Implications of Lorentz covariance for the guidance equation in two-slit quantum interference

It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wavefunction is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie-Bohm ones, such as crossing of the axis of symmetry.Comment: 27 pages including 6 pages of figure

A selective role for neuronal activity regulated pentraxin in the processing of sensory-specific incentive value

Neuronal activity regulated pentraxin (Narp) is a secreted neuronal product which clusters AMPA receptors and regulates excitatory synaptogenesis. Although Narp is selectively enriched in brain, its role in behavior is not known. As Narp is expressed prominently in limbic regions, we examined whether Narp deletion affects performance on tasks used to assess motivational consequences of food-rewarded learning. Narp knock-out (KO) mice were unimpaired in learning simple pavlovian discriminations, instrumental lever pressing, and in acquisition of at least two aspects of pavlovian incentive learning, conditioned reinforcement and pavlovian-instrumental transfer. In contrast, Narp deletion resulted in a substantial deficit in the ability to use specific outcome expectancies to modulate instrumental performance in a devaluation task. In this task, mice were trained to respond on two levers for two different rewards. After training, mice were prefed with one of the two rewards, devaluing it. Responding on both levers was then assessed in extinction. Whereas control mice showed a significant preference in responding on the lever associated with the nondevalued reward, Narp KO mice responded equally on both levers, failing to suppress responding on the lever associated with the devalued reward. Both groups consumed more of the nondevalued reward in a subsequent choice test, indicating Narp KO mice could distinguish between the rewards themselves. These data suggest Narp has a selective role in processing sensory-specific information necessary for appropriate devaluation performance, but not in general motivational effects of reward-predictive cues on performance

Chaotic zone boundary for low free eccentricity particles near an eccentric planet

We consider particles with low free or proper eccentricity that are orbiting near planets on eccentric orbits. Via collisionless particle integration we numerically find the location of the boundary of the chaotic zone in the planet's corotation region. We find that the distance in semi-major axis between the planet and boundary depends on the planet mass to the 2/7 power and is independent of the planet eccentricity, at least for planet eccentricities below 0.3. Our integrations reveal a similarity between the dynamics of particles at zero eccentricity near a planet in a circular orbit and with zero free eccentricity particles near an eccentric planet. The 2/7 law has been previously explained by estimating the semi-major at which the first order mean motion resonances are large enough to overlap. Orbital dynamics near an eccentric planet could differ due to first order corotation resonances that have strength proportional to the planet's eccentricity. However, we find the corotation resonance width at low free eccentricity is small. Also the first order resonance width at zero free eccentricity is the same as that for a zero eccentricity particle near a planet in a circular orbit. This accounts for insensitivity of the chaotic zone width to planet eccentricity. Particles at zero free eccentricity near an eccentric planet have similar dynamics to those at zero eccentricity near a planet in a circular orbit.Comment: accepted for publication in MNRA

B2B analytics in the airline market: Harnessing the power of consumer big data

This paper utilizes market-level data to explore the relative performance of individual companies amongst defined competitors. We show the potential of using consumer clickstream data, an important type of big data, to create a new set of B2B analytical frameworks. In the markets where complex interactions between competitors, search intermediaries and consumers create a network, B2B relationships can be inferred from consumer search patterns, and can then be modeled to gauge the online performance. A commercial dataset from ComScore's US panel of one million users is used to illustrate a new approach to measure and evaluate the online performance of competitors in the US airline market. The methodology and associated performance framework demonstrate the potential for new forms of market intelligence based on the visualization of market networks, online performance calculated from matrix algorithms, the measurement of the impact of search intermediaries, and the identification of latent relationships. This research makes theoretical and empirical contributions to the debate on the use of big data for B2B market analytics. B2B managers can use this approach to extend their network horizon from an egocentric to a network view of competition and map out their competitive landscape from the perspective of the customer

Schrodinger dynamics as a two-phase conserved flow: an alternative trajectory construction of quantum propagation

It is shown that the Schrodinger equation can be cast in the form of two coupled real conservation equations, in Euclidean spacetime in the free case and in a five-dimensional Eisenhart geometry in the presence of an external potential. This implies a novel two-phase quantum hydrodynamic model whose Lagrangian picture provides an exact scheme to calculate the time-dependent wavefunction from a continuum of deterministic trajectories where two points are linked by at most two orbits. Properties of the model are examined, including the appearance of entangled trajectories in separable states. Wavefunction constructions employing alternative two-phase models are proposed.Comment: To appear in J. Phys.

Immediate Response Strategy and Shift to Place Strategy in Submerged T-Maze

A considerable amount of research has demonstrated that animals can use different strategies when learning about, and navigating within, their environment. Since the influential research of Keywords: spatial strategy, place, response, aversive, motivation In spatial navigation tasks, animals can attend to many sources of information. In particular, psychologists have long debated the extent to which animals use cues from either external location or internal movement to guide their behavior in maze learning tasks It has been widely accepted that animals initially learn about relational information found in the configuration of environmental cues (place learning) and, subsequently, switch to a more automatic, and less cognitively effortful, response strategy over time Demonstrations of these strategy shifts are dominated by appetitively motivated tasks, with food reinforcement. In Experiment 1, we examined performance in a similar, but aversively motivated task: rats escaped a submerged maze by swimming to a hidden platform. Remarkably, we observed a response strategy early in training followed by a switch to a place strategy, which persisted over extended training. This observation was opposite of the pattern of data described in the appetitive maze General Method Subjects Male Long Evans rats (275Ϫ325 g; Charles River Laboratories, Raleigh, North Carolina) were housed individually in a temperature-controlled room, with lights on from 7:00 a.m. to 7:00 p.m. Rats in Experiment 1 (n ϭ 34) had free access to food (Teklad Chow 2018; Harlan Laboratories, Madison, Wisconsin) and water

Role of social environment and social clustering in spread of opinions in co-evolving networks

Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the co-evolving network voter model of opinion formation, studied by Holme and Newman [1]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for the asymmetric influences in relationships among individuals in a social group. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We have investigated the influences of these modifications on the outcomes of the simulations of this model. We found that varying the shape of the distribution of probability of accepting or rejecting opinions can lead to the emergence of two qualitatively distinct final states, one having several isolated connected components each in internal consensus leading to the existence of diverse set of opinions and the other having one single dominant connected component with each node within it having the same opinion. Furthermore, and more importantly, we found that the initial clustering in network can also induce similar transitions. Our investigation also brings forward that these transitions are governed by a weak and complex dependence on system size. We found that the networks in the final states of the model have rich structural properties including the small world property for some parameter regimes. [1] P. Holme and M. Newman, Phys. Rev. E 74, 056108 (2006)

A non inflationary model with scale invariant cosmological perturbations

We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced during an almost matter dominated era in the contraction phase. This is achieved using Bohmian solutions of the canonical Wheeler-de Witt equation, thus treating both the background and the perturbations in a fully quantum manner. We find a very slightly blue spectrum ($n_{_\mathrm{S}}-1>0$). Taking into account the spectral index constraint as well as the CMB normalization measure yields an equation of state that should be less than $\omega\lesssim 8\times 10^{-4}$, implying $n_{_\mathrm{S}}-1 \sim \mathcal{O}(10^{-4})$, and that the characteristic size of the Universe at the bounce is $L_0 \sim 10^3 \ell_\mathrm{Planck}$, a region where one expects that the Wheeler-DeWitt equation should be valid without being spoiled by string or loop quantum gravity effects.Comment: 9 pages, 4 figure