Translation from Classical Two-Way Automata to Pebble Two-Way Automata

We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it is not known whether there exists a polynomial trade-off, in the number of states, between the nondeterministic and deterministic pebble two-way automata. However, we show that these two machine models are not independent: if there exists a polynomial trade-off for the classical two-way automata, then there must also exist a polynomial trade-off for the pebble two-way automata. Thus, we have an upward collapse (or a downward separation) from the classical two-way automata to more powerful pebble automata, still staying within the class of regular languages. The same upward collapse holds for complementation of nondeterministic two-way machines. These results are obtained by showing that each pebble machine can be, by using suitable inputs, simulated by a classical two-way automaton with a linear number of states (and vice versa), despite the existing exponential blow-up between the classical and pebble two-way machines

Method and Apparatus for a Miniature Bioreactor System for Long-Term Cell Culture

A bioreactor and method that permits continuous and simultaneous short, moderate, or long term cell culturing of one or more cell types or tissue in a laminar flow configuration is disclosed, where the bioreactor supports at least two laminar flow zones, which are isolated by laminar flow without the need for physical barriers between the zones. The bioreactors of this invention are ideally suited for studying short, moderate and long term studies of cell cultures and the response of cell cultures to one or more stressors such as pharmaceuticals, hypoxia, pathogens, or any other stressor. The bioreactors of this invention are also ideally suited for short, moderate or long term cell culturing with periodic cell harvesting and/or medium processing for secreted cellular components

Miniature Bioreactor System for Long-Term Cell Culture

A prototype miniature bioreactor system is designed to serve as a laboratory benchtop cell-culturing system that minimizes the need for relatively expensive equipment and reagents and can be operated under computer control, thereby reducing the time and effort required of human investigators and reducing uncertainty in results. The system includes a bioreactor, a fluid-handling subsystem, a chamber wherein the bioreactor is maintained in a controlled atmosphere at a controlled temperature, and associated control subsystems. The system can be used to culture both anchorage-dependent and suspension cells, which can be either prokaryotic or eukaryotic. Cells can be cultured for extended periods of time in this system, and samples of cells can be extracted and analyzed at specified intervals. By integrating this system with one or more microanalytical instrument(s), one can construct a complete automated analytical system that can be tailored to perform one or more of a large variety of assays

The Magic Number Problem for Subregular Language Families

We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has alpha states, for all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n). A number alpha not satisfying this condition is called a magic number (for n). It was shown in [11] that no magic numbers exist for general regular languages, while in [5] trivial and non-trivial magic numbers for unary regular languages were identified. We obtain similar results for automata accepting subregular languages like, for example, combinational languages, star-free, prefix-, suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free languages, showing that there are only trivial magic numbers, when they exist. For finite languages we obtain some partial results showing that certain numbers are non-magic.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Descriptional Complexity of Three-Nonterminal Scattered Context Grammars: An Improvement

Recently, it has been shown that every recursively enumerable language can be generated by a scattered context grammar with no more than three nonterminals. However, in that construction, the maximal number of nonterminals simultaneously rewritten during a derivation step depends on many factors, such as the cardinality of the alphabet of the generated language and the structure of the generated language itself. This paper improves the result by showing that the maximal number of nonterminals simultaneously rewritten during any derivation step can be limited by a small constant regardless of other factors

Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation

Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept and generate, respectively, type-3 (regular) languages. Based on our previous work, this paper analyzes effects of graph manipulations on corresponding RE. In this present, starting stage we assume that the DG under consideration contains no cycles. Graph manipulation is performed by deleting or inserting of nodes or arcs. Combined and/or multiple application of these basic operators enable a great variety of transformations of DG (and corresponding RE) that can be seen as mutants of the original DG (and corresponding RE). DG are popular for modeling complex systems; however they easily become intractable if the system under consideration is complex and/or large. In such situations, we propose to switch to corresponding RE in order to benefit from their compact format for modeling and algebraic operations for analysis. The results of the study are of great potential interest to mutation testing

