The theory of border bases for zero-dimensional ideals has attracted several researchers in symbolic computation due to their numerical stability and mathematical elegance. As shown in (Francis & Dukkipati, J. Symb. Comp., 2014), one can extend the c...
In this paper, we draw a connection between ideal lattices and Gröbner bases in the multivariate polynomial rings over integers. We study extension of ideal lattices in $\mathbb{Z}[x]/\langle f \rangle$ (Lyubashevsky \& Micciancio, 2006) to ideal la...
In 2015, Francis Comets shared with me a clever way to relate a model of directed last passage percolation with i.i.d. Gumbel edge weights to a special case of the log-gamma directed polymer model. To my knowledge, he never wrote this down. In the wa...
3 days ago · From everyday use to special occasions, this Mini Slouchy Chain Handbag from Universal Thread™ will be your go-to favorite. This mini slouchy bag features a polyester shell in a brown hue …
Hi all, First, I just want to make it clear that this is absolutely a serious question. If you go to my account and read my former post in /r/polyamory, you can read about my situation (throwaway ac...
Slush generator to create Custom Elements using Polymer, X-Tag or VanillaJS (⭐ 41)
Feb 8, 2024 · Gynecologists specialize in diagnosing and treating reproductive health disorders like endometriosis, infertility, polycystic ovary syndrome (PCOS), certain types of reproductive cancers …
Igusa proved in 1958 that the polynomial determining the supersingularity of elliptic curve in Legendre form is separable. In this paper, we get an analogous result for curves of genus $2$ in Rosenhain form. More precisely we show that the ideal dete...
We note that the recent polynomial proofs of the spherical and complex plank covering problems by Zhao and Ortega-Moreno give some general information on zeros of real and complex polynomials restricted to the unit sphere. As a corollary of these res...
Protein splicing is a post-translational autocatalystic excision of internal protein sequence (intein) with the subsequent ligation of the flanking polypeptides (exteins). The high specificity of excision ensured by intein makes it possible to use...
Despite its remoteness from other continents, the Antarctic region cannot escape the aftermath of human activities as it is highly influenced by anthropogenic impacts that occur both in the regional and global context. Contamination by microplastics,...
a simple collection of 2d collision/intersects functions. Supports points, circles, ellipses, lines, axis-aligned boxes, and polygons (⭐ 562)
The second author and Norbury initiated the enumeration of lattice points in the Deligne-Mumford compactifications of moduli spaces of curves. They showed that the enumeration may be expressed in terms of polynomials, whose top and bottom degree coef...
We show a parallelism between the expansion and compression of the atmosphere in the secondary cycle of a tropical cyclone with the fast expansion and compression of wet air in a bottle. We present a simple model in order to understand how the system...
We propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u) du$ for a function $f$, which depend on a smoothness parameter $r\in\mathbb{N}$. The first estimator integrates exactly the polynomials of degrees $p<r$ and achieves the o...
Pawns is a programming language under development which supports pure functional programming (including algebraic data types, higher order programming and parametric polymorphism) and imperative programming (including pointers, destructive update of...
Pawns is a programming language under development that supports algebraic data types, polymorphism, higher order functions and "pure" declarative programming. It also supports impure imperative features including destructive update of shared data str...
We generalize the Rubik's cube, together with its group of configurations, to any abstract regular polytope. After discussing general aspects, we study the Rubik's simplex of arbitrary dimension and provide a complete description of the associated gr...
The tangram and Sei Shonagon Chie no Ita are popular dissection puzzles consisting of seven pieces. Each puzzle can be formed by identifying edges from sixteen identical right isosceles triangles. It is known that the tangram can form 13 convex polyg...
In this short note we show the existence of an epimorphism between groups of $2$-bridge knots by means of an elementary argument using the Riley polynomial. As a corollary, we give a classification of $2$-bridge knots by Riley polynomials....