1,315 research outputs found
Structure Space of Model Proteins --A Principle Component Analysis
We study the space of all compact structures on a two-dimensional square
lattice of size . Each structure is mapped onto a vector in
-dimensions according to a hydrophobic model. Previous work has shown that
the designabilities of structures are closely related to the distribution of
the structure vectors in the -dimensional space, with highly designable
structures predominantly found in low density regions. We use principal
component analysis to probe and characterize the distribution of structure
vectors, and find a non-uniform density with a single peak. Interestingly, the
principal axes of this peak are almost aligned with Fourier eigenvectors, and
the corresponding Fourier eigenvalues go to zero continuously at the
wave-number for alternating patterns (). These observations provide a
stepping stone for an analytic description of the distribution of structural
points, and open the possibility of estimating designabilities of realistic
structures by simply Fourier transforming the hydrophobicities of the
corresponding sequences.Comment: 14 pages, 12 figures, Conclusion has been modifie
BTZ Black Hole Entropy from Ponzano-Regge Gravity
The entropy of the BTZ black hole is computed in the Ponzano-Regge
formulation of three-dimensional lattice gravity. It is seen that the correct
semi-classical behaviour of entropy is reproduced by states that correspond to
all possible triangulations of the Euclidean black hole.Comment: 11 pages LaTeX, 3 eps figures, some minor clarifications added,
result unchange
Current Oscillations, Interacting Hall Discs and Boundary CFTs
In this paper, we discuss the behavior of conformal field theories
interacting at a single point. The edge states of the quantum Hall effect (QHE)
system give rise to a particular representation of a chiral Kac-Moody current
algebra. We show that in the case of QHE systems interacting at one point we
obtain a ``twisted'' representation of the current algebra. The condition for
stationarity of currents is the same as the classical Kirchoff's law applied to
the currents at the interaction point. We find that in the case of two discs
touching at one point, since the currents are chiral, they are not stationary
and one obtains current oscillations between the two discs. We determine the
frequency of these oscillations in terms of an effective parameter
characterizing the interaction. The chiral conformal field theories can be
represented in terms of bosonic Lagrangians with a boundary interaction. We
discuss how these one point interactions can be represented as boundary
conditions on fields, and how the requirement of chirality leads to
restrictions on the interactions described by these Lagrangians. By gauging
these models we find that the theory is naturally coupled to a Chern-Simons
gauge theory in 2+1 dimensions, and this coupling is completely determined by
the requirement of anomaly cancellation.Comment: 32 pages, LateX. Uses amstex, amssymb. Typos corrected. To appear in
Int. J. Mod. Phys.
Electromagnetic Interaction of Massive Spin-3 State from String Theory
In the given work we study an interaction of second massive state of an open
boson string with the constant electromagnetic field. This state contains
massive fields with spins 3 and 1. Using the method of an open string BRST
quantization, we receive gauge-invariant lagrangian, describing the
electromagnetic interaction of these fields. From the explicit view of
transformations and lagrangian it follows that the presence of external
constant e/m field leads to the mixing of the given level states. Most likely
that the presence of the external field will lead to the mixing of the states
at other mass string levels as well.Comment: 17 pages, LaTeX, no figure
Symplectic potentials and resolved Ricci-flat ACG metrics
We pursue the symplectic description of toric Kahler manifolds. There exists
a general local classification of metrics on toric Kahler manifolds equipped
with Hamiltonian two-forms due to Apostolov, Calderbank and Gauduchon(ACG). We
derive the symplectic potential for these metrics. Using a method due to Abreu,
we relate the symplectic potential to the canonical potential written by
Guillemin. This enables us to recover the moment polytope associated with
metrics and we thus obtain global information about the metric. We illustrate
these general considerations by focusing on six-dimensional Ricci flat metrics
and obtain Ricci flat metrics associated with real cones over L^{pqr} and
Y^{pq} manifolds. The metrics associated with cones over Y^{pq} manifolds turn
out to be partially resolved with two blowup parameters taking special
(non-zero)values. For a fixed Y^{pq} manifold, we find explicit metrics for
several inequivalent blow-ups parametrised by a natural number k in the range
