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This paper presents a novel approach for optimal control of nonlinear stochastic systems using infinitesimal generator learning within infinite-dimensional reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the diffusion operator of a controlled Fokker-Planck-Kolmogorov equation in an infinite-dimensional hypothesis space. This operator models the continuous-time evolution of the probability measure of the control system's state. We demonstrate that this approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problem. Furthermore, our statistical learning framework includes nonparametric estimators for uncontrolled forward infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control.

Segmenting 3D blood vessels is a critical yet challenging task in medical image analysis. This is due to significant imaging modality-specific variations in artifacts, vascular patterns and scales, signal-to-noise ratios, and background tissues. These variations, along with domain gaps arising from varying imaging protocols, limit the generalization of existing supervised learning-based methods, requiring tedious voxel-level annotations for each dataset separately. While foundation models promise to alleviate this limitation, they typically fail to generalize to the task of blood vessel segmentation, posing a unique, complex problem. In this work, we present vesselFM, a foundation model designed specifically for the broad task of 3D blood vessel segmentation. Unlike previous models, vesselFM can effortlessly generalize to unseen domains. To achieve zero-shot generalization, we train vesselFM on three heterogeneous data sources: a large, curated annotated dataset, data generated by a domain randomization scheme, and data sampled from a flow matching-based generative model. Extensive evaluations show that vesselFM outperforms state-of-the-art medical image segmentation foundation models across four (pre-)clinically relevant imaging modalities in zero-, one-, and few-shot scenarios, therefore providing a universal solution for 3D blood vessel segmentation.

This study explores the semiclassical limit of an integrable-chaotic bosonic many-body quantum system, providing nuanced insights into its behavior. We examine classical-quantum correspondences across different interaction regimes of bosons in a triple-well potential, ranging from the integrable to the self-trapping regime, and including the chaotic one. The close resemblance between the phase-space mean projections of classical trajectories and those of Husimi distributions evokes the Principle of Uniform Semiclassical Condensation (PUSC) of Wigner functions of eigenstates. Notably, the resulting figures also exhibit patterns reminiscent of Jason Gallas's "shrimp" shapes., Comment: 8 pages, 9 figures

Early identification of stroke is crucial for intervention, requiring reliable models. We proposed an efficient retinal image representation together with clinical information to capture a comprehensive overview of cardiovascular health, leveraging large multimodal datasets for new medical insights. Our approach is one of the first contrastive frameworks that integrates graph and tabular data, using vessel graphs derived from retinal images for efficient representation. This method, combined with multimodal contrastive learning, significantly enhances stroke prediction accuracy by integrating data from multiple sources and using contrastive learning for transfer learning. The self-supervised learning techniques employed allow the model to learn effectively from unlabeled data, reducing the dependency on large annotated datasets. Our framework showed an AUROC improvement of 3.78% from supervised to self-supervised approaches. Additionally, the graph-level representation approach achieved superior performance to image encoders while significantly reducing pre-training and fine-tuning runtimes. These findings indicate that retinal images are a cost-effective method for improving cardiovascular disease predictions and pave the way for future research into retinal and cerebral vessel connections and the use of graph-based retinal vessel representations., Comment: Accepted as oral paper at ML-CDS workshop, MICCAI 2024

We derive a version of the so-called "best Fokker-Planck approximation" (BFPA) to describe the spatial properties of interacting active Ornstein-Uhlenbeck particles (AOUPs) in arbitrary spatial dimensions. In doing so, we also take into account the odd-diffusive contribution of the Lorentz force acting on a charged particle in a spatially dependent magnetic field, sticking to the overdamped limit. While the BFPA itself does not turn out to be widely useful, our general approach allows to deduce an appropriate generalization of the Fox approximation, which we use to characterize the stationary behavior of a single active particle in an external potential by deriving analytic expressions for configurational probability distributions (or effective potentials). In agreement with computer simulations, our theory predicts that the Lorentz force reduces the effective attraction and thus the probability to find an active particle in the vicinity of a repulsive wall. Even for an inhomogeneous magnetic field, our theoretical findings provide useful qualitative insights, specifically regarding the location of accumulation regions.

