High-throughput volumetric adaptive optical imaging using compressed time-reversal matrix

Deep-tissue optical imaging suffers from the reduction of resolving power due to tissue-induced optical aberrations and multiple scattering noise. Reflection matrix approaches recording the maps of backscattered waves for all the possible orthogonal input channels have provided formidable solutions for removing severe aberrations and recovering the ideal diffraction-limited spatial resolution without relying on fluorescence labeling and guide stars. However, measuring the full input–output response of the tissue specimen is time-consuming, making the real-time image acquisition difficult. Here, we present the use of a time-reversal matrix, instead of the reflection matrix, for fast high-resolution volumetric imaging of a mouse brain. The time-reversal matrix reduces two-way problem to one-way problem, which effectively relieves the requirement for the coverage of input channels. Using a newly developed aberration correction algorithm designed for the time-reversal matrix, we demonstrated the correction of complex aberrations using as small as 2% of the complete basis while maintaining the image reconstruction fidelity comparable to the fully sampled reflection matrix. Due to nearly 100-fold reduction in the matrix recording time, we could achieve real-time aberration-correction imaging for a field of view of 40 × 40 µm2 (176 × 176 pixels) at a frame rate of 80 Hz. Furthermore, we demonstrated high-throughput volumetric adaptive optical imaging of a mouse brain by recording a volume of 128 × 128 × 125 µm3 (568 × 568 × 125 voxels) in 3.58 s, correcting tissue aberrations at each and every 1 µm depth section, and visualizing myelinated axons with a lateral resolution of 0.45 µm and an axial resolution of 2 µm.

Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs

In this paper, we consider a three-dimensional Brownian-driven tandem queue with intermediate inputs, which corresponds to a three-dimensional semimartingale reflecting Brownian motion whose reflection matrix is triangular. For this three-node tandem queue, no closed form formula is known, not only for its stationary distribution but also for the corresponding transform. We are interested in exact tail asymptotics for stationary distributions. By generalizing the kernel method, and using extreme value theory and copula, we obtain exact tail asymptotics for the marginal stationary distribution of the buffer content in the third buffer and for the joint stationary distribution.

HOUSEHOLDER TRANSFORMATION IN THE INVERSE PROBLEM FOR A COMPLEX VIBRONIC ANALOGUE OF THE FERMI RESONANCE

In the inverse problem for a complex vibronic analogue of the Fermi resonance, the matrix elements of the electron-vibration interaction should be obtained from experimental data, energies Ek and intensities Ik (k = 1, 2, …, n; n ≥ 3), a “conglomerate” of lines in the spectrum. This problem in the direct-coupling model, where the Hamiltonian HDIR is specified by the energies of the “dark” states Ai and the matrix elements of their coupling with the “bright” state Bi (i = 1, 2, …, n –1), was solved by the author on the basisof algebraic methods. It is shown that the Hamiltonian HDW of the doorway-coupling model, in which the “bright” state has “interaction” with only single distinguished |DW> state, can be obtained from the Hamiltonian HDIR using the Householder triangularization method, namely, by the similarity transformation HDW = PHDIRP, where P is the reflection matrix which is constructed from the Bi values. The expressions for main elements of the doorway model, namely, the energy of the |DW> state and the matrix element of its coupling with the "bright" state, are obtained. For pyrazine and acetylene molecules, the matrix elements of the Hamiltonian HDW are calculated using the data of the electronic-vibrational-rotational spectra.

String integrability of defect CFT and dynamical reflection matrices

The D3-D5 probe-brane system is holographically dual to a defect CFT which is known to be integrable. The evidence comes mainly from the study of correlation functions at weak coupling. In the present work we shed light on the emergence of integrability on the string theory side. We do so by constructing the double row transfer matrix which is conserved when the appropriate boundary conditions are imposed. The corresponding reflection matrix turns out to be dynamical and depends both on the spectral parameter and the string embedding coordinates.

Simulating Floquet topological phases in static systems

We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not suffer from decoherence and heating.

The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary

The S-matrix bootstrap is extended to a 1+1d theory with O(N) symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed R-matrices is an infinite dimensional convex space from which we plot a two dimensional section given by a convex domain on a 2d plane. In certain cases, at the boundary of the domain, we find vertices corresponding to integrable R-matrices with no free parameters. In other cases, when there is a one-parameter family of integrable R-matrices, the whole boundary represents integrable theories. We also consider R-matrices which are analytic in an extended region beyond the physical cuts, thus forbidding poles (resonances) in that region. In certain models, this drastically reduces the allowed space of R-matrices leading to new vertices that again correspond to integrable theories. We also work out the dual problem, in particular in the case of extended analyticity, the dual function has cuts on the physical line whenever unitarity is saturated. For the periodic Yang-Baxter solution that has zero transmission, we computed the R-matrix initially using the bootstrap and then derived its previously unknown analytic form.