0<k<p. We also show that all known examples of resolved metrics such as the
resolved conifold and the resolution of C^3/Z_3 also fit the ACG
classification.Comment: LaTeX, 34 pages, 4 figures (v2)presentation improved, typos corrected
and references added (v3)matches published versio
Nonlocal regularisation of noncommutative field theories
We study noncommutative field theories, which are inherently nonlocal, using
a Poincar\'e-invariant regularisation scheme which yields an effective,
nonlocal theory for energies below a cut-off scale. After discussing the
general features and the peculiar advantages of this regularisation scheme for
theories defined in noncommutative spaces, we focus our attention onto the
particular case when the noncommutativity parameter is inversely proportional
to the square of the cut-off, via a dimensionless parameter . We work out
the perturbative corrections at one-loop order for a scalar theory with quartic
interactions, where the signature of noncommutativity appears in
-dependent terms. The implications of this approach, which avoids the
problems related to UV-IR mixing, are discussed from the perspective of the
Wilson renormalisation program. Finally, we remark about the generality of the
method, arguing that it may lead to phenomenologically relevant predictions,
when applied to realistic field theories.Comment: 1+11 pages, 6 figures; v2: references added, typos corrected,
conclusions unchange
N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models
We study N=2 nonlinear two dimensional sigma models with boundaries and their
massive generalizations (the Landau-Ginzburg models). These models are defined
over either Kahler or bihermitian target space manifolds. We determine the most
general local N=2 superconformal boundary conditions (D-branes) for these sigma
models. In the Kahler case we reproduce the known results in a systematic
fashion including interesting results concerning the coisotropic A-type branes.
We further analyse the N=2 superconformal boundary conditions for sigma models
defined over a bihermitian manifold with torsion. We interpret the boundary
conditions in terms of different types of submanifolds of the target space. We
point out how the open sigma models correspond to new types of target space
geometry. For the massive Landau-Ginzburg models (both Kahler and bihermitian)
we discuss an important class of supersymmetric boundary conditions which
admits a nice geometrical interpretation.Comment: 48 pages, latex, references and minor comments added, the version to
appear in JHE
Preventing transition to turbulence: a viscosity stratification does not always help
In channel flows a step on the route to turbulence is the formation of
streaks, often due to algebraic growth of disturbances. While a variation of
viscosity in the gradient direction often plays a large role in
laminar-turbulent transition in shear flows, we show that it has, surprisingly,
little effect on the algebraic growth. Non-uniform viscosity therefore may not
always work as a flow-control strategy for maintaining the flow as laminar.Comment: 9 pages, 8 figure
A family of thermostable fungal cellulases created by structure-guided recombination
SCHEMA structure-guided recombination of 3 fungal class II cellobiohydrolases (CBH II cellulases) has yielded a collection of highly thermostable CBH II chimeras. Twenty-three of 48 genes sampled from the 6,561 possible chimeric sequences were secreted by the Saccharomyces cerevisiae heterologous host in catalytically active form. Five of these chimeras have half-lives of thermal inactivation at 63°C that are greater than the most stable parent, CBH II enzyme from the thermophilic fungus Humicola insolens, which suggests that this chimera collection contains hundreds of highly stable cellulases. Twenty-five new sequences were designed based on mathematical modeling of the thermostabilities for the first set of chimeras. Ten of these sequences were expressed in active form; all 10 retained more activity than H. insolens CBH II after incubation at 63°C. The total of 15 validated thermostable CBH II enzymes have high sequence diversity, differing from their closest natural homologs at up to 63 amino acid positions. Selected purified thermostable chimeras hydrolyzed phosphoric acid swollen cellulose at temperatures 7 to 15°C higher than the parent enzymes. These chimeras also hydrolyzed as much or more cellulose than the parent CBH II enzymes in long-time cellulose hydrolysis assays and had pH/activity profiles as broad, or broader than, the parent enzymes. Generating this group of diverse, thermostable fungal CBH II chimeras is the first step in building an inventory of stable cellulases from which optimized enzyme mixtures for biomass conversion can be formulated
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