4,939 research outputs found
RNNs Implicitly Implement Tensor Product Representations
Recurrent neural networks (RNNs) can learn continuous vector representations
of symbolic structures such as sequences and sentences; these representations
often exhibit linear regularities (analogies). Such regularities motivate our
hypothesis that RNNs that show such regularities implicitly compile symbolic
structures into tensor product representations (TPRs; Smolensky, 1990), which
additively combine tensor products of vectors representing roles (e.g.,
sequence positions) and vectors representing fillers (e.g., particular words).
To test this hypothesis, we introduce Tensor Product Decomposition Networks
(TPDNs), which use TPRs to approximate existing vector representations. We
demonstrate using synthetic data that TPDNs can successfully approximate linear
and tree-based RNN autoencoder representations, suggesting that these
representations exhibit interpretable compositional structure; we explore the
settings that lead RNNs to induce such structure-sensitive representations. By
contrast, further TPDN experiments show that the representations of four models
trained to encode naturally-occurring sentences can be largely approximated
with a bag of words, with only marginal improvements from more sophisticated
structures. We conclude that TPDNs provide a powerful method for interpreting
vector representations, and that standard RNNs can induce compositional
sequence representations that are remarkably well approximated by TPRs; at the
same time, existing training tasks for sentence representation learning may not
be sufficient for inducing robust structural representations.Comment: Accepted to ICLR 201
Brillouin Cooling
We analyze how to exploit Brillouin scattering for the purpose of cooling
opto-mechanical devices and present a quantum-mechanical theory for Brillouin
cooling. Our analysis shows that significant cooling ratios can be obtained
with standard experimental parameters. A further improvement of cooling
efficiency is possible by increasing the dissipation of the optical anti-Stokes
resonance.Comment: 4 pages 3 figure
Continuous-wave Cascaded-Harmonic Generation and Multi-Photon Raman Lasing in Lithium Niobate Whispering-Gallery Resonators
We report experimental demonstration of continuous-wave cascaded-harmonic
generation and Raman lasing in a millimeter-scale lithium niobate
whispering-gallery resonator pumped at a telecommunication-compatible infrared
wavelength. Intensity enhancement through multiple recirculations in the
whispering-gallery resonator and quasi phase-matching through a nonuniform
crystal poling enable simultaneous cascaded-harmonic generation up to the
fourth-harmonic accompanied by stimulated Raman, two-photon, three-photon, and
four-photon Raman scattering corresponding the molecular vibrational
wavenumbers 632 cm-1 and 255 cm-1 in z-cut lithium niobate at pump power levels
as low as 200mW. We demonstrate simultaneous cascaded-harmonic generation and
Raman lasing by observing the spectrum of the scattered light from the
resonator and by capturing the image of the decoupled light from the resonator
on a color CCD camera
Design and Fabrication of Memristors
This paper details the design and fabrication of memristors in the RIT Semiconductor and Microsystem Fabrication Laboratory. Two methods of partially oxidizing titanium were explored, reactive sputtering and thermal oxidation. It is determined that thermal oxidation allows for greater control over the oxidation process due to an inability to sufficiently control the gas flow in the sputter chamber. Electron beam lithography is used to define holes in oxide in which the memristors will be fabricated. Due to issues with the lithography, fabrication is incomplete and ongoing
Quantum Key Distribution with Classical Bob
Secure key distribution among two remote parties is impossible when both are
classical, unless some unproven (and arguably unrealistic)
computation-complexity assumptions are made, such as the difficulty of
factorizing large numbers. On the other hand, a secure key distribution is
possible when both parties are quantum.
What is possible when only one party (Alice) is quantum, yet the other (Bob)
has only classical capabilities? We present a protocol with this constraint,
and prove its robustness against attacks: we prove that any attempt of an
adversary to obtain information (and even a tiny amount of information)
necessarily induces some errors that the legitimate users could notice.Comment: 4 and a bit pages, 1 figure, RevTe
Tidal scattering of stars on supermassive black holes in galactic centers
Some of the mass that feeds the growth of a massive black hole (BH) in a
galactic center is supplied by tidal disruption of stars that approach it on
unbound, low angular momentum orbits. For each star that is disrupted, others
narrowly escape after being subjected to extreme tidal distortion, spin-up,
mixing and mass-loss, which may affect their evolution and appearance. We show
that it is likely that a significant fraction of the stars around massive BHs
in galactic centers have undergone such extreme tidal interactions and survived
subsequent total disruption, either by being deflected off their orbit or by
missing the BH due to its Brownian motion. We discuss possible long-term
observable consequences of this process, which may be relevant for
understanding the nature of stars in galactic centers, and may provide a
signature of the existence of massive BHs there.Comment: 5 pages 4 figures. ApJL in press, minor changes to reflect journal
version including redifinition of unbound tidally disturbed stars and
additional reference
Near-Infrared Microlensing of Stars by the Super-Massive Black Hole in the Galactic Center
We investigate microlensing amplification of faint stars in the dense stellar
cluster in the Galactic Center (GC) by the super-massive black hole (BH). Such
events would appear very close to the position of the radio source SgrA*, which
is thought to coincide with the BH, and could be observed during the monitoring
of stellar motions in the GC. We use the observed K-band (2.2 um) luminosity
function (KLF) in the GC and in Baade's Window, as well as stellar population
synthesis computations, to construct KLF models for the inner 300 pc of the
Galaxy. These, and the observed dynamical properties of this region, are used
to compute the rates of microlensing events, which amplify stars above
specified detection thresholds. We present computations of the lensing rates
and amplifications as functions of the event durations (weeks to years), for a
range of detection thresholds. We find that short events dominate the total
rate and that long events tend to have large amplifications. For the current
detection limit of K=17 mag, the total microlensing rate is 0.003 1/yr, and the
rate of events with durations >1 yr is 0.001 1/yr. Recent GC proper motion
studies have revealed the possible presence of one or two variable K-band
sources very close to SgrA* (Genzel et al 97; Ghez et al 98). These sources may
have attained peak brightnesses of K~15 mag, about 1.5-2 mag above the
observational detection limits, and appear to have varied on a timescale of ~1
yr. This behavior is consistent with long-duration microlensing of faint stars
by the BH. However, we estimate that the probability that such an event could
have been detected during the course of the recent proper motion studies is
\~0.5%. A ten-fold improvement in the detection limit and 10 yr of monthly
monitoring would increase the total detection probability to ~20%. (Abridged)Comment: 29 p. with 5 figs. To appear in ApJ. Changed to reflect published
version. Short discussions of solar metallicity luminosity function and
star-star microlensing adde
Lifts of convex sets and cone factorizations
In this paper we address the basic geometric question of when a given convex
set is the image under a linear map of an affine slice of a given closed convex
cone. Such a representation or 'lift' of the convex set is especially useful if
the cone admits an efficient algorithm for linear optimization over its affine
slices. We show that the existence of a lift of a convex set to a cone is
equivalent to the existence of a factorization of an operator associated to the
set and its polar via elements in the cone and its dual. This generalizes a
theorem of Yannakakis that established a connection between polyhedral lifts of
a polytope and nonnegative factorizations of its slack matrix. Symmetric lifts
of convex sets can also be characterized similarly. When the cones live in a
family, our results lead to the definition of the rank of a convex set with
respect to this family. We present results about this rank in the context of
cones of positive semidefinite matrices. Our methods provide new tools for
understanding cone lifts of convex sets.Comment: 20 pages, 2 figure
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