Probabilistic properties of neuron spiking time-series obtained in vivo

Probabilistic properties of spiking time-series obtained in vivo from singular neurons belonging to Red Nucleus of brain are analyzed for two groups of rats: genetically defined rat model of depression (Flinders Sensitive Rat Line - FSL) and a control (healthy) group. The FSL group shows a distribution of interspike intervals with a much longer tail than that found for normal rats. The former distribution (for the FSL group) indicates a power-law with exponent α = - 1±0.1. A simple thermodynamic (noise) model is elaborated to explain obtained results. Received 13 May 2001 and Received in final form 20 September 2001     

Critical behavior of a three-state Potts model on a Voronoi lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8 000 sites. We consider the effect of an exponential decay of the interactions with the distance, , with a>0, and observe that this system seems to have critical exponents and which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for a=0 and as a logarithmic divergence for a=0.5 and a=1.0 Received 5 April 2000     

Theoretical Analysis of Kinesin KIF1A Transport Along Microtubule

Recently, a three-state model is presented to describe the intracellular traffic of unconventional (single-headed) kinesin KIF1A (Phys. Rev. Lett. 95:118101, 2005), in which each motor can bind strongly or weakly to its microtubule track, and each binding site of the track might be empty or occupied by one motor. As the usual two-state model, i.e. the totally asymmetric simple exclusion process (TASEP) with motor detachment and attachment, in steady state of the system, this three-state model also exhibits shock (or domain wall separating the high-density and low density phases) and boundary layers. In this study, using mean-field analysis, the conditions of existence of shock and boundary layers are obtained theoretically. Combined with numerical calculations, the properties of shock are also studied. This study will be helpful to understand the biophysical properties of the collective transport of kinesin KIF1A.     

Adiabatic population transfer in multistate chains via dressed intermediate states

The well-known process of stimulated Raman adiabatic passage (STIRAP) provides a robust technique for achieving complete population transfer between the first and last state of a three-state chain, with little population, even transiently, in the intermediate state. The extension of STIRAP to general N-state chainwise-linked systems continues to generate interest. Recently Malinovsky and Tannor (Phys. Rev. A 56, 4929 (1997)) have shown with numerical simulation that a resonant pulse sequence, which they term “straddle STIRAP”, can produce (under appropriate conditions, including specific pulse areas) complete population transfer with very little population in intermediate states. Their proposal supplements a pair of counterintuitively ordered delayed laser pulses, driving the first and last transition of the chain and corresponding to the pump and Stokes pulses in STIRAP, with one or more additional strong pulses of longer duration which couple the intermediate transition(s) and overlap both the pump and the Stokes pulses. In this paper, we modify the “straddling” Malinovsky-Tannor pulse sequence so that the intermediate couplings are constant (and strong), at least during the times when the pump and Stokes pulses are present, and the intermediate states therefore act as a strongly coupled subsystem with constant eigenvalues. Under this condition, we show that the original N-state chain is mathematically equivalent to a system comprising N-2 parallel -transitions, in which the initial state is coupled simultaneously to N-2 dressed intermediate states, which in turn are coupled to the final state. The population transfer is optimized by suitably tuning the pump and Stokes frequencies to resonance with one of these dressed intermediate states, which effectively acts as the single intermediate state in a three-state STIRAP-like process. We show that tuning to a dressed intermediate state turns the system (for both odd N and even N) into a three-state system - with all of the properties of conventional STIRAP (complete population transfer, little transient population in the intermediate states, insensitivity to variations in the laser parameters, such as pulse area). The success of the tuning-to-dressed-state idea is explained by using simple analytic approaches and illustrated with numerical simulations for four-, five-, six- and seven-state systems. Received: 17 April 1998 / Accepted: 15 June 1998     

Isomorphous phase transition and orientational freezing in hexagonal mixed crystal C 70(1 - x) C60x. A pseudospin model

