576 research outputs found
Complexity of Equivalence and Learning for Multiplicity Tree Automata
We consider the complexity of equivalence and learning for multiplicity tree
automata, i.e., weighted tree automata over a field. We first show that the
equivalence problem is logspace equivalent to polynomial identity testing, the
complexity of which is a longstanding open problem. Secondly, we derive lower
bounds on the number of queries needed to learn multiplicity tree automata in
Angluin's exact learning model, over both arbitrary and fixed fields.
Habrard and Oncina (2006) give an exact learning algorithm for multiplicity
tree automata, in which the number of queries is proportional to the size of
the target automaton and the size of a largest counterexample, represented as a
tree, that is returned by the Teacher. However, the smallest
tree-counterexample may be exponential in the size of the target automaton.
Thus the above algorithm does not run in time polynomial in the size of the
target automaton, and has query complexity exponential in the lower bound.
Assuming a Teacher that returns minimal DAG representations of
counterexamples, we give a new exact learning algorithm whose query complexity
is quadratic in the target automaton size, almost matching the lower bound, and
improving the best previously-known algorithm by an exponential factor
Surface states in nearly modulated systems
A Landau model is used to study the phase behavior of the surface layer for
magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz
point marking the boundary between modulated and homogeneous bulk phases. The
model incorporates surface and bulk fields and includes a term in the free
energy proportional to the square of the second derivative of the order
parameter in addition to the usual term involving the square of the first
derivative. In the limit of vanishing bulk field, three distinct types of
surface ordering are possible: a wetting layer, a non-wet layer having a small
deviation from bulk order, and a different non-wet layer with a large deviation
from bulk order which decays non-monotonically as distance from the wall
increases. In particular the large deviation non-wet layer is a feature of
systems at the Lifshitz point and also those having only homogeneous bulk
phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.
Towards an efficient biosensor for the detection of lipopolysaccharide in sepsis using molecularly imprinted polymers
Image-potential band-gap narrowing at a metal/semiconductor interface
GW approximation is used to systematically revisit the image-potential
band-gap narrowing at metal/semiconductor interfaces proposed by Inkson in the
1970's. Here we have questioned how the narrowing as calculated from
quasi-particle energy spectra for the jellium/Si interface depends on of
the jellium. The gap narrowing is found to only weakly depend on (i.e.,
narrowing eV even for a large . Hence we can turn to
smaller polarizability in the semiconductor side as an important factor in
looking for larger narrowing.Comment: 6 pages, 7 figure
Electronic properties of metal induced gap states at insulator/metal interfaces -- dependence on the alkali halide and the possibility of excitonic mechanism of superconductivity
Motivated from the experimental observation of metal induced gap states
(MIGS) at insulator/metal interfaces by Kiguchi {\it et al.} [Phys. Rev. Lett.
{\bf 90}, 196803 (2003)], we have theoretically investigated the electronic
properties of MIGS at interfaces between various alkali halides and a metal
represented by a jellium with the first-principles density functional method.
We have found that, on top of the usual evanescent state, MIGS generally have a
long tail on halogen sites with a -like character, whose penetration depth
() is as large as half the lattice constant of bulk alkali halides.
This implies that , while little dependent on the carrier density in
the jellium, is dominated by the lattice constant (hence by energy gap) of the
alkali halide, where . We also propose a possibility of the MIGS working favorably for the
exciton-mediated superconductivity.Comment: 7 pages, 9 figure
Light scattering study of the “pseudo-layer” compression elastic constant in a twist-bend nematic liquid crystal
The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or “pseudo-layers”, each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining “layer” compression and bending ought to be characterized by an effective layer compression elastic constant Beff and average director splay constant Keff1. The magnitude of Keff1 is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, Beff could differ substantially from the typical value of ∼10⁶ Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the “pseudo-layer” structure of the TB phase with Beff in the range 10³–10⁴ Pa. We show additionally that the temperature dependence of Beff at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director
Strong Enhancement of Superconducting Correlation in a Two-Component Fermion Gas
We study high-density electron-hole (e-h) systems with the electron density
slightly larger than the hole density. We find a new superconducting phase, in
which the excess electrons form Cooper pairs moving in an e-h BCS phase. The
coexistence of the e-h and e-e orders is possible because e and h have opposite
charges, whereas analogous phases are impossible in the case of two fermion
species that have the same charge or are neutral. Most strikingly, the e-h
order enhances the superconducting e-h order parameter by more than one order
of magnitude as compared with that given by the BCS formula, for the same value
of the effective e-e attractive potential \lambda^{ee}. This new phase should
be observable in an e-h system created by photoexcitation in doped
semiconductors at low temperatures.Comment: 5 pages including 5 PostScript figure
Second harmonic light scattering induced by defects in the twist-bend nematic phase of liquid crystal dimers
The nematic twist-bend (NTB) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase -- the first distinct nematic variant discovered in many years. The NTB phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The NTB structure thus provides another fascinating example of spontaneous chiral symmetry breaking in nature. The order parameter driving the formation of the heliconical state has been theoretically conjectured to be a polarization field, deriving from the bent conformation of the dimers, that rotates helically with the same nanoscale pitch as the director field. It therefore presents a significant challenge for experimental detection. Here we report a second harmonic light scattering (SHLS) study on two achiral, NTB-forming LCs, which is sensitive to the polarization field due to micron-scale distortion of the helical structure associated with naturally-occurring textural defects. These defects are parabolic focal conics of smectic-like ``pseudo-layers", defined by planes of equivalent phase in a coarse-grained description of the NTB state. Our SHLS data are explained by a coarse-grained free energy density that combines a Landau-deGennes expansion of the polarization field, the elastic energy of a nematic, and a linear coupling between the two
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