Search

The separation of physical forces acting on the tip of a magnetic force microscope (MFM) is essential for correct magnetic imaging. Electrostatic forces can be modulated by varying the tip-sample potential and minimized to map the local Kelvin potential. However, distinguishing magnetic forces from van der Waals forces typically requires two measurements with opposite tip magnetizations under otherwise identical measurement conditions. Here, we present an inverted magnetic force microscope where the sample is mounted on a flat cantilever for force sensing, and the magnetic tip is attached to a miniaturized electromagnet that periodically flips the tip magnetization. This setup enables the extraction of magnetic tip-sample interactions from the sidebands occurring at the switching rate in the cantilever oscillation spectrum. Our method achieves the separation of magnetic signals from other force contributions in a single-scan mode. Future iterations of this setup may incorporate membrane, trampoline, or string resonators with ultra-high quality factors, potentially improving measurement sensitivity by up to three orders of magnitude compared to the state-of-the-art MFM systems using cantilevers., Comment: 7 pages, 4 figures in Main and 3 pages, 3 figures in supplement

In regions with high shares of distributed energy resources (DERs), massive disconnection of small-scale DERs in low-voltage distribution grids during disturbances poses a serious threat to power system security. However, modeling this effect in a computationally efficient way remains challenging. This paper proposes a novel proportional-integral aggregate model for predicting the fraction of tripped DERs based on the voltage at the substation connection point. The model effectively captures the cumulative behavior of the system, is simple to implement, and includes seven parameters for undervoltage tripping and seven for overvoltage tripping behavior, each with a distinct physical meaning. We further propose an optimization-based approach to tune the model parameters. Simulation results show significantly more accurate predictions compared to the DER\_A model -- a standard dynamic model for aggregate DER behavior -- even when the latter is optimized, with only a minor increase in model complexity.

The integration of experimental technologies with large language models (LLMs) is transforming scientific research, positioning AI as a versatile research assistant rather than a mere problem-solving tool. In the field of power systems, however, managing simulations -- one of the essential experimental technologies -- remains a challenge for LLMs due to their limited domain-specific knowledge, restricted reasoning capabilities, and imprecise handling of simulation parameters. To address these limitations, we propose a feedback-driven, multi-agent framework that incorporates three proposed modules: an enhanced retrieval-augmented generation (RAG) module, an improved reasoning module, and a dynamic environmental acting module with an error-feedback mechanism. Validated on 69 diverse tasks from Daline and MATPOWER, this framework achieves success rates of 93.13% and 96.85%, respectively, significantly outperforming the latest LLMs (ChatGPT 4o and o1-preview), which achieved a 27.77% success rate on standard simulation tasks and 0% on complex tasks. Additionally, our framework also supports rapid, cost-effective task execution, completing each simulation in approximately 30 seconds at an average cost of 0.014 USD for tokens. Overall, this adaptable framework lays a foundation for developing intelligent LLM-based assistants for human researchers, facilitating power system research and beyond.

New results on the behavior of the double-mode RR Lyrae V338 Boo are presented. The Transiting Exoplanet Survey Satellite (TESS) observed this star again in 2022, and an observing campaign of the American Association of Variable Star Observers (AAVSO) was completed after the TESS observations as a follow-up. We find that the first overtone pulsation mode in this star completely disappears during the TESS observing window. This mode reappears at the end of the TESS observations, and the AAVSO observing campaign shows that in the months that followed, the first overtone mode was not only present, but was the dominant mode of pulsation. This star, and potentially others like it, could hold the key to finally solving the mystery of the Blazhko effect in RR Lyrae., Comment: 11 pages, 7 figures; published in ApJ

Barthe, Schechtman and Schmuckenschl\"ager proved that the cube maximizes the mean width of symmetric convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball, and the regular crosspolytope minimizes the mean width of symmetric convex bodies whose L\"owner ellipsoid is the Euclidean unit ball. Here we prove close to be optimal stronger stability versions of these results, together with their counterparts about the $\ell$-norm based on Gaussian integrals. We also consider related stability results for the mean width and the $\ell$-norm of the convex hull of the support of even isotropic measures on the unit sphere.

