We study a continuum model for stochastic reinforcement learning in repeated market entry games. Starting from a discrete-time microscopic learning rule, we derive a Fokker--Planck-type equation for the distribution of agents' propensities and, using a kinetic closure, obtain a nonlinear one-particle equation of a mean-field type. For the resulting Cauchy problem, we prove existence and uniqueness of solutions and analyze their long-time behavior. The PDE captures two key phenomena observed in market entry dynamics: aggregate learning (the average number of entrants approaches market capacity) and sorting (propensities concentrate near extreme behaviors). The model also yields explicit characteristic time scales, showing that aggregate learning occurs faster than sorting, in agreement with experimental and computational evidence.

The Galaxy UV Legacy Project (GULP) is a Cycle 28 Treasury program with the Hubble Space Telescope (HST) designed to characterize resolved massive stars, OB associations, and young star clusters (YSCs) in 26 nearby star-forming galaxies. Utilizing the ACS/SBC F150LP and WFC3/UVIS F218W filters, combined with extensive archival observations, GULP provides an unprecedented panchromatic 8-band view from the Far-UV to the I-band. The target galaxies were carefully selected to span a broad range of metallicities, masses, morphological types, and star formation rates, thereby enabling detailed studies of star formation processes across different galactic environments. This paper introduces the GULP survey, detailing its observational strategy, data processing, and initial scientific results for the irregular barred starburst dwarf galaxy NGC 4449, used as a test case. We derived the physical parameters and ages for thousands of stars using the Binary Populations And Spectral Synthesis (BPASS) models, and found that the younger stars and clusters are predominantly concentrated along the galaxy's central bar, and that over the past <50 Myr star formation progressively migrated from northeast to southwest. We used the F150LP, F218W, and F275W filters to investigate how the UV-bump at lambda 2175 A correlates with the intensity of the UV radiation. The UV-bump is detected in many areas of the galaxy, but is absent in the regions of most intense and recent star formation. This strongly supports the scenario where UV radiation from young, massive stars effectively destroys the small dust grains responsible for the UV-bump.

Particle in Cell (PIC) simulations have become a vital tool for the investigation of kinetic processes in plasma physics. Many of the systems investigated with PIC simulations contain particles with relativistic velocities. The correct integration and the knowledge of possible sources of errors in relativistic particle trajectories is of importance to accurately judge the validity of the simulation results. Over the past few decades, various new integration schemes for relativistic particle trajectories in PIC simulations have been proposed. These are aimed at improving numerical accuracy in specific scenarios. This article presents a comprehensive comparison of particle pushers with a focus on explicit schemes. An important class of these schemes is found to be generalisable to arbitrary high order. A comparison of the fourth order variants of these schemes with their second order counterpart is also presented.

The Sanford Underground Research Facility (SURF) began operation in 2007 as a facility dedicated to advancing compelling multidisciplinary scientific research. SURF is one of the deepest laboratory sites and offers the largest footprint in the world for scientific pursuits, including physics campuses on the 4850-foot level where the LUX-ZEPLIN, MAJORANA DEMONSTRATOR, and CASPAR experiments are located. SURF is also home to the Long-Baseline Neutrino Facility (LBNF) that will host the international Deep Underground Neutrino Experiment (DUNE). SURF provides ultra-low background environments, low-background assay capabilities, and electroformed copper is produced at the facility. In this review, we discuss the history, features and status of the facility, as well as the current scientific program and future evolution and plans.

Existing models of political violence often emphasize discrete transitions, when conflicts emerge, escalate, or subside, without considering the longer trajectories of violence that accumulate across time and space. This paper introduces a spatially explicit longitudinal sequence analysis to address this gap. Using event-level data from the Armed Conflict Location and Event Dataset covering Africa from 1997 to 2024, we classify locations according to the intensity and spatial concentration of violence, tracing how these states evolve into distinct conflict trajectories. Applying optimal matching and clustering techniques, we identify six recurrent patterns ranging from short-lived, localized outbreaks to protracted high-intensity conflicts. We further assess how these trajectories align across neighboring areas, revealing evidence of spatial interdependence, particularly in border regions. By highlighting the temporal rhythms and geographic linkages of political violence, the study advances conflict research beyond isolated transitions and provides a framework for understanding the life cycles of violence.

