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PubMed2003

Prediction of protein coarse contact maps.

Prediction of topological representations of proteins that are geometrically invariants can contribute towards the solution of fundamental open problems in structural genomics like folding. In this paper we focus on coarse grained protein contact maps, a representation that describes the spatial neighborhood relation between secondary structure elements such as helices, beta sheets, and random coils. Our methodology is based on searching the graph space. The search algorithm is guided by an adaptive evaluation function computed by a specialized noncausal recursive connectionist architecture. The neural network is trained using candidate graphs generated during examples of successful searches. Our results demonstrate the viability of the approach for predicting coarse contact maps.

Algorithms↗

PubMed2005

A high-order graph generating self-organizing structure.

A large class of neural network models have their units organized in a lattice with fixed topology or generate their topology during the learning process. These network models can be used as neighborhood preserving map of the input manifold, but such a structure is difficult to manage since these maps are graphs with a number of nodes that is just one or two orders of magnitude less than the number of input points (i.e., the complexity of the map is comparable with the complexity of the manifold) and some hierarchical algorithms were proposed in order to obtain a high-level abstraction of these structures. In this paper a general structure capable to extract high order information from the graph generated by a large class of self-organizing networks is presented. This algorithm will allow to build a two layers hierarchical structure starting from the results obtained by using the suitable neural network for the distribution of the input data. Moreover the proposed algorithm is also capable to build a topology preserving map if it is trained using a graph that is also a topology preserving map.

Algorithms↗

PubMed2006

The brainstem reticular formation is a small-world, not scale-free, network.

Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called 'small-world' and 'scale-free' networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain--the medial reticular formation (RF) of the brainstem--and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement.

Animals↗

PubMed2006

An improved neural network model for the two-page crossing number problem.

The simplest graph drawing method is that of putting the vertices of a graph on a line and drawing the edges as half-circles either above or below the line. Such drawings are called two-page book drawings. The smallest number of crossings over all two-page drawings of a graph G is called the two-page crossing number of G. Cimikowski and Shope have solved the two-page crossing number problem for an n-vertex and m-edge graph by using a Hopfield network with 2 m neurons. We present here an improved Hopfield model with m neurons. The new model achieves much better performance in the quality of solutions and is more efficient than the model of Cimikowski and Shope for all graphs tested. The parallel time complexity of the algorithm, without considering the crossing number calculations, is O(m) for the new Hopfield model with m processors clearly outperforming the previous algorithm.

Algorithms↗

PubMed2004

An improved transiently chaotic neural network for the maximum independent set problem.

By analyzing the dynamic behaviors of the transiently chaotic neural network and greedy heuristic for the maximum independent set (MIS) problem, we present an improved transiently chaotic neural network for the MIS problem in this paper. Extensive simulations are performed and the results show that this proposed transiently chaotic neural network can yield better solutions to p-random graphs than other existing algorithms. The efficiency of the new model is also confirmed by the results on the complement graphs of some DIMACS clique instances in the second DIMACS challenge. Moreover, the improved model uses fewer steps to converge to stable state in comparison with the original transiently chaotic neural network.

Algorithms↗

PubMed2006

Schizophrenic speech as a disordered trajectory in a collapsed cognitive "Small-World".

New theoretical instruments, as goal-directed neural networks models and geometric representations based on semantic graphs, open new approaches for our understanding of the schizophrenic speech. The neuropathologic disorders of the schizophrenia can be simulated using neural models, and these models can eventually explain the origin of goal confusion and incoherence in the schizophrenic discourse trajectory. Moreover, these models are useful to evaluate the different hypothesis about the pathogenic mechanisms of the disease. At the same time, a geometric representation of the trajectory of the speech can be obtained from real data. Our conjecture is that a context-dependent graph can be constructed in order to explore if, when the disease became more severe, a transition from a quasi ordered graph to a nearly completely random graph occurs. Plausibly, there exists a wide region where the graph has the properties of a "small-world". This kind of analyses could be potentially carried out using data coming from the spontaneous speech of schizophrenic patients, and can help to evaluate the progress of the disease. At the same time, these geometrical representations could help to evaluate the effect of treatments.

Attitude↗

PubMed2004

Disulfide connectivity prediction using recursive neural networks and evolutionary information.

