Bifurcations of mixed-mode oscillations in a stellate cell model

Experimental recordings of the membrane potential of stellate cells within the entorhinal cortex show a transition from subthreshold oscillations (STOs) via mixed-mode oscillations (MMOs) to relaxation oscillations under increased injection of depolarizing current. Acker et al. introduced a 7D conductance based model which reproduces many features of the oscillatory patterns observed in these experiments. For the first time, we present a comprehensive bifurcation analysis of this model by using the software package AUTO. In particular, we calculate the stable MMO branches within the bifurcation diagram of this model, as well as other MMO patterns which are unstable. We then use geometric singular perturbation theory to demonstrate how the bifurcations are governed by a 3D reduced model introduced by Rotstein et al. We extend their analysis to explain all observed MMO patterns within the bifurcation diagram. A key role in this bifurcation analysis is played by a novel homoclinic bifurcation structure connecting to a saddle equilibrium on the unstable branch of the corresponding critical manifold. This type of homoclinic connection is possible due to canards of folded node (folded saddle-node) type.     

Can spontaneous cell movements be modelled as Lévy walks?

Spontaneous cell movement is a random motion that takes place in the absence of external guiding stimuli. The spontaneous movements of HaCaT and NHDF cells (cells of the epidermis) are well represented as continuous Markovian processes driven by multiplicative noise [D. Selmeczi, S. Mosler, P.H. Hagedorn, N.B. Larsen, H. Flyvbjerg, Biophysical Journal 89 (2005) 912]. Model components are, however, ad hoc as they are inspired by fits to experimental data. As a consequence, model agreement with experimental data does not add much to our understanding of spontaneous movements of these cells beyond demonstrating that they can be modelled phenomenologically. Here it is noted that a slight re-parameterization and re-interpretation of the driving noise leads to the model of Lubashevsky et al. (2009) [I. Lubashevsky, R. Friedrich, A. Heuer, Physical Review E 79 (2009) 011110] that realises Lévy walks as Markovian stochastic processes. This brings forth new biological insight as Lévy walks are advantageous when searching in the absence of external stimuli and without knowledge of the target distribution, as may be the case with cells of the epidermis that form new tissue by locating and then attaching on to one another. The Hänggi-Klimontovich interpretation of the driving noise in the model of Lubashevsky et al. (2009) and Cauchy distributions of predicted velocities do, however, appear problematic, even unphysical. Here it is shown that these are perceived rather than actual difficulties. Intermittent stop-start motions of the kind displayed by some cells and protozoan are found to underlie the formulation of the model of Lubashevsky et al. (2009) and the velocities of starved Dictyostelium discoideum (a unicellular organism) are found to be Cauchy distributed to a good approximation. It is therefore suggested that the model of Lubashevsky et al. (2009) can describe the spontaneous movements of some cells, and that some cells have spontaneous movement patterns that can be approximated by Lévy walks, as first proposed by Schuster and Levandowsky (1996) [F.L. Schuster, M. Levandowsky, Journal of Eukaryotic Microbiology 43 (1996) 150].     

Unusual ferromagnetism in nanoparticles of doped oxides and manganites

The observation of unusually large ferromagnetism in the nanoparticles of doped oxides and enhanced ferromagnetic tendencies in manganite nanoparticles have been in focus recently. For the transition metal doped oxide nanoparticles a phenomenological ‘charge transfer ferromagnetism’ model has been recently proposed by Coey et al. From a microscopic calculation with charge transfer between the defect band and mixed valent dopants, acting as reservoir, we show how the unusually high ferromagnetic response develops. The puzzle of nanosize-induced ferromagnetic tendencies in manganites is also addressed within the same framework where lattice imperfections and uncompensated charges at the surface of the nanoparticle are shown to reorganize the surface electronic structures with enhanced double exchange.     

