Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has strong generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training

Supporting High-Uncertainty Decisions through AI and Logic-Style Explanations

A common criteria for Explainable AI (XAI) is to support users in establishing appropriate trust in the AI - rejecting advice when it is incorrect, and accepting advice when it is correct. Previous findings suggest that explanations can cause an over-reliance on AI (overly accepting advice). Explanations that evoke appropriate trust are even more challenging for decision-making tasks that are difficult for humans and AI. For this reason, we study decision-making by non-experts in the high-uncertainty domain of stock trading. We compare the effectiveness of three different explanation styles (influenced by inductive, abductive, and deductive reasoning) and the role of AI confidence in terms of a) the users' reliance on the XAI interface elements (charts with indicators, AI prediction, explanation), b) the correctness of the decision (task performance), and c) the agreement with the AI's prediction. In contrast to previous work, we look at interactions between different aspects of decision-making, including AI correctness, and the combined effects of AI confidence and explanations styles. Our results show that specific explanation styles (abductive and deductive) improve the user's task performance in the case of high AI confidence compared to inductive explanations. In other words, these styles of explanations were able to invoke correct decisions (for both positive and negative decisions) when the system was certain. In such a condition, the agreement between the user's decision and the AI prediction confirms this finding, highlighting a significant agreement increase when the AI is correct. This suggests that both explanation styles are suitable for evoking appropriate trust in a confident AI. Our findings further indicate a need to consider AI confidence as a criterion for including or excluding explanations from AI interfaces. In addition, this paper highlights the importance of carefully selecting an explanation style according to the characteristics of the task and data

Interference of a first-order transition with the formation of a spin-Peierls state in alpha'-NaV2O5?

We present results of high-resolution thermal-expansion and specific-heat measurements on single crystalline alpha'-NaV2O5. We find clear evidence for two almost degenerate phase transitions associated with the formation of the dimerized state around 33K: A sharp first-order transition at T1=(33+-0.1)K slightly below the onset of a second-order transition at T2onset around (34+-0.1)K. The latter is accompanied by pronounced spontaneous strains. Our results are consistent with a structural transformation at T1 induced by the incipient spin-Peierls (SP) order parameter above T2=TSP.Comment: 5 pages, 7 figure

Application of Proximal Alternating Linearized Minimization (PALM) and inertial PALM to dynamic 3D CT

The foot and ankle is a complex structure consisting of 28 bones and 30 joints that changes from being completely mobile when positioning the foot on the floor to a rigid closed pack position during propulsion such as when running or jumping. An understanding of this complex structure has largely been derived from cadaveric studies. In vivo studies have largely relied on skin surface markers and multi-camera systems that are unable to differentiate small motions between the bones of the foot. MRI and CT based studies have struggled to interpret functional weight bearing motion as imaging is largely static and non-load bearing. Arthritic diseases of the foot and ankle are treated either by fusion of the joints to remove motion, or joint replacement to retain motion. Until a better understanding of the biomechanics of these joints can be achieved

Electric-field controlled spin reversal in a quantum dot with ferromagnetic contacts

Manipulation of the spin-states of a quantum dot by purely electrical means is a highly desirable property of fundamental importance for the development of spintronic devices such as spin-filters, spin-transistors and single-spin memory as well as for solid-state qubits. An electrically gated quantum dot in the Coulomb blockade regime can be tuned to hold a single unpaired spin-1/2, which is routinely spin-polarized by an applied magnetic field. Using ferromagnetic electrodes, however, the properties of the quantum dot become directly spin-dependent and it has been demonstrated that the ferromagnetic electrodes induce a local exchange-field which polarizes the localized spin in the absence of any external fields. Here we report on the experimental realization of this tunneling-induced spin-splitting in a carbon nanotube quantum dot coupled to ferromagnetic nickel-electrodes. We study the intermediate coupling regime in which single-electron states remain well defined, but with sufficiently good tunnel-contacts to give rise to a sizable exchange-field. Since charge transport in this regime is dominated by the Kondo-effect, we can utilize this sharp many-body resonance to read off the local spin-polarization from the measured bias-spectroscopy. We show that the exchange-field can be compensated by an external magnetic field, thus restoring a zero-bias Kondo-resonance, and we demonstrate that the exchange-field itself, and hence the local spin-polarization, can be tuned and reversed merely by tuning the gate-voltage. This demonstrates a very direct electrical control over the spin-state of a quantum dot which, in contrast to an applied magnetic field, allows for rapid spin-reversal with a very localized addressing.Comment: 19 pages, 11 figure

Magnetic bound states in the quarter-filled ladder system α′−NaV2O5\alpha'-NaV_{2}O_{5}}

Raman scattering in the quarter-filled spin ladder system alpha'-NaV_2O_5 shows in the dimerized singlet ground state ($T \leq T_{SP}=35K$) an unexpected sequence of three magnetic bound states. Our results suggest that the recently proposed mapping onto an effective spin chain for $T > T_{SP}$ has to be given up in favor of the full topology and exchange paths of a ladder in the dimerized phase for $T < T_{SP}$. As the new ground state we propose a dynamic superposition of energetically nearly degenerate dimer configurations on the ladder.Comment: 5 pages, 4 figures, to be published in PRB, brief reports, Dec. 199

Spin dependent quantum interference in non-local graphene spin valves

Spin dependent electron transport measurements on graphene are of high importance to explore possible spintronic applications. Up to date all spin transport experiments on graphene were done in a semi-classical regime, disregarding quantum transport properties such as phase coherence and interference. Here we show that in a quantum coherent graphene nanostructure the non-local voltage is strongly modulated. Using non-local measurements, we separate the signal in spin dependent and spin independent contributions. We show that the spin dependent contribution is about two orders of magnitude larger than the spin independent one, when corrected for the finite polarization of the electrodes. The non-local spin signal is not only strongly modulated but also changes polarity as a function of the applied gate voltage. By locally tuning the carrier density in the constriction we show that the constriction plays a major role in this effect and indicates that it can act as a spin filter device. Our results show the potential of quantum coherent graphene nanostructures for the use in future spintronic devices