Potential Applications of Active Antenna Technologies for Emerging NASA Space Communications Scenarios

AbstractThe National Aeronautics and Space Administration (NASA) is presently embarking on the implementation of far-reaching changes within the framework of both space and aeronautics communications architectures. For example, near earth relays are looking to transition from the traditional few large geostationary satellites to satellite constellations consisting of thousands of small low earth orbiting satellites while lunar space communications will require the need to relay data from many assets distributed on the lunar surface back to earth. Furthermore, within the aeronautics realm, satellite communications for beyond line of sight (BLOS) links are being investigated in tandem with the proliferation of unmanned aerial systems (UAS) within the urban air mobility (UAM) environment. In all of these scenarios, future communications architectures will demand the need to connect and quickly transition between many nodes for large data volume transport. As such, NASA Glenn Research Center (GRC) has been heavily investigating the development of low cost phased array technologies that can readily address these various scenario conditions. In particular, GRC is presently exploring 5G-based beamformer technologies to leverage commercial timescale and volume production cycles which have heretofore not existed within the frequency allocations utilized for NASA applications. In this paper, an overview of the potential future applications of phased arrays being envisioned by NASA are discussed, along with technology feasibility demonstrations being conducted by GRC implementing low cost, 5G based beamformer technologies

Parameterized Algorithms for Graph Partitioning Problems

We study a broad class of graph partitioning problems, where each problem is specified by a graph $G=(V,E)$, and parameters $k$ and $p$. We seek a subset $U\subseteq V$ of size $k$, such that $\alpha_1m_1 + \alpha_2m_2$ is at most (or at least) $p$, where $\alpha_1,\alpha_2\in\mathbb{R}$ are constants defining the problem, and $m_1, m_2$ are the cardinalities of the edge sets having both endpoints, and exactly one endpoint, in $U$, respectively. This class of fixed cardinality graph partitioning problems (FGPP) encompasses Max $(k,n-k)$-Cut, Min $k$-Vertex Cover, $k$-Densest Subgraph, and $k$-Sparsest Subgraph. Our main result is an $O^*(4^{k+o(k)}\Delta^k)$ algorithm for any problem in this class, where $\Delta \geq 1$ is the maximum degree in the input graph. This resolves an open question posed by Bonnet et al. [IPEC 2013]. We obtain faster algorithms for certain subclasses of FGPPs, parameterized by $p$, or by $(k+p)$. In particular, we give an $O^*(4^{p+o(p)})$ time algorithm for Max $(k,n-k)$-Cut, thus improving significantly the best known $O^*(p^p)$ time algorithm

Seven exercises planned to stimulate the flow of ideas in creative composition

Thesis (Ed.M.)--Boston Universit

Parameterized Complexity of the k-anonymity Problem

The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization that has been recently proposed is the $k$-anonymity. This approach requires that the rows of a table are partitioned in clusters of size at least $k$ and that all the rows in a cluster become the same tuple, after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is known to be APX-hard even when the records values are over a binary alphabet and $k=3$, and when the records have length at most 8 and $k=4$ . In this paper we study how the complexity of the problem is influenced by different parameters. In this paper we follow this direction of research, first showing that the problem is W[1]-hard when parameterized by the size of the solution (and the value $k$). Then we exhibit a fixed parameter algorithm, when the problem is parameterized by the size of the alphabet and the number of columns. Finally, we investigate the computational (and approximation) complexity of the $k$-anonymity problem, when restricting the instance to records having length bounded by 3 and $k=3$. We show that such a restriction is APX-hard.Comment: 22 pages, 2 figure

Parameterized Inapproximability of Target Set Selection and Generalizations

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex $v$ is activated during the propagation process if at least $thr(v)$ of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions $f$ and $\rho$ this problem cannot be approximated within a factor of $\rho(k)$ in $f(k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results

Counting dependent and independent strings

The paper gives estimations for the sizes of the the following sets: (1) the set of strings that have a given dependency with a fixed string, (2) the set of strings that are pairwise \alpha independent, (3) the set of strings that are mutually \alpha independent. The relevant definitions are as follows: C(x) is the Kolmogorov complexity of the string x. A string y has \alpha -dependency with a string x if C(y) - C(y|x) \geq \alpha. A set of strings {x_1, \ldots, x_t} is pairwise \alpha-independent if for all i different from j, C(x_i) - C(x_i | x_j) \leq \alpha. A tuple of strings (x_1, \ldots, x_t) is mutually \alpha-independent if C(x_{\pi(1)} \ldots x_{\pi(t)}) \geq C(x_1) + \ldots + C(x_t) - \alpha, for every permutation \pi of [t]

