor and measurability in inner models. The general thrust of these is that very general mutual stationarity properties on small cardinals, such as the ℵns, is a large cardinal property. A number of open problems, theorems, and conjectures are stated.

We construct a model where every increasing ω-sequence of regular cardinals carries a mutually stationary sequence which is not tightly stationary, and show that this property is preserved under a class of Prikry-type forcings. Along the way, we give examples in the Cohen and Prikry models of ω-sequences of regular cardinals for which there is a non-tightly stationary sequence of stationary subsets consisting of cofinality ω_1 ordinals, and show that such stationary sequences are mutually stationary in the presence of interleaved (...) supercompact cardinals. (shrink)

Global co-stationarity of the ground model from an N₂-c.c, forcing which adds a new subset of N₁ is internally consistent relative to an ω₁-Erdös hyperstrong cardinal and a sufficiently large measurable above.

This study investigated the stationarity of electrodermal time series collected in situations where turn taking in human interactions are involved. In this context, the stationarity of the time series is the extent to which a simple model can be used to fit the entire time series. The experiment involved seven participants in an emergency response simulation against one opponent. They generated 48 time series across six simulations, which were split and re-spliced to separate the team’s turns and the (...) opponent’s turns. Significant differences in R2 coefficients were found for both linear and nonlinear statistical models between experimental conditions, but the difference only amounted to 3% of the accuracy of those models relative to the original data. It was thus concluded that the impact of turn taking on stationarity was a small effect at most. A comparison of synchronization coefficients for the team data, which rely on the collective accuracy of the individual time series models, indicated stronger synchronization during periods when the team was watching the opponent’s actions compared to when they took their own turns. It was thus concluded, furthermore, that the common focus of attention prevailed against any non-stationarity that was introduced by turn taking. (shrink)

This paper attempts to present and organize several problems in the theory of Singular Cardinals. The most famous problems in the area (bounds for the ℶ-function at singular cardinals) are well known to all mathematicians with even a rudimentary interest in set theory. However, it is less well known that the combinatorics of singular cardinals is a thriving area with results and problems that do not depend on a solution of the Singular Cardinals Hypothesis. We present here an annotated collection (...) of representative problems with some references. Where the problems are novel, attribution is attempted and it is noted where money is attached to particular problems. Three closely related themes are represented in these problems: stationary sets and stationary set reflection, variations of square and approachability, and the singular cardinals hypothesis. Underlying many of them are ideas from Shelah's PCF theory. Important subthemes were mutual stationarity, Aronszajn trees, and superatomic Boolean Algebras. The author notes considerable overlap between this paper and the unpublished report submitted to the Banff Center for the Workshop on Singular Cardinals Combinatorics, May 1–5, 2004. (shrink)

Changing and often class-dependent non-stationarities of signals are a big challenge in the transfer of common findings in cognitive workload estimation using Electroencephalography (EEG) from laboratory experiments to realistic scenarios or other experiments. Additionally, it often remains an open question whether actual cognitive workload reflected by brain signals was the main contribution to the estimation or discriminative and class-dependent muscle and eye activity, which can be secondary effects of changing workload levels. Within this study, we investigated a novel approach to (...) spatial filtering based on beamforming adapted to changing settings. We compare it to no spatial filtering and Common Spatial Patterns (CSP). We used a realistic maneuvering task, as well as an auditoryn-backsecondary task on a tugboat simulator as two different conditions to induce workload changes on professional tugboat captains. Apart from the typical within condition classification, we investigated the ability of the different classification methods to transfer between then-backcondition and the maneuvering task. The results show a clear advantage of the proposed approach over the others in the challenging transfer setting. While no filtering leads to lowest within-condition normalized classification loss on average in two scenarios (22 and 10%), our approach using adaptive beamforming (30 and 18%) performs comparably to CSP (33 and 15%). Importantly, in the transfer from one to another setting, no filtering and CSP lead to performance around chance level (45 to 53%), while our approach in contrast is the only one capable of classifying in all other scenarios (34 and 35%) with a significant difference from chance level. The changing signal composition over the scenarios leads to a need to adapt the spatial filtering in order to be transferable. With our approach, the transfer is successful due to filtering being optimized for the extraction of neural components and additional investigation of their scalp patterns revealed mainly neural origin. Interesting findings are that rather the patterns slightly change between conditions. We conclude that the approaches with low normalized loss depend on eye and muscle activity which is successful for classification within conditions, but fail in the classifier transfer since eye and muscle contributions are highly condition-specific. (shrink)