On coupling between the orientation and the shape of a vesicle under a shear flow

A simple 2D model of deformable vesicles tumbling in a shear under flow is introduced in order to account for the main qualitative features observed experimentally as shear rates are increased. The simplicity of the model allows for a full analytical tractability while retaining the essential physical ingredients. The model reveals that the main axes of the vesicle undergo oscillations which are coupled to the vesicle orientation in the flow. The model reproduces and sheds light on the main novel features reported in recent experiments [M. Mader et al., Eur. Phys. J. E. 19, 389 (2006)], namely that both coefficients A and B that enter the Keller-Skalak equation, dψ/dt = A+Bcos(2 ψ) (ψ is the vesicle orientation angle in the shear flow), undergo a collapse upon increasing shear rate.     

Michaelis-Menten mechanism for single-enzyme and multi-enzyme system under stochastic noise and spatial diffusion

The investigation of enzymatic reaction under stochastic effect and spatial effect is an interesting problem. By virtue of Monte Carlo simulation, the stochastic dynamic of enzyme and the related Michaelis-Menten mechanism with stochastic internal noise and spatial diffusion are explored in this article. (i) For the single-enzyme system, two cases, including the fast phosphorylation case [X. S. Xie, et al., J. Phys. Chem. B 109 (2005) 19068] and slow phosphorylation case [X. S. Xie, et al., Nat. Chem. Biol. 2 (2006) 87] are considered. It is found the micro enzymatic velocity rate shows a rough hyperbolic dependence on the substrate concentration, hence obeys the Michaelis-Menten law qualitatively. In addition, our result reveals that diffusion rate can adjust the Michaelis-Menten curve; especially, it is shown that increasing diffusion rate enhances the micro enzyme rate. (ii) For the multi-enzyme system, a typical example, i.e., MAPK signaling pathway is used. We apply the Michaelis-Menten mechanism to the MAPK cascade and give a simple comparison for the signaling ability between the Michaelis-Menten mechanism and the single collision mechanism [J. W. Locasale et al., PLOS Comput. Biol. 4 (2008) e1000099].     

Spectral variations in the optical transition matrix element and their impact on the optical properties associated with hydrogenated amorphous silicon

Using an empirical model for the density of states functions associated with hydrogenated amorphous silicon, in conjunction with an elementary model for the optical transition matrix elements, we aim to explore how variations in the matrix elements impact upon the spectral dependence of the optical properties associated with this material. We also wish to ascertain as to whether or not the hydrogenated amorphous silicon mobility gap result suggested by Jackson et al. [W.B. Jackson, S.M. Kelso, C.C. Tsai, J.W. Allen, S.-J. Oh, Phys. Rev. B 31 (1985) 5187] is consistent with the results of the experiment. We find that the mobility gap value suggested by Jackson et al. is too large. An upper bound on the mobility gap associated with hydrogenated amorphous silicon of 1.68 eV is suggested instead. Electrical measurements performed on undoped hydrogenated amorphous silicon yield a mobility gap value that is consistent with this bound.     

An investigation of equivalence between the bulk-based and the brane-based approaches for anisotropic models

We investigate the relation between the brane-based and the bulk-based approaches for anisotropic case in brane-world models. In the brane-based approach, the brane is chosen to be fixed on a coordinate system, whereas in the bulk-based approach it is no longer static as it moves along the extra dimension. It was shown that these two approaches are equivalent for specific models in Mukohyama et al. (Phys Rev D 62:024028, 2000), Bowcock et al. (Class Quant Gravit 17:4745–4764, 2000). In this paper, it is aimed to get general formalism of the equivalence obtained in Mukohyama et al. (Phys Rev D 62:024028, 2000). We found that calculations driven by a general anisotropic bulk-based metric yield a brane-based metric in Gaussian Normal Coordinates by conserving spatial anisotropy. We also derive solutions for an anisotropic bulk-based model and get the corresponding brane-based metric of the model.     

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.     

Generation of entanglement via atomic coherence in a two-mode three-level cascade atomic system

The generation of continuous variable entanglement via atomic coherence in a two-mode three-level cascade atomic system is discussed according to the entanglement criterion proposed by Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)]. Atomic coherence between the top and bottom levels is induced with two photons of a strong external pump field. It shows that entanglement for the two-mode field in the cavity can be generated under certain conditions. Moreover, by means of the input-output theory, we show that the two-mode entanglement could also be approached at the output.     

