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Journal articles on the topic 'Forcing (Model theory) Topology'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

van den Berg, Benno, and Ieke Moerdijk. "The axiom of multiple choice and models for constructive set theory." Journal of Mathematical Logic 14, no. 01 (June 2014): 1450005. http://dx.doi.org/10.1142/s0219061314500056.

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We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory (hence acceptable from a constructive and generalized-predicative standpoint). In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as well as more general sheaf extensions. As a result, methods from our earlier work can be applied to show that this extension satisfies various derived rules, such as a derived compactness rule for Cantor space and a derived continuity rule for Baire space. Finally, we show that this extension is robust in the sense that it is also reflected by the model constructions from algebraic set theory just mentioned.

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2

Farah, Ilijas. "Completely Additive Liftings." Bulletin of Symbolic Logic 4, no. 1 (March 1998): 37–54. http://dx.doi.org/10.2307/421005.

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The purpose of this communication is to survey a theory of liftings, as developed in author's thesis ([8]). The first result in this area was Shelah's construction of a model of set theory in which every automorphism of P(ℕ)/ Fin, where Fin is the ideal of finite sets, is trivial, or inother words, it is induced by a function mapping integers into integers ([33]). (It is a classical result of W. Rudin [31] that under the Continuum Hypothesis there are automorphisms other than trivial ones.) Soon afterwards, Velickovic ([47]), was able to extract from Shelah's argument the fact that every automorphism of P(ℕ)/ Fin with a Baire-measurable lifting has to be trivial. This, for instance, implies that in Solovay's model ([36]) all automorphisms are trivial. Later on, an axiomatic approach was adopted and Shelah's conclusion was drawn first from the Proper Forcing Axiom (PFA) ([34]) and then from the milder Open Coloring Axiom (OCA) and Martin's Axiom (MA) ([48], see §5 for definitions). Both shifts from the quotient P(ℕ)/ Fin to quotients over more general ideals P(ℕ)/I and from automorphisms to arbitrary ho-momorphisms were made by Just in a series of papers ([14]-[17]), motivated by some problems in algebra ([7, pp. 38–39], [43, I.12.11], [45, Q48]) and topology ([46, p. 537]).

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3

Avigad, Jeremy. "Forcing in Proof Theory." Bulletin of Symbolic Logic 10, no. 3 (September 2004): 305–33. http://dx.doi.org/10.2178/bsl/1102022660.

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AbstractPaul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments.

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4

Kunen, Kenneth. "Forcing and Differentiable Functions." Order 29, no. 2 (April 1, 2011): 293–310. http://dx.doi.org/10.1007/s11083-011-9210-8.

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5

ANTOS, CAROLIN, and SY-DAVID FRIEDMAN. "HYPERCLASS FORCING IN MORSE-KELLEY CLASS THEORY." Journal of Symbolic Logic 82, no. 2 (June 2017): 549–75. http://dx.doi.org/10.1017/jsl.2016.74.

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AbstractIn this article we introduce and study hyperclass-forcing (where the conditions of the forcing notion are themselves classes) in the context of an extension of Morse-Kelley class theory, called MK**. We define this forcing by using a symmetry between MK** models and models of ZFC− plus there exists a strongly inaccessible cardinal (called SetMK**). We develop a coding between β-models ${\cal M}$ of MK** and transitive models M+ of SetMK** which will allow us to go from ${\cal M}$ to M+ and vice versa. So instead of forcing with a hyperclass in MK** we can force over the corresponding SetMK** model with a class of conditions. For class-forcing to work in the context of ZFC− we show that the SetMK** model M+ can be forced to look like LK*[X], where κ* is the height of M+, κ strongly inaccessible in M+ and $X \subseteq \kappa$. Over such a model we can apply definable class forcing and we arrive at an extension of M+ from which we can go back to the corresponding β-model of MK**, which will in turn be an extension of the original ${\cal M}$. Our main result combines hyperclass forcing with coding methods of [3] and [4] to show that every β-model of MK** can be extended to a minimal such model of MK** with the same ordinals. A simpler version of the proof also provides a new and analogous minimality result for models of second-order arithmetic.

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6

Dasgupta, Soham. "Sd - Topology over the theory of a Model." IARJSET 7, no. 12 (December 30, 2020): 46–48. http://dx.doi.org/10.17148/iarjset.2020.71209.

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7

Hamel, Clovis, and Franklin D. Tall. "Model theory for Cp-theorists." Topology and its Applications 281 (August 2020): 107197. http://dx.doi.org/10.1016/j.topol.2020.107197.

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8

Malliaris, M., and S. Shelah. "Cofinality spectrum theorems in model theory, set theory, and general topology." Journal of the American Mathematical Society 29, no. 1 (April 9, 2015): 237–97. http://dx.doi.org/10.1090/jams830.

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9

Baldwin, J. T., M. C. Laskowski, and S. Shelah. "Forcing isomorphism." Journal of Symbolic Logic 58, no. 4 (December 1993): 1291–301. http://dx.doi.org/10.2307/2275144.

