7,113 research outputs found
The SIC Question: History and State of Play
Recent years have seen significant advances in the study of symmetric
informationally complete (SIC) quantum measurements, also known as maximal sets
of complex equiangular lines. Previously, the published record contained
solutions up to dimension 67, and was with high confidence complete up through
dimension 50. Computer calculations have now furnished solutions in all
dimensions up to 151, and in several cases beyond that, as large as dimension
844. These new solutions exhibit an additional type of symmetry beyond the
basic definition of a SIC, and so verify a conjecture of Zauner in many new
cases. The solutions in dimensions 68 through 121 were obtained by Andrew
Scott, and his catalogue of distinct solutions is, with high confidence,
complete up to dimension 90. Additional results in dimensions 122 through 151
were calculated by the authors using Scott's code. We recap the history of the
problem, outline how the numerical searches were done, and pose some
conjectures on how the search technique could be improved. In order to
facilitate communication across disciplinary boundaries, we also present a
comprehensive bibliography of SIC research.Comment: 16 pages, 1 figure, many references; v3: updating bibliography,
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Detection of subthreshold pulses in neurons with channel noise
Neurons are subject to various kinds of noise. In addition to synaptic noise,
the stochastic opening and closing of ion channels represents an intrinsic
source of noise that affects the signal processing properties of the neuron. In
this paper, we studied the response of a stochastic Hodgkin-Huxley neuron to
transient input subthreshold pulses. It was found that the average response
time decreases but variance increases as the amplitude of channel noise
increases. In the case of single pulse detection, we show that channel noise
enables one neuron to detect the subthreshold signals and an optimal membrane
area (or channel noise intensity) exists for a single neuron to achieve optimal
performance. However, the detection ability of a single neuron is limited by
large errors. Here, we test a simple neuronal network that can enhance the
pulse detecting abilities of neurons and find dozens of neurons can perfectly
detect subthreshold pulses. The phenomenon of intrinsic stochastic resonance is
also found both at the level of single neurons and at the level of networks. At
the network level, the detection ability of networks can be optimized for the
number of neurons comprising the network.Comment: 14 pages, 9 figure
Multimodal transition and stochastic antiresonance in squid giant axons
The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G.
Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant
axons stimulated by periodic sequence of short current pulses is interpreted
within the Hodgkin-Huxley model. The minimum of the firing rate as a function
of the stimulus amplitude in the high-frequency regime is due to the
multimodal transition. Below this singular point only odd multiples of the
driving period remain and the system is highly sensitive to noise. The
coefficient of variation has a maximum and the firing rate has a minimum as a
function of the noise intensity which is an indication of the stochastic
coherence antiresonance. The model calculations reproduce the frequency of
occurrence of the most common modes in the vicinity of the transition. A linear
relation of output frequency vs. for above the transition is also
confirmed.Comment: 5 pages, 9 figure
Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator
In a system of non-linear chemical reactions called the Brusselator, we show
that {\it intrinsic noise} can be regulated to drive it to exhibit resonance in
the presence of a sub-threshold signal. The phenomena of periodic stochastic
resonance and aperiodic stochastic resonance, hitherto studied mostly with
extrinsic noise, is demonstrated here to occur with inherent systemic noise
using exact stochastic simulation algorithm due to Gillespie. The role of
intrinsic noise in a couple of other phenomena is also discussed.Comment: 7 pages, 5 figure
Brain natriuretic peptide and NT-proBNP levels reflect pulmonary artery systolic pressure in trekkers at high altitude.
Our objective was to evaluate the utility of the natriuretic peptides BNP (brain natriuretic peptide) and NT-proBNP as markers of pulmonary artery systolic pressure (PASP) in trekkers ascending to high altitude (HA). 20 participants had BNP and NT-proBNP assayed and simultaneous echocardiographic assessment of PASP performed during a trek to 5150 m. PASP increased significantly (p=0.006) with ascent from 24+/-4 to 39+/-11 mm Hg at 5150 m. At 5150 m those with a PASP>/=40 mm Hg (n=8) (versus those with PASP/=400 pg/ml) rise in NT-proBNP at 5150 m (n=4) PASP was significantly higher: 45.9+/-7.5 vs. 32.2+/-6.2 mm Hg (p=0.015). BNP and NT-proBNP may reflect elevated PASP, a central feature of high altitude pulmonary oedema, at HA
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