Showing 1–15 of 15 results for author: Cheng, T S

In-situ Silicon Doped hBN by High-Temperature Molecular Beam Epitaxy Enables Single Photon Emission

Authors: Jiyun Kim, Nika Teran, Juliette Plo, Jonathan Bradford, Guillaume Cassabois, Amy F. M. Collins, Tin S. Cheng, Christopher J. Mellor, Shery L. Y. Chang, Sergei V. Novikov, Igor Aharonovich

Abstract: Hexagonal boron nitride (hBN) has emerged as a leading host for optically active quantum defects. Yet introduction of specific impurity species other than carbon remains unexplored. Here, we demonstrate an in-situ silicon doping of hBN grown by high-temperature molecular beam epitaxy (HT-MBE). By systematically varying the growth temperature from 900 to 1390 °C under a constant silicon flux, we es… ▽ More Hexagonal boron nitride (hBN) has emerged as a leading host for optically active quantum defects. Yet introduction of specific impurity species other than carbon remains unexplored. Here, we demonstrate an in-situ silicon doping of hBN grown by high-temperature molecular beam epitaxy (HT-MBE). By systematically varying the growth temperature from 900 to 1390 °C under a constant silicon flux, we establish an optimal window for Si incorporation to host a diverse range of emitters from 430-750 nm at room temperature. By transferring silicon-doped hBN film on SiO$_2$ substrate, we verified that single photon emitter activity was sustained in the hBN, demonstrating compatibility with device integration. The plausible origins of the observed optical transitions were discussed, and several potential candidates were proposed. Our results demonstrate a step toward a comprehensive understanding of in-situ doping of hBN and its utilization for quantum photonic applications. △ Less

Submitted 1 June, 2026; originally announced June 2026.

Optimizer choice matters for the emergence of Neural Collapse

Authors: Jim Zhao, Tin Sum Cheng, Wojciech Masarczyk, Aurelien Lucchi

Abstract: Neural Collapse (NC) refers to the emergence of highly symmetric geometric structures in the representations of deep neural networks during the terminal phase of training. Despite its prevalence, the theoretical understanding of NC remains limited. Existing analyses largely ignore the role of the optimizer, thereby suggesting that NC is universal across optimization methods. In this work, we chall… ▽ More Neural Collapse (NC) refers to the emergence of highly symmetric geometric structures in the representations of deep neural networks during the terminal phase of training. Despite its prevalence, the theoretical understanding of NC remains limited. Existing analyses largely ignore the role of the optimizer, thereby suggesting that NC is universal across optimization methods. In this work, we challenge this assumption and demonstrate that the choice of optimizer plays a critical role in the emergence of NC. The phenomenon is typically quantified through NC metrics, which, however, are difficult to track and analyze theoretically. To overcome this limitation, we introduce a novel diagnostic metric, NC0, whose convergence to zero is a necessary condition for NC. Using NC0, we provide theoretical evidence that NC cannot emerge under decoupled weight decay in adaptive optimizers, as implemented in AdamW. Concretely, we prove that SGD, SignGD with coupled weight decay (a special case of Adam), and SignGD with decoupled weight decay (a special case of AdamW) exhibit qualitatively different NC0 dynamics. Also, we show the accelerating effect of momentum on NC (beyond convergence of train loss) when trained with SGD, being the first result concerning momentum in the context of NC. Finally, we conduct extensive empirical experiments consisting of 3,900 training runs across various datasets, architectures, optimizers, and hyperparameters, confirming our theoretical results. This work provides the first theoretical explanation for optimizer-dependent emergence of NC and highlights the overlooked role of weight-decay coupling in shaping the implicit biases of optimizers. △ Less

Submitted 25 February, 2026; v1 submitted 18 February, 2026; originally announced February 2026.

