Construction and Applications of CRT Sequences

Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of throughput due to delay offsets, we want to construct protocol sequences whose pairwise Hamming cross-correlation is as close to a constant as possible. In this paper, we present a construction of protocol sequences which is based on the bijective mapping between one-dimensional sequence and two-dimensional array by the Chinese Remainder Theorem (CRT). In the application to the collision channel without feedback, a worst-case lower bound on system throughput is derived.Comment: 16 pages, 5 figures. Some typos in Section V are correcte

Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics

Single-shot real-time characterization of optical waveforms with sub-picosecond resolution is essential for investigating various ultrafast optical dynamics. However, the finite temporal recording length of current techniques hinders comprehensive understanding of many intriguing ultrafast optical phenomena that evolve over a time scale much longer than their fine temporal details. Inspired by the space-time duality and by stitching of multiple microscopic images to achieve a larger field of view in the spatial domain, here a panoramic-reconstruction temporal imaging (PARTI) system is devised to scale up the temporal recording length without sacrificing the resolution. As a proof-of-concept demonstration, the PARTI system is applied to study the dynamic waveforms of slowly-evolved dissipative Kerr solitons in an ultrahigh-Q microresonator. Two 1.5-ns-long comprehensive evolution portraits are reconstructed with 740-fs resolution and dissipative Kerr soliton transition dynamics, in which a multiplet soliton state evolves into stable singlet soliton state, are depicted

Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments

We propose and evaluate a technique for instrumental variables estimation of linear models with conditional heteroskedasticity. The technique uses approximating parametric models for the projection of right hand side variables onto the instrument space, and for conditional heteroskedasticity and serial correlation of the disturbance. Use of parametric models allows one to exploit information in all lags of instruments, unconstrained by degrees of freedom limitations. Analytical calculations and simulations indicate that there sometimes are large asymptotic and finite sample efficiency gains relative to conventional estimators (Hansen (1982)), and modest gains or losses depending on data generating process and sample size relative to quasi-maximum likelihood. These results are robust to minor misspecification of the parametric models used by our estimator.

A New Hybrid Framework to Efficiently Model Lines of Sight to Gravitational Lenses

In strong gravitational lens systems, the light bending is usually dominated by one main galaxy, but may be affected by other mass along the line of sight (LOS). Shear and convergence can be used to approximate the contributions from less significant perturbers (e.g. those that are projected far from the lens or have a small mass), but higher order effects need to be included for objects that are closer or more massive. We develop a framework for multiplane lensing that can handle an arbitrary combination of tidal planes treated with shear and convergence and planes treated exactly (i.e., including higher order terms). This framework addresses all of the traditional lensing observables including image positions, fluxes, and time delays to facilitate lens modelling that includes the non-linear effects due to mass along the LOS. It balances accuracy (accounting for higher-order terms when necessary) with efficiency (compressing all other LOS effects into a set of matrices that can be calculated up front and cached for lens modelling). We identify a generalized multiplane mass sheet degeneracy, in which the effective shear and convergence are sums over the lensing planes with specific, redshift-dependent weighting factors.Comment: 13 pages, 2 figure

A General Upper Bound on the Size of Constant-Weight Conflict-Avoiding Codes

Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper bound on the size of conflict-avoiding codes is proved. This upper bound is general in the sense that it is applicable to all code lengths and all Hamming weights. Several existing constructions for conflict-avoiding codes, which are known to be optimal for Hamming weights equal to four and five, are shown to be optimal for all Hamming weights in general.Comment: 10 pages, 1 figur

Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments

We propose and evaluate a technique for instrumental variables estimation of linear models with conditional heteroskedasticity. The technique uses approximating parametric models for the projection of right hand side variables onto the instrument space, and for conditional heteroskedasticity and serial correlation of the disturbance. Use of parametric models allows one to exploit information in all lags of instruments, unconstrained by degrees of freedom limitations. Analytical calculations and simulations indicate that there sometimes are large asymptotic and finite sample efficiency gains relative to conventional estimators (Hansen (1982)), and modest gains or losses depending on data generating process and sample size relative to quasi-maximum likelihood. These results are robust to minor misspecification of the parametric models used by our estimator.