Freiheitsentziehende Maßnahmen in Altenpflegeheimen sind unter pflegerischen und ethischen, aber auch betreuungsrechtlichen und vor allem strafrechtlichen Gesichtspunkten von besonderer Bedeutung. Häufig sind eingeschränkte Mobilität, Verringerung der kognitiven Funktionen, große Hilfsbedürftigkeit des älteren Menschen der auslösende Faktor für den Einsatz derartiger Einschränkungen. Daneben gibt es jedoch Hinweise, dass die Anwendung freiheitsentziehender Maßnahmen auch mit organisatorischen Abläufen in Altenpflegeeinrichtungen zusammenhängt. Der vorliegende Beitrag diskutiert, wieweit freiheitsentziehende und freiheitsbeschränkende Maßnahmen bei alten Menschen überhaupt zulässig sind und zeigt auf, dass die Entwicklung von alternativen (...) Betreuungs- und Versorgungsansätzen dazu beitragen kann, dass durch weniger freiheitsentziehende Maßnahmen in der stationären Pflege die Würde der alten Menschen gewahrt bleibt. (shrink)

Die Komplexität ethischer Fragen und Alltagskonflikte in Einrichtungen der stationären Altenpflege verlangen Gesprächsforen für Ethikberatung und Fortbildung zur ethischen Entscheidungsfindung. Noch ist in Deutschland die Einrichtung von Ethikkomitees in Altenpflegeheimen in den Anfängen. Es kommt nun vordringlich darauf an, bei der Institutionalisierung die spezifischen strukturellen und personellen Bedingungen eines Altenpflegeheims zu berücksichtigen, um zum Wohle aller Betroffenen mit der erforderlichen Kontextsensitivität zu einer verbesserten ethischen Entscheidungskultur beizutragen. Wesentliche Merkmale eines Altenpflegeheims werden dargestellt und anhand der Psychopharmakaversorgung einige typische ethische Probleme (...) diskutiert. (shrink)

This paper analyzes the ergodic hypothesis in the context of Boltzmann’s late work in statistical mechanics, where Boltzmann lays the foundations for what is today known as the typicality account. I argue that, based on the concepts of stationarity (of the measure) and typicality (of the equilibrium state), the ergodic hypothesis, as an idealization, is a consequence rather than an assumption of Boltzmann’s account. More precisely, it can be shown that every system with a stationary measure and an equilibrium (...) state (be it a typical state with respect to the phase space or the time average) behaves essentially as if it were ergodic. I claim that Boltzmann was aware of this fact as it grounds both his notion of equilibrium, relating it to the thermodynamic notion of equilibrium, and his estimate of the fluctuation rates. (shrink)

Since Economics survey by Windrum et al., research on empirical validation of agent-based Agent-based model in Economics has made substantial advances, thanks to a constant flow of high-quality contributions. This Chapter attempts to take stock of such recent literature to offer an updated critical review of the existing validation techniques. We sketch a simple theoretical framework that conceptualizes existing validation approaches, which we examine along three different dimensions: Comparison between artificial and real-world Data; Calibration and estimation of model parameters; and (...) parameter space Exploration. Finally, we discuss open issues in the field of ABM validation and Estimation. In particular, we argue that more research efforts should be devoted toward advancing HypothesisTesting in ABM, with specific emphasis on model stationarity and ergodicity. (shrink)