In recent years there has been a lot of interest in the study of isometry invariant Poisson processes of $k$-flats in $d$-dimensional hyperbolic space $\mathbb{H}^d$, for $0\le k\le d-1$. A phenomenon that has no counterpart in euclidean geometry arises in the investigation of the total $k$-dimensional volume $F_r$ of the process inside a spherical observation window $B_r$ of radius $r$ when one lets $r$ tend to infinity. While $F_r$ is asymptotically normally distributed for $2k\leq d+1$, it has been shown to obey a nonstandard central limit theorem for $2k>d+1$. The intersection process of order $m$, for $d-m(d-k) \geq 0$, of the original process $\eta$ consists of all intersections of distinct flats $E_1,\ldots,E_m \in \eta$ with $\dim(E_1\cap\ldots\cap E_m) = d-m(d-k)$. For this intersection process, the total $d-m(d-k)$-dimensional volume $F^{(m)}_r$ of the process in $B_r$, again as $r \to \infty$, is of particular interest. For $2k \leq d+1$ it has been shown that $F^{(m)}_r$ is again asymptotically normally distributed. For $m \geq 2$, the limit is so far unknown, although it has been shown for certain $d$ and $k$ that it cannot be a normal distribution. We determine the limit distribution for all values of $d,k,m$. In addition, we establish explicit rates of convergence in the Kolmogorov distance and discuss properties of the limit distribution. Furthermore we show that the asymptotic covariance matrix of the vector $(F^{(1)}_r,\ldots,F^{(m)}_r)^\top$ has full rank when $2k < d+1$ and rank one when $2k \geq d+1$.

Magnetic nanoparticle-based hyperthermia has emerged as a promising therapeutic modality for treating malignant solid tumors that exhibit resistance to conventional cancer treatments, including chemotherapy and radiation. Despite the clinical approval of superparamagnetic iron oxide nanoparticles (SPIONs) for the adjunct treatment of recurrent glioblastoma, their therapeutic potential is undercut by chemical synthesis-inherent limitations such as low saturation magnetization, superparamagnetic characteristics, and a wide nanoparticle size distribution. Here, we introduce an micromagnetic modelling-based SAF-MDP design with in-plane magnetization, optimized through specific uniaxial anisotropy adjustments to avert the spin-flop phenomenon and eliminate hysteresis-free hard-axis magnetization loops, paired with a mechanofluidic modeling approach to assess the alignment of the SAF-MDP to the applied alternating magnetic field (AMF). Magnetic Force Microscopy characterization provides unprecedented insights into the particle switching behaviour on a single particle scale. This comprehensive strategy spanning micromagnetics and advanced magnetic characterization enables the design of particles with heating efficiencies to approach the theoretical maximum, dictated by the saturation magnetization of the utilized materials and limited solely by the biologically acceptable frequencies and amplitudes of the oscillating magnetic field. Our work not only addresses the limitations encountered by previous methodologies but also sets the stage for the development of advanced SAF-MDP designs and alignment techniques. This opens a new avenue to hyperthermia-based cancer therapy, delineated only by the boundaries of physical laws and biological safety standards., Comment: 9 pages, 5 figures, 3 pages Methods

The union of the particles of a stationary Poisson process of compact (convex) sets in Euclidean space is called Boolean model and is a classical topic of stochastic geometry. In this paper, Boolean models in hyperbolic space are considered, where one takes the union of the particles of a stationary Poisson process in the space of compact (convex) subsets of the hyperbolic space. Geometric functionals such as the volume of the intersection of the Boolean model with a compact convex observation window are studied. In particular, the asymptotic behavior for balls with increasing radii as observation windows is investigated. Exact and asymptotic formulas for expectations, variances, and covariances are shown and univariate and multivariate central limit theorems are derived. Compared to the Euclidean framework, some new phenomena can be observed.