Towards molecular computers that operate in a biological environment

Even though electronic computers are the only computer species we are accustomed to, the mathematical notion of a programmable computer has nothing to do with electronics. In fact, Alan Turing’s notional computer [L.M. Turing, On computable numbers, with an application to the entcheidungsproblem, Proc. Lond. Math. Soc. 42 (1936) 230-265], which marked in 1936 the birth of modern computer science and still stands at its heart, has greater similarity to natural biomolecular machines such as the ribosome and polymerases than to electronic computers. This similarity led to the investigation of DNA-based computers [C.H. Bennett, The thermodynamics of computation — Review, Int. J. Theoret. Phys. 21 (1982) 905-940; A.M. Adleman, Molecular computation of solutions to combinatorial problems, Science 266 (1994) 1021-1024]. Although parallelism, sequence specific hybridization and storage capacity, inherent to DNA and RNA molecules, can be exploited in molecular computers to solve complex mathematical problems [Q. Ouyang, et al., DNA solution of the maximal clique problem, Science 278 (1997) 446-449; R.J. Lipton, DNA solution of hard computational problems, Science 268 (1995) 542-545; R.S. Braich, et al., Solution of a 20-variable 3-SAT problem on a DNA computer, Science 296 (2002) 499-502; Liu Q., et al., DNA computing on surfaces, Nature 403 (2000) 175-179; D. Faulhammer, et al., Molecular computation: RNA solutions to chess problems, Proc. Natl. Acad. Sci. USA 97 (2000) 1385-1389; C. Mao, et al., Logical computation using algorithmic self-assembly of DNA triple-crossover molecules, Nature 407 (2000) 493-496; A.J. Ruben, et al., The past, present and future of molecular computing, Nat. Rev. Mol. Cell. Biol. 1 (2000) 69-72], we believe that the more significant potential of molecular computers lies in their ability to interact directly with a biochemical environment such as the bloodstream and living cells. From this perspective, even simple molecular computations may have important consequences when performed in a proper context. We envision that molecular computers that operate in a biological environment can be the basis of “smart drugs”, which are potent drugs that activate only if certain environmental conditions hold. These conditions could include abnormalities in the molecular composition of the biological environment that are indicative of a particular disease. Here we review the research direction that set this vision and attempts to realize it.     

Derivation of diffusion coefficient of a Brownian particle in tilted periodic potential from the coordinate moments

In this research, diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity VN and effective diffusion coefficient DN of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31 (1983) 433]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient Deff of the Brownian particle also has been obtained [P. Reimann, et al., Phys. Rev. E 65 (2002) 031104]. In this research, we'll give another analytical expression of the effective diffusion coefficient Deff from the moments of the particle's coordinate.     

Quantum-like dynamics of decision-making

In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the “rational strategy” provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can explain this effect (“irrationality” of players) Asano et al. (2010, 2011) [23] and [24]. Our model is based on the mathematical formalism of quantum mechanics, because psychological fluctuations inducing the irrationality are formally represented as quantum fluctuations Asano et al. (2011) [55]. In this paper, we reconsider the process of quantum-like decision-making more closely and redefine it as a well-defined quantum dynamics by using the concept of lifting channel, which is an important concept in quantum information theory. We also present numerical simulation for this quantum-like mental dynamics. It is non-Markovian by its nature. Stabilization to the steady state solution (determining subjective probabilities for decision making) is based on the collective effect of mental fluctuations collected in the working memory of a decision maker.     

Reply to comment on “Negative refraction in 1D photonic crystals”

I refute the criticisms of Srivastava et al. (2008) [13] raised in Bénédicto et al. [14].     

Dimensional reduction of the 5D Kaluza–Klein geodesic deviation equation

In the work of Kerner et al. (Phys Rev D 63:027502, 2001) the problem of the geodesic deviation in a 5D Kaluza–Klein background is faced. The 4D space–time projection of the resulting equation coincides with the usual geodesic deviation equation in the presence of the Lorenz force, provided that the fifth component of the deviation vector satisfies an extra constraint which takes into account the q/m conservation along the path. The analysis was performed setting as a constant the scalar field which appears in Kaluza–Klein model. Here we focus on the extension of such a work to the model where the presence of the scalar field is considered. Our result coincides with that of Kerner et al. when the minimal case f = 1{\phi=1} is considered, while it shows some departures in the general case. The novelty due to the presence of f{\phi} is that the variation of the q/m between the two geodesic lines is not conserved during the motion; an exact law for such a behaviour has been derived.     