We report the epitaxial stabilization of GdAuSb films and GdAuSb/LaAuSb superlattices via molecular beam epitaxy on (0001)-oriented Al$_{2}$O$_{3}$ substrates. GdAuSb crystallize in the Au-Au dimerized YPtAs structure type (space group $P6_{3}/mmc$), the same structure as the Dirac semimetal LaAuSb. Angle-resolved photoemission spectroscopy (ARPES) measurements show similar near $E_F$ bandstructures for GdAuSb and LaAuSb, plus a rigid band shift for GdAuSb towards more hole-like behavior and core-like Gd $4f$ states $\sim 9$~eV below the Fermi energy. LaAuSb/GdAuSb superlattices exhibit sharp superlattice fringes by X-ray diffraction and atomically-precise interfaces by scanning transmission electron microscopy. Superlattices display two transitions in temperature-dependent resistvity, compared to a single Néel temperature for thick GdAuSb films. Superlattices of $Ln$AuSb materials ($Ln=$ rare earth) with atomically abrupt interfaces offer a new epitaxial platform for control of magnetic and topological order via tunable intralayer exchange and reduced dimensionality.

In this paper, we consider the near-critical dimer model in the setup of isoradial superpositions with Temperleyan boundary conditions. We show that the centered height function converges as the mesh size tends to zero to a limiting field which agrees with the (electromagnetically tilted) sine-Gordon model, whose derivative correlations are described by Grassmann variables (or equivalently determinants involving a massive Dirac operator). This answers a longstanding question in the field. A crucial part of the work is to develop a notion of discrete massive holomorphic functions and the tools to study such functions, in particular finding an exact discrete form of the massive Cauchy--Riemann equations, which is satisfied by the inverse Kasteleyn matrix. In comparison with previous studies, a key novelty of this part of our work is that the mass is not only allowed to be non-constant but can be complex-valued.

Estimating brain microstructure has important applications in medicine and neuroscience. Diffusion-weighted magnetic resonance imaging enables measuring microstructure \textit{in vivo}. Conventional biophysical model fitting can be accurate but is slow and impractical for time-critical clinical use, where machine learning can offer a potential route to rapid estimation. We address the problem of microstructure estimation under arbitrary acquisition protocols where most existing learning-based methods fail due to protocol assumptions, requiring retraining when the protocol changes. We present a graph neural network that represents input data as a point cloud in the 3D space where diffusion-weighted measurements are made and performs rotation-invariant message passing with permutation-invariant pooling, producing fixed-size embeddings that encode microstructure. The inductive biases of our relatively small model were guided by the underlying physics and symmetries of the problem rather than by generic model architectures. Trained on randomised simulated data, our model demonstrates domain generalisation, accurately estimating microstructure from data with unseen real-world protocols without retraining. This approach represents a step towards a "train once, deploy anywhere" architecture, bringing rapid learning-based microstructure mapping closer to clinical deployment.

This paper investigates the role of the augmentation parameter in the Finite Selection Model (FSM) and its impact on estimator performance. Through a comprehensive Monte Carlo simulation study, we analyze the sensitivity of bias, variance, and mean squared error to different values of the augmentation parameter. The results demonstrate that moderate augmentation improves covariate balance while maintaining estimation efficiency. However, excessive augmentation may increase variance and reduce estimator stability. The findings provide practical guidelines for selecting the augmentation parameter in applied experimental design settings.

In this paper we consider the operad of holomorphic disk embeddings of the unit disk $\mathbb D \subset \mathbb C$. We introduce a suboperad $\mathbb{CE}_2^{HS}$ defined by square-integrability conditions and show that the symmetric algebra $\mathrm{Sym} A^{2}(\mathbb D)$ of the Bergman space carries a natural $\mathbb{CE}_2^{HS}$-algebra structure. Conformally flat factorization homology with coefficients in $\mathrm{Sym} A^{2}(\mathbb D)$ then yields metric-dependent invariants of two-dimensional Riemannian manifolds. Moreover, $\mathrm{Sym} A^{2}(\mathbb D)$ is identified with the ind-Hilbert space completion of the affine Heisenberg vertex operator algebra.

Here, we present a simple, low-cost format for structured speaking and listening on historical, cultural, and equity-related topics within a physics institute. In this article, we describe how we run hour-long Learning Together sessions, including what you need, how to set expectations (this is not a debate, nor is it open discussion), and practical facilitation moves that help participants reflect safely on unfamiliar and sometimes difficult material. We aim to offer a replicable recipe that instructors and departments can adapt to their own contexts.