A four-state pseudospin model is constructed for the isomorphous phase transition hcp-2↦hcp-1 in pure C₇₀ and in C₇₀-rich mixed crystal C _{70(1 - x)} C_60x. With the specific anisotropic pseudospin interactions adapted to the C₇₀ crystal the model is equivalent to a two-state Ising model in a temperature-dependent field. Replica symmetric state of the model is shown to approach the critical point when the width of distribution of random fields and/or of random bonds increases. The temperature of the phase transition and the phase equilibrium temperature then are practically constant, whereas the experiment shows their strong decrease with x. The main effect of dilution resides in an x-dependence of the model parameters. Dilatometric data on the hexagonal C _{70(1 - x)} C_60x are used to fit these parameters. A metastable disordered phase subsisting below the phase transition is discovered in a range of the model parameters and is shown to be responsible for the macroscopic behaviour of the system. A good agreement with experimental data is obtained for the spontaneous strain and for the x-dependence of the hysteresis. Received 20 April 2001 and Received in final form 26 September 2001     

Modeling language evolution: Aromanian,an endangered language in Greece

Time evolution of the relative density of speakers of an endangered language, Aromanian, which is spoken by a bilingual community in North-Western Greece, is approached theoretically by means of a two-state model and a three-state model. The same prestige and volatility parameters are used in these two models. Furthermore, a culture parameter and a second exponent are introduced in the three-state model. The parameters of each model are fitted to the current status of Aromanian, on the basis of field evidence collected by us, and the first findings about the risk of the language’s extinction are presented.     

Magnetic reconstructions at the surface of the B2 FeV alloy

We present an ab initio study of the magnetic surface reconstructions of the B2 FeV alloy using a self-consistent tight-binding linearized muffin tin orbital method developed in the atomic spheres approximation. For (001) and (111), the surface reconstruction stabilizes configurations unstable in the bulk alloy. When Fe is at the (001) surface, a c(2×2) in-plane antiferromagnetic order is found to be the ground state with magnetic moments of -2.32 and 2.27. A p(1×1) ↓ ferromagnetic order is displayed in case of V toplayer with a magnetic moment of -1.83. At the (111) surface, we obtain for Fe toplayer two solutions p(1×1)↑ and p(2×1). The configuration p(1×1)↑ is found to be the ground state with a magnetic moment per atom of 2.34. For V toplayer, only the p(1×1) ↓ solution is obtained with a moment of -0.84. In all cases, the Fe-V coupling is always antiparallel like in the bulk. Our results are discussed and compared to experiments. Received 11 August 2000 and Received in final form 8 June 2001     

Zero-temperature TAP equations for the Ghatak-Sherrington model

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field D for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determined as a function of D. Received 25 November 1999     

Kink solutions of the classical transverse field Ising chain

We investigate stationary and travelling wave solutions of the classical one-dimensional transverse field Ising model. Results are given on the existence, shape and stability of kink solutions and periodic solutions. We review recent analytical results (e.g., the proof of existence of a one-parameter family of stationary kink solutions and the proof of existence of travelling wave kink solutions with nonzero velocity c≠ 0) and extend them by the use of numerical methods. Small oscillations arising in the tails of travelling kink solutions are investigated numerically. In the end, stability analysis puts some light on pinning effects. Received 23 February 2001 and Received in final form 4 October 2001     

The association of octadecyl-end-capped poly-(sodium 2-acrylamido-2-methylpropanesulfonates) in water and salt solutions: A study by fluorescence spectroscopy and isothermal titration calorimetry

Steady-state fluorescence spectroscopy and isothermal titration calorimetry (ITC) have been used to study the aggregation in aqueous solutions of poly-(2-acrylamido)-2-methylpropanesulfonic acids, sodium salt mono-endcapped with either N,N-di-n-octadecyl or N-4-[(1-pyrenyl)butyl]-N-n-octadecyl which were prepared by free radical polymerization of 2-(acrylamido)-2-methylpropane sulfonic acid (AMPS) initiated with the azo compounds, 4,4'-azobis{cyano-N,N-di-n-octadecyl}pentanamide and 4,4'-azobis{cyano-N,N-[4-(1-pyrenyl)butyl]-n-octadecyl}pentanamide, respectively. Both techniques indicate the occurrence of multimolecular aggregates in solutions of the polymers in water and in 0.2 M NaCl. The concentration range for aggregation is about 1-14 mmol AMPS l^-1 (0.5-2.7 g l^-1) in 0.2 M NaCl and the enthalpy of micellization, estimated from ITC data, is ∼100 J [mol AMPS]^-1. The accessibility of the chromophores to neutral molecules and to cationic species was assessed by quenching of fluorescence with nitromethane and thallium nitrate, respectively. The association of the mono-endcapped polymers is compared to that of PAMPS derivatives carrying hydrophobic groups randomly attached along the chain. Received 7 August 2000 and Received in final form 26 October 2000     

