A Self-Occulting Accretion Disk in the SW Sex Star DW UMa

We present the ultraviolet spectrum of the SW Sex star and nova-like variable DW UMa in an optical low state, as observed with the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope (HST). The data are well described by a synthetic white dwarf (WD) spectrum with T_eff = 46,000 +/- 1000 K, log g = 7.60 +/- 0.15, v*sin(i) = 370 +/- 100 km/s and Z/Z_solar = 0.47 +/- 0.15. For this combination of T_eff and log g, WD models predict M_WD = 0.48 +/- 0.06 M_solar and R_WD = (1.27 +/- 0.18) * 10^9 cm. Combining the radius estimate with the normalization of the spectral fit, we obtain a distance estimate of d = 830 +/-150 pc. During our observations, DW UMa was approximately 3 magnitudes fainter in V than in the high state. A comparison of our low-state HST spectrum to a high-state spectrum obtained with the International Ultraviolet Explorer shows that the former is much bluer and has a higher continuum level shortward of 1450 A. Since DW UMa is an eclipsing system, this suggests that an optically thick accretion disk rim blocks our view of the WD primary in the high state. If self-occulting accretion disks are common among the SW Sex stars, we can account for (i) the preference for high-inclination systems within the class and (ii) their V-shaped continuum eclipses. Moreover, even though the emission lines produced by a self-obscured disk are generally still double-peaked, they are weaker and narrower than those produced by an unobscured disk. This may allow a secondary line emission mechanism to dominate and produce the single-peaked, optical lines that are a distinguishing characteristic of the SW Sex stars.Comment: 9 pages, including 2 figures; accepted for publication in Astrophysical Journal Letters; New version matches version in press (footnote added to discussion section; figures now use color

Load-Aware Modeling and Analysis of Heterogeneous Cellular Networks

Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For a K-tier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the $i^{th}$ tier are assumed to transmit independently with probability $p_i$, which models the load. Assuming - reasonably - that smaller cells are more lightly loaded than macrocells, the analysis shows that adding such access points to the network always increases the coverage probability. We also observe that fully loaded models are quite pessimistic in terms of coverage.Comment: to appear, IEEE Transactions on Wireless Communication

Fundamentals of Heterogeneous Cellular Networks with Energy Harvesting

We develop a new tractable model for K-tier heterogeneous cellular networks (HetNets), where each base station (BS) is powered solely by a self-contained energy harvesting module. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power and deployment density. Since a BS may not always have enough energy, it may need to be kept OFF and allowed to recharge while nearby users are served by neighboring BSs that are ON. We show that the fraction of time a k^{th} tier BS can be kept ON, termed availability \rho_k, is a fundamental metric of interest. Using tools from random walk theory, fixed point analysis and stochastic geometry, we characterize the set of K-tuples (\rho_1, \rho_2, ... \rho_K), termed the availability region, that is achievable by general uncoordinated operational strategies, where the decision to toggle the current ON/OFF state of a BS is taken independently of the other BSs. If the availability vector corresponding to the optimal system performance, e.g., in terms of rate, lies in this availability region, there is no performance loss due to the presence of unreliable energy sources. As a part of our analysis, we model the temporal dynamics of the energy level at each BS as a birth-death process, derive the energy utilization rate, and use hitting/stopping time analysis to prove that there exists a fundamental limit on \rho_k that cannot be surpassed by any uncoordinated strategy.Comment: submitted to IEEE Transactions on Wireless Communications, July 201

Semi-infinite parabolic IC-sheaf

Let G be a connected reductive group, P its parabolic subgroup. We consider the parabolic semi-infinite category of sheaves on the affine Grassmanian of G and construct the parabolic version of the semi-infinite IC-sheaf of each orbit. We establish some of its properties and relate it to sheaves on the Drinfeld compactification of the moduli stack Bun_P of P-torsors on a curve. We also relate the parabolic semi-infinite IC-sheaf with the dual baby Verma object on the spectral side.Comment: 85

Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular Networks

Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given SINR, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR.Comment: IEEE Journal on Selected Areas in Communications, vol. 30, no. 3, pp. 550 - 560, Apr. 201