A sum-over-histories account of an EPR(B) experiment

We analyze a variant of the EPRB experiment within a framework for quantum mechanics that rests on a radical interpretation of the sum over histories. Within this framework, reality is (just as classically) a single history, e.g. a definite collection of particles undergoing definite motions; and quantum dynamics appears as a kind of stochastic law of motion for that history, a law formulated in terms of non-classical probability-amplitudes. No state vectors enter this framework, and their attendant nonlocality is therefore absent as well.1. That is, before pair creations and annihilations were discovered. (The electronic and nuclear spins might also be regarded as new aspects of their kinematics. But perhaps spin is better construed, within the sum-over-histories framework, as a quality of a more dynamical character, namely as a generalized sort of probability-amplitude.)2. A possible escape would be the so-called Everett interpretation, in which the collapse never occurs, but its effects are supposed to be recovered via a more careful analysis of closed systems in which measurement-like processes take place. Among other things, this approach tends to lead either to the view that nothing really happens [1] or to the view that everything really happens [2] (which perhaps is not that different from the former view).3. For example, the rule, collapse occurs along the past light cone (in the Heisenberg picture), appears to be consistent.4. And Bell's inequality shows thatany theory formulated in terms of an instantaneous state evolving in time would encounter the same trouble. Indeed, the trouble shows up even more glaringly if one adapts Bell's argument to spin-1 systems, using the results of Kochen and Specker[10]. In order to use the Kochen-Specker results in the EPR manner one needs a scheme for measuring the relevant observables, but this can be accomplished by means of suitably concatenated Stern-Gerlach analyzers with recombining beams [13]. Then, as Allen Stairs has pointed out [14], even the perfect correlations become impossible to reproduce, and no reference to probability theory is needed to establish a contradiction with locality. Recently, an analogous experiment using three spin 1/2 particles instead of two spin 1 particles has also been given [15].5. No technical problem obstructs an extension to fermionic fields (indeed the functional integral formalism for Quantum Field Theory is probably the most popular at present), but the realistic interpretation of the individual histories seems to get lost. One way out would be if all fermions were composites or collective excitations of fields quantized according to bosonic commutation relations. Another would be if the particle formulation were taken as basic, with the complementary field formulation being merely a mathematical artifice (at least for fermions).6. In the approach of Gell-Mann-Hartle and Griffiths for example, only a small subset of the possible partitions is granted meaning, in such a way that all interference terms are suppressed and quantum probabilities reduce to classical ones.7. In stating these rules we consider an idealized situation in which the spatio-temporal indeterminacy of particle-locationwithin a given one of our trajectories is ignored; or if you prefer, you can take the experiment as only a Gedanken one affording a simplified illustration of how EPR-like correlations are understood within the sum-over-histories framework. In this connection recall also that the semiclassical propagator is in fact exact for a free particle.8. This can be interpreted either as part of the specification of the initial conditions, or (as suggested by a referee) merely as an example of relativization of probabilities.9. Thus a state vector may be defined as an equivalence-class of sets of partial histories.10. One such generalization applies to open systems, for example to a particle in contact with a heat reservoir. For this example see [11], wherein the two-way path formalism of §5 above is used, and the influence of the reservoir results in an effective dynamics for the particle in which the forward and backward portions of its world-line are coupled to each other by a certain interaction term in the amplitude. In this type of situation a density-operator (though not a state vector ) can still be introduced, but it no longer summarizes all the relevant information about the past (and correspondingly its evolution lacks the Markov property that(t + dt) is determined by(t) alone). For quantum gravity, it may be that not even such a non-Markov will be exactly definable, and only the global probabilities themselves will make sense.11. Ironically it is just this property of the amplitudes which, as mentioned above, makes possible the introduction of the state vectors whose collapse then introduces such a strong appearance ofnonlocality into the theory.     

Nucleophilic dephosphorylation of p-nitrophenyl diphenyl phosphate in cationic micellar media

The kinetics of nucleophilic dephosphorylation of p-nitrophenyl diphenyl phosphate by hydroxamate ions (R'(C=O)N(RO-)) have been investigated in aqueous cationic micellar media at pH 9.12 and 27 degrees C. The pseudo-first-order rate constant-surfactant profiles show micelle-assisted bimolecular reactions involving interfacial ion exchange between bulk aqueous media and micellar pseudophase. N-Substituted hydroxamate ion shows higher reactivity over the unsubstituted hydroxamate ions in cationic micellar media. The kinetic data are discussed in terms of the pseudophase ion exchange model.     

High-performance thin layer chromatography method for quantitative determination of four major anthraquinone derivatives in Rheum emodi

A high-performance thin layer chromatographic (HPTLC) method for the rapid and simple quantification of the four major anthraquinone derivatives i.e. physcion, chrysophanol, emodin and chrysophanol glycoside in Rheum emodi is described. HPTLC of anthraquinone derivatives was performed on pre-coated RP-18 F254S HPTLC plates. For achieving good separation, the mobile phase of methanol-water-formic acid (80:19:1, v/v/v) was used. The densitometric determination of anthraquinone derivatives was carried out at 445 nm in reflection/absorption mode. The calibration curves were linear in the range of 20-100 ng for physcion, 80-400 ng for chrysophanol and emodin, and 200-1000 ng for chrysophanol glycoside. The method was found to be reproducible and convenient for quantitative analysis of anthraquinone derivatives in the methanolic extract of rhizomes of R. emodi collected from three different locations of Western Himalaya, India.     

