The Electric Propulsion Electrostatic Analyzer Experiment (ÈPÈE) is a compact ion energy bandpass filter deployed on the International Space Station (ISS) in March 2023 and providing continuous measurements through April 2024. This period coincides with the Solar Cycle 25 maximum, capturing unique observations of solar activity extremes in the mid- to low-latitude regions of the topside ionosphere. From these in situ spectra we derive plasma parameters that inform space-weather impacts on satellite navigation and radio communication. We present a statistical processing pipeline for ÈPÈE that (i) estimates the instrument noise floor, (ii) accounts for irregular temporal sampling, and (iii) extracts ionospheric signals. Rather than discarding noisy data, the method learns a baseline noise model and fits the measurement surface using a scaled Vecchia Gaussian process approximation, recovering values typically rejected by thresholding. The resulting products increase data coverage and enable noise-assisted monitoring of ionospheric variability.

Topology optimization (TO) of 3D surface-enhanced Raman scattering (SERS) substrates faces challenges in managing field singularities and modeling orientation-averaged anisotropic molecules. We present 3D TO for manufacturable SERS substrates that maximize spatially averaged signals from randomly oriented, anisotropic molecules in both elastic and inelastic scattering. A new trace formulation provides a closed-form rotational average of anisotropic Raman tensors, which are not equivalent to isotropic molecules because of tensor nonlinearity. Optimized silver and Si3N4 devices show that lengthscale constraints are sufficient to suppress designs that rely on unphysical mathematical field divergences at sharp corners. Metallic designs deliver broadband enhancement and remain robust to typical Raman shifts, whereas dielectric designs yield narrower, quality-factor-limited gains that are inferior to metallic designs for quality factors below about 500. Our approach readily incorporates additional physics, such as a nonlinear damage model. Together, these results provide a practical route to improved manufacturable SERS substrates and extend naturally to other distributed-emitter design problems.

Techniques for detecting critical phenomena -- phase transitions where correlation length diverges and small perturbations have large effects -- have been developed across multiple fields over nine decades. We survey between six and twelve disciplines (depending on classification criteria) where researchers derived functionally corresponding measures of correlation scaling, with little documented awareness of each other's work. The physicist's correlation length $ξ$, the cardiologist's DFA scaling exponent $α$, the financial analyst's Hurst exponent $H$, and the machine learning engineer's spectral radius $χ$ all detect critical signatures under different notation. We classify each surveyed domain as independent derivation, domain transfer, or empirical precursor, and present citation network evidence that cross-domain citations remained significantly below random-mixing expectations (under a simple null model of domain mixing) during the formative period (1987--2010). The framework that motivated this investigation -- derived from distributed systems engineering and presented in the Supplementary Material -- is excluded from the survey count given the authors' dual role. Building on prior syntheses -- notably Sornette's 2004 textbook -- this paper contributes a taxonomy of discovery types and quantitative documentation of the convergence pattern.

Motivated by recent experimental refinements of stellar reaction rates, we establish a non-perturbative Green's function formalism based on the exact solution of the Dyson equation for sub-barrier proton-nucleus resonant scattering. By utilizing bare Green's functions to map the quantum tunneling problem onto a scattering formalism, we demonstrate that the summation of infinite quantum paths recovers the exact tunneling coefficients, enabling an analytical solution of the Dyson equation where the strong nuclear force is modeled as a surface delta-shell impurity embedded within the Coulomb field. Applying this framework to the astrophysically relevant $p + {}^{7}\text{Li}$, $p + {}^{14}\text{N}$, and $p + {}^{23}\text{Na}$ systems, we achieve precise agreement with experimental resonance energies while revealing a fundamental physical distinction in resonance formation. The heavier ${}^{23}\text{Na}$ system is identified as a saturated state, residing on a geometric plateau where the resonance energy becomes insensitive to the interaction strength; our calculated value of $2.11$~MeV aligns remarkably well with the experimental level of $2.08$~MeV. In contrast, the lighter ${}^7\text{Li}$ and ${}^{14}\text{N}$ systems emerge as threshold states in a weak-coupling window, where the resonance energy is highly sensitive to the potential parameters and is sustained near the continuum edge. In this regime, our model yields energies of $0.489$~MeV and $1.067$~MeV, closely reproducing the experimental benchmarks of $0.441$~MeV and $1.058$~MeV, respectively. We demonstrate that these threshold states are characterized by a significant enhancement of the resonant cross-section, driven by the inverse relationship between the tunneling width and the spectral density peak.

