High temperature superconductors, especially YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO), are considered a key enabling technology towards a clean energy future. Hole doping in YBCO is a prerequisite for the emergence of its unchallenged superconducting properties. Up to now, research was focused on the under- and optimally doped region, due to practical limitations in reaching the overdoped state, despite being highly interesting from fundamental and applied aspects as competing orders vanish and critical current densities are expected to peak. Here, we deploy for the first time an electrochemical method to access the mostly uncharted overdoped region. We demonstrate precise control over the bulk oxygen concentration in YBCO thin films across the full off-stoichiometry window (0$\leδ\le$1) using electrochemical oxidation combined with in situ XRD and electrical measurements. Resulting high doping states and critical current densities are confirmed using a multi modal approach, including x-ray diffraction, electrical, Hall and magnetic characterization. Thus, this work opens a promising pathway based on electrochemical oxidation towards electronically clean, oxygen overdoped cuprate superconductors and therefore will assist to further push the critical current density to its intrinsic limit.

This paper evaluates the performance of reconfigurable intelligent surface (RIS) optimization algorithms, which utilize channel estimation methods, in ray tracing (RT) simulations within urban digital twin environments. Beyond Sionna's native capabilities, we implement and benchmark additional RIS optimization algorithms based on channel estimation, enabling an evaluation of RIS strategies under various deployment conditions. Coverage maps for RIS-assisted communication systems are generated through the integration of Sionna's RT simulations. Moreover, real-world experimentation underscores the necessity of validating algorithms in near-realistic simulation environments, as minor variations in measurement setups can significantly affect performance.

We consider the electronic and magnetic properties of the Hubbard model on a square lattice with the Fermi level near van Hove singularity and the ratio of the next-nearest-neighbor and nearest-neighbor hoppings $t'/t=-0.45$, which favours the ferromagnetic instability. We find, that a self-consistent consideration of the ferromagnetic fluctuations within the D-TRILEX approach results in the splitting of the electronic spectral function at low temperatures. This splitting exhibits only a weak momentum dependence, and only one of the split bands crosses the Fermi level. As a result, the Fermi surface itself remains unsplit, but its area increases, reflecting the presence of non-Fermi-liquid electronic excitations. We show that both the self-consistent account of the non-local contributions to the electronic self-energy and the proper treatment of electron interaction vertices in D-TRILEX are important to obtain this behaviour.

Adopting explicitly correlated Kolos-Wolniewicz-type basis functions, the Born-Oppenheimer potential curves of a number of excited $Σ$ states of the hydrogen-antihydrogen system ($\bar{\rm H}$) were calculated for both, even and odd, Q symmetries, including also free positronium states. It is demonstrated that the excited leptonic states support ro-vibrational states with energies close to the ground-state dissociation threshold. As a consequence, the excited leptonic states need to be considered in theoretical treatments of ground-state H-$\bar{\mathrm{H}}$ collisions.

With the rapid development of the internet industry, online social networks have come to play an increasingly significant role in everyday life. In recent years, content-based emerging platforms such as TikTok, Instagram, and Bilibili have diverged fundamentally in their underlying logic from traditional connection-based social platforms like Facebook and LinkedIn. Empirical data on follower counts and follower-count-based rankings reveal that the distribution of social power varies significantly across different types of platforms, with content-based platforms exhibiting notably greater inequality. Here we propose two fundamental network formation mechanisms: a meritocracy-based model and a Matthew-effect-based model, designed to capture the formation logic underlying traditional and emerging social networks, respectively. Through theoretical and numerical analysis, we demonstrate that both models replicate salient statistical features of social networks including scale-free and small-world property, while also closely match empirical patterns on the relationship between in-degrees and in-degree rankings, thereby capturing the distinctive distributions of social power in respective platforms. Moreover, networks such as academic collaboration networks, where the distribution of social power usually lies between that of traditional and emerging platorms, can be interpreted through a hybrid of the two proposed mechanisms. Deconstructing the formation mechanisms of online social networks offers valuable insights into the evolution of the content ecosystems and the behavioral patterns of content creators on online social platforms.

NF set theory using intuitionistic logic is called iNF. We develop the theories of finite sets and their power sets and mappings, finite cardinals and their ordering, cardinal exponentiation, addition, and multiplication. We follow Rosser and Specker with appropriate constructive modifications, especially replacing ``arbitrary subset'' by ``separable subset'' in the definitions of exponentiation and order. It is not known whether iNF proves that the set of finite cardinals is infinite, so the whole development must allow for the possibility that there is a maximum integer; arithmetical computations might ``overflow'' as in a computer or odometer, and theorems about them must be carefully stated to allow for this possibility. The work presented here is intended as a substrate for further investigations of iNF, including the development of Bishop-style constructive mathematics in iNF.

