Nonsymmetric Interactions Research Articles

Effects of heterogeneous opinion interactions in many-agent systems for epidemic dynamics

<abstract><p>In this work we define a kinetic model for understanding the impact of heterogeneous opinion formation dynamics on epidemics. The considered many-agent system is characterized by nonsymmetric interactions which define a coupled system of kinetic equations for the evolution of the opinion density in each compartment. In the quasi-invariant limit we may show positivity and uniqueness of the solution of the problem together with its convergence towards an equilibrium distribution exhibiting bimodal shape. The tendency of the system towards opinion clusters is further analyzed by means of numerical methods, which confirm the consistency of the kinetic model with its moment system whose evolution is approximated in several regimes of parameters.</p></abstract>

Effects of heterogeneous opinion interactions in many-agent systems for epidemic dynamics

<abstract><p>In this work we define a kinetic model for understanding the impact of heterogeneous opinion formation dynamics on epidemics. The considered many-agent system is characterized by nonsymmetric interactions which define a coupled system of kinetic equations for the evolution of the opinion density in each compartment. In the quasi-invariant limit we may show positivity and uniqueness of the solution of the problem together with its convergence towards an equilibrium distribution exhibiting bimodal shape. The tendency of the system towards opinion clusters is further analyzed by means of numerical methods, which confirm the consistency of the kinetic model with its moment system whose evolution is approximated in several regimes of parameters.</p></abstract>

Spin liquid in twisted homobilayers of group-VI dichalcogenides

Twisted transition metal dichalcogenide (TMD) homobilayers have recently emerged as a powerful platform for studying correlated insulating states. In the strongly correlated limit, we construct an effective spin Hamiltonian on a honeycomb lattice that includes the Heisenberg interaction and nonsymmetric interactions such as a Dzyaloshinskii-Moriya interaction and a Kane-Mele coupling for the Mott-insulating phase at half-filling. For the twisted TMD homobilayers, the spin-orbit coupling in the Hubbard model, which is expected to induce the antisymmetric exchange couplings in the effective spin Hamiltonian, is a highly tunable and experimentally accessible quantity that can be tuned by an applied electric field. In this study, we investigate classical and quantum phase diagrams of the effective spin Hamiltonian using analytical and numerical methods. We show that the model exhibits a rich classical phase diagram including an antiferromagnetic (AFM) phase, a planar spiral ordered phase with high classical degeneracy, a $z$-AFM phase, a noncoplanar phase, a noncollinear phase, and a 120$^{\circ}$-AFM phase. In the quantum treatment, we calculate low-energy magnon excitation spectrum, ground state energy, and static spin structure factor using linear spin-wave theory and density matrix renormalization group methods to compose the quantum phase diagram of the effective spin Hamiltonian. Beyond the Heisenberg interaction, we find that the existence of these antisymmetric couplings is responsible for the quantum spin liquid, $z$-AFM, noncoplanar, and 120$^{\circ}$ phases. Twisted TMD homobilayers, therefore, offer rich platforms for realizing rich phases of matter such as quantum spin liquid, noncoplanar, and 120$^{\circ}$, resulting from the spin-orbit coupling.

Radon measure solutions for steady hypersonic-limit Euler flows passing two-dimensional finite non-symmetric obstacles and interactions of free concentration layers

Radon measure solutions for steady hypersonic-limit Euler flows passing two-dimensional finite non-symmetric obstacles and interactions of free concentration layers

Nonsymmetric Interactions Trigger Collective Swings in Globally Ordered Systems

Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In condensed matter systems, order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing with system size. Several biological systems, however, are less stable and spontaneously change their global state on relatively short time scales. Here we show that there are two crucial ingredients in these systems that enhance the effect of noise, leading to collective changes of state on finite time scales and off-equilibrium behavior: the nonsymmetric nature of interactions between individuals, and the presence of local heterogeneities in the topology of the network. Our results might explain what is observed in several living systems and are consistent with recent experimental data on bird flocks and other animal groups.

