Tropical Geometry of Statistical Models

This paper presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. The question addressed here is how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. A key role is played by the Newton polytope of a statistical model. Our results are applied to the hidden Markov model and to the general Markov model on a binary tree.Comment: 14 pages, 3 figures. Major revision. Applications now in companion paper, "Parametric Inference for Biological Sequence Analysis

Observation of Scalar Aharonov-Bohm Effect with Longitudinally Polarized Neutrons

We have carried out a neutron interferometry experiment using longitudinally polarized neutrons to observe the scalar Aharonov-Bohm effect. The neutrons inside the interferometer are polarized parallel to an applied pulsed magnetic field B(t). The pulsed B field is spatially uniform so it exerts no force on the neutrons. Its direction also precludes the presence of any classical torque to change the neutron polarization

Scalar Aharonov-Bohm effect with longitudinally polarized neutrons

In the scalar Aharonov-Bohm effect, a charged particle (electron) interacts with the scalar electrostatic potential U in the field-free (i.e., force-free) region inside an electrostatic cylinder (Faraday cage). Using a perfect single-crystal neutron interferometer we have performed a “dual” scalar Aharonov-Bohm experiment by subjecting polarized thermal neutrons to a pulsed magnetic field. The pulsed magnetic field was spatially uniform, precluding any force on the neutrons. Aligning the direction of the pulsed magnetic field to the neutron magnetic moment also rules out any classical torque acting to change the neutron polarization. The observed phase shift is purely quantum mechanical in origin. A detailed description of the experiment, performed at the University of Missouri Research Reactor, and its interpretation is given in this paper

Topology, Locality, and Aharonov-Bohm Effect with Neutrons

Recent neutron interferometry experiments have been interpreted as demonstrating a new topological phenomenon similar in principle to the usual Aharonov-Bohm (AB) effect, but with the neutron's magnetic moment replacing the electron's charge. We show that the new phenomenon, called Scalar AB (SAB) effect, follows from an ordinary local interaction, contrary to the usual AB effect, and we argue that the SAB effect is not a topological effect by any useful definition. We find that SAB actually measures an apparently novel spin autocorrelation whose operator equations of motion contain the local torque in the magnetic field. We note that the same remarks apply to the Aharonov-Casher effect.Comment: 9 page

³¹P Saturation Transfer and Phosphocreatine Imaging in the Monkey Brain

³¹P magnetic resonance imaging with chemical-shift discrimination by selective excitation has been employed to determine the phosphocreatine (PCr) distribution in the brains of three juvenile macaque monkeys. PCr images were also obtained while saturating the resonance of the {gamma}-phosphate of ATP, which allowed the investigation of the chemical exchange between PCr and the {gamma}-phosphate of ATP catalyzed by creatine kinase. Superposition of the PCr images over the proton image of the same monkey brain revealed topological variations in the distribution of PCr and creatine kinase activity. PCr images were also obtained with and without visual stimulation. In two out of four experiments, an apparently localized decrease in PCr concentration was noted in visual cortex upon visual stimulation. This result is interpreted in terms of a possible role for the local ADP concentration in stimulating the accompanying metabolic response

Temporal and spatial dynamics of spawning, settlement, and growth of gray snapper (Lutjanus griseus) from the West Florida shelf as determined from otolith microstructures

The goal of our study was to understand the spatial and temporal variation in spawning and settlement of gray snapper (Lutjanus griseus) along the West Florida shelf (WFS). Juvenile gray snapper were collected over two consecutive years from seagrass meadows with a benthic scrape and otter trawl. Spawning, settlement, and growth patterns were compared across three sampling regions (Panhandle, Big bend, and Southwest) by using otolith microstructure. Histology of adult gonads was also used for an independent estimate of spawning time. Daily growth increments were visible in the lapilli of snapper 11–150 mm standard length; ages ranged from 38 to 229 days and estimated average planktonic larval duration was 25 days. Estimated growth rates ranged from 0.60 to 1.02 mm/d and did not differ among the three sampling regions, but did differ across sampling years. Back-calculated fertilization dates from otoliths indicated that juveniles in the Panhandle and Big Bend were mainly summer spawned fish, whereas Southwest juveniles had winter and summer fertilization dates. Settlement occurred during summer both years and in the winter of 1997 for the southern portion of the WFS. Moon phase did not appear to be strongly correlated with fertilization or settlement. Histological samples of gonads from adults collected near the juvenile sampling areas indicated a summer spawning period

Classical and Quantum Interaction of the Dipole

A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic dipoles are obtained. Four new experiments are proposed, three of which would observe topological phase shifts.Comment: 10 pages, Latex/Revtex. Some minor errors have been correcte

Heralded quantum steering over a high-loss channel

Entanglement is the key resource for many long-range quantum information tasks, including secure communication and fundamental tests of quantum physics. These tasks require robust verification of shared entanglement, but performing it over long distances is presently technologically intractable because the loss through an optical fiber or free-space channel opens up a detection loophole. We design and experimentally demonstrate a scheme that verifies entanglement in the presence of at least $14.8\pm0.1$ dB of added loss, equivalent to approximately $80$ km of telecommunication fiber. Our protocol relies on entanglement swapping to herald the presence of a photon after the lossy channel, enabling event-ready implementation of quantum steering. This result overcomes the key barrier in device-independent communication under realistic high-loss scenarios and in the realization of a quantum repeater.Comment: 8 pages, 5 figure