The vascular network in the human body is characterized by blood vessels exhibiting drastic structural variations in radius, length, topological properties, and branching patterns. This heterogeneity, together with location-specific anatomical background variations, poses a significant challenge for robust, large-scale analysis of the entire cardiovascular system. As a result, most research has focused on narrow, isolated segments of the vascular network. While such targeted studies provide valuable insights, they inherently limit the ability to assess the systemic health and functional integrity of the vascular network as a whole. In this work, we aim to bridge this gap to advance both clinical diagnostics and our fundamental understanding of vascular physiology. We propose the task of segmenting all vessels in CT images, ranging from the largest components of the cardiovascular system to even minuscule mesenteric vessels. To this end, we introduce vesselFM-CT, the first model capable of robustly segmenting all blood vessels in 3D CT images. VesselFM-CT is trained via an iterative, multi-step process and optimizes our proposed TubeLoss loss function, effectively addressing the inh
We introduce the first iterative algorithm for constructing a $\varepsilon$-coreset that guarantees deterministic $\ell_p$ subspace embedding for any $p \in [1,\infty)$ and any $\varepsilon > 0$. For a given full rank matrix $\mathbf{X} \in \mathbb{R}^{n \times d}$ where $n \gg d$, $\mathbf{X}' \in \mathbb{R}^{m \times d}$ is an $(\varepsilon,\ell_p)$-subspace embedding of $\mathbf{X}$, if for every $\mathbf{q} \in \mathbb{R}^d$, $(1-\varepsilon)\|\mathbf{Xq}\|_{p}^{p} \leq \|\mathbf{X'q}\|_{p}^{p} \leq (1+\varepsilon)\|\mathbf{Xq}\|_{p}^{p}$. Specifically, in this paper, $\mathbf{X}'$ is a weighted subset of rows of $\mathbf{X}$ which is commonly known in the literature as a coreset. In every iteration, the algorithm ensures that the loss on the maintained set is upper and lower bounded by the loss on the original dataset with appropriate scalings. So, unlike typical coreset guarantees, due to bounded loss, our coreset gives a deterministic guarantee for the $\ell_p$ subspace embedding. For an error parameter $\varepsilon$, our algorithm takes $O(\mathrm{poly}(n,d,\varepsilon^{-1}))$ time and returns a deterministic $\varepsilon$-coreset, for $\ell_p$ subspace embedding whose s
Analyzing human vasculature and vessel-like, tubular structures, such as airways, is crucial for disease diagnosis and treatment. Current methods often rely on small sub-regions or simplified tree-like structures, rendering analysis of entire organ-level networks at clinical resolution computationally challenging. To this end, we propose VAEsselSparse, an efficient encoder-decoder model to obtain a meaningful yet compact representation of the entire organ-level vascular network at sub-millimeter resolution. VAEsselSparse leverages the inherent sparsity of 3D vascular structures via sparse convolutions and attention mechanisms, achieving substantial spatial compression rates of 8 x 8 x 8. We demonstrate superior reconstruction performance compared to dense counterparts and previous methods. Importantly, the resulting latent space retains clinically relevant discriminative features readily usable for classification tasks, such as aneurysm/stenosis or subvariants of the circle of Willis. Moreover, the compact latent space of VAEsselSparse serves as an effective representation for learning vessel-specific priors through generative models, enabling the synthesis of realistic vasculature
Let $\mathbb{F}_{q}$ be a finite field, and $A:=\mathbb{F}_{q}[T]$. In this article, we give explicit criteria, involving concrete valuations, on the coefficients of the Drinfeld $A$-modules of rank $r$ for $r=2,3$, which ensure the surjectivity of the associated $(T)$-adic Galois representation. As a result, we shall calculate the densities of such Drinfeld $A$-modules.
