Locality is not violated for the singlet spin state

The use of Bell inequality for the singlet spin state is analyzed. Due to superselection rules the singlet spin state is entangled with spatial spherical wave functions. Bell inequalities are violated only for subensembles which are not pure states. Locality is not violated.     

An efficient time-step-based self-adaptive algorithm for predictor-corrector methods of Runge-Kutta type

Finding an efficient implementation variant for the numerical solution of problems from computational science and engineering involves many implementation decisions that are strongly influenced by the specific hardware architecture. The complexity of these architectures makes it difficult to find the best implementation variant by manual tuning. For numerical solution methods from linear algebra, auto-tuning techniques based on a global search engine as they are used for ATLAS or FFTW can be used successfully. These techniques generate different implementation variants at installation time and select one of these implementation variants either at installation time or at runtime, before the computation starts. For some numerical methods, auto-tuning at installation time cannot be applied directly, since the best implementation variant may strongly depend on the specific numerical problem to be solved. An example is solution methods for initial value problems (IVPs) of ordinary differential equations (ODEs), where the coupling structure of the ODE system to be solved has a large influence on the efficient use of the memory hierarchy of the hardware architecture. In this context, it is important to use auto-tuning techniques at runtime, which is possible because of the time-stepping nature of ODE solvers.In this article, we present a sequential self-adaptive ODE solver that selects the best implementation variant from a candidate pool at runtime during the first time steps, i.e., the auto-tuning phase already contributes to the progress of the computation. The implementation variants differ in the loop structure and the data structures used to realize the numerical algorithm, a predictor-corrector (PC) iteration scheme with Runge-Kutta (RK) corrector considered here as an example. For those implementation variants in the candidate pool that use loop tiling to exploit the memory hierarchy of a given hardware platform we investigate the selection of tile sizes. The self-adaptive ODE solver combines empirical search with a model-based approach in order to reduce the search space of possible tile sizes. Runtime experiments demonstrate the efficiency of the self-adaptive solver for different IVPs across a range of problem sizes and on different hardware architectures.     

Quaternion-based improved LPP method for color face recognition

In recent years, pattern recognition and computer vision have increasingly become the focus of research. Locality preserving projection (LPP) is a very important learning method in these two fields and has been widely used. Using LPP to perform face recognition, we usually can get a high accuracy. However, the face recognition application of LPP suffers from a number of problems and the small sample size is the most famous one. Moreover, though the face image is usually a color image, LPP cannot sufficiently exploit the color and we should first convert the color image into the gray image and then apply LPP to it. Transforming the color image into the gray image will cause a serious loss of image information. In this paper, we first use the quaternion to represent the color pixel. As a result, an original training or test sample can be denoted as a quaternion vector. Then we apply LPP to the quaternion vectors to perform feature extraction for the original training and test samples. The devised quaternion-based improved LPP method is presented in detail. Experimental results show that our method can get a higher classification accuracy than other methods.     

Abstract elementary classes stable in ℵ0

We study abstract elementary classes (AECs) that, in ${\mathrm{?}}_0$, have amalgamation, joint embedding, no maximal models and are stable (in terms of the number of orbital types). Assuming a locality property for types, we prove that such classes exhibit superstable-like behavior at ${\mathrm{?}}_0$. More precisely, there is a superlimit model of cardinality ${\mathrm{?}}_0$ and the class generated by this superlimit has a type-full good ${\mathrm{?}}_0$-frame (a local notion of nonforking independence) and a superlimit model of cardinality ${\mathrm{?}}_1$. We also give a supersimplicity condition under which the locality hypothesis follows from the rest.     

Einstein-Podolsky-Rosen experiments: the structure of the probability space. I

Incompatibility of measurements, central to quantum mechanics, is captured in the formalism of empirical logic, which is based on a generalization of the notion of a sample space in Kolmogoroff's axiomatic theory of probability. In composite empirical systems of the kind considered in the Einstein-Podolsky-RosenGedankenexperiment, incompatibility gives rise to the notion of influence, which is closely related to stochastic independence.These concepts are used to study the methodological structure of a large class of Einstein-Podolsky-Rosen type experiments, linking a series of much debated issues such as scientific Realism, ontological and epistemic uncertainty, determinism, locality, separability, factorizability, completeness, conservation, correlation, Bell-Clauser-Horne inequalities, and hidden-variables models to an axiomatic probability theory.1. My translation. Fine infers a missing not in the first part of the sentence and translates I can not reconcile myself to the following, that a manipulation undertaken on A has an influence on B.... I do not dispute that Einstein could not reconcile himself with such a postulate of influence, and thus I agree with Fine's comments on this sentence. However, the German original needs no negation if one surmises that Einstein writes about the consequences of ahypothesis of influence.2. The quasimanualAB consists of all subsets ofXY of the form _xE xF _x, whereE A andF _x B for allx E can be chosen in all possible ways, together with the symmetrical subsets ofXY, where the rôle ofA andB is exchanged. See Refs. [22,43,55] for the technical details.     

Causality and Bell-CHSH Inequalities Violations in?Entanglement Swapping Schemes

An ample amount of evidence supporting the violation of locality has been presented in quantum theory. If such an instantaneous influencing is possible, it is worth considering the possibility of a causality violation in quantum theory, i.e., a future event influencing the past. Motivated by the delayed-choice gedanken experiment, we provide two protocols of entanglement swapping that are subtle in involving causality conditions. In particular, we present protocols in which locality constraints are identical to causality conditions and closely examine Bell-inequalities violation based on these protocols. These protocols will provide a clear picture of how quantum theory still preserves causality while locality is violated. We also discuss a potential threat to the entanglement-based key distribution schemes.     

A Simple Relation between Non-locality and a Corrected Entropy

Within the framework of a statistical interpretation of quantum mechanics entanglement (in a mathematical sense) manifests itself in the non-separability of the statistical operator ρ representing the ensemble in question. In experiments, on the other hand, entanglement can be detected, in the form of non-locality, by the violation of Bell’s inequality Δ≤2. How do these different viewpoints match? We employ a corrected von Neumann entropy to measure the (mathematical) degree of entanglement and show that, at least in the case of 2×2 dimensions, this function is directly related to Bell’s correlation function Δ. This relation can be well approximated by an ellipse equation which, for the first time, allows for a direct comparison of the two faces of entanglement.     

Local cardinal interpolation by C2 cubic B2-splines with a tunable shape parameter

A $C^2$ cubic local interpolating B2-spline, controllable by a shape parameter, is introduced and its properties are analyzed. An algorithm for the automatic selection of the free parameter is developed and tested on several examples. Finally, a two-phase subdivision scheme for its efficient evaluation at dyadic points is presented.     

A Local Realistic Theory for Mermin’s EPR Experiment

As another counterexample to prevalent conventional belief, a realistic theory, which is local and reproduces all the probabilistic predictions of quantum theory, is presented for Mermin’s version of the Einstein-Podolsky-Rosen (EPR) experiment.