Deterministic Sampling and Range Counting in Geometric Data Streams

We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.Comment: 12 pages, 1 figur

Heliospheric plasma sheets

[1] As a high-beta feature on scales of hours or less, the heliospheric plasma sheet (HPS) encasing the heliospheric current sheet shows a high degree of variability. A study of 52 sector boundaries identified in electron pitch angle spectrograms in Wind data from 1995 reveals that only half concur with both high-beta plasma and current sheets, as required for an HPS. The remaining half lack either a plasma sheet or current sheet or both. A complementary study of 37 high-beta events reveals that only 5 contain sector boundaries while nearly all (34) contain local magnetic field reversals, however brief. We conclude that high-beta plasma sheets surround current sheets but that most of these current sheets are associated with fields turned back on themselves. The findings are consistent with the hypothesis that high-beta plasma sheets, both at and away from sector boundaries, are the heliospheric counterparts of the small coronal transients observed at the tips of helmet streamers, in which case the proposed mechanism for their release, interchange reconnection, could be responsible for the field inversions

Feedback Controlled Software Systems

Software systems generally suffer from a certain fragility in the face of disturbances such as bugs, unforeseen user input, unmodeled interactions with other software components, and so on. A single such disturbance can make the machine on which the software is executing hang or crash. We postulate that what is required to address this fragility is a general means of using feedback to stabilize these systems. In this paper we develop a preliminary dynamical systems model of an arbitrary iterative software process along with the conceptual framework for stabilizing it in the presence of disturbances. To keep the computational requirements of the controllers low, randomization and approximation are used. We describe our initial attempts to apply the model to a faulty list sorter, using feedback to improve its performance. Methods by which software robustness can be enhanced by distributing a task between nodes each of which are capable of selecting the best input to process are also examined, and the particular case of a sorting system consisting of a network of partial sorters, some of which may be buggy or even malicious, is examined

On Detection Issues in the SC-based Uplink of a MU-MIMO System with a Large Number of BS Antennas

This paper deals with SC/FDE within a MU-MIMO system where a large number of BS antennas is adopted. In this context, either linear or reduced-complexity iterative DF detection techniques are considered. Regarding performance evaluation by simulation, appropriate semi-analytical methods are proposed. This paper includes a detailed evaluation of BER performances for uncoded 4-Quadrature Amplitude Modulation (4-QAM) schemes and a MU-MIMO channel with uncorrelated Rayleigh fading. The accuracy of performance results obtained through the semi-analytical simulation methods is assessed by means of parallel conventional Monte Carlo simulations, under the assumptions of perfect power control and perfect channel estimation. The performance results are discussed in detail, with the help of selected performance bounds. We emphasize that a moderately large number of BS antennas is enough to closely approximate the SIMO MFB performance, especially when using the suggested low-complexity iterative DF technique, which does not require matrix inversion operations. We also emphasize the achievable "massive MIMO" effects, even for strongly reduced-complexity linear detection techniques, provided that the number of BS antennas is much higher than the number of antennas which are jointly employed in the terminals of the multiple autonomous users.Comment: 7 pages, 4 figure

Spitzer and z' Secondary Eclipse Observations of the Highly Irradiated Transiting Brown Dwarf KELT-1b

We present secondary eclipse observations of the highly irradiated transiting brown dwarf KELT-1b. These observations represent the first constraints on the atmospheric dynamics of a highly irradiated brown dwarf, and the atmospheres of irradiated giant planets at high surface gravity. Using the Spitzer Space Telescope, we measure secondary eclipse depths of 0.195+/-0.010% at 3.6um and 0.200+/-0.012% at 4.5um. We also find tentative evidence for the secondary eclipse in the z' band with a depth of 0.049+/-0.023%. These measured eclipse depths are most consistent with an atmosphere model in which there is a strong substellar hotspot, implying that heat redistribution in the atmosphere of KELT-1b is low. While models with a more mild hotspot or even with dayside heat redistribution are only marginally disfavored, models with complete heat redistribution are strongly ruled out. The eclipse depths also prefer an atmosphere with no TiO inversion layer, although a model with TiO inversion is permitted in the dayside heat redistribution case, and we consider the possibility of a day-night TiO cold trap in this object. For the first time, we compare the IRAC colors of brown dwarfs and hot Jupiters as a function of effective temperature. Importantly, our measurements reveal that KELT-1b has a [3.6]-[4.5] color of 0.07+/-0.11, identical to that of isolated brown dwarfs of similarly high temperature. In contrast, hot Jupiters generally show redder [3.6]-[4.5] colors of ~0.4, with a very large range from ~0 to ~1. Evidently, despite being more similar to hot Jupiters than to isolated brown dwarfs in terms of external forcing of the atmosphere by stellar insolation, KELT-1b has an atmosphere most like that of other brown dwarfs. This suggests that surface gravity is very important in controlling the atmospheric systems of substellar mass bodies.Comment: 14 pages, 3 tables, 11 figures. Accepted by ApJ. Updated to reflect the accepted versio

