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The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
Genotypic fitness landscapes are constructed by assessing the fitness of all possible combinations of a given number of mutations. In the last years, several experimental fitness landscapes have been completely resolved. As fitness…
A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual…
If a system undergoing phase transitions exhibits some characteristics of both first and second order, it is said to be of 'mixed order' or to display the Thouless effect. Such a transition is present in a simple model of a dynamic social…
When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial…
Unlike primates, training artificial neural networks on changing data distributions leads to a rapid decrease in performance on old tasks. This phenomenon is commonly referred to as catastrophic forgetting. In this paper, we investigate the…
The paramagnetic-to-ferromagnetic phase transition is believed to proceed through a critical point, at which power laws and scaling invariance, associated with the existence of one diverging characteristic length scale -- the so called…
Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
Given the ease of creating synthetic data from machine learning models, new models can be potentially trained on synthetic data generated by previous models. This recursive training process raises concerns about the long-term impact on…
Building on the work of Fyodorov (2004) and Fyodorov and Nadal (2012) we examine the critical behaviour of population of saddles with fixed instability index $k$ in high dimensional random energy landscapes. Such landscapes consist of a…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
Muller's ratchet, in its prototype version, models a haploid, asexual population whose size~$N$ is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying…
A simulation model of a population having internal (genetic) structure is presented. The population is subject to selection pressure coming from the environment which is the same in the whole system but changes in time. Reproduction has a…
Melting is often understood in purely equilibrium terms, where crystalline order disappears once the free energy of the solid equals that of the liquid. Yet at the microscopic level, the initiating events for melting can often be traced to…
We study the phase transition phenomenon inherent in the shuffled (permuted) regression problem, which has found numerous applications in databases, privacy, data analysis, etc. In this study, we aim to precisely identify the locations of…
Fitness effects of mutations fall on a continuum ranging from lethal to deleterious to beneficial. The distribution of fitness effects (DFE) among random mutations is an essential component of every evolutionary model and a mathematical…
Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones. Recent theoretical studies have pointed out that the resulting fitness dynamics is…
The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model…
The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is…