An SDP Approach For Solving Quadratic Fractional Programming Problems

This paper considers a fractional programming problem (P) which minimizes a ratio of quadratic functions subject to a two-sided quadratic constraint. As is well-known, the fractional objective function can be replaced by a parametric family of quadratic functions, which makes (P) highly related to, but more difficult than a single quadratic programming problem subject to a similar constraint set. The task is to find the optimal parameter $\lambda^*$ and then look for the optimal solution if $\lambda^*$ is attained. Contrasted with the classical Dinkelbach method that iterates over the parameter, we propose a suitable constraint qualification under which a new version of the S-lemma with an equality can be proved so as to compute $\lambda^*$ directly via an exact SDP relaxation. When the constraint set of (P) is degenerated to become an one-sided inequality, the same SDP approach can be applied to solve (P) {\it without any condition}. We observe that the difference between a two-sided problem and an one-sided problem lies in the fact that the S-lemma with an equality does not have a natural Slater point to hold, which makes the former essentially more difficult than the latter. This work does not, either, assume the existence of a positive-definite linear combination of the quadratic terms (also known as the dual Slater condition, or a positive-definite matrix pencil), our result thus provides a novel extension to the so-called "hard case" of the generalized trust region subproblem subject to the upper and the lower level set of a quadratic function.Comment: 26 page

Preoperative electrophysiological characterization of patients with primary macula-involving rhegmatogenous retinal detachment

Purpose: To determine 1) which components of retinal function are impaired after rhegmatogenous retinal detachment, 2) which outer retinal pathways (rod- or cone-driven) are more severely affected, and 3) whether there is concomitant inner retinal dysfunction. Methods: We conducted a prospective observational study in a large academic institution. We performed preoperative electroretinography on eight patients to assess outer and inner retinal function. In all cases, a comparison between the eye with the detached retina and the control fellow eye was made. Results: Eyes with a detached retina had significantly lower a-wave and b-wave amplitudes with respect to both rod- and cone-dominated testing parameters (P < 0.05) and reduced 30 Hz flicker responses compared to fellow eyes (P < 0.05); the effect size was similar for all significantly reduced parameters (r~0.6). There were no significant differences between eyes with detached retinas and control fellow eyes with respect to b/a-wave ratios, a-wave latencies, or b-wave latencies. Conclusion: Patients with rhegmatogenous retinal detachment have preoperative outer retinal dysfunction equally affecting both rod- and cone-driven pathways, and they have minimal inner retinal dysfunction

Triplet-Tuning: A Novel Family of Non-Empirical Exchange-Correlation Functionals

In the framework of DFT, the lowest triplet excited state, T$_1$, can be evaluated using multiple formulations, the most straightforward of which are UDFT and TDDFT. Assuming the exact XC functional is applied, UDFT and TDDFT provide identical energies for T$_1$ ($E_{\rm T}$), which is also a constraint that we require our XC functionals to obey. However, this condition is not satisfied by most of the popular XC functionals, leading to inaccurate predictions of low-lying, spectroscopically and photochemically important excited states, such as T$_1$ and S$_1$. Inspired by the optimal tuning strategy for frontier orbital energies [Stein, Kronik, and Baer, {\it J. Am. Chem. Soc.} {\bf 2009}, 131, 2818], we proposed a novel and non-empirical prescription of constructing an XC functional in which the agreement between UDFT and TDDFT in $E_{\rm T}$ is strictly enforced. Referred to as "triplet tuning", our procedure allows us to formulate the XC functional on a case-by-case basis using the molecular structure as the exclusive input, without fitting to any experimental data. The first triplet tuned XC functional, TT-$\omega$PBEh, is formulated as a long-range-corrected hybrid of PBE and HF functionals [Rohrdanz, Martins, and Herbert, {\it J. Chem. Phys.} {\bf 2009}, 130, 054112] and tested on four sets of large organic molecules. Compared to existing functionals, TT-$\omega$PBEh manages to provide more accurate predictions for key spectroscopic and photochemical observables, including but not limited to $E_{\rm T}$, $E_{\rm S}$, $\Delta E_{\rm ST}$, and $I$, as it adjusts the effective electron-hole interactions to arrive at the correct excitation energies. This promising triplet tuning scheme can be applied to a broad range of systems that were notorious in DFT for being extremely challenging

Two Energy Release Processes for CMEs: MHD Catastrophe and Magnetic Reconnection

It remains an open question how magnetic energy is rapidly released in the solar corona so as to create solar explosions such as solar flares and coronal mass ejections (CMEs). Recent studies have confirmed that a system consisting of a flux rope embedded in a background field exhibits a catastrophic behavior, and the energy threshold at the catastrophic point may exceed the associated open field energy. The accumulated free energy in the corona is abruptly released when the catastrophe takes place, and it probably serves as the main means of energy release for CMEs at least in the initial phase. Such a release proceeds via an ideal MHD process in contrast with nonideal ones such as magnetic reconnection. The catastrophe results in a sudden formation of electric current sheets, which naturally provide proper sites for fast magnetic reconnection. The reconnection may be identified with a solar flare associated with the CME on one hand, and produces a further acceleration of the CME on the other. On this basis, several preliminary suggestions are made for future observational investigations, especially with the proposed KuaFu satellites, on the roles of the MHD catastrophe and magnetic reconnection in the magnetic energy release associated with CMEs and flares.Comment: 7 pages, 4 figures, Adv. Spa. Res., in press