Cosmological studies of the Lyman-Alpha (Lya) forest typically constrain parameters using two-point statistics. However, higher-order statistics, such as the three-point function (or its Fourier counterpart, the bispectrum) offer additional information and help break the degeneracy between the mean flux and power spectrum amplitude, albeit at a significant computational cost. To address this, we extend an existing highly informative compression of the bispectrum, the skew spectra, to the Lya forest. We derive the tree-level bispectrum of Lya forest fluctuations in the framework of effective field theory (EFT) directly in redshift space and validate our methodology on synthetic Lya forest data. We measure the anisotropic cross-spectra between the transmitted flux fraction and all quadratic operators arising in the bispectrum, yielding a set of 26 skew spectra. Using idealized 3D Gaussian smoothing (R=10 Mpc/h), we find good agreement (1-2 sigma level based on the statistical errors of the mocks) with the theoretical tree-level bispectrum prediction for monopole and quadrupole up to k <= 0.17 h/Mpc. To enable the cosmological analysis of Lya forest data from the currently observing Dark Energy Spectroscopic Instrument (DESI), where we cannot do 3D smoothing, we use a line-of-sight smoothing and introduce a new statistic, the shifted skew spectra. These probe non-squeezed bispectrum triangles and avoid locally applying quadratic operators to the field by displacing one copy of the field in the radial direction. Using a fixed displacement of 40 Mpc/h (and line-of-sight smoothing of 10 Mpc/h) yields a similar agreement with the theory prediction. For the special case of correlating the squared (and displaced) field with the original one, we analytically forward model the window function making this approach readily applicable to DESI data.

(Scanning) transmission electron microscopy ((S)TEM) has significantly advanced materials science but faces challenges in correlating precise atomic structure information with the functional properties of devices due to its time-intensive nature. To address this, we introduce an analytical workflow for the holistic characterization, modelling, and simulation of device heterostructures. This workflow automates the experimental (S)TEM data analysis, providing an in-depth characterization of crystallographic information, 3D orientation, elemental composition, and strain distribution. It reduces a process that typically takes days for a trained human into an automatic routine solved in minutes. Utilizing a physics-guided artificial intelligence model, it generates representative descriptions of materials and samples. The workflow culminates in creating digital twins, 3D finite element and atomic models of millions of atoms, enabling simulations that provide crucial insights into device behaviour in practical applications. Demonstrated with SiGe planar heterostructures for scalable spin qubits, the workflow links digital twins to theoretical properties, revealing how atomic structure impacts materials and functional properties such as spatially-resolved phononic or electronic characteristics, or (inverse) spin orbit lengths. The versatility of our workflow is demonstrated through its application to a wide array of materials systems, device configurations, and sample morphologies.

It is well known that the current-biased Josephson junction (CBJJ) can serve as a Josephson threshold detector (JTD) for the sensitive detection of weak microwave signals. Based on the recent work (PRB {\bf 111}, 024501 (2025)) on the detection sensitive limit of the usual equilibrium JTD, here we numerically demonstrate that a non-equilibrium JTD can be alternatively utilized to implement the higher sensitive detection of a weak microwave signal, arriving at its energy quantum limit. In the presence of thermal noise, we numerically simulate the phase dynamics for the CBJJ in the JTD with the different sweep rates of the biased currents, and find that the SCDs of the JTD with and without the microwave signal input show different behaviors. It is demonstrated that, depending on how high the sweep rate of the biased current being applied, the JTD can be operated in either the equilibrium- or the non-equilibrium state. Specifically, under the rapidly non-adiabatic driving, the SCDs of the JTD are obviously insensitive to the thermal noises, which means that the non-equilibrium JTD can possess a higher achievable detection sensitivity, compared with its equilibrium state counterpart. Consequently, the non-equilibrium JTD can be utilized to implement the desired single microwave-photon detection. Also, some of the achievable performance indexes, such as the dynamic range, detection bandwidth, and the photon-number resolvability, etc., of the non-equilibrium JTD have been estimated, when it serves as a wideband microwave single-photon detector.

