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and monographs devoted to this theory where one can find the detailed exposition of many difficult results as well as historical references.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

The Parameterized Complexity of Domination-type Problems and Application to Linear Codes

We study the parameterized complexity of domination-type problems. (sigma,rho)-domination is a general and unifying framework introduced by Telle: a set D of vertices of a graph G is (sigma,rho)-dominating if for any v in D, |N(v)\cap D| in sigma and for any $v\notin D, |N(v)\cap D| in rho. We mainly show that for any sigma and rho the problem of (sigma,rho)-domination is W[2] when parameterized by the size of the dominating set. This general statement is optimal in the sense that several particular instances of (sigma,rho)-domination are W[2]-complete (e.g. Dominating Set). We also prove that (sigma,rho)-domination is W[2] for the dual parameterization, i.e. when parameterized by the size of the dominated set. We extend this result to a class of domination-type problems which do not fall into the (sigma,rho)-domination framework, including Connected Dominating Set. We also consider problems of coding theory which are related to domination-type problems with parity constraints. In particular, we prove that the problem of the minimal distance of a linear code over Fq is W[2] for both standard and dual parameterizations, and W[1]-hard for the dual parameterization. To prove W[2]-membership of the domination-type problems we extend the Turing-way to parameterized complexity by introducing a new kind of non deterministic Turing machine with the ability to perform `blind' transitions, i.e. transitions which do not depend on the content of the tapes. We prove that the corresponding problem Short Blind Multi-Tape Non-Deterministic Turing Machine is W[2]-complete. We believe that this new machine can be used to prove W[2]-membership of other problems, not necessarily related to dominationComment: 19 pages, 2 figure

Zero-Gravity Vortex Vent and PVT Gaging System

Space Station and satellite reservicing will require the ability to vent gas on orbit from liquid supply or storage tanks and to gage liquid quantity under microgravity conditions. In zero gravity, (zero-g) the vortex vent is capable of venting gas from a tank of liquid containing gas randomly distributed as bubbles. The concept uses a spinning impeller to create centrifugal force inside a vortex tube within a tank. This creates a gas pocket and forces the liquid through a venturi and back into the tank. Gas is then vented from the gas pocket through a liquid detector and then out through an exhaust port. If the liquid detector senses liquid in the vent line, the fluid is directed to the low-pressure port on the venturi and is returned to the tank. The advantages of this system is that it has no rotating seals and is compatible with most corrosive and cryogenic fluids. A prototype was designed and built at the NASA Johnson Space Center and flown on the KC-135 zero-g aircraft. During these test flights, where microgravity conditions are obtained for up to 30 sec, the prototype demonstrated that less than 0.10 percent of the volume of fluid vented was liquid when the tank was half full of liquid. The pressure volume temperature (PVT) gaging system is used in conjunction with the vortex vent to calculate the amount of liquid remaining in a tank under microgravity conditions. The PVT gaging system is used in conjunction with the vortex vent to gage liquid quantity in zero or low gravity. The system consists of a gas compressor, accumulator, and temperature and pressure instrumentation. To measure the liquid in a tank a small amount of gas is vented from the tank to the compressor and compressed into the accumulator. Pressure and temperature in the tank and accumulator are measured before and after the gas transfer occurs. Knowing the total volume of the tank, the volume of the accumulator, the volume of the intermediate lines, and initial and final pressures and temperatures, the mass of the gas leaving the tank is equated to the mass of the gas entering the accumulator. The volume of liquid remaining in the tank is calculated using the ideal gas law

The Hardness of Embedding Grids and Walls

The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of "pattern graphs" can be embedded into a given graph $H$ (that is, is isomorphic to a subgraph of $H$) is fixed-parameter tractable if $K$ is a class of graphs of bounded tree width and $W[1]$-complete otherwise. Towards this conjecture, we prove that the embedding problem is $W[1]$-complete if $K$ is the class of all grids or the class of all walls

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,

Steady-state evoked potentials possibilities for mental-state estimation

The use of the human steady-state evoked potential (SSEP) as a possible measure of mental-state estimation is explored. A method for evoking a visual response to a sum-of-ten sine waves is presented. This approach provides simultaneous multiple frequency measurements of the human EEG to the evoking stimulus in terms of describing functions (gain and phase) and remnant spectra. Ways in which these quantities vary with the addition of performance tasks (manual tracking, grammatical reasoning, and decision making) are presented. Models of the describing function measures can be formulated using systems engineering technology. Relationships between model parameters and performance scores during manual tracking are discussed. Problems of unresponsiveness and lack of repeatability of subject responses are addressed in terms of a need for loop closure of the SSEP. A technique to achieve loop closure using a lock-in amplifier approach is presented. Results of a study designed to test the effectiveness of using feedback to consciously connect humans to their evoked response are presented. Findings indicate that conscious control of EEG is possible. Implications of these results in terms of secondary tasks for mental-state estimation and brain actuated control are addressed

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

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