Emotion recognition plays an important part in human-computer interaction. Currently, the main challenge in electroencephalogram -based emotion recognition is the non-stationarity of EEG signals, which causes performance of the trained model decreasing over time. In this paper, we propose a two-level domain adaptation neural network to construct a transfer model for EEG-based emotion recognition. Specifically, deep features from the topological graph, which preserve topological information from EEG signals, are extracted using a deep neural network. These features are then passed (...) through TDANN for two-level domain confusion. The first level uses the maximum mean discrepancy to reduce the distribution discrepancy of deep features between source domain and target domain, and the second uses the domain adversarial neural network to force the deep features closer to their corresponding class centers. We evaluated the domain-transfer performance of the model on both our self-built data set and the public data set SEED. In the cross-day transfer experiment, the ability to accurately discriminate joy from other emotions was high: sadness, anger, and fear on the self-built data set. The accuracy reached 74.93% on the SEED data set. In the cross-subject transfer experiment, the ability to accurately discriminate joy from other emotions was equally high: sadness, anger, and fear on the self-built data set. The average accuracy reached 87.9% on the SEED data set, which was higher than WGAN-DA. The experimental results demonstrate that the proposed TDANN can effectively handle the domain transfer problem in EEG-based emotion recognition. (shrink)

How should one discount utility across time? The conventional wisdom in social science is that one should use an exponential discount function. Such a function is a representation of the axioms that provide a well-defined utility function plus a condition known as stationarity. Yet stationarity doesnt really have much intuitive normative pull on its own. Here I try to cast it in a normative glow by deriving stationarity from two explicitly normative premises, both suggested by the philosophical (...) thesis of temporal neutralism. Putting the argument in this form helps us better understand exponential discounting and challenges to it. (shrink)

In Part I of this series [A. Poveda, A. Rinot and D. Sinapova, Sigma-Prikry forcing I: The axioms, Canad. J. Math. 73(5) (2021) 1205–1238], we introduced a class of notions of forcing which we call [Formula: see text]-Prikry, and showed that many of the known Prikry-type notions of forcing that center around singular cardinals of countable cofinality are [Formula: see text]-Prikry. We showed that given a [Formula: see text]-Prikry poset [Formula: see text] and a [Formula: see text]-name for a non-reflecting (...) stationary set [Formula: see text], there exists a corresponding [Formula: see text]-Prikry poset that projects to [Formula: see text] and kills the stationarity of [Formula: see text]. In this paper, we develop a general scheme for iterating [Formula: see text]-Prikry posets and, as an application, we blow up the power of a countable limit of Laver-indestructible supercompact cardinals, and then iteratively kill all non-reflecting stationary subsets of its successor. This yields a model in which the singular cardinal hypothesis fails and simultaneous reflection of finite families of stationary sets holds. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. In Part I of this series [A. Poveda, A. Rinot and D. Sinapova, Sigma-Prikry forcing I: The axioms, Canad. J. Math. 73(5) (2021) 1205–1238], we introduced a class of notions of forcing which we call [math]-Prikry, and showed that many of the known Prikry-type notions of forcing that center around singular cardinals of countable cofinality are [math]-Prikry. We showed that given a [math]-Prikry poset [math] and a [math]-name for a non-reflecting (...) stationary set [math], there exists a corresponding [math]-Prikry poset that projects to [math] and kills the stationarity of [math]. In this paper, we develop a general scheme for iterating [math]-Prikry posets and, as an application, we blow up the power of a countable limit of Laver-indestructible supercompact cardinals, and then iteratively kill all non-reflecting stationary subsets of its successor. This yields a model in which the singular cardinal hypothesis fails and simultaneous reflection of finite families of stationary sets holds. (shrink)

This study aims to analyze the impact of Foreign Direct Investment, external debt and population growth on economic progress of Pakistan by using time series data from 1980 to 2014. It analyzes the correlation between Gross Domestic Product,FDI, external debt and population growth. Augmented Dickey Fuller test has been used to check stationarity in time series data. To evaluate the empirical results multiple regression method is used. GDP has been used as a dependent variable while FDI, external debt and (...) population as independent variables. Findings of this paper show the positive and significant impact of FDI, and population growth on GDP but external debt has negative impact on GDP. (shrink)