Continuous-Time Simultaneous Localization And Mapping (CTSLAM) has become a promising approach for fusing asynchronous and multi-modal sensor suites. Unlike discrete-time SLAM, which estimates poses discretely, CTSLAM uses continuous-time motion parametrizations, facilitating the integration of a variety of sensors such as rolling-shutter cameras, event cameras and Inertial Measurement Units (IMUs). However, CTSLAM approaches remain computationally demanding and are conventionally posed as centralized Non-Linear Least Squares (NLLS) optimizations. Targeting these limitations, we not only present the fastest SymForce-based [Martiros et al., RSS 2022] B- and Z-Spline implementations achieving speedups between 2.43x and 110.31x over Sommer et al. [CVPR 2020] but also implement a novel continuous-time Gaussian Belief Propagation (GBP) framework, coined Hyperion, which targets decentralized probabilistic inference across agents. We demonstrate the efficacy of our method in motion tracking and localization settings, complemented by empirical ablation studies., Comment: To be published in ECCV 2024

The integration of experiment technologies with large language models (LLMs) is transforming scientific research, offering AI capabilities beyond specialized problem-solving to becoming research assistants for human scientists. In power systems, simulations are essential for research. However, LLMs face significant challenges in power system simulations due to limited pre-existing knowledge and the complexity of power grids. To address this issue, this work proposes a modular framework that integrates expertise from both the power system and LLM domains. This framework enhances LLMs' ability to perform power system simulations on previously unseen tools. Validated using 34 simulation tasks in Daline, a (optimal) power flow simulation and linearization toolbox not yet exposed to LLMs, the proposed framework improved GPT-4o's simulation coding accuracy from 0% to 96.07%, also outperforming the ChatGPT-4o web interface's 33.8% accuracy (with the entire knowledge base uploaded). These results highlight the potential of LLMs as research assistants in power systems.

Coordinate transformations significantly simplify power systems computations. Most notably, the classical Clarke and dq0 transformations are widely used in three-phase systems, as together they transform balanced abc quantities into constant-valued signals. However, during unbalanced operation, the utility of these transformations diminishes, since a null 0 coordinate cannot be ensured and oscillating signals emerge. While recently proposed transformations ensure a null 0 coordinate, they still do not lead to constant-valued signals in the dq0 domain. In this letter, we propose a generalized vector locus transformation that ensures both a null 0 coordinate and constant-valued signals. Moreover, we show that, in the balanced case, the classical amplitude-invariant Clarke transformation is an instance of the proposed transformation.

This two-part tutorial dives into the field of data-driven power flow linearization (DPFL), a domain gaining increased attention. DPFL stands out for its higher approximation accuracy, wide adaptability, and better ability to implicitly incorporate the latest system attributes. This renders DPFL a potentially superior option for managing the significant fluctuations from renewable energy sources, a step towards realizing a more sustainable energy future, by translating the higher model accuracy into increased economic efficiency and less energy losses. To conduct a deep and rigorous reexamination, this tutorial first classifies existing DPFL methods into DPFL training algorithms and supportive techniques. Their mathematical models, analytical solutions, capabilities, limitations, and generalizability are systematically examined, discussed, and summarized. In addition, this tutorial reviews existing DPFL experiments, examining the settings of test systems, the fidelity of datasets, and the comparison made among a limited number of DPFL methods. Further, this tutorial implements extensive numerical comparisons of all existing DPFL methods (40 methods in total) and four classic physics-driven approaches, focusing on their generalizability, applicability, accuracy, and computational efficiency. Through these simulationmethodss, this tutorial aims to reveal the actual performance of all the methods (including the performances exposed to data noise or outliers), guiding the selection of appropriate linearization methods. Furthermore, this tutorial discusses future directions based on the theoretical and numerical insights gained. As the first part, this paper reexamines DPFL theories, covering all the training algorithms and supportive techniques. Capabilities, limitations, and aspects of generalizability, which were previously unmentioned in the literature, have been identified., Comment: 20 pages

