arXiv subjects

Dongwei Chen

Publications and source records attributed to Dongwei Chen.

13 recordsLinked to original sources

arXiv2026

A Land of Oblique Duality for Frames and Probabilistic Frames

Functions or distributions used to sample and to reconstruct signals often occur in different domains, like the Dirac delta and a band-limited bump function in classical sampling. Oblique dual frames generalize this phenomenon. In this paper, we provide new tools to study oblique dual frames and introduce a probabilistic variant of oblique dual frames. We first present the oblique dual frame potential and show that it is minimized precisely when the oblique dual coincides with the canonical oblique dual. We then define oblique dual probabilistic frames and oblique approximately dual probabilistic frames. In particular, we prove that for a given oblique dual probabilistic frame, the associated oblique dual probabilistic frame potential is minimized if and only if the frame is tight and the oblique dual is canonical. Moreover, the tightness assumption can be removed when the minimization is restricted to oblique dual probabilistic frames of pushforward type. Finally, we investigate perturbations of oblique dual probabilistic frames and show that if a probability measure is sufficiently close to an oblique dual probabilistic frame pair in the $2$-Wasserstein topology, then it forms an oblique approximately dual probabilistic frame.

math.FA↗

arXiv2025

A note on the c-monotonicity in optimal transport with capacity constraints

This paper studies the geometry of the optimizer for the optimal transport problem with capacity constraints. We introduce the concept of c-capacity monotonicity, which is a generalization of c-cyclical monotonicity in optimal transport. We show that the optimizer of the optimal transport problem with capacity constraints is c-capacity monotone.

math.OC↗

arXiv2025

Approximately Dual and Pseudo-Dual Probabilistic Frames

This paper studies properties of dual probabilistic frames -- in particular in relation to redundancy -- and introduces both approximately dual probabilistic frames and pseudo-dual probabilistic frames. We show that the canonical dual probabilistic frame is the only dual frame of pushforward type of a probabilistic frame with zero redundancy. Furthermore, we show that probabilistic frames with finite redundancy are atomic and finite. Approximately dual probabilistic frames generalize duality, with pseudo-duality being a further generalization. We introduce these concepts and prove certain structural results. In particular, every probabilistic frame has a discrete finite frame as an approximate dual.

math.FA↗

arXiv2025

Beta-Generalized Lindley Distribution: A Novel Probability Model for Wind Speed

Wind speed distribution has many applications, such as the assessment of wind energy and building design. Applying an appropriate statistical distribution to fit the wind speed data, especially on its heavy right tail, is of great interest. In this study, we introduce a novel four-parameter class of generalized Lindley distribution, called the beta-generalized Lindley (BGL) distribution, to fit the wind speed data, which are derived from the annual and long-term measurements of the Flatirons M2 meteorological tower from the years 2010 to 2020 at heights of 10, 20, 50, and 80 meters. In terms of the density fit and various goodness-of-fit metrics, the BGL model outperforms its submodels (beta-Lindley, generalized Lindley, and Lindley) and other reference distributions, such as gamma, beta-Weibull, Weibull, beta-exponential, and Log-Normal. Furthermore, the BGL distribution is more accurate at modeling the long right tail of wind speed, including the $95^{th}$ and $99^{th}$ percentiles and Anderson-Darling statistics at different heights. Therefore, we conclude that the BGL distribution is a strong alternative model for the wind speed distribution.

stat.AP↗

arXiv2025

Probabilistic Dual Frames and Minimization of Dual Frame Potentials

This paper studies probabilistic dual frames and the associated dual frame potentials from the perspective of optimal mass transport. The main contribution of this work shows that given a probabilistic frame, its associated dual frame potential is minimized if and only if the probabilistic frame is tight and the probabilistic dual frame is the canonical dual. In particular, the tightness condition can be dropped if the probabilistic dual frame potential is minimized only among probabilistic dual frames of pushforward type.