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If two models of a first-order theory are isomorphic, then they remain isomorphic in any forcing extension of the universe of sets. In general however, such a forcing extension may create new isomorphisms. For example, any forcing that collapses cardinals may easily make formerly nonisomorphic models isomorphic. However, if we place restrictions on the partially-ordered set to ensure that the forcing extension preserves certain invariants, then the ability to force nonisomorphic models of some theory T to be isomorphic implies that the invariants are not sufficient to characterize the models of T.A countable first-order theory is said to be classifiable if it is superstable and does not have either the dimensional order property (DOP) or the omitting types order property (OTOP). If T is not classifiable, Shelah has shown in [5] that sentences in L∞,λ do not characterize models of T of power λ. By contrast, in [8] Shelah showed that if a theory T is classifiable, then each model of cardinality λ is described by a sentence of L∞,λ. In fact, this sentence can be chosen in the . ( is the result of enriching the language by adding for each μ < λ a quantifier saying the dimension of a dependence structure is greater than μ) Further work ([3], [2]) shows that ⊐+ can be replaced by ℵ1.

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10

Malliaris, M., and S. Shelah. "General topology meets model theory, on p and t." Proceedings of the National Academy of Sciences 110, no. 33 (July 8, 2013): 13300–13305. http://dx.doi.org/10.1073/pnas.1306114110.

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11

Ekstrand, Jason, Craig Erickson, H. Tracy Hall, Diana Hay, Leslie Hogben, Ryan Johnson, Nicole Kingsley, et al. "Positive semidefinite zero forcing." Linear Algebra and its Applications 439, no. 7 (October 2013): 1862–74. http://dx.doi.org/10.1016/j.laa.2013.05.020.

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12

FUCHS, GUNTER, and RALF SCHINDLER. "INNER MODEL THEORETIC GEOLOGY." Journal of Symbolic Logic 81, no. 3 (July 21, 2016): 972–96. http://dx.doi.org/10.1017/jsl.2015.64.

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AbstractOne of the basic concepts of set theoretic geology is the mantle of a model of set theory V: it is the intersection of all grounds of V, that is, of all inner models M of V such that V is a set-forcing extension of M. The main theme of the present paper is to identify situations in which the mantle turns out to be a fine structural extender model. The first main result is that this is the case when the universe is constructible from a set and there is an inner model with a Woodin cardinal. The second situation like that arises if L[E] is an extender model that is iterable in V but not internally iterable, as guided by P-constructions, L[E] has no strong cardinal, and the extender sequence E is ordinal definable in L[E] and its forcing extensions by collapsing a cutpoint to ω (in an appropriate sense). The third main result concerns the Solid Core of a model of set theory. This is the union of all sets that are constructible from a set of ordinals that cannot be added by set-forcing to an inner model. The main result here is that if there is an inner model with a Woodin cardinal, then the solid core is a fine-structural extender model.

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13

Liu, Zhengyu, Yishuai Jin, and Xinyao Rong. "A Theory for the Seasonal Predictability Barrier: Threshold, Timing, and Intensity." Journal of Climate 32, no. 2 (December 21, 2018): 423–43. http://dx.doi.org/10.1175/jcli-d-18-0383.1.

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Abstract A theory is developed in a stochastic climate model for understanding the general features of the seasonal predictability barrier (PB), which is characterized by a band of maximum decline in autocorrelation function phase-locked to a particular season. Our theory determines the forcing threshold, timing, and intensity of the seasonal PB as a function of the damping rate and seasonal forcing. A seasonal PB is found to be an intrinsic feature of a stochastic climate system forced by either seasonal growth rate or seasonal noise forcing. A PB is generated when the seasonal forcing, relative to the damping rate, exceeds a modest threshold. Once generated, all the PBs occur in the same calendar month, forming a seasonal PB. The PB season is determined by the decline of the seasonal forcing as well as the delayed response associated with damping. As such, for a realistic weak damping, the PB season is locked close to the minimum SST variance under the seasonal growth-rate forcing, but after the minimum SST variance under the seasonal noise forcing. The intensity of the PB is determined mainly by the amplitude of the seasonal forcing. The theory is able to explain the general features of the seasonal PB of the observed SST variability over the world. In the tropics, a seasonal PB is generated mainly by a strong seasonal growth rate, whereas in the extratropics a seasonal PB is generated mainly by a strong seasonal noise forcing. Our theory provides a general framework for the understanding of the seasonal PB of climate variability.

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14

Neeman, Itay, and Jindřich Zapletal. "Proper forcing and L(ℝ)." Journal of Symbolic Logic 66, no. 2 (June 2001): 801–10. http://dx.doi.org/10.2307/2695045.

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AbstractWe present two ways in which the model L(ℝ) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing: we show further that a set of ordinals in V cannot be added to L(ℝ) by small forcing. The large cardinal needed corresponds to the consistency strength of ADL(ℝ): roughly ω Woodin cardinals.

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15

Goldberg, Felix, and Abraham Berman. "Zero forcing for sign patterns." Linear Algebra and its Applications 447 (April 2014): 56–67. http://dx.doi.org/10.1016/j.laa.2013.11.049.

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16

Onose, Hiroshi. "Nonoscillation of nonlinear first order differential equations with forcing term." Hiroshima Mathematical Journal 16, no. 3 (1986): 617–24. http://dx.doi.org/10.32917/hmj/1206130313.