Building on the theoretical insights of Part I, this paper, as the second part of the tutorial, dives deeper into data-driven power flow linearization (DPFL), focusing on comprehensive numerical testing. The necessity of these simulations stems from the theoretical analysis's inherent limitations, particularly the challenge of identifying the differences in real-world performance among DPFL methods with overlapping theoretical capabilities and/or limitations. The absence of a comprehensive numerical comparison of DPFL approaches in the literature also motivates this paper, especially given the fact that over 95% of existing DPFL studies have not provided any open-source codes. To bridge the gap, this paper first reviews existing DPFL experiments, examining the adopted test scenarios, load fluctuation settings, data sources, considerations for data noise/outliers, and the comparison made so far. Subsequently, this paper evaluates a total of 44 methods, containing over 30 existing DPFL approaches, some innovative DPFL techniques, and several classic physics-driven power flow linearization methods for benchmarking. The evaluation spans various dimensions, including generalizability, applicability, accuracy, and computational efficiency, using various different test cases scaling from 9-bus to 1354-bus systems. The numerical analysis identifies and examines significant trends and consistent findings across all methods under various test cases. It also offers theoretical insights into phenomena like under-performance, failure, excessive computation times, etc. Overall, this paper identifies the differences in the performances of the wide range of DPFL methods, reveals gaps not evident from theoretical discussions, assists in method selection for real-world applications, and provides thorough discussions on open questions within DPFL research, indicating ten potential future directions., Comment: 26 pages

The flexibilities provided by the distributed energy resources (DERs) in distribution systems enable the coordination of transmission system operator (TSO) and distribution system operators (DSOs). At the distribution level, the flexibilities should be optimized for participation in the transmission system operation. This paper first proposes a flexibility quantification method that quantifies the costs of providing flexibilities and their values to the DSO in the TSO-DSO coordination. Compared with traditional power-range-based quantification approaches that are mainly suitable for generators, the proposed method can directly capture the time-coupling characteristics of DERs' individual and aggregated flexibility regions. Based on the quantification method, we further propose a DSO optimization model to activate the flexibilities from DER aggregators in the distribution system for energy arbitrage and ancillary services provision in the transmission system, along with a revenue allocation strategy that ensures a non-profit DSO. Numerical tests on the IEEE test system verify the proposed methods.

In this paper, a novel Energy Management System (EMS) algorithm to achieve optimal Electric Vehicle (EV) charging scheduling at the parking lots of electric railway stations is proposed. The proposed approach uncovers the potential of leveraging EV charging flexibility to prevent overloading in the combined EV charging and railway operation along with renewable generation, railway regenerative capabilities, and energy storage. Specifically, to realize end-user flexibility, each EV state of charge at departure time is introduced as an optimization variable. Peak load constraints are included in the railway EMS to properly adjust EV charging requirements during periods of high railway demand. A comprehensive numerical study using a scenario-tree approach on an actual railway line in Switzerland demonstrates the effectiveness and the feasibility of the proposed method in a practical setting under multiple scenarios., Comment: to appear in Electric Power Systems Research (also to be presented at Power Systems Computation Conference, June 2024)

An appropriate data basis grants one of the most important aspects for training and evaluating probabilistic trajectory prediction models based on neural networks. In this regard, a common shortcoming of current benchmark datasets is their limitation to sets of sample trajectories and a lack of actual ground truth distributions, which prevents the use of more expressive error metrics, such as the Wasserstein distance for model evaluation. Towards this end, this paper proposes a novel approach to synthetic dataset generation based on composite probabilistic B\'ezier curves, which is capable of generating ground truth data in terms of probability distributions over full trajectories. This allows the calculation of arbitrary posterior distributions. The paper showcases an exemplary trajectory prediction model evaluation using generated ground truth distribution data.

