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This paper presents a comprehensive analysis of critical point sets in two-layer neural networks. To study such complex entities, we introduce the critical embedding operator and critical reduction operator as our tools. Given a critical…
This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability,…
This article determines and characterizes the minimal number of actuators needed to ensure structural controllability of a linear system under structural alterations that can severe the connection between any two states. We assume that…
Intracellular networks process cellular-level information and control cell fate. They can be computationally modeled using Boolean networks, which are implicit-time causal models of discrete binary events. These networks can be embedded in…
Biological circuits such as neural or gene regulation networks use internal states to map sensory input to an adaptive repertoire of behavior. Characterizing this mapping is a major challenge for systems biology, and though experiments that…
Recent years have seen the emergence of many new neural network structures (architectures and layers). To solve a given task, a network requires a certain set of abilities reflected in its structure. The required abilities depend on each…
In the event of an observation of neutrinoless double beta decay, a relevant question would be: what lepton number violating physics is responsible for the decay? The exchange of Majorana neutrinos and/or supersymmetric particles may…
In this paper, a method is presented to synthesize neural network controllers such that the feedback system of plant and controller is dissipative, certifying performance requirements such as L2 gain bounds. The class of plants considered…
While deep neural networks have surpassed human performance in multiple situations, they are prone to catastrophic forgetting: upon training a new task, they rapidly forget previously learned ones. Neuroscience studies, based on idealized…
The nematode Caenorhabditis elegans (C. elegans) is used as a model organism to better understand developmental biology and neurobiology. C. elegans features an invariant cell lineage, which has been catalogued and observed using…
Local perturbations of individual metabolic reactions may result in different levels of lethality, depending on their roles in metabolism and the size of subsequent cascades induced by their failure. Moreover, essentiality of individual…
The Synthetic Control method (SC) has become a valuable tool for estimating causal effects. Originally designed for single-treated unit scenarios, it has recently found applications in high-dimensional disaggregated settings with multiple…
We study the dynamic range of a cellular automaton model for a neuronal network with electrical and chemical synapses. The neural network is separated into two layers, where one layer corresponds to inhibitory, and the other corresponds to…
Evolving biomolecular networks have to combine the stability against perturbations with flexibility allowing their constituents to assume new roles in the cell. Gene duplication followed by functional divergence of associated proteins is a…
Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under…
Leptogenesis in left-right symmetric theories is studied. The usual see-saw mechanism is modified by the presence of a left-handed Higgs triplet. A simple connection between the properties of the light left-handed and heavy right-handed…
Neuronal spikes directly drive muscles and endow animals with agile movements, but applying the spike-based control signals to actuators in artificial sensor-motor systems inevitably causes a collapse of learning. We developed a system that…
Ablation studies have been widely used in the field of neuroscience to tackle complex biological systems such as the extensively studied Drosophila central nervous system, the vertebrate brain and more interestingly and most delicately, the…
Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of…
Spontaneous symmetry breaking (SSB) occurs when modes of asymmetric profile appear in a symmetric, double-well potential, due to the nonlinearity of the potential exceeding a critical value. In this study, we examine SSB in a periodic…