The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations between th...
Consider the following hat guessing game. A bear sits on each vertex of a graph $G$, and a demon puts on each bear a hat colored by one of $h$ colors. Each bear sees only the hat colors of his neighbors. Based on this information only, each bear has...
Nowadays three-dimensional (3D) printing has been widely used for producing geometrically complex 3D structures from a broad range of materials such as ceramics, metals, polymers, semiconductors, etc. Although it has been demonstrated that a fabricat...
Motivated by suggestions of Paolo Cotta-Ramusino's work at the physical level of rigor relating BF theory to the Donaldson polynomials, we provide a construction applicable to the Turaev/Viro and Crane/Yetter invariants of *a priori* finer invarian...
A Nullstellensatz is a theorem providing information on polynomials that vanish on a certain set: David Hilbert's Nullstellensatz (1893) is a cornerstone of algebraic geometry, and Noga Alon's Combinatorial Nullstellensatz (1999) is a powerful tool i...
An enteric coating is a polymer barrier applied to oral medication that prevents its dissolution or disintegration in the gastric environment. This helps
Biomedical image segmentation is a very important part in disease diagnosis. The term "colonic polyps" refers to polypoid lesions that occur on the surface of the colonic mucosa within the intestinal lumen. In clinical practice, early detection of po...
Traditional segmentation methods for colonic polyps are mainly designed based on low-level features. They could not accurately extract the location of small colonic polyps. Although the existing deep learning methods can improve the segmentation accu...
We utilize Cauchy's argument principle in combination with the Jacobian of a holomorphic function in several complex variables and the first moment of a ratio of two correlated complex normal random variables to prove explicit formulas for the densit...
We study zero distribution of random linear combinations of the form $$P_n(z)=\sum_{j=0}^nη_jφ_j(z),$$ in any Jordan region $Ω\subset \mathbb C$. The basis functions $φ_j$ are orthogonal polynomials on the unit circle (OPUC) that are real-valued...
The behavior of mobile linkers connecting two semi-flexible charged polymers, such as polyvalent counterions connecting DNA or F-actin chains, is studied theoretically. The chain bending rigidity induces an effective repulsion between linkers at la...
Metric spaces defined within convex polygons, such as the Thompson, Funk, reverse Funk, and Hilbert metrics, are subjects of recent exploration and study in computational geometry. This paper contributes an educational piece of software for understan...
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...
I am not OP. Originally posted in [](https://www.reddit.com/r/relationship_advice/) by [](https://www.reddit.com/user/LostMonokumaKub/) This was a BORU post with only one update, posted two years ago...
We reported a systematic change in the average magnetic relaxation rate, after the application and removal of a 5 T magnetic field, in a polycrystalline sample of La0.5Ca0.5MnO3. Magnetic relaxation measurements and magnetization versus field curve...
Let $K$ be a field of positive characteristic with no algebraically closed subfield. Let $F$ be a function field over $K$ and $t \in F$ transcendental over $K$. Refining a result of Eisentr{ä}ger and Shlapentokh, we show that there is no algorithm w...
We prove $L^{p_1}(\mathbb R^d)\times \dots \times L^{p_{n+2}}(\mathbb R^{d})$ polynomial growth estimates for the Christ-Journé multilinear singular integral forms and suitable generalizations....
We show that nontrivial classical pretzel knots L(p,q,r) are hyperbolic with eight exceptions which are torus knots. We find Conway polynomials of n-pretzel links using a new computation tree. As applications, we compute the genera of n-pretzel lin...
This paper presents the design and implementation of Juniper: a functional reactive programming language (FRP) targeting the Arduino and related microcontroller systems. Juniper provides a number of high level features, including parametric polymorph...
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