Intelligent decisions in response to external informative input can allow organisms to achieve their biological goals while spending very little of their own resources. In this paper, we develop and study a minimal model for a navigational task, performed by an otherwise completely motorless particle that possesses the ability of \textit{hitchhiking} in a bath of active Brownian particles (ABPs). Hitchhiking refers to identifying and attaching to suitable surrounding bath particles. Using a reinforcement learning algorithm, such an agent, which we refer to as intelligent hitchhiking particle (IHP), is enabled to persistently navigate in the desired direction. This relatively simple IHP can also anticipate and react to characteristic motion patterns of their hosts, which we exemplify for a bath of chiral ABPs (cABPs). To demonstrate that the persistent motion of the IHP will outperform that of the bath particles in view of long-time ballistic motion, we calculate the mean-squared displacement and discuss its dependence on the density and persistence time of the bath ABPs by means of an analytic model.

Let $E$ be the class of finite (resp. probability) measures absolutely continuous with respect to a $\sigma$-finite Radon measure on a Polish space. We present a criterion on the quasi-regularity of Dirichlet forms on $E$ in terms of upper bound conditions given by the uniform $(L^1+L^\infty)$-norm of the extrinsic derivative. As applications, we construct a class of general type Markov processes on $E$ via quasi-regular Dirichlet forms containing the diffusion, jump and killing terms. Moreover, stochastic extrinsic derivative flows on $E$ are studied by using quasi-regular Dirichlet forms, which in particular provide martingale solutions to SDEs on these two spaces, with drifts given by the extrinsic derivative of entropy functionals.

This article provides a scaling limit for a family of skew interacting Brownian motions in the context of mesoscopic interface models. Let $d\in\mathbb N$, $y_1,\dots,y_M\in\mathbb R$ and $f\in C_b(\mathbb R)$ be fixed. For each $N\in\mathbb N$ we consider a $k_N$-dimensional, skew reflecting distorted Brownian motion $(X^{N,i}_t)_{i=1,\dots,k_N}$, $t\geq 0$, and investigate the scaling limits for $N\to\infty$. The drift includes skew reflections at height levels $\tilde y_j:=N^{1-\frac{d}{2}}y_j$ with intensities $\beta_j/N^d$ for $j=1,\dots,M$. The corresponding SDE is given by \begin{equation} d X^{N,i}_t=-\big(A_N X^{N}_t\big)_id t-\frac{1}{2}N^{-\tfrac{d}{2}-1}\,f\big(N^{\frac{d}{2}-1}X^{N,i}_t\big)d t \\+\sum_{j=1}^M\tfrac{1-e^{-\beta_j/N^d}}{1+e^{-\beta_j/N^d}}d l_t^{N,i, \tilde y_j} +d B_t^{N,i}, \end{equation} where ${(B_t^{N,i})}_{t\geq 0}$, $i=1,\dots, k_N$, are independent Brownian motions and $ l_t^{N,i, \tilde y_j}$ denotes the local time of ${(X^{N,i}_t)}_{t\geq 0}$ at $\tilde y_j$. We prove the weak convergence of the equilibrium laws of \begin{equation*} u_t^N=\Lambda_N\circ X^{N}_{N^2t},\quad t\geq 0, \end{equation*} for $N\to\infty$, choosing suitable injective, linear maps $\Lambda_N:\mathbb R^{k_N}\to \{h\,|\,h:D\to\mathbb R\}$. The scaling limit is a distorted Ornstein-Uhlenbeck process whose state space is the Hilbert space $H=L^2(D, dz)$. We characterize a class of height maps, such that the scaling limit of the dynamic is not influenced by the particular choice of ${(\Lambda_N)}_{N\in\mathbb N}$ within that class.

We investigate the potential performance improvements of double-hybrid density functionals by replacing the standard opposite-spin-scaled MP2 (SOS-MP2) with the modified opposite-spin-scaled MP2 (MOS-MP2) in the nonlocal correlation component. Using the large and diverse GMTKN55 dataset, we find that MOS-double hybrids provide significantly better accuracy compared to SOS-MP2-based double hybrids when empirical dispersion correction is not employed. The non-covalent interaction subsets account for the majority of this improvement. Adding the DFT-D4 dispersion correction to MOS-type double hybrids does not provide any superior performance over conventional dispersion-corrected SOS-MP2-based double hybrids. Nevertheless, for nine tested transition metal sets, dispersion-corrected spin-component-scaled (SCS) double hybrids are still significantly better than any MOS-double hybrid functional.

