Symmetries of coupled harmonic oscillators

It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2)

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

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

Iwasawa Effects in Multi-layer Optics

There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two space-like and one time-like dimensions, or the $Sp(2)$ group which is a standard theoretical tool in optics. Among the interesting mathematical properties of this group, the Iwasawa decomposition drastically simplifies the matrix algebra under certain conditions, and leads to a concise expression for the S-matrix for transmitted and reflected rays. It is shown that the Iwasawa effect can be observed in multi-layer optics, and a sample calculation of the S-matrix is given.Comment: RevTex 10 pages including 1 psfi

Reduction of Activation Energy Barrier of Stone-Wales Transformation in Endohedral Metallofullerenes

We examine effects of encapsulated metal atoms inside a C$_{60}$ molecule on the activation energy barrier to the Stone-Wales transformation using {\it ab initio} calculations. The encapsulated metal atoms we study are K, Ca and La which nominally donate one, two and three electrons to the C$_{60}$ cage, respectively. We find that isomerization of the endohedral metallofullerene via the Stone-Wales transformation can occur more easily than that of the empty fullerene owing to the charge transfer. When K, Ca and La atoms are encapsulated inside the fullerene, the activation energy barriers are lowered by 0.30, 0.55 and 0.80 eV, respectively compared with that of the empty C$_{60}$ (7.16 eV). The lower activation energy barrier of the Stone-Wales transformation implies the higher probability of isomerization and coalescence of metallofullerenes, which require a series of Stone-Wales transformations.Comment: 13 pages, 3 figures, 1 tabl

Squeezed states, time-energy uncertainty relation, and Feynman's rest of the universe

Two illustrative examples are given for Feynman's rest of the universe. The first example is the two-mode squeezed state of light where no measurement is taken for one of the modes. The second example is the relativistic quark model where no measurement is possible for the time-like separation fo quarks confined in a hadron. It is possible to illustrate these examples using the covariant oscillator formalism. It is shown that the lack of symmetry between the position-momentum and time-energy uncertainty relations leads to an increase in entropy when the system is different Lorentz frames

The language of Einstein spoken by optical instruments

Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell's equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics is largely based on two-by-two matrices or $ABCD$ matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincar\'e sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations which correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.Comment: LaTex 8 pages, presented at the 10th International Conference on Quantum Optics (Minsk, Belarus, May-June 2004), to be published in the proceeding