Distribution Of Coupling Strengths Research Articles

Hysteresis in a generalized Kuramoto model with a first-order approximate coupling function and inhomogeneous coupling strengths

We investigate hysteresis in a generalized Kuramoto model with identical oscillators, focusing on coupling strength inhomogeneity, which results in oscillators being coupled to others with varying strength, and a first-order approximation of general coupling functions. With the coupling function and the coupling strength inhomogeneity, each oscillator acquires an effective intrinsic frequency proportional to its individual coupling strength. This is analogous to the positive coupling strength-frequency correlation introduced explicitly or implicitly in some previous models with nonidentical oscillators that show explosive synchronization and hysteresis. Through numerical simulations and analysis using truncated Gaussian, uniform, and truncated power-law coupling strength distributions, we observe that the system can exhibit abrupt phase transitions and hysteresis. The distribution of coupling strengths significantly affects the hysteresis regions within the parameter space of the coupling function. Additionally, numerical simulations of models with weighted networks including a brain network confirm the existence of hysteresis due to the first-order approximate coupling function and coupling strength inhomogeneity, suggesting the broad applicability of our findings to complex real-world systems.

Hydrothermal Factors Influence on Spatial-Temporal Variation of Evapotranspiration-Precipitation Coupling over Climate Transition Zone of North China

As a land–atmosphere coupling “hot spot”, the northern China climate transition zone has a sharp spatial gradient of hydrothermal conditions, which plays an essential role in shaping the spatial and temporal pattern of evapotranspiration-precipitation coupling, but whose mechanisms still remain unclear. This study analyzes the spatial and temporal variation in land–atmosphere coupling strength (CS) in the climate transitional zone of northern China and its relationship with soil moisture and air temperature. Results show that CS gradually transitions from strong positive in the northwest to negative in the southeast and northeast corners. The spatial distribution of CS is closely related to climatic hydrothermal conditions, where soil moisture plays a more dominant role: CS increases first, and then decreases with increasing soil moisture, with the threshold of soil moisture at 0.2; CS gradually transitions from positive to negative at soil moisture between 0.25 and 0.35; CS shows an exponential decreasing trend with increasing temperature. In terms of temporal variation, CS is strongest in spring and weakens sequentially in summer, autumn, and winter, and has significant interdecadal fluctuations. The trend in CS shifts gradually from significantly negative in the west to a non-significant positive in the east. Soil moisture variability dominates the intra-annual variability of CS in the study regions, and determines the interannual variation of CS in arid and semi-arid areas. Moreover, the main reason for the positive and negative spatial differences in CS in the study area is the different driving regime of evapotranspiration (ET). ET is energy-limited in the southern part of the study area, leading to a positive correlation between ET and lifting condensation level (LCL), while in most of the northern part, ET is water-limited and is negatively correlated with LCL; LCL has a negative correlation with P across the study area, thus leading to a negative ET-P coupling in the south and a positive coupling in the north.

Phase and amplitude dynamics of coupled oscillator systems on complex networks.

We investigated locking behaviors of coupled limit-cycle oscillators with phase and amplitude dynamics. We focused on how the dynamics are affected by inhomogeneous coupling strength and by angular and radial shifts in coupling functions. We performed mean-field analyses of oscillator systems with inhomogeneous coupling strength, testing Gaussian, power-law, and brain-like degree distributions. Even for oscillators with identical intrinsic frequencies and intrinsic amplitudes, we found that the coupling strength distribution and the coupling function generated a wide repertoire of phase and amplitude dynamics. These included fully and partially locked states in which high-degree or low-degree nodes would phase-lead the network. The mean-field analytical findings were confirmed via numerical simulations. The results suggest that, in oscillator systems in which individual nodes can independently vary their amplitude over time, qualitatively different dynamics can be produced via shifts in the coupling strength distribution and the coupling form. Of particular relevance to information flows in oscillator networks, changes in the non-specific drive to individual nodes can make high-degree nodes phase-lag or phase-lead the rest of the network.

