Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview <s> Linear Feasibility Test <s> We present a new polynomial-time algorithm for linear programming. The running-time of this algorithm is O ( n 3-5 L 2 ), as compared to O ( n 6 L 2 ) for the ellipsoid algorithm. We prove that given a polytope P and a strictly interior point a e P , there is a projective transformation of the space that maps P , a to P' , a' having the following property. The ratio of the radius of the smallest sphere with center a' , containing P' to the radius of the largest sphere with center a' contained in P' is O ( n ). The algorithm consists of repeated application of such projective transformations each followed by optimization over an inscribed sphere to create a sequence of points which converges to the optimal solution in polynomial-time. <s> BIB001 </s> Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview <s> Linear Feasibility Test <s> On a Theory of the Collapse of the Wave Function.- On the Measurement Problem of Quantum Mechanics.- A New Characteristic of a Quantum System Between Two Measurements - A "Weak Value".- Can the Quantum Measurement Process be put into QED?.- Chained Bell Inequalities.- From George Boole to John Bell - The Origins of Bell's Inequality.- The Logic of Quantum Nonseparability.- Bell's Theorem and Mermin's Gedanken Experiment.- Searching for Mutually Unbiased Observables.- Going Beyond Bell's Theorem.- Quantum Field Theory, Bell's Inequalities and the Problem of Hidden Variables.- What Locality Isn't: A Response to Jarrett.- Bell's Theorem: The Forgotten Loophole and How to Exploit It.- Are More Economical Escapes From Bell's Strictures Possible?.- Concerning Theories Free From Bell's Constraint.- The EPR Paradox, Actions at a Distance and the Theory of Relativity.- Conditionals, Probability and Bell's Theorem.- Relativity and Probability, Classical or Quantal.- Relativistic Probability Amplitudes and State Preparation.- Non-Linearity and Post-Bell Quantum Mechanics.- Observable Effects of the Uncertainty Relations in the Covariant Phase Space Representation of Quantum Mechanics.- Geometry of Cyclic Quantum Evolutions.- On the Computer Simulation of the EPR-Bohm Experiment.- Discrete Phase-Space Model for Quantum Mechanics.- A Possible Explanation of Quantum Mechanics Behavior by a Classical Cellular Automaton Construction.- Quantum Mechanical Information is Ubiquitous.- The Unobservability of Spinor Structure.- Teaching QM: True, Trivial, Inevitable.- Quantum Cosmology and Quantum Mechanics.- Cosmology, EPR Correlations and Separability.- Bell's Theorem: Form and Information in the Quantum Theory.- Horizons of Knowledge in Cosmology.- The Ontological Status of the Cosmological Singularity.- Quantum Cosmological Generality of Inflation in Anisotropic Spacetime.- Mass Generation in the Early Universe.- Massive Photons and Monopoles.- The Large-Scale Streaming of Galaxies.- The Numerically Simple Universe.- Size of a Least Unit.- Bell, Book and Candle: The Limning of a Mystery.- Complementarity and Space-Time Description.- Complementarity and Cosmology.- Quantum Ontologies.- Henry P. Stapp on Quantum Theory and Reality.- For Whom the Bell Tolls: A Plea for Fundamental Ontology.- The Role of Consciousness in Physical Reality.- The Significance of Human Observation in Measurement in Quantum Mechanics The Nature of the Traditional Separation Between Psychology and Physics.- The Universe in the Light of Contemporary Scientific Developments.- Name Index. <s> BIB002 </s> Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview <s> Linear Feasibility Test <s> We construct a set of ${2}^{{2}^{n}}$ independent Bell-correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are satisfied if and only if the correlations considered allow a local classical model. All these inequalities can be summarized in a single, albeit nonlinear inequality. We show that quantum correlations satisfy this condition provided the state has positive partial transpose with respect to any grouping of the n systems into two subsystems. We also provide an efficient algorithm for finding the maximal quantum-mechanical violation of each inequality, and show that the maximum is always attained for the generalized GHZ state. <s> BIB003 </s> Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview <s> Linear Feasibility Test <s> We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of generalized Bell inequalities are summarized. We investigate maximal violations of Bell inequalities as well as states not violating (certain) Bell inequalities. Finally, we discuss the relation between Bell inequality violations and entanglement properties currently discussed in quantum information theory. <s> BIB004 </s> Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview <s> Linear Feasibility Test <s> Strong nonlocality allows signals faster than light. Weak nonlocality is a statistical property of classical events for which there is no realistic local theory. This requires the violation of at least one general Bell inequality. The theory of ideal quantum measurements predicts weak nonlocality but not strong nonlocality. Bell experiment here refers to any experiment designed to demonstrate weak nonlocality. BellTest is a computer program generally available on the Web to help planning and analysis of such Bell experiments. In Mode 1 it obtains general Bell inequalities. In Mode 2 it tests for their violation. We describe its use, with some new results for illustration. <s> BIB005 </s> Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview <s> Linear Feasibility Test <s> Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one determine, for each of the outputs, which of the inputs it is influenced by? The problem has applications ranging from modeling pairwise comparisons to reconstructing mental processing architectures to conjoint testing. A necessary and sufficient condition for a given pattern of selective influences is provided by the Joint Distribution Criterion, according to which the problem of"what influences what"is equivalent to that of the existence of a joint distribution for a certain set of random variables. For inputs and outputs with finite sets of values this criterion translates into a test of consistency of a certain system of linear equations and inequalities (Linear Feasibility Test) which can be performed by means of linear programming. While new in the behavioral context, both this test and the Joint Distribution Criterion on which it is based have been previously proposed in quantum physics, in dealing with generalizations of Bell inequalities for the quantum entanglement problem. The parallels between this problem and that of selective influences in behavioral sciences is established by observing that noncommuting measurements in quantum physics are mutually exclusive and can therefore be treated as different levels of one and the same factor. <s> BIB006
The Linear Feasibility Test (LFT) is a criterion for selective influences in all situations involving finite sets of inputs/outputs, Λ = {1, . . . , n}, with the ith input and ith output having finite sets of values, {1, . . . , k i } and {1, . . . , m i }, respectively BIB006 . In other situations LFT can be used as a necessary condition because every set of possible values can be discretized. The distributions of H φ = H 1 j1 , . . . , H n jn are represented by probabilities with φ = (j 1 , . . . , j n ) ∈ Φ and We consider this probability the [(a 1 , . . . , a n ) , (j 1 , . . . , j n )]th component of the m 1 · · · m n t-vector P (with t denoting the number of treatments in Φ). The joint distribution of H in JDC, if it exists, is represented by probabilities We consider this probability the h  has a solution (is feasible). This is a linear programming task in the standard form (with a constant objective function). Let L (P ) be a Boolean function equal to 1 if and only if this system is feasible. L (P ) is known to be computable, its time complexity being polynomial BIB001 . The potential of JDC to lead to LFT and provide an ultimate criterion for the Bohmian entanglement problem has not been utilized in quantum physics until relatively recently, when LFT was proposed in BIB003 BIB004 and BIB005 . But the essence of the idea can be found in  . Given a set of numerical (experimentally estimated or theoretical) probabilities, computing L (P ) is always preferable to dealing with explicit inequalities as their number becomes very large even for moderate-size vectors P . The classical Bell-CHSH-Fine inequalities (27)-(28) for n = 2, k 1 = k 2 = 2, m 1 = m 2 = 2 (assuming that the marginal selectivity equalities hold) number just 8, but already for n = 2, k 1 = k 2 = 2 with m 1 = m 2 = 3 (describing, e.g., an EPR experiment with two spin-1 particles, or two spin-1 /2 ones and inefficient detectors), our computations yield 1080 inequalitiies equivalent to L (P ) = 1. For n = 3, k 1 = k 2 = k 3 = 2 and m 1 = m 2 = m 3 = 2, corresponding to the GHZ paradigm BIB002 with three spin-1 /2 particles, this number is 53792. Lists of such inequalities can be derived "mechanically" from the format of matrix M using well-known facet enumeration algorithms (see, e.g., program lrs at http://cgm.cs.mcgill.ca/~avis/C/lrs.html). Once such a system of inequalities S is derived, one can use it to prove necessity (or sufficiency) of any other system S ′ by showing, with the aid of a linear programming algorithm, that S ′ is redundant when added to S (respectively, S is redundant when added to S ′ ).