A new model for broadband waveguide to microstrip transition design

A new model is presented which permits the prediction of the resonant frequencies created by antipodal finline waveguide to microstrip transitions. The transition is modeled as a tapered transmission line in series with an infinite set of coupled resonant circuits. The resonant circuits are modeled as simple microwave resonant cavities of which the resonant frequencies are easily determined. The model is developed and the resonant frequencies determined for several different transitions. Experimental results are given to confirm the models

Single-Photon Counting Detector Scalability for High Photon Efficiency Optical Communications Links

For high photon-efficiency deep space or low power optical communications links, such as the Orion Artemis-2 Optical Communications System (O2O) project, the received optical signal is attenuated to the extent that single- photon detectors are required. For direct-detection receivers operating at 1.55 m wavelength, single-photon detectors including Geiger-mode InGaAs avalanche photon diodes (APDs), and in particular superconducting nanowire single-photon detectors (SNSPDs) offer the highest sensitivity and fastest detection speeds. However, these photon detectors exhibit a recovery time between registered input pulses, effectively reducing the detection efficiency over the recovery interval, resulting in missed photon detections, reduced count rate, and ultimately limiting the achievable data rate. A method to overcome this limitation is to divide the received optical signal into multiple detectors in parallel. Here we analyze this approach for a receiver designed to receive a high photon efficiency serially concatenated pulse position modulation (SCPPM) input waveform. From measured count rate and efficiency data using commercial SNSPDs, we apply a model from which we determine the effective detection efficiency, or blocking loss, for different input signal rates. We analyze the scalability of adding detectors in parallel for different modulation orders and background levels to achieve desired data rates. Finally we show tradeoffs between the number of detectors and the required received optical power, useful for real link design considerations

Detector Channel Combining Results from a High Photon Efficiency Optical Communications Link Test Bed

The National Aeronautics and Space Administration (NASA) Glenn Research Center (GRC) is developing a low cost, scalable, photon-counting receiver prototype for space-to-ground optical communications links. The receiver is being tested in a test bed that emulates photon-starved space-to-ground optical communication links. The receiver uses an array of single-pixel fiber-coupled superconducting nanowire single-photon detectors. The receiver is designed to receive the high photon efficiency serially concatenated pulse position modulation (SCPPM) waveform specified in the Consultative Committee for Space Data Systems (CCSDS) Optical Communications Coding and Synchronization Blue Book Standard. The optical receiver consists of an array of single-pixel superconducting nanowire detectors, analog phase shifters for channel alignment, digitizers for each detector channel, and digital processing of the received signal. An overview of the test bed and arrayed receiver system is given. Simulation and system characterization results are presented. The data rate increase of using a four-channel arrayed detector system over using one single pixel nanowire detector is characterized. Results indicate that a single-pixel detector is capable of receiving data at a rate of 40 Mbps and a four-channel arrayed detector system is capable of receiving data at a rate of 130 Mbps

The parameterized complexity of some geometric problems in unbounded dimension

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in \Rd, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in \Rd, decide whether they can be separated by two hyperplanes. iii) Given a system of $n$ linear inequalities with $d$ variables, find a maximum-size feasible subsystem. We show that (the decision versions of) all these problems are W[1]-hard when parameterized by the dimension $d$. %and hence not solvable in ${O}(f(d)n^c)$ time, for any computable function $f$ and constant $c$ %(unless FPT=W[1]). Our reductions also give a $n^{\Omega(d)}$-time lower bound (under the Exponential Time Hypothesis)

Monolithic microwave integrated circuits: Interconnections and packaging considerations

Monolithic microwave integrated circuits (MMIC's) above 18 GHz were developed because of important potential system benefits in cost reliability, reproducibility, and control of circuit parameters. The importance of interconnection and packaging techniques that do not compromise these MMIC virtues is emphasized. Currently available microwave transmission media are evaluated to determine their suitability for MMIC interconnections. An antipodal finline type of microstrip waveguide transition's performance is presented. Packaging requirements for MMIC's are discussed for thermal, mechanical, and electrical parameters for optimum desired performance

Dimension Spectra of Lines

This paper investigates the algorithmic dimension spectra of lines in the Euclidean plane. Given any line L with slope a and vertical intercept b, the dimension spectrum sp(L) is the set of all effective Hausdorff dimensions of individual points on L. We draw on Kolmogorov complexity and geometrical arguments to show that if the effective Hausdorff dimension dim(a, b) is equal to the effective packing dimension Dim(a, b), then sp(L) contains a unit interval. We also show that, if the dimension dim(a, b) is at least one, then sp(L) is infinite. Together with previous work, this implies that the dimension spectrum of any line is infinite

Systems of Linear Equations over F2\mathbb{F}_2 and Problems Parameterized Above Average

In the problem Max Lin, we are given a system $Az=b$ of $m$ linear equations with $n$ variables over $\mathbb{F}_2$ in which each equation is assigned a positive weight and we wish to find an assignment of values to the variables that maximizes the excess, which is the total weight of satisfied equations minus the total weight of falsified equations. Using an algebraic approach, we obtain a lower bound for the maximum excess. Max Lin Above Average (Max Lin AA) is a parameterized version of Max Lin introduced by Mahajan et al. (Proc. IWPEC'06 and J. Comput. Syst. Sci. 75, 2009). In Max Lin AA all weights are integral and we are to decide whether the maximum excess is at least $k$, where $k$ is the parameter. It is not hard to see that we may assume that no two equations in $Az=b$ have the same left-hand side and $n={\rm rank A}$. Using our maximum excess results, we prove that, under these assumptions, Max Lin AA is fixed-parameter tractable for a wide special case: $m\le 2^{p(n)}$ for an arbitrary fixed function $p(n)=o(n)$. Max $r$-Lin AA is a special case of Max Lin AA, where each equation has at most $r$ variables. In Max Exact $r$-SAT AA we are given a multiset of $m$ clauses on $n$ variables such that each clause has $r$ variables and asked whether there is a truth assignment to the $n$ variables that satisfies at least $(1-2^{-r})m + k2^{-r}$ clauses. Using our maximum excess results, we prove that for each fixed $r\ge 2$, Max $r$-Lin AA and Max Exact $r$-SAT AA can be solved in time $2^{O(k \log k)}+m^{O(1)}.$ This improves $2^{O(k^2)}+m^{O(1)}$-time algorithms for the two problems obtained by Gutin et al. (IWPEC 2009) and Alon et al. (SODA 2010), respectively

Augmenting graphs to minimize the diameter

We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT 4-approximation algorithm for the problem.Comment: 15 pages, 3 figure

Silyl trifluoromethanesulfonate-activated para-methoxybenzyl methyl ether as an alkylating agent for thiols and aryl ketones

para-Methoxybenzyl methyl ether acts as an alkylating agent for thiols in the presence of trimethylsilyl trifluoromethanesulfonate and trialkylamine base in good yields (58-96%). Aryl ketones are alkylated under similar conditions, probably through an enol silane intermediate, also in high yields (67-95%). The active alkylating species is likely a p-methoxybenzyl cation