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Register a new userGranger-faithfulness and link orientation in network reconstruction
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Networked dynamic systems are often abstracted as directed graphs, where the observed system processes form the vertex set and directed edges are used to represent non-zero transfer functions. Recovering the exact underlying graph structure of such a networked dynamic system, given only observational data, is a challenging task. Under relatively mild well-posedness assumptions on the network dynamics, there are state-of-the-art methods which can guarantee the absence of false positives. However, in this article we prove that under the same well-posedness assumptions, there are instances of networks for which any method is susceptible to inferring false negative edges or false positive edges. Borrowing a terminology from the theory of graphical models, we say those systems are unfaithful to their networks. We formalize a variant of faithfulness for dynamic systems, called Granger-faithfulness, and for a large class of dynamic networks, we show that Granger-unfaithful systems constitute a Lebesgue zero-measure set. For the same class of networks, under the Granger-faithfulness assumption, we provide an algorithm that reconstructs the network topology with guarantees for no false positive and no false negative edges in its output. We augment the topology reconstruction algorithm with orientation rules for some of the inferred edges, and we prove the rules are consistent under the Granger-faithfulness assumption.
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An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved. Assuming a partial finite-order Markov property, conditions are then derived under which Granger causality between them can be reliably inferred from the second order moments of the quantized processes. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through measurements quantized via non-uniform, uniform or high resolution quantizers. This approach does not require the statistics of the underlying Gaussian signals to be estimated, or a system model to be identified. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations. The effectiveness of the proposed method is illustrated by simulation results.
In the last decade, the growing influence of open source software has necessitated the need to reduce the abstraction levels in hardware design. Open source hardware significantly reduces the development time, increasing the probability of first-pass success and enable developers to optimize software solutions based on hardware features, thereby reducing the design costs. The recent introduction of open source Process Development Kit (OpenPDK) by Skywater technologies in June 2020 has eliminated the barriers to Application-Specific Integrated Circuit (ASIC) design, which is otherwise considered expensive and not easily accessible. The OpenPDK is the first concrete step towards achieving the goal of open source circuit blocks that can be imported to reuse and modify in ASIC design. With process technologies scaling down for better performance, the need for entirely digital designs, which can be synthesized in any standard Automatic Place-and-Route (APR) tool, has increased considerably, for mapping physical design to the new process technology. This work presents the first open source all-digital Serializer/Deserializer (SerDes) for multi-GHz serial links designed using Skywater OpenPDK 130nm process node. To ensure that the design is fully synthesizable, the SerDes uses CMOS inverter-based drivers at the Tx, while the Rx front end comprises a resistive feedback inverter as a sensing element, followed by sampling elements. A fully digital oversampling CDR at the Rx recovers the Tx clock for proper decoding of data bits. The physical design flow utilizes OpenLANE, which is an end-to-end tool for generating GDS from RTL. Virtuoso has been used for extracting parasitics for post-layout simulations, which exhibit the SerDes functionality at 2 Gbps for 34 dB channel loss while consuming 438 mW power. The GDS and netlist files of the SerDes are uploaded in a GitHub repository for public access.
ReLU (rectified linear units) neural network has received significant attention since its emergence. In this paper, a univariate ReLU (UReLU) neural network is proposed to both modelling the nonlinear dynamic system and revealing insights about the system. Specifically, the neural network consists of neurons with linear and UReLU activation functions, and the UReLU functions are defined as the ReLU functions respect to each dimension. The UReLU neural network is a single hidden layer neural network, and the structure is relatively simple. The initialization of the neural network employs the decoupling method, which provides a good initialization and some insight into the nonlinear system. Compared with normal ReLU neural network, the number of parameters of UReLU network is less, but it still provide a good approximation of the nonlinear dynamic system. The performance of the UReLU neural network is shown through a Hysteretic benchmark system: the Bouc-Wen system. Simulation results verify the effectiveness of the proposed method.
This paper provides an optimized cable path planning solution for a tree-topology network in an irregular 2D manifold in a 3D Euclidean space, with an application to the planning of submarine cable networks. Our solution method is based on total cost minimization, where the individual cable costs are assumed to be linear to the length of the corresponding submarine cables subject to latency constraints between pairs of nodes. These latency constraints limit the cable length and number of hops between any pair of nodes. Our method combines the Fast Marching Method (FMM) and a new Integer Linear Programming (ILP) formulation for Minimum Spanning Tree (MST) where there are constraints between pairs of nodes. We note that this problem of MST with constraints is NP-complete. Nevertheless, we demonstrate that ILP running time is adequate for the great majority of existing cable systems. For cable systems for which ILP is not able to find the optimal solution within an acceptable time, we propose an alternative heuristic algorithm based on Prims algorithm. In addition, we apply our FMM/ILP-based algorithm to a real-world cable path planning example and demonstrate that it can effectively find an MST with latency constraints between pairs of nodes.
We consider a detection problem where sensors experience noisy measurements and intermittent communication opportunities to a centralized fusion center (or cloud). The objective of the problem is to arrive at the correct estimate of event detection in the environment. The sensors may communicate locally with other sensors (local clusters) where they fuse their noisy sensor data to estimate the detection of an event locally. In addition, each sensor cluster can intermittently communicate to the cloud, where a centralized fusion center fuses estimates from all sensor clusters to make a final determination regarding the occurrence of the event across the deployment area. We refer to this hybrid communication scheme as a cloud-cluster architecture. Minimizing the expected loss function of networks where noisy sensors are intermittently connected to the cloud, as in our hybrid communication scheme, has not been investigated to our knowledge. We leverage recently improved concentration inequalities to arrive at an optimized decision rule for each cluster and we analyze the expected detection performance resulting from our hybrid scheme. Our analysis shows that clustering the sensors provides resilience to noise in the case of low communication probability with the cloud. For larger clusters, a steep improvement in detection performance is possible even for a low communication probability by using our cloud-cluster architecture.
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