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Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of Mathematical Selection, where we generally, deal with problems subjecting to Operation Research, Artificial Intelligence and many more promising domains. In a broader sense, an optimization problem entails maximising or minimising a real function by systematically selecting input values from within an allowed set and computing the function's value. A broad region of applied mathematics is the generalisation of metaheuristic theory and methods to other formulations. More broadly, optimization entails determining the finest virtues of some fitness function, offered a fixed space, which may include a variety of distinct types of decision variables and contexts. In this work, we will be working on the famous Balanced Assignment Problem, and will propose a comparative analysis on the Complexity Metrics of Computational Time for different Notions of solving the Balanced Assignment Problem.

Bayesian and causal inference are fundamental processes for intelligence. Bayesian inference models observations: what can be inferred about y if we observe a related variable x? Causal inference models interventions: if we directly change x, how will y change? Predictive coding is a neuroscience-inspired method for performing Bayesian inference on continuous state variables using local information only. In this work, we go beyond Bayesian inference, and show how a simple change in the inference process of predictive coding enables interventional and counterfactual inference in scenarios where the causal graph is known. We then extend our results, and show how predictive coding can be generalized to cases where this graph is unknown, and has to be inferred from data, hence performing causal discovery. What results is a novel and straightforward technique that allows us to perform end-to-end causal inference on predictive-coding-based structural causal models, and demonstrate its utility for potential applications in machine learning.

The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In this study, we apply advanced network-based information filtering techniques to design a novel deep neural network unit characterized by a sparse higher-order graphical architecture built over the homological structure of underlying data. We demonstrate its effectiveness in two application domains which are traditionally challenging for deep learning: tabular data and time series regression problems. Results demonstrate the advantages of this novel design which can tie or overcome the results of state-of-the-art machine learning and deep learning models using only a fraction of parameters.

Artificial Intelligence (AI) systems are increasingly used in high-stakes domains of our life, increasing the need to explain these decisions and to make sure that they are aligned with how we want the decision to be made. The field of Explainable AI (XAI) has emerged in response. However, it faces a significant challenge known as the disagreement problem, where multiple explanations are possible for the same AI decision or prediction. While the existence of the disagreement problem is acknowledged, the potential implications associated with this problem have not yet been widely studied. First, we provide an overview of the different strategies explanation providers could deploy to adapt the returned explanation to their benefit. We make a distinction between strategies that attack the machine learning model or underlying data to influence the explanations, and strategies that leverage the explanation phase directly. Next, we analyse several objectives and concrete scenarios the providers could have to engage in this behavior, and the potential dangerous consequences this manipulative behavior could have on society. We emphasize that it is crucial to investigate this issue now, before these methods are widely implemented, and propose some mitigation strategies.

There has been growing interest in using the QUIC transport protocol for the Internet of Things (IoT). In lossy and high latency networks, QUIC outperforms TCP and TLS. Since IoT greatly differs from traditional networks in terms of architecture and resources, IoT specific parameter tuning has proven to be of significance. While RFC 9006 offers a guideline for tuning TCP within IoT, we have not found an equivalent for QUIC. This paper is the first of our knowledge to contribute empirically based insights towards tuning QUIC for IoT. We improved our pure HTTP/3 publish-subscribe architecture and rigorously benchmarked it against an alternative: MQTT-over-QUIC. To investigate the impact of transport-layer parameters, we ran both applications on Raspberry Pi Zero hardware. Eight metrics were collected while emulating different network conditions and message payloads. We enumerate the points we experimentally identified (notably, relating to authentication, MAX\_STREAM messages, and timers) and elaborate on how they can be tuned to improve resource consumption and performance. Our application offered lower latency than MQTT-over-QUIC with slightly higher resource consumption, making it preferable for reliable time-sensitive dissemination of information.

Most link prediction methods return estimates of the connection probability of missing edges in a graph. Such output can be used to rank the missing edges, from most to least likely to be a true edge, but it does not directly provide a classification into true and non-existent. In this work, we consider the problem of identifying a set of true edges with a control of the false discovery rate (FDR). We propose a novel method based on high-level ideas from the literature on conformal inference. The graph structure induces intricate dependence in the data, which we carefully take into account, as this makes the setup different from the usual setup in conformal inference, where exchangeability is assumed. The FDR control is empirically demonstrated for both simulated and real data.

