On FO2 quantifier alternation over words

We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. We then use the notion of condensed rankers, a refinement of the rankers defined by Weis and Immerman, to produce a decidable hierarchy of varieties which is interwoven with the quantifier alternation hierarchy -- and conjecturally equal to it. It follows that the latter hierarchy is decidable within one unit: given a formula alpha in FO^2[<], one can effectively compute an integer m such that alpha is equivalent to a formula with at most m+1 alternating blocks of quantifiers, but not to a formula with only m-1 blocks. This is a much more precise result than what is known about the quantifier alternation hierarchy within FO[<], where no decidability result is known beyond the very first levels

From algebra to logic: there and back again -- the story of a hierarchy

This is an extended survey of the results concerning a hierarchy of languages that is tightly connected with the quantifier alternation hierarchy within the two-variable fragment of first order logic of the linear order.Comment: Developments in Language Theory 2014, Ekaterinburg : Russian Federation (2014

The Ca2+/Cl− dependent L-[3H]glutamate binding: a new receptor or a particular transport process?

AbstractCa2+/Cl− increases the L-[3H]glutamate binding to rat brain synaptic membranes. It was suggested that Ca2+/Cl− expresses a new class of glutamate receptors. We report several lines of evidence suggesting that Ca2+/Cl− in fact favours a glutamate transport into membrane vesicles. This finding may serve to reconcile most of the discrepancies found in the literature on the glutamate binding and its pharmacology

Molecular Signatures in the Near Infrared Dayside Spectrum of HD 189733b

We have measured the dayside spectrum of HD 189733b between 1.5 and 2.5 microns using the NICMOS instrument on the Hubble Space Telescope. The emergent spectrum contains significant modulation, which we attribute to the presence of molecular bands seen in absorption. We find that water (H2O), carbon monoxide (CO), and carbon dioxide (CO2) are needed to explain the observations, and we are able to estimate the mixing ratios for these molecules. We also find temperature decreases with altitude in the ~0.01 < P < ~1 bar region of the dayside near-infrared photosphere and set an upper limit to the dayside abundance of methane (CH4) at these pressures.Comment: 13 pages, 3 figures. accepted in Astrophysical Journal Letter

Dilution effects in Ho2−x_{2-x}Yx_xSn2_2O7_7: from the Spin Ice to the single-ion magnet

A study of the modifications of the magnetic properties of Ho$_{2-x}$Y$_x$Sn$_2$O$_7$ upon varying the concentration of diamagnetic Y$^{3+}$ ions is presented. Magnetization and specific heat measurements show that the Spin Ice ground-state is only weakly affected by doping for $x\leq 0.3$, even if non-negligible changes in the crystal field at Ho$^{3+}$ occur. In this low doping range $\mu$SR relaxation measurements evidence a modification in the low-temperature dynamics with respect to the one observed in the pure Spin Ice. For $x\to 2$, or at high temperature, the dynamics involve fluctuations among Ho$^{3+}$ crystal field levels which give rise to a characteristic peak in $^{119}$Sn nuclear spin-lattice relaxation rate. In this doping limit also the changes in Ho$^{3+}$ magnetic moment suggest a variation of the crystal field parameters.Comment: 4 pages, 5 figures, proceedings of HFM2008 Conferenc

Complexity of checking whether two automata are synchronized by the same language

A deterministic finite automaton is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton to a particular one. We prove that it is a PSPACE-complete problem to check whether the language of reset words for a given automaton coincides with the language of reset words for some particular automaton.Comment: 12 pages, 4 figure

Towards A Holographic Model of D-Wave Superconductors

The holographic model for S-wave high T_c superconductors developed by Hartnoll, Herzog and Horowitz is generalized to describe D-wave superconductors. The 3+1 dimensional gravitational theory consists a symmetric, traceless second-rank tensor field and a U(1) gauge field in the background of the AdS black hole. Below T_c the tensor field which carries the U(1) charge undergoes the Higgs mechanism and breaks the U(1) symmetry of the boundary theory spontaneously. The phase transition characterized by the D-wave condensate is second order with the mean field critical exponent beta = 1/2. As expected, the AC conductivity is isotropic below T_c and the system becomes superconducting in the DC limit but has no hard gap.Comment: 14 pages, 2 figures, Some typos corrected, Matched with the published versio

Optimization in task--completion networks

We discuss the collective behavior of a network of individuals that receive, process and forward to each other tasks. Given costs they store those tasks in buffers, choosing optimally the frequency at which to check and process the buffer. The individual optimizing strategy of each node determines the aggregate behavior of the network. We find that, under general assumptions, the whole system exhibits coexistence of equilibria and hysteresis.Comment: 18 pages, 3 figures, submitted to JSTA

Synchronizing Automata on Quasi Eulerian Digraph

In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in $n$. Thus the main problem here is to prove quadratic (in $n$) upper bounds. Since 1964, this problem has been solved for few special classes of \sa. One of this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In this paper we introduce a new approach to prove quadratic upper bounds and explain it in terms of Markov chains and Perron-Frobenius theories. Using this approach we obtain a quadratic upper bound for a generalization of Eulerian automata.Comment: 8 pages, 1 figur

Partially Ordered Two-way B\"uchi Automata

We introduce partially ordered two-way B\"uchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way B\"uchi automata are B\"uchi automata which can change the direction in which the input is processed with the constraint that whenever a state is left, it is never re-entered again. Nondeterministic partially ordered two-way B\"uchi automata coincide with the first-order fragment Sigma2. Our main contribution is that deterministic partially ordered two-way B\"uchi automata are expressively complete for the first-order fragment Delta2. As an intermediate step, we show that deterministic partially ordered two-way B\"uchi automata are effectively closed under Boolean operations. A small model property yields coNP-completeness of the emptiness problem and the inclusion problem for deterministic partially ordered two-way B\"uchi automata.Comment: The results of this paper were presented at CIAA 2010; University of Stuttgart, Computer Scienc