相关论文: Parametric transformation functions in the Kapreka…

We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of $n$-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the…

Many algorithms are specified with respect to a fixed but unspecified parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is…

The switch process alternates independently between 1 and -1, with the first switch to 1 occurring at the origin. The expected value function of this process is defined uniquely by the distribution of switching times. The relation between…

Trained transformer models have been found to implement interpretable procedures for tasks like arithmetic and associative recall, but little is understood about how the circuits that implement these procedures originate during training. To…

We introduce a class of "inverse parametric optimization" problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We…

A calculation formula of volume of revolution with integration by parts of definite integral is derived based on monotone function, and extended to a general case that curved trapezoids is determined by continuous, piecewise strictly…

We consider the wavelet transform of a finite, rooted, node-ranked, $p$-way tree, focusing on the case of binary ($p = 2$) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through…

We analyze the problem of comparing unitary transformations. The task is to decide, with minimal resources and maximal reliability, whether two given unitary transformations are identical or different. It is possible to make such…

There are several approaches to study occurrences of consecutive patterns in permutations such as the inclusion-exclusion method, the tree representations of permutations, the spectral approach and others. We propose yet another approach to…

The Arithmetic Fourier Transform is a numerical formulation for computing Fourier series and Taylor series coefficients. It competes with the Fast Fourier Transform in terms of speed and efficiency, requiring only addition operations and…

Using the frame formalism we determine some possible metrics and metric-compatible connections on the noncommutative differential geometry of the real quantum plane. By definition a metric maps the tensor product of two 1-forms into a…

This paper is devoted to the study of source reconstruction algorithms for coupled systems of heat equations, with either constant or spatially dependent coupling terms, where internal measurements are available from a reduced number of…

We study parametric integration of functions from the class C^r([0,1]^{d_1+d_2}) to C([0,1]^{d_1}) in the quantum model of computation. We analyze the convergence rate of parametric integration in this model and show that it is always…

Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation…

We have developed an algorithm that constructs a model of a reconfigurable optical interferometer, independent of specific architectural constraints. The programming of unitary transformations on the interferometer's optical modes relies on…

A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…

Here we define a procedure for evaluating KL-projections (I- and rI-projections) of channels. These can be useful in the decomposition of mutual information between input and outputs, e.g. to quantify synergies and interactions of different…

Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the first of a…

We address the general mathematical problem of computing the inverse $p$-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary $p$-th roots and their inverses of…

A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan…