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A tensor-based formula for solving the linear system involving Kronecker sum is proposed. It is shown that the linear system involving Kronecker sum of matrices is directly related to the matrix and tensor forms of Sylvester equation. The new tensor-based formula indicates that a Sylvester tensor equation has a unique solution if the sum of spectra of the matrices does not contain zero. As an application, we solve the discretized Poisson equation on a rectangular domain and Dirichlet boundary conditions. In 2d, we show that both the new formula and the fast Poisson solver based on diagonalization have the same cost $\mathcal {O}(n^{3/2})$. In 3d, the new formula has the cost $\mathcal {O}(n^{4/3})$ while cyclic reduction and successive over-relaxation methods have a complexity of $\mathcal {O}(n^{3/2})$.

Accurate modeling is essential in integer-valued real phenomena, including the distribution of entire data, zero-inflated (ZI) data, and discrete exceedances. The Poisson and Negative Binomial distributions, along with their ZI variants, are considered suitable for modeling the entire data distribution, but they fail to capture the heavy tail behavior effectively alongside the bulk of the distribution. In contrast, the discrete generalized Pareto distribution (DGPD) is preferred for high threshold exceedances, but it becomes less effective for low threshold exceedances. However, in some applications, the selection of a suitable high threshold is challenging, and the asymptotic conditions required for using DGPD are not always met. To address these limitations, extended versions of DGPD are proposed. These extensions are designed to model one of three scenarios: first, the entire distribution of the data, including both bulk and tail and bypassing the threshold selection step; second, the entire distribution along with ZI; and third, the tail of the distribution for low threshold exceedances. The proposed extensions offer improved estimates across all three scenarios compared to existing models, providing more accurate and reliable results in simulation studies and real data applications., Comment: 17 pages, Figures 8, tables 3

Personalized Federated Learning (pFL) holds immense promise for tailoring machine learning models to individual users while preserving data privacy. However, achieving optimal performance in pFL often requires a careful balancing act between memory overhead costs and model accuracy. This paper delves into the trade-offs inherent in pFL, offering valuable insights for selecting the right algorithms for diverse real-world scenarios. We empirically evaluate ten prominent pFL techniques across various datasets and data splits, uncovering significant differences in their performance. Our study reveals interesting insights into how pFL methods that utilize personalized (local) aggregation exhibit the fastest convergence due to their efficiency in communication and computation. Conversely, fine-tuning methods face limitations in handling data heterogeneity and potential adversarial attacks while multi-objective learning methods achieve higher accuracy at the cost of additional training and resource consumption. Our study emphasizes the critical role of communication efficiency in scaling pFL, demonstrating how it can significantly affect resource usage in real-world deployments.

In recent years, financial analysts have been trying to develop models to predict the movement of a stock price index. The task becomes challenging in vague economic, social, and political situations like in Pakistan. In this study, we employed efficient models of machine learning such as long short-term memory (LSTM) and quantum long short-term memory (QLSTM) to predict the Karachi Stock Exchange (KSE) 100 index by taking monthly data of twenty-six economic, social, political, and administrative indicators from February 2004 to December 2020. The comparative results of LSTM and QLSTM predicted values of the KSE 100 index with the actual values suggested QLSTM a potential technique to predict stock market trends.