math.FA↗

arXiv2025

Probabilistic frames and Wasserstein distances

We use Wasserstein distances to characterize and study probabilistic frames. Adapting results from Olkin and Pukelsheim, from Gelbrich and from Cuesta-Albertos, Matran-Bea and Tuero-Diaz to frame operators, we show that the sets of probabilistic frames with given frame operator are homeomorphic by an optimal linear push-forward. Using the Wasserstein distances, we generalize several recent results in probabilistic frame theory and show path connectedness of the set of probabilistic frames with a fixed frame operator. We also describe transport duals that do not arise as push-forwards and characterize those that are push-forwards.

math.PR↗

arXiv2024

On the Probabilistic Approximation in Reproducing Kernel Hilbert Spaces

This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer theorem to our setting, and especially when the probability measure is finitely supported, or the Hilbert space is finite-dimensional, we show that the probabilistic approximation problem turns out to be a measure quantization problem, which connects the probabilistic function approximation to the sampling theory. Some discussions and examples are also given when the reproducing kernel Hilbert space is infinite-dimensional and the measure is infinitely supported.

math.FA↗

arXiv2023

Paley-Wiener Theorem for Probabilistic Frames

This paper establishes Paley-Wiener perturbation theorems for probabilistic frames. The classical Paley-Wiener perturbation theorem shows that if a sequence is close to a basis in a Banach space, then this sequence is also a basis. Similar perturbation results have been established for frames in Hilbert spaces. In this work, we show that if a probability measure is sufficiently close to a probabilistic frame in an appropriate sense, then this probability measure is also a probabilistic frame. Moreover, we obtain explicit frame bounds for such probability measures that are close to a given probabilistic frame in the $2$-Wasserstein metric. This yields an alternative proof of the fact that the set of probabilistic frames is open in $\mathcal{P}_2(\mathbb{R}^n)$ under the $2$-Wasserstein topology.

math.FA↗

arXiv2023

Rediscover Climate Change during Global Warming Slowdown via Wasserstein Stability Analysis

Climate change is one of the key topics in climate science. However, previous research has predominantly concentrated on changes in mean values, and few research examines changes in Probability Distribution Function (PDF). In this study, a novel method called Wasserstein Stability Analysis (WSA) is developed to identify PDF changes, especially the extreme event shift and non-linear physical value constraint variation in climate change. WSA is applied to 21st-century warming slowdown period and is compared with traditional mean-value trend analysis. The result indicates that despite no significant trend, the central-eastern Pacific experienced a decline in hot extremes and an increase in cold extremes, indicating a La Nina-like temperature shift. Further analysis at two Arctic locations suggests sea ice severely restricts the hot extremes of surface air temperature. This impact is diminishing as sea ice melts. Overall, based on detecting PDF changes, WSA is a useful method for re-discovering climate change.

physics.ao-ph↗

arXiv2021

Densely connected neural networks for nonlinear regression

Densely connected convolutional networks (DenseNet) behave well in image processing. However, for regression tasks, convolutional DenseNet may lose essential information from independent input features. To tackle this issue, we propose a novel DenseNet regression model where convolution and pooling layers are replaced by fully connected layers and the original concatenation shortcuts are maintained to reuse the feature. To investigate the effects of depth and input dimension of proposed model, careful validations are performed by extensive numerical simulation. The results give an optimal depth (19) and recommend a limited input dimension (under 200). Furthermore, compared with the baseline models including support vector regression, decision tree regression, and residual regression, our proposed model with the optimal depth performs best. Ultimately, DenseNet regression is applied to predict relative humidity, and the outcome shows a high correlation (0.91) with observations, which indicates that our model could advance environmental data analysis.

cs.LG↗

arXiv2020

S3Library: Automatically Eliminating C/C++ Buffer Overflow using Compatible Safer Libraries

