Abstract

We review the main applications of machine learning models that are not fully supervised in particle physics, i.e., clustering, anomaly detection, detector simulation, and unfolding. Unsupervised methods are ideal for anomaly detection tasks—machine learning models can be trained on background data to identify deviations if we model the background data precisely. The learning can also be partially unsupervised when we can provide some information about the anomalies at the data level. Generative models are useful in speeding up detector simulations—they can mimic the computationally intensive task without large resources. They can also efficiently map detector-level data to parton-level data (i.e., data unfolding). In this review, we focus on interesting ideas and connections and briefly overview the underlying techniques wherever necessary.

Abstract

We present a hypergraph coloring based approach to pliable index coding (PICOD). We represent the given PICOD problem using a hypergraph consisting of m messages as vertices and the request-sets of the n clients as hyperedges. A conflict- free coloring of a hypergraph is an assignment of colors to its vertices so that each hyperedge contains a uniquely colored vertex. We show that various parameters arising out of conflict- free colorings (and some new variants) of the PICOD hypergraph result in new upper bounds for the optimal PICOD length. Using these new upper bounds, we show the existence of single-request PICOD schemes with length O(log2 Γ), where Γ is the maximum number of hyperedges overlapping with any hyperedge. For the t-request PICOD scenario, we show the existence of PICOD schemes of length max(O(log Γ log m), O(t log m)), under some mild conditions on the graph parameters. These results improve upon earlier work in general. We also show that our achievable lengths in the t-request case are asymptotically optimal, up to a multiplicative factor of log t. Our existence results are accompanied by randomized constructive algorithms, which have complexity polynomial in the parameters of the PICOD problem, in expectation or with high probability. Index Terms—Index Coding, Pliabl

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Abstract

Monitoring water flow helps to identify leaks and wastage, leading to better management of water resources and conservation of this precious resource. To address this challenge, there is a need for an efficient and sustainable water management system. This paper presents an Internet of Things (IoT) based solution that involves retrofitting existing analog water meters using readily available off-the-shelf electronic components. Real-time data collection and analysis are performed through edge computation, which locally processes water meter images captured by the camera and extracts water meter readings. These readings are transmitted to the cloud for storage and further analysis. Various strategies have been implemented to optimize supply-current usage, preserving charge-discharge cycles of solar-powered batteries even in adverse environmental conditions. To streamline the firmware update process for multiple connected devices, a broadcasting technique is employed, offering the benefits of reduced manual labor and time savings. To assess the reliability and performance of developed solution, field deployment is conducted over several months, enabling the characterization of water usage patterns across different locations. Integrating energy harvesting capabilities into system reduces maintenance costs and promotes eco-friendly energy practices. Overall, this solution offers an effective and comprehensive approach towards achieving efficient and sustainable water management.

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Abstract

We study a family of subcodes of the $m$-dimensional product code $mathscr{C}^{otimes m}$ (`subproduct codes') that have a recursive Plotkin-like structure, and which include Reed-Muller (RM) codes and Dual Berman codes as special cases. We denote the codes in this family as $mathscr{C}^{otimes [r,m]}$, where mbox{$0 leq r leq m$} is the `order' of the code. These codes allow a `projection' operation that can be exploited in iterative decoding, viz., the sum of two carefully chosen subvectors of any codeword in $mathscr{C}^{otimes [r,m]}$ belongs to $mathscr{C}^{otimes [r-1,m-1]}$. Recursive subproduct codes provide a wide range of rates and block lengths compared to RM codes while possessing several of their structural properties, such as the Plotkin-like design, the projection property, and fast ML decoding of first-order codes. Our simulation results for first-order and second-order codes, that are based on a belief propagation decoder and a local graph search algorithm, show instances of subproduct codes that perform either better than or within $0.5$~dB of comparable RM codes and CRC-aided Polar codes.

Abstract

The concept of sum labelling was introduced in 1990 by Harary. A graph is a sum graph if its vertices can be labelled by distinct positive integers in such a way that two vertices are connected by an edge if and only if the sum of their labels is the label of another vertex in the graph. It is easy to see that every sum graph has at least one isolated vertex, and every graph can be made a sum graph by adding at most n2 isolated vertices to it. The minimum number of isolated vertices that need to be added to a graph to make it a sum graph is called the sum number of the graph. The sum number of several prominent graph classes (e.g., cycles, trees, complete graphs) is already well known. We examine the effect of taking the disjoint union of graphs on the sum number. In particular, we provide a complete characterisation of the sum number of graphs of maximum degree two, since every such graph is the disjoint union of paths and cycles

Abstract

In this paper, we determine the computational complexity of recognizing two graph classes, grounded 𝖫-graphs and stabbable grid intersection graphs. An 𝖫-shape is made by joining the bottom end-point of a vertical (|) segment to the left end-point of a horizontal (−) segment. The top end- point of the vertical segment is known as the anchor of the 𝖫-shape. Grounded 𝖫-graphs are the intersection graphs of 𝖫-shapes such that all the 𝖫-shapes’ anchors lie on the same horizontal line. We show that recognizing grounded 𝖫-graphs is 𝖭𝖯-complete. This answers an open question asked by Jelínek & Töpfer (Electron. J. Comb., 2019). Grid intersection graphs are the intersection graphs of axis-parallel line segments in which two vertical (similarly, two horizontal) segments cannot intersect. We say that a (not necessarily axis-parallel) straight line 𝓁 stabs a segment 𝑠, if 𝑠 intersects 𝓁. A graph 𝐺 is a stabbable grid intersection graph (S TAB GIG) if there is a grid intersection representation of 𝐺 in which the same line stabs all its segments. We show that recognizing S TAB GIG graphs is 𝖭𝖯-complete, even on a restricted class of graphs. This answers an open question asked by Chaplick et al. (Order, 2018).

Abstract

In this article, an incoherent beam combination of higher-order Gaussian beams through atmospheric turbulence is studied. An analytical expression of the combined intensity and spot size of higher-order Gaussian beams such as Hermite Gaussian (HG), Laguerre Gaussian (LG), and Bessel Gaussian (BG) are derived. The performance of these higher-order Gaussian beams is analyzed in various modes including the effect of beam wander, jitter, bore-sight error, Strehl ratio, and Visibility. A series of analytical simulations shows the intensity variation of 19 higher-order combined beams. Spot size, peak, and average intensity comparisons are made between various modes of higher-order Gaussian beam combinations. It is seen that the spot size of the combined beam increases rapidly in a higher mode of HG and LG beam. We evaluate the efficiency of combining beams at different distances, noting that it increases with higher mode orders and reaches its maximum with the 𝐻𝐺22 mode. Additionally, we explore the performance of higher-order Gaussian beam combinations under varying ground turbulence conditions. We observe that higher modes such as 𝐻𝐺22 and 𝐿𝐺22 are more susceptible to strong turbulence compared to lower modes.

Abstract

In this letter, we have modeled and analyzed the impact of alignment errors in fiber lasers and collimating lens arrays on incoherent beam combination systems. The combined intensity expression is calculated considering different errors, and efficiency comparisons are made between 7 and 61 laser beam arrays. The results show that the misalignment error also increases with an increase in the number of beam arrays, leading to a decrease in the combination efficiency. We observed that to achieve more than 80% combination efficiency, maximum error tolerances should be 3 µm, 0.3 mm, and 4 mrad for displacement, focal and tilt errors, respectively. The findings presented in this letter have practical relevance for enhancing the design, operation, and optimization of beam combination systems.