When generating light with orbital angular momentum by imprinting orbital phase onto a standard Gaussian beam, it is often assumed that the propagation of the generated spatial mode is a Laguerre-Gaussian. However, the true propagation of this beam in a realistic, aperture-limited optical system is non-trivial and has not been thoroughly explored in existing literature. We explore a numerical model that shows the development of an optical vortex mode, propagating from the plane of phase modulation, and the relation of these dynamics to the orbital phase factor $\ell$ and the spatial bandwidth of the optical system. The results of this model are compared to experimental data for beams with $\ell$ values 1, 2, 5, and 10 propagating through a range of spatial filters, with the described model showing agreement in the near field regime.

The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hidden $\text{SU}(2) \times \text{SU}(2)$ symmetry, we discuss the quantum Kepler problem for a spin-$\frac{1}{2}$ particle. We show that the Hilbert space $\mathcal{H}$ of bound states for this problem is unitarily equivalent, as a representation of $\text{SU}(2) \times \text{SU}(2)$, to the Hilbert space of solutions of the Weyl equation on the spacetime $\mathbb{R} \times S^3$. This equation describes a massless left-handed spin-$\frac{1}{2}$ particle. We then form the fermionic Fock space on $\mathcal{H}$ and show this is unitarily equivalent to the Hilbert space of a massless left-handed spin-$\frac{1}{2}$ free quantum field on $\mathbb{R} \times S^3$, again as representations of $\text{SU}(2) \times \text{SU}(2)$. By modifying the Hamiltonian of this free field theory, we obtain the well-known "Madelung rules". These give a reasonable approximation to the observed filling of subshells as we consider elements with more and more electrons, and match the rough overall structure of the periodic table.

We use a slave-boson approach to study the band renormalization and pair susceptibility in the normal state of Iron-based superconductors in presence of strong Coulomb repulsion and Hund's interaction. Our results show orbital selectivity toward localization of $xy$ orbitals and its interplay with superconductivity. We also compare the recently proposed triplet resonating valence bond theory of superconductivity in Iron-based superconductors with the more conventional $s_\pm$ pairing and show that both favor a superconductivity when the $xy$ orbital is delocalized.

In this work, we propose performing key operations in quantum computation and communication using room-temperature atoms moving across a grid of high-quality-factor, small-mode-volume cavities. These cavities enable high-cooperativity interactions with single atoms to be achieved with a characteristic timescale much shorter than the atomic transit time, allowing multiple coherent operations to take place. We study scenarios where we can drive a Raman transition to generate photons with specific temporal shapes and to absorb, and hence detect, single photons. The strong atom-cavity interaction can also be used to implement the atom-photon controlled-phase gate, which can then be used to construct photon-photon gates, create photonic cluster states, and perform non-demolition detection of single photons. We provide numerics validating our methods and discuss the implications of our results for several applications.

Pump-probe spectroscopy is a powerful tool to study ultrafast exciton dynamics, revealing the underlying complex interactions on the electronic scale. Despite significant advances in experimental techniques, developing a comprehensive and rigorous theoretical framework for modeling and interpreting the transient response in photoexcited materials remains a challenge. Here, we present a first-principles approach to simulating pump-probe spectroscopy and disentangling the electronic and thermal contributions underlying exciton dynamics. We showcase our method to three materials, representative for different classes of solids: the transition-metal dichalcogenides WSe$_2$, the halide perovskite CsPbBr$_3$, and the transition-metal oxide TiO$_2$, showing remarkable agreement with experimental counterparts. We find that (i) photoinduced Coulomb screening is the primary electronic effect, responsible for a blue shift of exciton resonances, while (ii) Pauli blocking plays a minor role, and (iii) thermal lattice expansion leads to a red shift of the spectra. We further demonstrate how key parameters such as excitation density, pump photon energy, and pump polarization modulate the transient absorption spectra, offering direct control over the exciton-resonance energy. Our approach establishes a quantitative and predictive framework for interpreting pump-probe experiments, providing actionable insights for the design of energy-selective optoelectronic devices through exciton engineering.

In clinical trials with recurrent events, such as repeated hospitalizations terminating with death, it is important to consider the patient events overall history for a thorough assessment of treatment effects. The occurrence of fewer events due to early deaths can lead to misinterpretation, emphasizing the importance of a while-alive strategy as suggested in Schmidli et al. (2023). In this study, we focus on the patient weighted while-alive estimand, represented as the expected number of events divided by the time alive within a target window, and develop efficient estimation for this estimand. Specifically, we derive the corresponding efficient influence function and develop a one-step estimator initially applied to the simpler irreversible illness-death model. For the broader context of recurrent events, due to the increased complexity, this one-step estimator is practically intractable due to likely misspecification of the needed conditional transition intensities that depend on a patient's unique history. Therefore, we suggest an alternative estimator that is expected to have high efficiency, focusing on the randomized treatment setting. Additionally, we apply our proposed estimator to two real-world case studies, demonstrating the practical applicability of this second estimator and benefits of this while-alive approach over currently available alternatives.

There are three long-known types of restricted integer compositions whose counts match the Fibonacci sequence:\ one from ancient India and two from 19th century England. We give proofs of these enumeration results using tiling arguments and discuss how these can be used in combinatorial proofs of several Fibonacci number identities. With MacMahon's notion of conjugation, we show that, for every $n \ge 2$, the compositions of $n$ include subsets whose sizes satisfy the Fibonacci recurrence.

It has been argued for many years that models used to analyze data from crossover designs are not appropriate when simple carryover effects are assumed. Furthermore, a statistical model that could estimate complex carry-over effects in crossover designs had never been found. However, in this paper, the estimability conditions of the complex carryover effects and a theoretical result that supports them are found. In addition, a simulation example is developed in a non-linear dose-response test for a typical AB/BA crossover design with repeated measures. This simulation shows that a semiparametric model can detect complex carryover effects and that this estimation improves the precision of the estimators of the treatment effect. It is concluded that when there are at least five replicates in each observation period per individual, semiparametric statistical models provide a good estimator of the treatment effect and reduce bias with respect to models that assume the absence of carryover effects or simplex carryover effects. Furthermore, an application of the methodology is shown and the wealth of analysis gained by estimating complex carryover effects is evident.

We estimate the number of ends of smooth and singular Ricci shrinkers focussing first on general ends and later on asymptotically conical ones. In particular, we obtain a variety of applications to sequences of Ricci shrinkers converging in a weak pointed sense to a possibly singular limit Ricci shrinker, for instance no new conical end can form in the limit.

We demonstrate that assuming the "discrete" vacuum geometry in the Minkowskian Higgs model with vacuum BPS monopole solutions can justify the Dirac fundamental quantization of that model. The important constituent of this quantization is getting various rotary effects, including collective solid rotations inside the physical BPS monopole vacuum, and just assuming the "discrete" vacuum geometry seems to be that thing able to justify these rotary effects. More precisely, assuming the "discrete" geometry for the appropriate vacuum manifold implies the presence of thread topological defects (side by side with point hedgehog topological defects and walls between different topological domains) inside this manifold in the shape of specific (rectilinear) threads: gauge and Higgs fields located in the spatial region intimately near the axis $z$ of the chosen (rest) reference frame. This serves as the source of collective solid rotations proceeding inside the BPS monopole vacuum suffered the Dirac fundamental quantization. It will be argued that indeed the first-order phase transition occurs in the Minkowskian Higgs model with vacuum BPS monopoles quantized by Dirac. This comes to the coexistence of two thermodynamic phases inside the appropriate BPS monopole vacuum. There are the thermodynamic phases of collective solid rotations and superfluid potential motions.

Quantum heuristics have shown promise in solving various optimization problems, including lattice protein folding. Equally relevant is the inverse problem, protein design, where one seeks sequences that fold to a given target structure. The latter problem is often split into two steps: (i) searching for sequences that minimize the energy in the target structure, and (ii) testing whether the generated sequences fold to the desired structure. Here, we investigate the utility of variational quantum algorithms for the first of these two steps on today's noisy intermediate-scale quantum devices. We focus on the sequence optimization task, which is less resource-demanding than folding computations. We test the quantum approximate optimization algorithm and variants of it, with problem-informed quantum circuits, as well as the hardware-efficient ansatz, with problem-agnostic quantum circuits. While the former algorithms yield acceptable results in noiseless simulations, their performance drops under noise. With the problem-agnostic circuits, which are more compatible with hardware constraints, an improved performance is observed in both noisy and noiseless simulations. However, the results deteriorate when running on a real quantum device. We attribute this discrepancy to features not captured by the simulated noise model, such as the temporal aspect of the hardware noise.

In this paper, we introduce a certain random variable closely related to the value-distribution of the Hurwitz zeta-function with algebraic parameter. We prove a version of the limit theorem, where the limit measure is presented by the law of this random variable. Then we apply it to show that any complex number can be approximated by values of the Hurwitz zeta-function for algebraic irrational parameters but with finite exceptions.

