Minimal Forbidden Factors of Circular Words

Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have different (antifactorial) sets of minimal forbidden factors. There exist algorithms for computing the minimal forbidden factors of a word, as well as of a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an algorithm that, given the trie recognizing a finite antifactorial language $M$, computes a DFA recognizing the language whose set of minimal forbidden factors is $M$. In the same paper, they showed that the obtained DFA is minimal if the input trie recognizes the minimal forbidden factors of a single word. We generalize this result to the case of a circular word. We discuss several combinatorial properties of the minimal forbidden factors of a circular word. As a byproduct, we obtain a formal definition of the factor automaton of a circular word. Finally, we investigate the case of minimal forbidden factors of the circular Fibonacci words.Comment: To appear in Theoretical Computer Scienc

Degree of Sequentiality of Weighted Automata

Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the semantics is given by the set of weights of accepting runs. We focus on multi-sequential WA that are defined as finite unions of sequential WA. The problem we address is to minimize the size of this union. We call this minimum the degree of sequentiality of (the relation realized by) the WA. For a given positive integer k, we provide multiple characterizations of relations realized by a union of k sequential WA over an infinitary finitely generated group: a Lipschitz-like machine independent property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata. When possible, we effectively translate a WA into an equivalent union of k sequential WA. We also provide a decision procedure for our twinning property for commutative computable groups thus allowing to compute the degree of sequentiality. Last, we show that these results also hold for word transducers and that the associated decision problem is PSPACE -complete

Minimal Absent Words in Rooted and Unrooted Trees

We extend the theory of minimal absent words to (rooted and unrooted) trees, having edges labeled by letters from an alphabet of cardinality. We show that the set of minimal absent words of a rooted (resp. unrooted) tree T with n nodes has cardinality (resp.), and we show that these bounds are realized. Then, we exhibit algorithms to compute all minimal absent words in a rooted (resp. unrooted) tree in output-sensitive time (resp. assuming an integer alphabet of size polynomial in n

On Functionality of Visibly Pushdown Transducers

Visibly pushdown transducers form a subclass of pushdown transducers that (strictly) extends finite state transducers with a stack. Like visibly pushdown automata, the input symbols determine the stack operations. In this paper, we prove that functionality is decidable in PSpace for visibly pushdown transducers. The proof is done via a pumping argument: if a word with two outputs has a sufficiently large nesting depth, there exists a nested word with two outputs whose nesting depth is strictly smaller. The proof uses technics of word combinatorics. As a consequence of decidability of functionality, we also show that equivalence of functional visibly pushdown transducers is Exptime-Complete.Comment: 20 page

Field-tunable magnetic phases in a semiconductor-based two-dimensional Kondo lattice

We show the existence of intrinsic localized spins in mesoscopic high-mobility GaAs/AlGaAs heterostructures. Non-equilibrium transport spectroscopy reveals a quasi-regular distribution of the spins, and indicates that the spins interact indirectly via the conduction electrons. The interaction between spins manifests in characteristic zero-bias anomaly near the Fermi energy, and indicates gate voltage-controllable magnetic phases in high-mobility heterostructures. To address this issue further, we have also designed electrostatically tunable Hall devices, that allow a probing of Hall characteristics at the active region of the mesoscopic devices. We show that the zero field Hall coefficient has an anomalous contribution, which can be attributed to scattering by the localized spins. The anomalous contribution can be destroyed by an increase in temperature, source drain bias, or field range.Comment: To be published in PhysicaE EP2DS proceedin

Electronic states on a twin boundary of a d-wave superconductor

We show that an induced $s$-wave harmonic in the superconducting gap of an orthorhombic $d_{x^2-y^2}$ superconductor strongly affects the excitation spectrum near a twinning plane. In particular, it yields bound states of zero energy with areal density proportional to the relative weight of the $s$-wave component. An unusual scattering process responsible for the thermal conductivity across the twin boundary at low temperatures is also identified.Comment: 4 pages, ReVTEX, 2 PS-figure

