On the (non)rigidity of the Frobenius Endomorphism over Gorenstein Rings

It is well-known that for a large class of local rings of positive characteristic, including complete intersection rings, the Frobenius endomorphism can be used as a test for finite projective dimension. In this paper, we exploit this property to study the structure of such rings. One of our results states that the Picard group of the punctured spectrum of such a ring $R$ cannot have $p$-torsion. When $R$ is a local complete intersection, this recovers (with a purely local algebra proof) an analogous statement for complete intersections in projective spaces first given in SGA and also a special case of a conjecture by Gabber. Our method also leads to many simply constructed examples where rigidity for the Frobenius endomorphism does not hold, even when the rings are Gorenstein with isolated singularity. This is in stark contrast to the situation for complete intersection rings. Also, a related length criterion for modules of finite length and finite projective dimension is discussed towards the end.Comment: Minor changes in Example 2.2 and Theorem 2.9. Conjecture 1.2 was added

Spontaneous and Superfluid Chiral Edge States in Exciton-Polariton Condensates

We present a scheme of interaction-induced topological bandstructures based on the spin anisotropy of exciton-polaritons in semiconductor microcavities. We predict theoretically that this scheme allows the engineering of topological gaps, without requiring a magnetic field or strong spin-orbit interaction (transverse electric-transverse magnetic splitting). Under non-resonant pumping, we find that an initially topologically trivial system undergoes a topological transition upon the spontaneous breaking of phase symmetry associated with polariton condensation. Under resonant coherent pumping, we find that it is also possible to engineer a topological dispersion that is linear in wavevector -- a property associated with polariton superfluidity.Comment: 6 pages, 4 figure

On-Line Portfolio Selection with Moving Average Reversion

On-line portfolio selection has attracted increasing interests in machine learning and AI communities recently. Empirical evidences show that stock's high and low prices are temporary and stock price relatives are likely to follow the mean reversion phenomenon. While the existing mean reversion strategies are shown to achieve good empirical performance on many real datasets, they often make the single-period mean reversion assumption, which is not always satisfied in some real datasets, leading to poor performance when the assumption does not hold. To overcome the limitation, this article proposes a multiple-period mean reversion, or so-called Moving Average Reversion (MAR), and a new on-line portfolio selection strategy named "On-Line Moving Average Reversion" (OLMAR), which exploits MAR by applying powerful online learning techniques. From our empirical results, we found that OLMAR can overcome the drawback of existing mean reversion algorithms and achieve significantly better results, especially on the datasets where the existing mean reversion algorithms failed. In addition to superior trading performance, OLMAR also runs extremely fast, further supporting its practical applicability to a wide range of applications.Comment: ICML201

Chiral field theory of 0−+0^{-+} glueball

A chiral field theory of $0^{-+}$ glueball is presented. By adding a $0^{-+}$ glueball field to a successful Lagrangian of chiral field theory of pseudoscalar, vector, and axial-vector mesons, the Lagrangian of this theory is constructed. The couplings between the pseodoscalar glueball field and mesons are via U(1) anomaly revealed. Qualitative study of the physical processes of the $0^{-+}$ glueball of $m=1.405\textrm{GeV}$ is presented. The theoretical predictions can be used to identify the $0^{-+}$ glueball.Comment: 29 page

Averaged null energy condition in Loop Quantum Cosmology

Wormhole and time machine are very interesting objects in general relativity. However, they need exotic matters which are impossible in classical level to support them. But if we introduce the quantum effects of gravity into the stress-energy tensor, these peculiar objects can be constructed self-consistently. Fortunately, loop quantum cosmology (LQC) has the potential to serve as a bridge connecting the classical theory and quantum gravity. Therefore it provides a simple way for the study of quantum effect in the semiclassical case. As is well known, loop quantum cosmology is very successful to deal with the behavior of early universe. In the early stage, if taken the quantum effect into consideration, inflation is natural because of the violation of every kind of local energy conditions. Similar to the inflationary universe, the violation of the averaged null energy condition is the necessary condition for the traversable wormholes. In this paper, we investigate the averaged null energy condition in LQC in the framework of effective Hamiltonian, and find out that LQC do violate the averaged null energy condition in the massless scalar field coupled model.Comment: 5 page

Correlated Spectral and Temporal Variability in the High-Energy Emission from Blazars

Blazar flare data show energy-dependent lags and correlated variability between optical/X-ray and GeV-TeV energies, and follow characteristic trajectories when plotted in the spectral-index/flux plane. This behavior is qualitatively explained if nonthermal electrons are injected over a finite time interval in the comoving plasma frame and cool by radiative processes. Numerical results are presented which show the importance of the effects of synchrotron self-Compton cooling and plasmoid deceleration. The use of INTEGRAL to advance our understanding of these systems is discussed.Comment: 8 pages, 5 figures, uses epsf.sty, rotate.sty Invited paper in "The Extreme Universe," 3rd INTEGRAL Workshop, 14-18 September 1998, Taorimina, Ital

Method and apparatus for positioning a robotic end effector

A robotic end effector and operation protocol for a reliable grasp of a target object irrespective of the target's contours is disclosed. A robotic hand includes a plurality of jointed fingers, one of which, like a thumb, is in opposed relation to the other. Each finger is comprised of at least two jointed sections, and provided with reflective proximity sensors, one on the inner surface of each finger section. Each proximity sensor comprises a transmitter of a beam of radiant energy and means for receiving reflections of the transmitted energy when reflected by a target object and for generating electrical signals responsive thereto. On the fingers opposed to the thumb, the proximity sensors on the outermost finger sections are aligned in an outer sensor array and the sensors on the intermediate finger sections and sensors on the innermost finger sections are similarly arranged to form an intermediate sensor array and an inner sensor array, respectively. The invention includes a computer system with software and/or circuitry for a protocol comprising the steps in sequence of: (1) approach axis alignment to maximize the number of outer layer sensors which detect the target; (2) non-contact contour following the target by the robot fingers to minimize target escape potential; and (3) closing to rigidize the target including dynamically re-adjusting the end effector finger alignment to compensate for target motion. A signal conditioning circuit and gain adjustment means are included to maintain the dynamic range of low power reflection signals

Type I planet migration in nearly laminar disks - long term behavior

We carry out 2-D high resolution numerical simulations of type I planet migration with different disk viscosities. We find that the planet migration is strongly dependent on disk viscosities. Two kinds of density wave damping mechanisms are discussed. Accordingly, the angular momentum transport can be either viscosity dominated or shock dominated, depending on the disk viscosities. The long term migration behavior is different as well. Influences of the Rossby vortex instability on planet migration are also discussed. In addition, we investigate very weak shock generation in inviscid disks by small mass planets and compare the results with prior analytic results.Comment: Accepted for publication in Ap