Motivated by recent experiments of motile bacteria crossing liquid-liquid interfaces of isotropic- nematic coexistence (Cheon et al., Soft Matter 20: 7313-7320, 2024), we study the dynamics of prolate microswimmers traversing clean liquid-liquid interfaces. Using large-scale lattice Boltzmann simulations, we observe that neutrally wetting swimmers can be either trapped or cross the in- terface, depending on their initial angle, swimming speed and the interfacial tension between the two fluids. The simulation results are rationalized by considering a competition between interfacial (thermodynamic) and active (hydrodynamic) forces. The swimmers get trapped at the interface due to a thermodynamic trapping force, akin to Pickering effect, when the forces from interfacial tension dominate over the swimming forces. The trapping behavior can be captured by calculating a critical capillary number by balancing the interfacial and active energies. This prediction agrees remarkably well with the numerical simulations as well as the bacterial experiments of Cheon et al., (Soft Matter 20: 7313-7320, 2024). Finally, our results demonstrate that the torque resulting in a reorientation of the swimmers parallel to the interface have both hydro and thermodynamic components.

We study the asymptotic behavior of solutions to the fully nonlinear Hamilton-Jacobi equation $H(x, Du, λu) = 0$ in $\mathbb{R}^n$ as $λ\to 0^+$. Under the assumption that the Aubry set is localized, we employ a variational approach to derive limiting Mather-type measures and formulate a selection principle. Central to our analysis is a modified variational formula that bridges global and local state-constraint solutions, thereby extending localization techniques to the nonlinear framework.

Social media is transforming various aspects of offline life, from everyday decisions such as dining choices to the progression of conflicts. In this study, we propose a coupled modelling framework with an online social network layer to analyse how engagement on a specific topic spills over into offline protest activities. We develop a stochastic model and derive several mean-field models of varying complexity. These models allow us to estimate the reproductive number and anticipate when surges in activity are likely to occur. A key factor is the transmission rate between the online and offline domains; for offline outbursts to emerge, this rate must fall within a critical range, neither too low nor too high. Additionally, using synthetic networks, we examine how network structure influences the accuracy of these approximations. Our findings indicate that low-density networks need more complex approximations, whereas simpler models can effectively represent higher-density networks. When tested on two real-world networks, however, increased complexity did not enhance accuracy.

The $ϕ$-Assouad dimensions are a family of dimensions which interpolate between the upper box and Assouad dimensions. They are a generalization of the well-studied Assouad spectrum with a more general form of scale sensitivity that is often closely related to "phase-transition" phenomena in sets. In this article we establish a number of key properties of the $ϕ$-Assouad dimensions which help to clarify their behaviour. We prove for any bounded doubling metric space $F$ and $α\in\mathbb{R}$ satisfying $\overline{\operatorname{dim}}_{\mathrm{B}}F<α\leq\operatorname{dim}_{\mathrm{A}} F$ that there is a function $ϕ$ so that the $ϕ$-Assouad dimension of $F$ is equal to $α$. We further show that the "upper" variant of the dimension is fully determined by the $ϕ$-Assouad dimension, and that homogeneous Moran sets are in a certain sense generic for these dimensions. Further, we study explicit examples of sets where the Assouad spectrum does not reach the Assouad dimension. We prove a precise formula for the $ϕ$-Assouad dimensions for Galton--Watson trees that correspond to a general class of stochastically self-similar sets, including Mandelbrot percolation. This result follows from two results which may be of general interest: a sharp large deviations theorem for Galton--Watson processes with bounded offspring distribution, and a Borel--Cantelli-type lemma for infinite structures in random trees. Finally, we obtain results on the $ϕ$-Assouad dimensions of overlapping self-similar sets and decreasing sequences with decreasing gaps.

Recent advances in quantum simulators permit unitary evolution interspersed with locally resolved mid-circuit measurements. This paves the way for the observation of large-scale space-time structures in quantum trajectories and opens a window for the \emph{in situ} analysis of complex dynamical processes. We demonstrate this idea using a paradigmatic dissipative spin model, which can be implemented, e.g., on Rydberg quantum simulators. Here, already the trajectories of individual experimental runs reveal surprisingly complex statistical phenomena. In particular, we exploit free-energy functionals for trajectory ensembles to identify dynamical features reminiscent of hydrophobic behavior observed near the liquid-vapor transition in the presence of solutes in water. We show that these phenomena are observable in experiments and discuss the impact of common imperfections, such as readout errors and disordered interactions.

