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Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…
Pose Machines provide a sequential prediction framework for learning rich implicit spatial models. In this work we show a systematic design for how convolutional networks can be incorporated into the pose machine framework for learning…
We study the typical properties of polynomial Support Vector Machines within a Statistical Mechanics approach that allows us to analyze the effect of different normalizations of the features. If the normalization is adecuately chosen, there…
We prove that polynomial valuations on vector lattices correspond to orthosymmetric multilinear maps. As a consequence we obtain a concise proof of the equivalence of orthosymmetry and orthogonal additivity.
We propose an explicit construction of a weighted generalised Grassmannian. For a weighted Grassmannian (i.e., for series A) we obtain an effective parametrisation of possible $\mathbb{Z}$-gradings on Pl\"{u}cker coordinates, and provide…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
Semialgebraic graphs are graphs whose vertices are points in $\mathbb{R}^d$, and adjacency between two vertices is determined by the truth value of a semialgebraic predicate of constant complexity. We show how to harness polynomial…
We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating…
This paper describes valuation-based systems for representing and solving discrete optimization problems. In valuation-based systems, we represent information in an optimization problem using variables, sample spaces of variables, a set of…
Starting from de la Vall\'ee Poussin type (VP) interpolation, the authors have recently introduced a family of interpolating polynomial scaling and wavelet bases generating the approximation and detail spaces of a non-standard…
Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of…
In this paper we study systems of autonomous algebraic ODEs in several differential indeterminates. We develop a notion of algebraic dimension of such systems by considering them as algebraic systems. Afterwards we apply differential…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…
In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are…
We introduce a new class of evaluation linear codes by evaluating polynomials at the roots of a suitable trace function. We give conditions for self-orthogonality of these codes and their subfield-subcodes with respect to the Hermitian…
Let R and S be two irreducible root systems spanning the same vector space and having the same Weyl group W, such that S (but not necessarily R) is reduced. For each such pair (R,S) we construct a family of W-invariant orthogonal…
The authors proposed a general way to find particular solutions for overdetermined systems of PDEs previously, where the number of equations is greater than the number of unknown functions. In this paper, we propose an algorithm for finding…
The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…