Variational Quantum Algorithms are a vital part of quantum computing. It is a blend of quantum and classical methods for tackling tough problems in machine learning, chemistry, and combinatorial optimization. Yet as these algorithms scale up, they cannot escape the barren-plateau phenomenon. As systems grow, gradients can vanish so quickly that training deep or randomly initialized circuits becomes nearly impossible. To overcome the barren plateau problem, we introduce a two-stage optimization framework. First comes the convex initialization stage. Here, we shape the quantum energy landscape, the Hilmaton landscape, into a smooth, low-energy basin. This step makes gradients easier to spot and keeps noise from derailing the process. Once we have gotten a stable gradient flow, we move to the second stage: nonconvex refinement. In this phase, we let the algorithm wander through different energy minima, making the model more expressive. We show that our proposed algorithm theoretically reduces the dependence on the condition number of the underlying quantum least squares approximate matrix via Riemannian manifold optimization. Finally, we used our two-stage solution to perform quantum cryptanalysis of quantum key distribution protocol (i.e., BB84) to determine the optimal cloning strategies. The simulation results showed that our proposed two-stage solution outperforms its random initialization counterpart.

Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor networks naturally accommodate non-unitary maps. This flexibility lets us design quantum-inspired methods that start from a quantum algorithmic structure, yet go beyond unitarity to achieve speedups. Here we introduce a tensor-network approach to compute the discrete Laplace transform, a non-unitary, aperiodic transform (in contrast to the Fourier transform). We encode a length-$N$ signal on two paired $n$-qubit registers and decompose the overall map into a non-unitary exponential Damping Transform followed by a Quantum Fourier Transform, both compressed in a single matrix-product operator. This decomposition admits strong MPO compression to low bond dimension resulting in significant acceleration. We demonstrate simulations up to $N=2^{30}$ input data points, with up to $2^{60}$ output data points, and quantify how bond dimension controls runtime and accuracy, including precise and efficient pole identification.

Context. Understanding the survival and orbital evolution of brown dwarf (BD) companions during the post-main-sequence (MS) evolution of their host stars is increasingly important, especially with recent discoveries of many substellar companions around white dwarfs (WDs). Aims. We investigate the long-term evolution and final outcomes of BDs orbiting low-mass MS stars as these evolve into WDs. By comparing forward-modeling populations with observed WD-BD binaries, we test evolutionary models and predict the existence of yet-undetected systems. Methods. We employ the COMPAS binary population synthesis code to evolve observed MS-BD systems through the post-MS phases of their host stars into the WD stage, tracking orbital changes driven by mass loss, tides, and common-envelope (CE) evolution. Results. Our simulations reproduce a period gap in the distribution of detached WD-BD binaries, consistent with observations. We also identify a boundary separating detached and semi-detached systems on the period-mass diagram, located at orbital periods of $\sim$1-2 hours depending on the BD mass. Conclusions. We predict that a subset of currently known MS-BD binaries will survive post-MS evolution and emerge as detached WD-BD systems, while others will undergo CE evolution and potentially form cataclysmic variables with BD donors. Our results reproduce the observed period gap in WD-BD binaries and provide quantitative predictions for the role of CE efficiency in shaping their distribution. This work predicts that many WD-BD systems remain undetected, motivating targeted searches with microlensing and high-contrast imaging techniques using next-generation large telescopes.

We propose a variational formulation of an inverse problem in continuous-time stochastic control, aimed at identifying control costs consistent with a given distribution over trajectories. The formulation is based on minimizing the suboptimality gap of observed behavior. We establish a connection between the inverse problem and a generalized dynamic Schrödinger problem, showing that their optimal values coincide. This result links inverse stochastic control with stochastic optimal transport, offering a new conceptual viewpoint on inverse inference in controlled diffusions.