Various synchronous states due to coupling strength inhomogeneity and coupling functions in systems of coupled identical oscillators.

We study the effects of coupling strength inhomogeneity and coupling functions on locking behaviors of coupled identical oscillators, some of which are relatively weakly coupled to others while some are relatively strongly coupled. Through the stability analysis and numerical simulations, we show that several categories of fully locked or partially locked states can emerge and obtain the conditions for these categories. In this system with coupling strength inhomogeneity, locked and drifting subpopulations are determined by the coupling strength distribution and the shape of the coupling functions. Even the strongly coupled oscillators can drift while weakly coupled oscillators can be locked. The simulation results with Gaussian and power-law distributions for coupling strengths are compared and discussed.

Electrophysiological and firing properties of neurons: Categorizing soloists and choristers in primary visual cortex

Visual processing in the cortex involves various aspects of neuronal properties such as morphological, electrophysiological and molecular. In particular, the neural firing pattern is an important indicator of dynamic circuitry within a neuronal population. Indeed, in microcircuits, neurons act as soloists or choristers wherein the characteristical activity of a ‘soloist’ differs from the firing pattern of a ‘chorister’. Both cell types correlate their respective firing rate with the global populational activity in a unique way. In the present study, we sought to examine the relationship between the spike shape (thin spike neurons and broad spike neurons) of cortical neurons recorded from V1, their firing levels and their propensity to act as soloists or choristers. We found that thin spike neurons, which exhibited higher levels of firing, generally correlate their activity with the neuronal population (choristers). On the other hand, broad spike neurons showed lower levels of firing and demonstrated weak correlations with the assembly (soloists). A major consequence of the present study is: estimating the correlation of neural spike trains with their neighboring population is a predictive indicator of spike waveforms and firing level. Indeed, we found a continuum distribution of coupling strength ranging from weak correlation-strength (attributed to low-firing neurons) to high correlation-strength (attributed to high-firing neurons). The tendency to exhibit high- or low-firing is conducive to the spike shape of neurons. Our results offer new insights into visual processing by showing how high-firing rate neurons (mostly thin spike neurons) could modulate the neuronal responses within cell-assemblies.

Entrainment range of nonidentical circadian oscillators by a light-dark cycle

The suprachiasmatic nucleus (SCN) is a principal circadian clock in mammals, which controls physiological and behavioral daily rhythms. The SCN has two main features: Maintaining a rhythmic cycle of approximately 24 h in the absence of a light-dark cycle (free-running period) and the ability to entrain to external light-dark cycles. Both free-running period and range of entrainment vary from one species to another. To understand this phenomenon, we investigated the diversity of a free-running period by the distribution of coupling strengths in our previous work [Phys. Rev. E 80, 030904(R) (2009)]. In this paper we numerically found that the dispersion of intrinsic periods among SCN neurons influence the entrainment range of the SCN, but has little influence on the free-running periods under constant darkness. This indicates that the dispersion of coupling strengths determines the diversity in free-running periods, while the dispersion of intrinsic periods determines the diversity in the entrainment range. A theoretical analysis based on two coupled neurons is presented to explain the results of numerical simulations.

Excitonic Coupling in Linear and Trefoil Trimer Perylenediimide Molecules Probed by Single-Molecule Spectroscopy

Perylenediimide (PDI) molecules are promising building blocks for photophysical studies of electronic interactions within multichromophore arrays. Such PDI arrays are important materials for fabrication of molecular nanodevices such as organic light-emitting diodes, organic semiconductors, and biosensors because of their high photostability, chemical and physical inertness, electron affinity, and high tinctorial strength over the entire visible spectrum. In this work, PDIs have been organized into linear (L3) and trefoil (T3) trimer molecules and investigated by single-molecule fluorescence microscopy to probe the relationship between molecular structures and interchromophoric electronic interactions. We found a broad distribution of coupling strengths in both L3 and T3 and hence strong/weak coupling between PDI units by monitoring spectral peak shifts in single-molecule fluorescence spectra upon sequential photobleaching of each constituent chromophore. In addition, we used a wide-field defocused imaging technique to resolve heterogeneities in molecular structures of L3 and T3 embedded in a PMMA polymer matrix. A systematic comparison between the two sets of experimental results allowed us to infer the correlation between intermolecular interactions and molecular structures. Our results show control of the PDI intermolecular interactions using suitable multichromophoric structures.

