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The emergence of distinct local mark behaviours is becoming increasingly common in the applications of spatial marked point processes. This dynamic highlights the limitations of existing global mark correlation functions in accurately identifying the true patterns of mark associations/variations among points as distinct mark behaviours might dominate one another, giving rise to an incomplete understanding of mark associations. In this paper, we introduce a family of local indicators of mark association (LIMA) functions for spatial marked point processes. These functions are defined on general state spaces and can include marks that are either real-valued or function-valued. Unlike global mark correlation functions, which are often distorted by the existence of distinct mark behaviours, LIMA functions reliably identify all types of mark associations and variations among points. Additionally, they accurately determine the interpoint distances where individual points show significant mark associations. Through simulation studies, featuring various scenarios, and four real applications in forestry, criminology, and urban mobility, we study spatial marked point processes in $\R^2$ and on linear networks with either real-valued or function-valued marks, demonstrating that LIMA functions significantly outperform the existing global mark correlation functions., Comment: Submitted for publication

The immense progress in data collection and storage capacities have yielded rather complex, challenging spatial event-type data, where each event location is augmented by a non-simple mark. Despite the growing interest in analysing such complex event patterns, the methodology for such analysis is not embedded well in the literature. In particular, the literature lacks statistical methods to analyse marks which are characterised by an inherent relational structure, i.e.\ where the mark is graph-valued. Motivated by epidermal nerve fibre data, we introduce different mark summary characteristics, which investigate the average variation or association between pairs of graph-valued marks, and apply some of the methods to the nerve data., Comment: submitted for publication

Quantum many-body scars are energy eigenstates which fail to reproduce thermal expectation values of local observables in systems, where the rest of the many-body spectrum fulfils eigenstate thermalization. Experimental observation of quantum many-body scars has so far been limited to models with multiple scar states. Here we propose protocols to observe single scars in architectures of fixed-frequency, fixed-coupling superconducting qubits. We first adapt known models possessing the desired features into a form particularly suited for the experimental platform. We develop protocols for the implementation of these models, through trotterized sequences of two-qubit cross-resonance interactions, and verify the existence of the approximate scar state in the stroboscopic effective Hamiltonian. Since a single scar cannot be detected from coherent revivals in the dynamics, differently from towers of scar states, we propose and numerically investigate alternative and experimentally-accessible signatures. These include the dynamical response of the scar to local state deformations, to controlled noise, and to the resolution of the Lie-Suzuki-Trotter digitization., Comment: 16 pages, 7 figures, Submission to SciPost

A mathematical description of the reduced dynamics of an open quantum system can often be given in terms of a completely positive and trace preserving (CPTP) map, also known as quantum channel. In a seminal work by Wolf et al. [Phys. Rev. Lett. 101, 150402 (2008)], it was shown that deciding whether a given quantum channel was generated from an underlying effective Markovian dynamics, with time-independent Lindbladian generator, is generally an NP-hard problem. In this work we show that in cases where one has access to the full reduced dynamics at all previous times (the dynamical map) one can significantly facilitate the search for an effective generator by making use of Floquet theory. By performing a spectral unwinding such that the effective micromotion is minimized, the effective Floquet generator is often an excellent candidate for an effective Lindblad generator, hence significantly reducing the complexity of the search for an effective Lindblad generator in many (though not all) cases. Our results are relevant for engineering Floquet Lindbladians in complex many-body systems.

We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or decay, according to the strength of spatially nonlocal intra- and interspecific interactions. The two cell phenotypes are interchangeable, the transitions depending on the environmental acidity. We prove global existence of a weak solution to the considered PDE-ODE-PDE system and perform numerical simulations in 1D to informally investigate boundedness and patterning behavior in dependence of the system's parameters and kernels involved in the nonlocal terms.

Electrocardiogram (ECG) recordings have long been vital in diagnosing different cardiac conditions. Recently, research in the field of automatic ECG processing using machine learning methods has gained importance, mainly by utilizing deep learning methods on raw ECG signals. A major advantage of models like convolutional neural networks (CNNs) is their ability to effectively process biomedical imaging or signal data. However, this strength is tempered by challenges related to their lack of explainability, the need for a large amount of training data, and the complexities involved in adapting them for unsupervised clustering tasks. In addressing these tasks, we aim to reintroduce shallow learning techniques, including support vector machines and principal components analysis, into ECG signal processing by leveraging their semi-structured, cyclic form. To this end, we developed and evaluated a transformation that effectively restructures ECG signals into a fully structured format, facilitating their subsequent analysis using shallow learning algorithms. In this study, we present this adaptive transformative approach that aligns R-peaks across all signals in a dataset and resamples the segments between R-peaks, both with and without heart rate dependencies. We illustrate the substantial benefit of this transformation for traditional analysis techniques in the areas of classification, clustering, and explainability, outperforming commercial software for median beat transformation and CNN approaches. Our approach demonstrates a significant advantage for shallow machine learning methods over CNNs, especially when dealing with limited training data. Additionally, we release a fully tested and publicly accessible code framework, providing a robust alignment pipeline to support future research, available at https://github.com/imi-ms/rlign.

