scholarly journals Higher-order simplicial synchronization of coupled topological signals

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Reza Ghorbanchian ◽  
Juan G. Restrepo ◽  
Joaquín J. Torres ◽  
Ginestra Bianconi
Keyword(s):  
Algebraic Topology ◽  
Network Models ◽  
Simplicial Complexes ◽  
Higher Order ◽  
Large Network ◽  
Underlying Network ◽  
Discontinuous Phase ◽  
Fully Connected ◽  
The Brain ◽  
Fully Connected Networks

AbstractSimplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of simplicial complexes. In particular we consider topological signals, i.e., dynamical signals defined on simplices of different dimension, here taken to be nodes and links for simplicity. We show that coupling between signals defined on nodes and links leads to explosive topological synchronization in which phases defined on nodes synchronize simultaneously to phases defined on links at a discontinuous phase transition. We study the model on real connectomes and on simplicial complexes and network models. Finally, we provide a comprehensive theoretical approach that captures this transition on fully connected networks and on random networks treated within the annealed approximation, establishing the conditions for observing a closed hysteresis loop in the large network limit.

scholarly journals Higher-Order Networks

2021 ◽  
Author(s):  
Ginestra Bianconi
Keyword(s):  
Complex Systems ◽  
Network Topology ◽  
Simplicial Complexes ◽  
Higher Order ◽  
Topological Data Analysis ◽  
Mathematical Framework ◽  
Wide Range ◽  
Underlying Network ◽  
Many Body Interactions ◽  
Higher Order Networks

Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.

scholarly journals Recommendation algorithm based on attributed multiplex heterogeneous network

2021 ◽  
Vol 7 ◽  
pp. e822
Author(s):  
Zhisheng Yang ◽  
Jinyong Cheng
Keyword(s):  
Heterogeneous Network ◽  
Area Under Curve ◽  
Network Models ◽  
Attention Mechanism ◽  
Large Network ◽  
Sigmoid Function ◽  
Large Networks ◽  
Model Tuning ◽  
Characteristic Area ◽  
Fully Connected

In the field of deep learning, the processing of large network models on billions or even tens of billions of nodes and numerous edge types is still flawed, and the accuracy of recommendations is greatly compromised when large network embeddings are applied to recommendation systems. To solve the problem of inaccurate recommendations caused by processing deficiencies in large networks, this paper combines the attributed multiplex heterogeneous network with the attention mechanism that introduces the softsign and sigmoid function characteristics and derives a new framework SSN_GATNE-T (S represents the softsign function, SN represents the attention mechanism introduced by the Softsign function, and GATNE-T represents the transductive embeddings learning for attribute multiple heterogeneous networks). The attributed multiplex heterogeneous network can help obtain more user-item information with more attributes. No matter how many nodes and types are included in the model, our model can handle it well, and the improved attention mechanism can help annotations to obtain more useful information via a combination of the two. This can help to mine more potential information to improve the recommendation effect; in addition, the application of the softsign function in the fully connected layer of the model can better reduce the loss of potential user information, which can be used for accurate recommendation by the model. Using the Adam optimizer to optimize the model can not only make our model converge faster, but it is also very helpful for model tuning. The proposed framework SSN_GATNE-T was tested for two different types of datasets, Amazon and YouTube, using three evaluation indices, ROC-AUC (receiver operating characteristic-area under curve), PR-AUC (precision recall-area under curve) and F1 (F1-score), and found that SSN_GATNE-T improved on all three evaluation indices compared to the mainstream recommendation models currently in existence. This not only demonstrates that the framework can deal well with the shortcomings of obtaining accurate interaction information due to the presence of a large number of nodes and edge types of the embedding of large network models, but also demonstrates the effectiveness of addressing the shortcomings of large networks to improve recommendation performance. In addition, the model is also a good solution to the cold start problem.

scholarly journals The topology of higher-order complexes associated with brain hubs in human connectomes

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Miroslav Andjelković ◽  
Bosiljka Tadić ◽  
Roderick Melnik
Keyword(s):  
Complex Dynamics ◽  
Simplicial Complexes ◽  
Brain Regions ◽  
Higher Order ◽  
Core Networks ◽  
Right Cerebral Hemisphere ◽  
Left And Right ◽  
Order Complexes ◽  
The Brain