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17

Crook, N. Andrew, and Donna F. Tucker. "Flow over Heated Terrain. Part I: Linear Theory and Idealized Numerical Simulations." Monthly Weather Review 133, no. 9 (September 1, 2005): 2552–64. http://dx.doi.org/10.1175/mwr2964.1.

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Abstract The flow past heated topography is examined with both linear and nonlinear models. It is first shown that the forcing of an obstacle with horizontally homogenous surface heating can be approximated by the forcing of an obstacle with surface heating isolated over the obstacle. The small-amplitude flow past an obstacle with isolated heating is then examined with a linear model. Under the linear approximation, the flow response to heated topography is simply the addition of the separate responses to thermal and orographic forcing. These separate responses are first considered individually and then the combined response is examined. Nondimensional parameters are developed that measure the relative importance of thermal and orographic forcing. Nonaxisymmetric forcing is then considered by examining the flow along and across a heated elliptically shaped obstacle. It is shown that the low-level lifting is maximized when the flow is along the major axis of the obstacle. The linear solutions are then tested in a nonlinear anelastic model. The response to a heat source and orography are first examined separately. Good agreement is found between nonlinear and linear models for the individual responses to thermal and orographic forcing. The case of uniformly heated flow past an obstacle is then examined. In these simulations, the thermal response is isolated by subtracting the orographic-only response from the full thermal–orographic response. The numerical simulations are able to capture the main features of the thermal response. Finally, numerical simulations of the flow along and across an elliptically shaped heated obstacle are examined, where it is verified that the lifting is maximized when the flow is along the major axis of the obstacle. These results are extended in Part II of this study to examine the moist convective response to flow over both idealized terrain and the complex terrain of the Rocky Mountains of the United States.

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18

Hausmann, Markus. "Symmetric spectra model global homotopy theory of finite groups." Algebraic & Geometric Topology 19, no. 3 (May 21, 2019): 1413–52. http://dx.doi.org/10.2140/agt.2019.19.1413.

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19

CALÇADA, DULCE, SUSANA VINGA, ANA T. FREITAS, and ARLINDO L. OLIVEIRA. "QUANTITATIVE MODELING OF THE SACCHAROMYCES CEREVISIAE FLR1 REGULATORY NETWORK USING AN S-SYSTEM FORMALISM." Journal of Bioinformatics and Computational Biology 09, no. 05 (October 2011): 613–30. http://dx.doi.org/10.1142/s0219720011005690.

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In this study we address the problem of finding a quantitative mathematical model for the genetic network regulating the stress response of the yeast Saccharomyces cerevisiae to the agricultural fungicide mancozeb. An S-system formalism was used to model the interactions of a five-gene network encoding four transcription factors (Yap1, Yrr1, Rpn4 and Pdr3) regulating the transcriptional activation of the FLR1 gene. Parameter estimation was accomplished by decoupling the resulting system of nonlinear ordinary differential equations into a larger nonlinear algebraic system, and using the Levenberg–Marquardt algorithm to fit the models predictions to experimental data. The introduction of constraints in the model, related to the putative topology of the network, was explored. The results show that forcing the network connectivity to adhere to this topology did not lead to better results than the ones obtained using an unrestricted network topology. Overall, the modeling approach obtained partial success when trained on the nonmutant datasets, although further work is required if one wishes to obtain more accurate prediction of the time courses.

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20

Alexandru, Andrei, and Gabriel Ciobanu. "A Topological Approach in the Extended Fraenkel-Mostowski Model of Set Theory." Annals of the Alexandru Ioan Cuza University - Mathematics 60, no. 2 (November 24, 2014): 261–77. http://dx.doi.org/10.2478/aicu-2013-0029.

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Abstract Lattices of subgroups are presented as algebraic domains. Given an arbitrary group, we define the Scott topology over the subgroups lattice of that group. A basis for this topology is expressed in terms of finitely generated subgroups. Several properties of the continuous functions with respect the Scott topology are obtained; they provide new order properties of groups. Finally there are expressed several properties of the group of permutations of atoms in a permutative model of set theory. We provide new properties of the extended interchange function by presenting some topological properties of its domain. Several order and topological properties of the sets in the Fraenkel-Mostowski model remains also valid in the Extended Fraenkel-Mostowski model, even one axiom in the axiomatic description of the Extended Fraenkel-Mostowski model is weaker than its homologue in the axiomatic description of the Fraenkel-Mostowski model.

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21

Jaroš, Jaroslav. "Oscillation criteria for functional-differential inequalities with strongly bounded forcing term." Hiroshima Mathematical Journal 16, no. 3 (1986): 639–49. http://dx.doi.org/10.32917/hmj/1206130316.

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22

CHEN, YIXIN, DONG HUA, and FANG LIU. "GENERALIZED LATENT CLASS ANALYSIS BASED ON MODEL DOMINANCE THEORY." International Journal on Artificial Intelligence Tools 18, no. 05 (October 2009): 739–55. http://dx.doi.org/10.1142/s021821300900038x.

