Browsing by Subject "mathematical analysis"

Now showing 1 - 9 of 9

Open Access
Almost quantum correlations
(Nature Publishing Group, 2015) Navascués, M.; Guryanova, Y.; Hoban, M.J.; Acín, A.
Quantum theory is not only successfully tested in laboratories every day but also constitutes a robust theoretical framework: small variations usually lead to implausible consequences, such as faster-than-light communication. It has even been argued that quantum theory may be special among possible theories. Here we report that, at the level of correlations among different systems, quantum theory is not so special. We define a set of correlations, dubbed 'almost quantum', and prove that it strictly contains the set of quantum correlations but satisfies all-but-one of the proposed principles to capture quantum correlations. We present numerical evidence that the remaining principle is satisfied too. © 2015 Macmillan Publishers Limited.
Open Access
Direct measurement of molecular stiffness and damping in confined water layers
(The American Physical Society, 2004) Jeffery, S.; Hoffmann, P. M.; Pethica, J. B.; Ramanujan, C.; Özer, H. Ö.; Oral, A.
We present direct and linear measurements of the normal stiffness and damping of a confined, few molecule thick water layer. The measurements were obtained by use of a small amplitude (0.36 Å), off-resonance atomic force microscopy technique. We measured stiffness and damping oscillations revealing up to seven molecular layers separated by 2.526 ± 0.482 Å. Relaxation times could also be calculated and were found to indicate a significant slow-down of the dynamics of the system as the confining separation was reduced. We found that the dynamics of the system is determined not only by the interfacial pressure, but more significantly by solvation effects which depend on the exact separation of tip and surface. The dynamic forces reflect the layering of the water molecules close to the mica surface and are enhanced when the tip-surface spacing is equivalent to an integer multiple of the size of the water molecules. We were able to model these results by starting from the simple assumption that the relaxation time depends linearly on the film stiffness.
Open Access
GOPred: GO molecular function prediction by combined classifiers
(2010) Saraç Ö.S.; Atalay V.; Cetin-Atalay, R.
Functional protein annotation is an important matter for in vivo and in silico biology. Several computational methods have been proposed that make use of a wide range of features such as motifs, domains, homology, structure and physicochemical properties. There is no single method that performs best in all functional classification problems because information obtained using any of these features depends on the function to be assigned to the protein. In this study, we portray a novel approach that combines different methods to better represent protein function. First, we formulated the function annotation problem as a classification problem defined on 300 different Gene Ontology (GO) terms from molecular function aspect. We presented a method to form positive and negative training examples while taking into account the directed acyclic graph (DAG) structure and evidence codes of GO. We applied three different methods and their combinations. Results show that combining different methods improves prediction accuracy in most cases. The proposed method, GOPred, is available as an online computational annotation tool (http://kinaz.fen.bilkent.edu.tr/gopred). © 2010 Saraç et al.
Open Access
Is the largest Lyapunov exponent preserved in embedded dynamics?
(2000) Dechert W.Davis, Gençay, R.
The method of reconstruction for an n-dimensional system from observations is to form vectors of m consecutive observations, which for m > 2n, is generically an embedding. This is Takens' result. Our analytical examples show that it is possible to obtain spurious Lyapunov exponents that are even larger than the largest Lyapunov exponent of the original system. Therefore, we present examples where the largest Lyapunov exponent may not be preserved under Takens' embedding theorem. (C) 2000 Elsevier Science B.V.
Open Access
Model boson fluid with disorder in the self-consistent field approximation
(2001) Yurtsever, A.; Tanatar, Bilal
We study the ground-state properties of a model neutral boson fluid in the presence of disorder effects. The effective interaction between the bosons is obtained through the self-consistent field method which renormalizes the bare interaction consisting of a hard-core repulsive potential with an attractive tail at zero temperature. We introduce disorder effects within a number-conserving approximation by modifying the density - density response function. Our results for the static structure factor and the collective mode dispersion reflect the effect of disorder in qualitative agreement with other calculational approaches. © 2001 Elsevier Science B.V. All reserved.