Impossibility of independence amplification in Kolmogorov complexity theory

The paper studies randomness extraction from sources with bounded independence and the issue of independence amplification of sources, using the framework of Kolmogorov complexity. The dependency of strings $x$ and $y$ is ${\rm dep}(x,y) = \max\{C(x) - C(x \mid y), C(y) - C(y\mid x)\}$, where $C(\cdot)$ denotes the Kolmogorov complexity. It is shown that there exists a computable Kolmogorov extractor $f$ such that, for any two $n$-bit strings with complexity $s(n)$ and dependency $\alpha(n)$, it outputs a string of length $s(n)$ with complexity $s(n)- \alpha(n)$ conditioned by any one of the input strings. It is proven that the above are the optimal parameters a Kolmogorov extractor can achieve. It is shown that independence amplification cannot be effectively realized. Specifically, if (after excluding a trivial case) there exist computable functions $f_1$ and $f_2$ such that ${\rm dep}(f_1(x,y), f_2(x,y)) \leq \beta(n)$ for all $n$-bit strings $x$ and $y$ with ${\rm dep}(x,y) \leq \alpha(n)$, then $\beta(n) \geq \alpha(n) - O(\log n)$

Structural parameterizations for boxicity

The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for every fixed $d \ge 2$. We show that boxicity is fixed-parameter tractable when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Adiga et al., that boxicity is fixed-parameter tractable in the vertex cover number. Moreover, we show that boxicity admits an additive $1$-approximation when parameterized by the pathwidth of the input graph. Finally, we provide evidence in favor of a conjecture of Adiga et al. that boxicity remains NP-complete when parameterized by the treewidth.Comment: 19 page

Sources contributing to background surface ozone in the US Intermountain West

We quantify the sources contributing to background surface ozone concentrations in the US Intermountain West by using the GEOS-Chem chemical transport model with 1 / 2° × 2 / 3° horizontal resolution to interpret the Clean Air Status and Trends Network (CASTNet) ozone monitoring data for 2006–2008. We isolate contributions from lightning, wildfires, the stratosphere, and California pollution. Lightning emissions are constrained by observations and wildfire emissions are estimated from daily fire reports. We find that lightning increases mean surface ozone in summer by 10 ppbv in the Intermountain West, with moderate variability. Wildfire plumes generate high-ozone events in excess of 80 ppbv in GEOS-Chem, but CASTNet ozone observations in the Intermountain West show no enhancements during these events nor do they show evidence of regional fire influence. Models may overestimate ozone production in fresh fire plumes because of inadequate chemistry and grid-scale resolution. The highest ozone concentrations observed in the Intermountain West (> 75 ppbv) in spring are associated with stratospheric intrusions. The model captures the timing of these intrusions but not their magnitude, reflecting numerical diffusion intrinsic to Eulerian models. This can be corrected statistically through a relationship between model bias and the model-diagnosed magnitude of stratospheric influence; with this correction, models may still be useful to forecast and interpret high-ozone events from stratospheric intrusions. We show that discrepancy between models in diagnosing stratospheric influence is due in part to differences in definition, i.e., whether stratospheric ozone is diagnosed as produced in the stratosphere (GEOS-Chem definition) or as transported from above the tropopause. The latter definition can double the diagnosed stratospheric influence in surface air by labeling as "stratospheric" any ozone produced in the troposphere and temporarily transported to the stratosphere. California pollution influence in the Intermountain West frequently exceeds 10 ppbv but is generally not correlated with the highest ozone events

Infrared Instrumentation and Astronomy

Contains research objectives and summary of research on five research projects.Joint Services Electronics Program (Contract DAAB07-76-C-1400)M.I.T. Sloan Fund for Basic ResearchNational Aeronautics and Space Administration (Contract NAS5-23731)National Aeronautics and Space Administration (Grant NGR 22-009-526