The coverage depth problem in DNA data storage is about computing the expected number of reads needed to recover all encoded strands. Given a generator matrix of a linear code, this quantity equals the expected number of randomly drawn columns required to obtain full rank. While MDS codes are optimal when they exist, i.e., over large fields, practical scenarios may rely on structured code families defined over small fields. In this work, we develop combinatorial tools to solve the DNA coverage depth problem for various linear codes, based on duality arguments and the notion of extended weight enumerator. Using these methods, we derive closed formulas for the simplex, Hamming, ternary Golay, extended ternary Golay, and first-order Reed-Muller codes. The centerpiece of this paper is a general expression for the coverage depth of a linear code in terms of the weight distributions of its higher-field extensions.

We establish a unified, symmetry-driven framework that combines the alternating spin splitting of altermagnets with valley topology to realize and electrically interconvert helical and chiral topological phases within a single material platform. We first demonstrate a magnetic analogue of the quantum spin Hall effect in altermagnets, hosting helical spin-valley-momentum-locked (SVML) edge states characterized by a composite spin-valley Chern number Csv = 2. Large-scale quantum transport simulations show these SVML edge states exhibit fully quantized spin conductance robust against nonmagnetic and long-range magnetic disorder, reflecting their dual topological protection, while remaining vulnerable to short-range magnetic disorder. Exploiting that the counterpropagating SVML modes are linked by crystal rotation symmetry, we introduce a gate-tunable sublattice-staggered potential that selectively gaps one valley and converts the helical state into a chiral quantum anomalous Hall phase with Csv = 1, robust against all disorder types. Reversing the potential switches the transmitted spin-valley polarization. Our first-principles calculations identify monolayer V2STeO and VO families as realistic platforms supporting both helical and chiral topological phases and their electrical switching. These results establish altermagnets as electrically programmable platforms for robust topological devices across charge, spin, and valley.

In this paper we combine methods from additive combinatorics and Diophantine geometry to study the generalised sum-product phenomenon in algebraic groups. As an application of this circle of ideas, we resolve a conjecture of Bremner on arithmetic progressions in coordinates of elliptic curves, along with various other generalisations studied in the literature. We also prove a uniform Bourgain--Chang-type sum-product estimate for general $1$-dimensional algebraic groups $G$ over $\mathbb{C}$. Using these ideas, we provide an alternative solution to a problem of Bays--Breuillard. Furthermore, we show an Elekes--Szabó type result in the same setting for sets with small doubling, improving upon an earlier result of Bays--Breuillard when $G$ is not $\mathbb{G}_a$. Our power saving here can be shown to be quantitatively optimal. We use a combination of deep, classical results in Diophantine geometry due to David--Philippon, Laurent and Evertse--Schmidt--Schlickewei along with the recent breakthrough work on the weak Polynomial Freiman--Ruzsa conjecture over integers due to Gowers--Green--Manners--Tao.

We present a rigorous formulation of the Quantum Big Bounce for the closed isotropic Universe, filled with a self-interacting scalar field, that emerges from the interaction with an ekpyrotic potential. Working in a covariant approach to the minisuperspace, we demonstrate the quantum equivalence between parametrizations in terms of the logarithmic scale factor and the volume variable. The analogy between the Wheeler-DeWitt equation and the Klein-Gordon equation, alongside a proper definition of asymptotic states, allows the identification of two different bouncing scenarios: one in which the transition occurs over a fixed direction of the internal time arrow, corresponding to a LQC-like scenario, and one involving a reversal of the internal time flow. The high-energy divergence in the former case shows the incompleteness of the WDW theory and the need for regularization. Therefore, the WDW theory is valid up to a given energy threshold. The latter transition, corresponding to an ekpyrotic scenario, is instead well-posed at any energy scale at the first perturbative order. While the Ashtekar school Big Bounce is expected to be recovered when high-energy corrections are included in this scheme, the WDW alone can avoid the cosmological singularity in a quantum mechanical fashion.

We combine data for extragalactic systems to quantify a relation between the observed baryonic mass $M_b$ and the enclosed dynamical mass $M_{200}$ inferred from kinematics or gravitational lensing. Our sample covers nine orders of magnitude in baryonic mass, including galaxies with kinematic or weak gravitational lensing data and groups and clusters of galaxies with new gravitational lensing data. For rich clusters with $M_b > 10^{14}\;\mathrm{M}_{\odot}$, the observed baryon fraction is consistent with the cosmic value, $f_b = 0.157$. For lower masses, the baryon fraction decreases systematically with mass. The variation is well described by $M_b/M_{200} = f_b \tanh(M_b/M_0)^{1/4}$ with $M_0 \approx 5 \times 10^{13}\;\mathrm{M}_{\odot}$. This relation is qualitatively similar to stellar mass-halo mass relations derived from abundance matching, but exhibits less scatter.

