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Saliency methods seek to explain the predictions of a model by producing an importance map across each input sample. A popular class of such methods is based on backpropagating a signal and analyzing the resulting gradient. Despite much…
We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangean similar to those used for spin systems. We are able to show that the low energy…
The brain must extract behaviorally relevant latent variables from the signals streamed by the sensory organs. Such latent variables are often encoded in the dynamics that generated the signal rather than in the specific realization of the…
Cells with the same genome can exist in different phenotypes. and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming…
The present document is devoted to structural properties of neural population dynamics and especially their differential flatness. Several applications of differential flatness in the present context can be envisioned, among which:…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
We present a general procedure to introduce electronic polarization into classical Molecular Dynamics (MD) force-fields using a Neural Network (NN) model. We apply this framework to the simulation of a solid-liquid interface where the…
Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of…
The spatial structure of the cell is highly organized at all levels: from small complexes and assemblies, to local nano- and micro-clusters, to global, micrometer scales across and between cells. We suggest that this multiscale spatial cell…
Multicellular organisms exhibit a high degree of structural organization with specific cell types always occurring in characteristic locations. The conventional framework for describing the emergence of such consistent spatial patterns is…
The growth and scaling of organs is a fundamental aspect of animal development. However, how organs grow to the right size and shape required by physiological demands, remains largely unknown. Here, we provide a framework combining theory…
A linear external perturbation is introduced in the action of the partition function of the random matrix model of RNA [G. Vernizzi, H. Orland and A. Zee, Phys. Rev. Lett. 94, 168103 (2005)]. It is seen that (i). the perturbation…
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…
The Weibull distribution is a commonly adopted choice for modeling the survival of systems subject to maintenance over time. When only proxy indicators and censored observations are available, it becomes necessary to express the…
Cell migration plays essential roles in development, wound healing, diseases, and in the maintenance of a complex body. Experiments in collective cell migration generally measure quantities such as cell displacement and velocity. The…
Many cellular processes require a polarization axis which generally initially emerges as an inhomogeneous distribution of molecular markers in the cell. We present a simple analytical model of a general mechanism of cell polarization taking…
A key problem of eukaryotic cell motility is the signaling mechanism of chemoattractant gradient sensing. Recent experiments have revealed the molecular correlate of gradient sensing: Frontness molecules, such as PI3P and Rac, localize at…
Recent progress in brain-guided image generation has improved the quality of fMRI-based reconstructions; however, fundamental challenges remain in preserving object-level structure and semantic fidelity. Many existing approaches overlook…
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and…
The fundamental biological processes of development of tissues and organs in multicellular organisms is governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in concentration…