Related papers: Replica Symmetry Breaking in the Random Replicant …
Model checking is the process of deciding whether a system satisfies a given specification. Often, when the setting comprises multiple processes, the specifications are over sets of input and output signals that correspond to individual…
Symmetry arguments are frequently used -- often implicitly -- in mathematical modeling of natural selection. Symmetry simplifies the analysis of models and reduces the number of distinct population states to be considered. Here, I introduce…
In models with dynamical electroweak symmetry breaking, this breaking is normally communicated to quarks and leptons by a set of vector bosons with masses generated via sequential breaking of a larger gauge symmetry. In reasonably…
Symmetry breaking--the phenomenon in which the symmetry of a system is not inherited by its stable states--underlies pattern formation, superconductivity, and numerous other effects. Recent theoretical work has established the possibility…
It is known that recursive training from generative models can lead to the so called `collapse' of the simulated probability distribution. This note shows that one in fact gets two different asymptotic behaviours depending on whether an…
Overfitting, which happens when the number of parameters in a model is too large compared to the number of data points available for determining these parameters, is a serious and growing problem in survival analysis. While modern medicine…
We model evolution of plants in a world, made up of different locations, with multiple environments (mutually exclusive and collectively exhaustive subsets of locations). Each environment (landmass) has temperature, rainfall, and other…
The spontaneous symmetry breaking in the quantum sine-Gordon model is studied by a density matrix renormalization group. A phase diagram in the coupling constant - system size plane is obtained.
We investigate the problem of speciation and coexistence in simple ecosystems when the competition among individuals is included in the Eigen model for quasi-species. By suggesting an analogy between the competition among strains and the…
Assessment of replicability is critical to ensure the quality and rigor of scientific research. In this paper, we discuss inference and modeling principles for replicability assessment. Targeting distinct application scenarios, we propose…
We investigate the replicator dynamics with "sparse" symmetric interactions which represent specialist-specialist interactions in ecological communities. By considering a large self interaction $u$, we conduct a perturbative expansion which…
We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry…
Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all…
We discuss general formation of complementary behaviors, functions and forms in biological species competing for resources. We call orthogonalization the related processes on macro and micro-level of a self-organized formation of…
The dynamical symmetry breaking associated with the existence and non-existence of breather solutions is studied. Here, nonlinear hyperbolic evolution equations are calculated using a high-precision numerical scheme. %%% First, for…
Within a Kuhn-Tucker cavity method introduced in a former paper, we study optimal stability learning for situations, where in the replica formalism the replica symmetry may be broken, namely (i) the case of a simple perceptron above the…
Recent 3D organ reconstitution studies show that a group of stem cells can establish a body axis and acquire different fates in a spatially organized manner. How such symmetry breaking happens in the absence of external spatial cues, and…
A formalism capable of handling the first step of hierarchical replica symmetry breaking in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field…
For a one-locus haploid infinite population with discrete generations, the celebrated Kingman's model describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability.…
An ongoing "reproducibility crisis" calls into question scientific discoveries across a variety of disciplines ranging from life to social sciences. Replication studies aim to investigate the validity of findings in published research, and…