Knowledge Graphs (KGs) are extensively used across different domains and in several applications. Often, these KGs are very large in size. Such KGs become unwieldy for tasks such as question answering and visualization. Summarization of KGs offers a viable alternative in such cases. Furthermore, personalized KG summarization is crucial in the current data-driven world as it captures the specific requirements of users based on their query patterns. Since it only maintains relevant information, the personalized summaries of KG are small, resulting in significantly smaller storage requirements and query runtime. In this work, we adapt the coreset theory to create personalized KG summaries. For a given dataset and a user-specific query workload, we present an approach that samples a relevant subset of triples using sensitivity-based importance sampling. We ensure that the subset approximates the characteristics of the full dataset with bounded approximation error. We define sensitivity scores that measure the importance of a triple with respect to a user's query workload, which are then used by our coreset construction algorithm. We explicitly focus on personalized knowledge graph summ
The real-time performance, adversarial resiliency, and privacy preservation are the most important metrics that need to be balanced to practice collision avoidance in large-scale multi-UAV (Unmanned Aerial Vehicle) systems. Current frameworks tend to prescribe monolithic solutions that are not only prohibitively computationally complex with a scaling cost of $O(n^2)$ but simply do not offer Byzantine fault tolerance. The proposed hierarchical framework presented in this paper tries to eliminate such trade-offs by stratifying a three-layered architecture. We spread the intelligence into three layers: an immediate collision avoiding local layer running on dense graph attention with latency of $<10 ms$, a regional layer using sparse attention with $O(nk)$ computational complexity and asynchronous federated learning with coordinate-wise trimmed mean aggregation, and lastly, a global layer using a lightweight Hashgraph-inspired protocol. We have proposed an adaptive differential privacy mechanism, wherein the noise level $(ε\in [0.1, 1.0])$ is dynamically reduced based on an evaluation of the measured real-time threat that in turn maximized the privacy-utility tradeoff. Through the u
Catastrophic forgetting is one of the fundamental issues of continual learning because neural networks forget the tasks learned previously when trained on new tasks. The proposed framework is a new path-coordinated framework of continual learning that unites the Neural Tangent Kernel (NTK) theory of principled plasticity bounds, statistical validation by Wilson confidence intervals, and evaluation of path quality by the use of multiple metrics. Experimental evaluation shows an average accuracy of 66.7% at the cost of 23.4% catastrophic forgetting on Split-CIFAR10, a huge improvement over the baseline and competitive performance achieved, which is very close to state-of-the-art results. Further, it is found out that NTK condition numbers are predictive indicators of learning capacity limits, showing the existence of a critical threshold at condition number $>10^{11}$. It is interesting to note that the proposed strategy shows a tendency of lowering forgetting as the sequence of tasks progresses (27% to 18%), which is a system stabilization. The framework validates 80% of discovered paths with a rigorous statistical guarantee and maintains 90-97% retention on intermediate tasks. T
Let $q = p^e \geq 7$ be an odd prime power, and set $A := \mathbb{F}_q[T]$. In this article, we construct an infinite two-parameter family of Drinfeld $A$-modules of rank $3$ such that, for every non-zero prime ideal $\mathfrak{l}$ of $A$, the associated mod-$\mathfrak{l}$, $\mathfrak{l}$-adic, and adelic Galois representations are surjective. These results generalise the specific example, constructed only for primes $p\equiv 1\pmod{3}$, in~\cite{Che22}.
The consensus strategies used in collaborative multi-agent systems (MAS) face notable challenges related to adaptability, scalability, and convergence certainties. These approaches, including structured workflows, debate models, and iterative voting, often lead to communication bottlenecks, stringent decision-making processes, and delayed responses in solving complex and evolving tasks. This article introduces a three-tier architecture, the Hierarchical Adaptive Consensus Network (\hacn), which suggests various consensus policies based on task characterization and agent performance metrics. The first layer collects the confidence-based voting outcomes of several local agent clusters. In contrast, the second level facilitates inter-cluster communication through cross-clustered partial knowledge sharing and dynamic timeouts. The third layer provides system-wide coordination and final arbitration by employing a global orchestration framework with adaptable decision rules. The proposed model achieves $\bigO(n)$ communication complexity, as opposed to the $\bigO(n^2)$ complexity of the existing fully connected MAS. Experiments performed in a simulated environment yielded a 99.9\% reduct
Autonomous Vehicles (AV) proliferation brings important and pressing security and reliability issues that must be dealt with to guarantee public safety and help their widespread adoption. The contribution of the proposed research is towards achieving more secure, reliable, and trustworthy autonomous transportation system by providing more capabilities for anomaly detection, data provenance, and real-time response in safety critical AV deployments. In this research, we develop a new framework that combines the power of Artificial Intelligence (AI) for real-time anomaly detection with blockchain technology to detect and prevent any malicious activity including sensor failures in AVs. Through Long Short-Term Memory (LSTM) networks, our approach continually monitors associated multi-sensor data streams to detect anomalous patterns that may represent cyberattacks as well as hardware malfunctions. Further, this framework employs a decentralized platform for securely storing sensor data and anomaly alerts in a blockchain ledger for data incorruptibility and authenticity, while offering transparent forensic features. Moreover, immediate automated response mechanisms are deployed using smar
The interplay of topology and disorder in quantum dynamics has recently attracted significant attention across diverse platforms, including solid-state devices, ultracold atoms, and photonic systems. Here, we report on a topological Anderson transition caused by quasiperiodic modulation of the stronger intra-cell couplings in photonic Su-Schrieffer-Heeger lattices. As the quasiperiodic strength is varied, the system exhibits a reentrant transition from a trivial phase to a topological phase and back to a trivial phase, accompanied by the closing and reopening of the band gap around zero energy. Unlike the traditional detection of photonic topological edge modes, we measure the mean chiral displacement from the transport of light in the bulk of the lattices. In our photonic lattices with a fixed length, the propagation dynamics is retrieved by varying the wavelength of light, which tunes the inter-waveguide couplings.
