44 research outputs found
Effective Hamiltonians for Thin Dirichlet Tubes with Varying Cross-Section
We show how to translate recent results on effective Hamiltonians for quantum
systems constrained to a submanifold by a sharply peaked potential to quantum
systems on thin Dirichlet tubes. While the structure of the problem and the
form of the effective Hamiltonian stays the same, the difficulties in the
proofs are different.Comment: 6 pages, 1 figur
Generalised Quantum Waveguides
We study general quantum waveguides and establish explicit effective
Hamiltonians for the Laplacian on these spaces. A conventional quantum
waveguide is an -tubular neighbourhood of a curve in
and the object of interest is the Dirichlet Laplacian on this
tube in the asymptotic limit . We generalise this by
considering fibre bundles over a -dimensional submanifold
with fibres diffeomorphic to ,
whose total space is embedded into an -neighbourhood of . From
this point of view takes the role of the curve and that of the
disc-shaped cross-section of a conventional quantum waveguide. Our approach
allows, among other things, for waveguides whose cross-sections are
deformed along and also the study of the Laplacian on the boundaries of
such waveguides. By applying recent results on the adiabatic limit of
Schr\"odinger operators on fibre bundles we show, in particular, that for small
energies the dynamics and the spectrum of the Laplacian on are reflected by
the adiabatic approximation associated to the ground state band of the normal
Laplacian. We give explicit formulas for the according effective operator on
in various scenarios, thereby improving and extending many of the
known results on quantum waveguides and quantum layers in
Particle Creation at a Point Source by Means of Interior-Boundary Conditions
We consider a way of defining quantum Hamiltonians involving particle
creation and annihilation based on an interior-boundary condition (IBC) on the
wave function, where the wave function is the particle-position representation
of a vector in Fock space, and the IBC relates (essentially) the values of the
wave function at any two configurations that differ only by the creation of a
particle. Here we prove, for a model of particle creation at one or more point
sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian
can indeed be rigorously defined in this way without the need for any
ultraviolet regularization, and that it is self-adjoint. We prove further that
introducing an ultraviolet cut-off (thus smearing out particles over a positive
radius) and applying a certain known renormalization procedure (taking the
limit of removing the cut-off while subtracting a constant that tends to
infinity) yields, up to addition of a finite constant, the Hamiltonian defined
by the IBC.Comment: 41 page
MEGAN: Multi-Explanation Graph Attention Network
Explainable artificial intelligence (XAI) methods are expected to improve
trust during human-AI interactions, provide tools for model analysis and extend
human understanding of complex problems. Explanation-supervised training allows
to improve explanation quality by training self-explaining XAI models on ground
truth or human-generated explanations. However, existing explanation methods
have limited expressiveness and interoperability due to the fact that only
single explanations in form of node and edge importance are generated. To that
end we propose the novel multi-explanation graph attention network (MEGAN). Our
fully differentiable, attention-based model features multiple explanation
channels, which can be chosen independently of the task specifications. We
first validate our model on a synthetic graph regression dataset. We show that
for the special single explanation case, our model significantly outperforms
existing post-hoc and explanation-supervised baseline methods. Furthermore, we
demonstrate significant advantages when using two explanations, both in
quantitative explanation measures as well as in human interpretability.
Finally, we demonstrate our model's capabilities on multiple real-world
datasets. We find that our model produces sparse high-fidelity explanations
consistent with human intuition about those tasks and at the same time matches
state-of-the-art graph neural networks in predictive performance, indicating
that explanations and accuracy are not necessarily a trade-off.Comment: 9 pages main text, 29 pages total, 19 figure
Mitigating Molecular Aggregation in Drug Discovery with Predictive Insights from Explainable AI
As the importance of high-throughput screening (HTS) continues to grow due to
its value in early stage drug discovery and data generation for training
machine learning models, there is a growing need for robust methods for
pre-screening compounds to identify and prevent false-positive hits. Small,
colloidally aggregating molecules are one of the primary sources of
false-positive hits in high-throughput screens, making them an ideal candidate
to target for removal from libraries using predictive pre-screening tools.
