Existence and Stability of Standing Pulses in Neural Networks : I Existence

We consider the existence of standing pulse solutions of a neural network integro-differential equation. These pulses are bistable with the zero state and may be an analogue for short term memory in the brain. The network consists of a single-layer of neurons synaptically connected by lateral inhibition. Our work extends the classic Amari result by considering a non-saturating gain function. We consider a specific connectivity function where the existence conditions for single-pulses can be reduced to the solution of an algebraic system. In addition to the two localized pulse solutions found by Amari, we find that three or more pulses can coexist. We also show the existence of nonconvex ``dimpled'' pulses and double pulses. We map out the pulse shapes and maximum firing rates for different connection weights and gain functions.Comment: 31 pages, 29 figures, submitted to SIAM Journal on Applied Dynamical System

Numerical Approximations Using Chebyshev Polynomial Expansions

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in connection to solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second order boundary value problems in fluid dynamics are presented.Comment: minor wording changes, some typos have been eliminate

Use of Plasmodium falciparum culture-adapted field isolates for in vitro exflagellation-blocking assay

International audienceA major requirement for malaria elimination is the development of transmission-blocking interventions. In vitro transmission-blocking bioassays currently mostly rely on the use of very few Plasmodium falciparum reference laboratory strains isolated decades ago. To fill a piece of the gap between laboratory experimental models and natural systems, the purpose of this work was to determine if culture-adapted field isolates of P. falciparum are suitable for in vitro transmission-blocking bioassays targeting functional maturity of male gametocytes: exflagellation. Plasmodium falciparum isolates were adapted to in vitro culture before being used for in vitro gametocyte production. Maturation was assessed by microscopic observation of gametocyte morphology over time of culture and the functional viability of male gametocytes was assessed by microscopic counting of exflagellating gametocytes. Suitability for in vitro exflagellation-blocking bioassays was determined using dihydroartemisinin and methylene blue. In vitro gametocyte production was achieved using two isolates from French Guiana and two isolates from Cambodia. Functional maturity of male gametocytes was assessed by exflagellation observations and all four isolates could be used in exflagellation-blocking bioassays with adequate response to methylene blue and dihydroartemisinin. This work shows that in vitro culture-adapted P. falciparum field isolates of different genetic background, from South America and Southeast Asia, can successfully be used for bioassays targeting the male gametocyte to gamete transition, exflagellation

Noise-induced perturbations of dispersion-managed solitons

We study noise-induced perturbations of dispersion-managed solitons by developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte-Carlo simulations and reconstruct the probability density functions of the solution parameters under the effect of noise.Comment: 12 pages, 6 figure

A statistical mechanics approach to autopoietic immune networks

The aim of this work is to try to bridge over theoretical immunology and disordered statistical mechanics. Our long term hope is to contribute to the development of a quantitative theoretical immunology from which practical applications may stem. In order to make theoretical immunology appealing to the statistical physicist audience we are going to work out a research article which, from one side, may hopefully act as a benchmark for future improvements and developments, from the other side, it is written in a very pedagogical way both from a theoretical physics viewpoint as well as from the theoretical immunology one. Furthermore, we have chosen to test our model describing a wide range of features of the adaptive immune response in only a paper: this has been necessary in order to emphasize the benefit available when using disordered statistical mechanics as a tool for the investigation. However, as a consequence, each section is not at all exhaustive and would deserve deep investigation: for the sake of completeness, we restricted details in the analysis of each feature with the aim of introducing a self-consistent model.Comment: 22 pages, 14 figur

Chemoenzymatic Probes for Detecting and Imaging Fucose-α(1-2)-galactose Glycan Biomarkers

The disaccharide motif fucose-α(1-2)-galactose (Fucα(1-2)Gal) is involved in many important physiological processes, such as learning and memory, inflammation, asthma, and tumorigenesis. However, the size and structural complexity of Fucα(1-2)Gal-containing glycans have posed a significant challenge to their detection. We report a new chemoenzymatic strategy for the rapid, sensitive detection of Fucα(1-2)Gal glycans. We demonstrate that the approach is highly selective for the Fucα(1-2)Gal motif, detects a variety of complex glycans and glycoproteins, and can be used to profile the relative abundance of the motif on live cells, discriminating malignant from normal cells. This approach represents a new potential strategy for biomarker detection and expands the technologies available for understanding the roles of this important class of carbohydrates in physiology and disease