This study leverages convolutional neural networks to enhance the temporal resolution of 3D angiography in intracranial aneurysms focusing on the reconstruction of volumetric contrast data from sparse and limited projections. Three patient-specific IA geometries were segmented and converted into stereolithography files to facilitate computational fluid dynamics simulations. These simulations first modeled blood flow under steady conditions with varying inlet velocities: 0.25 m/s, 0.35 m/s, and 0.45 m/s. Subsequently, 3D angiograms were simulated by labeling inlet particles to represent contrast bolus injections over durations of 0.5s, 1.0s, 1.5s, and 2.0s. The angiographic simulations were then used within a simulated cone beam C arm CT system to generate in-silico rotational DSAs, capturing projections every 10 ms over a 220-degree arc at 27 frames per second. From these simulations, both fully sampled (108 projections) and truncated projection datasets were generated the latter using a maximum of 49 projections. High fidelity volumetric images were reconstructed using a Parker weighted Feldkamp Davis Kress algorithm. A modified U Net CNN was subsequently trained on these datasets to reconstruct 3D angiographic volumes from the truncated projections. The network incorporated multiple convolutional layers with ReLU activations and Max pooling, complemented by upsampling and concatenation to preserve spatial detail. Model performance was evaluated using mean squared error (MSE). Evaluating our U net model across the test set yielded a MSE of 0.0001, indicating good agreement with ground truth reconstructions and demonstrating acceptable capabilities in capturing relevant transient angiographic features. This study confirms the feasibility of using CNNs for reconstructing 3D angiographic images from truncated projections.

We study in-depth those rings $R$ for which, there exists a fixed $n\geq 1$, such that $u^n-1$ lies in the subring $\Delta(R)$ of $R$ for every unit $u\in R$. We succeeded to describe for any $n\geq 1$ all reduced $\pi$-regular $(2n-1)$-$\Delta$U rings by showing that they satisfy the equation $x^{2n}=x$ as well as to prove that the property of being exchange and clean are tantamount in the class of $(2n-1)$-$\Delta$U rings. These achievements considerably extend results established by Danchev (Rend. Sem. Mat. Univ. Pol. Torino, 2019) and Ko\c{s}an et al. (Hacettepe J. Math. \& Stat., 2020). Some other closely related results of this branch are also established., Comment: 19 pages

Numerical wave functions (WFs), root mean square (RMS) radii, $E1$ and $M1$ radiative transitions, and branching ratios of $S, P, D$ and $F$ states of toponium mesons ($t\overline{t}$) are calculated using a non-relativistic quark potential model (NRQPM). Shooting method is used to solve the radial Schrodinger equation to find the radial wave functions which are used in the calculation of properties of mesons. Calculated masses are compared with the theoretical available data., Comment: 15 pages, 3 figures, 13 tables

Optical diffraction tomography (ODT) enables non-invasive information-rich 3D refractive index (RI) reconstruction of unimpaired transparent biological and technical samples, crucial in biomedical research, optical metrology, materials sciences, and other fields. ODT bypasses the inherent limitations of 2D integrated quantitative phase imaging methods. To increase the signal-to-noise ratio easy-to-implement common-path shearing interferometry setups are successfully combined with low spatiotemporal coherence of illumination. The need for self-interference generated holograms, with small shear values, critically impedes the analysis of dense and thick samples, e.g., cell cultures, tissue sections, and embryos/organoids. Phase gradient imaging techniques, deployed as a popular solution in the small shear regime, up to now were constrained to 2D integrated quasi-quantitative phase imaging and z-scanning for depth resolution. To fill this significant scientific gap, we propose a novel gradient optical diffraction tomography (GODT) method. The GODT uses coherence-tailored illumination-scanning sequence of phase gradient measurements to tomographically reconstruct, for the first time to the best of our knowledge, a derivative of the 3D RI distribution (in the shear direction) with clearly visible 3D sample structure and high sensitivity to its spatial variations. We present a mathematically rigorous theory based on the first-order Rytov approximation behind the new method, validate it using simulations deploying numerical Shepp-Logan target and corroborate experimentally via successful tomographic imaging of the calibrated nano-printed cell phantom and efficient examination of neural cells. This novel imaging modality opens new possibilities in biomedical quantitative phase imaging, advancing the field and putting forward a first of a kind contrast domain: 3D RI gradient., Comment: no comments

