arXiv subjects

Tuan Anh Pham

Publications and source records attributed to Tuan Anh Pham.

At least 19 recordsLinked to original sources

arXiv2026

Ideals of homomorphic images of the enveloping algebra of the Witt algebra

Let $W_{\geq -1} = \mathbb{C}[t]\partial$ and $W = \mathbb{C}[t, t^{-1}]\partial$ be the Witt algebra of algebraic vector fields on $\mathbb{C}$ and $\mathbb{C}^*$ respectively. In this paper, we make significant progress toward the open conjecture that the enveloping algebras $\mathrm{U}(W_{\geq -1})$ and $\mathrm{U}(W)$ satisfy the ascending chain condition (ACC) on two-sided ideals. We show that all homomorphic images of $\mathrm{U}(W_{\geq -1})$ and $\mathrm{U}(W)$ under the family of ``orbit homomorphisms'' of arbitrary Gelfand-Kirillov dimension satisfy ACC on ideals. These orbit homomorphisms were the key ingredient allowing us to ``lift'' the Dixmier map from finite-dimensional solvable settings to infinite-dimensional settings of the Witt and Virasoro algebras in our recent work [Pham, 2025, arXiv:2504.14670]. As a result, we completely classify the prime and primitive spectra of these homomorphic images. As these images approximate $\mathrm{U}(W_{\geq -1})$ better as their GK-dimension increases, this classification sheds new light on the two-sided and prime ideal structures of $\mathrm{U}(W_{\geq -1})$. Finally, we discuss several applications of our results to the Dixmier map for $W_{\geq -1}$.

math.RA↗

arXiv2026

An Indoor Navigation System for the Visually Impaired based on UWB Positioning and D* Lite Path Planning Algorithm

This paper proposes an indoor navigation system for the visually impaired, leveraging Ultra-Wideband (UWB) positioning technology and the D*Lite path planning algorithm. The system utilizes UWB sensors to provide precision localization in GPS-denied environments. The D* Lite algorithm is integrated to optimize travel trajectories and ensure rapid route re-planning in the presence of dynamic obstacles. Experimental results demonstrate that the system operates reliably with low latency, providing safety and flexibility for users in complex indoor spaces.

cs.RO↗

arXiv2026

On the boundary Carrollian conformal algebra

We initiate the mathematical study of the boundary Carrollian conformal algebra (BCCA), an infinite-dimensional Lie algebra recently discovered in the context of Carrollian physics. The BCCA is an intriguing object from both physical and mathematical perspectives, since it is a filtered but not graded Lie algebra. In this paper, we first construct some modules for the BCCA and one of its subalgebras, which we call $\mathcal{O}$, by restriction of well-known modules of the BMS$_3$ and Witt algebras respectively. Along the way, we prove the irreducibility criteria for the so-called ``induced modules'' of the BMS$_3$ algebra (which we prefer to call massive modules to avoid ambiguity) and show that this is the same criteria for the irreducibility of the Verma modules of the BMS$_3$ algebra. Interestingly, the modules generated by the action of the BCCA on the generating vector of the massive modules are also irreducible under the same criteria. When this criteria holds, every massive module decomposes into a direct sum of two BCCA-submodules, each of which we conjecture to be indecomposable. Meanwhile, restricting Verma modules to the BCCA and $\mathcal{O}$ leads to free or ``almost free'' modules, which are not particularly interesting from a representation-theoretic viewpoint. This motivates the construction of BCCA modules intrinsically. To do this, we go through some structure theory on the BCCA to define a new basis and a decreasing filtration on the algebra, using which we construct Whittaker modules over the BCCA and the subalgebra $\mathcal{O}$ and prove criteria for their irreducibility.

math.RT↗

arXiv2026

Max-Min Secrecy Rate Optimization for Secure ISAC Networks: Global Optimization and Low-Complexity Algorithm