Physico-chemical sciences are dominated by the deterministic interpretation. Scientific medicine has generally been assigned to the area of functional biology and thence to the physico-chemical sciences. In as much as diseases are alterations of physiological processes, they share the ontological status of the latter. However, many diseases cannot be accommodated within a deterministic interpretation. First, many diseases are initiated by errors in transmission of information and followed by natural selection. These diseases, such as tumoural transformations and autoimmune processes, behave as (...) evolutionary processes. Second, physiological processes do not cause irreversible changes while diseases may do so when not followed by restitutio ad integrum. The tendency of living organisms to maintain stationary states of great stability and minimum energy dissipation is largely due to intermolecular forces-stabilized structures, the information for which is selected during phylogenesis and decodified during ontogenesis. Diseases cause alterations of the biological structures, thereby shifting living organisms toward stationary states of lower stability and increased dissipation. The shift, reversible or irreversible, to less stable and efficient stationary states is a common thermodynamic feature of diseases. In spite of the uniqueness of their genotype, living organisms, during ontogenetic development, form spatio-temporal unrestricted classes of infinite membership. Neither stationarity nor environment-induced perturbations and consequent adaptations are sources of historicity because of the genomic programme constraint. Historicity is conferred, however, to each organism by the permanent record of such unique events as: a) the variation-selection processes occurring in the brain-mind and immunological systems; and b) irreversible alterations induced by diseases. The disease-induced changes have ontological and epistemological consequences. Since biological structures and functions are transformed into individual, historical entities, the laws of scientific medicine must be applied in clinical practice to higher levels of organization, namely to the ensembles or groups of individuals affected by the diseases. (shrink)

The rapid worldwide spread of COVID-19 forced many countries to enforce complete lockdown and strict quarantine policies. The strict lockdown and quarantine affect the psychological state of people toward cryptocurrency. The current research aims to examine the effect of COVID-19 on Bitcoin prices concerning cumulative deaths and confirmed cases. The research comprises daily data from January 20, 2020, to April 30, 2020, during the initial worldwide breakout of COVID-19. This research employed the augmented Dickey-Fuller test to check the stationarity (...) of data, the co-integration test for the interdependency of variables, and the vector error correction model for identifying the direction and long or short-run relationship between Bitcoin prices and COVID-19. The research results show that Bitcoin prices are negatively significant and related to COVID-19 in the short-run. A unidirectional relationship between Bitcoin prices and cumulative deaths is also observed. Investors and the public’s psychological state were positively significant to Bitcoin prices in the long-term because of cashless transactions, unbanked, and less risky virus traveling. The second reason behind the positive psychological relation is un-centralization and easy-to-make payments by Bitcoin. This study’s finding provides timely evidence to decision-makers on Bitcoin price volatility and its impacts on the public’s psychological states regarding COVID-19. (shrink)

We present a characterization of weakly compact cardinals in terms of generalized stationarity. We apply this characterization to construct a model with no partial square sequences.

In this article we consider an argument put forth by Selgin in support of the claim that there exists a mechanism for limiting coordinated expansions of fiduciary media under a system of fractional reserve free banking. Selgin argues that such banks hold risk-adjusted reserves against expected losses, and even if the expectation of reserve losses remains zero, the variance of such losses increases under an in-concert expansion . It is this increased variability that is claimed to act as a brake (...) on the expansion. We take issue with this argument on the basis of the fact that such a characterization of observed clearings would require that characteristics of the underlying data-generating process be obtainable from pathwise realizations of that process. In other words, there is an implicit assumption of stationarity in Selgin’s argument, and this assumption is at odds with well-known empirical facts of non-stationarity associated with most economic time series. We also point out ways in which techniques of risk management commonly found in the modern financial industry are unlikely to be effective in addressing this problem. (shrink)

Hoerl & McCormack's theory defines temporal behavior from an awareness of time, but lacks one critical element: the impact of “psychological presence” in the “moment now.” Central to experience of temporal non-stationarity: “Nowness” links future with past in the context of time flow. Does this differ between species? Evidence suggests not: Different temporal experiences between species requires greater critical evaluation.