Classical simulations of quantum circuits are essential for verifying and benchmarking quantum algorithms, particularly for large circuits, where computational demands increase exponentially with the number of qubits. Among available methods, the classical simulation of quantum circuits inspired by density functional theory -- the so-called QC-DFT method, shows promise for large circuit simulations as it approximates the quantum circuits using single-qubit reduced density matrices to model multi-qubit systems. However, the QC-DFT method performs very poorly when dealing with multi-qubit gates. In this work, we introduce a novel CNOT "functional" that leverages neural networks to generate unitary transformations, effectively mitigating the simulation errors observed in the original QC-DFT method. For random circuit simulations, our modified QC-DFT enables efficient computation of single-qubit marginal measurement probabilities, or single-qubit probability (SQPs), and achieves lower SQP errors and higher fidelities than the original QC-DFT method. Despite limitations in capturing full entanglement and joint probability distributions, we find potential applications of SQPs in simulating Shor's and Grover's algorithms for specific solution classes. These findings advance the capabilities of classical simulations for some quantum problems and provide insights into managing entanglement and gate errors in practical quantum computing., Comment: 6 pages, 2 figures, and supplemental materials

The rapid advancement of Large Language Models (LLMs) and their potential integration into autonomous driving systems necessitates understanding their moral decision-making capabilities. While our previous study examined four prominent LLMs using the Moral Machine experimental framework, the dynamic landscape of LLM development demands a more comprehensive analysis. Here, we evaluate moral judgments across 51 different LLMs, including multiple versions of proprietary models (GPT, Claude, Gemini) and open-source alternatives (Llama, Gemma), to assess their alignment with human moral preferences in autonomous driving scenarios. Using a conjoint analysis framework, we evaluated how closely LLM responses aligned with human preferences in ethical dilemmas and examined the effects of model size, updates, and architecture. Results showed that proprietary models and open-source models exceeding 10 billion parameters demonstrated relatively close alignment with human judgments, with a significant negative correlation between model size and distance from human judgments in open-source models. However, model updates did not consistently improve alignment with human preferences, and many LLMs showed excessive emphasis on specific ethical principles. These findings suggest that while increasing model size may naturally lead to more human-like moral judgments, practical implementation in autonomous driving systems requires careful consideration of the trade-off between judgment quality and computational efficiency. Our comprehensive analysis provides crucial insights for the ethical design of autonomous systems and highlights the importance of considering cultural contexts in AI moral decision-making., Comment: 20 pages, 6 figures

Large and Small Language Models (LMs) are typically pretrained using extensive volumes of text, which are sourced from publicly accessible platforms such as Wikipedia, Book Corpus, or through web scraping. These models, due to their exposure to a wide range of language data, exhibit impressive generalization capabilities and can perform a multitude of tasks simultaneously. However, they often fall short when it comes to domain-specific tasks due to their broad training data. This paper introduces SecEncoder, a specialized small language model that is pretrained using security logs. SecEncoder is designed to address the domain-specific limitations of general LMs by focusing on the unique language and patterns found in security logs. Experimental results indicate that SecEncoder outperforms other LMs, such as BERTlarge, DeBERTa-v3-large and OpenAI's Embedding (textembedding-ada-002) models, which are pretrained mainly on natural language, across various tasks. Furthermore, although SecEncoder is primarily pretrained on log data, it outperforms models pretrained on natural language for a range of tasks beyond log analysis, such as incident prioritization and threat intelligence document retrieval. This suggests that domain specific pretraining with logs can significantly enhance the performance of LMs in security. These findings pave the way for future research into security-specific LMs and their potential applications.

This paper introduces TIPS: Threat Actor Informed Prioritization using SecEncoder, a specialized language model for security. TIPS combines the strengths of both encoder and decoder language models to detect and prioritize compromised applications. By integrating threat actor intelligence, TIPS enhances the accuracy and relevance of its detections. Extensive experiments with a real-world benchmark dataset of applications demonstrate TIPS's high efficacy, achieving an F-1 score of 0.90 in identifying malicious applications. Additionally, in real-world scenarios, TIPS significantly reduces the backlog of investigations for security analysts by 87%, thereby streamlining the threat response process and improving overall security posture.