In this paper, we investigate a secure integrated sensing and communication (ISAC) system in which multiple communication users (CUs) coexist with multiple untrusted sensing users (SUs) that may eavesdrop on the confidential information intended for the CUs. To promote security fairness among users, we formulate a max-min secrecy rate optimization problem subject to a transmit power budget and sensing quality requirements characterized by beampattern matching error constraints. The resulting design problem is highly non-convex due to the secrecy rate expressions and non-convex sensing constraints. To address these challenges, we first reformulate the problem using semidefinite relaxation (SDR). Based on the reformulated problem, we develop a branch-and-bound (BB) framework combined with convex relaxations to obtain the globally optimal solution within a prescribed accuracy. To further reduce computational complexity, we propose a low-complexity algorithm based on successive convex approximation (SCA), which iteratively solves a sequence of convex subproblems and converges to a local solution. Numerical results demonstrate that the proposed BB algorithm achieves the global optimum and provides a benchmark for performance evaluation. Moreover, the proposed SCA-based algorithm attains near-optimal secrecy performance with significantly lower computational complexity, making it attractive for practical ISAC deployments.

eess.SP↗

arXiv2026

Electrostatic Gating of Ionic Conductance Through Heterogeneous van der Waals Nanopores

Nanofluidic ionic transistors typically require gate voltages above 1 V and operate only at sub millimolar ionic strengths, limiting their biocompatible applications. We demonstrate ionic transistors consisting of single sub 10 nm nanopores drilled in van der Waals (vdW) heterostructures with internal gate electrodes made of few layer graphene. These devices deliver up to 10fold current modulation at gate voltages as low as 0.3 V in 10 mM KCl, and 2fold modulation at near physiological 100 mM KCl. Baseline conductance with no gate shows surface charge dominated transport below 100 mM KCl consistent with negatively charged hBN walls and 5 nm opening of the pores. The surface charge and the electrochemical asymmetry introduced by the three electrode configuration govern the device behavior: negative gate voltage (VG) enriches ionic concentrations and enhances current, whereas positive VG induces a local depletion zone that suppresses transport. The current modulation by VG is dependent on the polarity of the transmembrane potential and leads to ion current rectification. Molecular dynamics simulations of a nanopore in a hBN graphene hBN stack reveal confinement and surface charge dependent suppression of relative permittivity of interfacial water. Continuum modeling with radially varying interfacial water permittivity reproduces the asymmetric IV characteristics and explains how the embedded gate sculpts local potential and ion concentrations. By enabling sub 0.5 V control of ionic transport at up to 100 mM salt concentrations, these devices address a key barrier in nanofluidics and open the pathway to low power ionic circuits and biosensing.

cond-mat.mtrl-sci↗

arXiv2025

Large Neighborhood and Hybrid Genetic Search for Inventory Routing Problems

The inventory routing problem (IRP) focuses on jointly optimizing inventory and distribution operations from a supplier to retailers over multiple days. Compared to other problems from the vehicle routing family, the interrelations between inventory and routing decisions render IRP optimization more challenging and call for advanced solution techniques. A few studies have focused on developing large neighborhood search approaches for this class of problems, but this remains a research area with vast possibilities due to the challenges related to the integration of inventory and routing decisions. In this study, we advance this research area by developing a new large neighborhood search operator tailored for the IRP. Specifically, the operator optimally removes and reinserts all visits to a specific retailer while minimizing routing and inventory costs. We propose an efficient tailored dynamic programming algorithm that exploits preprocessing and acceleration strategies. The operator is used to build an effective local search routine, and included in a state-of-the-art routing algorithm, i.e., Hybrid Genetic Search (HGS). Through extensive computational experiments, we demonstrate that the resulting heuristic algorithm leads to solutions of unmatched quality up to this date, especially on large-scale benchmark instances.

cs.NE↗

arXiv2025

Fairness-Aware Secure Communication in ISAC Systems with STAR-RIS and RSMA

In this paper, we investigate the integration of simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) with rate-splitting multiple access (RSMA) for improving physical layer security (PLS) in integrated sensing and communication (ISAC) systems. Specifically, we consider a multi-user, multi-sensing target scenario, where each sensing target is treated as a potential eavesdropper, reflecting realistic deployment conditions. To enable fairness-aware secure communication among users while maintaining sensing performance, we formulate a joint optimization problem that designs the base station beamforming vectors and STAR-RIS coefficients, aiming to maximize the minimum secrecy rate under a minimum beampattern gain constraint. To solve the resulting non-convex problem, we propose an efficient algorithm based on alternating optimization (AO) and the majorization-minimization (MM) method. Simulation results verify the fast convergence of the proposed algorithm and demonstrate significant improvements in secure communication performance.

