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 $g$ 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 $\chi$ 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-