Machine learning-based phenotypic imaging to characterise the targetable biology of <i>Plasmodium falciparum</i> male gametocytes for the development of transmission-blocking antimalarials

Preventing parasite transmission from humans to mosquitoes is recognised to be critical for achieving elimination and eradication of malaria. Consequently developing new antimalarial drugs with transmission-blocking properties is a priority. Large screening campaigns have identified many new transmission-blocking molecules, however little is known about how they target the mosquito-transmissible Plasmodium falciparum stage V gametocytes, or how they affect their underlying cell biology. To respond to this knowledge gap, we have developed a machine learning image analysis pipeline to characterise and compare the cellular phenotypes generated by transmission-blocking molecules during male gametogenesis. Using this approach, we studied 40 molecules, categorising their activity based upon timing of action and visual effects on the organisation of tubulin and DNA within the cell. Our data both proposes new modes of action and corroborates existing modes of action of identified transmission-blocking molecules. Furthermore, the characterised molecules provide a new armoury of tool compounds to probe gametocyte cell biology and the generated imaging dataset provides a new reference for researchers to correlate molecular target or gene deletion to specific cellular phenotype. Our analysis pipeline is not optimised for a specific organism and could be applied to any fluorescence microscopy dataset containing cells delineated by bounding boxes, and so is potentially extendible to any disease model

Geometry and symmetries of multi-particle systems

The quantum dynamical evolution of atomic and molecular aggregates, from their compact to their fragmented states, is parametrized by a single collective radial parameter. Treating all the remaining particle coordinates in d dimensions democratically, as a set of angles orthogonal to this collective radius or by equivalent variables, bypasses all independent-particle approximations. The invariance of the total kinetic energy under arbitrary d-dimensional transformations which preserve the radial parameter gives rise to novel quantum numbers and ladder operators interconnecting its eigenstates at each value of the radial parameter. We develop the systematics and technology of this approach, introducing the relevant mathematics tutorially, by analogy to the familiar theory of angular momentum in three dimensions. The angular basis functions so obtained are treated in a manifestly coordinate-free manner, thus serving as a flexible generalized basis for carrying out detailed studies of wavefunction evolution in multi-particle systems.Comment: 37 pages, 2 eps figure

The Ising model and Special Geometries

We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model ($n \le 6$) are homomorphic to their adjoint. This property of being self-adjoint up to operator homomorphisms, is equivalent to the fact that their symmetric square, or their exterior square, have rational solutions. The differential Galois groups are in the special orthogonal, or symplectic, groups. This self-adjoint (up to operator equivalence) property means that the factor operators we already know to be Derived from Geometry, are special globally nilpotent operators: they correspond to "Special Geometries". Beyond the small order factor operators (occurring in the linear differential operators associated with $\chi^{(5)}$ and $\chi^{(6)}$), and, in particular, those associated with modular forms, we focus on the quite large order-twelve and order-23 operators. We show that the order-twelve operator has an exterior square which annihilates a rational solution. Then, its differential Galois group is in the symplectic group $Sp(12, \mathbb{C})$. The order-23 operator is shown to factorize in an order-two operator and an order-21 operator. The symmetric square of this order-21 operator has a rational solution. Its differential Galois group is, thus, in the orthogonal group $SO(21, \mathbb{C})$.Comment: 33 page

Lattice Green functions in all dimensions

We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there is a close connection between the LGF of the $d$-dimensional hypercubic lattice and that of the $(d-1)$-dimensional diamond lattice. We give constant-term formulations of LGFs for all lattices and dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the s.c., b.c.c. and diamond LGFs and some Ramanujan-type formulae for $1/\pi.$Comment: 30 page