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The paper considers dynamics of Van der Pol–Duffing (VdPD) oscillator with attached nonlinear energy sink. Due to a cubic nonlinearity of the VdPD oscillator, a frequency of oscillations near the unstable origin strongly differs from the frequency of limit cycle oscillations (LCO). The paper demonstrates that, despite the strong nonlinearity of the model system, one can efficiently describe the dynamics with a combination of averaging and multiple scales methods. Global structure of possible response regimes is revealed. It is also demonstrated that the nonlinear energy sink can efficiently control and mitigate the undesired LCOs in this system.

Alzheimer's disease and Schizophrenia are two common diseases of the brain with significant differences in neuropathology, etiology and symptoms. This dissimilarity in the two diseases makes a comparison of the two ideal for detecting molecular substrates that are common to brain disorders in general.In this study, we compared gene expression profiles across multiple brain areas, taken postmortem from patients with well-characterized Alzheimer's disease and Schizophrenia, and from cognitively normal control group with no neuro- or psychopathology.Although the totality of gene expression changes in the two diseases is dissimilar, a subset of genes appears to play a role in both diseases in specific brain regions. We find at Brodmann area 22, the superior temporal gyrus, a statistically significant number of genes with apparently disregulated expression in both diseases. Furthermore, we found genes that differentiate the two diseases from the control across multiple brain regions, and note that these genes were usually down-regulated. Brodmann area 8, part of the superior frontal cortex, is relatively abundant with them.We show overwhelming statistical evidence for Alzheimer's and Schizophrenia sharing a specific molecular background at the superior temporal gyrus. We suggest that impairment of the regulation of autophagy pathway is shared, in BA 22, by the two diseases.

Two methods were proposed recently to derive energy parameters from known native protein conformations and corresponding sets of decoys. One is based on finding, by means of a perceptron learning scheme, energy parameters such that the native conformations have lower energies than the decoys. The second method maximizes the difference between the native energy and the average energy of the decoys, measured in terms of the width of the decoys' energy distribution (Z-score). Whereas the perceptron method is sensitive mainly to "outlier" (i.e., extremal) decoys, the Z-score optimization is governed by the high density regions in decoy-space. We compare the two methods by deriving contact energies for two very different sets of decoys: the first obtained for model lattice proteins and the second by threading. We find that the potentials derived by the two methods are of similar quality and fairly closely related. This finding indicates that standard, naturally occurring sets of decoys are distributed in a way that yields robust energy parameters (that are quite insensitive to the particular method used to derive them). The main practical implication of this finding is that it is not necessary to fine-tune the potential search method to the particular set of decoys used.

Unbiased samples of ground states were generated for the short-range Ising spin glass with J(ij) = +/-1, in three dimensions. Clustering the ground states revealed their hierarchical structure, which is explained by correlated spin domains, serving as cores for macroscopic zero energy "excitations."

We discuss the problem of representations of protein structure and give the definition of contact maps. We present a method to obtain a three-dimensional polypeptide conformation from a contact map. We also explain how to deal with the case of nonphysical contact maps. We describe a stochastic method to perform dynamics in contact map space. We explain how the motion is restricted to physical regions of the space. First, we introduce the exact free energy of a contact map and discuss two simple approximations to it. Second, we present a method to derive energy parameters based on perception learning. We prove in an extensive number of situations that the pairwise contact approximation both when alone and when supplemented with a hydrophobic term is unsuitable for stabilizing proteins' native states.

We introduce an energy function for contact maps of proteins. In addition to the standard term, that takes into account pair-wise interactions between amino acids, our potential contains a new hydrophobic energy term. Parameters of the energy function were obtained from a statistical analysis of the contact maps of known structures. The quality of our energy function was tested extensively in a variety of ways. In particular, fold recognition experiments revealed that for a fixed sequence the native map is identified correctly in an overwhelming majority of the cases tested. We succeeded in identifying the structure of some proteins that are known to pose difficulties for such tests (BPTI, spectrin, and cro-protein). In addition, many known pairs of homologous structures were correctly identified, even when the two sequences had relatively low sequence homology. We also introduced a dynamic Monte Carlo procedure in the space of contact maps, taking topological and polymeric constraints into account by restrictive dynamic rules. Various aspects of protein dynamics, including high-temperature melting and refolding, were simulated. Perspectives of application of the energy function and the method for structure checking and fold prediction are discussed.

A variational calculation yields an eigenstate representing a domain wall-type solution for various quantum-mechanical spin models. Heisenberg Hamiltonians with local and exchange anisotropy, and an Ising model in a transverse field (including its critical regime) are discussed in detail. The domain walls are viewed as localized solutions of non-linear equations. The extent to which the results for the transverse field Ising model may be mapped on to a currently interesting “double well” anhurmonic lattice problem are analysed.

Transitions from symmetry-adapted to symmetry-broken solutions of variational problems are classified according to the nature of the discontinuity involved. Two systems in which a second-order transition occurs are studied.

