For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities can be c...
In this paper, we investigate the degrees of freedom ($\dof$) of penalized $\ell_1$ minimization (also known as the Lasso) for linear regression models. We give a closed-form expression of the $\dof$ of the Lasso response. Namely, we show that for an...
I give a new integral representation for the degree five (standard) L-function for automorphic representations of GSp(4) that is a refinement of integral representation of Piatetski-Shapiro and Rallis. The new integral representation unfolds to produ...
Let $G = (V, E)$ be a finite simple graph. In this paper, we characterize the degree of the $h$-polynomial of the edge ideal of $G$ in terms of the independence number of $G$. The key tools are the value of the independence polynomial of $G$ at $-1$...
Jan 10, 2025 · 周杰伦最新合作单曲《Six Degrees》发布，展现独特音乐风格，引发乐迷期待。
Austin Community College offers more than 100 programs in 10 areas of study that lead to career certificates, associate degrees, bachelor’s degrees, or university transfer.
We reformulate a fundamental result due to Cook, Harbourne, Migliore and Nagel on the existence and irreduciblity of unexpected plane curves of a set of points $Z$ in $\mathbb{P}^2$, using the minimal degree of a Jacobian syzygy of the defining equat...
In this paper, we examine a specific type of random chains and propose an unified approach to studying the degree-based topological indices, including their extreme values. We derive explicit analytical expressions for the expected values and varianc...
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We provide elementary algorithms for two preservation theorems for first-order sentences (FO) on the class âd of all finite structures of degree at most d: For each FO-sentence that is preserved under extensions (homomorphisms) on âd, a âd-equiv...
Part I - WeatherPy In this example, you’ll be creating a Python script to visualize the weather of 500+ cities across the world of varying distance from the equator. To accomplish this, you’ll be utilizing a simple Python library, the OpenWeatherMap API, and a little common sense…
We introduce a series of generalized clustering coefficients based on String formalism given by Aoyama, using adjacent matrix in networks. We numerically evaluate Milgram condition proposed in order to explore q-th degrees of separation in scale free...
In this article we discuss six degrees of separation, which has been suggested by Milgram's famous experiment\cite{Milg},\cite{Milg2}, from a theoretical point of view again. Though Milgram's experiment was partly inspired to Pool and Kochen's stud...
Fix a number field $k$, integers $\ell, n \geq 2$, and a prime $p$. For all $r \geq 1$, we prove strong unconditional upper bounds on the $r$-th moment of $\ell$-torsion in the ideal class groups of degree $p$ extensions of $k$ and of degree $n$ $S_n...
We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to directed graphs,...
Paddleboarding Through Minus 40-Degree Air Paddleboarders glide through minus 40-degree air in Novosibirsk, Russia, where the Ob River's current refuses to freeze. The temperature gap between ...
received a Bachelor of Arts degree in mathematics (summa cum laude) from Cornell College in 1972, a Master of Science degree in electrical engineering (with
HIGHLY meaning: 1 : to a great degree; 2 : in an amount or number that is greater than usual to a high degree
This is a translation of Kronecker's "Über die Gleichungen fünften Grades" (On equations of fifth degree), excerpted from the monthly report to the Berlin Academy of Sciences from June 1861....
HIGHLY meaning: 1 : to a great degree; 2 : in an amount or number that is greater than usual to a high degree