However, a lack of understanding of the causes of molecular aggregation
introduces difficulty in the development of predictive tools for detecting
aggregating molecules. Herein, we present an examination of the molecular
features differentiating datasets of aggregating and non-aggregating molecules,
as well as a machine learning approach to predicting molecular aggregation. Our
method uses explainable graph neural networks and counterfactuals to reliably
predict and explain aggregation, giving additional insights and design rules
for future screening. The integration of this method in HTS approaches will
help combat false positives, providing better lead molecules more rapidly and
thus accelerating drug discovery cycles.Comment: 17 pages, plus S
A Quantitative Evaluation of Dense 3D Reconstruction of Sinus Anatomy from Monocular Endoscopic Video
Generating accurate 3D reconstructions from endoscopic video is a promising
avenue for longitudinal radiation-free analysis of sinus anatomy and surgical
outcomes. Several methods for monocular reconstruction have been proposed,
yielding visually pleasant 3D anatomical structures by retrieving relative
camera poses with structure-from-motion-type algorithms and fusion of monocular
depth estimates. However, due to the complex properties of the underlying
algorithms and endoscopic scenes, the reconstruction pipeline may perform
poorly or fail unexpectedly. Further, acquiring medical data conveys additional
challenges, presenting difficulties in quantitatively benchmarking these
models, understanding failure cases, and identifying critical components that
contribute to their precision. In this work, we perform a quantitative analysis
of a self-supervised approach for sinus reconstruction using endoscopic
sequences paired with optical tracking and high-resolution computed tomography
acquired from nine ex-vivo specimens. Our results show that the generated
reconstructions are in high agreement with the anatomy, yielding an average
point-to-mesh error of 0.91 mm between reconstructions and CT segmentations.
However, in a point-to-point matching scenario, relevant for endoscope tracking
and navigation, we found average target registration errors of 6.58 mm. We
identified that pose and depth estimation inaccuracies contribute equally to
this error and that locally consistent sequences with shorter trajectories
generate more accurate reconstructions. These results suggest that achieving
global consistency between relative camera poses and estimated depths with the
anatomy is essential. In doing so, we can ensure proper synergy between all
components of the pipeline for improved reconstructions that will facilitate
clinical application of this innovative technology
Effects of alirocumab on types of myocardial infarction: insights from the ODYSSEY OUTCOMES trial
Aims The third Universal Definition of Myocardial Infarction (MI) Task Force classified MIs into five types: Type 1, spontaneous; Type 2, related to oxygen supply/demand imbalance; Type 3, fatal without ascertainment of cardiac biomarkers; Type 4, related to percutaneous coronary intervention; and Type 5, related to coronary artery bypass surgery. Low-density lipoprotein cholesterol (LDL-C) reduction with statins and proprotein convertase subtilisin–kexin Type 9 (PCSK9) inhibitors reduces risk of MI, but less is known about effects on types of MI. ODYSSEY OUTCOMES compared the PCSK9 inhibitor alirocumab with placebo in 18 924 patients with recent acute coronary syndrome (ACS) and elevated LDL-C (≥1.8 mmol/L) despite intensive statin therapy. In a pre-specified analysis, we assessed the effects of alirocumab on types of MI. Methods and results Median follow-up was 2.8 years. Myocardial infarction types were prospectively adjudicated and classified. Of 1860 total MIs, 1223 (65.8%) were adjudicated as Type 1, 386 (20.8%) as Type 2, and 244 (13.1%) as Type 4. Few events were Type 3 (n = 2) or Type 5 (n = 5). Alirocumab