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and monographs devoted to this theory where one can find the detailed exposition of many difficult results as well as historical references.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

Say Goodbye to Frye: Missouri Supreme Court Clarifies Standard for Admitting Expert Testimony in Civil and Administrative Cases

In State Board of Registration for the Healing Arts v. McDonagh, the Supreme Court of Missouri clarified the standard of admissibility for expert testimony in civil cases and administrative proceedings. This Note will examine the different standards that Missouri courts have applied and explore how the new McDonagh standard will impact Missouri courts

On Resource-bounded versions of the van Lambalgen theorem

The van Lambalgen theorem is a surprising result in algorithmic information theory concerning the symmetry of relative randomness. It establishes that for any pair of infinite sequences $A$ and $B$, $B$ is Martin-L\"of random and $A$ is Martin-L\"of random relative to $B$ if and only if the interleaved sequence $A \uplus B$ is Martin-L\"of random. This implies that $A$ is relative random to $B$ if and only if $B$ is random relative to $A$ \cite{vanLambalgen}, \cite{Nies09}, \cite{HirschfeldtBook}. This paper studies the validity of this phenomenon for different notions of time-bounded relative randomness. We prove the classical van Lambalgen theorem using martingales and Kolmogorov compressibility. We establish the failure of relative randomness in these settings, for both time-bounded martingales and time-bounded Kolmogorov complexity. We adapt our classical proofs when applicable to the time-bounded setting, and construct counterexamples when they fail. The mode of failure of the theorem may depend on the notion of time-bounded randomness

Isolation and identification of cobalt- and caesium-resistant bacteria from a nuclear fuel storage pond

One of the issues facing the nuclear power industry is how to store spent nuclear fuel which is contaminated with radionuclides produced during nuclear fission, including caesium ((134)Cs(+), (135)Cs(+) and (137)Cs(+)) and cobalt ((60)Co(2+)). In this study, we have isolated Co(2+)- and Cs(+)-resistant bacteria from water collected from a nuclear fuel storage pond. The most resistant Cs(+) and Co(2+) isolates grew in the presence of 500 mM CsCl and 3 mM CoCl2. Strain Cs67-2 is resistant to fourfold more Cs(+) than Cupriavidus metallidurans str. CH34 making it the most Cs(+)-resistant strain identified to date. The Cs(+)-resistant isolates were closely related to bacteria in the Serratia and Yersinia genera, while the Co(2+)-resistant isolates were closely related to the Curvibacter and Tardiphaga genera. These new isolates could be used for bioremediation

Phase Transition and Strong Predictability

The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed in our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], where we introduced the notion of thermodynamic quantities into AIT. These quantities are real functions of temperature T>0. The values of all the thermodynamic quantities diverge when T exceeds 1. This phenomenon corresponds to phase transition in statistical mechanics. In this paper we introduce the notion of strong predictability for an infinite binary sequence and then apply it to the partition function Z(T), which is one of the thermodynamic quantities in AIT. We then reveal a new computational aspect of the phase transition in AIT by showing the critical difference of the behavior of Z(T) between T=1 and T<1 in terms of the strong predictability for the base-two expansion of Z(T).Comment: 5 pages, LaTeX2e, no figure

Natural transformation of the filamentous cyanobacterium Phormidium lacuna

Research for biotechnological applications of cyanobacteria focuses on synthetic pathways and bioreactor design, while little effort is devoted to introduce new, promising organisms in the field. Applications are most often based on recombinant work, and the establishment of transformation can be a risky, time-consuming procedure. In this work we demonstrate the natural transformation of the filamentous cyanobacterium Phormidium lacuna and insertion of a selection marker into the genome by homologous recombination. This is the first example for natural transformation filamentous non-heterocystous cyanobacterium. We found that Phormidium lacuna is polyploid, each cell has about 20–90 chromosomes. Transformed filaments were resistant against up to 14 mg/ml of kanamycin. Formerly, natural transformation in cyanobacteria has been considered a rare and exclusive feature of a few unicellular species. Our finding suggests that natural competence is more distributed among cyanobacteria than previously thought. This is supported by bioinformatic analyses which show that all protein factors for natural transformation are present in the majority of the analyzed cyanobacteria

Division of Student Affairs: Centennial History

This departmental history was written on the occasion of the UND Centennial in 1983.https://commons.und.edu/departmental-histories/1110/thumbnail.jp

Interpretation of Rayleigh-Wave Ellipticity Observed with Multicomponent Passive Seismic Interferometry at Hekla Volcano, Iceland

The 2010 eruption of Eyjafjallajökull has drawn increased attention to Iceland’s Eastern Volcanic Zone (EVZ) due to the threat it poses to the heavily used air-traffic corridors of the northern Atlantic Ocean. Within the EVZ, Hekla is historically one of the most active volcanoes and has exhibited a decadal eruption pattern for the past 40 years. Hekla most recently erupted in 2000 and is thus ripe for another decadal eruption. Because Hekla is generally aseismic, except for a brief time period (hours) leading up to an eruption, monitoring has previously depended on precursory deformation signals (Linde et al., 1993). As a result, seismic tomography of the internal structure of the volcano using phase arrivals of local earthquakes is not possible. Motivated by Hekla’s practically aseismic behavior in inter-eruptive periods, we installed a temporary network of four broadband seismometers around the volcanic edifice in late August 2010 with the intention of investigating the applicability of passive seismic interferometry (PSI) for imaging and monitoring the volcano

Time series analysis of water use and indirect reusewithin a HUC-4 basin (Wabash) over a nine year period

Anthropogenic water use and reuse represent major components of the water cycle. In the context of climate change, water reuse and recycling are considered necessary components for an integrated water management approach. Unplanned, or de facto, indirect water reuse occurs in most of the U.S. river systems, however, there is little real-time documentation of it. Despite the fact that there are national and state agencies that systematically collect data on water withdrawals and wastewater discharges, their databases are organized and managed in a way that makes it challenging to use them for water resource management analysis. The ability to combine reported water data to perform large scale analysis about water use and reuse is severely limited. In this paper, we apply a simple but effective methodology to complete a time series watershed-scale analysis of water use and unplanned indirect reuse for the Wabash River Watershed. Results document the occurrence of indirect water reuse, ranging from 3% to 134%, in a water-rich area of the U.S. The time series analysis shows that reported data effectively describe the water use trends through nine years, from 2009 to 2017, clearly reflecting both anthropogenic and natural events in the watershed, such as the retirement of thermoelectric power plants, and the occurrence of an extreme drought in 2012. We demonstrate the feasibility and significance of using available water datasets to perform large scale water use analysis, describe limitations encountered in the process, and highlight areas for improvement in water data management