Continuum dynamics of the intention field under weakly cohesive social interaction

We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. First, we derive a Fokker–Planck-type equation under the assumption that interactions between individuals produce little consensus of opinion (grazing collision approximation). Second, we study conditions under which the Fokker–Planck equation has non-trivial equilibria and derive the macroscopic limit (corresponding to the long-time dynamics and spatially localized interactions) for the evolution of the mean opinion. Finally, we compare two different types of interaction rates: the original one given in the work of Borghesi, Bouchaud and Jensen (symmetric binary interactions) and one inspired from works by Motsch and Tadmor (non-symmetric binary interactions). We show that the first case leads to a conservative model for the density of the mean opinion whereas the second case leads to a non-conservative equation. We also show that the speed at which consensus is reached asymptotically for these two rates has fairly different density dependence.

Theoretical Insights into Adsorption of Cobalt Phthalocyanine on Ag(111): A Combination of Chemical and van der Waals Bonding

In this article we study in detail the interaction of cobalt phthalocyanine (CoPc) with the Ag(111) surface by means of density functional theory calculations (DFT). We discuss the electronic and geometric differences of the adsorbed CoPc as it interacts with the different binding sites of the surface, yielding deeper insight into the adsorption mechanism of organometallic molecules with noble metal surfaces. We interpret the experimentally observed 4-fold to 2-fold symmetry reduction upon interaction of phthalocyanine molecules with metal surfaces as caused by electronic effects originating from nonsymmetric interactions between the molecule and the surface. To asses the role of dispersion forces in bonding of CoPc to the surface we employ a semiempirical dispersion correction to standard DFT and compare the obtained molecule–surface separation with experimental measurements. We show that, in the case of CoPc, the molecule bonds to the surface mostly due to covalent bonding between Co and Ag, but with a ...

Polymorphism, Fluorescence, and Optoelectronic Properties of a Borazine Derivative

We have prepared a new borazine derivative that bears mesityl substituents at the boron centers and displays exceptional chemical stability. Detailed crystallographic and solid-state fluorescence characterizations revealed the existence of several polymorphs, each of which showed different emission profiles. In particular, a bathochromic shift is observed when going from the lower- to the higher-density crystal. Computational investigations of the conformational dynamics of borazine 1 in both the gas phase and in the solid state using molecular dynamics (MD) simulations showed that the conformation of the peripheral aryl groups significantly varies when going from an isolated molecule (in which the rings are able to flip over the 90° barrier at RT) to the crystals (in which the rotation is locked by packing effects), thus generating specific nonsymmetric intermolecular interactions in the different polymorphs. To investigate the optoelectronic properties of these materials by fabrication and characterization of light-emitting diodes (LEDs) and light-emitting electrochemical cells (LECs), borazine 1 was incorporated as the active material in the emissive layer. The current and radiance versus voltage characteristics, as well as the electroluminescence spectra reported here for the first time are encouraging prospects for the engineering of future borazine-based devices.

Single-photon nonlinearities using arrays of cold polar molecules

We model single photon nonlinearities resulting from the dipole-dipole interactions of cold polar molecules. We propose utilizing ``dark state polaritons'' to effectively couple photon and molecular states; through this framework, coherent control of the nonlinearity can be expressed and potentially used in an optical quantum computation architecture. Due to the dipole-dipole interaction the photons pick up a measurable nonlinear phase even in the single photon regime. A manifold of protected symmetric eigenstates is used as basis. Depending on the implementation, major sources of decoherence result from non-symmetric interactions and phonon dispersion. We discuss the strength of the nonlinearity per photon and the feasibility of this system.

Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions

A stochastic model is applied to describe the spatial structure of a forest stand. We aim at quantifying the strength of the competition process between the trees in terms of interaction within and between different size classes of trees using multivariate Gibbs point processes with hierarchical interactions introduced in [Högmander, H., Särkkä, A., 1999. Multitype spatial point patterns with hierarchical interactions. Biometrics 55, 1051–1058]. The new model overcomes the main limitation of the traditional use of the Gibbs models allowing to describe systems with non-symmetric interactions between different objects. When analyzing interactions between neighbouring trees it is natural to assume that the size of a tree determines its hierarchical level: the largest trees are not influenced by any other trees than the trees in the same size class, while trees in the other size classes are influenced by the other trees in the same class as well as by all larger trees. In this paper, we describe a wide range of Gibbs models with both hierarchical and non-hierarchical interactions as well as a simulation algorithm and a parameter estimation procedure for the hierarchical models. We apply the hierarchical interaction model to the analysis of forest data consisting of locations and diameters of tree stems.

