Data transformation is an essential step in data science. While experts primarily use programming to transform their data, there is an increasing need to support non-programmers with user interface-based tools. With the rapid development in interacti...
We construct an infinite sequence of projectively flat manifolds by using castling transformations of prehomogeneous vector spaces. We also give a classification of manifolds equipped with a flat projective structure obtained by a finite number of ca...
Quantum groups have been widely explored as a tool to encode possible nontrivial generalisations of reference frame transformations, relevant in quantum gravity. In quantum information, it was found that the reference frames can be associated to quan...
This article explores the differences between frame and coordinate transformations in relativistic theories. We highlight the key role of tetrad fields in connecting spacetime and frame indices. Using Maxwell's electrodynamics as an example, we show...
We study the problem of computing the Fréchet distance between two polygonal curves under transformations. First, we consider translations in the Euclidean plane. Given two curves $π$ and $σ$ of total complexity $n$ and a threshold $δ\geq 0$, we...
It is conjectured that a class of n-fold integral transformations {I(alpha)|alpha in {C}} forms a mutually commutative family, namely, we have I(alpha) I(beta)=I(beta) I(alpha) for all alpha, beta in {C}. The commutativity of I(alpha) for the two-f...
Low-rank adaption (LoRA) is a widely used parameter-efficient finetuning method for LLM that reduces memory requirements. However, current LoRA optimizers lack transformation invariance, meaning the actual updates to the weights depends on how the tw...
We show an exact formula obtained in [1], which relates hatted and standard zeta-values to all orders of perturbation theory. The formula is based on the Landau-Khalatnikov-Fradkin (LKF) transformation between the massless propagators of charged part...
We develop a new model for phase transformation kinetics in metals by generalizing the Levitas-Preston (LP) phase field model of martensite phase transformations (see Levitas and Preston (2002a,b); Levitas, Preston and Lee (2003)) to arbitrary pressu...
Polly is the LLVM project's polyhedral loop nest optimizer. Recently, user-directed loop transformation pragmas were proposed based on LLVM/Clang and Polly. The search space exposed by the transformation pragmas is a tree, wherein each node represent...
A modification of the Holstein-Primakoff transformation is proposed such that creation and annihilation operators for a bosonic field are rewritten as operators of a $SU(2)$ algebra. Once it is applied to a quantum Hamiltonian, a subsequent applicati...
A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schrödinger matrix Hamiltonians is characterized...
The languages generated by interval exchange transformations have been characterized by Ferenczi-Zamboni (2008) and Belov-Cernyatev (2010) under some extra conditions on the system. Lifting these conditions leads us to consider successively natural c...
This volume constitutes the pre-proceedings of the 26th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2016), held on 6-8th September 2016 in Edinburgh, Scotland UK, and co-located with the 18th International Symp...
This paper introduces the Mechacnially prOgrammed Radius-adjustable PHysical (MORPH) wheel, a fully passive variable-radius wheel that embeds mechanical behavior logic for torque-responsive transformation. Unlike conventional variable transmission sy...
We describe situations in which chains of N degenerate quantum energy levels, coupled by time-dependent external fields, can be replaced by independent sets of chains of length N, N-1,...,2 and sets of uncoupled single states. The transformation is a...
Let T be a measurable transformation of a probability space $(E,\mathcal {E},π)$, preserving the measure π. Let X be a random variable with law π. Call K(\cdot, \cdot) a regular version of the conditional law of X given T(X). Fix $B\in \mathcal {E...
Special birational transformations $Φ:\p^r\da Z$ defined by quadric hypersurfaces are studied by means of the variety of lines $\mathcal L_z\subset\p^{r-1}$ passing through a general point $z\in Z$. Classification results are obtained when $Z$ is ei...
We apply the results of arXiv:1109.3573 to study quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps and obtain complete and explicit classifications...
Let φ: \mathbb{P}^{r}\dashrightarrow Z be a birational transformation with a smooth connected base locus scheme, where Z\subseteq\mathbb{P}^{r+c} is a nondegenerate prime Fano manifold. We call φa quadro-quadric special briational transformation if...