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There are two ways to compute Poincar\'e-Dulac normal forms of systems of ODEs. Under the original approach used by Poincar\'e the normalizing transformation is explicitly computed. On each step, the normalizing procedure requires the…
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
Shapley values have become a cornerstone of explainable AI, but they are computationally expensive to use, especially when features are dependent. Evaluating them requires approximating a large number of conditional expectations, either via…
Standard power systems are modeled using differential-algebraic equations (DAE). Following a transient event, voltage collapse can occur as a bifurcation of the transient load flow solutions which is marked by the system trajectory reaching…
The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent model of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general…
We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where $S$ servers share an entangled state and separately store classical data streams $W_1,\cdots, W_S$ over a finite field $\mathbb{F}_d$. A user aims…
The standard format of matrices belonging to Lie superalgebras consists of partitioning the matrices into even and odd blocks. In this paper, we study other possible matrix formats and in particular the so-called diagonal format which…
In this note, analysis of time delay systems using Lambert W function approach is reassessed. A common canonical form of time delay systems is defined. We extended the recent results of [6] for second order into nth order system. The…
We develop a complete and rigorous mathematical framework for the analysis of stochastic neural field equations under the influence of spatially extended additive noise. By comparing a solution to a fixed deterministic front profile it is…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
The reductions of a square complex matrix A to its canonical forms under transformations of similarity, congruence, or *congruence are unstable operations: these canonical forms and reduction transformations depend discontinuously on the…
Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…
In this work, we study early-warning signs for stochastic partial differential equations (SPDEs), where the linearization around a steady state has continuous spectrum. The studied warning sign takes the form of qualitative changes in the…
An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary…
$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations…
Sign language translation systems typically require English as an intermediary language, creating barriers for non-English speakers in the global deaf community. We present Canonical Semantic Form (CSF), a language-agnostic semantic…
The article deals with the subject of solving the problem of canonical-map synthesis for Hamiltonian systems. For this purpose, the controlling-function method has been developed that allows appropriate changes of the variables in terms of…
We present an algorithm for normalizing \emph{Batched Einstein Summation} expressions by mapping mathematically equivalent formulations to a unique normal form. Batches of einsums with the same Einstein notation that exhibit substantial…
When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…