eess.SP↗

arXiv2025

The Kernel and Image of Orbit Homomorphisms for the Witt Algebra

The Witt algebra $W_{\geq -1}$ is the Lie algebra of algebraic vector fields on a line. We investigate the two-sided ideal structure of its universal enveloping algebra, by studying the orbit homomorphisms $Ψ_n: U(W_{\geq -1}) \rightarrow T_n$, an infinite family of homomorphisms to noncommutative Noetherian algebras. The orbit homomorphisms lift primitive ideals from solvable Lie algebras to $U(W_{\geq -1})$, thereby playing a central role in the orbit method for the Witt algebra. We prove that the kernel of any orbit homomorphism is generated by an infinite set of differentiators as a one-sided ideal, whilst being generated by any single element of this set as a two-sided ideal. One consequence is an explicit description of primitive and semi-primitive ideals of $U(W_{\geq -1})$ corresponding to one-point local functions. We also prove that the image $B_n$ of the nth orbit homomorphism is both non-Noetherian and birational to the Noetherian algebra $T_n$. On the other hand, the degree zero subring of $B_n$ is left and right Noetherian, and we conjecture that the same holds for $U(W_{\geq -1})$.

math.RA↗

arXiv2025

The orbit method for the Virasoro algebra

Let $W = \mathbb{C}[t, t^{-1}]\partial_t$ be the Witt algebra of algebraic vector fields on $\mathbb{C}^\times$ and let $V\!ir$ be the Virasoro algebra, the unique nontrivial central extension of $W$. In 2023, Petukhov and Sierra showed that Poisson primitive ideals of $\mathrm{S}(W)$ and $\mathrm{S}(V\!ir)$ can be constructed from elements of $W^*$ and $V\!ir^*$ of a particular form, called local functions. In this paper, we show how to use a local function on $W$ or $V\!ir$ to construct a representation of the Lie algebra. We further show that the annihilators of these representations are new completely prime primitive ideals of $\mathrm{U}(W)$ and $\mathrm{U}(V\!ir)$. We use this to define a Dixmier map from the Poisson primitive spectrum of $\mathrm{S}(V\!ir)$, respectively $\mathrm{S}(W)$, to the primitive spectrum of $\mathrm{U}(V\!ir)$, respectively $\mathrm{U}(W)$, successfully extending the orbit method from finite-dimensional solvable Lie algebras to our countable-dimensional setting. Our method involves new ring homomorphisms from $\mathrm{U}(W)$ to the tensor product of a localized Weyl algebra and the enveloping algebra of a finite-dimensional solvable subquotient of $W$. We further show that the kernels of these homomorphisms are intersections of the primitive ideals constructed from natural subsets of $W^*$. As a corollary, we disprove the conjecture that any primitive ideal of $\mathrm{U}(W)$ is the kernel of some map from $\mathrm{U}(W)$ to the first Weyl algebra.

math.RA↗

arXiv2024

Molecular Fingerprints of Ice Surfaces in Sum Frequency Generation Spectra: a First Principles Machine Learning Study

Understanding the molecular-level structure and dynamics of ice surfaces is crucial for deciphering several chemical, physical, and atmospheric processes. Vibrational sum-frequency generation (SFG) spectroscopy is the most prominent tool for probing the molecular-level structure of the air--ice interface as it is a surface-specific technique, but the molecular interpretation of SFG spectra is challenging. This study utilizes a machine-learning potential, along with dipole and polarizability models trained on ab initio data, to calculate the SFG spectrum of the air--ice interface. At temperatures below ice surface premelting, our simulations support the presence of a proton-ordered arrangement at the Ice Ih surface, similar to that seen in Ice XI. Additionally, our simulations provide insight into the assignment of SFG peaks to specific molecular configurations where possible and assess the contribution of subsurface layers to the overall SFG spectrum. These insights enhance our understanding and interpretation of vibrational studies of environmental chemistry at the ice surface.

physics.chem-ph↗

arXiv2024

Nuclear Quantum Effects on the Electronic Structure of Water and Ice

The electronic properties and optical response of ice and water are intricately shaped by their molecular structure, including the quantum mechanical nature of hydrogen atoms. In spite of numerous studies appeared over decades, a comprehensive understanding of the effect of the nuclear quantum motion on the electronic structure of water and ice at finite temperatures remains elusive. Here, we utilize molecular simulations that harness the efficiency of machine-learning potentials and many-body perturbation theory to assess the impact of nuclear quantum effects on the electronic structure of water and hexagonal ice. By comparing the results of path-integral and classical simulations, we find that including nuclear quantum effects leads to a larger renormalization of the fundamental gap of ice, compared to that of water, eventually leading to a comparable gap in the two systems, consistent with experimental estimates. Our calculations suggest that the quantum fluctuations responsible for an increased delocalization of protons in ice, relative to water, are a key factor leading to the enhancement of nuclear quantum effects on the electronic structure of ice.

physics.chem-ph↗

arXiv2024

Distance-Dependent Evolution of Electronic States in Kagome- Honeycomb Lateral Heterostructures in FeSn

In this work, we demonstrate the formation and electronic influence of lateral heterointerfaces in FeSn containing Kagome and honeycomb layers. Lateral heterostructures offer spatially resolved property control, enabling the integration of dissimilar materials and promoting phenomena not typically observed in vertical heterostructures. Using the molecular beam epitaxy technique, we achieve a controllable synthesis of lateral heterostructures in the Kagome metal FeSn. With scanning tunneling microscopy/spectroscopy in conjunction with first-principles calculations, we provide a comprehensive understanding of the bonding motif connecting the Fe3Sn-terminated Kagome and Sn2-terminated honeycomb surfaces. More importantly, we reveal a distance-dependent evolution of the electronic states in the vicinity of the heterointerfaces. This evolution is significantly influenced by the orbital character of the flat bands. Our findings suggest an approach to modulate the electronic properties of the Kagome lattice, which should be beneficial for the development of future quantum devices.

cond-mat.str-el↗

arXiv2023

Spectroscopy-Guided Discovery of Three-Dimensional Structures of Disordered Materials with Diffusion Models

The ability to rapidly develop materials with desired properties has a transformative impact on a broad range of emerging technologies. In this work, we introduce a new framework based on the diffusion model, a recent generative machine learning method to predict 3D structures of disordered materials from a target property. For demonstration, we apply the model to identify the atomic structures of amorphous carbons ($a$-C) as a representative material system from the target X-ray absorption near edge structure (XANES) spectra--a common experimental technique to probe atomic structures of materials. We show that conditional generation guided by XANES spectra reproduces key features of the target structures. Furthermore, we show that our model can steer the generative process to tailor atomic arrangements for a specific XANES spectrum. Finally, our generative model exhibits a remarkable scale-agnostic property, thereby enabling generation of realistic, large-scale structures through learning from a small-scale dataset (i.e., with small unit cells). Our work represents a significant stride in bridging the gap between materials characterization and atomic structure determination; in addition, it can be leveraged for materials discovery in exploring various material properties as targeted.

cond-mat.mtrl-sci↗

arXiv2023

Robust Training of Machine Learning Interatomic Potentials with Dimensionality Reduction and Stratified Sampling

Machine learning interatomic potentials (MLIPs) enable the accurate simulation of materials at larger sizes and time scales, and play increasingly important roles in the computational understanding and design of materials. However, MLIPs are only as accurate and robust as the data they are trained on. In this work, we present DImensionality-Reduced Encoded Clusters with sTratified (DIRECT) sampling as an approach to select a robust training set of structures from a large and complex configuration space. By applying DIRECT sampling on the Materials Project relaxation trajectories dataset with over one million structures and 89 elements, we develop an improved materials 3-body graph network (M3GNet) universal potential that extrapolate more reliably to unseen structures. We further show that molecular dynamics (MD) simulations with universal potentials such as M3GNet can be used in place of expensive \textit{ab initio} MD to rapidly create a large configuration space for target materials systems. Combined with DIRECT sampling, we develop a highly reliable moment tensor potential for Ti-H system without the need for iterative optimization. This work paves the way towards robust high throughput development of MLIPs across any compositional complexity.

cond-mat.mtrl-sci↗

arXiv2023

Inorganic synthesis-structure maps in zeolites with machine learning and crystallographic distances