Comments: Published as a conference paper at ICLR 2026

Spectral Analysis of Molecular Features: When Richer Features Do Not Guarantee Better Generalization

Authors: Asma Jamali, Tin Sum Cheng, Rodrigo A. Vargas-Hernández

Abstract: The spectral properties of feature embeddings offer critical insights into model generalization and representation quality. While deep learning models are widely used for molecular property prediction, kernel methods remain competitive in low-data regimes, yet their spectral behavior is largely unexplored. We present the first comprehensive spectral analysis of kernel ridge regression across diver… ▽ More The spectral properties of feature embeddings offer critical insights into model generalization and representation quality. While deep learning models are widely used for molecular property prediction, kernel methods remain competitive in low-data regimes, yet their spectral behavior is largely unexplored. We present the first comprehensive spectral analysis of kernel ridge regression across diverse representations-including molecular fingerprints (ECFP), pretrained transformers, graph neural networks, and 3D descriptors-evaluated on QM9 and 3 MoleculeNet benchmarks. Surprisingly, richer spectral features do not consistently yield better generalization performance, contradicting common representation heuristics used in self-supervised learning (SSL). Across 4 spectral metrics, only ECFP-based kernels show a strictly positive correlation with performance. Transformer and global 3D representations exhibit mixed behavior, whereas local 3D representations show consistently negative correlations. Truncation analysis further emphasizes this disparity: for local 3D representations on thermodynamic targets, fewer than 2\% of eigenvalues (and occasionally as few as 0.02\%) are needed to recover 95\% of performance, whereas ECFP and transformer kernels require significantly more. By demonstrating a strong dependence on both task and representation, our results challenge the heuristic that richer spectra inherently improve generalization, providing new guidance for evaluating representations in SSL and in label-limited scientific tasks. △ Less

Submitted 12 June, 2026; v1 submitted 15 October, 2025; originally announced October 2025.

Comments: 11 pages, 7 figures, 3 tables, SI: 13 pages, 9 figures, 4 Tables

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data

Authors: Anastasis Kratsios, Tin Sum Cheng, Daniel Roy

Abstract: At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal, as they assume noiseless data and allow network parameters to be chosen freely, independent of algorithmic realism. This paper bridges that gap by introducing a… ▽ More At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal, as they assume noiseless data and allow network parameters to be chosen freely, independent of algorithmic realism. This paper bridges that gap by introducing an architecture-specific randomized training algorithm that constructs a uniform approximator from $N$ noisy training samples on the $d$-dimensional cube $[0,1]^d$. Our trained neural networks attain the minimax-optimal quantity of \textit{trainable} (non-random) parameters, subject to logarithmic factors which vanish under the idealized noiseless sampling assumed in classical UATs. Additionally, our trained models replicate key behaviours of real-world neural networks, absent in standard UAT constructions, by: (1) exhibiting sub-linear parametric complexity when fine-tuning on structurally related and favourable out-of-distribution tasks, (2) exactly interpolating the training data, and (3) maintaining reasonable Lipschitz regularity (after the initial clustering attention layer). These properties bring state-of-the-art UATs closer to practical machine learning, shifting the central open question from algorithmic implementability with noisy samples to whether stochastic gradient descent can achieve comparable guarantees. △ Less

Submitted 31 August, 2025; originally announced September 2025.

MSC Class: 68T07; 68Q32; 68T05; 41A65 ACM Class: F.1.3; G.1.2; F.1.3

Sharp Generalization Bounds for Foundation Models with Asymmetric Randomized Low-Rank Adapters

Authors: Anastasis Kratsios, Tin Sum Cheng, Aurelien Lucchi, Haitz Sáez de Ocáriz Borde

Abstract: Low-Rank Adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning (PEFT) technique for foundation models. Recent work has highlighted an inherent asymmetry in the initialization of LoRA's low-rank factors, which has been present since its inception and was presumably derived experimentally. This paper focuses on providing a comprehensive theoretical characterization of asy… ▽ More Low-Rank Adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning (PEFT) technique for foundation models. Recent work has highlighted an inherent asymmetry in the initialization of LoRA's low-rank factors, which has been present since its inception and was presumably derived experimentally. This paper focuses on providing a comprehensive theoretical characterization of asymmetric LoRA with frozen random factors. First, while existing research provides upper-bound generalization guarantees based on averages over multiple experiments, the behaviour of a single fine-tuning run with specific random factors remains an open question. We address this by investigating the concentration of the typical LoRA generalization gap around its mean. Our main upper bound reveals a sample complexity of $\tilde{\mathcal{O}}\left(\frac{\sqrt{r}}{\sqrt{N}}\right)$ with high probability for rank $r$ LoRAs trained on $N$ samples. Additionally, we also determine the fundamental limits in terms of sample efficiency, establishing a matching lower bound of $\mathcal{O}\left(\frac{1}{\sqrt{N}}\right)$. By more closely reflecting the practical scenario of a single fine-tuning run, our findings offer crucial insights into the reliability and practicality of asymmetric LoRA. △ Less