In the literature on spatial point processes, there is an emerging challenge in studying marked point processes with points being labelled by functions. In this paper, we focus on point processes living on linear networks and, from distinct points of view, propose several marked summary characteristics that are of great use in studying the average association and dispersion of the function-valued marks. Through a simulation study, we evaluate the performance of our proposed marked summary characteristics, both when marks are independent and when some sort of spatial dependence is evident among them. Finally, we employ our proposed mark summary characteristics to study the spatial structure of urban cycling profiles in Vancouver, Canada., Comment: submitted for publication

Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and is an extension of a mass-conserving model recently derived in arXiv:2308.05676. The admissible degeneracy of the diffusion tensor is characterised in terms of the upper box fractal dimension.

Topological and geometrical features arising in bosonic Bogoliubov-de Gennes (BdG) systems have mainly been studied by utilizing a generalized symplectic version of the Berry curvature and related Chern numbers. Here, we propose a symplectic quantum geometric tensor (SQGT), whose imaginary part leads to the previously studied symplectic Berry curvature, while the real part gives rise to a symplectic quantum metric, providing a natural distance measure in the space of bosonic Bogoliubov modes. We propose how to measure all components of the SQGT by extracting excitation rates in response to periodic modulations of the systems' parameters. Moreover, we connect the symplectic Berry curvature to a generalized symplectic anomalous velocity term for Bogoliubov Bloch wave packets. We test our results for a bosonic Bogoliubov-Haldane model., Comment: 8+23 pages, 3+2 figures

In string theory, black holes can be made from brane systems that are partially delocalized in string theory's extra dimensions. It is expected that they correspond to an ensemble of pure, horizonless microstates sourced by localized versions of this brane system. This thesis aims at studying the relationship between supersymmetric black holes and their microstates. In particular, we apply a concept called local supersymmetry enhancement to 1/4-BPS and 1/8-BPS systems that correspond to two-, three-, and four-charge black holes. This concept locally increases the number of preserved supercharges to 16 by adding dipole charges to the system. These bound states are then expected to be horizonless and describe the microstates of the black hole. First, we list all dipole charges for 1/4-BPS systems in Type II string theory. Then, we apply these to generate two structures to enhance 1/8-BPS systems, one with exclusively internal dipole charges and the other with a non-trivial shape in the non-compact dimensions. Thus, we identify the dipole charges for the microstates of various supersymmetric black holes, including new internal dipole charges for the D1-D5-P black hole and external ones for the D2-D2-D2-D6 black hole. These dipole charges reveal the local structure of the black hole's microstates and will be used in the construction of the corresponding supergravity solutions., Comment: 76 pages, 27 figures, Master thesis at the LMU and the Max Planck Institute for Physics in Munich

We are grateful to all discussants for their invaluable comments, suggestions, questions, and contributions to our article. We have attentively reviewed all discussions with keen interest. In this rejoinder, our objective is to address and engage with all points raised by the discussants in a comprehensive and considerate manner. Consistently, we identify the discussants, in alphabetical order, as follows: CJK for Cronie, Jansson, and Konstantinou, DS for Stoyan, GP for Grabarnik and Pommerening, MRS for Myllym\"aki, Rajala, and S\"arkk\"a, and MCvL for van Lieshout throughout this rejoinder., Comment: Response to commentary on arXiv:2309.01511

Recently, Nathan and Rudner derived a Gorini-Kossakowski-Sudarshan-Lindblad master equation from the Redfield equation. The claim is that the level of approximation is equal to that of the Redfield equation. Here we benchmark the Nathan-Rudner equation (NRE) against the exact solution of a damped harmonic oscillator and compare its performance to that of the time-dependent Redfield equation (RE). We find that which of the equations performs better depends on the regime considered. It turns out that the short-time dynamics is generally much better captured by the RE, whereas the NRE delivers results comparable to those of the rotating-wave approximation. For the steady state, in the high-temperature limit the RE again performs better and its solution approaches the exact result for ultrahigh temperatures. Nevertheless, here also the NR equation constitutes a good approximation. In the low-temperature limit, in turn, the NRE provides a better approximation than the RE. For too strong coupling, here the RE might even fail completely by predicting unphysical behaviour.