Enzymes are important proteins that catalyze chemical reactions. In recent years, machine learning methods have emerged to predict enzyme function from sequence; however, there are no standardized benchmarks to evaluate these methods. We introduce CARE, a benchmark and dataset suite for the Classification And Retrieval of Enzymes (CARE). CARE centers on two tasks: (1) classification of a protein sequence by its enzyme commission (EC) number and (2) retrieval of an EC number given a chemical reaction. For each task, we design train-test splits to evaluate different kinds of out-of-distribution generalization that are relevant to real use cases. For the classification task, we provide baselines for state-of-the-art methods. Because the retrieval task has not been previously formalized, we propose a method called Contrastive Reaction-EnzymE Pretraining (CREEP) as one of the first baselines for this task and compare it to the recent method, CLIPZyme. CARE is available at https://github.com/jsunn-y/CARE/.

The intimate correlation between the local atomic arrangement and electronic states in Li-ion battery cathode materials plays a crucial role in determining their electrochemical properties, including capacity, cycling stability, and rate capability. Despite almost 30 years of research efforts on high performance cathodes based on Ni rich layered oxides, there is still no consensus on LiNiO2 local atomic and electronic structure. Ni sites could be either Jahn-Teller distorted or bond disproportionated and the role of Ni and oxygen in the charge compensation mechanism remains unclear. In this study, we compare the local and electronic structure of LiNiO2 and NaNiO2, a long-range Jahn-Teller system, using a novel approach which aims at correlating the results from bulk spectroscopy techniques, particularly under operando conditions, obtained on standard samples to ensure sample interoperability and enhance the reliability and robustness of our results. Despite being a site-selective and local technique, XAS is unable to discriminate between the proposed scenarios, as confirmed also by theoretical calculations. On the contrary, Raman spectroscopy show local structural differences between monoclinic distorted NaNiO2 and rhombohedral LiNiO2. Additionally, HAXPES confirms the presence of multiple formal oxidation states for Ni, and RIXS data provides evidence of 3d8 states, confirming the negative charge transfer character of Ni and some degree of bond disproportionation in LiNiO2. Regarding the charge compensation mechanism, XRS and RIXS support the participation of oxygen holes in the redox activity, while Raman spectroscopy does not detect molecular oxygen. By combing several high-fidelity spectroscopy datasets, this study shows the value of correlative characterization workflows to provide insights into complex structural-electrochemical relationships.

While computer vision has achieved tremendous success with multimodal encoding and direct textual interaction with images via chat-based large language models, similar advancements in medical imaging AI, particularly in 3D imaging, have been limited due to the scarcity of comprehensive datasets. To address this critical gap, we introduce CT-RATE, the first dataset that pairs 3D medical images with corresponding textual reports. CT-RATE comprises 25,692 non-contrast 3D chest CT scans from 21,304 unique patients. Through various reconstructions, these scans are expanded to 50,188 volumes, totaling over 14.3 million 2D slices. Each scan is accompanied by its corresponding radiology report. Leveraging CT-RATE, we develop CT-CLIP, a CT-focused contrastive language-image pretraining framework designed for broad applications without the need for task-specific training. We demonstrate how CT-CLIP can be used in two tasks: multi-abnormality detection and case retrieval. Remarkably, in multi-abnormality detection, CT-CLIP outperforms state-of-the-art fully supervised models across all key metrics, effectively eliminating the need for manual annotation. In case retrieval, it efficiently retrieves relevant cases using either image or textual queries, thereby enhancing knowledge dissemination. By combining CT-CLIP's vision encoder with a pretrained large language model, we create CT-CHAT, a vision-language foundational chat model for 3D chest CT volumes. Finetuned on over 2.7 million question-answer pairs derived from the CT-RATE dataset, CT-CHAT surpasses other multimodal AI assistants, underscoring the necessity for specialized methods in 3D medical imaging. Collectively, the open-source release of CT-RATE, CT-CLIP, and CT-CHAT not only addresses critical challenges in 3D medical imaging but also lays the groundwork for future innovations in medical AI and improved patient care.