Photocatalytic performance of combustion-synthesized β and γ-Ga2O3 in the degradation of 1,4-dioxane in aqueous solution

Nanostructures of β and γ-Ga₂O₃ were prepared by the solution combustion route using urea as fuel. The synthesized nano photocatalysts were characterized by use of XRD, FT-IR, BET, TEM, TGA–DTA, DRS, and Raman spectroscopy. XRD and TEM investigations confirmed the nanostructures; particle size was in the range 3–5 nm for γ-Ga₂O₃ and 40–50 nm for β-Ga₂O₃. The specific surface area of γ-Ga₂O₃ was 91 m² g^?1 and that of β-Ga₂O₃ was 24.3 m² g^?1. The polymorphs of gallium oxide were used as photocatalysts for decomposition of 1,000 mg/l 1,4-dioxane. More than 90 % of the 1,4-dioxane could be degraded in less than 180 min by use of 10 mg/l photocatalyst + 0.5 ml H₂O₂. The efficiency of photocatalytic degradation of 1,4-dioxane by the synthesized photocatalysts was compared with that of P-25 TiO₂ and followed the order γ-Ga₂O₃ ≥ β-Ga₂O₃ > P-25 TiO₂. The degradation was found to follow pseudo first-order kinetics.     

Fast and scalable parallel layout decomposition in double patterning lithography

For 32/22 nm technology nodes and below, double patterning (DP) lithography has become the most promising interim solutions due to the delay in the deployment of next generation lithography (e.g., EUV). DP requires the partitioning of the layout patterns into two different masks, a procedure called layout decomposition. Layout decomposition is a key computational step that is necessary for double patterning technology. Existing works on layout decomposition are all single-threaded, which is not scalable in runtime and/or memory for large industrial layouts. This paper presents the first window-based parallel layout decomposition methods for improving both runtime and memory consumption. Experimental results are promising and show the presented parallel layout decomposition methods obtain upto 21× speedup in runtime and upto 7.5×reduction in peak memory consumption with acceptable solution quality.     

Anticancer Activity of Hydrogen‐Bond‐Stabilized Half‐Sandwich RuII Complexes with Heterocycles

Neutral half‐sandwich organometallic ruthenium(II) complexes of the type [(η⁶‐cymene)RuCl₂(L)] ( H1 – H10 ), where L represents a heterocyclic ligand, have been synthesized and characterized spectroscopically. The structures of five complexes were also established by single‐crystal X‐ray diffraction confirming a piano‐stool geometry with η⁶ coordination of the arene ligand. Hydrogen bonding between the N? H group of the heterocycle and a chlorine atom attached to Ru stabilizes the metal–ligand interaction. Complexes coordinated to a mercaptobenzothiazole framework ( H1 ) or mercaptobenzoxazole ( H6 ) showed high cytotoxicity against several cancer cells but not against normal cells. In vitro studies have shown that the inhibition of cancer cell growth involves primarily G1‐phase arrest as well as the generation of reactive oxygen species (ROS). The complexes are found to bind DNA in a non‐intercalative fashion and cause unwinding of plasmid DNA in a cell‐free medium. Surprisingly, the cytotoxic complexes H1 and H6 differ in their interaction with DNA, as observed by biophysical studies, they either cause a biphasic melting of the DNA or the inhibition of topoisomerase IIα activity, respectively. Substitution of the aromatic ring of the heterocycle or adding a second hydrogen‐bond donor on the heterocycle reduces the cytotoxicity.     

One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Coumarinyl azoimidazolyl complexes of osmium(II) hydridocarbonyls: spectroscopic and structural characterization,oxidation catalysis,photovoltaic effect and density functional theory computation

Os(II) hydridocarbonyl complexes of coumarinyl azoimidazoles, [Osh(CO)(PPh₃)₂(CZ‐4R‐R′)]^0/+ ( 3 , 4 ) (CZ‐R‐H = 2‐(coumarinyl‐6‐azo)‐4‐substituted imidazole or 1‐alkyl‐2‐(coumarinyl‐6‐azo)‐4‐substituted imidazole), were characterized from spectroscopic data and the single‐crystal X‐ray data for one of the complexes, [Osh(CO)(PPh₃)₂(CZ‐4‐Ph)] ( 3c ) (CZ‐4‐Ph = 2‐(coumarinyl‐6‐azo)‐4‐phenylimidazolate), confirmed the structure. The complexes show higher emission (quantum yield ? = 0.0163–0.16) and longer lifetime (τ = 1.4–10.3 ns) than free ligands (? = 0.0012–0.0185 and τ = 0.685–1.306 ns). Cyclic voltammetry shows quasi‐reversible metal oxidation at 0.67–0.94 V for [Os(III)/Os(II)] and 1.21–1.36 V for [Os(IV)/Os(III)] and subsequent azo reductions (?0.68 to ?0.95 V for [? N?N? ]/[? N N? ]^? and irreversible < ?1.2 V for [? N N? ]^?/[? N? N? ]^2?) of the chelated coumarinyl azoimidazole. The complexes are photostable and show better photovoltaic power conversion efficiency than free ligands. Also, the complexes were used as catalysts for the oxidation of primary/secondary alcohols to aldehydes/ketones using oxidizing agents like N‐methylmorpholine N‐oxide, t‐BuOOH and H₂O₂. Density functional theory computation was carried out from the optimized structures and the data obtained were used to interpret the electronic and photovoltaic properties. Copyright © 2016 John Wiley & Sons, Ltd.