4,251 research outputs found
Computing with the Integrate and Fire Neuron: Weber's Law, Multiplication and Phase Detection
The integrate and fire model (Stein, 1967) provides an analytically tractable formalism of neuronal firing rate in terms of a neuron's membrane time constant, threshold and refractory period. Integrate and fire (IAF) neurons have mainly been used to model physiologically realistic spike trains but little application of the IAF model appears to have been made in an explicitly computational context. In this paper we show that the transfer function of an IAF neuron provides, over a wide parameter range, a compressive nonlinearity sufficiently close to that of the logarithm so that IAF neurons can be used to multiply neural signals by mere addition of their outputs. Thus, although the IAF transfer function is not explicitly logarithmic, its compressive parameter regime supports a simple, single neuron model for multiplication. A simulation of the IAF multiplier shows that under a wide choice of parameters, the IAF neuron can multiply its inputs to within a 5% relative error. We also show that an IAF neuron under a different, yet biologically reasonable, parameter regime can have a quasi-linear transfer function, acting as an adder or a gain node. We then show an application in which the compressive transfer function of the IAF model provides a simple mechanism for phase-detection: multiplication of 40Hz phasic inputs followed by low-pass filtering yields an output that is a quasi-linear function of the relative phase of the inputs. This is a neural version of the heterodyne phase detection principle. Finally, we briefly discuss the precision and dynamic range of an IAF multiplier that is restricted to reasonable firing rates (in the range of 10-300 Hz) and reasonable computation time (in the range of 25-200 milliseconds).National Institute of Mental Health (5R01MH45969-04); Office of Naval Research (N00014-95-1-0409
Tweezers controlled resonator
We experimentally demonstrate trapping a microdroplet with an optical tweezer
and then enabling it as a microresonator by bringing it close to a tapered
fiber coupler. Our tweezers facilitated the tuning of the coupling from the
under-coupled to the critically coupled regime with an optical Q of 12 million
and microresonator size at the 85 mirons scale.Comment: 5 pages, 4 figure
Beaming Binaries - a New Observational Category of Photometric Binary Stars
The new photometric space-borne survey missions CoRoT and Kepler will be able
to detect minute flux variations in binary stars due to relativistic beaming
caused by the line-of-sight motion of their components. In all but very short
period binaries (P>10d), these variations will dominate over the ellipsoidal
and reflection periodic variability. Thus, CoRoT and Kepler will discover a new
observational class: photometric beaming binary stars. We examine this new
category and the information that the photometric variations can provide. The
variations that result from the observatory heliocentric velocity can be used
to extract some spectral information even for single stars.Comment: 15 pages, 4 figures, accpeted for publication in The Astrophysical
Journa
Semi-optimal Practicable Algorithmic Cooling
Algorithmic Cooling (AC) of spins applies entropy manipulation algorithms in
open spin-systems in order to cool spins far beyond Shannon's entropy bound. AC
of nuclear spins was demonstrated experimentally, and may contribute to nuclear
magnetic resonance (NMR) spectroscopy. Several cooling algorithms were
suggested in recent years, including practicable algorithmic cooling (PAC) and
exhaustive AC. Practicable algorithms have simple implementations, yet their
level of cooling is far from optimal; Exhaustive algorithms, on the other hand,
cool much better, and some even reach (asymptotically) an optimal level of
cooling, but they are not practicable. We introduce here semi-optimal
practicable AC (SOPAC), wherein few cycles (typically 2-6) are performed at
each recursive level. Two classes of SOPAC algorithms are proposed and
analyzed. Both attain cooling levels significantly better than PAC, and are
much more efficient than the exhaustive algorithms. The new algorithms are
shown to bridge the gap between PAC and exhaustive AC. In addition, we
calculated the number of spins required by SOPAC in order to purify qubits for
quantum computation. As few as 12 and 7 spins are required (in an ideal
scenario) to yield a mildly pure spin (60% polarized) from initial
polarizations of 1% and 10%, respectively. In the latter case, about five more
spins are sufficient to produce a highly pure spin (99.99% polarized), which
could be relevant for fault-tolerant quantum computing.Comment: 13 pages, 5 figure
Combining chromosomal arm status and significantly aberrant genomic locations reveals new cancer subtypes
Many types of tumors exhibit chromosomal losses or gains, as well as local
amplifications and deletions. Within any given tumor type, sample specific
amplifications and deletionsare also observed. Typically, a region that is
aberrant in more tumors,or whose copy number change is stronger, would be
considered as a more promising candidate to be biologically relevant to cancer.
We sought for an intuitive method to define such aberrations and prioritize
them. We define V, the volume associated with an aberration, as the product of
three factors: a. fraction of patients with the aberration, b. the aberrations
length and c. its amplitude. Our algorithm compares the values of V derived
from real data to a null distribution obtained by permutations, and yields the
statistical significance, p value, of the measured value of V. We detected
genetic locations that were significantly aberrant and combined them with
chromosomal arm status to create a succint fingerprint of the tumor genome.
This genomic fingerprint is used to visualize the tumors, highlighting events
that are co ocurring or mutually exclusive. We allpy the method on three
different public array CGH datasets of Medulloblastoma and Neuroblastoma, and
demonstrate its ability to detect chromosomal regions that were known to be
altered in the tested cancer types, as well as to suggest new genomic locations
to be tested. We identified a potential new subtype of Medulloblastoma, which
is analogous to Neuroblastoma type 1.Comment: 34 pages, 3 figures; to appear in Cancer Informatic
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