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An endhered (end-adhered) pattern is a subset of arcs in matchings, such that the corresponding starting points are consecutive and the same holds for the ending points. Such patterns are in one-to-one correspondence with the permutations.…
The evolutionary and ecological processes behind the origin of species are among the most fundamental problems in biology. In fact, many theoretical hypothesis on different type of speciation have been proposed. In particular, models of…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two…
Following the traditional paradigm of convolutional neural networks (CNNs), modern CNNs manage to keep pace with more recent, for example transformer-based, models by not only increasing model depth and width but also the kernel size. This…
Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…
We investigate the competition between two quasispecies residing on two disparate neutral networks. Under the assumption that the two neutral networks have different topologies and fitness levels, it is the mutation rate that determines…
The lack of large-scale, continuously evolving empirical data usually limits the study of networks to the analysis of snapshots in time. This approach has been used for verification of network evolution mechanisms, such as preferential…
Our work is concerned with the generation and targeted design of RNA, a type of genetic macromolecule that can adopt complex structures which influence their cellular activities and functions. The design of large scale and complex…
RNA viruses form genetically diverse populations structured as mutant spectra, or quasispecies, whose internal organization influences their evolutionary and adaptive dynamics. While genetic diversity has been extensively characterized, the…
A lattice model of RNA denaturation which fully accounts for the excluded volume effects among nucleotides is proposed. A numerical study shows that interactions forming pseudoknots must be included in order to get a sharp continuous…
We generalise Spatial Transformer Networks (STN) by replacing the parametric transformation of a fixed, regular sampling grid with a deformable, statistical shape model which is itself learnt. We call this a Statistical Transformer Network…
The conceptual landscape of convection has two simple gateways: optimal function and random form. Optimal convection adjusts toward a univariate ideal called neutrality. Convection form involves elements (parcels, bubbles, drafts) whose…
Neural networks have a number of shortcomings. Amongst the severest ones is the sensitivity to distribution shifts which allows models to be easily fooled into wrong predictions by small perturbations to inputs that are often imperceivable…
Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression…
Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to…
Spectral Graph Neural Networks (GNNs) are gaining attention for their ability to surpass the limitations of message-passing GNNs. They rely on supervision from downstream tasks to learn spectral filters that capture the graph signal's…
A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species.…