Carrying the insights of conditional probability to the quantum realm is notoriously difficult due to the non-commutative nature of quantum observables. Nevertheless, conditional expectations on von Neumann algebras have played a significant role in the development of quantum information theory, and especially the study of quantum error correction. In quantum gravity, it has been suggested that conditional expectations may be used to implement the holographic map algebraically, with quantum error correction underlying the emergence of spacetime through the generalized entropy formula. However, the requirements for exact error correction are almost certainly too strong for realistic theories of quantum gravity. In this note, we present a relaxed notion of quantum conditional expectation which implements approximate error correction. We introduce a generalization of Connes' spatial theory adapted to completely positive maps, and derive a chain rule allowing for the non-commutative factorization of relative modular operators into a marginal and conditional part, constituting a quantum Bayes' law. This allows for an exact quantification of the information gap occurring in the data processing inequality for arbitrary quantum channels. When applied to algebraic inclusions, this also provides an approach to factorizing the entropy of states into a sum of terms which, in the gravitational context, may be interpreted as a generalized entropy. We illustrate that the emergent area operator is fully non-commutative rather than central, except under the conditions of exact error correction. We provide some comments on how this result may be used to construct a fully algebraic quantum extremal surface prescription and to probe the quantum nature of black holes., Comment: V1: 30 pages, 1 figure

The Purcell effect, a common issue in qubit-resonator systems leading to fidelity loss is studied while its suppression is achieved using a novel qubit readout circuit design. Our approach utilizes a unique coupling architecture in which, the qubit first interacts with a filter resonator before linking to the readout resonator. This configuration enables precise control over the Purcell decay rate and ac Stark factor without impacting on measuring time. The mentioned factor is highly sensitive to the coupling strength between the readout resonator and the filter, meaning that the factor adjustment directly impacts the qubit state detection. A major advantage of this design is that tuning the resonator-filter coupling strength is relatively straightforward, offering flexibility in fine-tuning ac Stark factor.

The following paper presents a reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) system model scenario, where a base station communicates with a user, and a bi-static sensing unit, i.e. the passive radar (PR), senses targets using downlink signals. Given that the RIS aids with communication and sensing tasks, this paper introduces new interfering paths that can overwhelm the PR with unnecessarily high power, namely the path interference (PI), \textit{which is itself a combination of two interfering paths, the direct path interference (DPI) and the reflected path interference (RPI)}. For this, we formulate an optimization framework that allows the system to carry on with its ISAC tasks, through analog space-time beamforming at the sensing unit, in collaboration with RIS phase shift and statistical transmit covariance matrix optimization, while minimizing the PI power. As the proposed optimization problem is non-convex, we tailor a block-cyclic coordinate descent (BCCD) method to decouple the non-convex sub-problem from the convex one. A Riemannian conjugate gradient method is devised to generate the RIS and PR space-time beamforming phase shifts per BCCD iteration, while the convex sub-problem is solved via off-the-shelf solvers. Simulation results demonstrate the effectiveness of the proposed solver when compared with benchmarking ones., Comment: accepted in IEEE Journal on Selected Areas in Communications

Using thermodynamics-gravity conjecture, we present the formal derivation of the modified Friedmann equations inspired by the Barrow entropy, $S\sim A ^{1+\delta/2}$, where $0\leq\delta\leq 1$ is the Barrow exponent and $A$ is the horizon area. We then constrain the exponent $\delta$ by using Big-Bang Nucleosynthesis (BBN) observational data. In order to impose the upper bound on the Barrow exponent $\delta$, we set the observational bound on $\left| \frac{\delta T_f} {T_f }\right|$. We find out that the Barrow parameter $\delta$ should be around $ \delta \simeq 0.01$ in order not to spoil the BBN era. Next we derive the bound on the Barrow exponent $\delta$ in a different approach in which we analyze the effects of Barrow cosmology on the primordial abundances of light elements i.e. Helium $_{}^{4}\textit{He}$, Deuterium $D$ and Lithium $_{}^{7}\textit{Li}$. We observe that the deviation from standard Bekenstein-Hawking expression is small as expected. Additionally we present the relation between cosmic time $t$ and temperature $T$ in the context of modified Barrow cosmology. We confirm that the temperature of the early universe increases as the Barrow exponent $\delta$ (fractal structure of the horizon) increases, too., Comment: 9 pages, 5 figures

