16,833 research outputs found
How does bond percolation happen in coloured networks?
Percolation in complex networks is viewed as both: a process that mimics
network degradation and a tool that reveals peculiarities of the underlying
network structure. During the course of percolation, networks undergo
non-trivial transformations that include a phase transition in the
connectivity, and in some special cases, multiple phase transitions. Here we
establish a generic analytic theory that describes how structure and sizes of
all connected components in the network are affected by simple and
colour-dependant bond percolations. This theory predicts all locations where
the phase transitions take place, existence of wide critical windows that do
not vanish in the thermodynamic limit, and a peculiar phenomenon of colour
switching that occurs in small connected components. These results may be used
to design percolation-like processes with desired properties, optimise network
response to percolation, and detect subtle signals that provide an early
warning of a network collapse
Optimal designs in regression with correlated errors
This paper discusses the problem of determining optimal designs for
regression models, when the observations are dependent and taken on an
interval. A complete solution of this challenging optimal design problem is
given for a broad class of regression models and covariance kernels.
We propose a class of estimators which are only slightly more complicated
than the ordinary least-squares estimators. We then demonstrate that we can
design the experiments, such that asymptotically the new estimators achieve the
same precision as the best linear unbiased estimator computed for the whole
trajectory of the process. As a by-product we derive explicit expressions for
the BLUE in the continuous time model and analytic expressions for the optimal
designs in a wide class of regression models. We also demonstrate that for a
finite number of observations the precision of the proposed procedure, which
includes the estimator and design, is very close to the best achievable. The
results are illustrated on a few numerical examples.Comment: 38 pages, 5 figure
From in vitro evolution to protein structure
In the nanoscale, the machinery of life is mainly composed by macromolecules and macromolecular complexes that through their shapes create a network of interconnected mechanisms of biological processes. The relationship between shape and function of a biological molecule is the foundation of structural biology, that aims at studying the structure of a protein or a macromolecular complex to unveil the molecular mechanism through which it exerts its function. What about the reverse: is it possible by exploiting the function for which a protein was naturally selected to deduce the protein structure? To this aim we developed a method, called CAMELS (Coupling Analysis by Molecular Evolution Library Sequencing), able to obtain the structural features of a protein from an artificial selection based on that protein function. With CAMELS we tried to reconstruct the TEM-1 beta lactamase fold exclusively by generating and sequencing large libraries of mutational variants. Theoretically with this method it is possible to reconstruct the structure of a protein regardless of the species of origin or the phylogenetical time of emergence when a functional phenotypic selection of a protein is available. CAMELS allows us to obtain protein structures without needing to purify the protein beforehand
ARPES and NMTO Wannier Orbital Theory of LiMoO - Implications for Unusually Robust Quasi-One Dimensional Behavior
We present the results of a combined study by band theory and angle resolved
photoemission spectroscopy (ARPES) of the purple bronze,
LiMoO. Structural and electronic origins of its unusually
robust quasi-one dimensional (quasi-1D) behavior are investigated in detail.
The band structure, in a large energy window around the Fermi energy, is
basically 2D and formed by three Mo -like extended Wannier orbitals,
each one giving rise to a 1D band running at a 120 angle to the two
others. A structural "dimerization" from to gaps
the and bands while leaving the bands metallic in the gap, but
resonantly coupled to the gap edges and, hence, to the other directions. The
resulting complex shape of the quasi-1D Fermi surface (FS), verified by our
ARPES, thus depends strongly on the Fermi energy position in the gap, implying
a great sensitivity to Li stoichiometry of properties dependent on the FS, such
as FS nesting or superconductivity. The strong resonances prevent either a
two-band tight-binding model or a related real-space ladder picture from giving
a valid description of the low-energy electronic structure. We use our extended
knowledge of the electronic structure to newly advocate for framing
LiMoO as a weak-coupling material and in that framework can
rationalize both the robustness of its quasi-1D behavior and the rather large
value of its Luttinger liquid (LL) exponent . Down to a temperature of
6K we find no evidence for a theoretically expected downward
renormalization of perpendicular single particle hopping due to LL fluctuations
in the quasi-1D chains.Comment: 53 pages, 17 Figures, 6 year
On the prediction of stationary functional time series
This paper addresses the prediction of stationary functional time series.
Existing contributions to this problem have largely focused on the special case
of first-order functional autoregressive processes because of their technical
tractability and the current lack of advanced functional time series
methodology. It is shown here how standard multivariate prediction techniques
can be utilized in this context. The connection between functional and
multivariate predictions is made precise for the important case of vector and
functional autoregressions. The proposed method is easy to implement, making
use of existing statistical software packages, and may therefore be attractive
to a broader, possibly non-academic, audience. Its practical applicability is
enhanced through the introduction of a novel functional final prediction error
model selection criterion that allows for an automatic determination of the lag
structure and the dimensionality of the model. The usefulness of the proposed
methodology is demonstrated in a simulation study and an application to
environmental data, namely the prediction of daily pollution curves describing
the concentration of particulate matter in ambient air. It is found that the
proposed prediction method often significantly outperforms existing methods
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