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The paper focuses on studying strong geodetic sets and numbers in the context of corona-type products of graphs. Our primary focus is on three variations of the corona products: the generalized corona, generalized edge corona, and generalized neighborhood corona products. A strong geodetic set is a minimal subset of vertices that covers all vertices in the graph through unique geodesics connecting pairs from this subset. We obtain the strong geodetic set and number of the corona-type product graph using the strong 2-geodetic set and strong 2-geodetic number of the initial arbitrary graphs. We analyze how the structural properties of these corona products affect the strong geodetic number, providing new insights into geodetic coverage and the relationships between graph compositions. This work contributes to expanding research on the geodetic parameters of product graphs.

We investigate granular flows over an inclined rigid base, which is vibrated externally in a direction normal to itself, through discrete element simulations. We vary the base inclination angle theta, vibration frequency f, and amplitude A to study changes in the granular flow profile and the mass flow rate Q. We find that the flow velocity profiles for the vibrated bases are nonlinear, unlike their fixed base counterparts. Our study reveals that Q may be maintained nearly constant in flows over vibrated bases utilizing appropriate combinations of theta, A, and f. At the same time, by vibrating the base at a fixed inclination, we may increase the mass flow rate by as much as 30 times the value found in flows over a stationary base. Finally, we show that Q depends upon a nondimensional number S obtained by taking the ratio of vibrational and gravitational energies., Comment: 10 Pages, 10 figures. Accepted for publication in Physical Review Fluids. Abstract link: https://journals.aps.org/prfluids/accepted/82079S10F3413d0c620b91674f996f03498146df0

The spectrum of Laplacian and signless Laplacian matrix for a graph product is obtained, where both underlying graphs are regular. As an application of this, we have been able to generate the Kirchhoff Index and Wiener Index and determine the number of spanning trees. Additionally, we derived the conditions necessary for obtaining a Laplacian and signless Laplacian integral product graph.

Incorporating prior knowledge or specifications of input-output relationships into machine learning models has gained significant attention, as it enhances generalization from limited data and leads to conforming outputs. However, most existing approaches use soft constraints by penalizing violations through regularization, which offers no guarantee of constraint satisfaction -- an essential requirement in safety-critical applications. On the other hand, imposing hard constraints on neural networks may hinder their representational power, adversely affecting performance. To address this, we propose HardNet, a practical framework for constructing neural networks that inherently satisfy hard constraints without sacrificing model capacity. Specifically, we encode affine and convex hard constraints, dependent on both inputs and outputs, by appending a differentiable projection layer to the network's output. This architecture allows unconstrained optimization of the network parameters using standard algorithms while ensuring constraint satisfaction by construction. Furthermore, we show that HardNet retains the universal approximation capabilities of neural networks. We demonstrate the versatility and effectiveness of HardNet across various applications: fitting functions under constraints, learning optimization solvers, optimizing control policies in safety-critical systems, and learning safe decision logic for aircraft systems.

Accurate body weight estimation is critical in emergency medicine for proper dosing of weight-based medications, yet direct measurement is often impractical in urgent situations. This paper presents a non-invasive method for estimating body weight by calculating total body volume and height using 3D imaging technology. A RealSense D415 camera is employed to capture high-resolution depth maps of the patient, from which 3D models are generated. The Convex Hull Algorithm is then applied to calculate the total body volume, with enhanced accuracy achieved by segmenting the point cloud data into multiple sections and summing their individual volumes. The height is derived from the 3D model by identifying the distance between key points on the body. This combined approach provides an accurate estimate of body weight, improving the reliability of medical interventions where precise weight data is unavailable. The proposed method demonstrates significant potential to enhance patient safety and treatment outcomes in emergency settings., Comment: 6 pages

Craters form as the lander's exhaust interacts with the planetary surfaces. Understanding this phenomenon is imperative to ensure safe landings. We investigate crater morphology, where a turbulent air jet impinges on the granular surfaces. To reveal the fundamental aspect of this phenomenon, systematic experiments are performed with various air jet velocities, nozzle positions, and grain properties. The resultant crater morphology is characterized by an aspect ratio. We find a universal scaling law in which the aspect ratio is scaled by the dimensionless variable consisting of air velocity at the nozzle, speed of sound in air, nozzle diameter, nozzle tip distance from the surface, grain diameter, the density of grains, and density of air. The obtained scaling reveals the crossover of the length scales governing crater aspect ratio, providing a useful guideline for ensuring safe landings. Moreover, we report a novel drop shaped subsurface cratering phenomenon., Comment: 18 pages, 12 figures

This paper introduces the concept of the closed neighborhood corona product of the graph. We explore the mathematical features of this product graph, specifically in terms of its spectral characteristics. We have calculated the characteristic polynomials of the adjacency, Laplacian, and signless Laplacian matrices. Moreover, we investigate the conditions under which two graphs are cospectral regarding this product. A significant portion of our study is dedicated to computing the Kirchhoff index, the number of spanning trees and the sequence of non-cospectral equienergetic product graphs. We also outline specific criteria that determine when the product graph is integral.

