Abstract

Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a synthetical structure being furthermore perfectly reflected in the modular organization of the network's functioning. Our results solve a relevant problem of designing a desired set of clusters and are of generic application in all cases where a desired parallel functioning needs to be blueprinted.

Abstract

A balanced ecosystem with coexisting constituent species is often perturbed by different natural events that persist only for a finite duration of time. What becomes important is whether, in the aftermath, the ecosystem recovers its balance or not. Here we study the fate of an ecosystem by monitoring the dynamics of a particular species that encounters a sudden increase in death rate. For exploration of the fate of the species, we use Monte-Carlo simulation on a three-species cyclic rock-paper-scissor model. The density of the affected (by perturbation) species is found to drop exponentially immediately after the pulse is applied. In spite of showing this exponential decay as a short-time behavior, there exists a region in parameter space where this species surprisingly remains as a single survivor, wiping out the other two which had not been directly affected by the perturbation. Numerical simulations using stochastic differential equations of the species give consistency to our results.

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Abstract

We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates between sampling points from selected regions in the search space and de-emphasizing regions that may not lead to good solutions for MGPF. Our approach provides an asymptotic, 2-approximation guarantee for MGPF. We also present extensive numerical results to illustrate the advantages of our proposed approach over uniform sampling in terms of the quality of the solutions found and computation speed.

Abstract

Unsupervised Representation Learning on graphs is gaining traction due to the increasing abundance of unlabelled network data and the compactness, richness, and usefulness of the representations generated. In this context, the need to consider fairness and bias constraints while generating the representations has been well-motivated and studied to some extent in prior works. One major limitation of most of the prior works in this setting is that they do not aim to address the bias generated due to connectivity patterns in the graphs, such as varied node centrality, which leads to a disproportionate performance across nodes. In our work, we aim to address this issue of mitigating bias due to inherent graph structure in an unsupervised setting. To this end, we propose CAFIN, a centrality-aware fairness-inducing framework that leverages the structural information of graphs to tune the representations generated by existing frameworks. We deploy it on GraphSAGE (a popular framework in this domain) and showcase its efficacy on two downstream tasks – Node Classification and Link Prediction. Empirically, CAFIN consistently reduces the performance disparity across popular datasets (varying from 18 to 80% reduction in performance disparity) from various domains while incurring only a minimal cost of fairness.

Abstract

This paper presents a low power voltage reference and current reference in one circuit. The reference voltage is the sum of the complementary to absolute temperature (CTAT) gatesource voltage of a MOSFET operating in the subthreshold region and a scaled version of the proportional to absolute temperature (PTAT) ΔVGS of two MOSFETs operating in subthreshold region. The generated temperature independent reference current is the ratio of the reference voltage and a resistance. The proposed circuit does not use an operational transconductance amplifier (OTA) to generate the reference current, thereby eliminates the variation in current due to any offset of the OTA. Furthermore, the circuit uses a native MOSFET for ameliorating the DC PSRR. The proposed circuit is designed in a 130nm CMOS process. The circuit works with a minimum supply voltage of 1.2V while generating a reference voltage of around 0.7V and a reference current of around 100nA. A TC of 100 ppm/˚C for the reference voltage and a TC of 108 ppm/˚C for the reference current are noted for mismatch and process variations from Monte-Carlo simulations for 300 samples. The circuit consumes only 240nW of power, which makes it suitable for ultra-low power applications.

Abstract

Aspect-based summarization of a legal case file related to regulating bodies allows different stakeholders to consume information of interest therein efficiently. In this paper, we propose a multi-step process to achieve the same. First, we explore the semantic sentence segmentation of SEBI case files via classification. We also propose a dataset of Indian legal adjudicating orders which contain tags from carefully crafted domain-specific sentence categories with the help of legal experts. We experiment with various machine learning and deep learning methods for this multi-class classification. Then, we examine the performance of numerous summarization methods on the segmented document to generate persona-specific summaries. Finally, we develop a pipeline making use of the best methods in both sub-tasks to achieve high recall.

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Abstract

A leptophobic $Z^prime$ that does not couple with the Standard Model leptons can evade the stringent bounds from the dilepton-resonance searches. In our earlier paper [T. Arun et al., Search for the $Z'$ boson decaying to a right-handed neutrino pair in leptophobic $U(1)$ models,Phys. Rev. D, 106 (2022) 095035; arXiv:2204.02949], we presented two gauge anomaly-free $U(1)$ models---one based on the Green-Schwarz (GS) anomaly cancellation mechanism, and the other on a grand unified theory (GUT) framework with gauge kinetic mixing---where a heavy leptophobic $Z'$ is present along with right-handed neutrinos ($N_R$). We pointed out the interesting possibility of a correlated search for $Z'$ and $N_R$ at the LHC through the $ppto Z'to N_R N_R$ channel. This channel can probe a part of the $Z'$ parameter space beyond the reach of the standard dijet resonance searches. In this follow-up paper, we analyse the challenging monolepton final state arising from the decays of the $N_R$ pair with Deep Learning. We present the high-luminosity LHC discovery reaches for six different GUT embeddings and a benchmark point in the GS setup. We also update our previous estimates in the dilepton channel with Deep Learning. We identify parameter regions that can be probed with the proposed channel but will remain inaccessible to dijet searches at the HL-LHC