Submitted 17 June, 2025; originally announced June 2025.

Unpacking Softmax: How Temperature Drives Representation Collapse, Compression, and Generalization

Authors: Wojciech Masarczyk, Mateusz Ostaszewski, Tin Sum Cheng, Tomasz Trzciński, Aurelien Lucchi, Razvan Pascanu

Abstract: The softmax function is a fundamental building block of deep neural networks, commonly used to define output distributions in classification tasks or attention weights in transformer architectures. Despite its widespread use and proven effectiveness, its influence on learning dynamics and learned representations remains poorly understood, limiting our ability to optimize model behavior. In this pa… ▽ More The softmax function is a fundamental building block of deep neural networks, commonly used to define output distributions in classification tasks or attention weights in transformer architectures. Despite its widespread use and proven effectiveness, its influence on learning dynamics and learned representations remains poorly understood, limiting our ability to optimize model behavior. In this paper, we study the pivotal role of the softmax function in shaping the model's representation. We introduce the concept of rank deficit bias - a phenomenon in which softmax-based deep networks find solutions of rank much lower than the number of classes. This bias depends on the softmax function's logits norm, which is implicitly influenced by hyperparameters or directly modified by softmax temperature. Furthermore, we demonstrate how to exploit the softmax dynamics to learn compressed representations or to enhance their performance on out-of-distribution data. We validate our findings across diverse architectures and real-world datasets, highlighting the broad applicability of temperature tuning in improving model performance. Our work provides new insights into the mechanisms of softmax, enabling better control over representation learning in deep neural networks. △ Less

Submitted 2 June, 2025; originally announced June 2025.

Optically detected magnetic resonance of wafer-scale hexagonal boron nitride thin films

Authors: Sam C. Scholten, Jakub Iwański, Kaijian Xing, Johannes Binder, Aleksandra K. Dąbrowska, Hark H. Tan, Tin S. Cheng, Jonathan Bradford, Christopher J. Mellor, Peter H. Beton, Sergei V. Novikov, Jan Mischke, Sergej Pasko, Emre Yengel, Alexander Henning, Simonas Krotkus, Andrzej Wysmołek, Jean-Philippe Tetienne

Abstract: Hexagonal boron nitride (hBN) has recently been shown to host native defects exhibiting optically detected magnetic resonance (ODMR) with applications in nanoscale magnetic sensing and imaging. To advance these applications, deposition methods to create wafer-scale hBN films with controlled thicknesses are desirable, but a systematic study of the ODMR properties of the resultant films is lacking.… ▽ More Hexagonal boron nitride (hBN) has recently been shown to host native defects exhibiting optically detected magnetic resonance (ODMR) with applications in nanoscale magnetic sensing and imaging. To advance these applications, deposition methods to create wafer-scale hBN films with controlled thicknesses are desirable, but a systematic study of the ODMR properties of the resultant films is lacking. Here we perform ODMR measurements of thin films (3-2000nm thick) grown via three different methods: metal-organic chemical vapour deposition (MOCVD), chemical vapour deposition (CVD), and molecular beam epitaxy (MBE). We find that they all exhibit an ODMR response, including the thinnest 3nm film, albeit with different characteristics. The best volume-normalised magnetic sensitivity obtained is 30uT/sqrt(Hz um^3). We study the effect of growth temperature on a series of MOCVD samples grown under otherwise fixed conditions and find 800-900C to be an optimum range for magnetic sensitivity, with a significant improvement (up to two orders of magnitude) from post-growth annealing. This work provides a useful baseline for the magnetic sensitivity of hBN thin films deposited via standard methods and informs the feasibility of future sensing applications. △ Less

Submitted 27 May, 2025; originally announced May 2025.