Metric-affine gravity (GL(4) gauge theory) in 4-dimensions is coupled to a spacetime Dirac source field using the isomorphisms of the Lie algebra gl(4) to the Clifford algebras Cl(3,1) and Cl(2,2). A simple transformation relates the generators of Cl(3,1) to a real representation of Cl(2,2), while the real representation of Cl(2,2) serves directly as a basis for the Lie algebra gl(4). Therefore, although GL(4) does not contain a spinor representation of the Lorentz group, expanding its Lie algebra in the Cl(2,2) basis gives a Clifford valued connection with well-defined coupling to Dirac spinors. Variation of the expansion coefficients gives new Dirac sources for both torsion and nonmetricity, separated by identifying the so(3,1) basis within the gl(4) basis.

The formation channels of binary black hole (BBH) mergers detected by the LIGO/Virgo/KAGRA (LVK) network remain uncertain. While BBH mergers occurring inside active galactic nucleus (AGN) disks may interact with surrounding gas and generate observable optical flares. We test this scenario by quantifying the spatial and temporal correlation between BBH events in GWTC-4.0 and AGN flares identified from six years of the Zwicky Transient Facility (ZTF) DR23 data. Using 80 BBH mergers selected for adequate localization, redshift reach, observing-epoch overlap, and ZTF sky coverage, we construct a likelihood for the flare-associated fraction, $f_{\rm flare}$, that combines each event's 3D localization with a locally estimated flare number density derived from a 3D Voronoi tessellation, while explicitly accounting for survey boundaries and incomplete catalog coverage. Adopting a 200-day post-merger time window for potential counterparts, we infer $f_{\rm flare} = 0.07_{-0.05}^{+0.24}$ (90\% confidence level). This non-zero maximum-likelihood value is driven primarily by GW190412, for which a single flare candidate (J143041.67+355703.8) is consistent in both time and spatial position. The candidate's light curve is limited to two data points during its peak, so it remains classified only as a candidate AGN flare. Excluding GW190412 yields results consistent with no association and an upper limit of $f_{\rm flare} < 0.17$ at 90\% confidence level. The intrinsic properties of GW190412 and the characteristics of the candidate host AGN are broadly consistent with theoretical expectations for the AGN-disk formation channel, motivating continued, targeted electromagnetic follow-up of well-localized and highly asymmetric BBH mergers in current and upcoming time-domain surveys.

Adding a constant energy offset leaves classical dynamics unchanged. In quantum mechanics it changes the phase velocity of the wavefunction. The inclusion of the constant rest energy in the Klein-Gordon formulation leads to significantly higher phase velocities compared with the Schrödinger equation. The Schrödinger equation predicts an attenuation of the wavefunction along one of the paths in a Sagnac interferometer when a beamsplitter's trajectory along that path includes a segment where its speed exceeds the phase velocity of a free particle. Such an attenuation does not occur for electromagnetic waves nor for eigenstates of momentum in the Klein-Gordon equation since the speed of the beamsplitter cannot then exceed the phase velocity of the wave. This attenuation reduces the amplitude without introducing a phase shift, preserving the overall structure of the transmitted wave group. While a Klein-Gordon wave group undergoes three traversals of the beamsplitter that moved, it experiences attenuation equivalent to only a single pass, whereas the Schrödinger equation predicts the expected attenuation for three passes. This discrepancy highlights a fundamental incompatibility between the Klein-Gordon equation and the Schrödinger equation in a regime where their predictions should converge.

A pair of quantized spin-wave modes is driven by two-tone parallel pumping in a YIG microdisk. The nonlinear dynamics is experimentally investigated by probing the resulting steady state, which is found to critically depend on the chosen pair of modes, the detuning between the pump frequencies and the modes parametric resonance, as well as the temporal sequence of the two rf tones. A general theory of parametric excitation in confined structures based on magnetization normal modes is developed and quantitatively accounts for the observed dependence and non-commutative behaviors, which emerge from the interplay between the self and mutual nonlinear frequency shifts of the spin-wave modes. Owing to its high degree of external controllability and scalability to larger sets of modes, this dynamical system provides a model platform for exploring nonlinear phenomena and a promising route toward rf driven state mapping relevant to neuromorphic and unconventional computing.

