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Communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding is considered. The average bit error probability of an irregular LDPC code ensemble after a fixed number of…
We study how to sparsify connectivity in graphs under a tight deletion budget. Given a graph $G$ and integers $k,x \ge 0$, Critical Node Cut (CNC) asks whether we can delete at most $k$ vertices so that the number of remaining unordered…
We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with $\sqrt{n}$-rate on the assumption that the smoothness of the functionals is larger than the…
Traditional attempts for loop closure detection typically use hand-crafted features, relying on geometric and visual information only, whereas more modern approaches tend to use semantic, appearance or geometric features extracted from deep…
Polar codes were introduced in 2009 and proven to achieve the symmetric capacity of any binary-input discrete memoryless channel under low-complexity successive cancellation decoding. In this thesis, we construct cyclic polar codes based on…
Previous works studied how deep neural networks (DNNs) perceive image content in terms of their biases towards different image cues, such as texture and shape. Previous methods to measure shape and texture biases are typically…
Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions. In this work, we investigate the…
CCD light curves of the Algol type eclipsing binaries DP Cep, AL Gem, FG Gem, UU Leo, CF Tau and AW Vul were analysed using the Wilson-Deninney code and new geometric and absolute parameters were derived. Due to cyclic apparent orbital…
In their thought-provoking paper [1], Belkin et al. illustrate and discuss the shape of risk curves in the context of modern high-complexity learners. Given a fixed training sample size $n$, such curves show the risk of a learner as a…
We consider two-dimensional Ising models with randomly distributed ferromagnetic bonds and study the local critical behavior at defect lines by extensive Monte Carlo simulations. Both for ladder and chain type defects, non-universal…
We analyze the connection between the autocorrelation of a binary sequence and its run structure given by the run length encoding. We show that both the periodic and the aperiodic autocorrelation of a binary sequence can be formulated in…
Selection of descent direction at a point plays an important role in numerical optimization for minimizing a real valued function. In this article, a descent sequence is generated for the functions with bounded parameters to obtain a…
We present an explicit closed-form formula for the vertices of the classical cut polytope $\operatorname{CUT}(n)$, defined as the convex hull of cut vectors of the complete graph $K_n$. Our derivation proceeds via a related polytope,…
Kernel logistic regression (KLR) is a widely used supervised learning method for binary and multi-class classification, which provides estimates of the conditional probabilities of class membership for the data points. Unlike other kernel…
In safety-critical classification, the cost of failure is often asymmetric, yet Bayesian deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), that cannot distinguish whether a model's ignorance…
Unbreakable decomposition, introduced by Cygan et al. (SICOMP'19) and Cygan et al. (TALG'20), has proven to be one of the most powerful tools for parameterized graph cut problems in recent years. Unfortunately, all known constructions…
We propose a simple domain decomposition method for $d$-dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a space-filling curve to create equally…
In this paper, we propose to train convolutional neural networks (CNNs) with both binarized weights and activations, leading to quantized models specifically} for mobile devices with limited power capacity and computation resources.…
Due to wide applications of binary sequences with low correlation to communications, various constructions of such sequences have been proposed in literature. However, most of the known constructions via finite fields make use of the…
Two-dimensional error-correcting codes, where codewords are represented as $n \times n$ arrays over a $q$-ary alphabet, find important applications in areas such as QR codes, DNA-based storage, and racetrack memories. Among the possible…