arXiv subjects

Mehdi Moradi

Publications and source records attributed to Mehdi Moradi.

At least 19 recordsLinked to original sources

arXiv2026

On locally finite-dimensional traces II

We continue the study of locally finite-dimensional traces introduced in our earlier work. We give new characterizations of LFD traces in terms of finite-rank projections in irreducible representations and in the socle of the bidual. We show that, for separable nowhere scattered $C^*$-algebras, the set of all LFD traces is convex. We also prove that quasidiagonal traces form a face of the trace simplex and record applications to strongly self-absorbing $C^*$-algebras. We construct an exact tracially AF algebra not KK-equivalent to any nuclear $C^*$-algebra.

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arXiv2026

Multiscale Topological Inference for Marked Point Processes via Euler Characteristic Envelopes

The statistical analysis of marked point processes requires disentangling complex spatial arrangements from attribute-dependent interactions. While classical summary statistics are effective for second-order dependencies, they frequently fail to capture higher-order topological structures and non-linear interactions between marks and space. In this work, we propose a novel multiscale topological inference framework for marked point processes by integrating mark-weighted filtrations with Euler Characteristic envelopes. We redefine the underlying metric space using an exponential mark-weighted distance, which modulates connectivity based on attribute similarity, effectively accelerating the merger of connected components among homophilic neighbors. To ensure rigorous statistical inference, we apply non-parametric global envelope tests to the resulting Euler Characteristic Curves, allowing for formal hypothesis testing against the null model of random labeling. Furthermore, we introduce a local decomposition of the topological signal via Z-scores at the critical filtration scale to identify and localize structural hubs and topological barriers. Systematic simulations across various scenarios demonstrate the framework's high specificity and sensitivity to attribute-space dependencies while remaining robust against purely geometric effects. This methodology provides a comprehensive and interpretable toolkit for identifying, quantifying, and localizing complex structural dependencies in marked spatial data, bridging the gap between topological data analysis and classical point process statistics.

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arXiv2025

Quasidiagonality of Kazhdan Groups

It is shown that infinite, discrete, Kazhdan property (T) groups never have the {\it finite-dimensional density} (FDD) property. This answers a conjecture of Lubotzky and Shalom affirmatively.

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arXiv2025

Inhomogeneous mark correlation functions for general marked point processes

Spatial phenomena in environmental and biological contexts often involve events that are unevenly distributed across space and carry attributes, whose associations/variations are space-dependent. In this paper, we introduce the class of inhomogeneous mark correlation functions, capturing mark associations/variations, while explicitly accounting for the spatial inhomogeneity of events. The proposed functions are designed to quantify how, on average, marks vary or associate with one another as a function of pairwise spatial distances. We develop nonparametric estimators and evaluate their performance through simulation studies covering a range of scenarios with mark association or variation, spanning from nonstationary point patterns without spatial interaction to those characterised by clustering tendencies. Our simulations reveal the shortcomings of traditional methods in the presence of spatial inhomogeneity, underscoring the necessity of our approach. Furthermore, the results show that our estimators accurately identify both the positivity/negativity and effective spatial range for detected mark associations/variations. The proposed inhomogeneous mark correlation functions are then applied to two distinct forest ecosystems: Longleaf pine trees in southern Georgia, USA, marked by their diameter at breast height, and Scots pine trees in Pfynwald, Switzerland, marked by their height. Our findings reveal that the inhomogeneous mark correlation functions provide deeper and more detailed insights into tree growth patterns compared to traditional methods

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arXiv2024

Local Indicators of Mark Association for Spatial Marked Point Processes

The emergence of distinct local mark behaviours is becoming increasingly common in the applications of spatial marked point processes. This dynamic highlights the limitations of existing global mark correlation functions in accurately identifying the true patterns of mark associations/variations among points as distinct mark behaviours might dominate one another, giving rise to an incomplete understanding of mark associations. In this paper, we introduce a family of local indicators of mark association (LIMA) functions for spatial marked point processes. These functions are defined on general state spaces and can include marks that are either real-valued or function-valued. Unlike global mark correlation functions, which are often distorted by the existence of distinct mark behaviours, LIMA functions reliably identify all types of mark associations and variations among points. Additionally, they accurately determine the interpoint distances where individual points show significant mark associations. Through simulation studies, featuring various scenarios, and four real applications in forestry, criminology, and urban mobility, we study spatial marked point processes in $\R^2$ and on linear networks with either real-valued or function-valued marks, demonstrating that LIMA functions significantly outperform the existing global mark correlation functions.

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arXiv2024

Function-valued marked spatial point processes on linear networks: application to urban cycling profiles

In the literature on spatial point processes, there is an emerging challenge in studying marked point processes with points being labelled by functions. In this paper, we focus on point processes living on linear networks and, from distinct points of view, propose several marked summary characteristics that are of great use in studying the average association and dispersion of the function-valued marks. Through a simulation study, we evaluate the performance of our proposed marked summary characteristics, both when marks are independent and when some sort of spatial dependence is evident among them. Finally, we employ our proposed mark summary characteristics to study the spatial structure of urban cycling profiles in Vancouver, Canada.

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arXiv2024

Rejoinder on "Marked spatial point processes: current state and extensions to point processes on linear networks"

We are grateful to all discussants for their invaluable comments, suggestions, questions, and contributions to our article. We have attentively reviewed all discussions with keen interest. In this rejoinder, our objective is to address and engage with all points raised by the discussants in a comprehensive and considerate manner. Consistently, we identify the discussants, in alphabetical order, as follows: CJK for Cronie, Jansson, and Konstantinou, DS for Stoyan, GP for Grabarnik and Pommerening, MRS for Myllym\"aki, Rajala, and S\"arkk\"a, and MCvL for van Lieshout throughout this rejoinder.

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arXiv2023

Marked spatial point processes: current state and extensions to point processes on linear networks

Within the applications of spatial point processes, it is increasingly becoming common that events are labeled by marks, prompting an exploration beyond the spatial distribution of events by incorporating the marks in the undertaken analysis. In this paper, we first consider marked spatial point processes in $\R^2$, where marks are either integer-valued, real-valued, or object-valued, and review the state-of-the-art to analyze the spatial structure and type of interaction/correlation between marks. More specifically, we review cross/dot-type summary characteristics, mark-weighted summary characteristics, various mark correlation functions, and frequency domain approaches. Second, we propose novel cross/dot-type higher-order summary characteristics, mark-weighted summary characteristics, and mark correlation functions for marked point processes on linear networks. Through a simulation study, we show that ignoring the underlying network gives rise to erroneous conclusions about the interaction/correlation between marks. Finally, we consider two applications: the locations of two types of butterflies in Melbourne, Australia, and the locations of public trees along the street network of Vancouver, Canada, where trees are labeled by their diameters at breast height.

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arXiv2022

Towards Automatic Prediction of Outcome in Treatment of Cerebral Aneurysms

Intrasaccular flow disruptors treat cerebral aneurysms by diverting the blood flow from the aneurysm sac. Residual flow into the sac after the intervention is a failure that could be due to the use of an undersized device, or to vascular anatomy and clinical condition of the patient. We report a machine learning model based on over 100 clinical and imaging features that predict the outcome of wide-neck bifurcation aneurysm treatment with an intravascular embolization device. We combine clinical features with a diverse set of common and novel imaging measurements within a random forest model. We also develop neural network segmentation algorithms in 2D and 3D to contour the sac in angiographic images and automatically calculate the imaging features. These deliver 90% overlap with manual contouring in 2D and 83% in 3D. Our predictive model classifies complete vs. partial occlusion outcomes with an accuracy of 75.31%, and weighted F1-score of 0.74.

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arXiv2022

CheXRelNet: An Anatomy-Aware Model for Tracking Longitudinal Relationships between Chest X-Rays

Despite the progress in utilizing deep learning to automate chest radiograph interpretation and disease diagnosis tasks, change between sequential Chest X-rays (CXRs) has received limited attention. Monitoring the progression of pathologies that are visualized through chest imaging poses several challenges in anatomical motion estimation and image registration, i.e., spatially aligning the two images and modeling temporal dynamics in change detection. In this work, we propose CheXRelNet, a neural model that can track longitudinal pathology change relations between two CXRs. CheXRelNet incorporates local and global visual features, utilizes inter-image and intra-image anatomical information, and learns dependencies between anatomical region attributes, to accurately predict disease change for a pair of CXRs. Experimental results on the Chest ImaGenome dataset show increased downstream performance compared to baselines. Code is available at https://github.com/PLAN-Lab/ChexRelNet

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arXiv2022

On locally finite dimensional traces

We partially resolve three open questions on approximation properties of traces on simple C*-algebras. We partially answer two questions raised by Nate Brown by showing that locally finite dimensional (LFD) traces form a convex set on simple C*-algebras and that they are automatically uniformly LFD on locally reflexive C*-algebras. We prove that all the traces on the reduced \C-algebra $C^*_r(\Gamma)$ of a discrete amenable ICC group $\Gamma$ are uniformly LFD, and conclude that $C^*_r(\Gamma)$ is strong-NF in the sense of Blackadar-Kirchberg in this case. This partially answers another open question raised by Brown.

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arXiv2022

Quasitriangular operator algebras

We give characterizations of quasitriangular operator algebras along the line of Voiculescu's characterization of quasidiagonal $C^*$-algebras.

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arXiv2022

3D Segmentation with Fully Trainable Gabor Kernels and Pearson's Correlation Coefficient

The convolutional layer and loss function are two fundamental components in deep learning. Because of the success of conventional deep learning kernels, the less versatile Gabor kernels become less popular despite the fact that they can provide abundant features at different frequencies, orientations, and scales with much fewer parameters. For existing loss functions for multi-class image segmentation, there is usually a tradeoff among accuracy, robustness to hyperparameters, and manual weight selections for combining different losses. Therefore, to gain the benefits of using Gabor kernels while keeping the advantage of automatic feature generation in deep learning, we propose a fully trainable Gabor-based convolutional layer where all Gabor parameters are trainable through backpropagation. Furthermore, we propose a loss function based on the Pearson's correlation coefficient, which is accurate, robust to learning rates, and does not require manual weight selections. Experiments on 43 3D brain magnetic resonance images with 19 anatomical structures show that, using the proposed loss function with a proper combination of conventional and Gabor-based kernels, we can train a network with only 1.6 million parameters to achieve an average Dice coefficient of 83%. This size is 44 times smaller than the original V-Net which has 71 million parameters. This paper demonstrates the potentials of using learnable parametric kernels in deep learning for 3D segmentation.

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arXiv2021

Basis Scaling and Double Pruning for Efficient Inference in Network-Based Transfer Learning

Network-based transfer learning allows the reuse of deep learning features with limited data, but the resulting models can be unnecessarily large. Although network pruning can improve inference efficiency, existing algorithms usually require fine-tuning that may not be suitable for small datasets. In this paper, using the singular value decomposition, we decompose a convolutional layer into two layers: a convolutional layer with the orthonormal basis vectors as the filters, and a "BasisScalingConv" layer which is responsible for rescaling the features and transforming them back to the original space. As the filters in each decomposed layer are linearly independent, when using the proposed basis scaling factors with the Taylor approximation of importance, pruning can be more effective and fine-tuning individual weights is unnecessary. Furthermore, as the numbers of input and output channels of the original convolutional layer remain unchanged after basis pruning, it is applicable to virtually all architectures and can be combined with existing pruning algorithms for double pruning to further increase the pruning capability. When transferring knowledge from ImageNet pre-trained models to different target domains, with less than 1% reduction in classification accuracies, we can achieve pruning ratios up to 74.6% for CIFAR-10 and 98.9% for MNIST in model parameters.

