MILD-Net: Minimal Information Loss Dilated Network for Gland Instance Segmentation in Colon Histology Images

The analysis of glandular morphology within colon histopathology images is an important step in determining the grade of colon cancer. Despite the importance of this task, manual segmentation is laborious, time-consuming and can suffer from subjectivity among pathologists. The rise of computational pathology has led to the development of automated methods for gland segmentation that aim to overcome the challenges of manual segmentation. However, this task is non-trivial due to the large variability in glandular appearance and the difficulty in differentiating between certain glandular and non-glandular histological structures. Furthermore, a measure of uncertainty is essential for diagnostic decision making. To address these challenges, we propose a fully convolutional neural network that counters the loss of information caused by max-pooling by re-introducing the original image at multiple points within the network. We also use atrous spatial pyramid pooling with varying dilation rates for preserving the resolution and multi-level aggregation. To incorporate uncertainty, we introduce random transformations during test time for an enhanced segmentation result that simultaneously generates an uncertainty map, highlighting areas of ambiguity. We show that this map can be used to define a metric for disregarding predictions with high uncertainty. The proposed network achieves state-of-the-art performance on the GlaS challenge dataset and on a second independent colorectal adenocarcinoma dataset. In addition, we perform gland instance segmentation on whole-slide images from two further datasets to highlight the generalisability of our method. As an extension, we introduce MILD-Net+ for simultaneous gland and lumen segmentation, to increase the diagnostic power of the network.Comment: Initial version published at Medical Imaging with Deep Learning (MIDL) 201

Online Matrix Completion with Side Information

We give an online algorithm and prove novel mistake and regret bounds for online binary matrix completion with side information. The mistake bounds we prove are of the form $\tilde{O}(D/\gamma^2)$. The term $1/\gamma^2$ is analogous to the usual margin term in SVM (perceptron) bounds. More specifically, if we assume that there is some factorization of the underlying $m \times n$ matrix into $P Q^\intercal$ where the rows of $P$ are interpreted as "classifiers" in $\mathcal{R}^d$ and the rows of $Q$ as "instances" in $\mathcal{R}^d$, then $\gamma$ is the maximum (normalized) margin over all factorizations $P Q^\intercal$ consistent with the observed matrix. The quasi-dimension term $D$ measures the quality of side information. In the presence of vacuous side information, $D= m+n$. However, if the side information is predictive of the underlying factorization of the matrix, then in an ideal case, $D \in O(k + \ell)$ where $k$ is the number of distinct row factors and $\ell$ is the number of distinct column factors. We additionally provide a generalization of our algorithm to the inductive setting. In this setting, we provide an example where the side information is not directly specified in advance. For this example, the quasi-dimension $D$ is now bounded by $O(k^2 + \ell^2)$

Quantum Correlations in Two-Fermion Systems

We characterize and classify quantum correlations in two-fermion systems having 2K single-particle states. For pure states we introduce the Slater decomposition and rank (in analogy to Schmidt decomposition and rank), i.e. we decompose the state into a combination of elementary Slater determinants formed by mutually orthogonal single-particle states. Mixed states can be characterized by their Slater number which is the minimal Slater rank required to generate them. For K=2 we give a necessary and sufficient condition for a state to have a Slater number of 1. We introduce a correlation measure for mixed states which can be evaluated analytically for K=2. For higher K, we provide a method of constructing and optimizing Slater number witnesses, i.e. operators that detect Slater number for some states.Comment: 9 pages, some typos corrected and introduction modified, version to be published in Phys. Rev.

Fast and exact search for the partition with minimal information loss

In analysis of multi-component complex systems, such as neural systems, identifying groups of units that share similar functionality will aid understanding of the underlying structures of the system. To find such a grouping, it is useful to evaluate to what extent the units of the system are separable. Separability or inseparability can be evaluated by quantifying how much information would be lost if the system were partitioned into subsystems, and the interactions between the subsystems were hypothetically removed. A system of two independent subsystems are completely separable without any loss of information while a system of strongly interacted subsystems cannot be separated without a large loss of information. Among all the possible partitions of a system, the partition that minimizes the loss of information, called the Minimum Information Partition (MIP), can be considered as the optimal partition for characterizing the underlying structures of the system. Although the MIP would reveal novel characteristics of the neural system, an exhaustive search for the MIP is numerically intractable due to the combinatorial explosion of possible partitions. Here, we propose a computationally efficient search to precisely identify the MIP among all possible partitions by exploiting the submodularity of the measure of information loss. Mutual information is one such submodular information loss functions, and is a natural choice for measuring the degree of statistical dependence between paired sets of random variables. By using mutual information as a loss function, we show that the search for MIP can be performed in a practical order of computational time for a reasonably large system. We also demonstrate that MIP search allows for the detection of underlying global structures in a network of nonlinear oscillators

Compressing medical images with minimal information loss

This thesis aims to explore the potentialities of neural networks as compression algorithms for medical images. The objective is to develop a compressed image representation suitable for image comparison. In particular we studied different autoencoder architectures, varying the encoding mechanism in order to achieve a high degree of compression while also retaining a meaningful feature space. Our work is focused on mammograms but the methods introduced here can be extrapolated to other types of medical images

Characterization of Vehicle Behavior with Information Theory

This work proposes the use of Information Theory for the characterization of vehicles behavior through their velocities. Three public data sets were used: i.Mobile Century data set collected on Highway I-880, near Union City, California; ii.Borl\"ange GPS data set collected in the Swedish city of Borl\"ange; and iii.Beijing taxicabs data set collected in Beijing, China, where each vehicle speed is stored as a time series. The Bandt-Pompe methodology combined with the Complexity-Entropy plane were used to identify different regimes and behaviors. The global velocity is compatible with a correlated noise with f^{-k} Power Spectrum with k >= 0. With this we identify traffic behaviors as, for instance, random velocities (k aprox. 0) when there is congestion, and more correlated velocities (k aprox. 3) in the presence of free traffic flow

Exploring the flavour structure of the MSSM with rare K decays

We present an extensive analysis of rare K decays, in particular of the two neutrino modes K+->pi+ nu nu-bar and KL->pi0 nu nu-bar, in the Minimal Supersymmetric extension of the Standard Model. We analyse the expectations for the branching ratios of these modes, both within the restrictive framework of the minimal flavour violation hypothesis and within a more general framework with new sources of flavour-symmetry breaking. In both scenarios, the information that can be extracted from precise measurements of the two neutrino modes turn out to be very useful in restricting the parameter space of the model, even after taking into account the possible information on the mass spectrum derived from high-energy colliders, and the constraints from B-physics experiments. In the presence of new sources of flavour-symmetry breaking, additional significant constraints on the model can be derived also from the two KL->pi0 l+l- modes.Comment: 22 pages, 10 figures (high quality figures available on request

Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory

We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the separability problem in quantum information theory. We show that the matrix norms that define the k-minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k-positive linear maps and bound entanglement. Similarly, we investigate the k-super minimal and k-super maximal operator systems that were recently introduced and show that their cones of positive elements are exactly the cones of k-block positive operators and (unnormalized) states with Schmidt number no greater than k, respectively. We characterize a class of norms on the k-super minimal operator systems and show that the completely bounded versions of these norms provide a criterion for testing the Schmidt number of a quantum state that generalizes the recently-developed separability criterion based on trace-contractive maps.Comment: 17 pages, to appear in JF