The White-Box Adversarial Data Stream Model

We study streaming algorithms in the white-box adversarial model, where the stream is chosen adaptively by an adversary who observes the entire internal state of the algorithm at each time step. We show that nontrivial algorithms are still possible. We first give a randomized algorithm for the $L_1$-heavy hitters problem that outperforms the optimal deterministic Misra-Gries algorithm on long streams. If the white-box adversary is computationally bounded, we use cryptographic techniques to reduce the memory of our $L_1$-heavy hitters algorithm even further and to design a number of additional algorithms for graph, string, and linear algebra problems. The existence of such algorithms is surprising, as the streaming algorithm does not even have a secret key in this model, i.e., its state is entirely known to the adversary. One algorithm we design is for estimating the number of distinct elements in a stream with insertions and deletions achieving a multiplicative approximation and sublinear space; such an algorithm is impossible for deterministic algorithms. We also give a general technique that translates any two-player deterministic communication lower bound to a lower bound for {\it randomized} algorithms robust to a white-box adversary. In particular, our results show that for all $p\ge 0$, there exists a constant $C_p>1$ such that any $C_p$-approximation algorithm for $F_p$ moment estimation in insertion-only streams with a white-box adversary requires $\Omega(n)$ space for a universe of size $n$. Similarly, there is a constant $C>1$ such that any $C$-approximation algorithm in an insertion-only stream for matrix rank requires $\Omega(n)$ space with a white-box adversary. Our algorithmic results based on cryptography thus show a separation between computationally bounded and unbounded adversaries. (Abstract shortened to meet arXiv limits.)Comment: PODS 202

Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.beThe general discussion of the data flow algorithmic models, and the linear programming problem with the variating by data flow criterion function coefficients are presented. The general problem is widely known in different names - data streams, incremental and online algorithms, etc. The more studied algorithmic models include mathematical statistics and clustering, histograms and wavelets, sorting, set cover, and others. Linear programming model is an addition to this list. Large theoretical knowledge exists in this as the simplex algorithm and as interior point methods but the flow analysis requires another interpretation of optimal plans and plan transition with variate coefficients. An approximate model is devised which predicts the boundary stability point for the current optimal plan. This is valuable preparatory information of applications, moreover when a parallel computational facility is supposed

Everything Matters in Programmable Packet Scheduling

Programmable packet scheduling allows the deployment of scheduling algorithms into existing switches without need for hardware redesign. Scheduling algorithms are programmed by tagging packets with ranks, indicating their desired priority. Programmable schedulers then execute these algorithms by serving packets in the order described in their ranks. The ideal programmable scheduler is a Push-In First-Out (PIFO) queue, which achieves perfect packet sorting by pushing packets into arbitrary positions in the queue, while only draining packets from the head. Unfortunately, implementing PIFO queues in hardware is challenging due to the need to arbitrarily sort packets at line rate based on their ranks. In the last years, various techniques have been proposed, approximating PIFO behaviors using the available resources of existing data planes. While promising, approaches to date only approximate one of the characteristic behaviors of PIFO queues (i.e., its scheduling behavior, or its admission control). We propose PACKS, the first programmable scheduler that fully approximates PIFO queues on all their behaviors. PACKS does so by smartly using a set of strict-priority queues. It uses packet-rank information and queue-occupancy levels at enqueue to decide: whether to admit packets to the scheduler, and how to map admitted packets to the different queues. We fully implement PACKS in P4 and evaluate it on real workloads. We show that PACKS: better-approximates PIFO than state-of-the-art approaches and scales. We also show that PACKS runs at line rate on existing hardware (Intel Tofino).Comment: 12 pages, 12 figures (without references and appendices