A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression

Authors: Tin Sum Cheng, Aurelien Lucchi, Anastasis Kratsios, David Belius

Abstract: This paper conducts a comprehensive study of the learning curves of kernel ridge regression (KRR) under minimal assumptions. Our contributions are three-fold: 1) we analyze the role of key properties of the kernel, such as its spectral eigen-decay, the characteristics of the eigenfunctions, and the smoothness of the kernel; 2) we demonstrate the validity of the Gaussian Equivalent Property (GEP),… ▽ More This paper conducts a comprehensive study of the learning curves of kernel ridge regression (KRR) under minimal assumptions. Our contributions are three-fold: 1) we analyze the role of key properties of the kernel, such as its spectral eigen-decay, the characteristics of the eigenfunctions, and the smoothness of the kernel; 2) we demonstrate the validity of the Gaussian Equivalent Property (GEP), which states that the generalization performance of KRR remains the same when the whitened features are replaced by standard Gaussian vectors, thereby shedding light on the success of previous analyzes under the Gaussian Design Assumption; 3) we derive novel bounds that improve over existing bounds across a broad range of setting such as (in)dependent feature vectors and various combinations of eigen-decay rates in the over/underparameterized regimes. △ Less

Submitted 23 October, 2024; originally announced October 2024.

Characterizing Overfitting in Kernel Ridgeless Regression Through the Eigenspectrum

Authors: Tin Sum Cheng, Aurelien Lucchi, Anastasis Kratsios, David Belius

Abstract: We derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in the over-parameterized regime for a fixed input dimension. For kernels with polynomial spectral decay, we recover the bound from previous work; for exponential decay, our bound is non-trivial and novel. Our contribution is… ▽ More We derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in the over-parameterized regime for a fixed input dimension. For kernels with polynomial spectral decay, we recover the bound from previous work; for exponential decay, our bound is non-trivial and novel. Our contribution is two-fold: (i) we rigorously prove the phenomena of tempered overfitting and catastrophic overfitting under the sub-Gaussian design assumption, closing an existing gap in the literature; (ii) we identify that the independence of the features plays an important role in guaranteeing tempered overfitting, raising concerns about approximating KRR generalization using the Gaussian design assumption in previous literature. △ Less

Submitted 29 May, 2024; v1 submitted 2 February, 2024; originally announced February 2024.

A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression

Authors: Tin Sum Cheng, Aurelien Lucchi, Ivan Dokmanić, Anastasis Kratsios, David Belius

Abstract: Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a pre-trained deep neural network's last layer to adapt it to a novel task when performing transfer learning. We address this gap for finite-rank kernel ridge regres… ▽ More Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a pre-trained deep neural network's last layer to adapt it to a novel task when performing transfer learning. We address this gap for finite-rank kernel ridge regression (KRR) by deriving sharp non-asymptotic upper and lower bounds for the KRR test error of any finite-rank KRR. Our bounds are tighter than previously derived bounds on finite-rank KRR, and unlike comparable results, they also remain valid for any regularization parameters. △ Less

Submitted 3 October, 2023; v1 submitted 2 October, 2023; originally announced October 2023.

A Tale of Two Cultures: Comparing Interpersonal Information Disclosure Norms on Twitter

Authors: Mainack Mondal, Anju Punuru, Tyng-Wen Scott Cheng, Kenneth Vargas, Chaz Gundry, Nathan S Driggs, Noah Schill, Nathaniel Carlson, Josh Bedwell, Jaden Q Lorenc, Isha Ghosh, Yao Li, Nancy Fulda, Xinru Page