Raman measurements performed on dense H2, D2 and H2+D2 in a wide pressure-temperature range reveal the presence of the ΔJ=0 rotational excitation. In the gas/fluid state this excitation has zero Raman shift, but in the solid, the crystal field drive s it away from the zero value e.g. 75 cm-1 at around 50 GPa and 10 K for both isotopes and their mixture. In the case of deuterium, the ΔJ=0 mode splits upon entering phase II suggesting a very complex molecular environment of the broken symmetry phase (BSP). In the fluid state and phases I and II the frequencies (energies) of the ΔJ=0 transition for H2 and D2 do not scale either as rotational (by factor of 2) nor vibrational (by square 2) modes and appear to be completely isotope independent. This independence on mass marks this transition as unique and a fundamentally different type of excitation from the commonly considered harmonic oscillator and quantum rotor.

Transfer learning aims to improve performance on a target task by leveraging information from related source tasks. We propose a nonparametric regression transfer learning framework that explicitly models heterogeneity in the source-target relationship. Our approach relies on a local transfer assumption: the covariate space is partitioned into finitely many cells such that, within each cell, the target regression function can be expressed as a low-complexity transformation of the source regression function. This localized structure enables effective transfer where similarity is present while limiting negative transfer elsewhere. We introduce estimators that jointly learn the local transfer functions and the target regression, together with fully data-driven procedures that adapt to unknown partition structure and transfer strength. We establish sharp minimax rates for target regression estimation, showing that local transfer can mitigate the curse of dimensionality by exploiting reduced functional complexity. Our theoretical guarantees take the form of oracle inequalities that decompose excess risk into estimation and approximation terms, ensuring robustness to model misspecification. Numerical experiments illustrate the benefits of the proposed approach.

In 2016, Dannan and Sitnik established the notable Damascus inequality, which features a symmetric structure under a multiplicative constraint. In this study, we consider the natural generalisation of this inequality by characterising all positive integers $m$ and $n$ such that the inequality \[\sum_{j=1}^m\frac{x_j^n-1}{x_{j}^{n+1}+1}\leqslant 0\] holds for any positive real numbers $x_1, \ldots, x_m$ with $\prod_{j=1}^mx_j=1$. Our approach relies on the theories of GA-convexity and Sturm's sequence. For the cases where the inequality fails, we also investigate the topological properties of the set of non-solutions.

Let $F$ be a non-archimedean local field or a finite field. Let $π$ be a principal series representation of $GL_{2n}(F)$ induced from any of its maximal standard parabolic subgroups. Let $N$ be the unipotent radical of the maximal parabolic subgroup $P$ of $GL_{2n}(F)$ corresponding to the partition $(n,n).$ In this article, we describe the structure of the twisted Jacquet module $π_{N,ψ}$ of $π$ with respect to $N$ and a non-degenerate character $ψ$ of $N.$ We also provide a necessary and sufficient condition for $π_{N,ψ}$ to be non-zero and show that the twisted Jacquet module is non-zero under certain assumptions on the inducing data. As an application of our results, we obtain the structure of twisted Jacquet modules of certain non-generic irreducible representations of $GL_{2n}(F)$ and establish the existence of their Shalika model in the non-archimedean case. We conclude our article with a conjecture by Dipendra Prasad classifying the smooth irreducible representations of $GL_{2n}(F)$ with a non-zero twisted Jacquet module.

When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-network structure has been employed to find good solutions within a reasonable time limit. For such methods, a lower per-iteration cost is advantageous when solving larger models. The contribution of this paper is two-fold. First, we propose a gradient-based algorithm with lower per-iteration cost than existing methods. Second, we further adapt this algorithm to exploit the piecewise-linear structure of neural networks that use Rectified Linear Units (ReLUs). In line with prior research, our methods become competitive with -- and then dominant over -- other local search methods as the optimization models become larger.

