Abstract

We identify a family of binary codes whose structure is similar to Reed-Muller (RM) codes and which include RM codes as a strict subclass. The codes in this family are denoted as Cn(r,m) , and their duals are denoted as Bn(r,m) . The length of these codes is nm , where n≥2 , and r is their ‘order’. When n=2 , Cn(r,m) is the RM code of order r and length 2m . The special case of these codes corresponding to n being an odd prime was studied by Berman (1967) and Blackmore and Norton (2001). Following the terminology introduced by Blackmore and Norton, we refer to Bn(r,m) as the Berman code and Cn(r,m) as the dual Berman code. We identify these codes using a recursive Plotkin-like construction, and we show that these codes have a rich automorphism group, they are generated by the minimum weight codewords, and that they can be decoded up to half the minimum distance efficiently. Using a result of Kumar et al. (2016), we show that these codes achieve the capacity of the binary erasure channel (BEC) under bit-MAP decoding. Furthermore, except double transitivity, they satisfy all the code properties used by Reeves and Pfister to show that RM codes achieve the capacity of binary-input memoryless symmetric channels. Finally, when n is odd, we identify a large class of abelian codes that includes Bn(r,m) and Cn(r,m) and which achieves BEC capacity.

Abstract

We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called cache ) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. One of the chief drawbacks of many of these existing constructions is the large subpacketization level, which denotes the number of times a file should be split for the schemes to provide coding gain. In this work, using a new binary matrix model, we present several novel constructions for coded caching based on the various types of combinatorial designs and their q -analogs, which are also called subspace designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement, they provide a rate that is either constant or decreasing, and moreover require competitively small levels of subpacketization, which is an extremely important feature in practical applications of coded caching. We also apply our constructions to the distributed computing framework of MapReduce, which consists of three phases, the Map phase, the Shuffle phase and the Reduce phase. Using our binary matrix framework, we present a new simple generic coded data shuffling scheme. Employing our designs-based constructions in conjunction with this new shuffling scheme, we obtain new coded computing schemes which have low file complexity, with marginally higher communication load compared to the optimal scheme for equivalent parameters. We show that our schemes can neatly extend to the scenario with full and partial stragglers also.

Abstract

This paper presents a novel algorithm for a swarm of unmanned aerial vehicles to search for an unknown source. The proposed method is inspired by the well-known particle swarm optimization (PSO) algorithm and is called accelerationbased particle swarm optimization (APSO) to address the sourceseeking problem with no a priori information. Unlike the conventional particle swarm optimization algorithm, where the particle velocity is updated based on the self-cognition and socialcognition information, here the update is performed on the particle acceleration. A theoretical analysis is provided, showing the stability and convergence of the proposed acceleration-based particle swarm optimization algorithm. Conditions on the parameters of the resulting third-order update equations are obtained using Jury’s stability test. High-fidelity simulations performed in CoppeliaSim, show the improved performance of the proposed acceleration-based particle swarm optimization algorithm for searching an unknown source when compared with the state-ofthe-art particle swarm-based source-seeking algorithms. From the obtained results, it is observed that the proposed method performs better than the existing methods under scenarios like different inter unmanned aerial vehicle communication network topologies, varying numbers of unmanned aerial vehicles in the swarm, different sizes of search regions, restricted source movement, and in the presence of measurements noise.

Abstract

Humans have a natural ability to perform semantic associations with the surrounding objects in the environment. This allows them to create a mental map of the environment, allowing them to navigate on-demand when given linguistic instructions. A natural goal in Vision Language Navigation (VLN) research is to impart autonomous agents with similar capabilities. Recent works take a step towards this goal by creating a semantic spatial map representation of the environment without any labeled data. However, their representations are limited for practical applicability as they do not distinguish between different instances of the same object. In this work, we address this limitation by integrating instance-level information into spatial map representation using a community detection algorithm and utilizing word ontology learned by large language models (LLMs) to perform open-set semantic associations in the mapping representation. The resulting map representation improves the navigation performance by two-fold (233%) on realistic language commands with instance-specific descriptions compared to the baseline. We validate the practicality and effectiveness of our approach through extensive qualitative and quantitative experiments.

Abstract

Positive phase coupling plays an attractive role in inducing in-phase synchrony in an ensemble of phase oscillators. Positive coupling involving both amplitude and phase continues to be attractive, leading to complete synchrony in identical oscillators (limit cycle or chaotic) or phase coherence in oscillators with heterogeneity of parameters. In contrast, purely positive phase velocity coupling may originate a repulsive effect on pendulumlike oscillators (with rotational motion) to bring them into a state of diametrically opposite phases or a splay state. Negative phase velocity coupling is necessary to induce synchrony or coherence in the general sense. The contrarian roles of phase coupling and phase velocity coupling on the synchrony of networks of second-order phase oscillators have been explored here. We explain our proposition using networks of two model systems, a second-order phase oscillator representing the pendulum or the superconducting Josephson junction dynamics, and a voltage-controlled oscillations in neurons model. Numerical as well as semianalytical approaches are used to confirm our result

Abstract

Achieving perfect synchronization in a complex network, specially in the presence of higher-order interactions (HOIs) at a targeted point in the parameter space, is an interesting, yet challenging task. Here we present a theoretical framework to achieve the same under the paradigm of the Sakaguchi-Kuramoto (SK) model. We analytically derive a frequency set to achieve perfect synchrony at some desired point in a complex network of SK oscillators with higher-order interactions. Considering the SK model with HOIs on top of the scale-free, random, and small world networks, we perform extensive numerical simulations to verify the proposed theory. Numerical simulations show that the analytically derived frequency set not only provides stable perfect synchronization in the network at a desired point but also proves to be very effective in achieving a high level of synchronization around it compared to the other choices of frequency sets. The stability and the robustness of the perfect synchronization state of the system are determined using the low-dimensional reduction of the network and by introducing a Gaussian noise around the derived frequency set, respectively.

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.

Abstract

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Abstract

Historical manuscripts often contain dense unstructured text lines. The large diversity in sizes, scripts and appearance makes precise text line segmentation extremely challenging. Existing line segmentation approaches often associate diacritic elements incorrectly to text lines and also address above mentioned challenges inadequately. To tackle these issues, we introduce SeamFormer, a novel approach for high precision text line segmentation in handwritten manuscripts. In the first stage of our approach, a multi-task Transformer deep network outputs coarse line identifiers which we term ‘scribbles’ and the binarized manuscript image. In the second stage, a scribble-conditioned seam generation procedure utilizes outputs from first stage and feature maps derived from manuscript image to generate tight-fitting line segmentation polygons. In the process, we incorporate a novel diacritic feature map which enables improved diacritic and text line associations. Via experiments and evaluations on new and existing challenging palm leaf manuscript datasets, we show that SeamFormer outperforms competing approaches and generates precise text line segmentations.