Uncertainty modeling has become increasingly important in power system decision-making. The widely-used tractable uncertainty modeling method-chance constraints with Conditional Value at Risk (CVaR) approximation, can be overconservative and even turn an originally feasible problem into an infeasible one. This paper proposes a new approximation method for multiple joint chance constraints (JCCs) to model the uncertainty in dispatch problems, which solves the conservativeness and potential infeasibility concerns of CVaR. The proposed method is also convenient for controlling the risk levels of different JCCs, which is necessary for power system applications since different resources may be affected by varying degrees of uncertainty or have different importance to the system. We then formulate a data-driven distributionally robust chance-constrained programming model for the power system multiperiod dispatch problem and leverage the proposed approximation method to solve it. In the numerical simulations, two small general examples clearly demonstrate the superiority of the proposed method, and the results of the multiperiod dispatch problem on IEEE test cases verify its practicality.

Magnetic skyrmions are topologically protected local magnetic solitons that are promising for storage, logic or general computing applications. In this work, we demonstrate that we can use a skyrmion device based on [W/CoFeB/MgO] 1 0 multilayers for three-dimensional magnetic field sensing enabled by spin-orbit torques (SOT). We stabilize isolated chiral skyrmions and stripe domains in the multilayers, as shown by magnetic force microscopy images and micromagnetic simulations. We perform magnetic transport measurements to show that we can sense both in-plane and out-of-plane magnetic fields by means of a differential measurement scheme in which the symmetry of the SOT leads to cancelation of the DC offset. With the magnetic parameters obtained by vibrating sample magnetometry and ferromagnetic resonance measurements, we perform finite-temperature micromagnetic simulations, where we investigate the fundamental origin of the sensing signal. We identify the topological transformation between skyrmions, stripes and type-II bubbles that leads to a change in the resistance that is read-out by the anomalous Hall effect. Our study presents a novel application for skyrmions, where a differential measurement sensing concept is applied to quantify external magnetic fields paving the way towards more energy efficient applications in skyrmionics based spintronics., Comment: Main Text: 9 Pages, 6 Figures

We prove a functional version of the additive kinematic formula as an application of the Hadwiger theorem on convex functions together with a Kubota-type formula for mixed Monge-Amp\`ere measures. As an application, we give a new explanation for the equivalence of the representations of functional intrinsic volumes as singular Hessian valuations and as integrals with respect to mixed Monge-Amp\`ere measures. In addition, we obtain a new integral geometric formula for mixed area measures of convex bodies, where integration on $\operatorname{SO}(n-1)\times \operatorname{O}(1)$ is considered.

This paper proposes a real-time distributed operational architecture to efficiently coordinate intergrated transmission and distribution systems (ITD). At the distribution system level, the distribution system operator (DSO) computes the aggregated flexibility of all controllable devices by power-energy envelopes and provides them to the transmission system operators. At the transmission system level, a distributed nonlinear MPC approach is proposed to coordinate the economic dispatch of multiple TSOs, considering the aggregated flexibility of all distribution systems. The subproblems of the proposed approach are associated with different TSOs and individual time periods. In addition, the aggregated flexibility of controllable devices in distribution networks is encapsulated, re-calculated, and communicated through the power-energy envelopes, facilitating a reduction in computational complexity and eliminating redundant information exchanges between TSOs and DSOs, thereby enhancing privacy and security. The framework's effectiveness and applicability in real-world scenarios are validated through simulated operational scenarios on a summer day in Germany, highlighting its robustness in the face of significant prediction mismatches due to severe weather conditions.

Motivated by a problem for mixed Monge-Amp\`ere measures of convex functions, we address a special case of a conjecture of Schneider and show that for every convex body $K$ the support of the mixed area measure $S(K[j],B_L^{n-1}[n-1-j],\cdot)$ is given by the set of $(K[j],B_L^{n-1}[n-1-j])$-extreme unit normal vectors, where $B_L^{n-1}$ denotes the $(n-1)$-dimensional Euclidean unit ball in a hyperplane $L$. As a consequence, we see that the supports of these measures are nested. Our proof introduces a Kubota-type formula for mixed area measures, which involves integration over $j$-dimensional linear subspaces that contain a fixed $1$-dimensional subspace. We transfer these results to the analytic setting, where we obtain corresponding statements for (conjugate) mixed Monge-Amp\`ere measures of convex functions. Thereby, we establish a fundamental property for functional intrinsic volumes. In addition, we study connections between mixed Monge-Amp\`ere measures of convex functions and mixed area measures and mixed volumes of convex bodies.