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Latent class analysis is a popular statistical learning approach. A major challenge for learning generalized latent class is the complexity in searching the huge space of models and parameters. The computational cost is higher when the model topology is more flexible. In this paper, we propose the notion of dominance which can lead to strong pruning of the search space and significant reduction of learning complexity, and apply this notion to the Generalized Latent Class (GLC) models, a class of Bayesian networks for clustering categorical data. GLC models can address the local dependence problem in latent class analysis by assuming a very general graph structure. However, The flexible topology of GLC leads to large increase of the learning complexity. We first propose the concept of dominance and related theoretical results which is general for all Bayesian networks. Based on dominance, we propose an efficient learning algorithm for GLC. A core technique to prune dominated models is regularization, which can eliminate dominated models, leading to significant pruning of the search space. Significant improvements on the model.

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23

Moore, Andrew M., Javier Zavala-Garay, Youmin Tang, Richard Kleeman, Anthony T. Weaver, Jérôme Vialard, Kamran Sahami, David L. T. Anderson, and Michael Fisher. "Optimal Forcing Patterns for Coupled Models of ENSO." Journal of Climate 19, no. 18 (September 15, 2006): 4683–99. http://dx.doi.org/10.1175/jcli3870.1.

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Abstract The optimal forcing patterns for El Niño–Southern Oscillation (ENSO) are examined for a hierarchy of hybrid coupled models using generalized stability theory. Specifically two cases are considered: one where the forcing is stochastic in time, and one where the forcing is time independent. The optimal forcing patterns in these two cases are described by the stochastic optimals and forcing singular vectors, respectively. The spectrum of stochastic optimals for each model was found to be dominated by a single pattern. In addition, the dominant stochastic optimal structure is remarkably similar to the forcing singular vector, and to the dominant singular vectors computed in a previous related study using a subset of the same models. This suggests that irrespective of whether the forcing is in the form of an impulse, is time invariant, or is stochastic in nature, the optimal excitation for the eigenmode that describes ENSO in each model is the same. The optimal forcing pattern, however, does vary from model to model, and depends on air–sea interaction processes. Estimates of the stochastic component of forcing were obtained from atmospheric analyses and the projection of the dominant optimal forcing pattern from each model onto this component of the forcing was computed. It was found that each of the optimal forcing patterns identified may be present in nature and all are equally likely. The existence of a dominant optimal forcing pattern is explored in terms of the effective dimension of the coupled system using the method of balanced truncation, and was found to be O(1) for the models used here. The implications of this important result for ENSO prediction and predictability are discussed.

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24

Barioli, Francesco, Wayne Barrett, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Bryan Shader, P. van den Driessche, and Hein van der Holst. "Zero forcing parameters and minimum rank problems." Linear Algebra and its Applications 433, no. 2 (August 2010): 401–11. http://dx.doi.org/10.1016/j.laa.2010.03.008.

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25

Ansill, Thomas, Bonnie Jacob, Jaime Penzellna, and Daniel Saavedra. "Failed skew zero forcing on a graph." Linear Algebra and its Applications 509 (November 2016): 40–63. http://dx.doi.org/10.1016/j.laa.2016.07.019.

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26

Jaroš, Jaroslav. "Maintenance of oscillations under the effect of a strongly bounded forcing term." Hiroshima Mathematical Journal 17, no. 2 (1987): 405–13. http://dx.doi.org/10.32917/hmj/1206130077.

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27

Aizawa, Tamio. "Integrity Verification of Topology-based Shape Representation Model Data (A Basic Theory)." Transactions of the Japan Society of Mechanical Engineers Series C 61, no. 592 (1995): 4825–33. http://dx.doi.org/10.1299/kikaic.61.4825.

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28

Posmentier, E. S. "Response of an ocean-atmosphere climate model to Milankovic forcing." Nonlinear Processes in Geophysics 1, no. 1 (March 31, 1994): 26–30. http://dx.doi.org/10.5194/npg-1-26-1994.

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Abstract. There is considerable evidence in support of Milankovic's theory that variations in high-latitude summer insolation caused by Earth orbital variations are the cause of the Pleistocene ice cycles. The enigmatic discrepancy between the spectra of Milankovic forcing and of Pleistocene climate variations is believed to be resolved by the slow, nonlinear response of ice sheets to changes in solar seasonality. An experiment with a preliminary version of a 14-region atmosphere/snow/upper ocean climate model demonstrates that the response of the ocean-atmosphere system alone to Milankovic forcing is capable of driving ice cycles with the observed spectrum. This occurs because of the highly nonlinear response of both the thermal seasons and the annual mean temperature to solar seasons, which is caused in turn by the highly nonlinear feedback between temperature and snow and sea ice.

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29

Gálfi, Vera Melinda, Tamás Bódai, and Valerio Lucarini. "Convergence of Extreme Value Statistics in a Two-Layer Quasi-Geostrophic Atmospheric Model." Complexity 2017 (2017): 1–20. http://dx.doi.org/10.1155/2017/5340858.

