scholarly journals Computing Ground States of Bose--Einstein Condensates with Higher Order Interaction via a Regularized Density Function Formulation

2019 ◽  
Vol 41 (6) ◽  
pp. B1284-B1309
Author(s):  
Weizhu Bao ◽  
Xinran Ruan
Keyword(s):  
Density Function ◽  
Ground States ◽  
Higher Order ◽  
Order Interaction ◽  
Function Formulation ◽  
Bose Einstein

scholarly journals Ground states of Bose–Einstein condensates with higher order interaction

2019 ◽  
Vol 386-387 ◽  
pp. 38-48 ◽  
Author(s):  
Weizhu Bao ◽  
Yongyong Cai ◽  
Xinran Ruan
Keyword(s):  
Ground States ◽  
Higher Order ◽  
Order Interaction ◽  
Bose Einstein

Stable Competitive Dynamics Emerge from Multispike Interactions in a Stochastic Model of Spike-Timing-Dependent Plasticity

2006 ◽  
Vol 18 (10) ◽  
pp. 2414-2464 ◽  
Author(s):  
Peter A. Appleby ◽  
Terry Elliott
Keyword(s):  
Synaptic Plasticity ◽  
Stochastic Model ◽  
Higher Order ◽  
Spike Timing ◽  
Competitive Dynamics ◽  
Spike Timing Dependent Plasticity ◽  
Interaction Function ◽  
Dependent Plasticity ◽  
Order Interaction ◽  
Synaptic Dynamics

In earlier work we presented a stochastic model of spike-timing-dependent plasticity (STDP) in which STDP emerges only at the level of temporal or spatial synaptic ensembles. We derived the two-spike interaction function from this model and showed that it exhibits an STDP-like form. Here, we extend this work by examining the general n-spike interaction functions that may be derived from the model. A comparison between the two-spike interaction function and the higher-order interaction functions reveals profound differences. In particular, we show that the two-spike interaction function cannot support stable, competitive synaptic plasticity, such as that seen during neuronal development, without including modifications designed specifically to stabilize its behavior. In contrast, we show that all the higher-order interaction functions exhibit a fixed-point structure consistent with the presence of competitive synaptic dynamics. This difference originates in the unification of our proposed “switch” mechanism for synaptic plasticity, coupling synaptic depression and synaptic potentiation processes together. While three or more spikes are required to probe this coupling, two spikes can never do so. We conclude that this coupling is critical to the presence of competitive dynamics and that multispike interactions are therefore vital to understanding synaptic competition.

scholarly journals Higher-order temporal network effects through triplet evolution

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Qing Yao ◽  
Bingsheng Chen ◽  
Tim S. Evans ◽  
Kim Christensen
Keyword(s):  
Real World ◽  
Link Prediction ◽  
Higher Order ◽  
Prediction Algorithm ◽  
Interaction Patterns ◽  
Temporal Networks ◽  
World Systems ◽  
Order Interaction ◽  
Space And Time ◽  
Pairwise Interactions

AbstractWe study the evolution of networks through ‘triplets’—three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world data to a model based on pairwise interactions only. The significant differences between the computed matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world systems in space and time, such as our data sets. Furthermore, this also reveals that different patterns of higher-order interaction are involved in different real-world situations. To test our approach, we then use these transition matrices as the basis of a link prediction algorithm. We investigate our algorithm’s performance on four temporal networks, comparing our approach against ten other link prediction methods. Our results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as we find our method, along with two other methods based on non-local interactions, give the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems.

Symmetry-conserving higher-order interaction terms in the interacting boson model

1985 ◽  
Vol 32 (3) ◽  
pp. 1049-1056 ◽  
Author(s):  
G. Vanden Berghe ◽  
H. E. De Meyer ◽  
P. Van Isacker
Keyword(s):  
Higher Order ◽  
Interacting Boson Model ◽  
Order Interaction ◽  
Interaction Terms ◽  
Boson Model
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