The security of autonomous vehicle networks is facing major challenges, owing to the complexity of sensor integration, real-time performance demands, and distributed communication protocols that expose vast attack surfaces around both individual and network-wide safety. Existing security schemes are unable to provide sub-10 ms (milliseconds) anomaly detection and distributed coordination of large-scale networks of vehicles within an acceptable safety/privacy framework. This paper introduces a three-tier hybrid security architecture HAVEN (Hierarchical Autonomous Vehicle Enhanced Network), which decouples real-time local threat detection and distributed coordination operations. It incorporates a light ensemble anomaly detection model on the edge (first layer), Byzantine-fault-tolerant federated learning to aggregate threat intelligence at a regional scale (middle layer), and selected blockchain mechanisms (top layer) to ensure critical security coordination. Extensive experimentation is done on a real-world autonomous driving dataset. Large-scale simulations with the number of vehicles ranging between 100 and 1000 and different attack types, such as sensor spoofing, jamming, and adv
The optimization of urban traffic is threatened by the complexity of achieving a balance between transport efficiency and the maintenance of privacy, as well as the equitable distribution of traffic based on socioeconomically diverse neighborhoods. Current centralized traffic management schemes invade user location privacy and further entrench traffic disparity by offering disadvantaged route suggestions, whereas current federated learning frameworks do not consider fairness constraints in multi-objective traffic settings. This study presents a privacy-preserving federated learning framework, termed FedFair-Traffic, that jointly and simultaneously optimizes travel efficiency, traffic fairness, and differential privacy protection. This is the first attempt to integrate three conflicting objectives to improve urban transportation systems. The proposed methodology enables collaborative learning between related vehicles with data locality by integrating Graph Neural Networks with differential privacy mechanisms ($ε$-privacy guarantees) and Gini coefficient-based fair constraints using multi-objective optimization. The framework uses federated aggregation methods of gradient clipping an
Let $\mathbb{F}_q$ be a finite field with $q$ elements, where $q$ is a prime power and let $A:= \mathbb{F}_{q}[T]$. By~\cite{PR09}, the adelic image of the Galois representation attached to a rank $2$ Drinfeld $A$-module $\varphi$ is open, and determining when it is surjective remains a subtle problem. To resolve this question, in this article, we study the $\mathfrak{p}$-adic surjectivity of the Galois representations attached to $\varphi$, where $\mathfrak{p} \in Ω_A:= \mathrm{Spec}(A) \setminus \{ (0) \}$. There are two directions to investigate this problem: one by fixing the prime $\mathfrak{p}$, and the other by fixing $\varphi$. In the horizontal direction, for a fixed prime $\mathfrak{p} \in Ω_A$, we give explicit and easily verifiable conditions on Drinfeld $ A$-modules $\varphi$ of rank $2$ which ensure the surjectivity of the $\mathfrak{p}$-adic Galois representation $ρ_{\varphi,\mathfrak{p}}$. This work not only extends the work of~\cite{Ray24} for $\mathfrak{p}=(T)$, but also obtains a variant of~\cite{Ray24} under comparatively simpler conditions in the case $\mathfrak{p}=(T)$. In the vertical direction, we show that for a fixed rank $2$ Drinfeld $A$-module $\varphi$,
Clustering is a fundamental technique in data analysis, with the $k$-means being one of the widely studied objectives due to its simplicity and broad applicability. In many practical scenarios, data points come with associated weights that reflect their importance, frequency, or confidence. Given a weighted point set $P \subset R^d$, where each point $p \in P$ has a positive weight $w_p$, the goal is to compute a set of $k$ centers $C = \{ c_1, c_2, \ldots, c_k \} \subset R^d$ that minimizes the weighted clustering cost: $Δ_w(P,C) = \sum_{p \in P} w_p \cdot d(p,C)^2$, where $d(p,C)$ denotes the Euclidean distance from $p$ to its nearest center in $C$. Although most existing coreset-based algorithms for $k$-means extend naturally to the weighted setting and provide a PTAS, no prior work has offered a simple, coreset-free PTAS designed specifically for the weighted $k$-means problem. In this paper, we present a simple PTAS for weighted $k$-means that does not rely on coresets. Building upon the framework of Jaiswal, Kumar, and Sen (2012) for the unweighted case, we extend the result to the weighted setting by using the weighted $D^2$-sampling technique. Our algorithm runs in time $n