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We search for the signature of universal properties of extreme events, theoretically predicted for Axiom A flows, in a chaotic and high-dimensional dynamical system. We study the convergence of GEV (Generalized Extreme Value) and GP (Generalized Pareto) shape parameter estimates to the theoretical value, which is expressed in terms of the partial information dimensions of the attractor. We consider a two-layer quasi-geostrophic atmospheric model of the mid-latitudes, adopt two levels of forcing, and analyse the extremes of different types of physical observables (local energy, zonally averaged energy, and globally averaged energy). We find good agreement in the shape parameter estimates with the theory only in the case of more intense forcing, corresponding to a strong chaotic behaviour, for some observables (the local energy at every latitude). Due to the limited (though very large) data size and to the presence of serial correlations, it is difficult to obtain robust statistics of extremes in the case of the other observables. In the case of weak forcing, which leads to weaker chaotic conditions with regime behaviour, we find, unsurprisingly, worse agreement with the theory developed for Axiom A flows.

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Cullen, Mike. "The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM." Fluids 3, no. 4 (October 10, 2018): 72. http://dx.doi.org/10.3390/fluids3040072.

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A diagnostic method is presented for analysing the large-scale behaviour of the Met Office Unified Model, which is a comprehensive atmospheric model used for weather and climate prediction. Outside the boundary layer, on scales larger than the radius of deformation, semi-geostrophic theory will give an accurate approximation to the model evolution. In particular, the ageostrophic circulation required to maintain geostrophic and hydrostatic balance against prescribed forcing and a rate of change of the geostrophic pressure can be calculated. In the tropics, the balance condition degenerates to the weak temperature gradient approximation. Within the boundary layer, the semi-geotriptic approximation has to be used because friction and rotation are equally important. Assuming the calculated pressure tendency and ageotriptic circulation match the observed model behaviour, the influence of the large-scale state and the nature of the forcing on the model response can be deduced in a straightforward way. The capabilities of the diagnostic are illustrated by comparing predictions of the ageotriptic circulation from the theory and the model. It is then used to show that the effects of latent heat release can be included by modifying the static stability, and to show the effect of an idealised tropical heat source on the subtropical jet. Finally, the response of the ageotriptic flow to boundary layer heating in the tropics is demonstrated. These illustrations show that the model behaviour on large scales conforms with theoretical expectations, so that the results of the diagnostic can be used to aid the development of further improvements to the model, in particular investigating systematic errors and understanding the large-scale atmospheric response to forcing.

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Hamkins, Joel David, David Linetsky, and Jonas Reitz. "Pointwise definable models of set theory." Journal of Symbolic Logic 78, no. 1 (March 2013): 139–56. http://dx.doi.org/10.2178/jsl.7801090.

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AbstractA pointwise definable model is one in which every object is definable without parameters. In a model of set theory, this property strengthens V = HOD, but is not first-order expressible. Nevertheless, if ZFC is consistent, then there are continuum many pointwise definable models of ZFC. If there is a transitive model of ZFC, then there are continuum many pointwise definable transitive models of ZFC. What is more, every countable model of ZFC has a class forcing extension that is pointwise definable. Indeed, for the main contribution of this article, every countable model of Gödel-Bernays set theory has a pointwise definable extension, in which every set and class is first-order definable without parameters.

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32

Corcoran, Padraig. "Topology Based Object Tracking." Mathematical and Computational Applications 24, no. 3 (September 18, 2019): 84. http://dx.doi.org/10.3390/mca24030084.

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A model for tracking objects whose topological properties change over time is proposed. Such changes include the splitting of an object into multiple objects or the merging of multiple objects into a single object. The proposed model employs a novel formulation of the tracking problem in terms of homology theory whereby 0-dimensional homology classes, which correspond to connected components, are tracked. A generalisation of this model for tracking spatially close objects lying in an ambient metric space is also proposed. This generalisation is particularly suitable for tracking spatial-temporal phenomena such as rain clouds. The utility of the proposed model is demonstrated with respect to tracking communities in a social network and tracking rain clouds in radar imagery.

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33

COX, SEAN, and MARTIN ZEMAN. "IDEAL PROJECTIONS AND FORCING PROJECTIONS." Journal of Symbolic Logic 79, no. 4 (December 2014): 1247–85. http://dx.doi.org/10.1017/jsl.2013.24.

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AbstractIt is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman–Magidor–Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove:(1)If${\cal I}$is a normal ideal on$\omega _2 $which satisfiesstationary antichain catching, then there is an inner model with a Woodin cardinal;(2)For any$n \in \omega $, it is consistent relative to large cardinals that there is a normal ideal${\cal I}$on$\omega _n $which satisfiesprojective antichain catching, yet${\cal I}$is not saturated (or even strong). This provides a negative answer to Open Question number 13 from Foreman’s chapter in the Handbook of Set Theory ([7]).

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34

Stanley, M. C. "Outer models and genericity." Journal of Symbolic Logic 68, no. 2 (June 2003): 389–418. http://dx.doi.org/10.2178/jsl/1052669057.

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Why is forcing the only known method for constructing outer models of set theory?If V is a standard transitive model of ZFC, then a standard transitive model W of ZFC is an outer model of V if V ⊆ W and V ∩ OR = W ∩ OR.Is every outer model of a given model a generic extension? At one point Solovay conjectured that if 0# exists, then every real that does not construct 0# lies in L[G], for some G that is generic for some forcing ℙ ∈ L. Famously, this was refuted by Jensen's coding theorem. He produced a real that is generic for an L-definable class forcing property, but does not lie in any set forcing extension of L.Beller, Jensen, and Welch in Coding the universe [BJW] revived Solovay's conjecture by asking the following question: Let a ⊆ ω be such that L[a] ⊨ “0# does not exist”. Is there ab∈ L[a] such that a ∉ L[b] and a is set generic over L[b].

