Abstract--In this paper, we analyze the performance of the estimation of Laplacian matrices under general observatio n models. Laplacian matrix estimation involves structural c on-straints, including symmetry and null-space properties, a long with matrix sparsity. By exploiting a linear reparametriza tion that enforces the structural constraints, we derive closed -form matrix expressions for the Cram er-Rao Bound (CRB) specifically tailored to Laplacian matrix estimation. We further extend the derivation to the sparsity-constrained case, introduc ing two oracle CRBs that incorporate prior information of the suppo rt set, i.e. the locations of the nonzero entries in the Laplaci an matrix. We examine the properties and order relations betwe en the bounds, and provide the associated Slepian-Bangs formu la for the Gaussian case. We demonstrate the use of the new CRBs in three representative applications: (i) topology identi fication in power systems, (ii) graph filter identification in diffuse d models, and (iii) precision matrix estimation in Gaussian M arkov random fields under Laplacian constraints. The CRBs are eval - uated and compared with the mean-squared-errors (MSEs) of the constrained maximum likelihood estimator (CMLE), whic h integrates both equality and inequality constraints along with sparsity constraints, and of the oracle CMLE, which knows the locations of the nonzero entries of the Laplacian matrix . We perform this analysis for the applications of power syste m topology identification and graphical LASSO, and demonstra te that the MSEs of the estimators converge to the CRB and oracle CRB, given a sufficient number of measurements. Graph-structured data and signals arise in numerous applications, including power systems, communications, finance, social networks, and biological networks, for analysis and inference of networks [ 2 ], [ 3 ]. In this context, the Laplacian matrix, which captures node connectivity and edge weights, serves as a fundamental tool for clustering [ 4 ], modeling graph diffusion processes [ 5 ], [ 6 ], topology inference [ 6 ]-[ 12 ], anomaly detection [ 13 ], graph-based filtering [ 14 ]-[ 18 ], and analyzing smoothness on graphs [ 19 ]. M. Halihal and T. Routtenberg are with the School of Electric al and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel, e-mail: moradha@post.bgu.ac.il, tirzar@b gu.ac.il.

This paper demonstrates that pre-trained language models (PLMs) are strong foundation models for on-device meteorological variables modeling.

At least five people have been killed in Israeli attacks on several towns in southern Lebanon, the country's Health Ministry has said, amid a fragile ceasefire between Israel and Hezbollah. "An Israeli enemy drone strike on the town of Ainata killed one person and wounded another," the ministry said. An "Israeli strike on the town of Bint Jbeil killed three people," while a third "on Beit Lif killed one person", it added. There was no immediate comment from the Israeli military on the attacks. Israel's army escalated its attacks on Lebanon in late September after more than 11 months of cross-border exchanges of fire with the Lebanese armed group Hezbollah, which began firing rockets towards Israel after the Palestinian group Hamas's attack on southern Israel on October 7, 2023.

This paper demonstrates that pre-trained language models (PLMs) are strong foundation models for on-device meteorological variables modeling. We present LM-Weather, a generic approach to taming PLMs, that have learned massive sequential knowledge from the universe of natural language databases, to acquire an immediate capability to obtain highly customized models for heterogeneous meteorological data on devices while keeping high efficiency. Concretely, we introduce a lightweight personalized adapter into PLMs and endows it with weather pattern awareness. During communication between clients and the server, low-rank-based transmission is performed to effectively fuse the global knowledge among devices while maintaining high communication efficiency and ensuring privacy. Experiments on real-wold dataset show that LM-Weather outperforms the state-of-the-art results by a large margin across various tasks (e.g., forecasting and imputation at different scales). We provide extensive and in-depth analyses experiments, which verify that LM-Weather can (1) indeed leverage sequential knowledge from natural language to accurately handle meteorological sequence, (2) allows each devices obtain highly customized models under significant heterogeneity, and (3) generalize under data-limited and out-of-distribution (OOD) scenarios.

Yemen's Houthi rebels say they have targeted what they claim to be an Israeli cargo ship, the MSC Silver, in the Gulf of Aden near the entrance to the Red Sea with a number of missiles. Houthi military spokesperson Yahya Sarea did not elaborate, but in a statement on Tuesday said the group had also used drones to target a number of United States warships in the Red Sea and Arabian Sea as well as sites in the southern Israeli resort town of Eilat. However, the British maritime security firm Ambrey said the container ship targeted by the Houthis on Tuesday was Liberia-flagged and headed for Somalia. The operator was publicly listed as [in] cooperation with ZIM and regularly called [at] Israeli ports," the Ambrey advisory note said. Zim Integrated Shipping Services Ltd, commonly known as ZIM, is a publicly held Israeli international cargo shipping company based in Israel.