MOTIVATION: We focus on the prediction of disulfide bridges in proteins starting from their amino acid sequence and from the knowledge of the disulfide bonding state of each cysteine. The location of disulfide bridges is a structural feature that conveys important information about the protein main chain conformation and can therefore help towards the solution of the folding problem. Existing approaches based on weighted graph matching algorithms do not take advantage of evolutionary information. Recursive neural networks (RNN), on the other hand, can handle in a natural way complex data structures such as graphs whose vertices are labeled by real vectors, allowing us to incorporate multiple alignment profiles in the graphical representation of disulfide connectivity patterns. RESULTS: The core of the method is the use of machine learning tools to rank alternative disulfide connectivity patterns. We develop an ad-hoc RNN architecture for scoring labeled undirected graphs that represent connectivity patterns. In order to compare our algorithm with previous methods, we report experimental results on the SWISS-PROT 39 dataset. We find that using multiple alignment profiles allows us to obtain significant prediction accuracy improvements, clearly demonstrating the important role played by evolutionary information. AVAILABILITY: The Web interface of the predictor is available at http://neural.dsi.unifi.it/cysteines

Algorithms↗

PubMed2004

Semantic graphs and associative memories.

Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.

Journal Article↗

PubMed1996

New approaches in molecular structure prediction.

In the past years, much effort has been put on the development of new methodologies and algorithms for the prediction of protein secondary and tertiary structures from (sequence) data; this is reviewed in detail. New approaches for these predictions such as neural network methods, genetic algorithms, machine learning, and graph theoretical methods are discussed. Secondary structure prediction algorithms were improved mostly by considering families of related proteins; however, for the reliable tertiary structure modeling of proteins, knowledge-based techniques are still preferred. Methods and examples with more or less successful results are described. Also, programs and parameterizations for energy minimisations, molecular dynamics, and electrostatic interactions have been improved, especially with respect to their former limits of applicability. Other topics discussed in this review include the use of traditional and on-line databases, the docking problem and surface properties of biomolecules, packing of protein cores, de novo design and protein engineering, prediction of membrane protein structures, the verification and reliability of model structures, and progress made with currently available software and computer hardware. In summary, the prediction of the structure, function, and other properties of a protein is still possible only within limits, but these limits continue to be moved.

Chemical Phenomena↗

PubMed2000

FPNA: interaction between FPGA and neural computation.

Neural networks are usually considered as naturally parallel computing models. But the number of operators and the complex connection graph of standard neural models can not be directly handled by digital hardware devices. More particularly, several works show that programmable digital hardware is a real opportunity for flexible hardware implementations of neural networks. And yet many area and topology problems arise when standard neural models are implemented onto programmable circuits such as FPGAs, so that the fast FPGA technology improvements can not be fully exploited. Therefore neural network hardware implementations need to reconcile simple hardware topologies with complex neural architectures. The theoretical and practical framework developed, allows this combination thanks to some principles of configurable hardware that are applied to neural computation: Field Programmable Neural Arrays (FPNA) lead to powerful neural architectures that are easy to map onto FPGAs, thanks to a simplified topology and an original data exchange scheme. This paper shows how FPGAs have led to the definition of the FPNA computation paradigm. Then it shows how FPNAs contribute to current and future FPGA-based neural implementations by solving the general problems that are raised by the implementation of complex neural networks onto FPGAs.

Computers↗

PubMed1988

Automata with hierarchical control and evolutionary learning.

We propose an automata-theoretical framework for structured hierarchical control, in terms of rules and meta-rules, for sequences of moves on a graph. This leads to a notion of a "universal" hierarchically structured automaton mu which can move on a given graph in such a way as to emulate any automaton which moves on that graph in response to inputs. This emulation is achieved via a mapping of the inputs in the given automaton to those of mu, and we think of such a mapping as an encoding of the given automaton. We see in several examples that efficient encodings of graph-search algorithms correspond to their natural hierarchical structure (in terms of rules and meta-rules), and this leads one to a precise notion of the "depth" of an automaton which moves on a given graph. By way of application, we discuss a proposed structure of a series of stochastic neural networks which can learn, by example, to encode a given sequence of moves on a graph, so that the encoding obtained is structurally the "natural" one for the given sequence of moves. Thus, such a learning system would perform both structural pattern recognition (in terms of "patterns" of moves), and encoding based on a desired outcome.

Algorithms↗

PubMed2005

Learning protein secondary structure from sequential and relational data.

We propose a method for sequential supervised learning that exploits explicit knowledge of short- and long-range dependencies. The architecture consists of a recursive and bi-directional neural network that takes as input a sequence along with an associated interaction graph. The interaction graph models (partial) knowledge about long-range dependency relations. We tested the method on the prediction of protein secondary structure, a task in which relations due to beta-strand pairings and other spatial proximities are known to have a significant effect on the prediction accuracy. In this particular task, interactions can be derived from knowledge of protein contact maps at the residue level. Our results show that prediction accuracy can be significantly boosted by the integration of interaction graphs.