Optomechanical crystals (OMCs) enable coherent interactions between optical photons and microwave acoustic phonons, and represent a platform for implementing quantum transduction between microwave and optical signals. Optical absorption-induced thermal noise at cryogenic (millikelvin) temperatures is one of the primary limitations of performance for OMC-based quantum transducers. Here, we address this challenge with a two-dimensional silicon OMC resonator that is side-coupled to a mechanically detached optical waveguide, realizing a six-fold reduction in the heating rate of the acoustic resonator compared to prior state-of-the-art, while operating in a regime of high optomechanical-backaction and millikelvin base temperature. This reduced heating translates into a demonstrated phonon-to-photon conversion efficiency of 93.1 $\pm$ 0.8% at an added noise of 0.25 $\pm$ 0.01 quanta, representing a significant advance toward quantum-limited microwave-optical frequency conversion and optically-controlled quantum acoustic memories.

The field of remote-sensing image classification has seen immense progress with the rise of convolutional neural networks, and more recently, through vision transformers. These models, with their self-attention mechanism, can effectively capture global relationships and long-range dependencies between the image patches, in contrast with traditional convolutional models. This paper introduces StrideNET, a dual-branch transformer-based model developed for terrain recognition and surface roughness extraction. The terrain recognition branch employs the Swin Transformer to classify varied terrains by leveraging its capability to capture both local and global features. Complementing this, the roughness extraction branch utilizes a statistical texture-feature analysis technique to dynamically extract important land surface properties such as roughness and slipperiness. The model was trained on a custom dataset consisting of four terrain classes - grassy, marshy, sandy, and rocky, and it outperforms benchmark CNN and transformer based models, by achieving an average test accuracy of over 99 % across all classes. The applications of this work extend to different domains such as environmental monitoring, land use and cover classification, disaster response and precision agriculture., Comment: 6 pages, 5 figures, 3rd IEEE International Conference on Computer Vision and Machine Intelligence (IEEE CVMI)

A signed graph product is defined for a new product, and initially the unsigned graph product's Laplacian spectrum and signless Laplacian spectrum are found. Next, for the signed graph product, the adjacency spectrum, Laplacian spectrum, and signless Laplacian spectrum are found. In the end, we determined the prerequisite for the signed graph product to be integral and we also have generated a sequence of co-spectral signed graphs and a sequence of non-co-spectral equienergetic signed graphs., Comment: arXiv admin note: text overlap with arXiv:2312.12843

For unsigned graphs G and H, the characteristic polynomial of different graph matrices for edge corona, subdivision vertex neighbourhood corona and subdivision edge neighbourhood corona has already been studied using the concept of coronal. However, till date no work regarding the spectrum of these products has been studied for signed graphs. In our work, we have filled this gap and defined these variants of coronae by introducing the concept of reverse orientation (r-orientation). We analyzed the structural properties of these product. Also, the characteristic polynomial of adjacency matrix, Laplacian matrices (signed and signless) and normalized Laplacian matrix of these variants of corona product of regular signed graphs under $r$-orientation is obtained using the concept of signed coronal. These results help us to construct infinitely many families of pairs of cospectral signed graphs.

This paper introduces the concept of $\mu$-signed and duplication signed graphs and shows that both are always structurally balanced. Using the duplication signed graph, we define the corona product of the duplication signed graph (Duplication add vertex corona product and duplication vertex corona product) and explore their structural properties. Additionally, we provide the adjacency spectrum of both the products for any $\Gamma_1$ and $\Gamma_2$, and the Laplacian and signless Laplacian spectrum for regular $\Gamma_1$ and arbitrary $\Gamma_2$, in terms of the corresponding spectrum of $\Gamma_1$ and $\Gamma_2$. Finally, we discuss its application in generating integral and equienergetic signed graphs., Comment: arXiv admin note: text overlap with arXiv:2310.12814

Optomechanical crystals are a promising device platform for quantum transduction and sensing. Precise targeting of the optical and acoustic resonance frequencies of these devices is crucial for future advances on these fronts. However, fabrication disorder in these wavelength-scale nanoscale devices typically leads to inhomogeneous resonance frequencies. Here we achieve in-situ, selective frequency tuning of optical and acoustic resonances in silicon optomechanical crystals via electric field-induced nano-oxidation using an atomic-force microscope. Our method can achieve a tuning range >2 nm (0.13%) for the optical resonance wavelength in the telecom C-band, and >60 MHz (1.2%) for the acoustic resonance frequency at 5 GHz. The tuning resolution of 1.1 nm for the optical wavelength, and $150$ kHz for the acoustic frequency allows us to spectrally align multiple optomechanical crystal resonators using optimal oxidation patterns determined via an inverse design protocol. Our results establish a method for precise post-fabrication tuning of optomechancical crystals. This technique can enable coupled optomechanical resonator arrays, scalable resonant optomechanical circuits, and frequency matching of microwave-optical quantum transducers.