The q=3-state Potts model undergoes a first-order transition in three dimensions, and a continuous one in two dimensions. For a system of finite thickness L, the transition will be either first order (for L>Lx) or continuous (for L

The applicability of the n-replica method to an Ising system with positive and negative bonds of equal strength is investigated. It is shown that this method does reproduce the correct low-temperature and low-(negative bond) concentration series for the ground-state energy. It is essential, however, to take the low-temperature limit after the n to 0 limit. For a square lattice, the slope of the critical line near the pure-system transition point is found to be 2 square root 2/ln( square root 2+1). The onset of spin-glass order is conjectured to be associated with a negative bond concentration at which unfrustrated plaquettes no longer percolate the lattice. The estimated value of 16% is in agreement with Monte Carlo results.

It is suggested that phase transitions induced by a magnetic field H//(111) in certain type I FCC antiferromagnets provide a physical realisation of the q=3- and q=4-state Potts models. The (H, T) phase diagram associated with these antiferromagnets for a field lying in the (110) plane is studied using mean field approximation and renormalisation group calculations in d=- epsilon dimensions. The phase diagram exhibits a critical and two first-order surfaces connected by lines to tricritical and polycritical points.

By using the replica trick and a duality transformation, the bond-diluted random Ising model is mapped onto a new Hamiltonian. This demonstrates the higher order critical nature of the percolation point and identifies the appropriate crossover scaling variables. Taking the n to 0 limit of the replica method near the percolation point is shown to be equivalent to the q to 1 limit of the Potts model. The critical line near pc is calculated, yielding for a square lattice exp(-2Kc)=2ln2(p-1/2)+0(p-1/2)2.

Second quantization is used to expand the product of two harmonic oscillator wavefunctions, of two different particles, centred on different sites, in terms of relative and centre of mass coordinate dependent functions.

The use of localized Hartree-Fock states in the perturbation theory of ordered systems is shown to introduce off-diagonal single-particle terms into the perturbation. This is equivalent to the use of diagonal Hartree-Fock solutions of a rearranged Hamiltonian.

An approximate wavefunction can systematically be improved by requiring simultaneous satisfaction of any set of hypervirial relations. When the operators involved form a Lie algebra, the connection between the conditions for extremum and the hypervirial relations takes a particularly simple form. For this case stability conditions are also obtained.

The presence of a state of residual stress in a material can impair its structural quality by adversely affecting its elastic limit, yield point, etc.1 Most common nondestructive measurements of residual stress use x-ray techniques.2 However, these techniques determine only the surface residual stresses, while in many practical cases knowledge of the bulk residual stresses is desired. Ultrasonic methods3,4 appear most natural for measuring bulk residual stress but are used infrequently, in part because of difficulty in adequately measuring small effects and in part because of the absence of theoretical results treating the inhomogeneous nature of residual stress fields.

The sensitivity of the propagation of an elastic wave to changes in the microstructural details of a material is well known.1 In particular, numerous experiments have shown that the attenuation of the wave is sensitive to the inclusions, voids, cracks, grain boundaries, twin boundaries, interphase boundaries, magnetic domain walls, dislocations, substitutional impurities of a material. For attenuation studies in metals, ceramics and polycrystals, three formulas, each for different wavelength regimes, are generally used in the quantitative interpretation of experimental results.1–3 If λ is the wavelength of the elastic wave and is the average grain diameter, then in the Rayleigh regime (λ≫D), α = A1 3λ4, in the stochastic regime (λ≃D), α = A2 λ2, and in the diffusive regime (λ≪D), α = A3/ -1. By fitting the data to these formulas, one tries to infer .

The subject of Neural Networks does not fit naturally into the general context of a meeting on ”Competing Interactions & Microstructures: Statics and Dynamics”. Therefore, I will try to explain what Neural Networks are, why are (some) physicists interested in them, and why is it not completely absurd to have a talk on them in such a meeting. A much extended version of my strongly biased views on the subject is given in a review article [1], which also contains a more detailed list of references. Here I present only an extended abstract that summarizes the main points of my talk.

Time evolution of a Cellular Automaton that describes shrinking domains is studied. A singly connected domain of Ising spins, embedded in a sea of the opposite phase, develops at T = 0 according to a dynamic rule that does not allow its perimeter to increase. At long enough times the domain disappears; we have shown that the average lifetime of such a domain is proportional to its area. We also considered the T = 0 dynamics of a single infinite quadrant, and have shown that it maps onto a diffusion problem with exclusion in one dimension. This latter problem is mapped onto a critical 6-vertex model.