The kilohertz quasi-periodic oscillations during the Z and atoll phases of the unique transient XTE J1701--462

We analysed 866 observations of the neutron-star low-mass X-ray binary XTE J1701-462 during its 2006-2007 outburst. XTE J1701-462 is the only example so far of a source that during an outburst showed, beyond any doubt, spectral and timing characteristics both of the Z and atoll type. We found that the lower kHz QPO in the atoll phase has a significantly higher coherence and fractional rms amplitude than any of the kHz QPOs seen during the Z phase, and that in the same frequency range, atoll lower kHz QPOs show coherence and fractional rms amplitude, respectively, 2 and 3 times larger than the Z kHz QPOs. Out of the 707 observations in the Z phase, there is no single observation in which the kHz QPOs have a coherence or rms amplitude similar to those seen when XTE J1701-462 was in the atoll phase, even though the total exposure time was about 5 times longer in the Z than in the atoll phase. Since it is observed in the same source, the difference in QPO coherence and rms amplitude between the Z and atoll phase cannot be due to neutron-star mass, magnetic field, spin, inclination of the accretion disk, etc. If the QPO frequency is a function of the radius in the accretion disk in which it is produced, our results suggest that in XTE J1701-462 the coherence and rms amplitude are not uniquely related to this radius. Here we argue that this difference is instead due to a change in the properties of the accretion flow around the neutron star. Regardless of the precise mechanism, our result shows that effects other than the geometry of space time around the neutron star have a strong influence on the coherence and rms amplitude of the kHz QPOs, and therefore the coherence and rms amplitude of the kHz QPOs cannot be simply used to deduce the existence of the innermost stable circular orbit around a neutron star.Comment: 11 pages, 5 figures, 2 tables, submitted to MNRA

Towards Prediction of Non-Radiative Decay Pathways in Organic Compounds I: The Case of Naphthalene Quantum Yields

Many emerging technologies depend on human’s ability to control and manipulate the excited-state properties of molecular systems. These technologies include fluorescent labeling in biomedical imaging, light harvesting in photovoltaics, and electroluminescence in light-emitting devices. All of these systems suffer from non-radiative loss pathways that dissipate electronic energy as heat, which causes the overall system efficiency to be directly linked to quantum yield (Φ) of the molecular excited state. Unfortunately, Φ is very difficult to predict from first principles because the description of a slow non-radiative decay mechanism requires an accurate description of long-timescale excited-state quantum dynamics. In the present study, we introduce an efficient semiempirical method of calculating the fluorescence quantum yield (Φfl) for molecular chromophores, which, based on machine learning, converts simple electronic energies computed using time-dependent density functional theory (TDDFT) into an estimate of Φfl. As with all machine learning strategies, the algorithm needs to be trained on fluorescent dyes for which Φfl’s are known, so as to provide a black-box method which can later predict Φfl’s for chemically similar chromophores that have not been studied experimentally. As a first illustration of how our proposed algorithm can be trained, we examine a family of 25 naphthalene derivatives. The simplest application of the energy gap law is found to be inadequate to explain the rates of internal conversion (IC) or intersystem crossing (ISC) – the electronic properties of at least one higher-lying electronic state (Sn or Tn) or one far-from-equilibrium geometry are typically needed to obtain accurate results. Indeed, the key descriptors turn out to be the transition state between the Franck–Condon minimum a distorted local minimum near an S0/S1 conical intersection (which governs IC) and the magnitude of the spin–orbit coupling (which governs ISC). The resulting Φfl’s are predicted with reasonable accuracy (±22%), making our approach a promising ingredient for high-throughput screening and rational design of the molecular excited states with desired Φ’s. We thus conclude that our model, while semi-empirical in nature, does in fact extract sound physical insight into the challenge of describing non-radiative relaxations

Understanding brønsted-acid catalyzed monomolecular reactions of Alkanes in Zeolite Pores by combining insights from experiment and theory

Acidic zeolites are effective catalysts for the cracking of large hydrocarbon molecules into lower molecular weight products required for transportation fuels. However, the ways in which the zeolite structure affects the catalytic activity at BrOnsted protons are not fully understood. One way to characterize the influence of the zeolite structure on the catalysis is to study alkane cracking and dehydrogenation at very low conversion, conditions for which the kinetics are well defined. To understand the effects of zeolite structure on the measured rate coefficient (k(app)), it is necessary to identify the equilibrium constant for adsorption into the reactant state (Kads-H+) and the intrinsic rate coefficient of the reaction (k(int)) at reaction temperatures, since k(app) is proportional to the product of Kads-H+ and k(int). We show that Kads-H+ cannot be calculated from experimental adsorption data collected near ambient temperature, but can, however, be estimated accurately from configurational-bias Monte Carlo (CBMC) simulations. Using monomolecular cracking and dehydrogenation of C-3-C-6 alkanes as an example, we review recent efforts aimed at elucidating the influence of the acid site location and the zeolite framework structure on the observed values of k(app) and its components, Kads-H+ and k(int)