Determining Sequential Micellization Steps of Bile Salts With Multi-cmc Modeling

Hypothesis Bile salts exhibit complex concentration-dependent micellization in aqueous solution, rooted in a long-standing hypothesis of increasing size in bile aggregation that has historically focused on the measurement of only one CMC detected by a given method, without resolving successive stepwise aggregates. Whether bile aggregation is continuous or discrete, at what concentration does the first aggregate form, and how many aggregation steps occur, all remain as open questions. Experiments Bile salt critical micelle concentrations (CMCs) were investigated with NMR chemical shift titrations and a multi-CMC phase separation modeling approach developed herein. The proposed strategy is to establish a correspondence of the phase separation and mass action models to treat the first CMC; subsequent micellization steps, involving larger micelles, are then treated as phase separation events. Findings The NMR data and the proposed multi-CMC model reveal and resolve multiple closely spaced sequential preliminary, primary, and secondary discrete CMCs in dihydroxy and trihydroxy bile salt systems in basic (pH 12) solutions with a single model of one NMR data set. Complex NMR data are closely explained by the model. Four CMCs are established in deoxycholate below 100 mM (298 K, pH 12): 3.8 ± 0.5 mM, 9.1 ± 0.3 mM, 27 ± 2 mM, and 57 ± 4 mM, while three CMCs were observed in multiple bile systems, also under basic conditions. Global fitting leverages the sensitivity of different protons to different aggregation stages. In resolving these closely spaced CMCs, the method also obtains chemical shifts of these spectroscopically inaccessible (aka dark) states of the distinct micelles

A Far-Ultraviolet Survey of 47 Tucanae.II The Long-Period Cataclysmic Variable AKO 9

We present time-resolved, far-ultraviolet (FUV) spectroscopy and photometry of the 1.1 day eclipsing binary system AKO 9 in the globular cluster 47 Tucanae. The FUV spectrum of AKO 9 is blue and exhibits prominent C IV and He II emission lines. The spectrum broadly resembles that of long-period, cataclysmic variables in the galactic field. Combining our time-resolved FUV data with archival optical photometry of 47 Tuc, we refine the orbital period of AKO 9 and define an accurate ephemeris for the system. We also place constraints on several other system parameters, using a variety of observational constraints. We find that all of the empirical evidence is consistent with AKO 9 being a long-period dwarf nova in which mass transfer is driven by the nuclear expansion of a sub-giant donor star. We therefore conclude that AKO 9 is the first spectroscopically confirmed cataclysmic variable in 47 Tuc. We also briefly consider AKO 9's likely formation and ultimate evolution. Regarding the former, we find that the system was almost certainly formed dynamically, either via tidal capture or in a 3-body encounter. Regarding the latter, we show that AKO 9 will probably end its CV phase by becoming a detached, double WD system or by exploding in a Type Ia supernova.Comment: 40 pages, 11 figures, to appear in the Dec 20 issue of ApJ; minor changes to match final published versio

Astrometric Control of the Inertiality of the Hipparcos Catalog

Based on the most complete list of the results of an individual comparison of the proper motions for stars of various programs common to the Hipparcos catalog, each of which is an independent realization of the inertial reference frame with regard to stellar proper motions, we redetermined the vector $\omega$ of residual rotation of the ICRS system relative to the extragalactic reference frame. The equatorial components of this vector were found to be the following: $\omega_x = +0.04\pm 0.15$ mas yr$^{-1}$, $\omega_y = +0.18\pm 0.12$ mas yr$^{-1}$, and $\omega_z = -0.35\pm 0.09$ mas yr$^{-1}$.Comment: 8 pages, 1 figur

Graph-Controlled Insertion-Deletion Systems

In this article, we consider the operations of insertion and deletion working in a graph-controlled manner. We show that like in the case of context-free productions, the computational power is strictly increased when using a control graph: computational completeness can be obtained by systems with insertion or deletion rules involving at most two symbols in a contextual or in a context-free manner and with the control graph having only four nodes.Comment: In Proceedings DCFS 2010, arXiv:1008.127