This paper reports on the shared tasks organized by the 21st IWSLT Conference. The shared tasks address 7 scientific challenges in spoken language translation: simultaneous and offline translation, automatic subtitling and dubbing, speech-to-speech translation, dialect and low-resource speech translation, and Indic languages. The shared tasks attracted 18 teams whose submissions are documented in 26 system papers. The growing interest towards spoken language translation is also witnessed by the constantly increasing number of shared task organizers and contributors to the overview paper, almost evenly distributed across industry and academia., Comment: IWSLT 2024; 59 pages

This paper reports on the theoretical investigation of charged Higgs bosons and their coupling to fermions within the Two Higgs Doublet Model (THDM). The study focuses on the discovery potential of charged Higgs bosons predicted in Types III and IV at the future Circular Hadron-Hadron Collider (FCC-hh) with a center-of-mass energy of (\sqrt{s} = 100) TeV. By analyzing their decays, couplings to fermions, branching ratios, and production cross-section via (pp \rightarrow tH^-), we investigate the signatures of charged Higgs bosons, including kinematical distributions based on the background processes of (b\bar{b}) quarks., Comment: 24 pages, 16 figures, 1 table

This paper studies the problem of optimal geographic placement of water quality (WQ) sensors in drinking water distribution networks (WDNs), with a specific focus on chlorine transport, decay, and reaction models. Such models are traditionally used as suitable proxies for WQ. The literature on this topic is indeed inveterate, but has a key limitation: it utilizes simplified single-species decay and reaction models that do not capture WQ transients for nonlinear, multi-species interactions. This results in sensor placements that do not account for nonlinear WQ dynamics. Furthermore, and as WQ simulations are parameterized by hydraulic profiles and demand patterns, the placement of sensors are often hydraulics-dependent. This study produces a simple algorithm that addresses the two aforementioned limitations. The presented algorithm is grounded in nonlinear dynamic system sciences and observability theory, and yields sensor placements that are robust to hydraulic changes. Thorough case studies on benchmark water networks are provided. The key findings provide practical recommendations for WDN operators.

We determine parameters of the renormalization group-consistent (RG-consistent) three-flavor color-superconducting Nambu-Jona-Lasinio (NJL) model that are suited to investigate possible compact-star configurations. Our goal is to provide viable quark-matter equation of state (EoS) that can generally be used for hybrid-star constructions. To that end, we mainly focus on quark-star properties in this work. By varying the vector and diquark coupling constants, we analyze their impact on the EoS, speed of sound (SoS), the maximum diquark gap, and the mass-radius relation. In almost all configurations, a stable color-flavor-locked (CFL) phase appears in the core of the maximum-mass configurations, typically spanning several kms in radius. In other cases, the star's two-flavor color-superconducting (2SC) branch of the EoS becomes unstable before reaching the CFL transition density. At neutron-star densities, the SoS squared reaches up to 0.6 and the CFL diquark gap up to 250 MeV. We argue that adding a hadronic EoS at lower densities by performing a Maxwell construction, does not increase the maximum mass substantially, thus we use the 2 solar mass constraint to constrain the NJL model parameters that are suited for the construction of hybrid-star EoS. We construct three examples of the hybrid star model, demonstrating that there is room for different CSC compositions. The hybrid EoS obtained in this way can have no 2SC matter or different ratios of 2SC and CFL quark matter in the core. We show that early hadron-quark transitions are possible that can modify the tidal deformability at 1.4 solar mass. We will provide tabulated EoS of the RG-consistent NJL model for these three parameter sets. We find that these EoS are consistent with the imposed constraints from astrophysics and perturbative QCD. They allow for different hybrid-star scenarios with a hadronic EoS that is soft at low densities., Comment: 21 pages, 12 figures, 2 tables Comments are welcomed