Considering the growing interest in magnetic materials for unconventional computing, data storage, and sensor applications, there is active research not only on material synthesis but also characterisation of their properties. In addition to structural and integral magnetic characterisations, imaging of magnetization patterns, current distributions and magnetic fields at nano- and microscale is of major importance to understand the material responses and qualify them for specific applications. In this roadmap, we aim to cover a broad portfolio of techniques to perform nano- and microscale magnetic imaging using SQUIDs, spin center and Hall effect magnetometries, scanning probe microscopies, x-ray- and electron-based methods as well as magnetooptics and nanoMRI. The roadmap is aimed as a single access point of information for experts in the field as well as the young generation of students outlining prospects of the development of magnetic imaging technologies for the upcoming decade with a focus on physics, materials science, and chemistry of planar, 3D and geometrically curved objects of different material classes including 2D materials, complex oxides, semi-metals, multiferroics, skyrmions, antiferromagnets, frustrated magnets, magnetic molecules/nanoparticles, ionic conductors, superconductors, spintronic and spinorbitronic materials.

Given the potential for technology to inflict harm and injustice on society, it is imperative that we cultivate a sense of social responsibility among our students as they progress through the Computer Science (CS) curriculum. Our students need to be able to examine the social complexities in which technology development and use are situated. Also, aligning students' personal goals and their ability to achieve them in their field of study is important for promoting motivation and a sense of belonging. Promoting communal goals while learning computing can help broaden participation, particularly among groups who have been historically marginalized in computing. Keeping these considerations in mind, we piloted an introductory Java programming course in which activities engaging students in ethical and socially responsible considerations were integrated across modules. Rather than adding social on top of the technical content, our curricular approach seeks to weave them together. The data from the class suggests that the students found the inclusion of the social context in the technical assignments to be more motivating and expressed greater agency in realizing social change. We share our approach to designing this new introductory socially responsible computing course and the students' reflections. We also highlight seven considerations for educators seeking to incorporate socially responsible computing.

Data pooling offers various advantages, such as increasing the sample size, improving generalization, reducing sampling bias, and addressing data sparsity and quality, but it is not straightforward and may even be counterproductive. Assessing the effectiveness of pooling datasets in a principled manner is challenging due to the difficulty in estimating the overall information content of individual datasets. Towards this end, we propose incorporating a data source prediction module into standard object detection pipelines. The module runs with minimal overhead during inference time, providing additional information about the data source assigned to individual detections. We show the benefits of the so-called dataset affinity score by automatically selecting samples from a heterogeneous pool of vehicle datasets. The results show that object detectors can be trained on a significantly sparser set of training samples without losing detection accuracy., Comment: Accepted at the International Conference on Robotics, Computer Vision and Intelligent Systems (ROBOVIS) 2024

Little is known whether peer reviewers use the same evaluation criteria and how they integrate the criteria into their overall judgment. This study therefore proposed two assessment styles based on theoretical perspectives and normative positions. According to the case-by-case style, referees use many and different criteria, weight criteria on a case-by-case basis, and integrate criteria in a complex, non-mechanical way into their overall judgment. According to the uniform style, referees use a small fraction of the available criteria, apply the same criteria, weight the criteria in the same way, and integrate the criteria based on simple rules (i.e., fast-and-frugal heuristics). These two styles were examined using a unique dataset from a career funding scheme that contained a comparatively large number of evaluation criteria. A heuristic (fast-and-frugal trees) and a complex procedure (logistic regression) were employed to describe how referees integrate the criteria into their overall judgment. The logistic regression predicted the referees' overall assessment with high accuracy and slightly more accurately than the fast-and-frugal trees. Overall, the results of this study support the uniform style but also indicate that the uniform style needs to be revised as follows: referees use many criteria and integrate the criteria using complex rules. However, and most importantly, the revised style could describe most - but not all - of the referees' judgments. Future studies should therefore examine how referees' judgments can be characterized in those cases where the uniform style failed. Moreover, the evaluation process of referees should be studied in more empirical and theoretical detail.