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Burgman, Robert J., Paul S. Schopf, and Ben P. Kirtman. "Decadal Modulation of ENSO in a Hybrid Coupled Model." Journal of Climate 21, no. 21 (November 1, 2008): 5482–500. http://dx.doi.org/10.1175/2008jcli1933.1.

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Abstract Decadal variations in the amplitude of El Niño and the Southern Oscillation have been the subject of great interest in the literature for the past decade. One theory suggests that ENSO is best described as a stable system driven by linear dynamics and that stochastic atmospheric forcing is responsible for the development and modulation of ENSO on interannual as well as decadal time scales. Another theory suggests that ENSO is driven by strong nonlinear coupled feedbacks between the ocean and atmosphere and low frequency changes in ENSO amplitude are driven by decadal changes in the tropical Pacific mean state. Unfortunately, the observed record is too short to collect reliable statistics for such low frequency behavior. A hybrid coupled model composed of a simple statistical atmosphere coupled to the Poseidon isopycnal ocean model has been developed for the study of ENSO decadal variability. The model simulates realistic ENSO variability on interannual and decadal time scales with negligible climate drift over 1000 years. Through analysis and experimentation the authors show that low frequency changes in the atmospheric “weather noise” drive changes in the tropical Pacific mean state leading to changes in the amplitude of ENSO on decadal time scales. Additional model simulations suggest that, while predictability is limited by the presence of atmospheric noise, there are extended periods when the coupled instability, strengthened by changes in the mean state, is insensitive to noise on interannual time scales. The relationship between decadal modulation of ENSO and mean state changes resides somewhere between the linear damped stochastically forced theory and the strongly unstable theory. Unlike the strongly unstable system, changes in ENSO amplitude on longer time scales are determined by the stochastic forcing. The stochastic forcing is not necessary in this model to sustain ENSO; however, its presence is crucial for low frequency changes in the mean state of the tropical Pacific. The strong relationship between the mean state and ENSO amplitude modulation in the model is in opposition to the linear damped stochastically forced theory. The fact that changes in the tropical Pacific mean state lead directly to changes in ENSO amplitude and predictability has positive implications for predictability.

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Schindler, Ralf-Dieter. "Proper Forcing and Remarkable Cardinals." Bulletin of Symbolic Logic 6, no. 2 (June 2000): 176–84. http://dx.doi.org/10.2307/421205.

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The present paper investigates the power of proper forcings to change the shape of the universe, in a certain well-defined respect. It turns out that the ranking among large cardinals can be used as a measure for that power. However, in order to establish the final result I had to isolate a new large cardinal concept, which I dubbed “remarkability.” Let us approach the exact formulation of the problem—and of its solution—at a slow pace.Breathtaking developments in the mid 1980s found one of its culminations in the theorem, due to Martin, Steel, and Woodin, that the existence of infinitely many Woodin cardinals with a measurable cardinal above them all implies that AD, the axiom of determinacy, holds in the least inner model containing all the reals, L(ℝ) (cf. [6[, p. 91). One of the nice things about AD is that the theory ZF + AD + V = L(ℝ) appears as a choiceless “completion” of ZF in that any interesting question (in particular, about sets of reals) seems to find an at least attractive answer in that theory (cf., for example, [5] Chap. 6). (Compare with ZF + V = L!) Beyond that, AD is very canonical as may be illustrated as follows.Let us say that L(ℝ) is absolute for set-sized forcings if for all posets P ∈ V, for all formulae ϕ, and for all ∈ ℝ do we have thatwhere is a name for the set of reals in the extension.

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Van Gorder, Robert A. "First-order soliton perturbation theory for a generalized KdV model with stochastic forcing and damping." Journal of Physics A: Mathematical and Theoretical 44, no. 1 (November 25, 2010): 015201. http://dx.doi.org/10.1088/1751-8113/44/1/015201.

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Song, In-Sun, and Hye-Yeong Chun. "Momentum Flux Spectrum of Convectively Forced Internal Gravity Waves and Its Application to Gravity Wave Drag Parameterization. Part I: Theory." Journal of the Atmospheric Sciences 62, no. 1 (January 1, 2005): 107–24. http://dx.doi.org/10.1175/jas-3363.1.

