Related papers: A Power Transform
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…
This paper designs a statistical quantification towards the intermittent power uncertainty in power systems. A negative-exponential forecast uncertainty function is constructed to represent the relationship between the statistics of…
This paper investigates the uncertain power flow analysis in distribution networks within the context of renewable power resources integration such as wind and solar power. The analysis aims to bound the worst-case voltage magnitude in any…
The Baker-Campbell-Hausdorff formula was recently resummed exactly in one variable, and left as a power series in the other (Moodie and Long 2021 J. Phys. A: Math. Theor. 54 015208). The coefficients of the power series were provided as a…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
This paper is a study of power series, where the coefficients are binomial expressions (iterated finite differences). Our results can be used for series summation, for series transformation, or for asymptotic expansions involving Stirling…
Power series are introduced that are simultaneously convergent for all real and p-adic numbers. Our expansions are in some aspects similar to those of exponential, trigonometric, and hyperbolic functions. Starting from these series and…
In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…
A new characterization for power function distributions is obtained which is based on products of order statistics. This result may be considered as a generalization of some recent results for contractions. We note that in this new result…
The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in…
Transformers are widely used in natural language processing due to their ability to model longer-term dependencies in text. Although these models achieve state-of-the-art performance for many language related tasks, their applicability…
A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations,…
The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…
We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of…
Power analyses are an important aspect of experimental design, because they help determine how experiments are implemented in practice. It is common to specify a desired level of power and compute the sample size necessary to obtain that…
The Transformed-Transformer family of distributions are the resulting family of distributions as transformed from a random variable $T$ through another transformer random variable $X$ using a weight function $\omega$ of the cumulative…
The power prior is a class of informative priors designed to incorporate historical data alongside current data in a Bayesian framework. It includes a power parameter that controls the influence of historical data, providing flexibility and…
A planar tree power series over a field $K$ is a formal expression $$\sum c_T \cdot T$$ where the sum is extended over all isomorphism classes of finite planar reduced rooted trees $T$ and where the coefficients $c_T$ are in $K$.…
Statistical power is a measure of the replicability of a categorical hypothesis test. Formally, it is the probability of detecting an effect, if there is a true effect present in the population. Hence, optimizing statistical power as a…
This document aims to be a self-contained, mathematically precise overview of transformer architectures and algorithms (*not* results). It covers what transformers are, how they are trained, what they are used for, their key architectural…