Around Kolmogorov complexity: basic notions and results

Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one can find the detailed exposition of many difficult results as well as historical references. However, it seems that a short survey of its basic notions and main results relating these notions to each other, is missing. This report attempts to fill this gap and covers the basic notions of algorithmic information theory: Kolmogorov complexity (plain, conditional, prefix), Solomonoff universal a priori probability, notions of randomness (Martin-L\"of randomness, Mises--Church randomness), effective Hausdorff dimension. We prove their basic properties (symmetry of information, connection between a priori probability and prefix complexity, criterion of randomness in terms of complexity, complexity characterization for effective dimension) and show some applications (incompressibility method in computational complexity theory, incompleteness theorems). It is based on the lecture notes of a course at Uppsala University given by the author

Computer aided design and manufacturing of composite propfan blades for a cruise missile wind tunnel model

One of the propulsion concepts being investigated for future cruise missiles is advanced unducted propfans. To support the evaluation of this technology applied to the cruise missile, a joint DOD and NASA test project was conducted to design and then test the characteristics of the propfans on a 0.55-scale, cruise missile model in a NASA wind tunnel. The configuration selected for study is a counterrotating rearward swept propfan. The forward blade row, having six blades, rotates in a counterclockwise direction, and the aft blade row, having six blades, rotates in a clockwise direction, as viewed from aft of the test model. Figures show the overall cruise missile and propfan blade configurations. The objective of this test was to evaluate propfan performance and suitability as a viable propulsion option for next generation of cruise missiles. This paper details the concurrent computer aided design, engineering, and manufacturing of the carbon fiber/epoxy propfan blades as the NASA Lewis Research Center

Characterization and Commissioning of a Ka-Band Ground Station for Cognitive Algorithm Development

In 2018, the Cognitive Communications and Propagation projects completed installation and checkout testing of a new Ka-Band ground station at the NASA Glenn Research Center in Cleveland, Ohio. The Cognitive Algorithms Demonstration Testbed (CADeT) was developed to provide a fully characterized and controllable dynamic link environment to researchers looking to demonstrate hardware and software aligned with atmospheric sensing and cognitive algorithms. CADeT integrates a host of precision control and measurement systems in addition to repurposing a 5.5 meter beam-waveguide dish platform previously used with the Advanced Communications Technology Satellite (ACTS). This paper will discuss the laboratory testing of ground station components with a emphasis on elements vital to achieving link budget requirements including characterization of the new Gallium Nitride (GaN) Solid State Power Amplifier (SSPA) and far-field measurements of the new antenna feed. Finally, the paper discusses in-situ tests conducted with CADeT and the Tracking and Data Relay Satellite System (TDRSS) to validate laboratory results and make necessary link budget adjustments before reviewing the lessons learned

Carbon isotope fractionation during aerobic biodegradation of trichloroethene by Burkholderia cepacia G4: a tool to map degradation mechanisms

The strain Burkholderia cepacia G4 aerobically mineralized trichloroethene (TCE) to CO2 over a time period of similar to20 h. Three biodegradation experiments were conducted with different bacterial optical densities at 540 nm (OD(540)s) in order to test whether isotope fractionation was consistent. The resulting TCE degradation was 93, 83.8, and 57.2% (i.e., 7.0, 16.2, and 42.8% TCE remaining) at OD(540)s of 2.0, 1.1, and 0.6, respectively. ODs also correlated linearly with zero-order degradation rates (1.99, 1.11, and 0.64 mumol h(-1)). While initial nonequilibrium mass losses of TCE produced only minor carbon isotope shifts (expressed in per mille delta C- 13(VPDB)), they were 57.2, 39.6, and 17.0parts per thousand between the initial and final TCE levels for the three experiments, in decreasing order of their OD(540)s. Despite these strong isotope shifts, we found a largely uniform isotope fractionation. The latter is expressed with a Rayleigh enrichment factor, E, and was -18.2 when all experiments were grouped to a common point of 42.8% TCE remaining. Although, decreases of epsilon to -20.7 were observed near complete degradation, our enrichment factors were significantly more negative than those reported for anaerobic dehalogenation of TCE. This indicates typical isotope fractionation for specific enzymatic mechanisms that can help to differentiate between degradation pathways

Valuing the biodiversity gains from protecting native plant communities from bitou bush (Chrysanthemoides monilifera subsp rotundata (DC.) T.Norl.) in New South Wales: application of the defensive expenditure method

Valuation of the gains from protection of biodiversity is difficult because the services that provide the benefits do not normally pass through markets where prices can form. But the services sometimes pass through markets where consumers or producers behave in a market-oriented manner, and so the values implicit in this behaviour can be identified and derived. Estimates of the benefits of biodiversity protection are derived from the costs of protecting native plant communities from a major weed in Australia, by following this approach. In 1999, invasion of coastal areas of New South Wales by bitou bush (Chrysanthemoides monilifera subsp. rotundata (DC.) T. Norl.) was listed as a key process threatening native plants under the NSW Threatened Species Conservation Act 1995. In accordance with the Act, the Department of Environment and Climate Change prepared a Threat Abatement Plan (TAP) to reduce the impacts of bitou bush on biodiversity at each threatened site. The costs of protecting sites vary closely with the number of priority native species and communities at each site. Following standard economic assumptions about market transactions, these costs are interpreted to provide values the benefits of protecting extra species, communities, and sites. Key words: Bitou bush, Chrysanthemoides monilifera, threat abatement plan, valuation of biodiversity, benefit-cost analysis, weed control, defensive-expenditure method.Bitou bush, Chrysanthemoides monilifera, threat abatement plan, valuation of biodiversity, benefit-cost analysis, weed control, defensive-expenditure method, Demand and Price Analysis, Environmental Economics and Policy,

On-Orbit Validation of a Framework for Spacecraft-Initiated Communication Service Requests with NASA's SCaN Testbed

We design, analyze, and experimentally validate a framework for demand-based allocation of high-performance space communication service in which the user spacecraft itself initiates a request for service. Leveraging machine-to-machine communications, the automated process has potential to improve the responsiveness and efficiency of space network operations. We propose an augmented ground station architecture in which a hemispherical-pattern antenna allows for reception of service requests sent from any user spacecraft within view. A suite of ground-based automation software acts upon these direct-to-Earth requests and allocates access to high-performance service through a ground station or relay satellite in response to immediate user demand. A software-defined radio transceiver, optimized for reception of weak signals from the helical antenna, is presented. Design and testing of signal processing equipment and a software framework to handle service requests is discussed. Preliminary results from on-orbit demonstrations with a testbed onboard the International Space Station are presented to verify feasibility of the concept

Degree spectra for transcendence in fields

We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e. degrees above an arbitrary fixed $\Delta^0_2$ degree. In other cases, these spectra may be characterized by the ability to enumerate an arbitrary $\Sigma^0_2$ set. This is the first proof that a computable field can fail to have a computable copy with a computable transcendence basis

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

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]

A note on the differences of computably enumerable reals

We show that given any non-computable left-c.e. real α there exists a left-c.e. real β such that α≠β+γ for all left-c.e. reals and all right-c.e. reals γ. The proof is non-uniform, the dichotomy being whether the given real α is Martin-Loef random or not. It follows that given any universal machine U, there is another universal machine V such that the halting probability of U is not a translation of the halting probability of V by a left-c.e. real. We do not know if there is a uniform proof of this fact