Related papers: Symmetry Properties of Nested Canalyzing Functions
Neuronal activity is found to lie on low-dimensional manifolds embedded within the high-dimensional neuron space. Variants of principal component analysis are frequently employed to assess these manifolds. These methods are, however,…
In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions which can be uniformly approximated by continuous…
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…
Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and…
Boolean networks constitute relevant mathematical models to study the behaviours of genetic and signalling networks. These networks define regulatory influences between molecular nodes, each being associated to a Boolean variable and a…
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\lambda$, and we…
A Boolean function is symmetric if it is invariant under all permutations of its arguments; it is quasi-symmetric if it is symmetric with respect to the arguments on which it actually depends. We present a test that accepts every…
Active nematic fluids confined in narrow channels generate spontaneous flows when the activity is sufficiently intense. Recently, it was shown that if the molecular anchoring at the channel walls is conflicting flows are initiated even in…
This paper presents a method to detect and recognize symmetries in Boolean functions. The idea is to use information theoretic measures of Boolean functions to detect sub-space of possible symmetric variables. Coupled with the new…
The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…
Correlation-immune (CI) multi-output Boolean functions have the property of keeping the same output distribution when some input variables are fixed. Recently, a new application of CI functions has appeared in the system of resisting…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
Although the classical density functional theory (DFT) of inhomogeneous fluids was formulated more than four decades ago, its application to broken symmetry phases of molecular systems remained a challenge. Approximate free energy…
The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present…
We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider $f(x_1, \dots, x_N)$, where $x_i \in \mathbb{R}^d$, and $f$ is invariant under permutations of its $N$…
Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making…
Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…
We introduce Neural Conjugate Flows (NCF), a class of neural network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous…
In a coupled-channel model, we explore the effects of coupling between configurations on the radial behavior of the wave function and, in particular, on the spectroscopic factor (SF) and the asymptotic normalization coefficient (ANC). We…