Structure and rheology of concentrated wormlike micelles [4]at the shear-induced isotropic-to-nematic transition

We have investigated the simple shear flow behavior of wormlike micelles using small-angle neutron scattering and mechanical measurements. Ternary surfactant solutions made of cetylpyridinium chloride, hexanol and brine (0.2 M NaCl) and hereafter abbreviated as CPCl-Hex were studied in the concentrated regime, . In a preliminary report (Berret et al. [#!ref16!#]), the discontinuity of slope observed in the shear stress versus shear rate curve was interpreted in terms of first-order phase transition between an isotropic state and a shear-induced nematic state ( transition). At the transition rate, , the solution exhibits a macroscopic phase separation into viscous and fluid layers (inhomogeneous shear flow). Above a second characteristic shear rate, the flow becomes homogeneous again, the sheared solution being nematic only. The neutron patterns obtained in the two-state inhomogeneous region have been re-examined. Based on a consistent analysis of both orientational and translational degrees of freedom related to the wormlike micelles, we emphasize new features for the transition. In the present paper, the shear rate variations of the relative proportions of each phase in the two-state region, as well as the viscosity ratio between isotropic and nematic phases are derived. We demonstrate in addition that slightly above the transition rate, the shear induced nematic phase is already strongly oriented, with an order parameter P ₂ = 0.65. The orientational state is that of a nematic flow-oriented monodomain. Finally, from the locations of the neutron scattering maxima for each isotropic and nematic contributions, we evaluate the concentrations for each phase and and derived a dynamical phase diagram of CPCl-Hex, in terms of the stress versus and . According to the classification by Schmitt et al. [#!ref22!#], the transition observed in CPCl-Hex micellar solutions could result from a positive flow-concentration coupling, in agreement with the observed monotonically increasing shear stress in the two-phase region. Received: 16 February 1998 / Revised: 18 February 1998 / Accepted: 24 May 1998     

Casimir amplitudes in a quantum spherical model with long-range interaction

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is . Received 3 June 1999 and Received in final form 16 August 1999     

On N-wave type systems and their gauge equivalent

The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra are derived and analyzed. They are written in terms of (x, t) ∈ satisfying r = rank nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat dressing method is appropriately modified to construct their soliton solutions. Received 20 October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Quasi-periodic and periodic solutions for dynamical systems related to Korteweg-de Vries equation

We consider quasi-periodic and periodic (cnoidal) wave solutions of a set of n-component dynamical systems related to Korteweg-de Vries equation. Quasi-periodic wave solutions for these systems are expressed in terms of Novikov polynomials. Periodic solutions in terms of Hermite polynomials and generalized Hermite polynomials for dynamical systems related to Korteweg-de Vries equation are found. Received 15 October 2001 / Received in final form 6 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: nakostov@ie.bas.bg     

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q ³. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. Received 12 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: stauffer@thp.uni-koeln.de     

Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

The dispersion state of sodium-sulphonated polystyrene ( NaPSS) star-branched polyelectrolytes was investigated in salt-free aqueous solutions, by use of the small-angle X-ray scattering technique. With respect to polystyrene (PS) star-branched polymers of identical functionality, the ordering phenomenon occurring in the neighborhood of the overlap concentration c^* is reinforced and observed in a larger range of concentrations. Moreover, the degree of order is no longer maximum at c^* and is improved as the concentration decreases. The dispersion state is then mainly controlled by the electrostatic interaction. A crystalline order should therefore be achieved with stars of lower functionality, provided the electrostatic interaction is added to the osmotic repulsion. On the other hand, unusual scattering patterns are measured for aqueous solutions of NaPSS star polyelectrolytes. Indeed, a diffuse scattering is revealed at high angles, in addition to the regular diffraction rings related to preferred interstar distances. It is similar to the broad scattering peak produced by semidilute solutions of NaPSS linear polyelectrolytes and associated to the electrostatic correlation hole within the isotropic model. In the dilute regime (c < c ^*), it is just an intramolecular characteristic and represents the electrostatic repulsion between arms belonging to the same star. In the semidilute regime (c > c ^*), it also reflects the electrostatic repulsion between arms of distinct stars. So, as the concentration increases, it is mainly caused by the interpenetration of NaPSS stars. Such an observation is in agreement with the composite structure earlier proposed by Daoud and Cotton for star semidilute solutions. For c > c ^*, NaPSS star aqueous solutions can therefore be pictured as effective stars immersed in a matrix formed by the overlap of the arm ends. With respect to the dilute regime, the effective stars are smaller; the higher the concentration the smaller the size. Received 14 May 1999 and Received in final form 15 March 2000     

Dynamic light scattering and <Superscript>31</Superscript>P NMR spectroscopy study of the self-assembly of deoxyguanosine 5'-monophosphate

Self-assembling properties of deoxyguanosine 5'-monophosphate in isotropic solutions of concentrations from 0.5 wt% to 15 wt% were investigated by dynamic light scattering (DLS) and ³¹P NMR spectroscopy. A slow diffusive mode with a diffusion coefficient D _slow∼ 10^-12 m²/s was detected by DLS for the whole concentration range. This mode is assigned to the translational motion of large globular aggregates, similar to those observed in DNA and other polyelectrolyte solutions. The existence of such aggregates was confirmed by freeze fracture electron microscopy. Close to the isotropic-cholesteric phase transition, at 4 wt% c 10 wt%, also a faster diffusive mode is observed in the polarized DLS response and a very fast mode is detected by depolarized DLS. These modes are related to translational and rotational diffusion of the columnar stacks of guanosine molecules, which are favorably formed in the relatively narrow pretransitional region. The stacking was also revealed from the appearance of a secondary resonance line in the ³¹P NMR spectra. Using the hydrodynamic theory of Tirado and Garcia de la Torre, the length of the cylindrical stacks was found to be L = 364±78 ?, which is significantly larger than the values reported for other guanosine derivatives. Received 13 July 2001 and Received in final form 17 October 2001     

Flexible linear polyelectrolytes in multivalent salt solutions: Solubility conditions

Single- and double-stranded DNA and many biological and synthetic polyelectrolytes undergo two structural transitions upon increasing the concentration of multivalent salt or molecules. First, the expanded-stretched chains in low monovalent salt solutions collapse into nearly neutral compact structures when the density of multivalent salt approaches that of the monomers. With further addition of multivalent salt the chains redissolve acquiring expanded-coiled conformations. We study the redissolution transition using a two-state model (F.J. Solis, M. Olvera de la Cruz, J. Chem. Phys. 112, 2030 (2000)). The redissolution occurs when there is a high degree of screening of the electrostatic interactions between monomers, thus reducing the energy of the expanded state. The transition is determined by the chemical potential of the multivalent ions in the solution, μ and the inverse screening length, κ. The transition point also depends on the charge distribution along the chain but is nearly independent of the molecular weight and degree of flexibility of the polyelectrolytes. We generate a diagram of μversusκ² where we find two regions of expanded conformations, one with charged chains and the other with overcharged (inverted charge) chains, separated by a collapsed nearly neutral conformation region. The collapse and redissolution transitions occur when the trajectory of the properties of the salt crosses the boundaries between these regions. We find that in most cases the redissolution occurs within the same expanded branch from which the chain precipitates. Received 15 May 2000 and Received in final form 28 June 2000     

Stratification of foam films made from polyelectrolyte solutions

Studies of thin liquid films, made from semidilute polyelectrolyte solutions, are presented. The disjoining pressure variation with film thickness exhibits oscillations, corresponding to film stratification. The oscillations become sharper as the polymer concentration c increases, and disappear when salt is added. The period of the oscillations scales as c ^-1/2. The observed stratification is related to the polymer network and the size of the steps to the mesh size ξ. Received 25 April 2000 and Received in final form 3 October 2000