We explore the topological significance of the Gukov-Manolescu knot series $F_K$. We show that the leading coefficient of $F_K$ is a monomial and express its exponent in terms of the Hopf invariant for all homogeneous braid knots, and for fibered knots up to 12 crossings. As an application, we deduce an explicit formula for the Hopf invariant in terms of colored Jones polynomials. For non-fibered strongly quasipositive knots, we study a relation between $F_K$ and the stability series of the colored Jones function, and explore similarities between $F_K$ and knot Floer homology. Finally, we propose a slope conjecture for $F_K$, relating it to the boundary slopes of the knot.

Curve-fold origami, composed of developable panels joined along a curved crease, exhibits rich dynamic behaviors relevant to metamaterials and soft robotic systems. Despite multiple approximated models, a comprehensive and exact dynamical theory for curve-fold origami remains absent, limiting the precise predictions of its dynamics, especially for those with wide panels. In this work, we develop an exact dimension-reduced theory that focuses on the dynamics of curve-fold origami, utilizing the intrinsic one-dimensional nature of developable surfaces. Starting from a single developable surface, we investigate the kinematics and kinetic energy of a moving developable surface. By overcoming the difficulty of describing the motion of local frames, we derive the exact velocity field of wide surfaces solely described by the motion of the reference curve, which leads to the kinetic energy of the entire surface. Owing to the one-dimensional feature, the Lagrangian of the system, composed of both kinetic and elastic energy, is a functional of the reference curve. Thus, we may variate the Lagrangian and derive a nonlinear dynamical theory for the reference curve, which comprises governing equations similar to the rod model but can precisely describe the motion of developable surfaces. The theory is validated consistently in both Lagrangian and Eulerian frameworks and is further extended to curved-fold origami modeled as a coupled bi-rod system. Utilizing our exact 1D model, we theoretically analyze the dynamical behaviors of various developable structures, revealing that the coupling of curvature and torsion along with the motion of local frames in our theory leads to the accurate modeling of arbitrarily deformed developable surfaces, which are validated by finite element analysis quantitatively.

The next-generation of $0νββ$ searches are targeting half-life sensitivities towards 10$^{27}$--10$^{28}$ years. Gaseous xenon time projection chamber (GXeTPC) detectors may be able to meet this challenge due to their excellent energy resolution and background rejection power through event visualization. This paper explores how the design choices of a next-generation GXeTPC time projection chamber can impact the overall performance of the experiment. We study the performance of systems using xenon enriched in the isotope $^{136}$Xe or natural xenon, focusing on scenarios that incorporate one tonne of $^{136}$Xe isotope. The detector size, copper shielding mass, energy resolution, density and corresponding levels of diffusion are surveyed to evaluate the overall performance dependencies on these parameters. A detector optimized for using enriched xenon is preferred over natural, due primarily to a factor of 10 lower background rate driven by the large intrinsic backgrounds introduced by the copper shielding used in the detector. The performance of three types of gas TPC technologies was also explored based on different gas additives used to reduce diffusion to different levels. For all TPC technologies, we find background rates of a fraction of a count per tonne year in the region of interest are achievable. These performance levels are contingent on suitable energy resolution and event position placement in the drift direction being achieved for the specific detector technology. Performance for enriched xenon TPCs varies mildly with pressure in the range 5 to 25 bars, reaching background levels below 0.2 events/tonne-year. Performance at one bar is worse by approximately a factor of four. When considerations for the construction of the detector in addition to the selection performance are included, there may be no clearly optimum pressure.