Abstract Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human connectome can be crucial for the brain complex dynamics. In this context, the best-connected brain areas, designated as hub nodes, play a central role in supporting integrated brain function. Here, we study the structure of simplicial complexes attached to eight global hubs in the female and male connectomes and identify the core networks among the affected brain regions. These eight hubs (Putamen, Caudate, Hippocampus and Thalamus-Proper in the left and right cerebral hemisphere) are the highest-ranking according to their topological dimension, defined as the number of simplexes of all orders in which the node participates. Furthermore, we analyse the weight-dependent heterogeneity of simplexes. We demonstrate changes in the structure of identified core networks and topological entropy when the threshold weight is gradually increased. These results highlight the role of higher-order interactions in human brain networks and provide additional evidence for (dis)similarity between the female and male connectomes.

Measuring the World

2018 ◽  
Author(s):  
Ann-Sophie Barwich
Keyword(s):  
Sensory Information ◽  
Network Models ◽  
Model System ◽  
Stimulus Input ◽  
Expectancy Effects ◽  
Neural Network Models ◽  
Perceptual Object ◽  
External Objects ◽  
The Common ◽  
The Brain

How much does stimulus input shape perception? The common-sense view is that our perceptions are representations of objects and their features and that the stimulus structures the perceptual object. The problem for this view concerns perceptual biases as responsible for distortions and the subjectivity of perceptual experience. These biases are increasingly studied as constitutive factors of brain processes in recent neuroscience. In neural network models the brain is said to cope with the plethora of sensory information by predicting stimulus regularities on the basis of previous experiences. Drawing on this development, this chapter analyses perceptions as processes. Looking at olfaction as a model system, it argues for the need to abandon a stimulus-centred perspective, where smells are thought of as stable percepts, computationally linked to external objects such as odorous molecules. Perception here is presented as a measure of changing signal ratios in an environment informed by expectancy effects from top-down processes.

Clique Here: On the Distributed Complexity in Fully-Connected Networks

2016 ◽  
Vol 26 (01) ◽  
pp. 1650004 ◽  
Author(s):  
Benny Applebaum ◽  
Dariusz R. Kowalski ◽  
Boaz Patt-Shamir ◽  
Adi Rosén
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Message Passing ◽  
Constant Number ◽  
Running Time ◽  
Message Size ◽  
Explicit Function ◽  
Randomized Protocols ◽  
Fully Connected ◽  
Fully Connected Networks

We consider a message passing model with n nodes, each connected to all other nodes by a link that can deliver a message of B bits in a time unit (typically, B = O(log n)). We assume that each node has an input of size L bits (typically, L = O(n log n)) and the nodes cooperate in order to compute some function (i.e., perform a distributed task). We are interested in the number of rounds required to compute the function. We give two results regarding this model. First, we show that most boolean functions require ‸ L/B ‹ − 1 rounds to compute deterministically, and that even if we consider randomized protocols that are allowed to err, the expected running time remains [Formula: see text] for most boolean function. Second, trying to find explicit functions that require superconstant time, we consider the pointer chasing problem. In this problem, each node i is given an array Ai of length n whose entries are in [n], and the task is to find, for any [Formula: see text], the value of [Formula: see text]. We give a deterministic O(log n/ log log n) round protocol for this function using message size B = O(log n), a slight but non-trivial improvement over the O(log n) bound provided by standard “pointer doubling.” The question of an explicit function (or functionality) that requires super constant number of rounds in this setting remains, however, open.

