arXiv subjects

Trung V. Phan

Publications and source records attributed to Trung V. Phan.

At least 19 recordsLinked to original sources

arXiv2026

DeepFaith: Evidence-Grounded LLMs for Faithful Incident Reporting in Multi-Stage APT Defense

Advanced Persistent Threats (APTs) are difficult to detect and interpret due to their multi-stage and stealthy nature. While recent autonomous defense systems leverage provenance graphs and learning-based models for detection and mitigation, their outputs remain largely machine-oriented and difficult for analysts to interpret. Large language models (LLMs) offer a promising interface for report generation, but often produce hallucinated or weakly grounded content. In this paper, we propose DeepFaith, an evidence-grounded framework for faithful incident reporting in multi-stage APT defense. DeepFaith transforms structured outputs from autonomous defense and explainability modules into natural-language reports that are explicitly aligned with underlying system evidence. The framework integrates a unified evidence representation, evidence-grounded prompting, faithfulness-aware generation, and post-generation verification to ensure that all generated statements are supported. Experiments in a realistic enterprise testbed demonstrate that DeepFaith improves faithfulness from 0.68 to 0.92, reduces unsupported claims from 0.32 to 0.08, and increases temporal consistency from 0.6 to 0.88, while maintaining concise reports and lower error rates than existing template-based and LLM-based solutions. These results show that evidence-grounded generation enables reliable, interpretable, and actionable reporting for security operations centers.

cs.CR↗

arXiv2026

Adaptive High-Level Tight Control of Prostate Cancer: A Path from From Terminal Disease to Chronic Condition

Metastatic prostate cancer is one of the leading causes of cancer-related morbidity and mortality worldwide. It is characterized by a high mortality rate and a poor prognosis. In this work, we explore how a clinical oncologist can apply a Stackelberg game-theoretic framework to prolong metastatic prostate cancer survival, or even make it chronic in duration. We utilize a Bayesian optimization approach to identify the optimal adaptive chemotherapeutic treatment policy for a single drug (Abiraterone) to maximize the time before the patient begins to show symptoms. We show that, with precise adaptive optimization of drug delivery, it is possible to significantly prolong the cancer suppression period, potentially converting metastatic prostate cancer from a terminal disease to a chronic disease for most patients, as supported by clinical and analytical evidence. We suggest that clinicians might explore the possibility of implementing a high-level tight control (HLTC) treatment, in which the trigger signals (i.e. biomarker levels) for drug administration and cessation are both high and close together, typically yield the best outcomes, as demonstrated through both computation and theoretical analysis. This simple insight could serve as a valuable guide for improving current adaptive chemotherapy treatments in other hormone-sensitive cancers.

q-bio.QM↗

arXiv2026

Learning the APT Kill Chain: Temporal Reasoning over Provenance Data for Attack Stage Estimation

Advanced Persistent Threats (APTs) evolve through multiple stages, each exhibiting distinct temporal and structural behaviors. Accurate stage estimation is critical for enabling adaptive cyber defense. This paper presents StageFinder, a temporal-graph learning framework for multi-stage attack progression inference from fused host and network provenance data. Provenance graphs are encoded using a graph neural network to capture structural dependencies among processes, files, and connections, while a long short-term memory (LSTM) model learns temporal dynamics to estimate stage probabilities aligned with the MITRE ATT&CK framework. The model is pretrained on the DARPA OpTC dataset and fine-tuned on labeled DARPA Transparent Computing data. Experimental results demonstrate that StageFinder achieves a macro F1-score of 0.96 and reduces prediction volatility by 31% compared to state-of-the-art baselines (Cyberian, NetGuardian). These results highlight the effectiveness of fused provenance-temporal learning for accurate and stable APT stage inference.

cs.CR↗

arXiv2026

DeepStage: Learning Autonomous Defense Policies Against Multi-Stage APT Campaigns

