A knotted protein refers to a type of protein structure that contains a knot-like configuration in its polypeptide chain. This can occur when a portion of the protein backbone loops around and passes through itself, creating a topological knot. Such configurations are rare in nature due to the constraints that the peptide chain must conform to, but they can provide unique stability and functional advantages. Knotted proteins have been observed in various organisms and are often characterized by their complex folding patterns.

A constructible polygon is a polygon that can be drawn using only a compass and straightedge as per the principles of classical Greek geometry. Specifically, a regular polygon (one where all sides and angles are equal) is considered constructible if the number of its sides \( n \) can be expressed in a very specific way.

A Hankel matrix is a specific type of structured matrix that has the property that each ascending skew-diagonal from left to right is constant. In more formal terms, a Hankel matrix is defined by its entries being determined by a sequence of numbers; the entry in the \(i\)-th row and \(j\)-th column of the matrix is given by \(h_{i,j} = a_{i+j-1}\), where \(a\) is a sequence of numbers.

The term "EP matrix" can refer to different concepts depending on the context. Here are a couple of interpretations: 1. **Eigenspace Projection (EP) Matrix**: In linear algebra, an EP matrix can be related to the projection onto an eigenspace associated with a specific eigenvalue of a matrix. The projection matrix is used to project vectors onto the subspace spanned by the eigenvectors corresponding to that eigenvalue.

Descartes' theorem, also known as the "kissing circles theorem," relates to the geometric properties of circles. Specifically, it provides a relationship between the curvatures (or bending) of four mutually tangent circles. In this context, the curvature of a circle is defined as the reciprocal of its radius (i.e., \( k = \frac{1}{r} \)).

Katherine Pollard is a prominent scientist known for her work in genomics and evolutionary biology. She is particularly noted for her research on the evolution of genomes, population genetics, and the role of genomic variation in disease. Pollard has contributed significantly to our understanding of how genomic changes can impact biological traits and disease susceptibility. She has held academic positions at institutions like the Gladstone Institutes and the University of California, San Francisco.

A nine-point conic is a relevant concept in projective geometry, particularly in relation to conic sections. Specifically, a nine-point conic relates to a configuration of points derived from a triangle. Given a triangle, the nine-point conic is defined using several key points: 1. The midpoints of each side of the triangle (3 points). 2. The feet of the altitudes from each vertex to the opposite side (3 points).

The mean, often referred to as the average, is a measure of central tendency in statistics. It is calculated by summing a set of values and then dividing that sum by the number of values in the set.

The Wilkinson matrix is a specific type of structured matrix used in numerical analysis, particularly in the study of matrix algorithms and eigenvalue problems. It is named after the mathematician and computer scientist James H. Wilkinson. The Wilkinson matrix is notable for its properties, especially its sensitivity to perturbations, which makes it useful for testing numerical algorithms for stability and accuracy.

Root Mean Square (RMS) is a statistical measure used to quantify the magnitude of a varying quantity. It is especially useful in contexts where alternating values are present, such as in electrical engineering, signal processing, and physics. The RMS value provides a way to express the average of a set of values, where all values are taken into account without regard to their sign (positive or negative).

Sensemaking is a cognitive process through which individuals and groups interpret and understand complex, ambiguous, or uncertain situations. It involves gathering information, interpreting data, and creating meaning from experiences. Sensemaking is particularly important in environments where information is incomplete or rapidly changing, such as in organizational decision-making, crisis management, or during transformative shifts in social or technological contexts.

The Bochner–Riesz means are a class of means associated with the Fourier transform, named after mathematicians Salomon Bochner and Hans Riesz. They generalize the concept of the Riesz means of Fourier series and are particularly useful in the study of convergence properties in harmonic analysis and functional analysis.

The quasi-arithmetic mean is a generalization of the arithmetic mean, and it is defined using a function that transforms the values before averaging them.

The term "Riesz mean" refers to a concept in mathematical analysis, specifically in the study of summability and convergence of series or functions. It is named after the Hungarian mathematician Frigyes Riesz. The Riesz mean is a way to assign a value to a divergent series or to improve the convergence properties of a series. It can be viewed as a generalization of the concept of taking limits.

Sepp Hochreiter is a prominent figure in the field of artificial intelligence and machine learning, particularly known for his contributions to deep learning. He is best known for co-developing the Long Short-Term Memory (LSTM) architecture, which is a type of recurrent neural network (RNN) designed to address the vanishing gradient problem, enabling the model to learn long-term dependencies in sequential data. Hochreiter earned his Ph.D.

The 60th meridian east is a line of longitude that is 60 degrees east of the Prime Meridian, which is defined as 0 degrees longitude. This meridian runs from the North Pole to the South Pole and passes through several countries as it spans the globe. In the northern hemisphere, the 60th meridian east traverses parts of Russia and Kazakhstan. In the southern hemisphere, it passes through Antarctica.