In many ways the solution to the Hedin equations represents an exact solution to the many body problem. However, for most systems of practical interest, the solution to the Hedin equations is rendered nearly numerically intractable because the Hedin equations are of functional derivative form. Integral equations, on the other hand, are much more numerically tractable, than functional derivative equations, as they can often be solved iteratively. In this work we present a systematic set of integral equations (with no functional derivatives) - Hedin approximations I, II, III, IV etc. - whose solutions converge to the solutions of the exact Hedin equations. The Hedin approximations are well suited to iterative numerical solutions (which we also describe). Furthermore Hedin approximation I is just the GW approximation (as such this work may be viewed as a systematic improvement of the GW approximation). We present a systematic study of the Hedin equations for zero dimensional field theory (which, in particular, is a method to enumerate Feynman diagrams for field theories in arbitrary dimensions) and show better and better convergence to the solutions of the Hedin equations for higher and higher Hedin approximations, with Hedin approximations I, II and III being explicitly studied. We, in particular, show that the higher Hedin approximations capture more and and more Feynman diagrams for the self energy. We also show that already Hedin approximation II captures more diagrams than the state of the art diagrammatic vertex corrections approach. Furthermore Hedin approximation III is a near perfect match to the exact solutions of the Hedin equations, at least in the zero dimensional case, and enumerates a large number of Feynman diagrams.

Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to $d$-level systems by conjugating an analog Hamiltonian block with single-qudit gates drawn from the Weyl-Heisenberg basis, which provides a natural set of operations for qudit architectures. More specifically, we propose a protocol to simulate arbitrary two-body Hamiltonians with at most $O(d^4 n^2)$ analog blocks. The power of this approach is illustrated by the simulation of many-body qudit spin Hamiltonians including magnetic quadrupolar terms.

In this paper we propose the analysis of the heavy quark photoproduction associated with a leading neutron in hadronic collisions at the LHC as an alternative to probe the pion gluon distribution in a kinematical range not covered by previous experiments. We perform an exploratory study of the charm and bottom photoproduction associated with a leading neutron in proton-proton ($pp$) and proton-lead ($pPb$) collisions, and present calculations for the rapidity distributions and cross-sections. Our predictions indicate that experimental studies of these processes are feasible, and that a future measurement of this final state will be useful to constrain the pion gluon distribution at small values of the Bjorken $x$ variable and to improve our understanding of the pion structure.

This work investigates the topological structure of multipartite entanglement in symmetric Dicke states $|D_n^{(k)}\rangle$. By viewing qubits as topological loops, we establish a direct correspondence between the recursive measurement dynamics of Dicke states and the stability of $n$-Hopf links. We utilize the Schmidt rank to quantify bipartite entanglement resilience and introduce the $l_1$-norm of quantum coherence as a measure of link fluidity. We demonstrate that unlike fragile states such as $ \left| GHZ \right \rangle$ (analogous to Borromean rings), Dicke states exhibit a robust, self-similar topology where local measurements preserve the global linking structure through non-vanishing residual coherence.

The dynamics of 2D long-range quantum magnets represents a current frontier in experimental physics such as in Rydberg atomic systems or trapped ions. In this work we address theoretical challenges in understanding these dynamics by combining large-scale neural quantum state simulations with an effective theory. Our findings uncover a mechanism for persistent coherent quantum dynamics and slow relaxation in 2D long-range quantum magnets. Demonstrated on the 2D transverse-field quantum Ising model with power-law decaying interactions, we observe long-lived oscillatory behavior after quenching the system from a ferromagnetic product state. We explain this phenomenon by the formation of magnon bound states, generated by effective attractive long-range magnon interactions. Our results highlight a generic mechanism for long-lived quantum coherence in 2D quantum magnets that can be directly observed in current quantum simulation platforms.

Algorithmic effects on social media platforms have come under recent scrutiny, with several studies reporting that right-leaning accounts tend to receive more exposure. In this paper, we expand upon this body of work using data collected from user feeds after Twitter's change of ownership but before its re-branding to X. We replicate findings from prior work regarding the increased exposure of right-leaning accounts to wider audiences in algorithmically curated compared to reverse-chronological feeds, and, crucially, we further unpack this effect to illuminate what correlated (and did not correlate) with these differences. Our results reveal that right-leaning accounts benefited not necessarily due to their political affiliation, but likely because they behaved in ways associated with algorithmic rewards; namely, posting more agitating content and receiving attention from the platform's owner, Elon Musk, who was the most central network account. We also demonstrate that legacy-verified accounts, like businesses and government officials, received less exposure in the algorithmic feed compared to non-verified or Twitter Blue-verified accounts. We discuss implications of these findings for the intersection between behavioral incentives for algorithmic reach and the health of online discourse.