The distribution of absorption lines in the spectra of distant quasars, called the Lyman-$α$ (Ly-$α$) forest, is a unique probe of cosmology and the intergalactic medium at high redshifts and small scales. The statistical power of ongoing redshift surveys demands precise theoretical tools to model the Ly-$α$ forest. We address this challenge by developing an analytic, perturbative forward model to predict the Ly-$α$ forest at the field level for a given set of cosmological initial conditions. Our model shows a remarkable performance when compared with the Sherwood hydrodynamic simulations: it reproduces the flux distribution, the Ly-$α$ - dark matter halo cross-correlations, and the count-in-cell statistics at the percent level down to scales of a few Mpc. Our work provides crucial tools that bridge analytic modeling on large scales with simulations on small-scales, enabling field-level inference from Ly-$α$ forest data and simulation-based priors for cosmological analyses. This is especially timely for realizing the full scientific potential of the Ly-$α$ forest measurements by the Dark Energy Spectroscopic Instrument.

We present a measurement of the amplitude of matter fluctuations over the redshift range 0.8 <= z <= 3.5 from the cross correlation of over 1.2 million spectroscopic quasars selected by the Dark Energy Spectroscopic Instrument (DESI) across 7,200 deg$^2$ (approx 170 quasars/deg$^2$) and Planck PR4 (NPIPE) cosmic microwave background (CMB) lensing maps. We perform a tomographic measurement in three bins centered at effective redshifts z=1.44, 2.27 and 2.75, which have ample overlap with the CMB lensing kernel. From a joint fit using the angular clustering of all three redshift bins (auto and cross-spectra), and including an $Ω_m$ prior from DESI DR1 baryon acoustic oscillations to break the $Ω_m-σ_8$ degeneracy, we constrain the amplitude of matter fluctuations in the matter-dominated regime to be $σ_8=0.929^{+0.059}_{-0.074}$ and $S_8\equiv σ_8(Ω_m/0.3)^{0.5} = 0.922^{+0.059}_{-0.073}$. We provide a growth of structure measurement with the largest spectroscopic quasar sample to date at high redshift, which is 1.5$σ$ higher than predictions from $Λ$CDM fits to measurements of the primary CMB from Planck PR4. The cross-correlation between PR4 lensing maps and DESI DR1 quasars is detected with a signal-to-noise ratio of 21.7 and the quasar auto-correlation at 27.2 for the joint analysis of all redshift bins. We combine our measurement with the CMB lensing auto-spectrum from the ground-based Atacama Cosmology Telescope (ACT DR6) and Planck PR4 to perform a sound-horizon-free measurement of the Hubble constant, yielding $H_0=69.1^{+2.2}_{-2.6}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ through its sensitivity to the matter-radiation equality scale.

To ensure security of supply in the power sector, many countries are already using or discussing the introduction of capacity mechanisms. Two main types of such mechanisms include capacity markets and capacity reserves. Simultaneously, the expansion of variable renewable energy sources increases the need for power sector flexibility, for which there are promising yet often under-utilized options on the demand side. In this paper, we analyze how a centralized capacity market and an advanced reliability reserve with a moderately high activation price affect investments in demand-side flexibility technologies. We do so for a German case study of 2030, using an open-source capacity expansion model and incorporating detailed demand-side flexibility potentials across industry, process heat, and district heating. We show that a centralized capacity market effectively caps peak prices in the wholesale electricity market and thus reduces incentives for investments in demand-side flexibility options. The advanced reliability reserve induces substantially higher flexibility investments while leading to similar overall electricity supply costs and ensuring a similar level of security of supply. The advanced reliability reserve could thus create a learning environment for flexibility technologies to support the transition to climate neutral energy systems. Additionally, an advanced reliability reserve could be introduced faster and is more flexible than a centralized capacity market. While concrete design parameters are yet to be specified, we argue that policymakers should consider the reliability reserve concept in upcoming decision on capacity mechanisms in Germany and beyond.

The problem of ordering of radial vs.\ orbital excitations is reviewed. It is shown that the current quark models cannot explain the location of the Roper resonance which is slightly lower than the lowest negative-parity excitations. We also study some related spectral problems, such as the dependence of the energies on the quark masses, and the possibility of bound states in simple chromelectric models.