Annex K of C11, bounds-checking interfaces, recently introduced a set of alternative functions to mitigate buffer overflows, primarily those caused by string/memory functions. However, poor compatibility limits their adoption. Failure oblivious computing can eliminate the possibility that an attacker can exploit memory errors to corrupt the address space and significantly increase the availability of systems. In this paper, we present S3Library (Saturation-Memory-Access Safer String Library), which is compatible with the standard C library in terms of function signature. Our technique automatically replaces unsafe deprecated memory/string functions with safer versions that perform bounds checking and eliminate buffer overflows via boundless memory. S3Library employs MinFat, a very compact pointer representation following the Less is More principle, to encode metadata into unused upper bits within pointers. In addition, S3Library utilizes Saturation Memory Access to eliminate illegal memory accesses into boundless padding area. Even if an out-of-bounds access is made, the fault program will not be interrupted. We implement our scheme within the LLVM framework on X86-64 and evaluate our approach on correctness, security, runtime performance and availability.

cs.CR↗

arXiv2020

Saturation Memory Access: Mitigating Memory Spatial Errors without Terminating Programs

Memory spatial errors, i.e., buffer overflow vulnerabilities, have been a well-known issue in computer security for a long time and remain one of the root causes of exploitable vulnerabilities. Most of the existing mitigation tools adopt a fail-stop strategy to protect programs from intrusions, which means the victim program will be terminated upon detecting a memory safety violation. Unfortunately, the fail-stop strategy harms the availability of software. In this paper, we propose Saturation Memory Access (SMA), a memory spatial error mitigation mechanism that prevents out-of-bounds access without terminating a program. SMA is based on a key observation that developers generally do not rely on out-of-bounds accesses to implement program logic. SMA modifies dynamic memory allocators and adds paddings to objects to form an enlarged object boundary. By dynamically correcting all the out-of-bounds accesses to operate on the enlarged protecting boundaries, SMA can tolerate out-of-bounds accesses. For the sake of compatibility, we chose tagged pointers to record the boundary metadata of a memory object in the pointer itself, and correct the address upon detecting out-of-bounds access. We have implemented the prototype of SMA on LLVM 10.0. Our results show that our compiler enables the programs to execute successfully through buffer overflow attacks. Experiments on MiBench show that our prototype incurs an overhead of 78\%. Further optimizations would require ISA supports.

cs.CR↗

arXiv2020

DangKiller: Eliminating Dangling Pointers Efficiently via Implicit Identifier

Use-After-Free vulnerabilities, allowing the attacker to access unintended memory via dangling pointers, are more threatening. However, most detection schemes can only detect dangling pointers and invalid them, but not provide a tolerance mechanism to repair the errors at runtime. Also, these techniques obtain and manage the metadata inefficiently with complex structures and too much scan (sweep). The goal of this paper is to use compiler instrumentation to eliminate dangling pointers automatically and efficiently. In this paper, we observe that most techniques lack accurate efficient pointer graph metadata maintaining methods, so they need to scan the log to reduce the redundancy and sweep the whole address space to find dangling pointers. Also, they lack a direct, efficiently obtaining metadata approach. The key insight of this paper is that a unique identifier can be used as a key to a hash or direct-map algorithm. Thus, this paper maintains the same implicit identifier with each memory object and its corresponding referent. Associating the unique ID with metadata for memory objects, obtaining and managing the pointer graph metadata can be efficiently. Therefore, with the delayed free technique adopted into C/C++, we present the DangKiller as a novel and lightweight dangling pointer elimination solution. We first demonstrate the MinFat Pointer, which can calculate unique implicit ID for each object and pointer quickly, and use hash algorithm to obtain metadata. Secondly, we propose the Log Cache and Log Compression mechanism based on the ID to decrease the redundancy of dangling pointer candidates. Coupled with the Address Tagging architecture on an ARM64 system, our experiments show that the DangKiller can eliminate use-after-free vulnerabilities at only 11% and 3% runtime overheads for the SPEC CPU2006 and 2017 benchmarks respectively, except for unique cases.

cs.CR↗