This paper presents a novel model order reduction technique tailored for power systems with a large share of inverter-based energy resources. Such systems exhibit an increased level of dynamic stiffness compared to traditional power systems, posing challenges for time-domain simulations and control design. Our approach involves rotation of the coordinate system of a linearized system using a transformation matrix derived from the real Jordan canonical form, leading to mode decoupling. The fast modes are then truncated in the rotated coordinate system to obtain a lower-order model with reduced stiffness. Applying the same transformation to the original nonlinear system results in an approximate separation of slow and fast states, which can be truncated to reduce the stiffness. The resulting reduced-order model demonstrates an accurate time-domain performance, the slow eigenvalues of the linearized system are correctly preserved, and a reduction in the model stiffness is achieved, allowing for accurate integration with increased step size. Our methodology is assessed in detail for a 3-bus system with generation units involving grid-forming/following converters and synchronous machines, where it allows for a computational speed-up of up to 100x compared to the original system. Several standard larger test systems are also considered., Comment: 8 pages, 5 figures, presented at PSCC 2024

Amidst the worldwide efforts to decarbonize power networks, Local Electricity Markets (LEMs) in distribution networks are gaining importance due to the increased adoption of renewable energy sources and prosumers. Considering that LEMs involve data exchange among independent entities, privacy and cybersecurity are some of the main practical challenges in LEM design. This paper proposes a secure market protocol using innovations from distributed optimization and Secure MultiParty Computation (SMPC). The considered LEM is formulated as an uncertainty-aware joint market for energy and reserves with affine balancing policies. To achieve scalability and enable the use of SMPC, market clearing is solved using the Consensus ADMM algorithm. Subsequently, the data exchange among participants via ADMM iterations is protected using the Shamir secret-sharing scheme to ensure privacy. The market protocol is further reinforced by a secure and verifiable settlement process that uses SMPC and ElGamal commitments to verify market quantities and by a secure recovery scheme for missing network measurements. Finally, the feasibility and performance of the proposed LEM are evaluated on a 15-bus test network.

Mixed volumes in $n$-dimensional Euclidean space are functionals of $n$-tuples of convex bodies $K,L,C_1,\ldots,C_{n-2}$. The Alexandrov--Fenchel inequalities are fundamental inequalities between mixed volumes of convex bodies. As very special cases they cover or imply many important inequalities between basic geometric functionals. A complete characterization of the equality cases in the Alexandrov--Fenchel inequality remains a challenging open problem. Major recent progress was made by Yair Shenfeld and Ramon van Handel \cite{SvH22,SvH23+}, in particular they resolved the problem in the cases where $C_1,\ldots,C_{n-2}$ are polytopes, zonoids or smooth bodies (under some dimensional restriction). In \cite{HugReichert23+} we introduced the class of polyoids, which are defined as limits of finite Minkowski sums of polytopes having a bounded number vertices. Polyoids encompass polytopes, zonoids and triangle bodies, and they can be characterized by means of generating measures. Based on this characterization and Shenfeld and van Handel's contribution, we extended their result to polyoids (or smooth bodies). Our previous result was stated in terms of the support of the mixed area measure associated with the unit ball $B^n$ and $C_1,\ldots,C_{n-2}$. This characterization result is completed in the present work which more generally provides a geometric description of the support of the mixed area measure of an arbitrary $(n-1)$-tuple of polyoids (or smooth bodies). The result confirms a long-standing conjecture by Rolf Schneider in the case of polyoids and hence, in particular, of zonoids.