Open Access
On the stability of delayed feedback controllers
(Elsevier, 2003) Morgül, Ö.
We consider the stability of delayed feedback control (DFC) scheme for one-dimensional discrete time systems. We first construct a map whose fixed points correspond to the periodic orbits of the uncontrolled system. Then the stability of the DFC is analyzed as the stability of the corresponding equilibrium point of the constructed map. For each periodic orbit, we construct a characteristic polynomial whose Schur stability corresponds to the stability of DFC. By using Schur-Cohn criterion, we can find bounds on the gain of DFC to ensure stability. © 2003 Elsevier B.V. All rights reserved.
Open Access
Schlesinger transformations for discrete second Painlevé equation: d-PII
(Elsevier BV * North-Holland, 2005) Muǧan, U.; Sakka, A.; Santini P. M.
A method to obtain the Schlesinger transformations for the standard discrete second Painlevé equation, d-PII, is given. The procedure involves formulating a Riemann-Hilbert problem for a transformation matrix which transforms the solution of the linear problem but leaves the associated monodromy data the same. © 2005 Elsevier B.V. All rights reserved.
Open Access
Six low-strain zinc-blende half metals: An ab initio investigation
(2003) Pask J.E.; Yang L.H.; Fong, C.Y.; Pickett W.E.; Dag, S.
A class of spintronic materials, the zinc-blende (ZB) half metals, has recently been synthesized in thin-film form. We apply all-electron and pseudopotential ab initio methods to investigate the electronic and structural properties of ZB Mn and Cr pnictides and carbides, and find six compounds to be half metallic at or near their respective equilibrium lattice constants, making them excellent candidates for growth at low strain. Based on these findings, we further propose substrates on which the growth may be accomplished with minimum strain. Our findings are supported by the recent successful synthesis of ZB CrAs on GaAs and ZB CrSb on GaSb, where our predicted equilibrium lattice constants are within 0.5% of the lattice constants of the substrates on which the growth was accomplished. We confirm previous theoretical results for ZB MnAs, but find ZB MnSb to be half metallic at its equilibrium lattice constant, whereas previous work has found it to be only nearly so. We report here two low-strain half metallic ZB compounds, CrP and MnC, and suggest appropriate substrates for each. Unlike the other five compounds, we predict ZB MnC to become/remain half metallic with compression rather than expansion, and to exhibit metallicity in the minority-rather than majority-spin channel. These fundamentally different properties of MnC can be connected to substantially greater p-d hybridization and d-d overlap, and correspondingly larger bonding-antibonding splitting and smaller exchange splitting. We examine the relative stability of each of the six ZB compounds against NiAs and MnP structures, and find stabilities for the compounds not yet grown comparable to those already grown.
Open Access
Stratonovich-to-Itô transition in noisy systems with multiplicative feedback
(Nature Publishing Group, 2013) Pesce G.; McDaniel, A.; Hottovy, S.; Wehr J.; Volpe G.
Intrinsically noisy mechanisms drive most physical, biological and economic phenomena. Frequently, the system's state influences the driving noise intensity (multiplicative feedback). These phenomena are often modelled using stochastic differential equations, which can be interpreted according to various conventions (for example, Itô calculus and Stratonovich calculus), leading to qualitatively different solutions. Thus, a stochastic differential equation-convention pair must be determined from the available experimental data before being able to predict the system's behaviour under new conditions. Here we experimentally demonstrate that the convention for a given system may vary with the operational conditions: we show that a noisy electric circuit shifts from obeying Stratonovich calculus to obeying Itô calculus. We track such a transition to the underlying dynamics of the system and, in particular, to the ratio between the driving noise correlation time and the feedback delay time. We discuss possible implications of our conclusions, supported by numerics, for biology and economics. © 2013 Macmillan Publishers Limited. All rights reserved.