Numerical simulation of the dynamics of molecular markers involved in cell polarisation

A cell is polarised when it has developed a main axis of organisation through the reorganisation of its cytosqueleton and its intracellular organelles. Polarisation can occur spontaneously or be triggered by external signals, like gradients of signaling molecules ... In this work, we study mathematical models for cell polarisation. These models are based on nonlinear convection-diffusion equations. The nonlinearity in the transport term expresses the positive loop between the level of protein concentration localised in a small area of the cell membrane and the number of new proteins that will be convected to the same area. We perform numerical simulations and we illustrate that these models are rich enough to describe the apparition of a polarisome.Comment: 15 page

Finding the "truncated" polynomial that is closest to a function

When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits. And yet, the polynomial approximations that are actually implemented do have coefficients that are represented with a finite - and sometimes small - number of bits: this is due to the finiteness of the floating-point representations (for software implementations), and to the need to have small, hence fast and/or inexpensive, multipliers (for hardware implementations). We then have to consider polynomial approximations for which the degree-$i$ coefficient has at most $m_i$ fractional bits (in other words, it is a rational number with denominator $2^{m_i}$). We provide a general method for finding the best polynomial approximation under this constraint. Then, we suggest refinements than can be used to accelerate our method.Comment: 14 pages, 1 figur

Determinant representation of the domain-wall boundary condition partition function of a Richardson-Gaudin model containing one arbitrary spin

In this work we present a determinant expression for the domain-wall boundary condition partition function of rational (XXX) Richardson-Gaudin models which, in addition to $N-1$ spins $\frac{1}{2}$, contains one arbitrarily large spin $S$. The proposed determinant representation is written in terms of a set of variables which, from previous work, are known to define eigenstates of the quantum integrable models belonging to this class as solutions to quadratic Bethe equations. Such a determinant can be useful numerically since systems of quadratic equations are much simpler to solve than the usual highly non-linear Bethe equations. It can therefore offer significant gains in stability and computation speed.Comment: 17 pages, 0 figure

Numerical simulation on a cell polarisation model: the polar case

20 pagesWhen it is polarised, a cell develops an asymmetric distribution of specific molecular markers, cytoskeleton and cell membrane shape. Polarisation can occur spontaneously or be triggered by external signals, like gradients of signalling molecules... In this work, we use the published models of cell polarisation and we set a numerical analysis for these models. They are based on nonlinear convection-diffusion equations and the nonlinearity in the transport term expresses the positive loop between the level of protein concentration localised in a small area of the cell membrane and the number of new proteins that will be convected to the same area. We perform numerical simulations and we illustrate that these models are rich enough to describe the apparition of a polarisome

Faults in Linux 2.6

In August 2011, Linux entered its third decade. Ten years before, Chou et al. published a study of faults found by applying a static analyzer to Linux versions 1.0 through 2.4.1. A major result of their work was that the drivers directory contained up to 7 times more of certain kinds of faults than other directories. This result inspired numerous efforts on improving the reliability of driver code. Today, Linux is used in a wider range of environments, provides a wider range of services, and has adopted a new development and release model. What has been the impact of these changes on code quality? To answer this question, we have transported Chou et al.'s experiments to all versions of Linux 2.6; released between 2003 and 2011. We find that Linux has more than doubled in size during this period, but the number of faults per line of code has been decreasing. Moreover, the fault rate of drivers is now below that of other directories, such as arch. These results can guide further development and research efforts for the decade to come. To allow updating these results as Linux evolves, we define our experimental protocol and make our checkers available

Correctly rounded multiplication by arbitrary precision constants

We introduce an algorithm for multiplying a floating-point number $x$ by a constant $C$ that is not exactly representable in floating-point arithmetic. Our algorithm uses a multiplication and a fused multiply accumulate instruction. We give methods for checking whether, for a given value of $C$ and a given floating-point format, our algorithm returns a correctly rounded result for any $x$. When it does not, our methods give the values $x$ for which the multiplication is not correctly rounded.Nous proposons un algorithme permettant de multiplier un nombre virgule flottante x par une constante C qui n’est pas exactement représentable en virgule flottante.Notre algorithme nécessite la disponibilité d’une instruction “multiplication-accumulation”. Nous donnons des méthodes pour tester si,pour une constante C et un format virgule flottante donnés, notre algorithme donnera un arrondi correct pour toutes les valeurs de x.Quand ce n’est pas le cas,nos méthodes permettent de connaître toutes les valeurs de x pour lesquelles la multiplication par C n’est pas arrondie correctement

(M,p,k)-friendly points: a table-based method for trigonometric function evaluation

International audienceWe present a new way of approximating the sine and cosine functions by a few table look-ups and additions. It consists in first reducing the input range to a very small interval by using rotations with "(M, p, k) friendly angles", proposed in this work, and then by using a bipartite table method in a small interval. An implementation of the method for 24- bit case is described and compared with CORDIC. Roughly, the proposed scheme offers a speedup of 2 compared with an unfolded double-rotation radix-2 CORDIC

Bidirectional partial power converter interface for energy storage systems to provide peak shaving in grid-tied PV plants

The ever growing participation of modern renewable resources in electric markets has shaken the paradigm of generation-demand constant match. Most modern renewables add intermittent behaviour and high variability to electric markets, forcing other renewables and themselves to perform power curtailment and/or having extra generating units connected to the network to compensate power, voltage and frequency variations. In order to handle this scenario, Energy Storage Systems (ESSs) have risen as enabling technologies capable to provide backup energy to compensate power, voltage and frequency fluctuations and, at the same time, offer additional benefits as ancillary services, peak shaving, load shifting, base load generation, etc. This paper presents a novel bidirectional Partial Power Converter (PPC), as an interface between a Battery ESS (BESS) and a grid-tied Photovoltaic (PV) plant. To obtain a better understanding of the converter, its mathematical model is presented and its operation modes are explained. The main purpose of this configuration is to provide peak shaving capability to a grid-tied PV plant, while providing a high efficiency BESS. Simulation results show the operation of the full system (grid-tied PV plant and BESS), performing peak shaving under a step-down and up in solar irradiation

Silicon hyperuniform disordered photonic materials with a pronounced gap in the shortwave infrared

The mesoscale fabrication of silicon hyperuniform disordered materials with a broad and pronounced photonic gap in the shortwave infrared is reported. Due to their unique structure and their high refractive index, these fascinating materials are predicted to possess a complete photonic bandgap in the absence of any long-range order

Integer and Floating-Point Constant Multipliers for FPGAs

International audienceReconfigurable circuits now have a capacity that allows them to be used as floating-point accelerators. They offer massive parallelism, but also the opportunity to design optimised floating-point hardware operators not available in microprocessors. Multiplication by a constant is an important example of such an operator. This article presents an architecture generator for the correctly rounded multiplication of a floating-point number by a constant. This constant can be a floating-point value, but also an arbitrary irrational number. The multiplication of the significands is an instance of the well-studied problem of constant integer multiplication, for which improvement to existing algorithms are also proposed and evaluated