Mixed volumes in $n$-dimensional Euclidean space are functionals of $n$-tuples consisting of convex bodies $K,L,C_1,\ldots,C_{n-2}$. The Alexandrov--Fenchel inequalities are fundamental inequalities between mixed volumes of convex bodies, which cover as very special cases many important inequalities between basic geometric functionals. The problem of characterizing completely the equality cases in the Alexandrov--Fenchel inequality is wide open. Major recent progress was made by Yair Shenfeld and Ramon van Handel \cite{SvH22,SvH23+}, in particular they resolved the problem in the cases where $K,L$ are general convex bodies and $C_1,\ldots,C_{n-2}$ are polytopes, zonoids or smooth bodies (under some dimensional restriction). We introduce the class of polyoids, which includes polytopes, zonoids and triangle bodies, and characterize polyoids by using generating measures. Based on this characterization and Shenfeld and van Handel's contribution, we extend their result to a class of convex bodies containing all polyoids and smooth bodies. Our result is stated in terms of the support of the mixed area measure of the unit ball $B^n$ and $C_1,\ldots,C_{n-2}$. A geometric description of this support is provided in the accompanying work \cite{HugReichert23+}.

The topic of this survey are geometric functionals of a Boolean model (in Euclidean space) governed by a stationary Poisson process of convex grains. The Boolean model is a fundamental benchmark of stochastic geometry and continuum percolation. Moreover, it is often used to model amorphous connected structures in physics, materials science and biology. Deeper insight into the geometric and probabilistic properties of Boolean models and the dependence on the underlying Poisson process can be gained by considering various geometric functionals of Boolean models. Important examples are the intrinsic volumes and Minkowski tensors. We survey here local and asymptotic density (mean value) formulas as well as second order properties and central limit theorems., Comment: This survey is a preliminary version of a chapter of the forthcoming book "Geometry and Physics of Spatial Random Systems'' edited and partially written by Daniel Hug, Michael Klatt, Klaus Mecke, Gerd Schr\"oder Turk and Wolfgang Weil

In this paper, an electric railway Energy Management System (EMS) with integration of an Energy Storage System (ESS), Regenerative Braking Energy (RBE), and renewable generation is proposed to minimize the daily operating costs of the railway station while meeting railway and Electric Vehicle (EV) charging demand. Compared to other railway EMS methods, the proposed approach integrates an optimal EV charging policy at the railway station to avoid high power demand due to charging requirements. Specifically, receding horizon control is leveraged to minimize the daily peak power spent on EV charging. The numerical study on an actual railway station in Chur, Switzerland shows that the proposed method that integrates railway demand and optimal EV charging along with ESS, RBE, and renewable generation can significantly reduce the average daily operating cost of the railway station over a large number of different scenarios while ensuring that peak load capacity limits are respected., Comment: to appear in IEEE PowerTech, Belgrade, Serbia, 2023

Cauchy's surface area formula says that for a convex body $K$ in $n$-dimensional Euclidean space the mean value of the $(n-1)$-dimensional volumes of the orthogonal projections of $K$ to hyperplanes is a constant multiple of the surface area of $K$. We prove an analogous formula, with the volumes of the projections replaced by their moment vectors. This requires to introduce a new vector-valued valuation on convex bodies.

This paper presents a novel safe reinforcement learning algorithm for strategic bidding of Virtual Power Plants (VPPs) in day-ahead electricity markets. The proposed algorithm utilizes the Deep Deterministic Policy Gradient (DDPG) method to learn competitive bidding policies without requiring an accurate market model. Furthermore, to account for the complex internal physical constraints of VPPs we introduce two enhancements to the DDPG method. Firstly, a projection-based safety shield that restricts the agent's actions to the feasible space defined by the non-linear power flow equations and operating constraints of distributed energy resources is derived. Secondly, a penalty for the shield activation in the reward function that incentivizes the agent to learn a safer policy is introduced. A case study based on the IEEE 13-bus network demonstrates the effectiveness of the proposed approach in enabling the agent to learn a highly competitive, safe strategic policy.