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Designing large coupling memory quasi-cyclic spatially-coupled LDPC (QC-SC-LDPC) codes with low error floors requires eliminating specific harmful substructures (e.g., short cycles) induced by edge spreading and lifting. Building on our…
From first principles, the author gathers a few general rules that need to be abided by in the calculation of the internal partition functions (IPFs) of individual molecules. These rules are violated in many schemes in the literature where…
Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different…
Let $\mathbf{K}$ be a field and $\phi$, $\mathbf{f} = (f_1, \ldots, f_s)$ in $\mathbf{K}[x_1, \dots, x_n]$ be multivariate polynomials (with $s < n$) invariant under the action of $\mathcal{S}_n$, the group of permutations of $\{1, \dots,…
The coupled nonlinear space fractional Ginzburg-Landau (CNLSFGL) equations with the fractional Laplacian have been widely used to model the dynamical processes in a fractal media with fractional dispersion. Due to the existence of…
Fault localization (FL) is a critical step in debugging, which typically relies on repeated executions to pinpoint faulty code regions. However, repeated executions can be impractical in the presence of non-deterministic failures or high…
Most conventional Federated Learning (FL) models are using a star network topology where all users aggregate their local models at a single server (e.g., a cloud server). That causes significant overhead in terms of both communications and…
Characterizing the express power of the Transformer architecture is critical to understanding its capacity limits and scaling law. Recent works provide the circuit complexity bounds to Transformer-like architecture. On the other hand,…
We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions, i.e., multivariate functions over the ring of integers modulo $d$, and investigate some of their structural properties. We also point out…
In this paper, we consider a secure multi-party computation problem (MPC), where the goal is to offload the computation of an arbitrary polynomial function of some massive private matrices (inputs) to a cluster of workers. The workers are…
Federated Learning (FL) is a machine learning paradigm in which many clients cooperatively train a single centralized model while keeping their data private and decentralized. FL is commonly used in edge computing, which involves placing…
Federated learning (FL) allows multiple medical institutions to collaboratively learn a global model without centralizing client data. It is difficult, if possible at all, for such a global model to commonly achieve optimal performance for…
Federated Learning (FL) has been becoming a popular interdisciplinary research area in both applied mathematics and information sciences. Mathematically, FL aims to collaboratively optimize aggregate objective functions over distributed…
Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…
Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors…
We investigate whether there are inherent limits of parallelization in the (randomized) massively parallel computation (MPC) model by comparing it with the (sequential) RAM model. As our main result, we show the existence of hard functions…
Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place,…
Despite their ubiquity in NLP tasks, Long Short-Term Memory (LSTM) networks suffer from computational inefficiencies caused by inherent unparallelizable recurrences, which further aggravates as LSTMs require more parameters for larger…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…