In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)
We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $ΣΠΣ$ circuits, we show that t...
Heine and Stieltjes in their studies of linear second-order differential equations with polynomial coefficients having a polynomial solution of a preassigned degree, discovered that the roots of such a solution are the coordinates of a critical poi...
Astronomy Engine: multi-language calculation of Sun, Moon, and planet positions. Predicts lunar phases, eclipses, transits, oppositions, conjunctions, equinoxes, solstices, rise/set times, and other events. Provides vector and angular coordinate transforms amo…
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate transforma...
For a semigroup $P_t$ generated by an elliptic operator on a smooth manifold $M$, we use straightforward martingale arguments to derive probabilistic formulae for $P_t(V(f))$, not involving derivatives of $f$, where $V$ is a vector field on $M$. For...
Spatiotemporal Arrays, Raster and Vector Data Cubes (⭐ 600)
Points: 638 | Comments: 388 | Author: eigen-vector
Manga is a fashionable Japanese-style comic form that is composed of black-and-white strokes and is generally displayed as raster images on digital devices. Typical mangas have simple textures, wide lines, and few color gradients, which are vectoriza...
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In this article we will construct a universal moduli space of stable parabolic vector bundles over the moduli space of marked Deligne-Mumford stable curves $\overline{M}_{_{g, n}}$. The objects that appear over the boundary of $\overline{M}_{_{g, n}}...
We study subsets of the $n$-dimensional vector space over the finite field $\mathbb{F}_q$, for odd $q$, which contain either a sphere for each radius or a sphere for each first coordinate of the center. We call such sets radii spherical Kakeya sets a...
Secret sharing provides a means to distribute shares of a secret such that any authorized subset of shares, specified by an access structure, can be pooled together to recompute the secret. The standard secret sharing model requires public access str...
We study the j-invariant of the canonical lifting of an elliptic curve as a Witt vector. We prove that its Witt coordinates lie in an open affine subset of the j-line and deduce the existence of a universal formula for the j-invariant of the canonica...
Constructing high-definition (HD) maps from sensory input requires accurately mapping the road elements in image space to the Bird's Eye View (BEV) space. The precision of this mapping directly impacts the quality of the final vectorized HD map. Exis...
Quantum machine learning (QML) is one of the most promising applications of quantum computation. However, it is still unclear whether quantum advantages exist when the data is of a classical nature and the search for practical, real-world application...
We prove an analogue of Kirwan surjectivity in the setting of equivariant basic cohomology of K-contact manifolds. If the Reeb vector field induces a free $S^1$-action, the $S^1$-quotient is a symplectic manifold and our result reproduces Kirwan's su...
Double Lie algebroids were discovered by Kirill Mackenzie from the study of double Lie groupoids and were defined in terms of rather complicated conditions making use of duality theory for Lie algebroids and double vector bundles. In this paper we es...
The promotion time cure rate model (PCM) is an extensively studied model for the analysis of time-to-event data in the presence of a cured subgroup. There are several strategies proposed in the literature to model the latency part of PCM. However, th...
The mixture cure rate model is the most commonly used cure rate model in the literature. In the context of mixture cure rate model, the standard approach to model the effect of covariates on the cured or uncured probability is to use a logistic funct...