628 research outputs found
Eigenelements of a General Aggregation-Fragmentation Model
We consider a linear integro-differential equation which arises to describe
both aggregation-fragmentation processes and cell division. We prove the
existence of a solution (\lb,\U,\phi) to the related eigenproblem. Such
eigenelements are useful to study the long time asymptotic behaviour of
solutions as well as the steady states when the equation is coupled with an
ODE. Our study concerns a non-constant transport term that can vanish at
since it seems to be relevant to describe some biological processes like
proteins aggregation. Non lower-bounded transport terms bring difficulties to
find estimates. All the work of this paper is to solve this problem
using weighted-norms
Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions
Topological Josephson junctions designed on the surface of a 3D-topological
insulator (TI) harbor Majorana bound states (MBS's) among a continuum of
conventional Andreev bound states. The distinct feature of these MBS's lies in
the -periodicity of their energy-phase relation that yields a fractional
ac Josephson effect and a suppression of odd Shapiro steps under
irradiation. Yet, recent experiments showed that a few, or only the first, odd
Shapiro steps are missing, casting doubts on the interpretation. Here, we show
that Josephson junctions tailored on the large bandgap 3D TI BiSe
exhibit a fractional ac Josephson effect acting on the first Shapiro step only.
With a modified resistively shunted junction model, we demonstrate that the
resilience of higher order odd Shapiro steps can be accounted for by thermal
poisoning driven by Joule overheating. Furthermore, we uncover a residual
supercurrent at the nodes between Shapiro lobes, which provides a direct and
novel signature of the current carried by the MBS. Our findings showcase the
crucial role of thermal effects in topological Josephson junctions and lend
support to the Majorana origin of the partial suppression of odd Shapiro steps.Comment: Revised article and Supplemental materia
The one-dimensional Keller-Segel model with fractional diffusion of cells
We investigate the one-dimensional Keller-Segel model where the diffusion is
replaced by a non-local operator, namely the fractional diffusion with exponent
. We prove some features related to the classical
two-dimensional Keller-Segel system: blow-up may or may not occur depending on
the initial data. More precisely a singularity appears in finite time when
and the initial configuration of cells is sufficiently concentrated.
On the opposite, global existence holds true for if the initial
density is small enough in the sense of the norm.Comment: 12 page
Automated multi-objective calibration of biological agent-based simulations
Computational agent-based simulation (ABS) is increasingly used to complement laboratory techniques in advancing our understanding of biological systems. Calibration, the identification of parameter values that align simulation with biological behaviours, becomes challenging as increasingly complex biological domains are simulated. Complex domains cannot be characterized by single metrics alone, rendering simulation calibration a fundamentally multi-metric optimization problem that typical calibration techniques cannot handle. Yet calibration is an essential activity in simulation-based science; the baseline calibration forms a control for subsequent experimentation and hence is fundamental in the interpretation of results. Here, we develop and showcase a method, built around multi-objective optimization, for calibrating ABSs against complex target behaviours requiring several metrics (termed objectives) to characterize. Multi-objective calibration (MOC) delivers those sets of parameter values representing optimal trade-offs in simulation performance against each metric, in the form of a Pareto front. We use MOC to calibrate a well-understood immunological simulation against both established a priori and previously unestablished target behaviours. Furthermore, we show that simulation-borne conclusions are broadly, but not entirely, robust to adopting baseline parameter values from different extremes of the Pareto front, highlighting the importance of MOC's identification of numerous calibration solutions. We devise a method for detecting overfitting in a multi-objective context, not previously possible, used to save computational effort by terminating MOC when no improved solutions will be found. MOC can significantly impact biological simulation, adding rigour to and speeding up an otherwise time-consuming calibration process and highlighting inappropriate biological capture by simulations that cannot be well calibrated. As such, it produces more accurate simulations that generate more informative biological predictions
Deflated GMRES for Systems with Multiple Shifts and Multiple Right-Hand Sides
We consider solution of multiply shifted systems of nonsymmetric linear
equations, possibly also with multiple right-hand sides. First, for a single
right-hand side, the matrix is shifted by several multiples of the identity.
Such problems arise in a number of applications, including lattice quantum
chromodynamics where the matrices are complex and non-Hermitian. Some Krylov
iterative methods such as GMRES and BiCGStab have been used to solve multiply
shifted systems for about the cost of solving just one system. Restarted GMRES
can be improved by deflating eigenvalues for matrices that have a few small
eigenvalues. We show that a particular deflated method, GMRES-DR, can be
applied to multiply shifted systems. In quantum chromodynamics, it is common to
have multiple right-hand sides with multiple shifts for each right-hand side.
We develop a method that efficiently solves the multiple right-hand sides by
using a deflated version of GMRES and yet keeps costs for all of the multiply
shifted systems close to those for one shift. An example is given showing this
can be extremely effective with a quantum chromodynamics matrix.Comment: 19 pages, 9 figure
Prevalence of resistance mutations related to integrase inhibitor S/GSK1349572 in HIV-1 subtype B raltegravir-naive and -treated patients
Objectives To compare the frequency of previously in vitro-selected integrase mutations (T124A, T124A/S153F, S153Y, T124A/S153Y and L101I/T124A/S153Y) conferring resistance to S/GSK1349572 between HIV-1 subtype B integrase inhibitor (INI)-naive and raltegravir-treated patients. Methods Integrase sequences from 650 INI-naive patients and 84 raltegravir-treated patients were analysed. Results The T124A mutation alone and the combination T124A/L101I were more frequent in raltegravir-failing patients than in INI-naive patients (39.3% versus 24.5%, respectively, Pâ=â0.005 for T124A and 20.2% versus 10.0%, respectively, Pâ=â0.008 for T124A/L101I). The S153Y/F mutations were not detected in any integrase sequence (except for S153F alone, only detected in one INI-naive patient). Conclusions T124A and T124A/L101I, more frequent in raltegravir-treated patients, could have some effect on raltegravir response and their presence could play a role in the selection of other mutations conferring S/GSK1349572 resistance. The impact of raltegravir-mediated changes such as these on the virological response to S/GSK1349572 should be studied further
Optical gain in 1.3-ÎŒm electrically driven dilute nitride VCSOAs
We report the observation of room-temperature optical gain at 1.3 ÎŒm in electrically driven dilute nitride vertical cavity semiconductor optical amplifiers. The gain is calculated with respect to injected power for samples with and without a confinement aperture. At lower injected powers, a gain of almost 10 dB is observed in both samples. At injection powers over 5 nW, the gain is observed to decrease. For nearly all investigated power levels, the sample with confinement aperture gives slightly higher gain
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