6,200 research outputs found
A categorial study of initiality in uniform topology
This thesis consists of two chapters, of which the first presents a categorial study of the concept of initiality (also known as projective generation) and the second gives applications in the theory of uniform and quasi-uniform spaces
Non-equilibrium Transport in the Anderson model of a biased Quantum Dot: Scattering Bethe Ansatz Phenomenology
We derive the transport properties of a quantum dot subject to a source-drain
bias voltage at zero temperature and magnetic field. Using the Scattering Bethe
Anstaz, a generalization of the traditional Thermodynamic Bethe Ansatz to open
systems out of equilibrium, we derive exact results for the quantum dot
occupation out of equilibrium and, by introducing phenomenological spin- and
charge-fluctuation distribution functions in the computation of the current,
obtain the differential conductance for large U/\Gamma. The Hamiltonian to
describe the quantum dot system is the Anderson impurity Hamiltonian and the
current and dot occupation as a function of voltage are obtained numerically.
We also vary the gate voltage and study the transition from the mixed valence
to the Kondo regime in the presence of a non-equilibrium current. We conclude
with the difficulty we encounter in this model and possible way to solve them
without resorting to a phenomenological method.Comment: 20 pages, 20 figures, published versio
Nonnormal amplification in random balanced neuronal networks
In dynamical models of cortical networks, the recurrent connectivity can
amplify the input given to the network in two distinct ways. One is induced by
the presence of near-critical eigenvalues in the connectivity matrix W,
producing large but slow activity fluctuations along the corresponding
eigenvectors (dynamical slowing). The other relies on W being nonnormal, which
allows the network activity to make large but fast excursions along specific
directions. Here we investigate the tradeoff between nonnormal amplification
and dynamical slowing in the spontaneous activity of large random neuronal
networks composed of excitatory and inhibitory neurons. We use a Schur
decomposition of W to separate the two amplification mechanisms. Assuming
linear stochastic dynamics, we derive an exact expression for the expected
amount of purely nonnormal amplification. We find that amplification is very
limited if dynamical slowing must be kept weak. We conclude that, to achieve
strong transient amplification with little slowing, the connectivity must be
structured. We show that unidirectional connections between neurons of the same
type together with reciprocal connections between neurons of different types,
allow for amplification already in the fast dynamical regime. Finally, our
results also shed light on the differences between balanced networks in which
inhibition exactly cancels excitation, and those where inhibition dominates.Comment: 13 pages, 7 figure
Anderson-like impurity in the one-dimensional t-J model: formation of local states and magnetic behaviour
We consider an integrable model describing an Anderson-like impurity coupled
to an open -- chain. Both the hybridization (i.e. its coupling to bulk
chain) and the local spectrum can be controlled without breaking the
integrability of the model. As the hybridization is varied, holon and spinon
bound states appear in the many body ground state. Based on the exact solution
we study the state of the impurity and its contribution to thermodynamic
quantities as a function of an applied magnetic field. Kondo behaviour in the
magnetic response of the impurity can be observed provided that its parameters
have been adjusted properly to the energy scales of the holon and spinon
excitations of the one-dimensional bulk.Comment: 32 pages, 11 figure
Production of human recombinant proapolipoprotein A-I in Escherichia coli: purification and biochemical characterization
A human liver cDNA library was used to isolate a clone coding for apolipoprotein A-I (Apo A-I). The clone
carries the sequence for the prepeptide (18 amino acids), the propeptide (6 amino acids), and the mature protein
(243 amino acids). A coding cassette for the proapo A-I molecule was reconstructed by fusing synthetic
sequences, chosen to optimize expression and specifying the amino-terminal methionine and amino acids -6
to +14, to a large fragment of the cDNA coding for amino acids 15-243. The module was expressed in
pOTS-Nco, an Escherichia coli expression vector carrying the regulatable X P^ promoter, leading to the production
of proapolipoprotein A-I at up to 10% of total soluble proteins. The recombinant polypeptide was
purified and characterized in terms of apparent molecular mass, isoelectric point, and by both chemical and
enzymatic peptide mapping. In addition, it was assayed in vitro for the stimulation of the enzyme lecithin:
cholesterol acyltransferase. The data show for the first time that proapo A-I can be produced efficiently in
