5,713 research outputs found
Information geometry of density matrices and state estimation
Given a pure state vector |x> and a density matrix rho, the function
p(x|rho)= defines a probability density on the space of pure states
parameterised by density matrices. The associated Fisher-Rao information
measure is used to define a unitary invariant Riemannian metric on the space of
density matrices. An alternative derivation of the metric, based on square-root
density matrices and trace norms, is provided. This is applied to the problem
of quantum-state estimation. In the simplest case of unitary parameter
estimation, new higher-order corrections to the uncertainty relations,
applicable to general mixed states, are derived.Comment: published versio
Efficient Simulation of Quantum State Reduction
The energy-based stochastic extension of the Schrodinger equation is a rather
special nonlinear stochastic differential equation on Hilbert space, involving
a single free parameter, that has been shown to be very useful for modelling
the phenomenon of quantum state reduction. Here we construct a general closed
form solution to this equation, for any given initial condition, in terms of a
random variable representing the terminal value of the energy and an
independent Brownian motion. The solution is essentially algebraic in
character, involving no integration, and is thus suitable as a basis for
efficient simulation studies of state reduction in complex systems.Comment: 4 pages, No Figur
Karen Rothenberg’s (Not So) Secret Roles and Contributions at the U.S. National Institutes of Health
Inferring Networks of Substitutable and Complementary Products
In a modern recommender system, it is important to understand how products
relate to each other. For example, while a user is looking for mobile phones,
it might make sense to recommend other phones, but once they buy a phone, we
might instead want to recommend batteries, cases, or chargers. These two types
of recommendations are referred to as substitutes and complements: substitutes
are products that can be purchased instead of each other, while complements are
products that can be purchased in addition to each other.
Here we develop a method to infer networks of substitutable and complementary
products. We formulate this as a supervised link prediction task, where we
learn the semantics of substitutes and complements from data associated with
products. The primary source of data we use is the text of product reviews,
though our method also makes use of features such as ratings, specifications,
prices, and brands. Methodologically, we build topic models that are trained to
automatically discover topics from text that are successful at predicting and
explaining such relationships. Experimentally, we evaluate our system on the
Amazon product catalog, a large dataset consisting of 9 million products, 237
million links, and 144 million reviews.Comment: 12 pages, 6 figure
Hidden variable interpretation of spontaneous localization theory
The spontaneous localization theory of Ghirardi, Rimini, and Weber (GRW) is a
theory in which wavepacket reduction is treated as a genuine physical process.
Here it is shown that the mathematical formalism of GRW can be given an
interpretation in terms of an evolving distribution of particles on
configuration space similar to Bohmian mechanics (BM). The GRW wavefunction
acts as a pilot wave for the set of particles. In addition, a continuous stream
of noisy information concerning the precise whereabouts of the particles must
be specified. Nonlinear filtering techniques are used to determine the dynamics
of the distribution of particles conditional on this noisy information and
consistency with the GRW wavefunction dynamics is demonstrated. Viewing this
development as a hybrid BM-GRW theory, it is argued that, besides helping to
clarify the relationship between the GRW theory and BM, its merits make it
worth considering in its own right.Comment: 13 page
The EPR experiment in the energy-based stochastic reduction framework
We consider the EPR experiment in the energy-based stochastic reduction
framework. A gedanken set up is constructed to model the interaction of the
particles with the measurement devices. The evolution of particles' density
matrix is analytically derived. We compute the dependence of the
disentanglement rate on the parameters of the model, and study the dependence
of the outcome probabilities on the noise trajectories. Finally, we argue that
these trajectories can be regarded as non-local hidden variables.Comment: 11 pages, 5 figure
Dynamical state reduction in an EPR experiment
A model is developed to describe state reduction in an EPR experiment as a
continuous, relativistically-invariant, dynamical process. The system under
consideration consists of two entangled isospin particles each of which undergo
isospin measurements at spacelike separated locations. The equations of motion
take the form of stochastic differential equations. These equations are solved
explicitly in terms of random variables with a priori known probability
distribution in the physical probability measure. In the course of solving
these equations a correspondence is made between the state reduction process
and the problem of classical nonlinear filtering. It is shown that the solution
is covariant, violates Bell inequalities, and does not permit superluminal
signaling. It is demonstrated that the model is not governed by the Free Will
Theorem and it is argued that the claims of Conway and Kochen, that there can
be no relativistic theory providing a mechanism for state reduction, are false.Comment: 19 pages, 3 figure
REACTIVITY OF CHLOROPHYLL a/b-PROTEINS AND MICELLAR TRITON X-100 COMPLEXES OF CHLOROPHYLLS a OR b WITH BOROHYDRIDE
The reaction of several plant chlorophyll-protein complexes with NaBH4 has been studied by absorption spectroscopy. In all the complexes studied, chlorophyll b is more reactive than Chi a, due to preferential reaction of its formyl substituent at C-7. The complexes also show large variations in reactivity towards NaBH4 and the order of reactivity is: LHCI > PSII complex > LHCII > PSI > P700 (investigated as a component of PSI). Differential pools of the same type of chlorophyll have been observed in several complexes.