Synchronization and coordination of sequences in two neural ensembles

There are many types of neural networks involved in the sequential motor behavior of animals. For high species, the control and coordination of the network dynamics is a function of the higher levels of the central nervous system, in particular the cerebellum. However, in many cases, especially for invertebrates, such coordination is the result of direct synaptic connections between small circuits. We show here that even the chaotic sequential activity of small model networks can be coordinated by electrotonic synapses connecting one or several pairs of neurons that belong to two different networks. As an example, we analyzed the coordination and synchronization of the sequential activity of two statocyst model networks of the marine mollusk Clione. The statocysts are gravity sensory organs that play a key role in postural control of the animal and the generation of a complex hunting motor program. Each statocyst network was modeled by a small ensemble of neurons with Lotka-Volterra type dynamics and nonsymmetric inhibitory interactions. We studied how two such networks were synchronized by electrical coupling in the presence of an external signal which lead to winnerless competition among the neurons. We found that as a function of the number and the strength of connections between the two networks, it is possible to coordinate and synchronize the sequences that each network generates with its own chaotic dynamics. In spite of the chaoticity, the coordination of the signals is established through an activation sequence lock for those neurons that are active at a particular instant of time.

Self-organization of hierarchical structures in non-locally coupled replicator models

We study a simple replicator model with non-symmetric and non-local interactions. Hierarchical structures with prey–predator relations are self-organized from a homogeneous state, induced by the dynamical instability of non-linear interactions.

A Database for Couette Flow Rate Considering the Effects of Non-Symmetric Molecular Interactions

A complete database for Couette flow rate (QCD,α1,α2,0.1⩽α1,α2⩽1.0,0.01⩽D⩽100, where D=inverse Knudsen number) for ultra-thin gas film lubrication problems is advanced. When the accommodation coefficients (AC) of the two lubricating surfaces are different α1≠α2, the Couette flow rate in the modified molecular gas film lubrication (MMGL) equation should be corrected. The linearized Boltzmann equation (under small Mach number conditions) is solved numerically for the case of non-symmetric molecular interactions α1≠α2. The Couette flow rate is then calculated, and the database is constructed. The present database can be easily implemented in the MMGL equation. In addition, the present database extends the previously published results for 0.1⩽α1,α2⩽0.7. The database for low ACs is valuable in the analysis and applications of MEMS devices (bushings of electrostatic micro motors, micro bearings, magnetic head/disk interfaces, etc.), and their future development.

Winnerless competition between sensory neurons generates chaos: A possible mechanism for molluscan hunting behavior.

In the presence of prey, the marine mollusk Clione limacina exhibits search behavior, i.e., circular motions whose plane and radius change in a chaotic-like manner. We have formulated a dynamical model of the chaotic hunting behavior of Clione based on physiological in vivo and in vitro experiments. The model includes a description of the action of the cerebral hunting interneuron on the receptor neurons of the gravity sensory organ, the statocyst. A network of six receptor model neurons with Lotka-Volterra-type dynamics and nonsymmetric inhibitory interactions has no simple static attractors that correspond to winner take all phenomena. Instead, the winnerless competition induced by the hunting neuron displays hyperchaos with two positive Lyapunov exponents. The origin of the chaos is related to the interaction of two clusters of receptor neurons that are described with two heteroclinic loops in phase space. We hypothesize that the chaotic activity of the receptor neurons can drive the complex behavior of Clione observed during hunting. (c) 2002 American Institute of Physics.

Single homopolymers in the relative density representation.

