Investigation of iterative image reconstruction in three-dimensional optoacoustic tomography

Iterative image reconstruction algorithms for optoacoustic tomography (OAT), also known as photoacoustic tomography, have the ability to improve image quality over analytic algorithms due to their ability to incorporate accurate models of the imaging physics, instrument response, and measurement noise. However, to date, there have been few reported attempts to employ advanced iterative image reconstruction algorithms for improving image quality in three-dimensional (3D) OAT. In this work, we implement and investigate two iterative image reconstruction methods for use with a 3D OAT small animal imager: namely, a penalized least-squares (PLS) method employing a quadratic smoothness penalty and a PLS method employing a total variation norm penalty. The reconstruction algorithms employ accurate models of the ultrasonic transducer impulse responses. Experimental data sets are employed to compare the performances of the iterative reconstruction algorithms to that of a 3D filtered backprojection (FBP) algorithm. By use of quantitative measures of image quality, we demonstrate that the iterative reconstruction algorithms can mitigate image artifacts and preserve spatial resolution more effectively than FBP algorithms. These features suggest that the use of advanced image reconstruction algorithms can improve the effectiveness of 3D OAT while reducing the amount of data required for biomedical applications

Spontaneous edge currents for the Dirac equation in two space dimensions

Spontaneous edge currents are known to occur in systems of two space dimensions in a strong magnetic field. The latter creates chirality and determines the direction of the currents. Here we show that an analogous effect occurs in a field-free situation when time reversal symmetry is broken by the mass term of the Dirac equation in two space dimensions. On a half plane, one sees explicitly that the strength of the edge current is proportional to the difference between the chemical potentials at the edge and in the bulk, so that the effect is analogous to the Hall effect, but with an internal potential. The edge conductivity differs from the bulk (Hall) conductivity on the whole plane. This results from the dependence of the edge conductivity on the choice of a selfadjoint extension of the Dirac Hamiltonian. The invariance of the edge conductivity with respect to small perturbations is studied in this example by topological techniques.Comment: 10 pages; final versio

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure

Generic critical points of normal matrix ensembles

The evolution of the degenerate complex curve associated with the ensemble at a generic critical point is related to the finite time singularities of Laplacian Growth. It is shown that the scaling behavior at a critical point of singular geometry $x^3 \sim y^2$ is described by the first Painlev\'e transcendent. The regularization of the curve resulting from discretization is discussed.Comment: Based on a talk given at the conference on Random Matrices, Random Processes and Integrable Systems, CRM Montreal, June 200

The bulk-edge correspondence for the quantum Hall effect in Kasparov theory

We prove the bulk-edge correspondence in $K$-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk topological invariants explicitly as a Kasparov product of boundary invariants with the extension class linking the algebras. This paper focuses on the example of the discrete integer quantum Hall effect, though our general method potentially has much wider applications.Comment: 16 pages. Minor corrections and introduction expanded. To appear in Letters in Mathematical Physic

Neural stress reactivity depends on individual characteristics

Acute and chronic stress are important factors in the etiology of affective disorders. While research has focused on alterations of the hypothalamus-pituitary-adrenal axis, only few studies have investigated alterations of the neural stress response and its recovery. Here, we characterized the neural and psychological stress response in a heterogenous patient sample (N =56) and healthy controls (HC, N =57), as variance in the stress response could be critical in phenotypic heterogeneity within patients. We used an adapted psychosocial stress paradigm (Elbau et al. 2019) to investigate the acute stress response as well as stress recovery. In addition to stress-induced activations and deactivations, we compared the similarity of brain activity Pre- and PostStress between patients and HC. Patients reported stronger changes in negative (p =.010) and positive emotions (p =.017). In contrast, stress-induced neural activation was not different in patients compared to HC. However, similarity of activation patterns Pre- and PostStress was lower in patients (p =.040). Crucially, highly similar or dissimilar activation patterns PostStress and PreStress were associated with greater subjectively experienced stress (multivariate p =.024). Furthermore, better-than-chance quantitative predictions of experienced emotions based on region-of-interest activation maps were associated with stress-induced changes in similarity (multivariate p =.0004). Patients with affective disorders were characterized by lower similarity of the brain response before and after stress. However, the absence of significant group differences suggests considerable heterogeneity in the neural stress response within patients. Thus, considering individual characteristics of patients will be critical to find underlying neural changes in affective disorders