_~icthods which serve to evaluate matrix elements of two-body interactions in a single-particle basis are applied in most branches of the physics. The most widely used single-particle basis is that of the harmonic oscillator cigenstates. ]"or interactions depending on the relative co-ordinate of the two particles, the Talmi expansion, which expresses the product of two harmonic oscillator wave functions in terms of relative and centre-of-mass dependent functions, is widely employed (1). The generalized Tallni expansion involves the product of two harmonic-oscillator wave functions with different well parameters (2), In the present communication the product ~,,(x~)~,,(~x2), where ~0,, are harmonicoscillator wave functions, and ~ %/im2w2)/(mlo~l), is expanded in terms of relative and generalized centre-of-mass co-ordinates dependent harmonic-oscillator wave functions, by a strictly algebraic t reatment . Use is made of the fact that 1) transition to relative and center-of-mass co-ordinates is obtained by a rotation in the xl-x 2 plane (3), and 2) the well parameter is affected by scaling of the corresponding co-ordinate. The product space {r n l , n 2 : 0 . . . . . ~} is isomorphic with that of a two-dimensional isotropie harmonic oscillator in the (x-y)-plane. l(otations in this plane 9 f t are generated by L z : ,(axa~--a~a,), where a, and a~ are harmonic-oscillator annihir , t t Jr lation operators. The three operators J l : (a~a~ma~a~)/2, J2=.Lz/2, J 3 : (a~a~--axa~)/2, which commute with the Hamil tonian of the two-dimensional isotropic harmonic oscillator, are the generators of SU, , and obey the usual angular-momentum commutat ion f relations. They commute with j2 = j~ + j~ HJ~ ~ (Ar/2)(N/2 -~ 1), where N = a,a , -~ ~-aCvav, qSn~(xl)qJm(x~): ]nx, n~} is an cigenstate of j2 and Ja, with eigenvalucs ](]"-k 1) and ~3 such that j = (n~ .--' n~)/2; ~'a = (n~--n~)/2. Therefore, In~, n~} _: 1], is). Define a transformation T=S~(~)R~(O/2), where S~(~) is represented in the (x-y)-space by the matrix

Isobenzimidazole-2-spirocyclohexane(1)can be made to react with nitrogen, oxygen, sulphur, and carbon nucleophiles to give mono-and di-substitied derivatives. On reductive ring-opening the correspondingly substituted o-phenylenediamine is obtained. The scope of this synthetic principle has been studied and the reaction used to prepare various heterocycles with substituents that are difficult to introduce by conventional methods. Selenadiazole or its 4-chloro and 4,5-dichloro derivatives were found to be unsuitable alternatives to (1).

Collective migration is an important cellular trait, which is intensely studied by both basic and translational researchers. Investigation of the underlying mechanisms necessitates high-throughput assays and computational algorithms capable of generating reproducible quantitative measurements of cell migration. We present a desktop tool that can be used easily by any researcher, to quantify both fluorescent and phase-contrast images produced in the course of commonly used gap closure ("scratch," "wound healing") collective migration assays. The software has a simple graphical interface that allows the user to tune the relevant parameters and process large numbers of images (or movies). The output contains segmented images and the numerical values inferred from them, allowing easy quantitative analysis of the results.

A large fraction of ductal carcinoma in situ (DCIS), a non-invasive precursor lesion of invasive breast cancer, overexpresses the HER2/neu oncogene. The ducts of DCIS are abnormally filled with cells that evade apoptosis, but the underlying mechanisms remain incompletely understood. We overexpressed HER2 in mammary epithelial cells and observed growth factor-independent proliferation. When grown in extracellular matrix as 3- dimensional spheroids, control cells developed a hollow lumen, but HER2-overexpressing cells populated the lumen by evading apoptosis. We demonstrate that HER2 overexpression in this cellular model of DCIS drives transcriptional up-regulation of multiple components of the Notch survival pathway. Importantly, luminal filling required up-regulation of a signaling pathway comprising Notch3, its cleaved intracellular domain (NICD) and the transcriptional regulator HES1, resulting in elevated levels of c-MYC and Cyclin D1. In line with HER2- Notch3 collaboration, drugs intercepting either arm reverted the DCIS-like phenotype. In addition, we report up-regulation of Notch3 in hyperplastic lesions of HER2 transgenic animals, as well as an association between HER2 levels and expression levels of components of the Notch pathway in tumor specimens of breast cancer patients. Therefore, it is conceivable that the integration of the Notch and HER2 signaling pathways contributes to the pathophysiology of DCIS.

The HER2/neu oncogene encodes a receptor-like tyrosine kinase whose overexpression in breast cancer predicts poor prognosis and resistance to conventional therapies. However, the mechanisms underlying aggressiveness of HER2 (human epidermal growth factor receptor 2)-overexpressing tumors remain incompletely understood. Because it assists epidermal growth factor (EGF) and neuregulin receptors, we overexpressed HER2 in MCF10A mammary cells and applied growth factors. HER2-overexpressing cells grown in extracellular matrix formed filled spheroids, which protruded outgrowths upon growth factor stimulation. Our transcriptome analyses imply a two-hit model for invasive growth: HER2-induced proliferation and evasion from anoikis generate filled structures, which are morphologically and transcriptionally analogous to preinvasive patients’ lesions. In the second hit, EGF escalates signaling and transcriptional responses leading to invasive growth. Consistent with clinical relevance, a gene expression signature based on the HER2/EGF-activated transcriptional program can predict poorer prognosis of a subgroup of HER2-overexpressing patients. In conclusion, the integration of a three-dimensional cellular model and clinical data attributes progression of HER2-overexpressing lesions to EGF-like growth factors acting in the context of the tumor's microenvironment.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.