Time-local quantum master equations that describe open quantum systems beyond the limit of ultraweak system-bath coupling are often not of Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. Prominent examples are the Redfield equation approximating general open quantum systems and the Hu-Paz-Zhang equation exactly describing a damped harmonic oscillator. Here, we show that not only the former, but also the latter can be brought to pseudo-Lindblad form, with a dissipator that resembles that of a GKSL equation, except for the fact that some of the terms have negative weights. Moreover, we systematically investigate transformations that leave the dissipator of pseudo-Lindblad equations unchanged, while changing the relative weight between its positive and negative terms. These can be used to minimize the weights of the negative terms, which is optimal both for the convergence of a recently developed quantum-trajectory unraveling of pseudo-Lindblad equations as well as for the truncation of the negative terms to obtain a GKSL equation.

We study, from the perspective of supersymmetry and space-time Killing spinors, the local brane densities involved in 1/4-BPS intersecting brane systems. In particular, we classify the possible local brane structures that have maximal (16) supersymmetries in 1/4-BPS intersecting brane backgrounds. Applied to BPS black holes, this classification reveals the allowed local microstructure for pure microstates. We further use these structures with local 16 supersymmetries as building blocks to generalise to 1/8-BPS systems. Moreover, we give examples of 1/8-BPS black holes for which the local supersymmetries are compatible with the combination of different entropy-generating effects from brane interaction. Finally, applying our classification to BPS domain walls, we illustrate how our formalism may possibly describe the local picture of the Hanany-Witten effect., Comment: V1: 34+25 pages, 28 figures/tables, many glues. V2: added a discussion on BPS domain walls and on the Hanany-Witten effect

Periodic driving can tune the quasistatic properties of quantum matter. A well-known example is the dynamical modification of tunneling by an oscillating electric field. Here we show experimentally that driving the phasonic degree of freedom of a cold-atom quasicrystal can continuously tune the effective quasi-disorder strength, reversibly toggling a localization-delocalization quantum phase transition. Measurements agree with fit-parameter-free theoretical predictions, and illuminate a fundamental connection between Aubry-Andr\'e localization in one dimension and dynamic localization in the associated two-dimensional Harper-Hofstadter model. These results open up new experimental possibilities for dynamical coherent control of quantum phase transitions., Comment: 5 pages, 4 figures, Supplementary information

As a prototype detector for the SHiP Surrounding Background Tagger (SBT), we constructed a cell (120 cm x 80 cm x 25 cm) made from corten steel that is filled with liquid scintillator (LS) composed of linear alkylbenzene (LAB) and 2,5-diphenyloxazole (PPO). The detector is equipped with two Wavelength-shifting Optical Modules (WOMs) for light collection of the primary scintillation photons. Each WOM consists of an acrylic tube that is dip-coated with a wavelength-shifting layer on its surface. Via internal total reflection, the secondary photons emitted by the molecules of the wavelength shifter are guided to a ring-shaped array of 40 silicon photomultipliers (SiPMs) coupled to the WOM for light detection. The granularity of these SiPM arrays provides an innovative method to gain spatial information on the particle crossing point. Several improvements in the detector design significantly increased the light yield with respect to earlier proof-of-principle detectors. We report on the performance of this prototype detector during an exposure to high-energy positrons at the DESY II test beam facility by measuring the collected integrated yield and the signal time-of-arrival in each of the SiPM arrays. The resulting detection efficiency and reconstructed energy deposition of the incident positrons are presented, as well as the spatial and time resolution of the detector. These results are then compared to Monte Carlo simulations., Comment: Corresponding authors: A. Brignoli, A. Hollnagel, H. Lacker, F. Lyons. Prepared for submission to JINST. Updated version v3: Minor revision of the manuscript with touch-up of figures and (sub)section titles

Out of thermal equilibrium, bosonic quantum systems can Bose-condense away from the ground state, featuring a macroscopic occupation of an excited state or even of multiple states in the so-called Bose-selection scenario. In previous work, a theory was developed that predicts, in which states a driven-dissipative ideal Bose gas condenses. Here, we address the inverse problem: Given a target state with desired condensate fractions in certain single-particle states, how can this configuration be achieved by tuning available control parameters? Which type of experimental setup allows for flexible condensation control? We solve these problems, on the one hand, by proposing a Bose `condenser', experimentally implementable in a superconducting circuit, where targeted Bose condensation into eigenstates of a chain of resonators is driven through the coupling to artificial quantum baths, realized via auxiliary two-level systems. On the other, we develop a theory to solve the inverse problem based on linear programming methods. We further discuss the engineering of transition points between different Bose condensation configurations, which may find application for amplification, heat-flow control, and the design of highly-structured quantum baths., Comment: 5 + 11 pages, 3 + 7 figures