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Deciphering the non-trivial interactions and mechanisms driving the evolution of time-varying complex networks (TVCNs) plays a crucial role in designing optimal control strategies for such networks or enhancing their causal predictive capabilities. In this paper, we advance the science of TVCNs by providing a mathematical framework through which we can gauge how local changes within a complex weighted network affect its global properties. More precisely, we focus on unraveling unknown geometric properties of a network and determine its implications on detecting phase transitions within the dynamics of a TVCN. In this vein, we aim at elaborating a novel and unified approach that can be used to depict the relationship between local interactions in a complex network and its global kinetics. We propose a geometric-inspired framework to characterize the network’s state and detect a phase transition between different states, to infer the TVCN’s dynamics. A phase of a TVCN is determined by its Forman–Ricci curvature property. Numerical experiments show the usefulness of the proposed curvature formalism to detect the transition between phases within artificially generated networks. Furthermore, we demonstrate the effectiveness of the proposed framework in identifying the phase transition phenomena governing the training and learning processes of artificial neural networks. Moreover, we exploit this approach to investigate the phase transition phenomena in cellular re-programming by interpreting the dynamics of Hi-C matrices as TVCNs and observing singularity trends in the curvature network entropy. Finally, we demonstrate that this curvature formalism can detect a political change. Specifically, our framework can be applied to the US Senate data to detect a political change in the United States of America after the 1994 election, as discussed by political scientists.

 

Controlling large-scale dynamical networks is crucial to understand and, ultimately, craft the evolution of complex behavior. While broadly speaking we understand how to control Markov dynamical networks, where the current state is only a function of its previous state, we lack a general understanding of how to control dynamical networks whose current state depends on states in the distant past (i.e. long-term memory). Therefore, we require a different way to analyze and control the more prevalent long-term memory dynamical networks. Herein, we propose a new approach to control dynamical networks exhibiting long-term power-law memory dependencies. Our newly proposed method enables us to find the minimum number of driven nodes (i.e. the state vertices in the network that are connected to one and only one input) and their placement to control a long-term power-law memory dynamical network given a specific time-horizon, which we define as the ‘time-to-control’. Remarkably, we provide evidence that long-term power-law memory dynamical networks require considerably fewer driven nodes to steer the network’s state to a desired goal for any given time-to-control as compared with Markov dynamical networks. Finally, our method can be used as a tool to determine the existence of long-term memory dynamics in networks.

 

Recent technological advances have contributed to the rapid increase in algorithmic complexity of applications, ranging from signal processing to autonomous systems. To control this complexity and endow heterogeneous computing systems with autonomous programming and optimization capabilities, we propose aunified, end-to-end, programmable graph representation learning(PGL) framework that mines the complexity of high-level programs down to low-level virtual machine intermediate representation, extracts specific computational patterns, and predicts which code segments run best on a core in heterogeneous hardware. PGL extracts multifractal features from code graphs and exploits graph representation learning strategies for automatic parallelization and correct assignment to heterogeneous processors. The comprehensive evaluation of PGL on existing and emerging complex software demonstrates a 6.42x and 2.02x speedup compared to thread-based execution and state-of-the-art techniques, respectively. Our PGL framework leads to higher processing efficiency, which is crucial for future AI and high-performance computing applications such as autonomous vehicles and machine vision.

 

We propose a systematic application-specific hardware design methodology for designing Spiking Neural Network (SNN), SNNOpt, which consists of three novel phases: 1) an Olliver-Ricci-Curvature (ORC)-based architecture-aware network partitioning, 2) a reinforcement learning mapping strategy, and 3) a Bayesian optimization algorithm for NoC design space exploration. Experimental results show that SNNOpt achieves a 47.45% less runtime and 58.64% energy savings over state-of-the-art approaches. 

