Weak MSO+U with Path Quantifiers over Infinite Trees

This paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier U and quantification over infinite paths. The proof is by reduction to emptiness for a certain automaton model, while emptiness for the automaton model is decided using profinite trees.Comment: version of an ICALP 2014 paper with appendice

Using the ecology model to describe the impact of asthma on patterns of health care

BACKGROUND: Asthma changes both the volume and patterns of healthcare of affected people. Most studies of asthma health care utilization have been done in selected insured populations or in a single site such as the emergency department. Asthma is an ambulatory sensitive care condition making it important to understand the relationship between care in all sites across the health service spectrum. Asthma is also more common in people with fewer economic resources making it important to include people across all types of insurance and no insurance categories. The ecology of medical care model may provide a useful framework to describe the use of health services in people with asthma compared to those without asthma and identify subgroups with apparent gaps in care. METHODS: This is a case-control study using the 1999 U.S. Medical Expenditure Panel Survey. Cases are school-aged children (6 to 17 years) and young adults (18 to 44 years) with self-reported asthma. Controls are from the same age groups who have no self-reported asthma. Descriptive analyses and risk ratios are placed within the ecology of medical care model and used to describe and compare the healthcare contact of cases and controls across multiple settings. RESULTS: In 1999, the presence of asthma significantly increased the likelihood of an ambulatory care visit by 20 to 30% and more than doubled the likelihood of making one or more visits to the emergency department (ED). Yet, 18.8% of children and 14.5% of adults with asthma (over a million Americans) had no ambulatory care visits for asthma. About one in 20 to 35 people with asthma (5.2% of children and 3.6% of adults) were seen in the ED or hospital but had no prior or follow-up ambulatory care visits. These Americans were more likely to be uninsured, have no usual source of care and live in metropolitan areas. CONCLUSION: The ecology model confirmed that having asthma changes the likelihood and pattern of care for Americans. More importantly, the ecology model identified a subgroup with asthma who sought only emergent or hospital services

Weak cost automata over infinite trees

Cost automata are traditional finite state automata enriched with a finite set of counters that can be manipulated on each transition. Based on the evolution of counter values, a cost automaton defines a function from the set of structures under consideration to the natural numbers extended with infinity, modulo a boundedness relation that ignores exact values but preserves boundedness properties.Historically, variants of cost automata have been used to solve problems in language theory such as the star height problem. They also have a rich theory in their own right as part of the theory of regular cost functions, which was introduced by Colcombet as an extension to the theory of regular languages. It subsumes the classical theory since a language can be associated with the function that maps every structure in the language to 0 and everything else to infinity; it is a strict extension since cost functions can count some behaviour within the input.Regular cost functions have been previously studied over finite words and trees. This thesis extends the theory to infinite trees, where classical parity automata are enriched with a finite set of counters. Weak cost automata, which have priorities {0,1} or {1,2} and an additional restriction on the structure of the transition function, are shown to be equivalent to a weak cost monadic logic. A new notion of quasi-weak cost automata is also studied and shown to arise naturally in this cost setting. Moreover, a decision procedure is given to determine whether or not functions definable using weak or quasi-weak cost automata are equivalent up to the boundedness relation, which also proves the decidability of the weak cost monadic logic over infinite trees.The semantics of these cost automata over infinite trees are defined in terms of cost-parity games which are two-player infinite games where one player seeks to minimize the counter values and satisfy the parity condition, and the other player seeks to maximize the counter values or sabotage the parity condition. The main contributions and key technical results involve proving that certain cost-parity games admit positional or finite-memory strategies.These results also help settle the decidability of some special cases of long-standing open problems in the classical theory. In particular, it is shown that it is decidable whether a regular language of infinite trees is recognizable using a nondeterministic co-Büchi automaton. Likewise, given a Büchi or co-Büchi automaton as input, it is decidable whether or not there is a weak automaton recognizing the same language.</p

Weak cost automata over infinite trees

Cost automata are traditional finite state automata enriched with a finite set of counters that can be manipulated on each transition. Based on the evolution of counter values, a cost automaton defines a function from the set of structures under consideration to the natural numbers extended with infinity, modulo a boundedness relation that ignores exact values but preserves boundedness properties.Historically, variants of cost automata have been used to solve problems in language theory such as the star height problem. They also have a rich theory in their own right as part of the theory of regular cost functions, which was introduced by Colcombet as an extension to the theory of regular languages. It subsumes the classical theory since a language can be associated with the function that maps every structure in the language to 0 and everything else to infinity; it is a strict extension since cost functions can count some behaviour within the input.Regular cost functions have been previously studied over finite words and trees. This thesis extends the theory to infinite trees, where classical parity automata are enriched with a finite set of counters. Weak cost automata, which have priorities {0,1} or {1,2} and an additional restriction on the structure of the transition function, are shown to be equivalent to a weak cost monadic logic. A new notion of quasi-weak cost automata is also studied and shown to arise naturally in this cost setting. Moreover, a decision procedure is given to determine whether or not functions definable using weak or quasi-weak cost automata are equivalent up to the boundedness relation, which also proves the decidability of the weak cost monadic logic over infinite trees.The semantics of these cost automata over infinite trees are defined in terms of cost-parity games which are two-player infinite games where one player seeks to minimize the counter values and satisfy the parity condition, and the other player seeks to maximize the counter values or sabotage the parity condition. The main contributions and key technical results involve proving that certain cost-parity games admit positional or finite-memory strategies.These results also help settle the decidability of some special cases of long-standing open problems in the classical theory. In particular, it is shown that it is decidable whether a regular language of infinite trees is recognizable using a nondeterministic co-Büchi automaton. Likewise, given a Büchi or co-Büchi automaton as input, it is decidable whether or not there is a weak automaton recognizing the same language.This thesis is not currently available via ORA

Locations of the lip, poxB, and ilvBN genes on the physical map of Escherichia coli.

The lip locus, located at ca. 14.5 min on the Escherichia coli chromosome (6), is thought to encode an enzyme (or enzymes) involved in the terminal step(s) of lipoic acid biosynthesis (1, 14). We have used a representative mutant (JRG26) from the single genetic class of lipoic acid-auxotro-phic strains described by Herbert and Guest (7) to identify the Kohara A phage which carries the complementing lip gene (Table 1). This phage also carries a DNA segment corresponding to a second genetic class of lipoic acid-auxotrophic mutants recently isolated in our laboratory (to be published elsewhere). Our restriction data from the lip locus are in general agreement with the data of Kohara et al. (9). However, we have not attempted to exhaustively verify the Kohara physical map of phage X168. Our restriction data (4, 5) for EcoRV, PvuII, BamHI, HindIII, EcoRI, KpnI, and PstI sites around the poxB gene are in agreement with the Kohara restriction map (9). The restriction data of Wek et al. (15) for the ilvBN gene agrees with the Kohara map except for an EcoRV site not present in the Kohara map. It should be noted that our result (ilvBN at 3860 kbp) is essentially identical to those of Kohara (8) and Brewer (2), who systematically compared the directly determined re-striction map (9) with that predicted from data base DNA sequences. In contrast, Medigue et al (10) and Rudd et al. (11) report ilvBN at 3919 and 3923 kbp, respectively. The apparent disagreement is due to computer-simulated rever-sal of the rrnD-rrnE inversion of strain W3110 mapped by TABLE 1. Physical locations of the poxB, ilvBN, and lip genes Genetic map Physical map Phage(s)