Given two signed graphs $\Gamma_1$ with nodes $\{u_1,u_2,\cdots,u_n\}$ and $\Gamma_2$, the neighbourhood corona, $\Gamma_1*\Gamma_2$ is the signed graph obtained by taking one copy of $\Gamma_1$ and $n_1$ copies of $\Gamma_2$, and joining every neighbour of the $i^{th}$ node with each nodes of the $i^{th}$ copy of $\Gamma_2$ by a new signed edge. In this paper we will determine the condition for $\Gamma_1*\Gamma_2$ to be balanced. We also determine the adjacency spectrum of $\Gamma_1*\Gamma_2$ for arbitrary $\Gamma_1$ and $\Gamma_2$, and Laplacian and signless Laplacian spectrum of $\Gamma_1*\Gamma_2$ for regular $\Gamma_1$ and arbitrary $\Gamma_2$, in terms of the corresponding spectrum of $\Gamma_1$ and $\Gamma_2$.

In the committee selection problem, the goal is to choose a subset of size $k$ from a set of candidates $C$ that collectively gives the best representation to a set of voters. We consider this problem in Euclidean $d$-space where each voter/candidate is a point and voters' preferences are implicitly represented by Euclidean distances to candidates. We explore fault-tolerance in committee selection and study the following three variants: (1) given a committee and a set of $f$ failing candidates, find their optimal replacement; (2) compute the worst-case replacement score for a given committee under failure of $f$ candidates; and (3) design a committee with the best replacement score under worst-case failures. The score of a committee is determined using the well-known (min-max) Chamberlin-Courant rule: minimize the maximum distance between any voter and its closest candidate in the committee. Our main results include the following: (1) in one dimension, all three problems can be solved in polynomial time; (2) in dimension $d \geq 2$, all three problems are NP-hard; and (3) all three problems admit a constant-factor approximation in any fixed dimension, and the optimal committee problem has an FPT bicriterion approximation., Comment: The paper will appear in the proceedings of ESA 2023

Despite exciting recent results showing vision-language systems' capacity to reason about images using natural language, their capacity for video reasoning remains under-explored. We motivate framing video reasoning as the sequential understanding of a small number of keyframes, thereby leveraging the power and robustness of vision-language while alleviating the computational complexities of processing videos. To evaluate this novel application, we introduce VIP, an inference-time challenge dataset designed to explore models' reasoning capabilities through video chain-of-thought. Inspired by visually descriptive scene plays, we propose two formats for keyframe description: unstructured dense captions and structured scene descriptions that identify the focus, action, mood, objects, and setting (FAMOuS) of the keyframe. To evaluate video reasoning, we propose two tasks: Video Infilling and Video Prediction, which test abilities to generate multiple intermediate keyframes and predict future keyframes, respectively. We benchmark GPT-4, GPT-3, and VICUNA on VIP, demonstrate the performance gap in these complex video reasoning tasks, and encourage future work to prioritize language models for efficient and generalized video reasoning., Comment: Accepted to the 2023 Conference on Empirical Methods in Natural Language Processing (EMNLP 2023)

Recent advances in large language models elicit reasoning in a chain-of-thought that allows models to decompose problems in a human-like fashion. Though this paradigm improves multi-step reasoning ability in language models, it is limited by being unimodal and applied mainly to question-answering tasks. We claim that incorporating visual augmentation into reasoning is essential, especially for complex, imaginative tasks. Consequently, we introduce VCoT, a novel method that leverages chain-of-thought prompting with vision-language grounding to recursively bridge the logical gaps within sequential data. Our method uses visual guidance to generate synthetic multimodal infillings that add consistent and novel information to reduce the logical gaps for downstream tasks that can benefit from temporal reasoning, as well as provide interpretability into models' multi-step reasoning. We apply VCoT to the Visual Storytelling and WikiHow summarization datasets and demonstrate through human evaluation that VCoT offers novel and consistent synthetic data augmentation beating chain-of-thought baselines, which can be used to enhance downstream performance.

Finite volume methods are popular tools for solving time-dependent partial differential equations, especially hyperbolic conservation laws. Over the past 40 years a popular way of enlarging their robustness was the enforcement of global or local entropy inequalities. This work focuses on a different entropy criterion proposed by Dafermos almost 50 years ago, stating that the weak solution should be selected that dissipates a selected entropy with the highest possible speed. We show that this entropy rate criterion can be used in a numerical setting if it is combined with the theory of optimal recovery. To date, this criterion has only seen limited use in Finite-Volume schemes and to the authors knowledge this work is the first in which this criterion is applied to a Finite-Volume scheme whose accuracy is based on reconstruction from mean values. This leads to a new family of schemes based on reconstruction providing an alternative to the popular ENO and WENO schemes.