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Abstract The phase-speed spectrum of momentum flux by convectively forced internal gravity waves is analytically formulated in two- and three-dimensional frameworks. For this, a three-layer atmosphere that has a constant vertical wind shear in the lowest layer, a uniform wind above, and piecewise constant buoyancy frequency in a forcing region and above is considered. The wave momentum flux at cloud top is determined by the spectral combination of a wave-filtering and resonance factor and diabatic forcing. The wave-filtering and resonance factor that is determined by the basic-state wind and stability and the vertical configuration of forcing restricts the effectiveness of the forcing, and thus only a part of the forcing spectrum can be used for generating gravity waves that propagate above cumulus clouds. The spectral distribution of the wave momentum flux is largely determined by the wave-filtering and resonance factor, but the magnitude of the momentum flux varies significantly according to spatial and time scales and moving speed of the forcing. The wave momentum flux formulation in the two-dimensional framework is extended to the three-dimensional framework. The three-dimensional momentum flux formulation is similar to the two-dimensional one except that the wave propagation in various horizontal directions and the three-dimensionality of forcing are allowed. The wave momentum flux spectrum formulated in this study is validated using mesoscale numerical model results and can reproduce the overall spectral structure and magnitude of the wave momentum flux spectra induced by numerically simulated mesoscale convective systems reasonably well.

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Chio, Cecilia Di, and Paolo Di Chio. "Evolution of language with spatial topology." Interaction Studies 10, no. 1 (March 24, 2009): 31–50. http://dx.doi.org/10.1075/is.10.1.03dic.

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In this paper, we propose two agent-based simulation models for the evolution of language in the framework of evolutionary language games. The theory of evolutionary language games arose from the union of evolutionary game theory, introduced by the English biologist John Maynard Smith, and language games, developed by the Austrian philosopher Ludwig Wittgenstein. The first model proposed is based on Martin Nowak’s work and is designed to reproduce and verify (or refute) the results Nowak obtained in his simplest mathematical model. For the second model, we extend the previous one with the introduction of a world where the languages live and evolve, and which influences interactions among individuals. The main goal of this research is to present a model which shows how the presence of a topological structure influences the communication among individuals and contributes to the emergence of clusters of different languages.

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Tabor, C. R., C. J. Poulsen, and D. Pollard. "Mending Milankovitch theory: obliquity amplification by surface feedbacks." Climate of the Past Discussions 9, no. 4 (July 5, 2013): 3769–87. http://dx.doi.org/10.5194/cpd-9-3769-2013.

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Abstract. Milankovitch theory states that orbitally induced changes in high-latitude summer insolation dictate the waxing and waning of ice-sheets. Accordingly, precession should dominate the ice-volume response because it most strongly modulates summer insolation intensity. However, Early Pleistocene (2.6–0.8 Ma) ice-volume proxy records vary almost exclusively at the frequency of the obliquity cycle. To explore this paradox, we use an Earth system model coupled with a dynamic ice-sheet to separate the climate responses to idealized transient orbits of obliquity and precession that maximize insolation changes. Our results show that positive surface albedo feedbacks between high-latitude annual-mean insolation, ocean heat flux and sea-ice coverage, and boreal forest/tundra exchange enhance the ice-volume response to obliquity forcing relative to precession forcing. These surface feedbacks, in combination with modulation of the precession cycle power by eccentricity, may explain the dominantly 41 kyr cycles in global ice volume of the Early Pleistocene.

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Tabor, C. R., C. J. Poulsen, and D. Pollard. "Mending Milankovitch's theory: obliquity amplification by surface feedbacks." Climate of the Past 10, no. 1 (January 10, 2014): 41–50. http://dx.doi.org/10.5194/cp-10-41-2014.

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Abstract. Milankovitch's theory states that orbitally induced changes in high-latitude summer insolation dictate the waxing and waning of ice sheets. Accordingly, precession should dominate the ice-volume response because it most strongly modulates summer insolation. However, early Pleistocene (2.588–0.781 Ma) ice-volume proxy records vary almost exclusively at the frequency of the obliquity cycle. To explore this paradox, we use an Earth system model coupled with a dynamic ice sheet to separate the climate responses to idealized transient orbits of obliquity and precession that maximize insolation changes. Our results show that positive surface albedo feedbacks between high-latitude annual-mean insolation, ocean heat flux and sea-ice coverage, and boreal forest/tundra exchange enhance the ice-volume response to obliquity forcing relative to precession forcing. These surface feedbacks, in combination with modulation of the precession cycle power by eccentricity, help explain the dominantly 41 kyr cycles in global ice volume of the early Pleistocene.

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Jevtic, Vladimir. "Multiverse and topology of time." Theoria, Beograd 56, no. 1 (2013): 47–57. http://dx.doi.org/10.2298/theo1301045j.

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Modern cosmological theories like theory of eternal chaotic inflation or cosmological model of brane universe, which represent implication of modern string theory, imply existence of ensemble of actual universes which create so-called multivers. Implication of this theories are of the great importance for philosophy of time. This paper concern topology of time in context of existence of the multiverse. We will show that topology of time in such multiverse, whose particular universes would be generated due to eternal chaotic inflation, should be non-standard and that in the case of existence of multiverse only model which include topology of brenching time should be acceptable like real description of multiverse. Moreover, we will show that, the existence of hypothetical entities like Kerr`s rotating black holes, also represent necessary and sufficient condition of branching spacetime in such multiverse.

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Ren, Yue Qing, and Zhi Qiang Zhang. "A Weighted Network Topology Model of WSN Based on Random Geometric Graph Method." Advanced Materials Research 962-965 (June 2014): 2898–902. http://dx.doi.org/10.4028/www.scientific.net/amr.962-965.2898.