Abstract: We present an exploration of cultural norms surrounding online disclosure of information about one's interpersonal relationships (such as information about family members, colleagues, friends, or lovers) on Twitter. The literature identifies the cultural dimension of individualism versus collectivism as being a major determinant of offline communication differences in terms of emotion, topic, and… ▽ More We present an exploration of cultural norms surrounding online disclosure of information about one's interpersonal relationships (such as information about family members, colleagues, friends, or lovers) on Twitter. The literature identifies the cultural dimension of individualism versus collectivism as being a major determinant of offline communication differences in terms of emotion, topic, and content disclosed. We decided to study whether such differences also occur online in context of Twitter when comparing tweets posted in an individualistic (U.S.) versus a collectivist (India) society. We collected more than 2 million tweets posted in the U.S. and India over a 3 month period which contain interpersonal relationship keywords. A card-sort study was used to develop this culturally-sensitive saturated taxonomy of keywords that represent interpersonal relationships (e.g., ma, mom, mother). Then we developed a high-accuracy interpersonal disclosure detector based on dependency-parsing (F1-score: 86%) to identify when the words refer to a personal relationship of the poster (e.g., "my mom" as opposed to "a mom"). This allowed us to identify the 400K+ tweets in our data set which actually disclose information about the poster's interpersonal relationships. We used a mixed methods approach to analyze these tweets (e.g., comparing the amount of joy expressed about one's family) and found differences in emotion, topic, and content disclosed between tweets from the U.S. versus India. Our analysis also reveals how a combination of qualitative and quantitative methods are needed to uncover these differences; Using just one or the other can be misleading. This study extends the prior literature on Multi-Party Privacy and provides guidance for researchers and designers of culturally-sensitive systems. △ Less

Submitted 26 September, 2023; originally announced September 2023.

Comments: This work will be presented at the 26th ACM Conference on Computer-Supported Cooperative Work and Social Computing (CSCW 2023). This paper will also be published in The Proceedings of the ACM on Human Computer Interaction

Cathodoluminescence spectroscopy of monolayer hexagonal boron nitride

Authors: K. Shima, T. S. Cheng, C. J. Mellor, P. H. Beton, C. Elias, P. Valvin, B. Gil, G. Cassabois, S. V. Novikov, S. F. Chichibu

Abstract: Cathodoluminescence (CL) spectroscopy is a powerful technique for studying emission properties of optoelectronic materials because CL is free from excitable bandgap limits and from ambiguous signals due to simple light scattering and resonant Raman scattering potentially involved in the photoluminescence (PL) spectra. However, direct CL measurements of atomically thin two-dimensional materials, su… ▽ More Cathodoluminescence (CL) spectroscopy is a powerful technique for studying emission properties of optoelectronic materials because CL is free from excitable bandgap limits and from ambiguous signals due to simple light scattering and resonant Raman scattering potentially involved in the photoluminescence (PL) spectra. However, direct CL measurements of atomically thin two-dimensional materials, such as transition metal dichalcogenides and hexagonal boron nitride (hBN), have been difficult due to the small excitation volume that interacts with high-energy electron beams (e-beams). Herein, distinct CL signals from a monolayer hBN, namely mBN, epitaxial film grown on a highly oriented pyrolytic graphite substrate are shown by using a home-made CL system capable of large-area and surface-sensitive excitation by an e-beam. The spatially resolved CL spectra at 13 K exhibited a predominant 5.5-eV emission band, which has been ascribed to originate from multilayered aggregates of hBN, markedly at thicker areas formed on the step edges of the substrate. Conversely, a faint peak at 6.04 eV was routinely observed from atomically flat areas. Since the energy agreed with the PL peak of 6.05 eV at 10 K that has been assigned as being due to the recombination of phonon-assisted direct excitons of mBN by Elias et al. [Nat. Commun. 10, 2639 (2019)], the CL peak at 6.04 eV is attributed to originate from the mBN epilayer. The CL results support the transition from indirect bandgap in bulk hBN to direct bandgap in mBN, in analogy with molybdenum disulfide. The results also encourage to elucidate emission properties of other low-dimensional materials with reduced excitation volumes by using the present CL configuration. △ Less

Submitted 17 May, 2023; originally announced May 2023.

