Sofic-Dyck shifts

We define the class of sofic-Dyck shifts which extends the class of Markov-Dyck shifts introduced by Inoue, Krieger and Matsumoto. Sofic-Dyck shifts are shifts of sequences whose finite factors form unambiguous context-free languages. We show that they correspond exactly to the class of shifts of sequences whose sets of factors are visibly pushdown languages. We give an expression of the zeta function of a sofic-Dyck shift

On the Commutative Equivalence of Context-Free Languages

The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated

Hypervelocity Stars. I. The Spectroscopic Survey

We discuss our targeted search for hypervelocity stars (HVSs), stars traveling with velocities so extreme that dynamical ejection from a massive black hole is their only suggested origin. Our survey, now half complete, has successfully identified a total of four probable HVSs plus a number of other unusual objects. Here we report the most recently discovered two HVSs: SDSS J110557.45+093439.5 and possibly SDSS J113312.12+010824, traveling with Galactic rest-frame velocities at least +508+-12 and +418+-10 km/s, respectively. The other late B-type objects in our survey are consistent with a population of post main-sequence stars or blue stragglers in the Galactic halo, with mean metallicity [Fe/H]=-1.3 and velocity dispersion 108+-5 km/s. Interestingly, the velocity distribution shows a tail of objects with large positive velocities that may be a mix of low-velocity HVSs and high-velocity runaway stars. Our survey also includes a number of DA white dwarfs with unusually red colors, possibly extremely low mass objects. Two of our objects are B supergiants in the Leo A dwarf, providing the first spectroscopic evidence for star formation in this dwarf galaxy within the last ~30 Myr.Comment: 10 pages, uses emulateapj, accepted by Ap

Interprocedural Reachability for Flat Integer Programs

We study programs with integer data, procedure calls and arbitrary call graphs. We show that, whenever the guards and updates are given by octagonal relations, the reachability problem along control flow paths within some language w1* ... wd* over program statements is decidable in Nexptime. To achieve this upper bound, we combine a program transformation into the same class of programs but without procedures, with an Np-completeness result for the reachability problem of procedure-less programs. Besides the program, the expression w1* ... wd* is also mapped onto an expression of a similar form but this time over the transformed program statements. Several arguments involving context-free grammars and their generative process enable us to give tight bounds on the size of the resulting expression. The currently existing gap between Np-hard and Nexptime can be closed to Np-complete when a certain parameter of the analysis is assumed to be constant.Comment: 38 pages, 1 figur

Silent Transitions in Automata with Storage

We consider the computational power of silent transitions in one-way automata with storage. Specifically, we ask which storage mechanisms admit a transformation of a given automaton into one that accepts the same language and reads at least one input symbol in each step. We study this question using the model of valence automata. Here, a finite automaton is equipped with a storage mechanism that is given by a monoid. This work presents generalizations of known results on silent transitions. For two classes of monoids, it provides characterizations of those monoids that allow the removal of \lambda-transitions. Both classes are defined by graph products of copies of the bicyclic monoid and the group of integers. The first class contains pushdown storages as well as the blind counters while the second class contains the blind and the partially blind counters.Comment: 32 pages, submitte

Slow group velocity and Cherenkov radiation

We theoretically study the effect of ultraslow group velocities on the emission of Vavilov-Cherenkov radiation in a coherently driven medium. We show that in this case the aperture of the group cone on which the intensity of the radiation peaks is much smaller than that of the usual wave cone associated with the Cherenkov coherence condition. We show that such a singular behaviour may be observed in a coherently driven ultracold atomic gas.Comment: 4 pages, 4 figure

Computational Complexity of Atomic Chemical Reaction Networks

Informally, a chemical reaction network is "atomic" if each reaction may be interpreted as the rearrangement of indivisible units of matter. There are several reasonable definitions formalizing this idea. We investigate the computational complexity of deciding whether a given network is atomic according to each of these definitions. Our first definition, primitive atomic, which requires each reaction to preserve the total number of atoms, is to shown to be equivalent to mass conservation. Since it is known that it can be decided in polynomial time whether a given chemical reaction network is mass-conserving, the equivalence gives an efficient algorithm to decide primitive atomicity. Another definition, subset atomic, further requires that all atoms are species. We show that deciding whether a given network is subset atomic is in $\textsf{NP}$, and the problem "is a network subset atomic with respect to a given atom set" is strongly $\textsf{NP}$-$\textsf{Complete}$. A third definition, reachably atomic, studied by Adleman, Gopalkrishnan et al., further requires that each species has a sequence of reactions splitting it into its constituent atoms. We show that there is a $\textbf{polynomial-time algorithm}$ to decide whether a given network is reachably atomic, improving upon the result of Adleman et al. that the problem is $\textbf{decidable}$. We show that the reachability problem for reachably atomic networks is $\textsf{Pspace}$-$\textsf{Complete}$. Finally, we demonstrate equivalence relationships between our definitions and some special cases of another existing definition of atomicity due to Gnacadja

Antidote-Controlled Platelet Inhibition Targeting von Willebrand Factor with Aptamers

Thrombus formation is initiated by platelets and leads to cardiovascular, cerebrovascular, and peripheral vascular disease, the leading causes of morbidity and mortality in the Western world. A number of antiplatelet drugs have improved clinical outcomes for thrombosis patients. However, their expanded use, especially in surgery, is limited by hemorrhage. Here, we describe an antiplatelet agent that can have its activity controlled by a matched antidote. We demonstrate that an RNA aptamer targeting von Willebrand factor (VWF) can potently inhibit VWF-mediated platelet adhesion and aggregation. By targeting this important adhesion step, we show that the aptamer molecule can inhibit platelet aggregation in PFA-100 and ristocetin-induced platelet aggregation assays. Furthermore, we show that a rationally designed antidote molecule can reverse the effects of the aptamer molecule, restoring platelet function quickly and effectively over a clinically relevant period. This aptamer-antidote pair represents a reversible antiplatelet agent inhibiting a platelet specific pathway. Furthermore, it is an important step towards creating safer drugs in clinics through the utilization of an antidote molecule.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63204/1/oli.2007.0089.pd

Unary Pushdown Automata and Straight-Line Programs

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs---one for the prefix, one for the lasso---that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is $\Pi_2 \mathrm P$-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply $\Pi_2 \mathrm P$-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards