arXiv subjects

Adam Marcus

Publications and source records attributed to Adam Marcus.

9 recordsLinked to original sources

arXiv2026

Stroke outcome and evolution prediction from CT brain using a spatiotemporal diffusion autoencoder

Stroke is a major cause of death and disability worldwide. Accurate outcome and evolution prediction has the potential to revolutionize stroke care by individualizing clinical decision-making leading to better outcomes. However, despite a plethora of attempts and the rich data provided by neuroimaging, modelling the ultimate fate of brain tissue remains a challenging task. In this work, we apply recent ideas in the field of diffusion probabilistic models to generate a self-supervised semantically meaningful stroke representation from Computed Tomography (CT) images. We then improve this representation by extending the method to accommodate longitudinal images and the time from stroke onset. The effectiveness of our approach is evaluated on a dataset consisting of 5,824 CT images from 3,573 patients across two medical centers with minimal labels. Comparative experiments show that our method achieves the best performance for predicting next-day severity and functional outcome at discharge.

cs.CV↗

arXiv2026

Identifying and Characterising Response in Clinical Trials: Development and Validation of a Machine Learning Approach in Colorectal Cancer

Precision medicine promises to transform health care by offering individualised treatments that dramatically improve clinical outcomes. A necessary prerequisite is to identify subgroups of patients who respond differently to different therapies. Current approaches are limited to static measures of treatment success, neglecting the repeated measures found in most clinical trials. Our approach combines the concept of partly conditional modelling with treatment effect estimation based on the Virtual Twins method. The resulting time-specific responses to treatment are characterised using survLIME, an extension of Local Interpretable Model-agnostic Explanations (LIME) to survival data. Performance was evaluated using synthetic data and applied to clinical trials examining the effectiveness of panitumumab to treat metastatic colorectal cancer. An area under the receiver operating characteristic curve (AUC) of 0.77 for identifying fixed responders was achieved in a 1000 patient simulation. When considering dynamic responders, partly conditional modelling increased the AUC from 0.597 to 0.685. Applying the approach to colorectal cancer trials found genetic mutations, sites of metastasis, and ethnicity as important factors for response to treatment. Our approach can accommodate a dynamic response to treatment while potentially providing better performance than existing methods in instances of a fixed response to treatment. When applied to clinical data we attain results consistent with the literature.

cs.LG↗

arXiv2023

Concurrent ischemic lesion age estimation and segmentation of CT brain using a Transformer-based network

The cornerstone of stroke care is expedient management that varies depending on the time since stroke onset. Consequently, clinical decision making is centered on accurate knowledge of timing and often requires a radiologist to interpret Computed Tomography (CT) of the brain to confirm the occurrence and age of an event. These tasks are particularly challenging due to the subtle expression of acute ischemic lesions and the dynamic nature of their appearance. Automation efforts have not yet applied deep learning to estimate lesion age and treated these two tasks independently, so, have overlooked their inherent complementary relationship. To leverage this, we propose a novel end-to-end multi-task transformer-based network optimized for concurrent segmentation and age estimation of cerebral ischemic lesions. By utilizing gated positional self-attention and CT-specific data augmentation, the proposed method can capture long-range spatial dependencies while maintaining its ability to be trained from scratch under low-data regimes commonly found in medical imaging. Furthermore, to better combine multiple predictions, we incorporate uncertainty by utilizing quantile loss to facilitate estimating a probability density function of lesion age. The effectiveness of our model is then extensively evaluated on a clinical dataset consisting of 776 CT images from two medical centers. Experimental results demonstrate that our method obtains promising performance, with an area under the curve (AUC) of 0.933 for classifying lesion ages <=4.5 hours compared to 0.858 using a conventional approach, and outperforms task-specific state-of-the-art algorithms.

eess.IV↗

arXiv2015

Finite free convolutions of polynomials

We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric additive and multiplicative convolutions were introduced by Walsh and Szeg\"o in different contexts, and have been studied for a century. The asymmetric additive convolution, and the connection of all of them with random matrices, is new. By developing the analogy with free probability, we prove that these convolutions produce real rooted polynomials and provide strong bounds on the locations of the roots of these polynomials.

math.CO↗

arXiv2013

Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem

We use the method of interlacing families of polynomials introduced to prove two theorems known to imply a positive solution to the Kadison--Singer problem. The first is Weaver's conjecture $KS_{2}$ \cite{weaver}, which is known to imply Kadison--Singer via a projection paving conjecture of Akemann and Anderson. The second is a formulation due to Casazza, et al., of Anderson's original paving conjecture(s), for which we are able to compute explicit paving bounds. The proof involves an analysis of the largest roots of a family of polynomials that we call the "mixed characteristic polynomials" of a collection of matrices.

math.CO↗

arXiv2013

Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees

We prove that there exist infinite families of regular bipartite Ramanujan graphs of every degree bigger than 2. We do this by proving a variant of a conjecture of Bilu and Linial about the existence of good 2-lifts of every graph. We also establish the existence of infinite families of `irregular Ramanujan' graphs, whose eigenvalues are bounded by the spectral radius of their universal cover. Such families were conjectured to exist by Linial and others. In particular, we prove the existence of infinite families of (c,d)-biregular bipartite graphs with all non-trivial eigenvalues bounded by sqrt{c-1}+sqrt{d-1}, for all c, d \geq 3. Our proof exploits a new technique for demonstrating the existence of useful combinatorial objects that we call the "method of interlacing polynomials'".

math.CO↗

arXiv2011

Human-powered Sorts and Joins

Crowdsourcing markets like Amazon's Mechanical Turk (MTurk) make it possible to task people with small jobs, such as labeling images or looking up phone numbers, via a programmatic interface. MTurk tasks for processing datasets with humans are currently designed with significant reimplementation of common workflows and ad-hoc selection of parameters such as price to pay per task. We describe how we have integrated crowds into a declarative workflow engine called Qurk to reduce the burden on workflow designers. In this paper, we focus on how to use humans to compare items for sorting and joining data, two of the most common operations in DBMSs. We describe our basic query interface and the user interface of the tasks we post to MTurk. We also propose a number of optimizations, including task batching, replacing pairwise comparisons with numerical ratings, and pre-filtering tables before joining them, which dramatically reduce the overall cost of running sorts and joins on the crowd. In an experiment joining two sets of images, we reduce the overall cost from $67 in a naive implementation to about $3, without substantially affecting accuracy or latency. In an end-to-end experiment, we reduced cost by a factor of 14.5.

cs.DB↗

arXiv2008

Entropy and set cardinality inequalities for partition-determined functions

A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these functions. Here a compound set means a set obtained by varying each argument of a function of several variables over a set associated with that argument, where all the sets are subsets of an appropriate algebraic structure so that the function is well defined. On the one hand, the entropy inequalities developed for partition-determined functions imply entropic analogues of general inequalities of Pl\"unnecke-Ruzsa type. On the other hand, the cardinality inequalities developed for compound sets imply several inequalities for sumsets, including for instance a generalization of inequalities proved by Gyarmati, Matolcsi and Ruzsa (2010). We also provide partial progress towards a conjecture of Ruzsa (2007) for sumsets in nonabelian groups. All proofs are elementary and rely on properly developing certain information-theoretic inequalities.

cs.IT↗

arXiv2005

Extensions of the linear bound in the Furedi-Hajnal conjecture

We present two extensions of the linear bound, due to Marcus and Tardos, on the number of 1's in an n by n 0-1 matrix avoiding a fixed permutation matrix. We first extend the linear bound to hypergraphs with ordered vertex sets and, using previous results of Klazar, we prove an exponential bound on the number of hypergraphs on n vertices which avoid a fixed permutation. This, in turn, solves various conjectures of Klazar as well as a conjecture of Branden and Mansour.We then extend the original Furedi-Hajnal problem from ordinary matrices to d-dimensional matrices and show that the number of 1's in a d-dimensional 0-1 matrix with side length n which avoids a d-dimensional permutation matrix is O(n^{d-1}).

math.CO↗