Comments: 7 pages, 3 figures

Band gap measurements of monolayer h-BN and insights into carbon-related point defects

Authors: Ricardo Javier Peña Román, Fábio J R Costa Costa, Alberto Zobelli, Christine Elias, Pierre Valvin, Guillaume Cassabois, Bernard Gil, Alex Summerfield, Tin S Cheng, Christopher J Mellor, Peter H Beton, Sergei V Novikov, Luiz F Zagonel

Abstract: Being a flexible wide band gap semiconductor, hexagonal boron nitride (h-BN) has great potential for technological applications like efficient deep ultraviolet light sources, building block for two-dimensional heterostructures and room temperature single photon emitters in the ultraviolet and visible spectral range. To enable such applications, it is mandatory to reach a better understanding of th… ▽ More Being a flexible wide band gap semiconductor, hexagonal boron nitride (h-BN) has great potential for technological applications like efficient deep ultraviolet light sources, building block for two-dimensional heterostructures and room temperature single photon emitters in the ultraviolet and visible spectral range. To enable such applications, it is mandatory to reach a better understanding of the electronic and optical properties of h-BN and the impact of various structural defects. Despite the large efforts in the last years, aspects such as the electronic band gap value, the exciton binding energy and the effect of point defects remained elusive, particularly when considering a single monolayer. Here, we directly measured the density of states of a single monolayer of h-BN epitaxially grown on highly oriented pyrolytic graphite, by performing low temperature scanning tunneling microscopy (STM) and spectroscopy (STS). The observed h-BN electronic band gap on defect-free regions is $(6.8\pm0.2)$ eV. Using optical spectroscopy to obtain the h-BN optical band gap, the exciton binding energy is determined as being of $(0.7\pm0.2)$ eV. In addition, the locally excited cathodoluminescence and photoluminescence show complex spectra that are typically associated to intragap states related to carbon defects. Moreover, in some regions of the monolayer h-BN we identify, using STM, point defects which have intragap electronic levels around 2.0 eV below the Fermi level. △ Less

Submitted 16 July, 2021; originally announced July 2021.

Comments: 50 Pages, 8 Figures, 100+ references

Journal ref: 2D Material 8 044001 (2021)

Identifying Carbon as the Source of Visible Single Photon Emission from Hexagonal Boron Nitride

Authors: Noah Mendelson, Dipankar Chugh, Jeffrey R. Reimers, Tin S. Cheng, Andreas Gottscholl, Hu Long, Christopher J. Mellor, Alex Zettl, Vladimir Dyakonov, Peter H. Beton, Sergei V. Novikov, Chennupati Jagadish, Hark Hoe Tan, Michael J. Ford, Milos Toth, Carlo Bradac, Igor Aharonovich

Abstract: Single photon emitters (SPEs) in hexagonal boron nitride (hBN) have garnered significant attention over the last few years due to their superior optical properties. However, despite the vast range of experimental results and theoretical calculations, the defect structure responsible for the observed emission has remained elusive. Here, by controlling the incorporation of impurities into hBN and by… ▽ More Single photon emitters (SPEs) in hexagonal boron nitride (hBN) have garnered significant attention over the last few years due to their superior optical properties. However, despite the vast range of experimental results and theoretical calculations, the defect structure responsible for the observed emission has remained elusive. Here, by controlling the incorporation of impurities into hBN and by comparing various synthesis methods, we provide direct evidence that the visible SPEs are carbon related. Room temperature optically detected magnetic resonance (ODMR) is demonstrated on ensembles of these defects. We also perform ion implantation experiments and confirm that only carbon implantation creates SPEs in the visible spectral range. Computational analysis of hundreds of potential carbon-based defect transitions suggest that the emission results from the negatively charged VBCN- defect, which experiences long-range out-of-plane deformations and is environmentally sensitive. Our results resolve a long-standing debate about the origin of single emitters at the visible range in hBN and will be key to deterministic engineering of these defects for quantum photonic devices. △ Less

Submitted 20 April, 2020; v1 submitted 2 March, 2020; originally announced March 2020.

Concept of a Value in Multilevel Security Databases

Authors: Jia Tao, Shashi Gadia, Tsz Shing Cheng

Abstract: This paper has been withdrawn. This paper has been withdrawn. △ Less

Submitted 29 June, 2009; v1 submitted 21 March, 2007; originally announced March 2007.

Comments: This paper has been withdrawn