Marginal empirical likelihood and sure independence feature screening

We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening procedure for linear models and the generalized linear models. Different from most existing feature screening approaches that rely on the magnitudes of some marginal estimators to identify true signals, the proposed screening approach is capable of further incorporating the level of uncertainties of such estimators. Such a merit inherits the self-studentization property of the empirical likelihood approach, and extends the insights of existing feature screening methods. Moreover, we show that our screening approach is less restrictive to distributional assumptions, and can be conveniently adapted to be applied in a broad range of scenarios such as models specified using general moment conditions. Our theoretical results and extensive numerical examples by simulations and data analysis demonstrate the merits of the marginal empirical likelihood approach.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1139 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Miniaturized Power Electronic Interfaces for Ultra-compact Electromechanical Systems

Advanced and ultra-compact electromechanical (EM) systems, such as kinetic energy harvesting and microrobotic systems are deemed as enabling solutions to provide efficient energy conversion. One of the most critical challenges in such systems is to develop tiny power electronic interfaces (PEIs) capable of addressing power conditioning between EM devices and energy storage units. This dissertation presents technologies and topological solutions toward fabricating miniaturized PEIs to efficiently regulate erratic power/voltage for kinetic energy harvesting and drive high-voltage actuators for microrobotic systems. High-frequency resonant-switching topologies are introduced as power stages of PEIs that allow small footprint of the circuit without suffering from switching losses. Two types of bridgeless resonant ac-dc converters are first introduced and developed to efficiently convert arbitrary input voltages into a regulated dc output voltage. The proposed topologies provide direct ac-dc power conversion with less number of components, in comparison to other resonant topologies. A 5-mm×6-mm, 100-mg, 2-MHz and 650-mW prototype is fabricated for validation of capability of converting very-low ac voltages into a relatively higher voltage. A resonant gate drive circuit is designed and utilized to further reduce gating losses under high-frequency switching and light-load condition. The closed-loop efficiency reaches higher than 70% across wide range of input voltages and output powers. In a multi-channel energy harvesting system, a multi-input bridgeless resonant ac-dc converter is developed to achieve ac-dc conversion, step up voltage and match optimal impedance. Alternating voltage of each energy harvesting channel is stepped up through the switching LC network and then rectified by a freewheeling diode. The optimal electrical impedance can be adjusted through resonance impedance matching and pulse-frequency-modulation (PFM) control. In addition, a six-input standalone prototype is fabricated to address power conditioning for a six-channel wind panel. Furthermore, the concepts of miniaturization are incorporated in the context of microrobots. In a mobile microrobotic system, conventional bulky power supplies and electronics used to drive electroactive polymer (EAP) actuators are not practical as on-board energy sources for microrobots. A bidirectional single-stage resonant dc-dc step-up converter is introduced and developed to efficiently drive high-voltage EAP actuators. The converter utilizes resonant capacitors and a coupled-inductor as a soft-switched LC network to step up low input voltages. The circuit is capable of generating explicit high-voltage actuation signals, with capability of recovering unused energy from EAP actuators. A 4-mm × 8-mm, 100-mg and 600-mW prototype has been designed and fabricated to drive an in-plane gap-closing electrostatic inchworm motor. Experimental validations have been carried out to verify the circuit’s ability to step up voltage from 2 V to 100 V and generate two 1-kHz, 100-V driving voltages at 2-nF capacitive loads

Cutting the traintracks: Cauchy, Schubert and Calabi-Yau

In this note we revisit the maximal-codimension residues, or leading singularities, of four-dimensional $L$-loop traintrack integrals with massive legs, both in Feynman parameter space and in momentum (twistor) space. We identify a class of "half traintracks" as the most general degenerations of traintracks with conventional (0-form) leading singularities, although the integrals themselves still have rigidity $\lfloor\frac{L-1}2\rfloor$ due to lower-loop "full traintrack'' subtopologies. As a warm-up exercise, we derive closed-form expressions for their leading singularities both via (Cauchy's) residues in Feynman parameters, and more geometrically using the so-called Schubert problems in momentum twistor space. For $L$-loop full traintracks, we compute their leading singularities as integrals of $(L{-}1)$-forms, which proves that the rigidity is $L{-}1$ as expected; the form is given by an inverse square root of an irreducible polynomial quartic with respect to each variable, which characterizes an $(L{-}1)$-dim Calabi-Yau manifold (elliptic curve, K3 surface, etc.) for any $L$. We also briefly comment on the implications for the "symbology" of these traintrack integrals.Comment: refs updated; 36 pages, 12 figure

Bootstrapping octagons in reduced kinematics from A2A_2 cluster algebras

Multi-loop scattering amplitudes/null polygonal Wilson loops in ${\mathcal N}=4$ super-Yang-Mills are known to simplify significantly in reduced kinematics, where external legs/edges lie in an $1+1$ dimensional subspace of Minkowski spacetime (or boundary of the $\rm AdS_3$ subspace). Since the edges of a $2n$-gon with even and odd labels go along two different null directions, the kinematics is reduced to two copies of $G(2,n)/T \sim A_{n{-}3}$. In the simplest octagon case, we conjecture that all loop amplitudes and Feynman integrals are given in terms of two overlapping $A_2$ functions (a special case of two-dimensional harmonic polylogarithms): in addition to the letters $v, 1+v, w, 1+w$ of $A_1 \times A_1$, there are two letters $v-w, 1- v w$ mixing the two sectors but they never appear together in the same term; these are the reduced version of four-mass-box algebraic letters. Evidence supporting our conjecture includes all known octagon amplitudes as well as new computations of multi-loop integrals in reduced kinematics. By leveraging this alphabet and conditions on first and last entries, we initiate a bootstrap program in reduced kinematics: within the remarkably simple space of overlapping $A_2$ functions, we easily obtain octagon amplitudes up to two-loop NMHV and three-loop MHV. We also briefly comment on the generalization to $2n$-gons in terms of $A_2$ functions and beyond.Comment: 26 pages, several figures and tables, an ancilary fil

Development and application of a packer-type drilling-free liner hanger

AbstractIn liner cementing, the upper cement plug and inner components of a common hanger needs to be drilled out after cementing, which will result in a poor cementing quality or even gas leakage at the flare opening. Therefore, a new packer-type drilling-free liner hanger has been developed, and a hydraulic setting-control packer, a flexible drilling-free seal box, and an auxiliary bearing back-off mechanism that go with the line hanger have been designed at the same time. Specific operation procedures include: (1) run in the liner string to the designed depth, then fully circulate the drilling fluid, finally drop the ball. When the tripping ball gets into the seat, the pressure will go up to cut off the hanging control pin and set the hanger; (2) continue to hold the pressure and cut off the ball seat pin to form circulation; (3) trip in the drill pipe to exert pressure on the hanger, back off to release the hanger from the running tool; (4) lower the drill pipe plug upon the completion of cement injection, cut off the releasing control pin of hollow casing plug, and run down further to bump with the bumping assembly; (5) remove the cementing head and connect the kelly driver, hold pressure again, then slowly pull up the drill tools, exert hydraulic pressure on the setting hydraulic cylinder of the packer assembly to cut off the setting control pin and set the packer; and (6) pull up the tools to the flare opening and wash out excessive cement slurry by circulating to realize free drilling of the whole hole. The successful application of the liner hanger in 127 mm diameter liner in Well BQ203-H1 indicates that the packer-type liner hanger has such advantages as easy hanging and back-off, accurate bumping, simple setting, and sound sealing performance