630 research outputs found
Constructive function approximation: theory and practice
In this paper we study the theoretical limits of finite constructive convex approximations of a given function in a Hilbert space using elements taken from a reduced subset. We also investigate the trade-off between the global error and the partial error during the iterations of the solution. These results are then specialized to constructive function approximation using sigmoidal neural networks. The emphasis then shifts to the implementation issues associated with the problem of achieving given approximation errors when using a finite number of nodes and a finite data set for training
Neural networks in fault detection: a case study
We study the applications of neural nets in the area of fault detection in real vibrational data. The study is one of the first to include a large set of real vibrational data and to illustrate the potential as well as the limitations of neural networks for fault detection
Number-Phase Wigner Representation for Efficient Stochastic Simulations
Phase-space representations based on coherent states (P, Q, Wigner) have been
successful in the creation of stochastic differential equations (SDEs) for the
efficient stochastic simulation of high dimensional quantum systems. However
many problems using these techniques remain intractable over long integrations
times. We present a number-phase Wigner representation that can be unraveled
into SDEs. We demonstrate convergence to the correct solution for an anharmonic
oscillator with small dampening for significantly longer than other phase space
representations. This process requires an effective sampling of a non-classical
probability distribution. We describe and demonstrate a method of achieving
this sampling using stochastic weights.Comment: 7 pages, 1 figur
Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier
The transmission of an interacting Bose-Einstein condensate incident on a
repulsive Gaussian barrier is investigated through numerical simulation. The
dynamics associated with interatomic interactions are studied across a broad
parameter range not previously explored. Effective 1D Gross-Pitaevskii equation
(GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE)
simulations in order to isolate purely coherent matterwave effects. Quantum
tunneling is then defined as the portion of the GPE transmission not described
by the classical BVE. An exponential dependence of transmission on barrier
height is observed in the purely classical simulation, suggesting that
observing such exponential dependence is not a sufficient condition for quantum
tunneling. Furthermore, the transmission is found to be predominately described
by classical effects, although interatomic interactions are shown to modify the
magnitude of the quantum tunneling. Interactions are also seen to affect the
amount of classical transmission, producing transmission in regions where the
non-interacting equivalent has none. This theoretical investigation clarifies
the contribution quantum tunneling makes to overall transmission in
many-particle interacting systems, potentially informing future tunneling
experiments with ultracold atoms.Comment: Close to the published versio
Non-destructive shadowgraph imaging of ultracold atoms
An imaging system is presented that is capable of far-detuned non-destructive
imaging of a Bose-Einstein condensate with the signal proportional to the
second spatial derivative of the density. Whilst demonstrated with application
to , the technique generalizes to other atomic species and is
shown to be capable of a signal to noise of at GHz detuning with
in-trap images showing no observable heating or atom loss. The technique
is also applied to the observation of individual trajectories of stochastic
dynamics inaccessible to single shot imaging. Coupled with a fast optical phase
lock loop, the system is capable of dynamically switching to resonant
absorption imaging during the experiment.Comment: 4 pages, 5 figure
Quantum entanglement between electronic and vibrational degrees of freedom in molecules
We consider the quantum entanglement of the electronic and vibrational
degrees of freedom in molecules with a tendency towards double welled
potentials using model coupled harmonic diabatic potential-energy surfaces. The
von Neumann entropy of the reduced density matrix is used to quantify the
electron-vibration entanglement for the lowest two vibronic wavefunctions in
such a bipartite system. Significant entanglement is found only in the region
in which the ground vibronic state contains a density profile that is bimodal
(i.e., contains two separate local minima). However, in this region two
distinct types of entanglement are found: (1) entanglement that arises purely
from the degeneracy of energy levels in the two potential wells and which is
destroyed by slight asymmetry, and (2) entanglement that involves strongly
interacting states in each well that is relatively insensitive to asymmetry.
These two distinct regions are termed fragile degeneracy-induced entanglement
and persistent entanglement, respectively. Six classic molecular systems
describable by two diabatic states are considered: ammonia, benzene,
semibullvalene, pyridine excited triplet states, the Creutz-Taube ion, and the
radical cation of the "special pair" of chlorophylls involved in
photosynthesis. These chemically diverse systems are all treated using the same
general formalism and the nature of the entanglement that they embody is
elucidated
Spin correlations as a probe of quantum synchronization in trapped ion phonon-lasers
We investigate quantum synchronization theoretically in a system consisting of two cold ions in microtraps. The ions' motion is damped by a standing-wave laser whilst also being driven by a blue-detuned laser which results in self-oscillation. Working in a non-classical regime, where these oscillations contain only a few phonons and have a sub-Poissonian number variance, we explore how synchronization occurs when the two ions are weakly coupled using a probability distribution for the relative phase. We show that strong correlations arise between the spin and vibrational degrees of freedom within each ion and find that when two ions synchronize their spin degrees of freedom in turn become correlated. This allows one to indirectly infer the presence of synchronization by measuring the ions' internal state
Functional significance may underlie the taxonomic utility of single amino acid substitutions in conserved proteins
We hypothesized that some amino acid substitutions in conserved proteins that are strongly fixed by critical functional roles would show lineage-specific distributions. As an example of an archetypal conserved eukaryotic protein we considered the active site of ß-tubulin. Our analysis identified one amino acid substitution—ß-tubulin F224—which was highly lineage specific. Investigation of ß-tubulin for other phylogenetically restricted amino acids identified several with apparent specificity for well-defined phylogenetic groups. Intriguingly, none showed specificity for “supergroups” other than the unikonts. To understand why, we analysed the ß-tubulin Neighbor-Net and demonstrated a fundamental division between core ß-tubulins (plant-like) and divergent ß-tubulins (animal and fungal). F224 was almost completely restricted to the core ß-tubulins, while divergent ß-tubulins possessed Y224. Thus, our specific example offers insight into the restrictions associated with the co-evolution of ß-tubulin during the radiation of eukaryotes, underlining a fundamental dichotomy between F-type, core ß-tubulins and Y-type, divergent ß-tubulins. More broadly our study provides proof of principle for the taxonomic utility of critical amino acids in the active sites of conserved proteins
- …