Related papers: An algorithm for computing syzygies on $V[X]$ when…
The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…
We propose an efficient algorithm for estimation of possibility based qualitative expected utility. It is useful for decision making mechanisms where each possible decision is assigned a multi-attribute possibility distribution. The…
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are rewritten as differential equations for sector-wise generating functions, so the…
Let X(F,G) be the G-character variety of F where G is a rank 1 complex affine algebraic group and F is a finitely presentable discrete group. We describe an algorithm, which we implement in Mathematica, SageMath, and in Python, that takes a…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
A well-known result of SGA4 shows how to compute the pseudo-colimit of a category-valued pseudo-functor on a 1-category. The main result of this paper gives a generalization of this computation by constructing the weighted pseudo-colimit of…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
We study families of cellular resolutions by looking at them as a category and applying tools from representation stability. We obtain sufficient conditions on the structure of the family to have a noetherian representation category and…
This paper discusses the extension of the Prototype Verification System (PVS) sub-theory for rings, part of the PVS algebra theory, with theorems related to the division algorithm for Euclidean rings and Unique Factorization Domains that…
Recent works have established a novel viewpoint that treats the eigenvalue spectra of disordered quantum systems as time-series, and corresponding algorithms such as singular-value-decomposition has proven its advantage in studying subtle…
For a discrete valuation domain $V$ with maximal ideal $\mathfrak{m}$ such that the residue field $V/\mathfrak{m}$ is finite, there exists a sequence of polynomials $(F_n(x))_{n \ge 0}$ defined over the quotient field $K$ of $V$ that forms…
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…
We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of…
We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve…
We present a new algorithm for computing a $\mu$-basis of the syzygy module of $n$ polynomials in one variable over an arbitrary field $\mathbb{K}$. The algorithm is conceptually different from the previously-developed algorithms by Cox,…
We consider the factorization of a rectangular matrix $X $ into a positive linear combination of rank-one factors of the form $u v^\top$, where $u$ and $v$ belongs to certain sets $\mathcal{U}$ and $\mathcal{V}$, that may encode specific…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
We propose a simple estimator that allows to calculate the absolute value of a system's partition function from a finite sampling of its canonical ensemble. The estimator utilizes a volume correction term to compensate the effect that the…