The novel guanylyl cyclase MsGC-I is strongly expressed in higher-order neuropils in the brain of Manduca sexta

2001 ◽  
Vol 204 (2) ◽  
pp. 305-314 ◽  
Author(s):  
A. Nighorn ◽  
P.J. Simpson ◽  
D.B. Morton
Keyword(s):  
Nervous System ◽  
Manduca Sexta ◽  
Guanylyl Cyclase ◽  
Higher Order ◽  
Adult Brain ◽  
Central Complex ◽  
Amino Acid Residues ◽  
Order Processing ◽  
Guanylyl Cyclases ◽  
The Brain

Guanylyl cyclases are usually characterized as being either soluble (sGCs) or receptor (rGCs). We have recently cloned a novel guanylyl cyclase, MsGC-I, from the developing nervous system of the hawkmoth Manduca sexta that cannot be classified as either an sGC or an rGC. MsGC-I shows highest sequence identity with receptor guanylyl cyclases throughout its catalytic and dimerization domains, but does not contain the ligand-binding, transmembrane or kinase-like domains characteristic of receptor guanylyl cyclases. In addition, MsGC-I contains a C-terminal extension of 149 amino acid residues. In this paper, we report the expression of MsGC-I in the adult. Northern blots show that it is expressed preferentially in the nervous system, with high levels in the pharate adult brain and antennae. In the antennae, immunohistochemical analyses show that it is expressed in the cell bodies and dendrites, but not axons, of olfactory receptor neurons. In the brain, it is expressed in a variety of sensory neuropils including the antennal and optic lobes. It is also expressed in structures involved in higher-order processing including the mushroom bodies and central complex. This complicated expression pattern suggests that this novel guanylyl cyclase plays an important role in mediating cyclic GMP levels in the nervous system of Manduca sexta.

scholarly journals Evolutionary modifications in human brain connectivity associated with schizophrenia

Brain ◽  
2019 ◽  
Vol 142 (12) ◽  
pp. 3991-4002 ◽  
Author(s):  
Martijn P van den Heuvel ◽  
Lianne H Scholtens ◽  
Siemon C de Lange ◽  
Rory Pijnenburg ◽  
Wiepke Cahn ◽  
...  
Keyword(s):  
Human Brain ◽  
Brain Connectivity ◽  
Brain Evolution ◽  
Higher Order ◽  
Brain Functions ◽  
Human Brain Evolution ◽  
The Brain

See Vértes and Seidlitz (doi:10.1093/brain/awz353) for a scientific commentary on this article. Is schizophrenia a by-product of human brain evolution? By comparing the human and chimpanzee connectomes, van den Heuvel et al. demonstrate that connections unique to the human brain show greater involvement in schizophrenia pathology. Modifications in service of higher-order brain functions may have rendered the brain more vulnerable to dysfunction.

scholarly journals Human Creativity and Consciousness: Unintended Consequences of the Brain’s Extraordinary Energy Efficiency?

2020 ◽  
Author(s):  
Tim Palmer
Keyword(s):  
Energy Efficiency ◽  
Human Brain ◽  
Quantum Physics ◽  
Unintended Consequences ◽  
Large Network ◽  
Active Neuron ◽  
Available Energy ◽  
Human Creativity ◽  
The One ◽  
The Brain

It is proposed that both human creativity and human consciousness are (unintended) consequences of the human brain’s extraordinary energy efficiency. The topics of creativity and consciousness are treated separately, though have a common sub-structure. It is argued that creativity arises from a synergy between two cognitive modes of the human brain (which broadly coincide with Kahneman’s Systems 1 and 2). In the first, available energy is spread across a relatively large network of neurons. As such, the amount of energy per active neuron is so small that the operation of such neurons is susceptible to thermal (ultimately quantum decoherent) noise. In the second, available energy is focussed on a small enough subset of neurons to guarantee a deterministic operation. An illustration of how this synergy can lead to creativity with implications for computing in silicon are discussed. Starting with a discussion of the concept of free will, the notion of consciousness is defined in terms of an awareness of what are perceived to be nearby counterfactual worlds in state space. It is argued that such awareness arises from an interplay between our memories on the one hand, and quantum physical mechanisms (where, unlike in classical physics, nearby counterfactual worlds play an indispensable dynamical role) in the ion channels of neural networks. As with the brain’s susceptibility to noise, it is argued that in situations where quantum physics plays a role in the brain, it does so for reasons of energy efficiency. As an illustration of this definition of consciousness, a novel proposal is outlined as to why quantum entanglement appears so counter-intuitive.

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