Segmentation of blood vessels in murine cerebral 3D OCTA images is foundational for in vivo quantitative analysis of the effects of neurovascular disorders, such as stroke or Alzheimer's, on the vascular network. However, to accurately segment blood vessels with state-of-the-art deep learning methods, a vast amount of voxel-level annotations is required. Since cerebral 3D OCTA images are typically plagued by artifacts and generally have a low signal-to-noise ratio, acquiring manual annotations poses an especially cumbersome and time-consuming task. To alleviate the need for manual annotations, we propose utilizing synthetic data to supervise segmentation algorithms. To this end, we extract patches from vessel graphs and transform them into synthetic cerebral 3D OCTA images paired with their matching ground truth labels by simulating the most dominant 3D OCTA artifacts. In extensive experiments, we demonstrate that our approach achieves competitive results, enabling annotation-free blood vessel segmentation in cerebral 3D OCTA images.

Implantable retinal prostheses offer a promising solution to restore partial vision by circumventing damaged photoreceptor cells in the retina and directly stimulating the remaining functional retinal cells. However, the information transmission between the camera and retinal cells is often limited by the low resolution of the electrode array and the lack of specificity for different ganglion cell types, resulting in suboptimal stimulations. In this work, we propose to utilize normalizing flow-based conditional invertible neural networks to optimize retinal implant stimulation in an unsupervised manner. The invertibility of these networks allows us to use them as a surrogate for the computational model of the visual system, while also encoding input camera signals into optimized electrical stimuli on the electrode array. Compared to other methods, such as trivial downsampling, linear models, and feed-forward convolutional neural networks, the flow-based invertible neural network and its conditional extension yield better visual reconstruction qualities w.r.t. various metrics using a physiologically validated simulation tool.

The observation of spin-dependent transmission of electrons through chiral molecules has led to the discovery of chiral-induced spin selectivity (CISS). The remarkably high efficiency of the spin polarizing effect has recently gained significant interest due to the high potential for novel sustainable hybrid chiral molecule magnetic applications. However, the fundamental mechanisms underlying the chiral-induced phenomena remain to be understood fully. In this work, we explore the impact of chirality on spin angular momentum in hybrid metal/ chiral molecule thin film heterostructures. For this, we inject a pure spin current via spin pumping and investigate the spin-to-charge conversion at the hybrid chiral interface. Notably, we observe a chiral-induced unidirectionality in the conversion. Furthermore, angle-dependent measurements reveal that the spin selectivity is maximum when the spin angular momentum is aligned with the molecular chiral axis. Our findings validate the central role of spin angular momentum for the CISS effect, paving the path toward three-dimensional functionalization of hybrid molecule-metal devices via chirality.

To study diffusion processes on the $p$-Wasserstein space $\scr P_p $ for $p\in [1,\infty)$ over a separable, reflexive Banach space $X$, we present a criterion on the quasi-regularity of Dirichlet forms in $L^2(\scr P_p,\Lambda)$ for a reference probability $\Lambda$ on $\scr P_p$. It is formulated in terms of an upper bound condition with the uniform norm of the intrinsic derivative. The condition is easy to check in relevant applications and allows to construct a type of Ornstein-Uhlenbeck process on $\scr P_p$. We find a versatile class of quasi-regular local Dirichlet forms on $\scr P_p$ by using images of Dirichlet forms on the tangent space $L^p(X\to X,\mu_0)$ at a reference point $\mu_0\in \scr P_p$. The Ornstein-Uhlenbeck type Dirichlet form is an important example in this class. An $L^2$-estimate for the corresponding heat kernel is derived, based on the eigenvalues of the covariance operator of the underlying Gaussian measure., Comment: Acknowledgments added; Application of Sect. 3.2 revised; Typos corrected

Nowadays, robots are applied in dynamic environments. For a robust operation, the motion planning module must consider other tasks besides reaching a specified pose: (self) collision avoidance, joint limit avoidance, keeping an advantageous configuration, etc. Each task demands different joint control commands, which may counteract each other. We present a hierarchical control that, depending on the robot and environment state, determines online a suitable priority among those tasks. Thereby, the control command of a lower-prioritized task never hinders the control command of a higher-prioritized task. We ensure smooth control signals also during priority rearrangement. Our hierarchical control computes reference joint velocities. However, the underlying concepts of hierarchical control differ when using joint accelerations or joint torques as control signals instead. So, as a further contribution, we provide a comprehensive discussion on how joint velocity control, joint acceleration control, and joint torque control differ in hierarchical task control. We validate our formulation in an experiment on hardware., Comment: 15 pages, 4 figures

