Natural killer (NK) cells serve as one of the first lines defense against viral infections and transformed cells. NK cell cytotoxicity is not dependent on antigen presentation by target cells, but integration activating inhibitory signals triggered receptor-ligand interactions formed at a tight intercellular contact between cell, i.e., immune synapse. We have studied single-cell migration behavior target-cell dynamics resting interleukin (IL)-2-activated human peripheral blood Small...

Mixed monotone systems form an important class of nonlinear that have recently received attention in the abstraction-based control design area. Slightly different definitions exist literature, and it remains a challenge to verify mixed monotonicity system general. In this paper, we first clarify relation between existing systems, then give two sufficient conditions for functions defined on Euclidean space. These are more general than ones from they suggest is very generic property. Some...

This paper considers the problem of synthesizing output-feedback control laws for a class discrete-time hybrid systems in order trajectories system to satisfy certain high-level specifications expressed linear temporal logic. By leveraging ideas from robust interpretation logic formulas and bounded-error estimation, we identify subclass which it is possible reduce state-feedback form. In particular, use locally superstable observers resolve partial information at continuous level. allows us...

Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, covariant formulation and analysis continuum models nonequilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce study a generalized Navier-Stokes model driven by active stresses in nonplanar geometries. The analytical tractability theory is demonstrated through exact stationary solutions case spherical bubble geometry. Direct numerical simulations...

Abstract Tensor decompositions such as the canonical format and tensor train have been widely utilized to reduce storage costs operational complexities for high‐dimensional data, achieving linear scaling with input dimension instead of exponential scaling. In this paper, we investigate even lower storage‐cost representations in ring format, which is an extension variable end‐ranks. Firstly, introduce two algorithms converting a full low cost. Secondly, detail rounding operation rings show...

The number of noisy images required for molecular reconstruction in single-particle cryo-electron microscopy (cryo-EM) is governed by the autocorrelations observed, randomly-oriented, projection images. In this work, we consider effect imposing sparsity priors on molecule. We use techniques from signal processing, optimization, and applied algebraic geometry to obtain new theoretical computational contributions challenging non-linear inverse problem with constraints. prove that structures...

.We study how the learning rate affects performance of a relaxed randomized Kaczmarz algorithm for solving \(A x \approx b + \varepsilon\) , where x=b\) is consistent linear system and \(\varepsilon\) has independent mean zero random entries. We derive schedule which optimizes bound on expected error that sharp in certain cases; contrast to exponential convergence standard algorithm, our optimized involves reciprocal Lambert- \(W\) function an exponential.Keywordslearning raterandomized...

Motivated by the problem of determining atomic structure macromolecules using single-particle cryo-electron microscopy (cryo-EM), we study sample and computational complexities sparse multi-reference alignment (MRA) model: estimating a signal from its noisy, circularly shifted copies. Based on tight connection to crystallographic phase retrieval problem, establish that if number observations is proportional square variance noise, then MRA statistically feasible for sufficiently signals. To...

Abstract Principal component analysis (PCA) plays an important role in the of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method estimating compressed representation 2-D covariance matrix noisy cryo-EM projection affected by radial point spread functions that enables PCA computation. Our is based on new algorithm expanding Fourier–Bessel basis (the harmonics disk), which provides...

We present a fast and numerically accurate method for expanding digitized

Following an approach by Exner et al. (Commun Math Phys 26:531–541, 2014), we establish Lieb–Thirring inequalities for general self-adjoint and second-degree differential operators with matrix valued potentials acting in one space-dimension. These include generalize the magnetic Schrödinger operator. Three different settings are considered, functions defined on whole real line, a semi-axis interval, respectively, leading to types of bounds. An interpretation result terms star graphs two...

We describe a simple, black-box compression format for tensors with multiscale structure. By representing the tensor as sum of compressed defined on increasingly coarse grids, we capture low-rank structures each grid-scale, and show how this leads to an increase in fixed accuracy. devise alternating algorithm represent given multiresolution prove local convergence guarantees. In two dimensions, provide examples that approach can beat Eckart--Young theorem, dimensions higher than two, achieve...

Single particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution 3-D structure biological macromolecules from many noisy and randomly oriented projection images. One notable approach to reconstruction, known as Kam's method, relies on moments 2-D Inspired by we introduce a rotationally invariant metric between two molecular structures, which does not require alignment. Further, stack images structure, rotations reflections performing...

The classical beltway problem entails recovering a set of points from their unordered pairwise distances on the circle. This can be viewed as special case crystallographic phase retrieval sparse signal its periodic autocorrelation. Based this interpretation, and motivated by cryo-electron microscopy, we suggest natural generalization to orthogonal groups: signal, up an transformation, autocorrelation over group. If support is collision-free, bound number solutions groups, prove that exactly...

Single-particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution three-dimensional (3D) structure biological macromolecules from many noisy and randomly oriented projection images. One notable approach to 3D reconstruction, known as Kam's method, relies on moments two-dimensional (2D) Inspired by we introduce a rotationally invariant metric between two molecular structures, which does not require alignment. Further, stack images...

When is heterogeneity in the composition of an autonomous robotic team beneficial and when it detrimental? We investigate answer this question context a minimally viable model that examines role heterogeneous speeds perimeter defense problems, where defenders share total allocated speed budget. consider two distinct problem settings develop strategies based on dynamic programming local interaction rules. present theoretical analysis both approaches our results are extensively validated using...

We devise fast and provably accurate algorithms to transform between an $N\times N \times N$ Cartesian voxel representation of a three-dimensional function its expansion into the ball harmonics, that is, eigenbasis Dirichlet Laplacian on unit in $\mathbb{R}^3$. Given $\varepsilon > 0$, our achieve relative $\ell^1$ - $\ell^\infty$ accuracy $\varepsilon$ time $O(N^3 (\log N)^2 + N^3 |\log \varepsilon|^2)$, while their dense counterparts have complexity $O(N^6)$. illustrate methods numerical examples.

Cryo-electron microscopy (Cryo-EM) is a widely-used technique for recovering the 3-D structure of biological molecules from large number experimentally generated noisy 2-D tomographic projection images structure, taken unknown viewing angles. Through computationally intensive algorithms, these observed are processed to reconstruct structures. Many popular computational methods rely on estimating angles as part reconstruction process, which becomes particularly challenging at low...

Mixed monotone systems form an important class of nonlinear that have recently received attention in the abstraction-based control design area. Slightly different definitions exist literature, and it remains a challenge to verify mixed monotonicity system general. In this paper, we first clarify relation between existing systems, then give two sufficient conditions for functions defined on Euclidean space. These are more general than ones from they suggest is very generic property. Some...