A UK vessel shot down a Houthi drone in the Red Sea, the United Kingdom's Ministry of Defence has said, as tensions in the Middle East soar amid the ongoing war in Gaza. "Yesterday HMS Diamond successfully repelled a drone attack from the Iranian-backed Houthis in the Red Sea," read a statement from the ministry published on Sunday on X. "Diamond destroyed a drone targeting her, with no injuries or damage sustained to Diamond or her crew," it added. There was no immediate comment from the Houthis. The Yemen-based group previously pledged to target Israel-linked vessels in the region as part of an effort to pressure the country's government to end its bombardment of Gaza and allow more humanitarian aid supplies into the coastal Palestinian enclave. Gaza has been under heavy bombardment by Israeli forces since October 7, when Hamas fighters stormed communities in southern Israel, killing at least 1,139 people and taking about 240 others captive, according to Israeli officials.

Aiming at selecting a small subset of nodes with maximum influence on networks, the Influence Maximization (IM) problem has been extensively studied. Since it is #P-hard to compute the influence spread given a seed set, the state-of-the-art methods, including heuristic and approximation algorithms, faced with great difficulties such as theoretical guarantee, time efficiency, generalization, etc. This makes it unable to adapt to large-scale networks and more complex applications. On the other side, with the latest achievements of Deep Reinforcement Learning (DRL) in artificial intelligence and other fields, lots of works have been focused on exploiting DRL to solve combinatorial optimization problems. Inspired by this, we propose a novel end-to-end DRL framework, ToupleGDD, to address the IM problem in this paper, which incorporates three coupled graph neural networks for network embedding and double deep Q-networks for parameters learning. Previous efforts to solve IM problem with DRL trained their models on subgraphs of the whole network, and then tested on the whole graph, which makes the performance of their models unstable among different networks. However, our model is trained on several small randomly generated graphs with a small budget, and tested on completely different networks under various large budgets, which can obtain results very close to IMM and better results than OPIM-C on several datasets, and shows strong generalization ability. Finally, we conduct a large number of experiments on synthetic and realistic datasets, and experimental results prove the effectiveness and superiority of our model.

The programme, developed by a company called SightBit, uses information collected from surveillance cameras to determine who is in the water -- an adult or child, for example -- if they are moving or limp, and the current's movement at that location. If a threat is determined, the programme sends an alert to a tablet held by the user -- a lifeguard, in this case -- with urgent instructions to act. SightBit's chief executive Netanel Eliav told AFP that he developed the technology after identifying a shortfall in how closed-circuit footage was being applied to boost safety in the water. The programme has been in use for more than a year in Ashdod, a city on Israel's Mediterranean coast that chose to deploy SightBit technology in an area at a distance from the nearest lifeguard. "We chose to locate the technology in areas away from the lifeguard towers, so the additional'eyes' there help the lifeguards very much," said Arie Turjeman, director of Ashdod's coast division.

Israel is holding its largest-ever air force exercise this week with the participation of several countries including the United Arab Emirates, with whom it normalised ties last year. Amir Lazar, chief of Israeli air force operations, told reporters at the southern Ovda airbase the drills "don't focus on Iran", but army officials have said Iran remains Israel's top strategic threat and at the centre of much of its military planning. Israel has held the so-called "Blue Flag" exercises every two years since 2013 in the Negev desert to synchronise different types of aircraft, piloted by different countries to counter armed drones and other threats. With more than 70 fighter jets and some 1,500 personnel participating, this year's drills are the largest-ever held in Israel, Lazar said. Among the nations taking part are France, the United States and Germany, as well as the United Kingdom, whose aircraft flew over Israeli territory for the first time since the Jewish state's creation in 1948.

Israeli researchers have found an apparently straightforward method to fool facial recognition software -- by applying conventional makeup to specific areas of the face according to a pattern determined by an artificial intelligence program. The study, conducted at Beersheba's Ben-Gurion University, found that when applying the computer-generated makeup pattern to test subjects, the systems were bypassed at a near 100% success rate. Twenty volunteers (10 men and 10 women) either had makeup applied to the most identifiable areas of the face according to the heatmap generated by the software, or random makeup applied, and finally no makeup at all. The test subjects then faced a real-world environment by walking down a hallway equipped with two cameras and a variety of lighting conditions. With the software-designed makeup pattern, subjects were correctly identified just 1.22% of the time, compared to 33.73% with random makeup and 47.57% without any makeup applied.