The federated learning (FL) technique was developed to mitigate data privacy issues in the traditional machine learning paradigm. While FL ensures that a user's data always remain with the user, the gradients are shared with the centralized server to build the global model. This results in privacy leakage, where the server can infer private information from the shared gradients. To mitigate this flaw, the next-generation FL architectures proposed encryption and anonymization techniques to protect the model updates from the server. However, this approach creates other challenges, such as malicious users sharing false gradients. Since the gradients are encrypted, the server is unable to identify rogue users. To mitigate both attacks, this paper proposes a novel FL algorithm based on a fully homomorphic encryption (FHE) scheme. We develop a distributed multi-key additive homomorphic encryption scheme that supports model aggregation in FL. We also develop a novel aggregation scheme within the encrypted domain, utilizing users' non-poisoning rates, to effectively address data poisoning attacks while ensuring privacy is preserved by the proposed encryption scheme. Rigorous security, privacy, convergence, and experimental analyses have been provided to show that FheFL is novel, secure, and private, and achieves comparable accuracy at reasonable computational cost.

Ensuring the confidentiality and privacy of sensitive information in cloud computing and outsourced databases is crucial. Homomorphic encryption (HE) offers a solution by enabling computations on encrypted data without decryption, allowing secure outsourcing while maintaining data confidentiality. However, HE faces performance challenges in query-intensive databases. To address this, we propose two novel optimizations, Silca and SilcaZ, tailored to outsourced databases in cloud computing. Silca utilizes a singular caching technique to reduce computational overhead, while SilcaZ leverages modular arithmetic operations to ensure the applicability of singular caching for intensive HE operations. We prove the semantic security of Silca and SilcaZ and implement them with CKKS and BGV in HElib as MySQL loadable functions. Extensive experiments with seven real-world datasets demonstrate their superior performance compared to existing HE schemes, bridging the gap between theoretical advancements and practical applications in applying HE schemes on outsourced databases in cloud computing.

The widespread adoption of cloud infrastructures has revolutionised data storage and access. However, it has also raised concerns regarding the privacy of sensitive data stored in the cloud. To address these concerns, encryption techniques have been widely used. However, traditional encryption schemes limit the efficient search and retrieval of encrypted data. To tackle this challenge, innovative approaches have emerged, such as the utilisation of Homomorphic Encryption (HE) in Searchable Encryption (SE) schemes. This paper provides a comprehensive analysis of the advancements in HE-based privacy-preserving techniques, focusing on their application in SE. The main contributions of this work include the identification and classification of existing SE schemes that utilize HE, a comprehensive analysis of the types of HE used in SE, an examination of how HE shapes the search process structure and enables additional functionalities, and the identification of promising directions for future research in HE-based SE. The findings reveal the increasing usage of HE in SE schemes, particularly Partially Homomorphic Encryption. The analysis also highlights the prevalence of index-based SE schemes using HE, the support for ranked search and multi-keyword queries, and the need for further exploration in functionalities such as verifiability and the ability to authorise and revoke users. Future research directions include exploring the usage of other encryption schemes alongside HE, addressing omissions in functionalities like fuzzy keyword search, and leveraging recent advancements in Fully Homomorphic Encryption schemes.

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics system, learning molecular fingerprints, predicting protein interface, and classifying diseases require that a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures, like the dependency tree of sentences and the scene graph of images, is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are connectionist models that capture the dependence of graphs via message passing between the nodes of graphs. Unlike standard neural networks, graph neural networks retain a state that can represent information from its neighborhood with an arbitrary depth. Although the primitive graph neural networks have been found difficult to train for a fixed point, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful learning with them. In recent years, systems based on graph convolutional network (GCN) and gated graph neural network (GGNN) have demonstrated ground-breaking performance on many tasks mentioned above. In this survey, we provide a detailed review over existing graph neural network models, systematically categorize the applications, and propose four open problems for future research.