The spatial Muller's ratchet is a model introduced by Foutel-Rodier and Etheridge to study the impact of cooperation and competition on the fitness of an expanding asexual population. The model is an interacting particle system consisting of particles performing symmetric random walks that reproduce and die with rates that depend on the local number of particles. For each particle, we keep track of the number of deleterious mutations that it carries, and after each birth event, with some positive probability, the offspring particle can acquire an additional mutation that gives it a lower reproduction rate than its parent. We show that under an appropriate scaling, the process converges weakly to the solution of an infinite system of partial differential equations (PDEs), confirming non-rigorous computations of Foutel-Rodier and Etheridge. In the PDE limit, when the reaction term of the system of PDEs is monostable, we establish bounds on the ratio between the density of particles with a given number of mutations and the density of particles without mutations. If the reaction term satisfies a Fisher-KPP condition, we can also rigorously determine the spreading speed of the population into an empty habitat. Finally, by considering the PDE limit of a form of tracer dynamics, we answer the question of whether deleterious mutations can surf population waves in this setting.

We show that a resonance due to gyroscopic motion of skyrmions, conceptually similar to the electron cyclotron resonance in metals, can be excited in a ferrimagnetic film by a spin current or microwaves. It must permit unambiguous measurement of the skyrmion mass for which a universal expression depending solely on the exchange interaction between spins belonging to two different ferrimagnetic sublattices is derived. The dependence of the skyrmion cyclotron frequency on parameters is computed for a TM/RE ferrimagnet, using CoGd as an example. The cyclotron frequency exhibits a dip near the angular momentum compensation point, where it hybridizes with the ferromagnetic resonance. The skyrmion cyclotron mode is studied for individual skyrmions and for skyrmion lattices, where the effect must be strong enough to be observed in microwave and spin-current experiments.

NGC 6316 is a poorly studied, distant, and massive globular cluster (GC) with prominent gamma-ray emission detected via the \textit{Fermi} Large Area Telescope (LAT). Based on gamma-ray spectral studies, NGC 6316 is expected to host tens of millisecond pulsars (MSPs). Using the Green Bank Telescope (GBT) and Murriyang, CSIRO's Parkes radio telescope (Parkes), we present the discovery and a 3.1 yr duration timing solution of the first millisecond pulsar found in the cluster. PSR J1716$-$2808A has a rotational period of 2.45 ms and is in a binary with a $\sim$0.1 M$_\odot$ companion with an orbital period of 0.42 d. This is a normal-looking MSP within a compact orbit with no evidence of eclipses. PSR J1716$-$2808A has a dispersion measure DM = 172.26 pc cm$^{-3}$, which is lower than predicted NE2001 and YMW16 electron density model values. The MSP is located within half a core radius from the cluster center and has a negative period derivative, implying that it is on the back side of the cluster and is being accelerated towards us. Given the negative period derivative, we report an upper limit on the maximum line-of-sight cluster acceleration, $a_{l,\textrm{max}}/c \approx$ 2.3$\times10^{-18}$ s$^{-1}$, experienced by the pulsar and constraints on the magnetic field to be $<\sim$3$\times$10$^{8}$ G. This confirms the pulsar to be within NGC 6316 despite the lower-than-expected dispersion measure. We can better constrain NGC 6316's properties through longer-term timing of PSR J1716$-$2808A or by finding more pulsars within the cluster. Based on the gamma-ray pulsar estimates and a cluster distance of 11.3 kpc, deeper, more sensitive searches would find many additional pulsars.

Ruelle gave an explicit second-order expansion at $c=0$ of the Hausdorff dimension of the Julia set of the quadratic family $f_c(z)=z^2+c$. McMullen later extended this result to polynomial perturbations of $z^d$ for arbitrary degree $d\geq 2$. In this paper we study an analogue of this problem for skew products in $\mathbb C^2$. Since holomorphic dynamical systems in higher dimensions are non-conformal, we replace the Hausdorff dimension by the \emph{volume dimension}, a dynamically defined notion we introduced in our earlier work and characterized as the zero of a natural pressure function. We consider families of holomorphic skew products of the form \[ f_t(z,w)=(z^d, w^d+t(c_1 (z) w^{d-1} +c_2(z)w^{d-2} + \cdots+c_d(z))). \] Our main result gives an explicit second-order expansion of the volume dimension of the Julia set $J(f_t)$ as $t\to0$ in terms of the coefficients $c_k(z)$.

