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Let $G=(V,E)$ be an $n$-vertex connected graph of maximum degree $\Delta$. Given access to $V$ and an oracle that given two vertices $u,v\in V$, returns the shortest path distance between $u$ and $v$, how many queries are needed to reconstruct $E$? We give a simple deterministic algorithm to reconstruct trees using $\Delta n\log_\Delta n+(\Delta+2)n$ distance queries and show that even randomised algorithms need to use at least $\frac1{100} \Delta n\log_\Delta n$ queries in expectation. The best previous lower bound was an information-theoretic lower bound of $\Omega(n\log n/\log \log n)$. Our lower bound also extends to related query models including distance queries for phylogenetic trees, membership queries for learning partitions and path queries in directed trees. We extend our deterministic algorithm to reconstruct graphs without induced cycles of length at least $k$ using $O_{\Delta,k}(n\log n)$ queries, which includes various graph classes of interest such as chordal graphs, permutation graphs and AT-free graphs. Since the previously best known randomised algorithm for chordal graphs uses $O_{\Delta}(n\log^2 n)$ queries in expectation, we both get rid off the randomness and get the optimal dependency in $n$ for chordal graphs and various other graph classes. Finally, we build on an algorithm of Kannan, Mathieu, and Zhou [ICALP, 2015] to give a randomised algorithm for reconstructing graphs of treelength $k$ using $O_{\Delta,k}(n\log^2n)$ queries in expectation.

The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game of infinitely many rational players. In addition to traditional initial and terminal conditions, one extra terminal condition is assumed to be known. Carleman estimates and a Carleman Weight Function play the key role. Numerical experiments demonstrate a good performance for complicated functions. Various versions of the convexification have been actively used by this research team for a number of years to numerically solve coefficient inverse problems.

The proliferation of resource-constrained devices has become prevalent across various digital applications, including smart homes, healthcare, the Internet of Vehicles, and the Internet of Flying Things, among others. However, the integration of these devices brings many security issues. To address these concerns, Blockchain technology has been widely adopted due to its robust security characteristics, including immutability, cryptography, and distributed consensus. However, implementing the blockchain within these networks is highly challenging due to the limited resources of the employed devices and the resource-intensive requirements of the blockchain. To overcome these challenges, a multitude of researchers have proposed lightweight blockchain solutions specifically designed for resource-constrained networks. In this paper, we present a taxonomy of lightweight blockchain solutions proposed in the literature. More precisely, we identify five areas within the "lightweight" concept, namely, blockchain architecture, device authentication, cryptography model, consensus algorithm, and storage method. We discuss the various methods employed in each "lightweight" category, highlighting existing gaps and identifying areas for improvement. Our review highlights the missing points in existing systems and paves the way to building a complete lightweight blockchain solution for networks of resource-constrained devices.

Blockchain's influence extends beyond finance, impacting diverse sectors such as real estate, oil and gas, and education. This extensive reach stems from blockchain's intrinsic ability to reliably manage digital transactions and supply chains. Within the oil and gas sector, the merger of blockchain with supply chain management and data handling is a notable trend. The supply chain encompasses several operations: extraction, transportation, trading, and distribution of resources. Unfortunately, the current supply chain structure misses critical features such as transparency, traceability, flexible trading, and secure data storage - all of which blockchain can provide. Nevertheless, it is essential to investigate blockchain's security and privacy in the oil and gas industry. Such scrutiny enables the smooth, secure, and usable execution of transactions. For this purpose, we reviewed 124 peer-reviewed academic publications, conducting an in-depth analysis of 21 among them. We classified the articles by their relevance to various phases of the supply chain flow: upstream, midstream, downstream, and data management. Despite blockchain's potential to address existing security and privacy voids in the supply chain, there is a significant lack of practical implementation of blockchain integration in oil and gas operations. This deficiency substantially challenges the transition from conventional methods to a blockchain-centric approach.

Many IoT use cases demand both secure storage and secure communication. Resource-constrained devices cannot afford having one set of crypto protocols for storage and another for communication. Lightweight application layer security standards are being developed for IoT communication. Extending these protocols for secure storage can significantly reduce communication latency and local processing. We present BLEND, combining secure storage and communication by storing IoT data as pre-computed encrypted network packets. Unlike local methods, BLEND not only eliminates separate crypto for secure storage needs, but also eliminates a need for real-time crypto operations, reducing the communication latency significantly. Our evaluation shows that compared with a local solution, BLEND reduces send latency from 630 microseconds to 110 microseconds per packet. BLEND enables PKI based key management while being sufficiently lightweight for IoT. BLEND doesn't need modifications to communication standards used when extended for secure storage, and can therefore preserve underlying protocols' security guarantees.

In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we deal with a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. We state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.

The issue of ensuring privacy for users who share their personal information has been a growing priority in a business and scientific environment where the use of different types of data and the laws that protect it have increased in tandem. Different technologies have been widely developed for static publications, i.e., where the information is published only once, such as k-anonymity and {\epsilon}-differential privacy. In the case where microdata information is published dynamically, although established notions such as m-invariance and {\tau}-safety already exist, developments for improving utility remain superficial. We propose a new heuristic approach for the NP-hard combinatorial problem of m-invariance and {\tau}-safety, which is based on a mathematical optimization column generation scheme. The quality of a solution to m-invariance and {\tau}-safety can be measured by the Information Loss (IL), a value in [0,100], the closer to 0 the better. We show that our approach improves by far current heuristics, providing in some instances solutions with ILs of 1.87, 8.5 and 1.93, while the state-of-the art methods reported ILs of 39.03, 51.84 and 57.97, respectively.

A "dark cloud" hangs over numerical optimization theory for decades, namely, whether an optimization algorithm $O(\log(n))$ iteration complexity exists. "Yes", this paper answers, with a new optimization algorithm and strict theory proof. It starts with box-constrained quadratic programming (Box-QP), and many practical optimization problems fall into Box-QP. Smooth quadratic programming (QP) and nonsmooth Lasso can be reformulated as Box-QP via duality theory. It is the first time to present an $O(\log(n))$ iteration complexity QP algorithm, in particular, which behaves like a "direct" method: the required number of iterations is deterministic with exact value $\left\lceil\log\left(\frac{3.125n}{\epsilon}\right)/\log(1.5625)\right\rceil$. This significant breakthrough enables us to transition from the $O(\sqrt{n})$ to the $O(\log(n))$ optimization algorithm, whose amazing scalability is particularly relevant in today's era of big data and artificial intelligence.

Australia is a leading AI nation with strong allies and partnerships. Australia has prioritised robotics, AI, and autonomous systems to develop sovereign capability for the military. Australia commits to Article 36 reviews of all new means and methods of warfare to ensure weapons and weapons systems are operated within acceptable systems of control. Additionally, Australia has undergone significant reviews of the risks of AI to human rights and within intelligence organisations and has committed to producing ethics guidelines and frameworks in Security and Defence. Australia is committed to OECD's values-based principles for the responsible stewardship of trustworthy AI as well as adopting a set of National AI ethics principles. While Australia has not adopted an AI governance framework specifically for Defence; Defence Science has published 'A Method for Ethical AI in Defence' (MEAID) technical report which includes a framework and pragmatic tools for managing ethical and legal risks for military applications of AI.