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Focus on the weakness of modeling WSN topology by the means of random graph theory, a new weighted topology model of WSN based on random geometric theory is proposed in this paper. For the proposed new network model, the weighting scheme of network edge take into account the property of distance decreasing effect for communication signal. It also defines the differential weight which can embody the energy consumption for network communication. Based on simulations and calculations of the measures for the network topology as well as comparison with other forms of network, the results indicate that the proposed network topology model can not only describe the interrelated connected relationship between different nodes but also verify the degree of node is subject to Poisson distribution. It also has prominent clustering effects. These properties are consist with real world networks.

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Brešar, Boštjan, Tim Kos, and Pablo Daniel Torres. "Grundy domination and zero forcing in Kneser graphs." Ars Mathematica Contemporanea 17, no. 2 (November 6, 2019): 419–30. http://dx.doi.org/10.26493/1855-3974.1881.384.

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Privé, Nikki C., and R. Alan Plumb. "Monsoon Dynamics with Interactive Forcing. Part I: Axisymmetric Studies." Journal of the Atmospheric Sciences 64, no. 5 (May 1, 2007): 1417–30. http://dx.doi.org/10.1175/jas3916.1.

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Abstract The applicability of axisymmetric theory of angular momentum conserving circulations to the large-scale steady monsoon is studied in a general circulation model with idealized representations of continental geometry and simple physics. Results from an aquaplanet setup with localized subtropical forcing are compared with a continental case. It is found that the meridional circulation that develops is close to angular momentum conserving for cross-equatorial circulation cells, both in the aquaplanet and in the continental cases. The equator proves to be a substantial barrier to boundary layer meridional flow; flow into the summer hemisphere from the winter hemisphere tends to occur in the free troposphere rather than in the boundary layer. A theory is proposed to explain the location of the monsoon; assuming quasiequilibrium, the poleward boundary of the monsoon circulation is collocated with the maximum in subcloud moist static energy, with the monsoon rains occurring near and slightly equatorward of this maximum. The model results support this theory of monsoon location, and it is found that the subcloud moist static energy distribution is determined by a balance between surface forcing and advection by the large-scale flow.

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Lin, Jephian C. H. "Zero forcing number, Grundy domination number, and their variants." Linear Algebra and its Applications 563 (February 2019): 240–54. http://dx.doi.org/10.1016/j.laa.2018.11.003.

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Haigh, Michael C., and Pavel S. Berloff. "Potential vorticity redistribution by localised transient forcing in the shallow-water model." Journal of Fluid Mechanics 852 (August 3, 2018): 199–225. http://dx.doi.org/10.1017/jfm.2018.547.

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This study is motivated by the need to develop stochastic parameterisations for representing the effects of mesoscale oceanic eddies in non-eddy-resolving and eddy-permitting ocean circulation models. A necessary logical step on the way to such parameterisations is the understanding of flow responses to spatially stationary and localised, time-dependent ‘plunger’ forcings intended to represent transient eddy flux divergences. Specifically, this study develops an understanding of the plunger-induced convergence of potential vorticity (PV) fluxes using the linearised single-layer shallow-water model. Time-periodic solutions are obtained and the ‘footprint’, defined as the time-mean, quasi-linear PV flux convergence, quantifies the cumulative PV redistribution induced by the plunger. Using the footprint, the equivalent eddy flux (EEF) is defined such that it succinctly quantifies the extent of the PV redistribution, and its dependencies on the forcing latitude and the background flow are examined in detail. For a uniform background flow the EEF is positive for all forcing latitudes, corresponding to net-poleward PV flux convergence, as expected by current theory of $\unicode[STIX]{x1D6FD}$-plane Rossby waves. The EEF also has a robust dependence on the direction and magnitude of a uniform background flow, which is a useful quality for the EEF to provide a basis for a parameterisation of eddy PV fluxes. We also examine the PV redistribution due to forcing on top of a Gaussian jet background flow and find that forcing proximity to the jet core is the primary factor in determining whether the jet is sharpened or broadened.

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Rogers, Christopher. "An explicit model for the homotopy theory of finite-type Lie n–algebras." Algebraic & Geometric Topology 20, no. 3 (May 27, 2020): 1371–429. http://dx.doi.org/10.2140/agt.2020.20.1371.

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MARTIN, Jérôme. "CHANGE OF SIGNATURE AND TOPOLOGY IN A FIVE-DIMENSIONAL COSMOLOGICAL MODEL." International Journal of Modern Physics D 03, no. 01 (March 1994): 231–35. http://dx.doi.org/10.1142/s0218271894000356.

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An, Bao Kun, and Yan Feng. "Complex Network Theory in the Application of Optimization Topology Network." Applied Mechanics and Materials 651-653 (September 2014): 1811–15. http://dx.doi.org/10.4028/www.scientific.net/amm.651-653.1811.

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Complex network theory is a new theory, which is rising with the rapid development of the computer. At present, the network structure of computers more complex network models already existed, has been unable to meet its topological properties. So, emerge as the times require complex network theory, provides a new development ideas and platform at the same time, complex network theory to the study of computer network topology. This paper firstly introduces the complex network theory, and then about the application of complex network theory in computer topology behavior, research on computer network topology and the experiment and model specific about complex network theory. More reduction.

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