Related papers: The Mystery of the Shape Parameter IV
Let $X$ be a compact toric extremal K\"ahler manifold. Using the work of Sz\'ekelyhidi, we provide a combinatorial criterion on the fan describing $X$ to ensure the existence of complex deformations of $X$ that carry extremal metrics. As an…
When filtering a topological space by a single parameter, the theory of quiver representations provides a complete framework for decomposing the resulting persistence module to obtain its barcode. This is achieved by interpreting the…
We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
The program of understanding Shape Theory layer by layer topologically and geometrically -- proposed in Part I -- is now addressed for 4 points in 1-$d$. Topological shape space graphs are far more complex here, whereas metric shape spaces…
We consider the algebra of invariants of binary forms of degree 9 with complex coefficients, find the 92 basic invariants, give an explicit system of parameters and show the existence of four more systems of parameters with different sets…
The full parameter space of Hermitian quark mass matrices with four texture zeros is explored by using current experimental data. We find that all ten free parameters of the four-zero quark mass matrices can well be constrained. In…
This paper proposes a new semi-parametric identification and estimation approach to multinomial choice models in a panel data setting with individual fixed effects. Our approach is based on cyclic monotonicity, which is a defining feature…
A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations…
We propose a novel quark mass matrix texture-pair with five free parameters, which fits the four quark mass ratios $m_s/m_b$, $m_d/m_b$, $m_c/m_t$, $m_u/m_t$, and the four CKM quark mixing observables. The matrices each have one texture…
In this paper, we classify the 1-Weierstrass points of the Kuribayashi quartic curves with three parameters $a,\,b$ and $c$ defined by the equation \[ C_{a,b,c}:x^{4}+y^{4}+z^{4}+ax^{2}y^{2}+bx^{2}z^2+cy^{2}z^{2}=0, \] such that…
We identified a set of four rephasing invariant parameters of the CKM matrix. They are found to exhibit hierarchies in powers of $\lambda^2$, from $\lambda^2$ to $\lambda^8$. It is shown that, at the present level of accuracy, only the…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
An updated determination of the parameters of the Cabibbo-Kobayashi-Maskawa matrix is presented.
Having been studied since long by statisticians, multivariate median concepts found their way into the image processing literature in the course of the last decades, being used to construct robust and efficient denoising filters for…
We review several key aspects of charm phenomenology which are important for the general program of determination of matrix elements of the Cabbibo-Kobayashi-Maskava (CKM) matrix. We argue that charm physics plays an important role in…
An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate…
This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in order to facilitate their study and then the stability of…
For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…
We extend to characteristic two recent results about isotropy of quadratic forms over function fields. In particular, we provide a characterization of function fields not only of quadratic forms but also more generally of polynomials in…