A single symmetric homopolymer is studied in the grand ensemble of its monomeric units. For an arbitrary external field but next neighbor interactions alone, such a system is represented as a functional of the local density to local fugacity ratio, conjugate to the fugacity, with the excess grand potential as thermodynamic generating function. A sample case in a spherical enclosure is solved, where a complementary exclusion from a spherical volume requires an extension to a grand ensemble of polymers. A preliminary extension is also made in mean field form to non-neighbor interactions, as well as to nonsymmetric interactions.

An invariance principle for markov processes and brownian particles with singular interaction

We prove an invariance principle for functionals of Markov processes. As an application we prove an invariance principle for tagged particles of Brownian particles with non-symmetric interactions.

Penalty function approach to recurrent neural network dynamics

The Hopfield dynamics for recurrent neural networks minimizes a certain quadratic form on the unit hypercube. I show here how the dynamical system can be derived from a standard method of optimization theory. I use the method to give a precise meaning to nonsymmetric interactions, and I discuss the possibility of introducing other types of dynamics.

A directed graph representation based on a statistical hypothesis testing and application to citation and association structures

A statistical hypothesis testing method is developed for generating a directed graph from a matrix of nonsymmetric interactions among elements of a system. Two threshold parameters are applied to an interaction matrix in order to generate edges of the graph. Chi-square goodness-of-fit test is considered. The generated graph is plotted on a plane as a figure with hierarchically order vertices. Two applications are considered: one is the structure of literature in computer applications and cybernetics based on citation relationships; the other is the structure of scientific notions of students based on an association test in educational psychology.

A Hierarchical Representation of Nonsymmetric Interactions in Information Systems

A method of graphical representation is developed to synthesize and to visualize nonsymmetric interactions among elements of information systems. An arbitrary pair of elements A and B is assumed to have two interaction measures m(A, B) and m(B, A), and the symmetry m(A, B) = m(B, A) does not hold in general. A directed graph is generated whose arcs are determined according to the ratio m(A, B)/m(B, A). That is, if this ratio exceeds a threshold, then an arc from A to B is given. The layout of the graph is made to be hierarchical so that the resulting figure has an understandable form. This method is applied to four examples concerning bibliographic information systems and educational psychology.

High resolution X-ray structure of yeast hexokinase, an allosteric protein exhibiting a non-symmetric arrangement of subunits

The structure determination of yeast hexokinase has been extended to 3.5 Å resolution for the dimer and to 2.7 Å resolution for the monomer using multiple isomorphous replacement. The electron density maps of both the monomer and dimer crystal forms have been substantially improved by an averaging procedure. From these maps the course of the polypeptide backbone and some aspects of the dimer interaction have been established. The hexokinase subunit arrangement is contrary to a major tenet of the Monod et al. (1965) theory of allosteric proteins which postulated that only symmetric or isologous interactions of subunits would occur in oligomeric proteins. One subunit of the dimer is related to the other by a 156 ° rotation about and a 13.8 Å translation along a molecular screw axis. In the hexokinase dimer the set of residues in one subunit that is interacting with the other subunit is different from the set of residues in the second subunit that is interacting with the first subunit. This heterologous or non-symmetric interaction of subunits is associated with some small differences in the structure of the two subunits, particularly at the subunit interface, and accounts for some of this enzyme's non-symmetric interactions with substrates and activators. Indeed, the non-symmetric subunit association may play an important role in the control of this enzyme's activity. The overall structure of hexokinase is considerably different than the known structures of the other enzymes in the glycolytic pathway. Although there is a striking similarity between the domain of hexokinase that binds AMP and the domain of lactate dehydrogenase that binds NAD, the former structure contains both antiparallel and parallel β-pleated strands, while the latter contains only parallel β-structure. In an attempt to assess the significance of this structural similarity, the structure of the nucleotide binding domains of hexokinase and lactate dehydrogenase are compared to a portion of carboxypeptidase A. The observed similarities among these structures suggests that a central β-pleated sheet flanked by α-helices is a common supersecondary structure that probably arose by convergent as well as divergent evolution. Thus, there appears to be no compelling evidence at this time to support the hypothesis that a part of hexokinase has evolved from the same gene as the dinucleotide binding domain of lactate dehydrogenase.