Perinatal grief following neonatal comfort care for lethal fetal condition

BACKGROUND: The objective of the study was to assess perinatal grief experienced after continuing pregnancy and comfort care in women diagnosed with lethal fetal condition compared with termination of pregnancy for fetal anomaly (TOPFA). METHODS: This was a retrospective observational study which included women who chose to continue their pregnancy after the diagnosis of lethal fetal condition with comfort care support at birth at the Prenatal Diagnosis Center of Rennes Hospital from January 2007 to January 2017. Women were matched with controls who underwent TOPFA for the same type of fetal anomaly, gestational age at diagnosis and year. Women were evaluated by a questionnaire including the Perinatal Grief Scale. RESULTS: There were 28 patients in the continuing pregnancy group matched with 56 patients in the TOPFA group. Interval between fetal loss and completion of questionnaire was 6±3 years. Perinatal grief score was similar at 61±22 vs 58±18 (p = 0.729) in the continuing pregnancy and TOPFA groups, respectively. Women in the TOPFA group expressed more guilt. The cesarean-section rate in the continuing pregnancy group was 25% . CONCLUSION: Perinatal grief experienced by women opting for continuing pregnancy and comfort care after diagnosis of a potentially lethal fetal anomaly is not more severe than for those choosing TOPFA

Angular position of nodes in the superconducting gap of YBCO

The thermal conductivity of a YBCO single crystal has been studied as a function of the relative orientation of the crystal axes and a magnetic field rotating in the Cu-O planes. Measurements were carried out at several temperatures below T_c and at a fixed field of 30 kOe. A four-fold symmetry characteristic of a superconducting gap with nodes at odd multiples of 45 degrees in k-space was resolved. Experiments were performed to exclude a possible macroscopic origin for such a four-fold symmetry such as sample shape or anisotropic pinning. Our results impose an upper limit of 10% on the weight of the s-wave component of the essentially d-wave superconducting order parameter of YBCO.Comment: 10 pages, 4 figure

Coupled CDW and SDW Fluctuations as an Origin of Anomalous Properties of Ferromagnetic Superconductor UGe_2

It is shown that anomalous properties of UGe_2 can be understood in a unified way on the basis of a single assumption that the superconductivity is mediated by the coupled SDW and CDW fluctuations induced by the imperfect nesting of the Fermi surface with majority spins at T=T_x(P) deep in the ferromagnetic phase. Excess growth of uniform magnetization is shown to develop in the temperature range T<T_x(P) as a mode-coupling effect of coupled growth of SDW and CDW orderings, which has been observed by two different types of experiments. The coupled CDW and SDW fluctuations are shown to be essentially ferromagnetic spin fluctuations which induce a spin-triplet p-wave attraction. These fluctuations consist of two modes, spin and charge fluctuations with large momentum transfer of the nesting vector. An anomalous temperature dependence of the upper critical field H_c2(T) such as crossing of H_c2(T) at P=11.4 kbar and P=13.5 kbar, can be understood by the strong-coupling-superconductivity formalism. Temperature dependence of the lattice specific heat including a large shoulder near T_x is also explained quite well as an effect of a kind of Kohn anomaly associated with coupled SDW-CDW transition.Comment: (12 pages, 10 eps figures) submitted to J. Phys. Soc. Jp

Anisotropic three-dimentional magnetic fluctuations in heavy fermion CeRhIn5

CeRhIn5 is a heavy fermion antiferromagnet that orders at 3.8 K. The observation of pressure-induced superconductivity in CeRhIn5 at a very high Tc of 2.1 K for heavy fermion materials has led to speculations regarding to its magnetic fluctuation spectrum. Using magnetic neutron scattering, we report anisotropic three-dimensional antiferromagnetic fluctuations with an energy scale of less than 1.7 meV for temperatures as high as 3Tc. In addition, the effect of the magnetic fluctuations on electrical resistivity is well described by the Born approximation.Comment: 4 pages, 4 figure