Observation of coherent many-body Rabi oscillations

A two-level quantum system coherently driven by a resonant electromagnetic field oscillates sinusoidally between the two levels at frequency $\Omega$ which is proportional to the field amplitude [1]. This phenomenon, known as the Rabi oscillation, has been at the heart of atomic, molecular and optical physics since the seminal work of its namesake and coauthors [2]. Notably, Rabi oscillations in isolated single atoms or dilute gases form the basis for metrological applications such as atomic clocks and precision measurements of physical constants [3]. Both inhomogeneous distribution of coupling strength to the field and interactions between individual atoms reduce the visibility of the oscillation and may even suppress it completely. A remarkable transformation takes place in the limit where only a single excitation can be present in the sample due to either initial conditions or atomic interactions: there arises a collective, many-body Rabi oscillation at a frequency $N^0.5\Omega$ involving all N >> 1 atoms in the sample [4]. This is true even for inhomogeneous atom-field coupling distributions, where single-atom Rabi oscillations may be invisible. When one of the two levels is a strongly interacting Rydberg level, many-body Rabi oscillations emerge as a consequence of the Rydberg excitation blockade. Lukin and coauthors outlined an approach to quantum information processing based on this effect [5]. Here we report initial observations of coherent many-body Rabi oscillations between the ground level and a Rydberg level using several hundred cold rubidium atoms. The strongly pronounced oscillations indicate a nearly complete excitation blockade of the entire mesoscopic ensemble by a single excited atom. The results pave the way towards quantum computation and simulation using ensembles of atoms.

Snow-atmosphere coupling strength in a global atmospheric model

[1] Large scale snow-atmosphere coupling strength (the degree to which the atmosphere responds to anomalies in snow cover) is quantitatively investigated using the Community Land Model (CLM 3.5) and its advanced snow scheme coupled to the Community Atmospheric Model (CAM). An index based on model ensemble statistics has been used to quantify the coupling strength. Multi-seasonal experiments reveal the spatial and temporal distribution of coupling strength during the snow depletion phase (March through June) over the Northern Hemisphere. The snow coupling strength was found to evolve in three distinct stages: before snowmelt, during snowmelt and after snowmelt. The coupling strength is strongest during snowmelt. The coupling strength after snowmelt, mainly due to hydrological effect (soil moisture impact), is stronger than coupling strength due to albedo effect (radiative impact) before snowmelt. A conceptual model is proposed to explain the mechanisms behind the spatial distribution of coupling strength.

Free-running period of neurons in the suprachiasmatic nucleus: Its dependence on the distribution of neuronal coupling strengths

The suprachiasmatic nucleus (SCN) pacemaker shows a free-running period ranging from 20 to 28 h for different species, which was usually explained from the angle of coupling strength. Based on the assumption of nonidentical coupling strengths in SCN, we find an alternative mechanism that the diversity of free-running period can be also caused by the distribution of coupling strengths. The free-running period is proportional to the average coupling strength and inverse proportional to the dispersion of couplings. Moreover, we present an analytic phase model to confirm our finding, which shows a solid foundation of our finding and opens a window to study the collective behaviors of SCN oscillators.

Interplay of noise and coupling in heterogeneous ensembles of phase oscillators

We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise can also be heterogeneous, representing diversity in the individual responses to external fluctuations. We show that the desynchronization transition induced by noise may be completely suppressed, even for arbitrarily large noise intensities, is the distribution of coupling strengths decays slowly enough for large couplings. Equivalently, if the response to noise of a sufficiently large fraction of the ensemble is weak enough, desynchronization cannot occur. The two effects combine with each other when the response to noise and the coupling strength of each oscillator are correlated. This combination is quantitatively characterized and illustrated with explicit examples.

