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We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence through a rigorous error analysis. Finally,…
Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of…
With the increasing number of components and further miniaturization the mean time between faults in supercomputers will decrease. System level fault tolerance techniques are expensive and cost energy, since they are often based on…
Multi-sector capacity expansion models play a crucial role in energy planning by providing decision support for policymaking in technology development. To ensure reliable support, these models require high technological, spatial, and…
It is well known that for a first order system of linear difference equations with rational function coefficients, a solution that is holomorphic in some left half plane can be analytically continued to a meromorphic solution in the whole…
When developing a software system, a change in one part of the system may lead to unwanted changes in other parts of the system. These affected parts may interfere with system performance, so regression testing is used to deal with these…
We propose new domain decomposition methods for systems of partial differential equations in two and three dimensions. The algorithms are derived with the help of the Smith factorization of the operator. This could also be validated by…
For processes involving structure functions and/or fragmentation functions, arguments that there is a part that dominates the NLO corrections are briefly reviewed. The arguments are tested against more recent NLO and in particular NNLO…
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future…
Modern generations of field-programmable gate arrays (FPGAs) allow for partial reconfiguration. In an online context, where the sequence of modules to be loaded on the FPGA is unknown beforehand, repeated insertion and deletion of modules…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
The trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…
This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas' algorithm is a symbolic method which splits a given system of…
In modern computing units, division operations are generally slower than other arithmetic operations and require more resources, such as area and power, than multiplication. To reduce the delay, fast division algorithms use an initial…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…
Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be…
We propose a new method for defragmenting the module layout of a reconfigurable device, enabled by a novel approach for dealing with communication needs between relocated modules and with inhomogeneities found in commonly used FPGAs. Our…