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Existing analyses of optimization in deep learning are either continuous, focusing on (variants of) gradient flow, or discrete, directly treating (variants of) gradient descent. Gradient flow is amenable to theoretical analysis, but is…
Cells sense and predict their environment via energy-dissipating pathways. However, it is unclear whether dissipation helps or harms prediction. Here we study dissipation and prediction for a minimal sensory module of receptors that…
Deep learning has achieved spectacular performance in image and speech recognition and synthesis. It outperforms other machine learning algorithms in problems where large amounts of data are available. In the area of measurement technology,…
Dictyostelium discoideum (D.d.) is a widely studied amoeba due to its capabilities of development, survival, and self-organization. During aggregation it produces and relays a chemical signal (cAMP) which shows spirals and target centers.…
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…
We study gradient magnetometry with an ensemble of atoms with arbitrary spin. We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. For quantum states that are invariant…
In this paper, we are concerned with the gradient estimate of the electric field due to two nearly touching dielectric inclusions, which is a central topic in the theory of composite materials. We derive accurate quantitative…
A deep equilibrium model uses implicit layers, which are implicitly defined through an equilibrium point of an infinite sequence of computation. It avoids any explicit computation of the infinite sequence by finding an equilibrium point…
We realise an intrinsic optically pumped magnetic gradiometer based on non-linear magneto-optical rotation. We show that our sensor can reach a gradiometric sensitivity of 18 $\text{fT}/\text{cm}/\sqrt{\text{Hz}}$ and can reject common mode…
In recent years experiments have demonstrated that living cells can measure low chemical concentrations with high precision, and much progress has been made in understanding what sets the fundamental limit to the precision of chemical…
We numerically study the coalescence dynamics of two sessile droplets with radii $R_0$. The droplets are placed on top of a rigid substrate with a contact angle of $\theta_{eq.} = \pi/9$. Having a highly wettable substrate ($\theta_{eq} \ll…
Artificially engineered biosensors are highly inefficient in accurately measuring the concentration of biomarkers, particularly, during early diagnosis of diseases. On the other hand, single cellular systems such as chemotactic bacteria can…
How many times a diffusing molecule can permeate across a membrane or be adsorbed on a substrate? We employ the encounter-based approach to find the statistics of adsorption or permeation events for molecular diffusion in a general…
Absorption of electromagnetic energy by a dissipative material is one of the most fundamental electromagnetic processes that underlies a plethora of applied problems, including sensing and molecular detection, radar detection, wireless…
How can cells embedded into a gradient concentration triangulate the position of the source and migrate toward their final destination? The source triangulation requires to recover the three dimensional coordinates of the source from the…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
Here we characterized an information measure for cell polarity that applies to non-motile cells responding to a chemical gradient. The central idea is that polarization represents information about the direction of the gradient. We applied…
This study presents physical observations and insights into particle migration characteristics throughout the suffusion process. Using a purpose-built coaxial permeameter cell, suffusion experiments were conducted on idealised internally…
Single-molecule fluorescence imaging of adsorption onto initially-bare surfaces shows that polymer chains need not localize immediately after arrival. In a system optimized to present limited adsorption sites (quartz surface to which…
The complex absorbing potential (CAP) technique is one of the commonly used Non-Hermitian quantum mechanics approaches for characterizing electronic resonances. CAP combined with various electronic structure methods has shown promising…