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Deep learning has achieved remarkable success in modeling sequential data, including event sequences, temporal point processes, and irregular time series. Recently, transformers have largely replaced recurrent networks in these tasks.…
Experimental particle physics uses machine learning for many tasks, where one application is to classify signal and background events. This classification can be used to bin an analysis region to enhance the expected significance for a mass…
Classification algorithms using Transformer architectures can be affected by the sequence length learning problem whenever observations from different classes have a different length distribution. This problem causes models to use sequence…
Normalization is a pre-processing step that converts the data into a more usable representation. As part of the deep neural networks (DNNs), the batch normalization (BN) technique uses normalization to address the problem of internal…
Time series analysis is a field of data science which is interested in analyzing sequences of numerical values ordered in time. Time series are particularly interesting because they allow us to visualize and understand the evolution of a…
Let s and t be variables. Define polynomials {n} in s, t by {0}=0, {1}=1, and {n}=s{n-1}+t{n-2} for n >= 2. If s, t are integers then the corresponding sequence of integers is called a Lucas sequence. Define an analogue of the binomial…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
We compare a piecewise linear map with constant slope beta>1 and a piecewise linear map with constant slope -beta. These maps are called the positive and negative beta-transformations. We show that for a certain set of beta's, the…
The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step…
In the derivation of Lorentz transformation, linear transformation between inertial frames is one of the most important steps. In teaching special relativity, we usually use the homogeneity and isotropy of spacetime to argue that the…
Transformer-based sequence-to-sequence architectures, while achieving state-of-the-art results on a large number of NLP tasks, can still suffer from overfitting during training. In practice, this is usually countered either by applying…
By means of a variational approach we find new series representations both for well known mathematical constants, such as $\pi$ and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we…
To prove that a measure, linearly representable by means of a finite set of nonnegative matrices $\mathcal M$, has the weak-Gibbs property, one check the uniform convergence (on $\mathcal M^\mathbb N$) of the sequence of vectors…
We study the use of a time series encoder to learn representations that are useful on data set types with which it has not been trained on. The encoder is formed of a convolutional neural network whose temporal output is summarized by a…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
We present a new training methodology for transformers using a multilevel, layer-parallel approach. Through a neural ODE formulation of transformers, our application of a multilevel parallel-in-time algorithm for the forward and…
The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinite numerical sequences, a criterion (i.e., a necessary and…
This work proposes a new image analysis tool called Label Consistent Transform Learning (LCTL). Transform learning is a recent unsupervised representation learning approach; we add supervision by incorporating a label consistency…
In this paper, we extend our previous work on the power series method for computing backstepping kernels. Our first contribution is the development of initial steps towards a MATLAB toolbox dedicated to backstepping kernel computation. This…
The standard approximation of a natural logarithm in statistical analysis interprets a linear change of \(p\) in \(\ln(X)\) as a \((1+p)\) proportional change in \(X\), which is only accurate for small values of \(p\). I suggest…