An Orthogonality Principle for Select-Maximum Estimation of Exponential Variables

It was recently proposed to encode the one-sided exponential source X via K parallel channels, Y1, ..., YK , such that the error signals X - Yi, i = 1,...,K, are one-sided exponential and mutually independent given X. Moreover, it was shown that the optimal estimator \hat{Y} of the source X with respect to the one-sided error criterion, is simply given by the maximum of the outputs, i.e., \hat{Y} = max{Y1,..., YK}. In this paper, we show that the distribution of the resulting estimation error X - \hat{Y} , is equivalent to that of the optimum noise in the backward test-channel of the one-sided exponential source, i.e., it is one-sided exponentially distributed and statistically independent of the joint output Y1,...,YK.Comment: 5 pages. Submitted to ISI

Incremental Refinements and Multiple Descriptions with Feedback

It is well known that independent (separate) encoding of K correlated sources may incur some rate loss compared to joint encoding, even if the decoding is done jointly. This loss is particularly evident in the multiple descriptions problem, where the sources are repetitions of the same source, but each description must be individually good. We observe that under mild conditions about the source and distortion measure, the rate ratio Rindependent(K)/Rjoint goes to one in the limit of small rate/high distortion. Moreover, we consider the excess rate with respect to the rate-distortion function, Rindependent(K, M) - R(D), in M rounds of K independent encodings with a final distortion level D. We provide two examples - a Gaussian source with mean-squared error and an exponential source with one-sided error - for which the excess rate vanishes in the limit as the number of rounds M goes to infinity, for any fixed D and K. This result has an interesting interpretation for a multi-round variant of the multiple descriptions problem, where after each round the encoder gets a (block) feedback regarding which of the descriptions arrived: In the limit as the number of rounds M goes to infinity (i.e., many incremental rounds), the total rate of received descriptions approaches the rate-distortion function. We provide theoretical and experimental evidence showing that this phenomenon is in fact more general than in the two examples above.Comment: 62 pages. Accepted in the IEEE Transactions on Information Theor

Lattice strategies for the dirty multiple access channel

A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa’s strategies (i.e. by a random binning scheme induced by Costa’s auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies (“lattice precoding”) can achieve positive rates independent of the interferences, and in fact in some cases- which depend on the noise variance and power constraints- they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a “helper ” to the other user), and for the “common interference ” case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit

ILLUMINATING THE DARKEST GAMMA-RAY BURSTS WITH RADIO OBSERVATIONS

We present X-ray, optical, near-infrared (IR), and radio observations of gamma-ray bursts (GRBs) 110709B and 111215A, as well as optical and near-IR observations of their host galaxies. The combination of X-ray detections and deep optical/near-IR limits establish both bursts as "dark." Sub-arcsecond positions enabled by radio detections lead to robust host galaxy associations, with optical detections that indicate z ≾ 4 (110709B) and z ≈ 1.8-2.9 (111215A). We therefore conclude that both bursts are dark due to substantial rest-frame extinction. Using the radio and X-ray data for each burst we find that GRB 110709B requires A_V^(host) ≳ 5.3 mag and GRB 111215A requires A_V^(host) ≳ 8.5 mag (assuming z = 2). These are among the largest extinction values inferred for dark bursts to date. The two bursts also exhibit large neutral hydrogen column densities of N H, int ≳ 10^(22) cm^(–2) (z = 2) as inferred from their X-ray spectra, in agreement with the trend for dark GRBs. Moreover, the inferred values are in agreement with the Galactic A_V -N_H relation, unlike the bulk of the GRB population. Finally, we find that for both bursts the afterglow emission is best explained by a collimated outflow with a total beaming-corrected energy of E_γ + E_K ≈ (7-9) × 10^(51) erg (z = 2) expanding into a wind medium with a high density, Ṁ ≈ (6-20) x 10^(-5) M_☉ yr^(–1) (n ≈ 100-350 cm^(–3) at ≈ 10^(17) cm). While the energy release is typical of long GRBs, the inferred density may be indicative of larger mass-loss rates for GRB progenitors in dusty (and hence metal rich) environments. This study establishes the critical role of radio observations in demonstrating the origin and properties of dark GRBs. Observations with the JVLA and ALMA will provide a sample with sub-arcsecond positions and robust host associations that will help to shed light on obscured star formation and the role of metallicity in GRB progenitors

Inflammatory Activation of Astrocytes Facilitates Melanoma Brain Tropism via the CXCL10-CXCR3 Signaling Axis

Melanoma is the deadliest skin cancer due to its high rate of metastasis, frequently to the brain. Brain metastases are incurable; therefore, understanding melanoma brain metastasis is of great clinical importance. We used a mouse model of spontaneous melanoma brain metastasis to study the interactions of melanomas with the brain microenvironment. We find that CXCL10 is upregulated in metastasis-associated astrocytes in mice and humans and is functionally important for the chemoattraction of melanoma cells. Moreover, CXCR3, the receptor for CXCL10, is upregulated in brain-tropic melanoma cells. Targeting melanoma expression of CXCR3 by nanoparticle-mediated siRNA delivery or by shRNA transduction inhibits melanoma cell migration and attenuates brain metastasis in vivo. These findings suggest that the instigation of pro-inflammatory signaling in astrocytes is hijacked by brain-metastasizing tumor cells to promote their metastatic capacity and that the CXCL10-CXCR3 axis may be a potential therapeutic target for the prevention of melanoma brain metastasis