E. coli as a stable and undegraded protein having physical and functional properties indistinguishable from
those of the natural product
Motion clouds: model-based stimulus synthesis of natural-like random textures for the study of motion perception
Choosing an appropriate set of stimuli is essential to characterize the
response of a sensory system to a particular functional dimension, such as the
eye movement following the motion of a visual scene. Here, we describe a
framework to generate random texture movies with controlled information
content, i.e., Motion Clouds. These stimuli are defined using a generative
model that is based on controlled experimental parametrization. We show that
Motion Clouds correspond to dense mixing of localized moving gratings with
random positions. Their global envelope is similar to natural-like stimulation
with an approximate full-field translation corresponding to a retinal slip. We
describe the construction of these stimuli mathematically and propose an
open-source Python-based implementation. Examples of the use of this framework
are shown. We also propose extensions to other modalities such as color vision,
touch, and audition
Hadamard Regularization
Motivated by the problem of the dynamics of point-particles in high
post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a
certain class of functions which are smooth except at some isolated points
around which they admit a power-like singular expansion. We review the concepts
of (i) Hadamard ``partie finie'' of such functions at the location of singular
points, (ii) the partie finie of their divergent integral. We present and
investigate different expressions, useful in applications, for the latter
partie finie. To each singular function, we associate a partie-finie (Pf)
pseudo-function. The multiplication of pseudo-functions is defined by the
ordinary (pointwise) product. We construct a delta-pseudo-function on the class
of singular functions, which reduces to the usual notion of Dirac distribution
when applied on smooth functions with compact support. We introduce and analyse
a new derivative operator acting on pseudo-functions, and generalizing, in this
context, the Schwartz distributional derivative. This operator is uniquely
defined up to an arbitrary numerical constant. Time derivatives and partial
derivatives with respect to the singular points are also investigated. In the
course of the paper, all the formulas needed in the application to the physical
problem are derived.Comment: 50 pages, to appear in Journal of Mathematical Physic
Local Leaders in Random Networks
We consider local leaders in random uncorrelated networks, i.e. nodes whose
degree is higher or equal than the degree of all of their neighbors. An
analytical expression is found for the probability of a node of degree to
be a local leader. This quantity is shown to exhibit a transition from a
situation where high degree nodes are local leaders to a situation where they
are not when the tail of the degree distribution behaves like the power-law
with . Theoretical results are verified by
computer simulations and the importance of finite-size effects is discussed.Comment: 4 pages, 2 figure
Probing the Density in the Galactic Center Region: Wind-Blown Bubbles and High-Energy Proton Constraints
Recent observations of the Galactic center in high-energy gamma-rays (above
0.1TeV) have opened up new ways to study this region, from understanding the
emission source of these high-energy photons to constraining the environment in
which they are formed. We present a revised theoretical density model of the
inner 5pc surrounding Sgr A* based on the fact that the underlying structure of
this region is dominated by the winds from the Wolf-Rayet stars orbiting Sgr
A*. An ideal probe and application of this density structure is this high
energy gamma-ray emission. We assume a proton-scattering model for the
production of these gamma-rays and then determine first whether such a model is
consistent with the observations and second whether we can use these
observations to further constrain the density distribution in the Galactic
center.Comment: 36 pages including 17 figures, submitted to ApJ, comments welcom
Edge-disjoint spanners in Cartesian products of graphs
AbstractA spanning subgraph S=(V,E′) of a connected graph G=(V,E) is an (x+c)-spanner if for any pair of vertices u and v, dS(u,v)⩽dG(u,v)+c where dG and dS are the usual distance functions in G and S, respectively. The parameter c is called the delay of the spanner. We study edge-disjoint spanners in graphs, focusing on graphs formed as Cartesian products. Our approach is to construct sets of edge-disjoint spanners in a product based on sets of edge-disjoint spanners and colorings of the component graphs. We present several results on general products and then narrow our focus to hypercubes
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