This paper presents DeepStage, a deep reinforcement learning (DRL) framework for adaptive and stage-aware defense against Advanced Persistent Threats (APTs). The enterprise environment is formulated as a partially observable Markov decision process (POMDP), in which host provenance and network telemetry are fused into unified provenance graphs. Building on our prior work (StageFinder), DeepStage employs a graph neural network encoder and an LSTM-based stage estimator to infer probabilistic attacker stages aligned with the MITRE ATT&CK framework. The resulting stage beliefs, together with graph embeddings, are used to guide a hierarchical Proximal Policy Optimization (PPO) agent that selects defense actions across monitoring, access control, containment, and remediation. Experiments in a realistic enterprise testbed with CALDERA-driven APT playbooks show that DeepStage achieves an average F1-score of 0.887 and a mitigation success rate of 84.7%, outperforming a risk-aware DRL baseline by 21.8% in F1-score and 16.2% in mitigation success. The results demonstrate effective stage-aware and cost-efficient autonomous cyber defense.

cs.CR↗

arXiv2026

DeepXplain: XAI-Guided Autonomous Defense Against Multi-Stage APT Campaigns

Advanced Persistent Threats (APTs) are stealthy, multi-stage attacks that require adaptive and timely defense. While deep reinforcement learning (DRL) enables autonomous cyber defense, its decisions are often opaque and difficult to trust in operational environments. This paper presents DeepXplain, an explainable DRL framework for stage-aware APT defense. Building on our prior DeepStage model, DeepXplain integrates provenance-based graph learning, temporal stage estimation, and a unified XAI pipeline that provides structural, temporal, and policy-level explanations. Unlike post-hoc methods, explanation signals are incorporated directly into policy optimization through evidence alignment and confidence-aware reward shaping. To the best of our knowledge, DeepXplain is the first framework to integrate explanation signals into reinforcement learning for APT defense. Experiments in a realistic enterprise testbed show improvements in stage-weighted F1-score (0.887 to 0.915) and success rate (84.7% to 89.6%), along with higher explanation confidence (0.86), improved fidelity (0.79), and more compact explanations (0.31). These results demonstrate enhanced effectiveness and trustworthiness of autonomous cyber defense.

cs.CR↗

arXiv2026

Generalizing Shell Theorem to Constant Curvature Spaces in All Dimensions and Topologies

A gravitational potential has the spherical property when the field outside any uniform spherical shell is indistinguishable from that of a point mass at the center. We present the general potentials that possess this property on constant curvature spaces, using the Euler-Poisson-Darboux identity for spherical means. Our results are consistent with known findings in flat three-dimensional space and reduce to Gurzadyan's cosmological theorem when the rescaling factor is exactly $1$. Our approach naturally extends to nontrivial spatial topologies.

physics.class-ph↗

arXiv2026

Quantum Kaczmarz Algorithm for Solving Linear Algebraic Equations

We introduce a quantum linear system solving algorithm based on the Kaczmarz method, a widely used workhorse for large linear systems and least-squares problems that updates the solution by enforcing one equation at a time. Its simplicity and low memory cost make it a practical choice across data regression, tomographic reconstruction, and optimization. In contrast to many existing quantum linear solvers, our method does not rely on oracle access to query entries, relaxing a key practicality bottleneck. In particular, when the rank of the system of interest is sufficiently small and the rows of the matrix of interest admit an appropriate structure, we achieve circuit complexity $\mathcal{O}\left(\frac{1}{\varepsilon}\log m\right)$, where $m$ is the number of variables and $\varepsilon$ is the target precision, without dependence on the sparsity $s$, and could possibly be without explicit dependence on condition number $κ$. This shows a significant improvement over previous quantum linear solvers where the dependence on $κ,s$ is at least linear. At the same time, when the rows have an arbitrary structure and have at most $s$ nonzero entries, we obtain the circuit depth $\mathcal{O}\left(\frac{1}{\varepsilon}\log s\right)$ using extra $\mathcal{O}(s)$ ancilla qubits, so the depth grows only logarithmically with sparsity $s$. When the sparsity $s$ grows as $\mathcal{O}(\log m)$, then our method can achieve an exponential improvement with respect to circuit depth compared to existing quantum algorithms, while using (asymptotically) the same amount of qubits.

quant-ph↗

arXiv2025

Self-Image Multiplicity in a Concave Cylindrical Mirror

Concave mirrors are fundamental optical elements, yet some easily observed behaviors are rarely addressed in standard textbooks, such as the formation of multiple reflected images. Here we investigate self-imaging -- where the observer is also the observed object -- using a concave cylindrical mirror. We predict the number of self-images visible from different observation points and classify space into regions by image count. We then test these predictions with an inexpensive stainless-steel concave cylindrical mirror commonly found in teaching labs. This activity links geometrical optics principles to direct observation and provides a ready-to-use classroom demonstration and student exercise.

physics.optics↗

arXiv2025

Informational Memory Shapes Collective Behavior in Intelligent Swarms

We present an experimental and theoretical study of 2-D swarms in which collective behavior emerges from both direct local mechanical coupling between agents and from the exchange and processing of information between agents. Each agent, an air-table drone endowed with internal memory and a binary decision variable, updates its state by integrating a time series of memories of local past collisions. This internal computation transforms the drone swarm into a dynamical information network in which history-dependent feedback drives spontaneous complete spin polarization, pitchfork bifurcated spin collectives, and chaotic switching between collective states. By tuning the depth of memory and the decision algorithm, we uncover a memory-induced phase transition that breaks spin symmetry at the population level. A minimal theoretical model maps these dynamics onto an effective potential landscape sculpted by informational feedback, revealing how temporally correlated computation can replace instantaneous forces as the driver of collective organization, informed by experiments. These results position physically interacting drone swarms as a model system for exploring the physics of informational drone ensembles whose emergent behavior arises from the interplay between physical interaction and information processing.

physics.soc-ph↗

arXiv2025

Quantum Algorithm for Estimating Ollivier-Ricci Curvature

We introduce a quantum algorithm for computing the Ollivier Ricci curvature, a discrete analogue of the Ricci curvature defined via optimal transport on graphs and general metric spaces. This curvature has seen applications ranging from signaling fragility in financial networks to serving as basic quantities in combinatorial quantum gravity. For inputs given as a point cloud with pairwise distances, we show that our algorithm can achieve an exponential speedup over the best-known classical methods for two particular classes of problem. Our work is another step toward quantum algorithms for geometrical problems that are capable of delivering practical value while also informing fundamental theory.

quant-ph↗

arXiv2025

Digitization Can Stall Swarm Transport: Commensurability Locking in Quantized-Sensing Chains

We present a minimal model for autonomous robotic swarms in one- and higher-dimensional spaces, where identical, field-driven agents interact pairwise to self-organize spacing and independently follow local gradients sensed through quantized digital sensors. We show that the collective response of a multi-agent train amplifies sensitivity to weak gradients beyond what is achievable by a single agent. We discover a fractional transport phenomenon in which, under a uniform gradient, collective motion freezes abruptly whenever the ratio of intra-agent sensor separation to inter-agent spacing satisfies a number-theoretic commensurability condition. This commensurability locking persists even as the number of agents tends to infinity. We find that this condition is exactly solvable on the rationals -- a dense subset of real numbers -- providing analytic, testable predictions for when transport stalls. Our findings establish a surprising bridge between number theory and emergent transport in swarm robotics, informing design principles with implications for collective migration, analog computation, and even the exploration of number-theoretic structure via physical experimentation.

cond-mat.soft↗

arXiv2025

Fractatomic Physics: An Invitation with Atomic Stability and Rydberg States in Fractal Spaces

We explore the physical quantum properties of atoms in fractal spaces, both as a theoretical generalization of normal integer-dimensional Euclidean spaces and as an experimentally realizable setting. We identify the threshold of fractality at which Ehrenfest atomic instability emerges, where the Schrödinger equation describing the wave-function of a single electron orbiting around an atom becomes scale-free, and discuss the potential of observing this phenomena in laboratory settings. We then study the Rydberg states of stable atoms using the Wentzel-Kramers-Brillouin approximation, along with a proposed extension for the Langer modification, in general fractal dimensionalities. We show that fractal space atoms near instability explode in size even at low-number excited state, making them highly suitable to induce strong entanglements and foster long-range many-body interactions. We argue that atomic physics in fractal spaces -- ``fractatomic physics'' -- is a rich research avenue deserving of further theoretical and experimental investigations.

quant-ph↗

arXiv2025

Size and Shape of Fuzzy Spheres from Matrix/Membrane Correspondence

We study the size and shape statistics of ground state fuzzy spheres when projected onto the transverse plane, utilizing the regularized SU(N=2) matrix model in D=(1+3)-dimensional spacetime. We show that they appear as ellipses, from matrix/membrane correspondence. With our numerical and analytical approximation for the ground state wavefunction, we provide estimations for their expectation surface areas, perimeters, eccentricities, and shape-parameters. These geometric constants of quantum membranes deviate drastically from classical mechanics.