At the beginning of the study of physical phenomena, the idea of "force" was widely used to explain the non-stationarity of observed phenomena, such as the movement of bodies. However, as mechanics and physical theories developed, the force notions gained own formal definitions and names, without the use of the term "force". So, the concept of kinetic energy arose instead of "vis viva", and "current" instead of "current strength" ets. Additionally, a number of new physical theories have been formulated (...) without the use of force concept. As a result, different types of forces have gradually been replaced by other more important concepts, such as energy and action, which are closely linked to fundamental physical principles. It is interesting to note that the general trend in the development of civilizations has been a shift from unrestricted power (expressed in the thesis "might makes right") to its subordination and incorporation into a legal framework. This is similar to the evolution of physics, which has seen the notion of force become eliminated or subordinated to more general principles and laws. (shrink)

While often presented as promising assistive technologies for motor-impaired users, electroencephalography (EEG)-based Brain-Computer Interfaces (BCIs) remain barely used outside laboratories due to low reliability in real-life conditions. There is thus a need to design long-term reliable BCIs that can be used outside-of-the-lab by end-users, e.g., severely motor-impaired ones. Therefore, we propose and evaluate the design of a multi-class Mental Task (MT)-based BCI for longitudinal training (20 sessions over 3 months) of a tetraplegic user for the CYBATHLON BCI series 2019. In (...) this BCI championship, tetraplegic pilots are mentally driving a virtual car in a racing video game. We aimed at combining a progressive user MT-BCI training with a newly designed machine learning pipeline based on adaptive Riemannian classifiers shown to be promising for real-life applications. We followed a two step training process: the first 11 sessions served to train the user to control a 2-class MT-BCI by performing either two cognitive tasks (REST and MENTAL SUBTRACTION) or two motor-imagery tasks (LEFT-HAND and RIGHT-HAND). The second training step (9 remaining sessions) applied an adaptive, session-independent Riemannian classifier that combined all 4 MT classes used before. Moreover, as our Riemannian classifier was incrementally updated in an unsupervised way it would capture both within and between-session non-stationarity. Experimental evidences confirm the effectiveness of this approach. Namely, the classification accuracy improved by about 30% at the end of the training compared to initial sessions. We also studied the neural correlates of this performance improvement. Using a newly proposed BCI user learning metric, we could show our user learned to improve his BCI control by producing EEG signals matching increasingly more the BCI classifier training data distribution, rather than by improving his EEG class discrimination. However, the resulting improvement was effective only on synchronous (cue-based) BCI and it did not translate into improved CYBATHLON BCI game performances. For the sake of overcoming this in the future, we unveil possible reasons for these limited gaming performances and identify a number of promising future research directions. Importantly, we also report on the evolution of the user's neurophysiological patterns and user experience throughout the BCI training and competition. (shrink)

We introduce a natural two-cardinal version of Bagaria’s sequence of derived topologies on ordinals. We prove that for our sequence of two-cardinal derived topologies, limit points of sets can be characterized in terms of a new iterated form of pairwise simultaneous reflection of certain kinds of stationary sets, the first few instances of which are often equivalent to notions related to strong stationarity, which has been studied previously in the context of strongly normal ideals. The non-discreteness of these two-cardinal (...) derived topologies can be obtained from certain two-cardinal indescribability hypotheses, which follow from local instances of supercompactness. Additionally, we answer several questions posed by the first author, Holy and White on the relationship between Ramseyness and indescribability in both the cardinal context and in the two-cardinal context. (shrink)

