The Geography of Giving: The Effect of Corporate Headquarters on Local Charities

We use data on the locations of the head offices of publicly traded U.S. firms to study the impact of corporate headquarters on the receipts of local charitable organizations. Cities like Houston, San Jose, and San Francisco gained significant numbers of corporate headquarters over the past two decades, while cities like Chicago and Los Angeles lost. Our analysis suggests that attracting or retaining the headquarters of an average firm yields approximately $10 million per year in contributions to local non-profits, while the headquarters of a larger firm (one ranked among the top 1000 in total market value) yields about$25 million per year. Likewise, we find that each $1000 increase in the market value of the firms headquartered in a city yields 70 cents or more to local non-profits. Most of the increase in charitable contributions arises from an effect on the number of highly-compensated individuals in a city, rather than through direct donations by the corporations themselves

Minimum Distance Distribution of Irregular Generalized LDPC Code Ensembles

In this paper, the minimum distance distribution of irregular generalized LDPC (GLDPC) code ensembles is investigated. Two classes of GLDPC code ensembles are analyzed; in one case, the Tanner graph is regular from the variable node perspective, and in the other case the Tanner graph is completely unstructured and irregular. In particular, for the former ensemble class we determine exactly which ensembles have minimum distance growing linearly with the block length with probability approaching unity with increasing block length. This work extends previous results concerning LDPC and regular GLDPC codes to the case where a hybrid mixture of check node types is used.Comment: 5 pages, 1 figure. Submitted to the IEEE International Symposium on Information Theory (ISIT) 201

On the Growth Rate of the Weight Distribution of Irregular Doubly-Generalized LDPC Codes

In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC) codes is derived. The expression is compact and generalizes existing results for LDPC and generalized LDPC (GLDPC) codes. Assuming that there exist check and variable nodes with minimum distance 2, it is shown that the growth rate depends only on these nodes. An important connection between this new result and the stability condition of D-GLDPC codes over the BEC is highlighted. Such a connection, previously observed for LDPC and GLDPC codes, is now extended to the case of D-GLDPC codes.Comment: 10 pages, 1 figure, presented at the 46th Annual Allerton Conference on Communication, Control and Computing (this version includes additional appendix

Spectral Shape of Check-Hybrid GLDPC Codes

This paper analyzes the asymptotic exponent of both the weight spectrum and the stopping set size spectrum for a class of generalized low-density parity-check (GLDPC) codes. Specifically, all variable nodes (VNs) are assumed to have the same degree (regular VN set), while the check node (CN) set is assumed to be composed of a mixture of different linear block codes (hybrid CN set). A simple expression for the exponent (which is also referred to as the growth rate or the spectral shape) is developed. This expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. Furthermore, it is shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function.Comment: 6 pages, 3 figures. Presented at the IEEE ICC 2010, Cape Town, South Africa. A minor typo in equation (9) has been correcte

Growth Rate of the Weight Distribution of Doubly-Generalized LDPC Codes: General Case and Efficient Evaluation

The growth rate of the weight distribution of irregular doubly-generalized LDPC (D-GLDPC) codes is developed and in the process, a new efficient numerical technique for its evaluation is presented. The solution involves simultaneous solution of a 4 x 4 system of polynomial equations. This represents the first efficient numerical technique for exact evaluation of the growth rate, even for LDPC codes. The technique is applied to two example D-GLDPC code ensembles.Comment: 6 pages, 1 figure. Proc. IEEE Globecom 2009, Hawaii, USA, November 30 - December 4, 200

Stability of Iterative Decoding of Multi-Edge Type Doubly-Generalized LDPC Codes Over the BEC

Using the EXIT chart approach, a necessary and sufficient condition is developed for the local stability of iterative decoding of multi-edge type (MET) doubly-generalized low-density parity-check (D-GLDPC) code ensembles. In such code ensembles, the use of arbitrary linear block codes as component codes is combined with the further design of local Tanner graph connectivity through the use of multiple edge types. The stability condition for these code ensembles is shown to be succinctly described in terms of the value of the spectral radius of an appropriately defined polynomial matrix.Comment: 6 pages, 3 figures. Presented at Globecom 2011, Houston, T

On the measurement of frequency and of its sample variance with high-resolution counters

A frequency counter measures the input frequency $\bar{\nu}$ averaged over a suitable time $\tau$, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by averaging multiple frequency measurements highly overlapped. In the presence of additive white noise or white phase noise, the square uncertainty improves from $\smash{\sigma^2_\nu\propto1/\tau^2}$ to $\smash{\sigma^2_\nu\propto1/\tau^3}$. Surprisingly, when a file of contiguous data is fed into the formula of the two-sample (Allan) variance $\smash{\sigma^2_y(\tau)=\mathbb{E}\{\frac12(\bar{y}_{k+1}-\bar{y}_k) ^2\}}$ of the fractional frequency fluctuation $y$, the result is the \emph{modified} Allan variance mod $\sigma^2_y(\tau)$. But if a sufficient number of contiguous measures are averaged in order to get a longer $\tau$ and the data are fed into the same formula, the results is the (non-modified) Allan variance. Of course interpretation mistakes are around the corner if the counter internal process is not well understood.Comment: 14 pages, 5 figures, 1 table, 18 reference

Impact of Beyond the Standard Model Physics in the Detection of the Cosmic Neutrino Background

We discuss the effect of Beyond the Standard Model charged current interactions on the detection of the Cosmic Neutrino Background by neutrino capture on tritium in a PTOLEMY-like detector. We show that the total capture rate can be substantially modified for Dirac neutrinos if scalar or tensor right-chiral currents, with strength consistent with current experimental bounds, are at play. We find that the total capture rate for Dirac neutrinos, $\Gamma_{\rm D}^{\rm BSM}$, can be between 0.3 to 2.2 of what is expected for Dirac neutrinos in the Standard Model, $\Gamma_{\rm D}^{\rm SM}$, so that it can be made as large as the rate expected for Majorana neutrinos with only Standard Model interactions. A non-negligible primordial abundance of right-handed neutrinos can only worsen the situation, increasing $\Gamma_{\rm D}^{\rm BSM}$ by 30 to 90\%. On the other hand, if a much lower total rate is measured than what is expected for $\Gamma_{\rm D}^{\rm SM}$, it may be a sign of new physics.Comment: Version published in JHEP. Some comments and references adde