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A detail study on the In-degree Distribution (ID) of Cellular Automata is obtained by exact enumeration. The results indicate large deviation from multiscaling and classification according to ID are discussed. We further augment the…
We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable…
Adam is a widely used optimization algorithm in deep learning, yet the specific class of objective functions where it exhibits inherent advantages remains underexplored. Unlike prior studies requiring external schedulers and $\beta_2$ near…
Anomaly detection of sequences is a hot topic in data mining. Anomaly Detection using Piecewise Aggregate approximation in the Amplitude Domain (called ADPAAD) is one of the widely used methods in anomaly detection of sequences. The core…
As the multiplexing power of spectroscopic instruments increases, so does the need for automated analysis. In practice, the bottleneck for speed is the calculation of model spectra to evaluate the likelihood of candidate parameters. This…
In this paper, we derive a modified InfoMax algorithm for the solution of Blind Signal Separation (BSS) problems by using advanced stochastic methods. The proposed approach is based on a novel stochastic optimization approach known as the…
We review some of the recent advances in the computation of one-loop scattering amplitudes which led to the construction of efficient and automated computational tools for NLO predictions. Particular attention is devoted to unitarity-based…
We present an algorithm for computing instanton numbers of curve singularities. A comparison is made between these and some other invariants of curve singularities. The algorithm has been implemented in the symbolic computer algebra program…
The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
We consider \emph{Alternating Direction Implicit} (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. for several imaging applications. The discretised scheme is shown…
We consider the problem of checking the differential privacy of online randomized algorithms that process a stream of inputs and produce outputs corresponding to each input. This paper generalizes an automaton model called DiP automata (See…
Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic…
A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
We consider the problem of existential quantifier elimination for Boolean formulas in Conjunctive Normal Form (CNF). We present a new method for solving this problem called Derivation of Dependency-Sequents (DDS). A Dependency-sequent…
We consider the computational complexity of tree transducers, depending on their separable sets of input variables.
Neural networks and deep learning are changing the way that artificial intelligence is being done. Efficiently choosing a suitable network architecture and fine-tune its hyper-parameters for a specific dataset is a time-consuming task given…
As modern software systems are increasingly developed for running in distributed environments, it is crucial to provide fundamental techniques such as dependence analysis for checking, diagnosing, and evolving those systems. However,…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…