Partially locked states in coupled oscillators due to inhomogeneous coupling

We investigate coupled identical phase oscillators with scale-free distribution of coupling strength. It is shown that partially locked states can occur due to the inhomogeneity in coupling and some properties of the coupling function. Various quantities of the partially locked states are computed through a self-consistency argument and the values show good agreement with simulation results.

Chaotic dynamics on large networks

Many systems in nature are governed by a large number of agents that interact nonlinearly through complex feedback loops. When the networks are sufficiently large and interconnected, they typically exhibit self-organization and chaos. This paper examines the prevalence and degree of chaos on large unweighted recurrent networks of ordinary differential equations with sigmoidal nonlinearities and unit coupling. The largest Lyapunov exponent is used as the signature and measure of the chaos, and the study includes the effects of damping, asymmetries in the distribution of coupling strengths, network symmetry, and sparseness of connections. Minimum conditions and optimal network architectures are determined for the existence of chaos. The results have implications for the design of social and other networks in the real world in which weak chaos is deemed desirable or as a way of understanding why certain networks might exist on "the edge of chaos."

Information-flux approach to multiple-spin dynamics

We introduce and formalize the concept of information flux in a many-body register as the influence that the dynamics of a specific element receive from any other element of the register. By quantifying the information flux in a protocol, we can design the most appropriate initial state of the system and, noticeably, the distribution of coupling strengths among the parts of the register itself. The intuitive nature of this tool and its flexibility, which allow for easily manageable numerical approaches when analytic expressions are not straightforward, are greatly useful in interacting many-body systems such as quantum spin chains. We illustrate the use of this concept in quantum cloning and quantum state transfer and we also sketch its extension to nonunitary dynamics.

Measurement of the coupling strength distribution in ferromagnetic (F)/antiferromagnetic (AF) exchange bias systems

We propose a method for determination of the distribution function P( j) of the coupling energy density j in polycrystalline textured ferromagnetic (F)/antiferromagnetic (AF) film systems. P( j) governs the entire film coupling J and the exchange bias field H e and was not measurable until now. The method is verified by torquemetry in a high magnetic field and by reversing its rotation sense. The transition to a new magnetic steady state after rotation reversal is analyzed within a Stoner–Wohlfarth model including thermal relaxation. This transition is completed earlier for strongly coupled grains than for grains with smaller j, which is reflected in the torque curves. We determined P( j) for a sputtered NiFe(16 nm)/IrMn(0.8 nm) film at T=50 K in the hysteretic range of coupling energies and found that P strongly decreases for increasing j.

Decoherence from ensembles of two-level fluctuators

1/f noise, the major source of dephasing in Josephson qubits, may be produced by an ensemble of two-level systems. Depending on the statistical properties of their distribution, the noise distribution can be Gaussian or non-Gaussian. The latter situation is realized, for instance, when the distribution of coupling strengths has a slowly decaying power-law tail. In this regime, questions of self-averaging and sample-to-sample fluctuations become crucial. We study the dephasing process for a class of distribution functions and analyse the self-averaging properties of the results.

Clustering in neural networks with heterogeneous and asymmetrical coupling strengths