Parallel work was undertaken on the reactivity of micellar complexes of chlorophyll a and of chlorophyll b with NaBH4 to study the effect of aggregation state on this reactivity. In these complexes, both chlorophyll a and b show large variations in reactivity in the order monomer > oligomer > polymer with chlorophyll b generally being more reactive than chlorophyll a. It is concluded that aggregation decreases the reactivity of chlorophylls towards NaBH4 in vitro, and may similarly decrease reactivity in naturally-occurring chlorophyll-protein complexes
Minimal Impairment in a Rat Model of Duration Discrimination Following Excitotoxic Lesions of Primary Auditory and Prefrontal Cortices
We present a behavioral paradigm for the study of duration perception in the rat, and report the result of neurotoxic lesions that have the goal of identifying sites that mediate duration perception. Using a two-alternative forced-choice paradigm, rats were either trained to discriminate durations of pure tones (range = [200,500] ms; boundary = 316 ms; Weber fraction after training = 0.24 ± 0.04), or were trained to discriminate frequencies of pure tones (range = [8,16] kHz; boundary = 11.3 kHz; Weber = 0.16 ± 0.11); the latter task is a control for non-timing-specific aspects of the former. Both groups discriminate the same class of sensory stimuli, use the same motions to indicate decisions, have identical trial structures, and are trained to psychophysical threshold; the tasks are thus matched in a number of sensorimotor and cognitive demands. We made neurotoxic lesions of candidate timing-perception areas in the cerebral cortex of both groups. Following extensive bilateral lesions of the auditory cortex, the performance of the frequency discrimination group was significantly more impaired than that of the duration discrimination group. We also found that extensive bilateral lesions of the medial prefrontal cortex resulted in little to no impairment of both groups. The behavioral framework presented here provides an audition-based approach to study the neural mechanisms of time estimation and memory for durations
Quantum noise and stochastic reduction
In standard nonrelativistic quantum mechanics the expectation of the energy
is a conserved quantity. It is possible to extend the dynamical law associated
with the evolution of a quantum state consistently to include a nonlinear
stochastic component, while respecting the conservation law. According to the
dynamics thus obtained, referred to as the energy-based stochastic Schrodinger
equation, an arbitrary initial state collapses spontaneously to one of the
energy eigenstates, thus describing the phenomenon of quantum state reduction.
In this article, two such models are investigated: one that achieves state
reduction in infinite time, and the other in finite time. The properties of the
associated energy expectation process and the energy variance process are
worked out in detail. By use of a novel application of a nonlinear filtering
method, closed-form solutions--algebraic in character and involving no
integration--are obtained for both these models. In each case, the solution is
expressed in terms of a random variable representing the terminal energy of the
system, and an independent noise process. With these solutions at hand it is
possible to simulate explicitly the dynamics of the quantum states of
complicated physical systems.Comment: 50 page
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