scholarly journals Global crystal bases for integrable modules over a quantum symmetric pair of type AIII

2021 ◽  
Vol 25 (2) ◽  
pp. 27-66
Author(s):  
Hideya Watanabe
Keyword(s):  
Symmetric Pair ◽  
Crystal Bases ◽  
Integrable Modules

Symmetric-pair antennas for beam steering, direction finding or isotropic-reception gain

1991 ◽  
Vol 138 (4) ◽  
pp. 368 ◽  
Author(s):  
R. Benjamin ◽  
W. Titze ◽  
P.V. Brennan ◽  
H.D. Griffiths
Keyword(s):  
Beam Steering ◽  
Direction Finding ◽  
Symmetric Pair

scholarly journals Crystal Bases and Monomials forUq(G2)-Modules

2006 ◽  
Vol 34 (1) ◽  
pp. 129-142 ◽  
Author(s):  
Dong-Uy Shin
Keyword(s):  
Crystal Bases

3D Printing — The Basins of Tristability in the Lorenz System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750128 ◽  
Author(s):  
Anda Xiong ◽  
Julien C. Sprott ◽  
Jingxuan Lyu ◽  
Xilu Wang
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Symmetric Pair ◽  
State Space Approach ◽  
3D Printers ◽  
The Lorenz System ◽  
Almost All ◽  
Space Approach

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

scholarly journals Autonomous emergence of connectivity assemblies via spike triplet interactions

2019 ◽  
Author(s):  
Lisandro Montangie ◽  
Julijana Gjorgjieva
Keyword(s):  
Random Network ◽  
Transmission Function ◽  
Higher Order ◽  
External Input ◽  
Spike Timing ◽  
Symmetric Pair ◽  
Graph Theoretic ◽  
Stdp Rule ◽  
Triplet Model ◽  
External Stimuli

AbstractNon-random connectivity can emerge without structured external input driven by activity-dependent mechanisms of synaptic plasticity based on precise spiking patterns. Here we analyze the emergence of global structures in recurrent networks based on a triplet model of spike timing dependent plasticity (STDP) which depends on the interactions of three precisely-timed spikes and can describe plasticity experiments with varying spike frequency better than the classical pair-based STDP rule. We describe synaptic changes arising from emergent higher-order correlations, and investigate their influence on different connectivity motifs in the network. Our motif expansion framework reveals novel motif structures under the triplet STDP rule, which support the formation of bidirectional connections and loops in contrast to the classical pair-based STDP rule. Therefore, triplet STDP drives the spontaneous emergence of self-connected groups of neurons, or assemblies, proposed to represent functional units in neural circuits. Assembly formation has often been associated with plasticity driven by firing rates or external stimuli. We propose that assembly structure can emerge without the need for externally patterned inputs or assuming a symmetric pair-based STDP rule commonly assumed in previous studies. The emergence of non-random network structure under triplet STDP occurs through internally-generated higher-order correlations, which are ubiquitous in natural stimuli and neuronal spiking activity, and important for coding. We further demonstrate how neuromodulatory mechanisms that modulate the shape of triplet STDP or the synaptic transmission function differentially promote connectivity motifs underlying the emergence of assemblies, and quantify the differences using graph theoretic measures.

scholarly journals Crystal Bases and Tensor Product Decompositions of Uq(G2)-Modules

1994 ◽  
Vol 163 (3) ◽  
pp. 675-691 ◽  
Author(s):  
S.J. Kang ◽  
K.C. Misra
Keyword(s):  
Tensor Product ◽  
Crystal Bases
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