reduced first MIs [hazard ratio (HR) 0.85, 95% confidence interval (CI) 0.77–0.95; P = 0.003], with reductions in both Type 1 (HR 0.87, 95% CI 0.77–0.99; P = 0.032) and Type 2 (0.77, 0.61–0.97; P = 0.025), but not Type 4 MI. Conclusion After ACS, alirocumab added to intensive statin therapy favourably impacted on Type 1 and 2 MIs. The data indicate for the first time that a lipid-lowering therapy can attenuate the risk of Type 2 MI. Low-density lipoprotein cholesterol reduction below levels achievable with statins is an effective preventive strategy for both MI types.For complete list of authors see http://dx.doi.org/10.1093/eurheartj/ehz299</p
Effect of alirocumab on mortality after acute coronary syndromes. An analysis of the ODYSSEY OUTCOMES randomized clinical trial
Background: Previous trials of PCSK9 (proprotein convertase subtilisin-kexin type 9) inhibitors demonstrated reductions in major adverse cardiovascular events, but not death. We assessed the effects of alirocumab on death after index acute coronary syndrome. Methods: ODYSSEY OUTCOMES (Evaluation of Cardiovascular Outcomes After an Acute Coronary Syndrome During Treatment With Alirocumab) was a double-blind, randomized comparison of alirocumab or placebo in 18 924 patients who had an ACS 1 to 12 months previously and elevated atherogenic lipoproteins despite intensive statin therapy. Alirocumab dose was blindly titrated to target achieved low-density lipoprotein cholesterol (LDL-C) between 25 and 50 mg/dL. We examined the effects of treatment on all-cause death and its components, cardiovascular and noncardiovascular death, with log-rank testing. Joint semiparametric models tested associations between nonfatal cardiovascular events and cardiovascular or noncardiovascular death. Results: Median follow-up was 2.8 years. Death occurred in 334 (3.5%) and 392 (4.1%) patients, respectively, in the alirocumab and placebo groups (hazard ratio [HR], 0.85; 95% CI, 0.73 to 0.98; P=0.03, nominal P value). This resulted from nonsignificantly fewer cardiovascular (240 [2.5%] vs 271 [2.9%]; HR, 0.88; 95% CI, 0.74 to 1.05; P=0.15) and noncardiovascular (94 [1.0%] vs 121 [1.3%]; HR, 0.77; 95% CI, 0.59 to 1.01; P=0.06) deaths with alirocumab. In a prespecified analysis of 8242 patients eligible for ≥3 years follow-up, alirocumab reduced death (HR, 0.78; 95% CI, 0.65 to 0.94; P=0.01). Patients with nonfatal cardiovascular events were at increased risk for cardiovascular and noncardiovascular deaths (P<0.0001 for the associations). Alirocumab reduced total nonfatal cardiovascular events (P<0.001) and thereby may have attenuated the number of cardiovascular and noncardiovascular deaths. A post hoc analysis found that, compared to patients with lower LDL-C, patients with baseline LDL-C ≥100 mg/dL (2.59 mmol/L) had a greater absolute risk of death and a larger mortality benefit from alirocumab (HR, 0.71; 95% CI, 0.56 to 0.90; Pinteraction=0.007). In the alirocumab group, all-cause death declined wit h achieved LDL-C at 4 months of treatment, to a level of approximately 30 mg/dL (adjusted P=0.017 for linear trend). Conclusions: Alirocumab added to intensive statin therapy has the potential to reduce death after acute coronary syndrome, particularly if treatment is maintained for ≥3 years, if baseline LDL-C is ≥100 mg/dL, or if achieved LDL-C is low. Clinical Trial Registration: URL: https://www.clinicaltrials.gov. Unique identifier: NCT01663402
Quantum waveguides with magnetic fields
International audienceWe study generalised quantum waveguides in the presence of moderate and strong external magnetic fields. Applying recent results on the adiabatic limit of the connection Laplacian we show how to construct and compute effective Hamiltonians that allow, in particular, for a detailed spectral analysis of magnetic waveguide Hamiltonians. We apply our general construction to a number of explicit examples, most of which are not covered by previous results