According to the traditional inferential theory of perception, percepts of object motion or stationarity stem from an evaluation of afferent retinal signals (which encode image motion) with the help of extraretinal signals (which encode eye movements). According to direct perception theory, on the other hand, the percepts derive from retinally conveyed information only. Neither view is compatible with a perceptual phenomenon that occurs during visually induced sensations of ego motion (vection). A modified version of inferential theory yields a model (...) in which the concept of extraretinal signals is replaced by that of reference signals, which do not encode how the eyes move in their orbits but how they move in space. Hence reference signals are produced not only during eye movements but also during ego motion (i.e., in response to vestibular stimulation and to retinal image flow, which may induce vection). The present theory describes the interface between self-motion and object-motion percepts. An experimental paradigm that allows quantitative measurement of the magnitude and gain of reference signals and the size of the just noticeable difference (JND) between retinal and reference signals reveals that the distinction between direct and inferential theories largely depends on: (1) a mistaken belief that perceptual veridicality is evidence that extraretinal information is not involved, and (2) a failure to distinguish between (the perception of) absolute object motion in space and relative motion of objects with respect to each other. The model corrects these errors, and provides a new, unified framework for interpreting many phenomena in the field of motion perception. (shrink)

Todorčević showed that Rado's Conjecture implies CC*, a strengthening of Chang's Conjecture. We generalize this by showing that also CC**, a global version of CC*, follows from RC. As a corollary we obtain that RC implies Semistationary Reflection and, i.e. the statement that all forcings that preserve the stationarity of subsets of ω1 are semiproper.

We show that if I is a precipitous ideal on ω₁ and if θ > ω₁ is a regular cardinal, then there is a forcing P = P(I, θ) which preserves the stationarity of all I-positive sets such that in $V^P $ , is a generic iterate of a countable structure . This shows that if the nonstationary ideal on ω₁ is precipitous and $H_\theta ^\# $ exists, then there is a stationary set preserving forcing which increases $\delta _2^1 (...) $ · Moreover, if Bounded Martin's Maximum holds and the nonstationary ideal on ω₁ is precipitous, then $\delta _2^1 $ = u₂ = ω₂. (shrink)

Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques proven to be the most (...) useful in the behavioral sciences. The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics. The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them. (shrink)

We examine the comportment of the global trajectory of a piecewisely conceived single species population growth model. Formulation relies on what we develop as the principle of limiting factors for population growth, adapted from the law of the minimum of Liebig and the law of the tolerance of Shelford. The ensuing paradigm sets natality and mortality rates to express through extreme values of population growth determining factor. Dynamics through time occur over different growth phases. Transition points are interpreted as thresholds (...) of viability, starvation, and intraspecific competition. In this delivery, we focus on the qualitative study of the global trajectory expressed on continuous time and on exploring the feasibility of analytical results against data on populations growing under experimental or natural conditions. All study cases sustained fittings of high reproducibility both at empirical and interpretative slants. Possible phase configurations include regimes with multiple stable equilibria, sigmoidal growth, extinction, or stationarity. Here, we also outline that the associating discrete-time piecewise model composes the logistic map applied over a particular region of the phase configuration. Preliminary exploratory analysis suggests that the logistic map’s chaos onset could surpass once the orbit enters a contiguous phase region. (shrink)

This paper examines collective decision-making with an infinite-time horizon setting. First, we establish a result on the collection of decisive sets: if there are at least four alternatives and Arrow’s axioms are satisfied on the selfish domain, then the collection of decisive sets forms an ultrafilter. Second, we impose generalized versions of stationarity axiom for social preferences, which are substantially weaker than the standard version. We show that if any of our generalized versions are satisfied in addition to Arrow’s (...) axioms, then some generation is dictatorial. Moreover, we specify a very weak stationarity axiom that guarantees a possibility result. (shrink)

The signals in numerous complex systems of engineering can be regarded as nonlinear parameter trend with noise which is identically distributed random signals or deterministic stationary chaotic signals. The commonly used methods for parameter estimation of nonlinear trend in signals are mainly based on least squares. It can cause inaccurate estimation results when the noise is complex. This paper proposes a calibration method for this issue in the case of single parameter via nonstationarity measure from the perspective of the (...) class='Hi'>stationarity of residual sequence. Some numerical studies are conducted for validation. Results of numerical studies show that the proposed calibration method performs well for various models with different noise strengths and types and can significantly improve the accuracy of initial estimates obtained by least squares method. This is the first time that the nonstationarity measure is applied to the parameter calibration. All these results will be a guide for future studies of other parameter calibrations. (shrink)