Grain boundaries in extremely confined colloidal smectics possess a topological fine structure with coexisting nematic and tetratic symmetry of the director field. An alternative way to approach the problem of smectic topology is via the layer structure, which is typically more accessible in experiments on molecular liquid crystals. Here, we consider exemplary density functional theory results for two-dimensional hard rods to illustrate how the concept of endpoint defects, which appear as tetratic disclinations of quarter charge in director topology, translates to smectic layer topology built around the networks formed by density maxima and minima. By doing so, we elaborate on further advantages of a topological concept evolving around the layer structure rather than the director field, such as providing insight in the structure of edge dislocations or virtual defects at the confining walls., Comment: The published article can be accessed via https://www.tandfonline.com/eprint/CDJCT5WAWQYYAVDRWK6J/full?target=10.1080/02678292.2024.2341860

In this work, we investigate the semiclassical limit of a simple bosonic quantum many-body system exhibiting both integrable and chaotic behavior. A classical Hamiltonian is derived using coherent states. The transition from regularity to chaos in classical dynamics is visualized through Poincar\'e sections. Classical trajectories in phase space closely resemble the projections of the Husimi functions of eigenstates with similar energy, even in chaotic cases. It is demonstrated that this correlation is more evident when projecting the eigenstates onto the Fock states. The analysis is carried out at a critical energy where the eigenstates are maximally delocalized in the Fock basis. Despite the imperfect delocalization, its influence is present in the classical and quantum properties under investigation. The study systematically establishes quantum-classical correspondence for a bosonic many-body system with more than two wells, even within the chaotic region., Comment: 14 pages, 19 figures

Dispersion-based graphene materials are promising candidates for various sensing applications. They offer the advantage of relatively simple and fast deposition via spin-coating, Langmuir-Blodgett deposition, or inkjet printing. Film uniformity and reproducibility remain challenging in all of these deposition methods. Here, we demonstrate, characterize, and successfully apply a scalable structuring method for graphene dispersions. The method is based on a standard lift-off process, is simple to implement, and increases the film uniformity of graphene devices. It is also compatible with standard semiconductor manufacturing methods. We investigate two different graphene dispersions via Raman spectroscopy and Atomic Force Microscopy and observe no degradation of the material properties by the structuring process. Furthermore, we achieve high uniformity of the structured patterns and homogeneous graphene flake distribution. Electrical characterizations show reproducible sheet resistance values correlating with material quantity and uniformity. Finally, repeatable humidity sensing is demonstrated with van der Pauw devices, with sensing limits of less than 1% relative humidity., Comment: 35 pages

Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems, since very few analytical results exist. In this work, we apply fundamental measure theory, which allows us to derive free energy functionals for hard particles from first principles and with high accuracy, to systems of hard cylinders, cones and spherotriangles. We provide a general recipe for incorporating biaxial liquid crystal order parameters into fundamental measure theory and use this framework to obtain the phase boundaries for the emergence of orientational order in the considered systems. Our results provide insights into the phase behavior of biaxial nematic liquid crystals and, in particular, into methods for their analytical investigation.

In an equilibrium thermal environment, random elastic collisions between background particles and a tracer establish the picture of Brownian motion fulfilling the celebrated Einstein relation between diffusivity and mobility. In nature, environments often comprise collections of autonomously moving objects that exhibit fascinating non-equilibrium phenomena and are nowadays termed active matter. We investigate experimentally the impact of an active background on a passive tracer using vibrationally excited active particles. They produce multiple correlated tapping collisions with the tracer, for which a persistent memory emerges in the dynamics. The system is described by a generalized active Einstein relation that constrains fluctuations, dissipation, and effective activity, by taking the emerging tracer memory into account. Since the resulting persistence can largely be tuned by the environmental density and motility, our findings can be useful to engineer properties of various active systems in biomedical applications, microfluidics, chemical engineering, or swarm robotics.