Research in vision and language has made considerable progress thanks to benchmarks such as COCO. COCO captions focused on unambiguous facts in English; ArtEmis introduced subjective emotions and ArtELingo introduced some multilinguality (Chinese and Arabic). However we believe there should be more multilinguality. Hence, we present ArtELingo-28, a vision-language benchmark that spans $\textbf{28}$ languages and encompasses approximately $\textbf{200,000}$ annotations ($\textbf{140}$ annotations per image). Traditionally, vision research focused on unambiguous class labels, whereas ArtELingo-28 emphasizes diversity of opinions over languages and cultures. The challenge is to build machine learning systems that assign emotional captions to images. Baseline results will be presented for three novel conditions: Zero-Shot, Few-Shot and One-vs-All Zero-Shot. We find that cross-lingual transfer is more successful for culturally-related languages. Data and code are provided at www.artelingo.org., Comment: 9 pages, Accepted at EMNLP 24, for more details see www.artelingo.org

This study investigates the use of symbolic computation in Matrix Structural Analysis (MSA) for continuous beams, leveraging the MATLAB Symbolic Math Toolbox. By employing symbolic MSA, analytical expressions for displacements, support reactions, and internal forces are derived, offering deeper insights into structural behavior. This approach facilitates efficient and scalable sensitivity analysis, where partial derivatives of outputs concerning input parameters can be directly computed, enhancing design exploration. The development includes an open-source MATLAB program, hosted on GitHub, enabling symbolic analysis of continuous beams subjected to point and uniform loads. This approach is invaluable for both engineering practice and pedagogy, enriching the understanding of structural mechanics and aiding in education by illustrating clear parameter relationships. The program supports deriving influence lines and identifying maximum response values.

In this work, we statistically analyze the radar cross section (RCS) of different test targets present in an indoor factory (InF) scenario specified by 3rd Generation Partnership Project considering bistatic configuration. The test targets that we consider are drones, humans, quadruped robot and a robotic arm. We consider two drones of different sizes and five human subjects for RCS characterization. For the drones, we measure the RCS when they are are flying over a given point and while they are rotating over the same point. For human subjects, we measure the RCS while standing still, sitting still and walking. For quadruped robot and robotic arm, we consider a continuous random motion emulating different tasks which they are supposed to perfom in typical InF scenario. We employ different distributions, such as Normal, Lognormal, Gamma, Rician, Weibull, Rayleigh and Exponential to fit the measurement data. From the statistical analysis, we gather that Lognormal distribution can fit all the considered targets in the InF scenario., Comment: the results are not correct

This paper presents a novel real-time, delay-aware cooperative perception system designed for intelligent mobility platforms operating in dynamic indoor environments. The system contains a network of multi-modal sensor nodes and a central node that collectively provide perception services to mobility platforms. The proposed Hierarchical Clustering Considering the Scanning Pattern and Ground Contacting Feature based Lidar Camera Fusion improve intra-node perception for crowded environment. The system also features delay-aware global perception to synchronize and aggregate data across nodes. To validate our approach, we introduced the Indoor Pedestrian Tracking dataset, compiled from data captured by two indoor sensor nodes. Our experiments, compared to baselines, demonstrate significant improvements in detection accuracy and robustness against delays. The dataset is available in the repository: https://github.com/NingMingHao/MVSLab-IndoorCooperativePerception