Animals↗

PubMedDate not supplied

Study of synaptic plasticity via random graphs.

The dynamical random graphs associated with a certain class of biological neural networks are introduced and studied. We describe the phase diagram revealing the parameters of a single neuron and of the synaptic strengths which allow formation of the stable strongly connected large groups of neurons. It is shown that the cycles are the most stable structures when the Hebb rule is implemented into the dynamics of the network of excitatory neurons. We discuss the role of cycles for the synchronization of the neuronal activity.

Neural Networks, Computer↗

PubMed1991

Structural analysis of neural circuits using the theory of directed graphs.

A new approach to analysis of structural properties of biological neural circuits is proposed based on their representation in the form of abstract structures called directed graphs. To exemplify this methodology, structural properties of a biological neural network and randomly wired circuits (RC) were compared. The analyzed biological circuit (BC) represented a sample of 39 neural nuclei which are responsible for the control of the cardiovascular function in higher vertebrates. Initially, direct connections of both circuits were stored in a square matrix format. Then, standard algorithms derived from the theory of directed graphs were applied to analyze the pathways of the circuits according to their length (in number of synapses), degree of connectedness, and structural strength. Thus, the BC was characterized by the presence of short, reciprocal, and unidirectional pathways which presented a high degree of heterogeneity in their strengths. This heterogeneity was mainly due to the existence of a small cluster of reciprocally connected neural nuclei in the circuit that have access, through short pathways, to most of the network. On the other hand, RCs were characterized by the presence of long and mainly reciprocal pathways which showed lower and absolute homogeneous strengths. Through this study the proposed methodology was demonstrated to be a simple and efficient way to store, analyze, and compare basic neuroanatomical information.

Animals↗

PubMed1998

Collective dynamics of 'small-world' networks.

Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

Animals↗

PubMed1999

Convergence properties of the softassign quadratic assignment algorithm.

The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.

Algorithms↗

PubMed2025

Interrogating functional connectivity of in vitro neural glia tissue model modulated through integrative control of matrix stiffness and a neurotrophic factor.

Brain function emerges from intricate cellular communication within neural networks. Both In silico neuronal models and primary neuron cells have revealed that the branching architecture of individual neurons determines the bioelectrical signal propagation pattern and dynamics. However, whether stem cell-differentiated neurons can build functional connectivity regulated by neuronal morphology has yet to be determined. Here, we hypothesized that neurite length, branching, or both factors would regulate the functional connectivity of the stem cell-differentiated neural network. We examined this hypothesis by differentiating mouse cortical neural stem cells (NSCs) on Matrigel substrates with varying storage moduli, both with and without basic fibroblast growth factor (bFGF). Interestingly, with bFGF, Matrigel with a storage modulus (G') of 100 Pa drives NSCs to differentiate into neurons with more dendritic branches, while the gel with G' of 50 Pa led to the development of longer neurites with fewer branches. Notably, branch-rich neural networks exhibited an increased frequency of calcium transients. Using a MATLAB-based analysis pipeline incorporating graph theory, we constructed spatial and temporal calcium activity maps, revealing that branching complexity, more than neurite length, correlates with the density and strength of functional neural circuits. Overall, this study demonstrates that the dendritic branching of neurons, modulated with matrix stiffness and neurotrophic factors, is a key element in enhancing the electrophysiological functionality of the stem cell-differentiated neural network. This finding will have a significant impact on efforts to reconstruct functional neural tissue models, advancing both regenerative therapies and unexplored applications, including biological computing.

Animals↗

PubMed2025

IGCN: integrative graph convolution networks for patient level insights and biomarker discovery in multi-omics integration.

MOTIVATION: Developing computational tools for integrative analysis across multiple types of omics data has been of immense importance in cancer molecular biology and precision medicine research. While recent advancements have yielded integrative prediction solutions for multi-omics data, these methods lack a comprehensive and cohesive understanding of the rationale behind their specific predictions. To shed light on personalized medicine and unravel previously unknown characteristics within integrative analysis of multi-omics data, we introduce a novel integrative neural network approach for cancer molecular subtype and biomedical classification applications, named Integrative Graph Convolutional Networks (IGCN). RESULTS: To demonstrate the superiority of IGCN, we compare its performance with other state-of-the-art approaches across different cancer subtype and biomedical classification tasks. Our experimental results show that our proposed model outperforms the state-of-the-art and baseline methods. IGCN identifies which types of omics data receive more emphasis for each patient when predicting a specific class. Additionally, IGCN has the capability to pinpoint significant biomarkers from a range of omics data types. AVAILABILITY AND IMPLEMENTATION: The source code is available at https://github.com/bozdaglab/IGCN.

Humans↗