We characterize the (κ, Λ, < μ)-distributive law in Boolean algebras in terms of cut and choose games $\scr{G}_{<\mu}^{\kappa}(\lambda)$ , when μ ≤ κ ≤ Λ and κ<κ = κ. This builds on previous work to yield game-theoretic characterizations of distributive laws for almost all triples of cardinals κ, Λ, μ with μ ≤ Λ, under GCH. In the case when μ ≤ κ ≤ Λ and κ<κ = κ, we show that it is necessary to consider whether the κ- (...) class='Hi'>stationarity of Pκ+Λ in the ground model is preserved by B. In this vein, we develop the theory of κ-club and κ-stationary subsets of Pκ+Λ. We also construct Boolean algebras in which Player I wins $\scr{G}_{\kappa}^{\kappa}(\kappa ^{+})$ but the (κ, ∞, κ)-d.1, holds, and, assuming GCH, construct Boolean algebras in which many games are undetermined. (shrink)

This note concerns the model theoretic properties of logics extending the first-order logic with monadic second-order variables equipped with the stationarity quantifier. The eight variations of the strong downward Löwenheim–Skolem Theorem down to <ℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<\aleph _2$$\end{document} for this logic with the interpretation of second-order variables as countable subsets of the structures are classified into four principles. The strongest of these four is shown to be equivalent to the conjunction of CH and (...) the Diagonal Reflection Principle for internally clubness of S. Cox. We show that a further strengthening of this SDLS and its variations follow from the Game Reflection Principle of B. König and its generalizations. (shrink)

An emerging perspective on human cognition and performance sees it as a kind of self-organizing phenomenon involving dynamic coordination across the body, brain and environment. Measuring this coordination faces a major challenge. Time series obtained from such cognitive, behavioral, and physiological coordination are often complicated in terms of non-stationarity and non-linearity, and in terms of continuous vs. categorical scales. Researchers have proposed several analytical tools and frameworks. One method designed to overcome these complexities is recurrence quantification analysis, developed in (...) the study of non-linear dynamics. It has been applied in various domains, including linguistic data or motion data. However, most previous studies have applied recurrence methods individually to categorical or continuous data. To understand how complex coordination works, an integration of these types of behavior is needed. We aimed to integrate these methods to investigate the relationship between language and motion directly. To do so, we added temporal information to categorical data, and applied joint recurrence analysis methods to visualize and quantify speech-motion coordination coupling during a rap performance. We illustrate how new dynamic methods may capture this coordination in a small case-study design on this expert rap performance. We describe a case study suggesting this kind of dynamic analysis holds promise, and end by discussing the theoretical implications of studying complex performances of this kind as a dynamic, coordinated phenomenon. (shrink)

A question of Foreman and Magidor asks if it is consistent for every sequence of stationary subsets of the ℵ n ’s for 1≤n<ω to be mutually stationary. We get a positive answer to this question in the context of the negation of the Axiom of Choice. We also indicate how a positive answer to a generalized version of this question in a choiceless context may be obtained.