In this paper, we explore a multi-task semantic communication (SemCom) system for distributed sources, extending the existing focus on collaborative single-task execution. We build on the cooperative multi-task processing introduced in [1], which divides the encoder into a common unit (CU) and multiple specific units (SUs). While earlier studies in multi-task SemCom focused on full observation settings, our research explores a more realistic case where only distributed partial observations are available, such as in a production line monitored by multiple sensing nodes. To address this, we propose an SemCom system that supports multi-task processing through cooperation on the transmitter side via split structure and collaboration on the receiver side. We have used an information-theoretic perspective with variational approximations for our end-to-end data-driven approach. Simulation results demonstrate that the proposed cooperative and collaborative multi-task (CCMT) SemCom system significantly improves task execution accuracy, particularly in complex datasets, if the noise introduced from the communication channel is not limiting the task performance too much. Our findings contribute to a more general SemCom framework capable of handling distributed sources and multiple tasks simultaneously, advancing the applicability of SemCom systems in real-world scenarios., Comment: This work has been submitted to the IEEE for possible publication

In this paper, we propose an approach that combines Vision Language Models (VLMs) and Behavior Trees (BTs) to address failures in robotics. Current robotic systems can handle known failures with pre-existing recovery strategies, but they are often ill-equipped to manage unknown failures or anomalies. We introduce VLMs as a monitoring tool to detect and identify failures during task execution. Additionally, VLMs generate missing conditions or skill templates that are then incorporated into the BT, ensuring the system can autonomously address similar failures in future tasks. We validate our approach through simulations in several failure scenarios.

This paper presents ARN-LSTM, a novel multi-stream action recognition model designed to address the challenge of simultaneously capturing spatial motion and temporal dynamics in action sequences. Traditional methods often focus solely on spatial or temporal features, limiting their ability to comprehend complex human activities fully. Our proposed model integrates joint, motion, and temporal information through a multi-stream fusion architecture. Specifically, it comprises a joint stream for extracting skeleton features, a temporal stream for capturing dynamic temporal features, and an ARN-LSTM block that utilizes Time-Distributed Long Short-Term Memory (TD-LSTM) layers followed by an Attention Relation Network (ARN) to model temporal relations. The outputs from these streams are fused in a fully connected layer to provide the final action prediction. Evaluations on the NTU RGB+D 60 and NTU RGB+D 120 datasets demonstrate the effectiveness of our model, achieving effective performance, particularly in group activity recognition.

Chlorine, the most widely used disinfectant, needs to be adequately distributed in water distribution networks (WDNs) to maintain consistent residual levels and ensure water safety. This is performed through control node injections at the treatment plant via booster stations scattered in WDNs. While previous studies have applied various optimization metrics for booster station placement, many have failed to consider the coverage of the station injections and the dynamic nature of WDNs. In particular, variations in hydraulics and demand significantly impact the reachability and efficacy of chlorine injections which then impact optimal placement of booster stations. This study introduces a novel formulation that combines control- and graph-theoretic approaches to solve the booster station placement problem. Unlike traditional methods, our approach emphasizes maximizing the system's ability to control disinfectant levels with minimal energy, taking into account the time-varying hydraulic profiles that lead to different optimal station placements. We propose a simple weighting technique to determine the placements by assessing the structural controllability of each configuration, based on the network's topology and independent of specific parameters like decay rates or pipe roughness. This method ensures effective chlorine coverage across the network. Our approach is validated on different networks, demonstrating its operational effectiveness, scalability, and practicality.

In this paper, we derive a novel Schwarzschild-like black hole (BH) solution describing a static and asymptotically flat BH surrounded by a dark matter (DM) halo with a Dehnen-type density distribution in the surrounding environment. We investigate the properties of the obtained BH by studying the curvature properties and energy conditions in Einstein gravity. Furthermore, we explore the features of a novel Schwarzschild-like BH embedded in a DM halo with Dehnen-type density profile by analyzing the timelike geodesics of particles along with BH observable properties., Comment: 20 pages, 7 captioned figures