Zeolites are inorganic materials known for their diversity of applications, synthesis conditions, and resulting polymorphs. Although their synthesis is controlled both by inorganic and organic synthesis conditions, computational studies of zeolite synthesis have focused mostly on organic template design. In this work, we use a strong distance metric between crystal structures and machine learning (ML) to create inorganic synthesis maps in zeolites. Starting with 253 known zeolites, we show how the continuous distances between frameworks reproduce inorganic synthesis conditions from the literature without using labels such as building units. An unsupervised learning analysis shows that neighboring zeolites according to our metric often share similar inorganic synthesis conditions, even in template-based routes. In combination with ML classifiers, we find synthesis-structure relationships for 14 common inorganic conditions in zeolites, namely Al, B, Be, Ca, Co, F, Ga, Ge, K, Mg, Na, P, Si, and Zn. By explaining the model predictions, we demonstrate how (dis)similarities towards known structures can be used as features for the synthesis space. Finally, we show how these methods can be used to predict inorganic synthesis conditions for unrealized frameworks in hypothetical databases and interpret the outcomes by extracting local structural patterns from zeolites. In combination with template design, this work can accelerate the exploration of the space of synthesis conditions for zeolites.

cond-mat.mtrl-sci↗

arXiv2022

Tuning the Many-body Interactions in a Helical Luttinger Liquid

In one-dimensional (1D) systems, electronic interactions lead to a breakdown of Fermi liquid theory and the formation of a Tomonaga-Luttinger Liquid (TLL). The strength of its many-body correlations can be quantified by a single dimensionless parameter, the Luttinger parameter $K$, characterising the competition between the electrons' kinetic and electrostatic energies. Recently, signatures of a TLL have been reported for the topological edge states of quantum spin Hall (QSH) insulators, strictly 1D electronic structures with linear (Dirac) dispersion and spin-momentum locking. Here we show that the many-body interactions in such helical Luttinger Liquid can be effectively controlled by the edge state's dielectric environment. This is reflected in a tunability of the Luttinger parameter $K$, distinct on different edges of the crystal, and extracted to high accuracy from the statistics of tunnelling spectra at tens of tunneling points. The interplay of topology and many-body correlations in 1D helical systems has been suggested as a potential avenue towards realising non-Abelian parafermions.

cond-mat.str-el↗

arXiv2022

Efficient, Interpretable Graph Neural Network Representation for Angle-dependent Properties and its Application to Optical Spectroscopy

Graph neural networks are attractive for learning properties of atomic structures thanks to their intuitive graph encoding of atoms and bonds. However, conventional encoding does not include angular information, which is critical for describing atomic arrangements in disordered systems. In this work, we extend the recently proposed ALIGNN encoding, which incorporates bond angles, to also include dihedral angles (ALIGNN-d). This simple extension leads to a memory-efficient graph representation that captures the complete geometry of atomic structures. ALIGNN-d is applied to predict the infrared optical response of dynamically disordered Cu(II) aqua complexes, leveraging the intrinsic interpretability to elucidate the relative contributions of individual structural components. Bond and dihedral angles are found to be critical contributors to the fine structure of the absorption response, with distortions representing transitions between more common geometries exhibiting the strongest absorption intensity. Future directions for further development of ALIGNN-d are discussed.

cs.LG↗

arXiv2020

Arc Routing with Time-Dependent Travel Times and Paths

Vehicle routing algorithms usually reformulate the road network into a complete graph in which each arc represents the shortest path between two locations. Studies on time-dependent routing followed this model and therefore defined the speed functions on the complete graph. We argue that this model is often inadequate, in particular for arc routing problems involving services on edges of a road network. To fill this gap, we formally define the time-dependent capacitated arc routing problem (TDCARP), with travel and service speed functions given directly at the network level. Under these assumptions, the quickest path between locations can change over time, leading to a complex problem that challenges the capabilities of current solution methods. We introduce effective algorithms for preprocessing quickest paths in a closed form, efficient data structures for travel time queries during routing optimization, as well as heuristic and exact solution approaches for the TDCARP. Our heuristic uses the hybrid genetic search principle with tailored solution-decoding algorithms and lower bounds for filtering moves. Our branch-and-price algorithm exploits dedicated pricing routines, heuristic dominance rules and completion bounds to find optimal solutions for problem counting up to 75 services. Based on these algorithms, we measure the benefits of time-dependent routing optimization for different levels of travel-speed data accuracy.

cs.DS↗