41,548 research outputs found
Assessing the impact of non-additive noise on modelling transcriptional regulation with Gaussian processes
In transcriptional regulation, transcription factors (TFs) are often
unobservable at mRNA level or may be controlled outside of the system being
modelled. Gaussian processes are a promising approach for dealing with these
difficulties as a prior distribution can be defined over the latent TF activity
profiles and the posterior distribution inferred from the observed expression levels
of potential target genes. However previous approaches have been based on the
assumption of additive Gaussian noise to maintain analytical tractability. We
investigate the influence of a more realistic form of noise on a biologically accurate
system based on Michaelis-Menten kinetics
Analysis of arching around shallow tunnels using the boundary element approach
This paper describes a study of the effect of soil arching around shallow tunnels using the Boundary Element Method. Due to the different stiffnesses of the soil and the underground structure, then, under surface loading, the differential displacements generate shearing (arching) forces which increase or decrease the load on the tunnel. Under elastic conditions, the soil parameters (elastic modulus (E) and Poisson’s ratio ( )) both affect these arching forces. The Boundary Element Method is an effective numerical technique to achieve accurate results as it deals directly with the tractions at the tunnel/soil interface. Moreover, it is more efficient than the Finite Element Method in this case because no elements are needed within the soil itself
Spectral Stability of the Neumann Laplacian
We prove the equivalence of Hardy- and Sobolev-type inequalities, certain
uniform bounds on the heat kernel and some spectral regularity properties of
the Neumann Laplacian associated with an arbitrary region of finite measure in
Euclidean space. We also prove that if one perturbs the boundary of the region
within a uniform H\"older category then the eigenvalues of the Neumann
Laplacian change by a small and explicitly estimated amount.
AMS subject classifications: 35P15, 35J25, 47A75, 47B25, 26D10, 46E35.
Keywords: Neumann Laplacian, Sobolev inequalities, Hardy inequalities,
spectral stability, H\"older continuity.Comment: 23 page
Treatment dilemmas in a young man presenting with narcolepsy and psychotic symptoms.
Psychotic features can be present in both narcolepsy and psychosis, which can result in challenges in diagnosis and management. The prevalence of both conditions is low and the reports in young people are scarce. Our report illustrates the relevance of a thorough differential diagnosis as well as the need to explore treatment avenues based on the evidence available for both narcolepsy and psychosis symptoms to try and maximise the therapeutic impact
Quantum wires in magnetic field: A comparative study of the Hartree-Fock and the spin density functional approaches
We present a detailed comparison of the self-consistent calculations based on
the Hartree-Fock and the spin density functional theory for a spit-gate quantum
wire in the IQH regime. We demonstrate that both approaches provide
qualitatively (and in most cases quantitatively) similar results for the
spin-resolved electron density, spin polarization, spatial spin separation at
the edges and the effective factor. The both approach give the same values
of the magnetic fields corresponding to the successive subband depopulation and
qualitatively similar evolution of the magnetosubbands. Quantitatively,
however, the HF and the DFT subbands are different (even though the
corresponding total electron densities are practically the same). In contrast
to the HF approach, the DFT calculations predict much larger spatial spin
separation near the wire edge for the low magnetic fields (when the
compressible strips for spinless electrons are not formed yet). In the opposite
limit of the large fields, the Hatree-Fock and the DFT approaches give very
similar values for the spatial spin separation.Comment: 5 pages, 3 figure
Measurements continuous in time and a posteriori states in quantum
Measurements continuous in time were consistently introduced in quantum
mechanics and applications worked out, mainly in quantum optics. In this
context a quantum filtering theory has been developed giving the reduced state
after the measurement when a certain trajectory of the measured observables is
registered (the a posteriori states). In this paper a new derivation of
filtering equations is presented, in the cases of counting processes and of
measurement processes of diffusive type. It is also shown that the equation for
the a posteriori dynamics in the diffusive case can be obtained, by a suitable
limit, from that one in the counting case. Moreover, the paper is intended to
clarify the meaning of the various concepts involved and to discuss the
connections among them. As an illustration of the theory, simple models are
worked out.Comment: 31 page. See also related papers at
http://www.maths.nott.ac.uk/personal/vpb/research/mes_fou.html and
http://www.maths.nott.ac.uk/personal/vpb/research/fil_con.htm
Self-consistent equilibrium of a two-dimensional electron system with a reservoir in a quantizing magnetic field: Analytical approach
An analytical approach has been developed to describe grand canonical
equilibrium between a three dimensional (3D) electron system and a two
dimensional (2D) one, an energy of which is determined self-consistently with
an electron concentration. Main attention is paid to a Landau level (LL)
pinning effect. Pinning means a fixation of the LL on a common Fermi level of
the 2D and the 3D systems in a finite range of the magnetic field due to an
electron transfer from the 2D to the 3D system. A condition and a start of LL
pinning has been found for homogeneously broadened LLs. The electronic transfer
from the 3D to the 2D system controls an extremely sharp magnetic dependency of
an energy of the upper filled LL at integer filling of the LLs. This can cause
a significant increase of inhomogeneous broadening of the upper LL that was
observed in recent local probe experiments.Comment: 12 pages, 2 figures, revtex
Statistics of Neutron Stars at the Stage of Supersonic Propeller
We analyze the statistical distribution of neutron stars at the stage of a
supersonic propeller. An important point of our analysis is allowance for the
evolution of the angle of inclination of the magnetic axis to the spin axis of
the neutron star for the boundary of the transition to the supersonic propeller
stage for two models: the model with hindered particle escape from the stellar
surface and the model with free particle escape. As a result, we have shown
that a consistent allowance for the evolution of the inclination angle in the
region of extinct radio pulsars for the two models leads to an increase in the
total number of neutron stars at the supersonic propeller stage. This increase
stems from he fact that when allowing for the evolution of the inclination
angle for neutron stars in the region of extinct radio pulsars and,
hence, for the boundary of the transition to the propeller stage, this
transition is possible at shorter spin periods (P~5-10 s) than assumed in the
standard model.Comment: 15 pages, 6 figures; scale corrected for figures 3-
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