Related papers: Complete intersection for equivariant models
Crossover is the process of recombining the genetic features of two parents. For many applications where crossover is applied to permutations, relevant genetic features are pairs of adjacent elements, also called edges in the permutation…
Mixed-effects models are among the most commonly used statistical methods for the exploration of multispecies data. In recent years, also Joint Species Distribution Models and Generalized Linear Latent Variale Models have gained in…
Complex interactions between genes or proteins contribute a substantial part to phenotypic evolution. Here we develop an evolutionarily grounded method for the cross-species analysis of interaction networks by {\em alignment}, which maps…
Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic…
The need for structures capable of accommodating complex evolutionary signals such as those found in, for example, wheat has fueled research into phylogenetic networks. Such structures generalize the standard phylogenetic tree model by also…
We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions…
The perfect phylogeny problem is a classic problem in computational biology, where we seek an unrooted phylogeny that is compatible with a set of qualitative characters. Such a tree exists precisely when an intersection graph associated…
We prove that the derived category of a smooth complete intersection variety is equivalent to a full subcategory of the derived category of a smooth projective Fano variety. This enables us to define some new invariants of smooth projective…
We give a Belyi-type characterisation of smooth complete intersections of general type over $\mathbb{C}$ which can be defined over $\bar{\mathbb{Q}}$. Our proof uses the higher-dimensional analogue of the Shafarevich boundedness conjecture…
We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large…
Fix a finite group $G$. We seek to classify varieties with $G$-action equivariantly birational to a representation of $G$ on affine or projective space. Our focus is odd-dimensional smooth complete intersections of two quadrics, relating…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
We study phylogenetic invariants of models of evolution whose group of symmetries is the cyclic group with 3 elements. We prove that projective schemes corresponding to the ideal I of phylogenetic invariants of such a model and to its…
We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are…
We study Fano schemes $F_k(X)$ for complete intersections $X$ in a projective toric variety $Y\subset \mathbb{P}^n$. Our strategy is to decompose $F_k(X)$ into closed subschemes based on the irreducible decomposition of $F_k(Y)$ as studied…
It is proved that a finite intersection of special preenveloping ideals in an exact category $({\mathcal A}; {\mathcal E})$ is a special preenveloping ideal. Dually, a finite intersection of special precovering ideals is a special…
The multiview variety of an arrangement of cameras is the Zariski closure of the images of world points in the cameras. The prime vanishing ideal of this complex projective variety is called the multiview ideal. We show that the bifocal and…
We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing…
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units…
Patch ideals encode neighbourhoods of a variety in GL_n/B. For Peterson varieties we determine generators for these ideals and show they are complete intersections, and thus Cohen-Macaulay and Gorenstein. Consequently, we combinatorially…