In medical imaging, generative models are increasingly relied upon for two distinct but equally critical tasks: reconstruction, where the goal is to restore medical imaging (usually inverse problems like inpainting or superresolution), and generation, where synthetic data is created to augment datasets or carry out counterfactual analysis. Despite shared architecture and learning frameworks, they prioritize different goals: generation seeks high perceptual quality and diversity, while reconstruction focuses on data fidelity and faithfulness. In this work, we introduce a "generative model zoo" and systematically analyze how modern latent diffusion models and autoregressive models navigate the reconstruction-generation spectrum. We benchmark a suite of generative models across representative cardiac medical imaging tasks, focusing on image inpainting with varying masking ratios and sampling strategies, as well as unconditional image generation. Our findings show that diffusion models offer superior perceptual quality for unconditional generation but tend to hallucinate as masking ratios increase, whereas autoregressive models maintain stable perceptual performance across masking leve
Two-dimensional semiconductors have attracted considerable interest for integration into emerging quantum photonic networks. Strain engineering of monolayer transition-metal dichalcogenides (ML-TMDs) enables the tuning of light-matter interactions and associated optoelectronic properties, and generates new functionalities, including the formation of quantum dots (QDs). Here, we combine spatially resolved micro-photoluminescence ($μ$-PL) spectroscopy from cryogenic (4$\text{-}$94 K) to room temperature with micro-Raman spectroscopy at room temperature to investigate the strain-dependent emission energies of thousands of individual QDs in ML-WS$_2$ and ML-WSe$_2$, integrated across multiple heterostructures and a piezoelectric device. Compared with delocalized excitons, QDs in both materials exhibit enhanced strain sensitivities of their emission energies $-$ approximately fourfold in WS$_2$ and twofold in WSe$_2$ $-$ leading to pronounced broadening of the ensemble emission linewidth. Temperature-dependent $μ$-PL spectroscopy combined with dynamic strain tuning experiments further reveal that the enhanced strain sensitivity of individual QDs originates from strengthened interactions
3D spatial graphs play a crucial role in biological and clinical research by modeling anatomical networks such as blood vessels,neurons, and airways. However, generating 3D biological graphs while maintaining anatomical validity remains challenging, a key limitation of existing diffusion-based methods. In this work, we propose a novel 3D biological graph generation method that adheres to structural and semantic plausibility conditions. We achieve this by using a novel projection operator during sampling that stochastically fixes inconsistencies. Further, we adopt a superior edge-deletion-based noising procedure suitable for sparse biological graphs. Our method demonstrates superior performance on two real-world datasets, human circle of Willis and lung airways, compared to previous approaches. Importantly, we demonstrate that the generated samples significantly enhance downstream graph labeling performance. Furthermore, we show that our generative model is a reasonable out-of-the-box link predictior.
Segmenting 3D blood vessels is a critical yet challenging task in medical image analysis. This is due to significant imaging modality-specific variations in artifacts, vascular patterns and scales, signal-to-noise ratios, and background tissues. These variations, along with domain gaps arising from varying imaging protocols, limit the generalization of existing supervised learning-based methods, requiring tedious voxel-level annotations for each dataset separately. While foundation models promise to alleviate this limitation, they typically fail to generalize to the task of blood vessel segmentation, posing a unique, complex problem. In this work, we present vesselFM, a foundation model designed specifically for the broad task of 3D blood vessel segmentation. Unlike previous models, vesselFM can effortlessly generalize to unseen domains. To achieve zero-shot generalization, we train vesselFM on three heterogeneous data sources: a large, curated annotated dataset, data generated by a domain randomization scheme, and data sampled from a flow matching-based generative model. Extensive evaluations show that vesselFM outperforms state-of-the-art medical image segmentation foundation mod