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arXiv2021

Chest ImaGenome Dataset for Clinical Reasoning

Despite the progress in automatic detection of radiologic findings from chest X-ray (CXR) images in recent years, a quantitative evaluation of the explainability of these models is hampered by the lack of locally labeled datasets for different findings. With the exception of a few expert-labeled small-scale datasets for specific findings, such as pneumonia and pneumothorax, most of the CXR deep learning models to date are trained on global "weak" labels extracted from text reports, or trained via a joint image and unstructured text learning strategy. Inspired by the Visual Genome effort in the computer vision community, we constructed the first Chest ImaGenome dataset with a scene graph data structure to describe $242,072$ images. Local annotations are automatically produced using a joint rule-based natural language processing (NLP) and atlas-based bounding box detection pipeline. Through a radiologist constructed CXR ontology, the annotations for each CXR are connected as an anatomy-centered scene graph, useful for image-level reasoning and multimodal fusion applications. Overall, we provide: i) $1,256$ combinations of relation annotations between $29$ CXR anatomical locations (objects with bounding box coordinates) and their attributes, structured as a scene graph per image, ii) over $670,000$ localized comparison relations (for improved, worsened, or no change) between the anatomical locations across sequential exams, as well as ii) a manually annotated gold standard scene graph dataset from $500$ unique patients.

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arXiv2021

AnaXNet: Anatomy Aware Multi-label Finding Classification in Chest X-ray

Radiologists usually observe anatomical regions of chest X-ray images as well as the overall image before making a decision. However, most existing deep learning models only look at the entire X-ray image for classification, failing to utilize important anatomical information. In this paper, we propose a novel multi-label chest X-ray classification model that accurately classifies the image finding and also localizes the findings to their correct anatomical regions. Specifically, our model consists of two modules, the detection module and the anatomical dependency module. The latter utilizes graph convolutional networks, which enable our model to learn not only the label dependency but also the relationship between the anatomical regions in the chest X-ray. We further utilize a method to efficiently create an adjacency matrix for the anatomical regions using the correlation of the label across the different regions. Detailed experiments and analysis of our results show the effectiveness of our method when compared to the current state-of-the-art multi-label chest X-ray image classification methods while also providing accurate location information.

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arXiv2021

Channel Scaling: A Scale-and-Select Approach for Transfer Learning

Transfer learning with pre-trained neural networks is a common strategy for training classifiers in medical image analysis. Without proper channel selections, this often results in unnecessarily large models that hinder deployment and explainability. In this paper, we propose a novel approach to efficiently build small and well performing networks by introducing the channel-scaling layers. A channel-scaling layer is attached to each frozen convolutional layer, with the trainable scaling weights inferring the importance of the corresponding feature channels. Unlike the fine-tuning approaches, we maintain the weights of the original channels and large datasets are not required. By imposing L1 regularization and thresholding on the scaling weights, this framework iteratively removes unnecessary feature channels from a pre-trained model. Using an ImageNet pre-trained VGG16 model, we demonstrate the capabilities of the proposed framework on classifying opacity from chest X-ray images. The results show that we can reduce the number of parameters by 95% while delivering a superior performance.

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arXiv2021

Statistical learning and cross-validation for point processes

This paper presents the first general (supervised) statistical learning framework for point processes in general spaces. Our approach is based on the combination of two new concepts, which we define in the paper: i) bivariate innovations, which are measures of discrepancy/prediction-accuracy between two point processes, and ii) point process cross-validation (CV), which we here define through point process thinning. The general idea is to carry out the fitting by predicting CV-generated validation sets using the corresponding training sets; the prediction error, which we minimise, is measured by means of bivariate innovations. Having established various theoretical properties of our bivariate innovations, we study in detail the case where the CV procedure is obtained through independent thinning and we apply our statistical learning methodology to three typical spatial statistical settings, namely parametric intensity estimation, non-parametric intensity estimation and Papangelou conditional intensity fitting. Aside from deriving theoretical properties related to these cases, in each of them we numerically show that our statistical learning approach outperforms the state of the art in terms of mean (integrated) squared error.

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