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CHSH and local hidden causality  [PDF]
J. F. Geurdes
Physics , 2010,
Abstract: Mathematics equivalent to Bell's derivation of the inequalities, also allows a local hidden variables explanation for the correlation between distant measurements.
On Lorentzian causality with continuous metrics  [PDF]
Piotr T. Chru?ciel,James D. E. Grant
Mathematics , 2011, DOI: 10.1088/0264-9381/29/14/145001
Abstract: We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when metrics which are merely continuous are considered. We show that existence of time functions remains true on domains of dependence with continuous metrics, and that $C^{0,1}$ differentiability of the metric suffices for many key results of the smooth causality theory.
Ambiguous volatility and asset pricing in continuous time  [PDF]
Larry G. Epstein,Shaolin Ji
Quantitative Finance , 2013,
Abstract: This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging arguments. Ambiguous volatility implies market incompleteness that rules out perfect hedging. Consequently, hedging arguments determine prices only up to intervals. However, sharper predictions can be obtained by assuming preference maximization and equilibrium. Thus we apply the model of utility to a representative agent endowment economy to study equilibrium asset returns. A version of the C-CAPM is derived and the effects of ambiguous volatility are described.
Ambiguous Volatility, Possibility and Utility in Continuous Time  [PDF]
Larry Epstein,Shaolin Ji
Quantitative Finance , 2011,
Abstract: This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both the drift and volatility of the driving process. At a technical level, the analysis requires a significant departure from existing continuous time modeling because it cannot be done within a probability space framework. This is because ambiguity about volatility leads invariably to a set of nonequivalent priors, that is, to priors that disagree about which scenarios are possible.
Locality and Causality in Hidden Variables Models of Quantum Theory  [PDF]
Stefan Teufel,Karin Berndl,Detlef Dürr,Sheldon Goldstein,Nino Zanghì
Physics , 1996, DOI: 10.1103/PhysRevA.56.1217
Abstract: Motivated by Popescu's example of hidden nonlocality, we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden variables model. We exhibit quantum states which either (i) are nontrivial counterexamples to this conjecture or (ii) possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we propose a nonlocality complexity classification scheme suggested by the latter possibility. Furthermore, we show that Werner's (and similar) hidden variables models can be extended to an important class of generalized observables. Finally a result of Fine on the equivalence of stochastic and deterministic hidden variables is generalized to causal models.
Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains  [PDF]
Michael Krumin,Shy Shoham
Computational Intelligence and Neuroscience , 2010, DOI: 10.1155/2010/752428
Abstract: Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ‘‘hidden’’ Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method. 1. Introduction The analysis of multivariate neurophysiological signals at the cellular (spike trains) and population scales (EEG/MEG, LFP, and ECOG) has developed almost independently, largely due to the mathematical differences between continuous and point-process signals. The analysis of multiple neural spike train data [1] has gained tremendous relevance recently with the advent and widespread application of arrays of microelectrodes in both basic and applied Neurosciences. Furthermore, emerging optical methods for network activity imaging [2] and control [3] are likely to further compound this growth. Currently, the analysis of multichannel spike trains is still largely limited to single-channel analyses, to bivariate cross-correlation and metric-space analyses [4], and to spike train filtering (“decoding”). In contrast, much of EEG/MEG time series analysis has revolved around linear and nonlinear models and analyses that are essentially multivariate, most prominently the multivariate autoregressive (MVAR) model. The MVAR framework is associated with a powerful set of time- and frequency-domain statistical tools for inferring directional and causal information flow based on Granger’s framework [5], including linear and nonlinear Granger causality, directed transfer function, directed coherence, and partial directed coherence (see [6–8] for reviews). Scattered attempts at applying this general framework to neural spike trains have relied on smoothing the spike trains to obtain a continuous process that can be fit with an MVAR model [9–12]. This approach has the clear
Strong causality from weak via continuous monitoring  [PDF]
John Jeffers
Physics , 2009, DOI: 10.1016/j.physleta.2009.03.055
Abstract: Repeated unbiased measurements cause a continual application of the weak causality principle, leading to an apparent arrow of time for continuously-monitored quantum systems.
Ambiguous Exhibitions, Ambiguous Institutions
Connell Vaughan
Skepsi , 2009,
Abstract: The institutional theory of art seeks to answer the question “what is art?” with the following ambiguous formula: something is art if conferred the status art by an art world. This position eliminates the issue of the ambiguity of art status by establishing a clear framework within which artefacts are considered art. Accordingly the concern of institutional theorists, such as Danto and Dickieet al,has been directed towards outlining those institutional apparatus of the art world such as galleries, museums and critics that confer the status of art and frame meaning. Once the institutional framework is accounted for, the ambiguity concerning art status is considered resolved. Although Howard Becker describes a pluralist vision of art worlds, art is still understood to be whatever is deemed art within such frameworks.This approach however, in overlooking the key role and changing nature of the institution itself, is problematic. Specifically the ambiguous nature of the art institution is missed. Using the relationship of graffiti and installation to the art institution I will discuss what could be called “ambiguous exhibitions”. These art forms maintain an unclear relationship to the established art world yet instances of exhibition and institutional structure are often visible. It is this realty that posits the problematic of the ambiguous nature of the art institution. The issue of what counts as an exhibition heralds a new debate concerning institutional aesthetics and ambiguity. In short it shows that there is scope for ambiguity in the meaning of the term “art world”. Instead of ambiguity operating on the level of art status, it is here operating on the level of institutional status. Consequently the ambiguous nature of such exhibitions brings back into the play the nature of the curator, the gallery, the critic, the museum, etc.
A local hidden variable model of quantum correlation exploiting the detection loophole  [PDF]
N. Gisin,B. Gisin
Physics , 1999, DOI: 10.1016/S0375-9601(99)00519-8
Abstract: A local hidden variable model exploiting the detection loophole to reproduce exactly the quantum correlation of the singlet state is presented. The model is shown to be compatible with both the CHSH and the CH Bell inequalities. Moreover, it bears the same rotational symmetry as spins. The reason why the model can reproduce the quantum correlation without violating the Bell theorem is that in the model the efficiency of the detectors depends on the local hidden variable. On average the detector efficiency is limited to 75%.
Analyticity of Entropy Rate of Continuous-State Hidden Markov Chains  [PDF]
Guangyue Han,Brian Marcus
Mathematics , 2012,
Abstract: We prove that under certain mild assumptions, the entropy rate of a hidden Markov chain, observed when passing a finite-state stationary Markov chain through a discrete-time continuous-output channel, is jointly analytic as a function of the input Markov chain parameters and the channel parameters. In particular, as consequences of the main theorems, we obtain analyticity for the entropy rate associated with representative channels: Cauchy and Gaussian.
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