quant-ph↗

arXiv2025

Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equations

The machine learning methods for data-driven identification of partial differential equations (PDEs) are typically defined for a given number of spatial dimensions and a choice of coordinates the data have been collected in. This dependence prevents the learned evolution equation from generalizing to other spaces. In this work, we reformulate the problem in terms of coordinate- and dimension-independent representations, paving the way toward what we call ``spatially liberated" PDE learning. To this end, we employ a machine learning approach to predict the evolution of scalar field systems expressed in the formalism of exterior calculus, which is coordinate-free and immediately generalizes to arbitrary dimensions by construction. We demonstrate the performance of this approach in the FitzHugh-Nagumo and Barkley reaction-diffusion models, as well as the Patlak-Keller-Segel model informed by in-situ chemotactic bacteria observations. We provide extensive numerical experiments that demonstrate that our approach allows for seamless transitions across various spatial contexts. We show that the field dynamics learned in one space can be used to make accurate predictions in other spaces with different dimensions, coordinate systems, boundary conditions, and curvatures.

cs.LG↗

arXiv2025

On the Derivation of the Cosmological Gurzadyan's Theorem

In cosmology, the Gurzadyan's theorem identifies the most general force law consistent with the finding of Newton's first shell theorem -- that a spherical symmetric mass exerts the same gravitational force as a point mass at its center. This theorem has found important applications in cosmological modeling, particularly in the context of MoND (Modified Newtonian Dynamics), which has recently gained renewed attention as a potential alternative to dark matter. The derivation by Gurzadyan is written in an extremely concise and dense style, making it difficult to follow. Recent proofs of the theorem based on power-series methods offer valuable perspectives, though they differ from the original derivation, which is based on perturbation analysis. Our note aims to clarify the underlying logic in a pedagogical way -- accessible to advanced high school or undergraduate students -- while preserving conceptual clarity and mathematical elegance of his insight.

physics.class-ph↗

arXiv2025

Quantum Algorithm for Estimating Intrinsic Geometry

High-dimensional datasets typically cluster around lower-dimensional manifolds but are also often marred by severe noise, obscuring the intrinsic geometry essential for downstream learning tasks. We present a quantum algorithm for estimating the intrinsic geometry of a point cloud -- specifically its local intrinsic dimension and local scalar curvature. These quantities are crucial for dimensionality reduction, feature extraction, and anomaly detection -- tasks that are central to a wide range of data-driven and data-assisted applications. In this work, we propose a quantum algorithm which takes a dataset with pairwise geometric distance, output the estimation of local dimension and curvature at a given point. We demonstrate that this quantum algorithm achieves an exponential speedup over its classical counterpart, and, as a corollary, further extend our main technique to diffusion maps, yielding exponential improvements even over existing quantum algorithms. Our work marks another step toward efficient quantum applications in geometrical data analysis, moving beyond topological summaries toward precise geometric inference and opening a novel, scalable path to quantum-enhanced manifold learning.

quant-ph↗

arXiv2024

Mechanical Attributes of Fractal Dragons

Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how the geometries of fractals can be exploited to determine their important mechanical properties, such as the first and second moments, which physically correspond to the center of mass and the moment of inertia, using a family of complex fractals known as the dragons.

cond-mat.stat-mech↗

arXiv2024

Social Physics of Bacteria: Avoidance of an Information Black Hole

Social physics explores responses to information exchange in a social network, and can be mapped down to bacterial collective signaling. Here, we explore how social inter-bacterial communication includes coordination of response to communication loss, as opposed to solitary searching for food, with collective response emergence at the population level. We present a 2-dimensional enclosed microfluidic environment that utilizes concentric rings of funnel ratchets, which direct motile E.coli bacteria towards a sole exit hole, an information ``black hole'', passage into the black hole irreversibly sweeps the bacteria away via hydrodynamic flow. We show that the spatiotemporal evolution of entropy production reveals how bacteria avoid crossing the hydrodynamic black hole information horizon.

physics.bio-ph↗