Finding strongly connected components (SCCs) and the diameter of a directed network play a key role in a variety of discrete optimization problems, and subsequently, machine learning and control theory problems. On the one hand, SCCs are used in solving the 2-satisfiability problem, which has applications in clustering, scheduling, and visualization. On the other hand, the diameter has applications in network learning and discovery problems enabling efficient internet routing and searches, as well as identifying faults in the power grid. In this paper, we leverage consensus-based principles to find the SCCs in a scalable and distributed fashion with a computational complexity of O(Ddmaxin−degree) , where D is the (finite) diameter of the network and dmaxin−degree is the maximum in-degree of the network. Additionally, we prove that our algorithm terminates in D+1 iterations, which allows us to retrieve the diameter of the network. We illustrate the performance of our algorithm on several random networks, including Erdö-Rényi, Barabási-Albert, and Watts-Strogatz networks. 

We address the problem of learning from demonstrations when the learner must satisfy safety and/or performance requirements expressed as Stochastic Temporal Logic (StTL) specifications. We extend the maximum causal entropy inverse reinforcement learning framework to account for StTL constraints and show how to encode them via a minimal set of mixed-integer linear constraints. Our method is based on a cut-and-generate algorithm that iterates between two phases: in the cut phase, we use cutting hyperplanes to approximate the feasible region of the non-linear constraint that encodes atomic predicates and in the generate phase, we propagate these hyperplanes through the schematics to generate constraints for arbitrary formulas. Our algorithmic contributions are validated in different environments and specifications. 

Cellular biological networks represent the molecular interactions that shape function of living cells. Uncovering the organization of a biological network requires efficient and accurate algorithms to determine the components, termed communities, underlying specific processes. Detecting functional communities is challenging because reconstructed biological networks are always incomplete due to technical bias and biological complexity, and the evaluation of putative communities is further complicated by a lack of known ground truth. To address these challenges, we developed a geometric-based detection framework based on Ollivier-Ricci curvature to exploit information about network topology to perform community detection from partially observed biological networks. We further improved this approach by integrating knowledge of gene function, termed side information, into the Ollivier-Ricci curvature algorithm to aid in community detection. This approach identified essential conserved and varied biological communities from partially observedArabidopsisprotein interaction datasets better than the previously used methods. We show that Ollivier-Ricci curvature with side information identified an expanded auxin community to include an important protein stability complex, the Cop9 signalosome, consistent with previous reported links to auxin response and root development. The results show that community detection based on Ollivier-Ricci curvature with side information can uncover novel components and novel communities in biological networks, providing novel insight into the organization and function of complex networks.

 

Time-evolution of partial differential equations is fundamental for modeling several complex dynamical processes and events forecasting, but the operators associated with such problems are non-linear. We propose a Pad´e approximation based exponential neural operator scheme for efficiently learning the map between a given initial condition and the activities at a later time. The multiwavelets bases are used for space discretization. By explicitly embedding the exponential operators in the model, we reduce the training parameters and make it more data-efficient which is essential in dealing with scarce and noisy real-world datasets. The Pad´e exponential operator uses a recurrent structure with shared parameters to model the non-linearity compared to recent neural operators that rely on using multiple linear operator layers in succession. We show theoretically that the gradients associated with the recurrent Pad´e network are bounded across the recurrent horizon. We perform experiments on non-linear systems such as Korteweg-de Vries (KdV) and Kuramoto–Sivashinsky (KS) equations to show that the proposed approach achieves the best performance and at the same time is data-efficient. We also show that urgent real-world problems like epidemic forecasting (for example, COVID- 19) can be formulated as a 2D time-varying operator problem. The proposed Pad´e exponential operators yield better prediction results (53% (52%) better MAE than best neural operator (non-neural operator deep learning model)) compared to state-of-the-art forecasting models. 

Assessing the stability of biological system models has aided in uncovering a plethora of new insights in genetics, neuroscience, and medicine. In this paper, we focus on analyzing the stability of neurological signals, including electroencephalogram (EEG) signals. Interestingly, spatiotemporal discrete-time linear fractional-order systems (DTLFOS) have been shown to accurately and efficiently represent a variety of neurological and physiological signals. Here, we leverage the conditions for stability of DTLFOS to assess a real-world EEG data set. By analyzing the stability of EEG signals during movement and rest tasks, we provide evidence of the usefulness of the quantification of stability as a bio-marker for cognitive motor control.