Related papers: A Determinantal Inequality for the Geometric Mean …
The geometric mean method (GMM) and the eigenvector method (EM) are well-known approaches to deriving information from pairwise comparison matrices in decision making processes. However, the original algorithms of these methods are…
Text-to-image diffusion models (DMs) develop at an unprecedented pace, supported by thorough theoretical exploration and empirical analysis. Unfortunately, the discrepancy between DMs and autoregressive models (ARMs) complicates the path…
We study the cone $\mathscr{P}_{\text{J}}$ of positive J-Hermitian matrices associated with an indefinite signature matrix J = $\text{Id}_{p,q}$. We show that the J-exponential map is bijective and use it to analyze the algebraic and…
We evaluate the determinant $\det_{1\leq i,j\leq n}(\binom{x+y+j}{x-i+2j}-\binom{x+y+j}{x+i+2j})$, which gives the number of lozenge tilings of a hexagon with cut off corners. A particularly interesting feature of this evaluation is that it…
State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs)…
The spatial resolution of a detector, using a reference detector telecscope, can be measured applying the geometric mean method, with tracks reconstructed from hits of all the detectors, including ($\sigma_\mathrm{in}$) and excluding…
There is a prevalent opinion that diffusion-based models outperform GAN-based counterparts in the Image Super Resolution (ISR) problem. However, in most studies, diffusion-based ISR models employ larger networks and are trained longer than…
The Toader-Qi mean of positive numbers $a$ and $b$ defined by \begin{equation*} TQ\left( a,b\right) =\frac{2}{\pi }\int_{0}^{\pi /2}a^{\cos ^{2}\theta }b^{\sin ^{2}\theta }d\theta \end{equation*} is related to the modified Bessel function…
In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calder\'on's and Zygmund's theory of first order…
We present a refinement, by selfimprovement, of the arithmetic geometric inequality.
Diffusion Models have demonstrated remarkable performance in image generation. However, their demanding computational requirements for training have prompted ongoing efforts to enhance the quality of generated images through modifications…
For a positive semidefinite matrix $H= \begin{bmatrix} A&X\\ X^{*}&B \end{bmatrix} $, we consider the norm inequality $ ||H||\leq ||A+B|| $. We show that this inequality holds under certain conditions. Some related topics are also…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
Image classification serves as the cornerstone of computer vision, traditionally achieved through discriminative models based on deep neural networks. Recent advancements have introduced classification methods derived from generative…
Recent work by M. Afifurrahman established the first asymptotic estimates with error terms for the number of $2\times 2$ matrices with fixed non-zero determinant $n\in\mathbb{N}$, and with coefficients bounded in absolute value by $X$. In…
The space of matrices of positive determinant GL^+_n inherits an extrinsic metric space structure from R^{n^2}. On the other hand, taking the infimum of the lengths of all paths connecting two points in GL^+_n gives an intrinsic metric. We…
A real symmetric matrix (resp., tensor) is said to be copositive if the associated quadratic (resp., homogeneous) form is greater than or equal to zero over the nonnegative orthant. The problem of detecting their copositivity is NP-hard.…
In this note, we present a simple proof of an analogue of the Cauchy-Schwarz inequality relevant to products of determinants. Specifically, we show that $$ |\det(A^*MB)|^2\leq \det(A^*MA)\cdot \det(B^*MB),\quad A,B\in \mathbb{C}^{m\times…
We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an…