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

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

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

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

Electron-vibration interaction in single-molecule junctions: from contact to tunneling regime

Point contact spectroscopy on a H2O molecule bridging Pt electrodes reveals a clear crossover between enhancement and reduction of the conductance due to electron-vibration interaction. As single channel models predict such a crossover at transmission probability of t=0.5, we used shot noise measurements to analyze the transmission and observed at least two channels across the junction where the dominant channel has t=0.51+/-0.01 transmission probability at the crossover conductance, which is consistent with the predictions for single-channel models.Comment: 4 pages, 1 table, 4 figure

Contributions of episodic retrieval and mentalizing to autobiographical thought: Evidence from functional neuroimaging, resting-state connectivity, and fMRI meta-analyses

A growing number of studies suggest the brain's "default network" becomes engaged when individuals recall their personal past or simulate their future. Recent reports of heterogeneity within the network raise the possibility that these autobiographical processes comprised of multiple component processes, each supported by distinct functional-anatomic subsystems. We previously hypothesized that a medial temporal subsystem contributes to autobiographical memory and future thought by enabling individuals to retrieve prior information and bind this information into a mental scene. Conversely, a dorsal medial subsystem was proposed to support social-reflective aspects of autobiographical thought, allowing individuals to reflect on the mental states of one's self and others (i.e. "mentalizing"). To test these hypotheses, we first examined activity in the default network subsystems as participants performed two commonly employed tasks of episodic retrieval and mentalizing. In a subset of participants, relationships among task-evoked regions were examined at rest, in the absence of an overt task. Finally, large-scale fMRI meta-analyses were conducted to identify brain regions that most strongly predicted the presence of episodic retrieval and mentalizing, and these results were compared to meta-analyses of autobiographical tasks. Across studies, laboratory-based episodic retrieval tasks were preferentially linked to the medial temporal subsystem, while mentalizing tasks were preferentially linked to the dorsal medial subsystem. In turn, autobiographical tasks engaged aspects of both subsystems. These results suggest the default network is a heterogeneous brain system whose subsystems support distinct component processes of autobiographical thought