Rare transition event with self-consistent theory of large-amplitude collective motion

A numerical simulation method, based on Dang et al.’s self-consistent theory of large-amplitude collective motion, for rare transition events is presented. The method provides a one-dimensional pathway without knowledge of the final configuration, which includes a dynamical effect caused by not only a potential but also kinetic term. Although it is difficult to apply the molecular dynamics simulation to a narrow-gate potential, the method presented is applicable to the case. A toy model with a high-energy barrier and/or the narrow gate shows that while the Dang et al. treatment is unstable for a changing of model parameters, our method stable for it.     

Performance comparison between classical and quantum control for a simple quantum system

Brańczyk et al. pointed out that the quantum control scheme is superior to the classical control scheme for a simple quantum system using simulation [A.M. Brańczyk, P.E.M.F. Mendonca, A. Gilchrist, A.C. Doherty, S.D. Barlett, Quantum control theory of a single qubit, Physical Review A 75 (2007) 012329 or arXiv e-print quant-ph/0608037]. Here we rigorously prove the result. Furthermore we will show that any quantum operation does not universally “correct” the dephasing noise.     

The Ho thickness dependence of spin-triplet supercurrents in Nb/Ho/Co/Ho/Nb films

Robinson et al. [J.W.A. Robinson, et al., Science 329 (2010) 59] reported control of spin-triplet supercurrents into ferromagnets by varying the thicknesses of the Ho injector and attributed the voltage peaks to non-integer spiral wavelengths of λ/2 and 5λ/2 in Ho. Here we demonstrate that these peaks correspond to λ/2 and 3λ/2.     

A one-dimensional continuous model for carbon nanotubes

The two-dimensional (2D) continuous elastic energy model for isotropic tubes is reduced to a one-dimensional (1D) curvature elastic energy model strictly. This 1D model is in accordance with the Kirchhoff elastic rod theory. Neglecting the in-plane strain energy in this model, it is suitable to investigate the nature features of carbon nanotubes (CNTs) with large deformations and can also reduce to the string model in [Z.C. Ou-Yang et al., Phys. Rev. Lett. 76, 4055 (1997)] when the deformation is small enough. For straight chiral shapes, this general model indicates that the difference of the chiral angle between two equilibrium states is about π/6, which is consistent with the lattice model. It also reveals that the helical shape has lower energy for per atom than the straight shape has in the same condition. By solving the corresponding equilibrium shape equations, the helical tube solution is in good agreement with the experimental result, and super helical shapes are obtained and we hope they can be found in future experiments.     

Derivation of generalized quantum jump operators and comparison of the microscopic single photon detector models

The recent experiment of Parigi et al. [Science 317, 1890 (2007)] shows, in agreement with theory, that subtraction of one photon can increase the expectation value of the number of photons in the thermal state. This observation agrees with the standard photon counting model in which the quantum jump superoperator (QJS) gives a count rate proportional to the number of photons. An alternate model for indirect photon counting has been introduced by Dodonov et al. [Phys. Rev. A 72, 023816 (2005)]. In their model the count rate is proportional to the probability that there are photons in the cavity, and the cavity field is bidirectionally coupled with a two state quantum system which is unidirectionally coupled to a counting device. We give a consistent first principle derivation of the QJSs for the indirect photon counting scheme and establish the complete relations between the physical measurement setup and the QJSs. It is shown that the time-dependent probability for photoelectron emission event must include normalization of the conditional probability. This normalization was neglected in the previous derivation of the QJSs. We include the normalization and obtain the correct photoelectron emission rates and the correct QJSs and show in which coupling parameter regimes these QJSs are applicable. Our analytical results are compared with the exact numerical solution of the Lindblad equation of the system. The derived QJSs enable analysis of experimental photon count rates in a case where a one-to-one correspondence does not exist between the decay of photons and the detection events.