A bijection between unicellular and bicellular maps

In this paper we present a combinatorial proof of a relation between the generating functions of unicellular and bicellular maps. This relation is a consequence of the Schwinger-Dyson equation of matrix theory. Alternatively it can be proved using representation theory of the symmetric group. Here we give a bijective proof by rewiring unicellular maps of topological genus $(g+1)$ into bicellular maps of genus $g$ and pairs of unicellular maps of lower topological genera. Our result has immediate consequences for the folding of RNA interaction structures, since the time complexity of folding the transformed structure is $O((n+m)^5)$, where $n,m$ are the lengths of the respective backbones, while the folding of the original structure has $O(n^6)$ time complexity, where $n$ is the length of the longer sequence.Comment: 18 pages, 13 figure

A n-qubit controlled phase gate with superconducting quantum interference devices coupled to a resonator

We present a way to realize a $n$-qubit controlled phase gate with superconducting quantum interference devices (SQUIDs) by coupling them to a superconducting resonator. In this proposal, the two logical states of a qubit are represented by the two lowest levels of a SQUID. An intermediate level of each SQUID is utilized to facilitate coherent control and manipulation of quantum states of the qubits. It is interesting to note that a $n$-qubit controlled phase gate can be achieved with $n$ SQUIDs by successively applying a $\pi /2$ Jaynes-Cummings pulse to each of the $n-1$ control SQUIDs before and after a $\pi$ Jaynes-Cummings pulse on the target SQUID.Comment: 9 pages, 4 figures, 1 table, RevTeX, Resubmitted to Phys. Rev.

Experimental study of contact transition control incorporating joint acceleration feedback

Joint acceleration and velocity feedbacks are incorporated into a classical internal force control of a robot in contact with the environment. This is intended to achieve a robust contact transition and force tracking performance for varying unknown environments, without any need of adjusting the controller parameters, A unified control structure is proposed for free motion, contact transition, and constrained motion in view of the consumption of the initial kinetic energy generated by a nonzero impact velocity. The influence of the velocity and acceleration feedbacks, which are introduced especially for suppressing the transition oscillation, on the postcontact tracking performance is discussed. Extensive experiments are conducted on the third joint of a three-link direct-drive robot to verify the proposed scheme for environments of various stiffnesses, including elastic (sponge), less elastic (cardboard), and hard (steel plate) surfaces. Results are compared with those obtained by the transition control scheme without the acceleration feedback. The ability of the proposed control scheme in resisting the force disturbance during the postcontact period is also experimentally investigated

Scalable Compression of Deep Neural Networks

Deep neural networks generally involve some layers with mil- lions of parameters, making them difficult to be deployed and updated on devices with limited resources such as mobile phones and other smart embedded systems. In this paper, we propose a scalable representation of the network parameters, so that different applications can select the most suitable bit rate of the network based on their own storage constraints. Moreover, when a device needs to upgrade to a high-rate network, the existing low-rate network can be reused, and only some incremental data are needed to be downloaded. We first hierarchically quantize the weights of a pre-trained deep neural network to enforce weight sharing. Next, we adaptively select the bits assigned to each layer given the total bit budget. After that, we retrain the network to fine-tune the quantized centroids. Experimental results show that our method can achieve scalable compression with graceful degradation in the performance.Comment: 5 pages, 4 figures, ACM Multimedia 201

Spherically symmetric trapping horizons, the Misner-Sharp mass and black hole evaporation

Understood in terms of pure states evolving into mixed states, the possibility of information loss in black holes is closely related to the global causal structure of spacetime, as is the existence of event horizons. However, black holes need not be defined by event horizons, and in fact we argue that in order to have a fully unitary evolution for black holes, they should be defined in terms of something else, such as a trapping horizon. The Misner-Sharp mass in spherical symmetry shows very simply how trapping horizons can give rise to black hole thermodynamics, Hawking radiation and singularities. We show how the Misner-Sharp mass can also be used to give insights into the process of collapse and evaporation of locally defined black holes.Comment: 9 pages, 10 figure

Unusual persistence of superconductivity against high magnetic fields in the strongly-correlated iron-chalcogenide film FeTe:Ox_{x}

We report an unusual persistence of superconductivity against high magnetic fields in the iron chalcogenide film FeTe:O$_{x}$ below ~ 2.5 K. Instead of saturating like a mean-field behavior with a single order parameter, the measured low-temperature upper critical field increases progressively, suggesting a large supply of superconducting states accessible via magnetic field or low-energy thermal fluctuations. We demonstrate that superconducting states of finite momenta can be realized within the conventional theory, despite its questionable applicability. Our findings reveal a fundamental characteristic of superconductivity and electronic structure in the strongly-correlated iron-based superconductors.Comment: 10 pages, 3 figure

Crossover from Kramers to phase-diffusion switching in hysteretic DC-SQUIDs

We have measured and propose a model for switching rates in hysteretic DC-SQUID in the regime where phase diffusion processes start to occur. We show that the switching rates in this regime are smaller than the rates given by Kramers' formula due to retrapping of Josephson phase. The retrapping process, which is affected by the frequency dependent impedance of the environment of the DC-SQUID, leads to a peaked second moment of the switching distribution as a function of temperature. The temperature where the peaks occur are proportional to the critical current of the DC- SQUID.Comment: 4 pages, 4 figure