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

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

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.

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.

Simulating the 21-cm signal from the Epoch of Reionization

In this thesis, the 21-cm signal from the epoch of reionization is simulated using a combination of N-Body techniques and semi-analytical models. Images, line-of-sight spectra and power spectra of the simulated 21-cm signal are presented. The N-Body code, GADGET-2, is used to obtain the distribution of dark matter and a friends-of-friends algorithm is used to identify dark matter halos to construct halo merger trees. We ran seven simulations with periodic boxes of volumes ranging from (10h(^-1)Mpc)(^3) to (140h(^-1)Mpc)(^3), and particle masses ranging from 6.46 x lO(^4)h(^-1)M(_ʘ) to 1.42 X 10(^9) h(^-1)M(_ʘ). These merger trees are used with the GALFORM semi-analytical model of galaxy formation to predict the locations of galaxies and their ionizing luminosities within the halos. We find that halos in a broad range of masses contribute significantly to the total ionizing emissivity of each simulation. The effect of suppressing gas cooling due to reionization in low mass halos in GALFORM was also investigated. For a redshift of reionization, z(_reion) = 15, this significantly reduces the number of ionizing photons produced at z < 15. This results in a prolonged period of reionization as the Universe makes the transition from neutral to fully ionized. Next, the 21-cm signal and ionization state of the hydrogen is calculated for the simulation box with a volume of (20h(^-1)Mpc)(^3) and a particle mass of 5.17 x 10(^5)h(^-1)M(_ʘ). The hydrogen is assumed to follow the dark matter, and the 21-cm differential brightness temperature is calculated from the distribution of neutral hydrogen. High resolution images and spectra of the 21-cm signal are generated from these neutral hydrogen density fields. A toy model is first investigated, randomly distributed ionized spheres of constant radii are generated to investigate the effect ionized regions have on the 21-cm power spectra. We find that this increases power on the scales of the size of the ionized spheres, but decreases power on small scales. The amount of change in power is sensitive to the overall ionized fraction of the simulation box, increasing the ionized fraction increases the power on the scales of the spheres while decreases the power on small scales. Next, the GALFORM model is investigated. The ionizing luminosities of GALFORM galaxies are used to calculate cosmological Strömgren spheres representing ionized regions. These spheres are "painted" around the location of the galaxies on the density field. We find that the power spectra lack any obvious features due to the range of sizes of the GALFORM ionized regions. However, the power spectra is sensitive to the ionized fraction of the simulation box. The slope of the power spectra decreases as ionized fraction increases. Finally, the temperature field is smoothed over a bandwidth of 200 kHz and a 2-D Gaussian beam with a FWHM of 3 arcmin to emulate the LOFAR telescope beam response. We find that only the largest features, such as large ionized regions, are still identifiable after smoothing. LOFAR should be able to detect the early stages of reionization, but may have difficulties during later stages when much of the brightest 21-cm signal is removed by reionization