Der „Entwurf eines Gesetzes zur strukturellen Weiterentwicklung der Pflegeversicherung“ vom 17. 10. 2007 sieht Regelungen zur Einbeziehung von stationären Pflegeeinrichtungen in die ambulante ärztliche GKV-Versorgung vor. Der vorliegende Beitrag analysiert und bewertet den Ansatz zur „heimärztlichen Versorgung“ unter rechtlichen Aspekten vor dem Hintergrund der Problematik der Psychopharmakaversorgung von Heimbewohnern und schon bestehender Möglichkeiten der Verzahnung der ambulanten ärztlichen und der stationären pflegerischen Versorgung. Das geplante Modell verfolgt das begrüßenswerte Ziel, die gelegentlich als unzureichend beschriebene ambulante ärztliche Betreuung von Pflegebedürftigen in (...) Pflegeheimen zu verbessern, Schnittstellenprobleme abzubauen und gleichzeitig der gesetzlichen Krankenversicherung unnötige Transport- und Krankenhauskosten zu ersparen. Es ist jedoch nur ein rudimentäres Heimarztmodell, da es gerade keine flächendeckende Versorgung der Heimbewohner mit Heimärzten erreichen will. Auch fehlen Anreize für eine Optimierung der ärztlichen und der pflegerischen Zusammenarbeit. Insofern können die Probleme, die sich im Rahmen der Psychopharmakaversorgung von stationär zu pflegenden Heimbewohnern abzeichnen, nur punktuell durch diese Reform verbessert werden. (shrink)

ZusammenfassungDer „Entwurf eines Gesetzes zur strukturellen Weiterentwicklung der Pflegeversicherung“ vom 17. 10. 2007 sieht Regelungen zur Einbeziehung von stationären Pflegeeinrichtungen in die ambulante ärztliche GKV-Versorgung vor. Der vorliegende Beitrag analysiert und bewertet den Ansatz zur „heimärztlichen Versorgung“ unter rechtlichen Aspekten vor dem Hintergrund der Problematik der Psychopharmakaversorgung von Heimbewohnern und schon bestehender Möglichkeiten der Verzahnung der ambulanten ärztlichen und der stationären pflegerischen Versorgung. Das geplante Modell verfolgt das begrüßenswerte Ziel, die gelegentlich als unzureichend beschriebene ambulante ärztliche Betreuung von Pflegebedürftigen in (...) Pflegeheimen zu verbessern, Schnittstellenprobleme abzubauen und gleichzeitig der gesetzlichen Krankenversicherung unnötige Transport- und Krankenhauskosten zu ersparen. Es ist jedoch nur ein rudimentäres Heimarztmodell, da es gerade keine flächendeckende Versorgung der Heimbewohner mit Heimärzten erreichen will. Auch fehlen Anreize für eine Optimierung der ärztlichen und der pflegerischen Zusammenarbeit. Insofern können die Probleme, die sich im Rahmen der Psychopharmakaversorgung von stationär zu pflegenden Heimbewohnern abzeichnen, nur punktuell durch diese Reform verbessert werden. (shrink)

For a regular cardinal κ with κ<κ = κ and κ ≤ λ , we construct generically a subset S of {x ∈ Pκλ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense but the stationarity of S can be destroyed by a κ+-c. c. forcing ℙ* which does not add any new element of Pκλ . Actually ℙ* can be chosen so that ℙ* is κ-strategically closed. However we show that (...) such ℙ* itself cannot be κ-strategically closed or even <κ-strategically closed if κ is inaccessible. (shrink)

In this article, we discuss the use of time series models in communication research. More specifically, we consider autoregressive and moving-average processes, which together constitute the autoregressive integrated moving average-framework. This approach provides a comprehensive framework to deal with the essential issue of stationarity and to model the dynamics of any time series by estimating the autocorrelation structure. Underlying the models are questions as to what extent news tends to reproduce itself and how news flows adjust after deviations from (...) the normal news stream. The data illustrating the models consist of visibility-scores of the immigration issue in Dutch national newspapers. The empirical analysis demonstrates that the impact of immigration figures on this visibility is not significant when the ARIMA-framework is applied, while an analysis using OLS suggests a positive influence. (shrink)

A formulation of probabilistic causality is given in terms of the theory of abstract dynamical systems. Causal factors are identified as invariants of motion of a system. Repetition of an experiment leads to the notion of stationarity, and causal factors yield a decomposition of the stationary probability law of the experiment into ergodic components. In these, statistical behaviour is uniform. Control of identified causal factors leads to a corresponding statistical law for the events, which is offered as a notion (...) of probabilistic causality. After a suggestion by Feller, randomization is identified as mixing, formulated in above terms. (shrink)