The unprecedented extension of the human lifespan necessitates a parallel evolution in how we quantify the quality of aging and its socioeconomic impact. Traditional metrics focusing on Healthspan (years free of disease) overlook the gradual erosion of physiological capacity that occurs even in the absence of illness, leading to declines in productivity and eventual lack of capacity to work. To address this critical gap, we introduce Peakspan: the age interval during which an individual maintains at least 90% of their peak functional performance in a specific physiological or cognitive domain. Our multi-system analysis reveals a profound misalignment: most biological systems reach maximal capacity in early adulthood, resulting in a Peakspan that is remarkably short relative to the total lifespan. This dissociation means humans now spend the majority of their adult lives in a "healthy but declined" state, characterized by a significant functional gap. We argue that extending Peakspan and developing strategies to restore function in post-peak individuals is the functional manifestation of rejuvenative biomedical progress and is essential for sustained economic growth in aging societies. Recognizing and tracking Peakspan, increasingly facilitated by artificial intelligence and foundational models of biological aging, is crucial for developing strategies to compress functional morbidity and maximize human potential across the life course.

The violation of the null energy condition (NEC) is essential for constructing nonsingular cosmological scenarios, such as Genesis cosmology, which avoids the initial singularity by initiating cosmic evolution from an asymptotically Minkowski state. To address theoretical concerns regarding the accumulation of negative energy, the smeared null energy condition (SNEC) has been proposed as a quantum-motivated, semi-local bound on NEC violation. In this work, we examine the implications of the SNEC conjecture for Genesis models, typically constructed within generalized Galileon theories. Our results demonstrate that SNEC imposes nontrivial restrictions on the viability of Genesis models, highlighting the SNEC conjecture as a powerful tool for constraining nonsingular cosmological scenarios.

The Sun produces a steady signal of high-energy gamma rays through interactions of Galactic cosmic rays (GCRs) with its atmosphere. Observations with Fermi-LAT and HAWC have revealed a gamma-ray flux significantly higher than early theoretical predictions, with unexpected temporal and spectral features that suggest a crucial role of the solar magnetic field. In this work, we model GCR-induced gamma-ray emission at the solar disk using the CRPropa framework with realistic hadronic interactions, chromospheric density profiles, and several magnetic field configurations over the solar cycle. This allows us to quantify the gamma-ray emission of the entire solar disk for different phases of the solar activity cycle and we present, for the first time, maps of the production locations of gamma rays on the solar surface. We consider both mono-energetic and realistic power-law injection spectra in a simplified dipole-quadrupole current sheet model and potential-field source surface (PFSS) extrapolations for Carrington rotations during solar maximum and minimum. Our results show that magnetic mirroring and large-scale field topology strongly affect the spectral shape and spatial distribution of the emission, with slightly enhanced fluxes predicted at solar minimum. While our simulated baseline fluxes remain below observations, additional effects, such as heavier nuclei, Parker-field mirroring, and deeper atmospheric interactions, could result in further enhancements of fluxes closer to observational values. Hadronic interactions do not only produce gamma rays but also neutrinos. We estimate the expected neutrino flux from the Sun based on our gamma-ray predictions. We find that the expected flux is slightly below current upper limits from IceCube.

A company provides a service at different time slots, each slot being endowed with a capacity. A non-atomic population of users is willing to purchase this service. The population is modeled as a continuous measure over the preferred times. Every user looks at the time slot that minimizes the sum of the price assigned by the company to this time slot and the distance to their preferred time. If this sum is non-negative, then the user chooses this time slot for getting the service. If this sum is positive, then the user rejects the service. We address the problem of finding prices that ensure that the volume of users choosing each time slot is below capacity, while maximizing the revenue of the company. For the case where the distance function is convex, we propose an exact algorithm for solving this problem in time $O(n^3|P|^3)$, where $P$ is the set of possible prices and $n$ is the number of time slots. For the case where the prices can be any real numbers, this algorithm can also be used to find asymptotically optimal solutions in polynomial time under mild extra assumptions on the distance function and the measure modeling the population.