The existence and stability of phase-clustered states have been studied previously in networks of weakly coupled oscillators with uniform coupling strengths [Physica D 63 (1993) 424]. However, several studies have shown that if the coupling is uniform and repulsive, it is hard to obtain stable phase-clustered states in networks of realistic neural oscillators when noise is present [Neural Comput. 7 (1995) 307; Phys. Rev. E 57 (1998) 2150]. This problem was avoided by introducing heterogeneity in the distribution of coupling strengths [J. Phys. Soc. Jpn. 72 (2003) 443]. It has been shown that heterogeneous coupling strengths make the occurrence of stable clustered states possible in small networks of repulsively coupled neural oscillators of all kinds [J. Comput. Neurosci. 14 (2003) 139; SIAM J. Appl. Math., submitted for publication]. The present work extends these results to large networks of N identical neurons that are globally coupled with heterogeneous and asymmetrical coupling strengths. Conditions for the existence and stability of a state of n synchronized clusters at evenly distributed phases, called the state of n splay-phase clusters, are derived. Clusters of different sizes, i.e. containing different numbers of neurons, are studied. The existence of such a state is guaranteed if the strength of the coupling originating from one neuron to other neurons is inversely proportional to the size of the cluster to which it belongs. This condition is called the rule of inverse cluster-size. At the state of n splay-phase clusters, the N-neuron network behaves like a network of n “big neurons”. Stability of this state is determined by n eigenvalues of which only one determines the stability of intra-cluster phase differences. The remaining n−1 conditions determine the stability of inter-cluster phase differences, but only n h=(n− mod (n,2))/2 of them have distinct real parts due to symmetry. Heterogeneous coupling makes the stability conditions depend on coupling strengths. This analysis not only reveals how clustered states occur in more general kinds of networks, but also illustrates how the stability of clustered states can be achieved in networks of repulsively coupled neural oscillators. Results on clustered states with phases that are not evenly distributed in the phase space are also presented. Potential applications of these results are discussed.

Tunneling splittings in model 2D potentials. III. . Generalization to N-dimensional case

Abstract Vibrational tunneling spectra for a ‘linear’ potential are calculated with the WKB trajectory method for a wide range of coupling strengths between coordinates, and compared to the quantum mechanical computations. Reasonable agreement is found between the WKB and quantum results, both in the tunneling splittings and wave functions at the ‘path-generated’ dividing line. The method is generalized to N-dimensional symmetric potentials with two equivalent minima. The results are exemplified by calculating the vibrational tunneling spectrum in a 3D ‘squeezed’ potential. The inhomogeneous broadening of tunneling doublets in supersonic beams is discussed. In rotationally excited states, the coupling strength depends on the rotational quantum number, because of the vibration-rotation interaction. The resultant line width is formed by an ensemble of coherently tunneling systems with a distribution of coupling strengths determined by the finite rotational temperature.

Sign-constrained linear learning and diluting in neural networks

For neural networks with predefined effects of the synapses, excitatory or inhibitory, the simplex algorithm is applied as a learning rule. It is assumed that the given signs of the synapses can never be changed during learning. The maximum possible dilution of synapses, as a result of the learning, is found at the maximum storage capacity of a model with only positive or randomly distributed signs. For the case of infinitely many neurons, a replica symmetric calculation of the free energy and the distribution of coupling strengths is presented. The linear algorithm is also applied to networks with a more suitable choice of sign constraints, with the result of a higher storage capacity.

Low-Temperature Thermal Expansion of Amorphous Solids

For most amorphous materials at temperatures below approx. = 1 K, the magnitudes and temperature dependences of specific heat, thermal conductivity and ultrasonic dispersion are qualitatively similar, independent of chemical composition. It has been suggested that thermal expansion also exhibits this universal behavior. The development of a dilatometer capable of resolving sample strains as small as 10/sup -12/ has permitted measurement of the linear thermal expansion of various glasses below 1 K. These investigations have demonstrated, however, that the low-temperature thermal expansion coefficient of glasses can be positive, negative, large or small. Analysis of measurements performed on two types of vitreous silica, two amorphous polymers, As/sub 2/S/sub 3/ and ZrO/sub 2/:Y/sub 2/O/sub 3/ is presented in the context of the phenomenological tunneling-states model. Consistency in explanation of thermal expansion and ultrasonic behavior is maintained by assuming a broad, weakly energy-dependent distribution of coupling strengths between phonons and the localized excitations thought to be characteristic of the glassy state.