Robust Registration of Calcium Images by Learned Contrast Synthesis

Multi-modal image registration is a challenging task that is vital to fuse complementary signals for subsequent analyses. Despite much research into cost functions addressing this challenge, there exist cases in which these are ineffective. In this work, we show that (1) this is true for the registration of in-vivo Drosophila brain volumes visualizing genetically encoded calcium indicators to an nc82 atlas and (2) that machine learning based contrast synthesis can yield improvements. More specifically, the number of subjects for which the registration outright failed was greatly reduced (from 40% to 15%) by using a synthesized image

Topological Bulk Lasing Modes Using an Imaginary Gauge Field

Topological edge modes, which are robust against disorders, have been used to enhance the spatial stability of lasers. Recently, it was revealed that topological lasers can be further stabilized using a novel topological phase in non-Hermitian photonic topological insulators. Here we propose a procedure to realize topologically protected modes extended over a d-dimensional bulk by introducing an imaginary gauge field. This generalizes the idea of zero-energy extended modes in the one-dimensional Su-Schrieffer-Heeger lattice into higher dimensional lattices allowing a d-dimensional bulky mode that is topologically protected. Furthermore, we numerically demonstrate that the topological bulk lasing mode can achieve high temporal stability superior to topological edge mode lasers. In the exemplified topological extended mode in the kagome lattice, we show that large regions of stability exist in its parameter space.Comment: 10 pages, 10 figure

A comparative study of overlap and staggered fermions in the Schwinger model

We investigate the validity of the square rooting procedure of the staggered determinant in the context of the Schwinger model. We find some evidence that at fixed physical quark mass the square root of the staggered determinant becomes proportional to the overlap determinant in the continuum limit. We also find that at fixed lattice spacing moderate smearing dramatically improves the chiral behavior of staggered fermions.Comment: Contribution to LATTICE 2004 (Chiral fermions

Understanding Pathologies of Deep Heteroskedastic Regression

Several recent studies have reported negative results when using heteroskedastic neural regression models to model real-world data. In particular, for overparameterized models, the mean and variance networks are powerful enough to either fit every single data point (while shrinking the predicted variances to zero), or to learn a constant prediction with an output variance exactly matching every predicted residual (i.e., explaining the targets as pure noise). This paper studies these difficulties from the perspective of statistical physics. We show that the observed instabilities are not specific to any neural network architecture but are already present in a field theory of an overparameterized conditional Gaussian likelihood model. Under light assumptions, we derive a nonparametric free energy that can be solved numerically. The resulting solutions show excellent qualitative agreement with empirical model fits on real-world data and, in particular, prove the existence of phase transitions, i.e., abrupt, qualitative differences in the behaviors of the regressors upon varying the regularization strengths on the two networks. Our work thus provides a theoretical explanation for the necessity to carefully regularize heteroskedastic regression models. Moreover, the insights from our theory suggest a scheme for optimizing this regularization which is quadratically more efficient than the naive approach.Comment: 19 pages, 8 figure

Exploration of novel topological lasing modes: their robustness and dynamics

Recently, topological photonics has been proven to be an attractive framework for manipulating the light in an extraordinary way. For instance, photonic topological insulators can exhibit modes that are robust against some defects such as fabrication imperfections, deformations and sharp bendings in waveguides. This thesis extends previous works on topological lasers by proposing new topological lasing modes, analysing the dynamic behaviours of those modes and adopting new topological classification methods with the aim to realise high-performance laser devices. In particular, I will cover some of my recent contributions in the research field, especially on topological edge modes in kagome photonic crystals, semiconductor topological laser cavities, and non-Hermitian topological bulk modes, as well as on a proposed data-driven approach for topological classification in topological insulator lasers. I will start with an all-dielectric reciprocal topological insulator based on the geometry of a kagome lattice, where I demonstrated broadband and highly efficient unidirectional photonic edge mode propagation for sharp bendings conserving the local symmetry. These topological edge modes working at telecommunication wavelengths will be used to construct semiconductor laser cavities insensitive to defects. In the topological cavity, I will show that two different regimes coexist where additional Fabry-Pérot modes are present in addition to the topological lasing modes. Finally, I will show how non-Hermiticity can give rise to new topological states. In particular, I will look at so-called topological bulk modes that arise from asymmetric couplings. In contrast to the topological edge modes, they are delocalised over the bulk while still being topologically protected. The topological bulk modes have been achieved in a two-dimensional kagome lattice, with rhombus geometry, by introducing an imaginary gauge field. I will show the possibility to achieve temporally stable, phase-locked broad area topological lasers in two-dimensional lattices. Further, I will propose a data-driven method in order to find new topological phases via reverse engineering

How Do People With Disabilities Cope While Waiting for Disability Insurance Benefits?

Disability Insurance waiting time varies from a few months to several years. We estimate the causal effect of longer waiting times on the use of five financial coping strategies. We find that SNAP benefits are the most responsive to longer waiting times. Moreover, while spousal employment is not responsive to longer wait times, spousal employment leads to longer waiting times, presumably because these applicants are more able to appeal. Together, these results suggest that coping strategies are used to both help applicants during the wait time and to extend the waiting time and increase their probability of success

Nature of topological protection in photonic spin and valley Hall insulators

Recent interest in optical analogs to the quantum spin Hall and quantum valley Hall effects is driven by the promise to establish topologically protected photonic edge modes at telecommunication and optical wavelengths on a simple platform suitable for industrial applications. While first theoretical and experimental efforts have been made, these approaches so far both lack a rigorous understanding of the nature of topological protection and the limits of backscattering immunity. We here use a generic group theoretical methodology to fill this gap and obtain general design principles for purely dielectric two-dimensional topological photonic systems. The method comprehensively characterizes possible two-dimensional hexagonal designs and reveals their topological nature, potential, and limits