We present new ASKAP/WALLABY HI observations of the nearby dwarf galaxy system ESO 179-013 (Kathryn's Wheel), the nearest known collisional ring galaxy, located 10 Mpc away in the Local Void. The system is composed of three previously known dwarf galaxies embedded in a large HI envelope, with a newly discovered fourth member identified through HI and radio continuum emission behind a bright foreground binary. Galaxy D exhibits the highest star formation rate in the group and deviates from the HI mass-diameter relation, suggesting it is a compact, gas-rich dwarf missed due to stellar foreground contamination. The HI data reveal for the first time an extended HI envelope around the whole system, the neutral gas counterpart of the star-forming ring and gas bridges among members, suggesting a more complex interaction history than the previously proposed collisional ring scenario. ESO 179-013 thus provides a rare opportunity to study hierarchical assembly and gas dynamics in underdense environments and demonstrates the power of blind HI surveys in identifying faint members of low-mass compact groups.

Broadband and low-loss superconducting switches can facilitate large-scale quantum information processors and cryogenic detectors by dynamically reconfiguring the connectivity of their circuits. The time dependent connectivity is enabled by the nonlinearity of lossless Josephson junctions, which are often wired into superconducting loops to be controlled by magnetic flux. However, this approach needs a power-consuming constant flux bias and dynamic flux actuation, both of which are hard to isolate from other switches or flux sensitive elements, limiting their integration density. Here, we design and characterize a microwave switch that implements a persistent current bias and direct current actuation to reduce static power consumption, actuation energy and potential crosstalk to other devices. We show that persistent current associated with tens of flux quanta is stable and long-lived, reducing the need for on-the-fly tuning. We further demonstrate that our switch has desirable performance for superconducting-circuit-based quantum information processing, including an off mode with more than 20 dB isolation comparable to commercial ferrite isolators, power handling larger than 100 pW sufficient for resonator readout tones and amplifier pumps, and modulation bandwidth broader than 600 MHz useful for multiplexing schemes.

KKMChh adapts the soft photon exponentiation of the program KKMC, initially for electron-positron annihilation, to hadron collisions, where it must interface to a parton shower and parton distribution functions (PDFs) which may already include effects of QED radiation. We describe the NISR (Negative Initial State Radiation) algorithm developed to consistently interface with PDFs including QED effects, and present results on its effect on some distributions of phenomenological interest.

The peculiar motions of galaxies are powerful cosmological probes that trace the growth of structures and the distribution of matter in the universe, providing a means to investigate the nature of dark energy and test gravity on cosmological scales. However, their direct observation is extremely challenging, as it requires independent and precise distance measurements to galaxies. We present a Bayesian approach to estimate the radial component of peculiar velocities of galaxies hosting Type Ia supernovae (SNe Ia), relying solely on the background cosmological model and the precision of the SNe Ia data. Unlike other peculiar velocity estimators based on Hubble residuals, our method does not assume local linearity of the magnitude-redshift relation or a fixed cosmology, making it unbiased even for large peculiar velocities and self-consistently avoiding bias due to a wrong cosmology. We validate our method using simulated supernova data with the precision of current and upcoming surveys, and further compare it with the linearized estimator to test its efficacy. We show that our estimator has lower bias than the standard estimator and remains consistent even for larger values of $v_{\rm p}/cz$. We also present a Bayesian derivation for the linearized estimator generalized to include the supernova magnitude covariance.

In this article, we consider a generalisation of the spatial Muller's ratchet introduced by Foutel-Rodier and Etheridge. This particle system is a spatial model of an asexual population, with birth and death rates that depend on the local population density. Particles live in discrete demes and migrate to neighbouring demes. Each particle carries some number of mutations (its `type'), and additional mutations can occur during birth events. Mutations are assumed to be deleterious, i.e.~carrying a higher number of mutations results in a lower birth rate. Our main result shows that this interacting particle system can be constructed even when the total initial number of particles is infinite. We also prove moment bounds on the local density of particles; these bounds are a crucial ingredient of the proof of a law of large numbers result for the particle system in the companion article. The construction of the particle system uses a sequence of approximating processes. Proving weak convergence of this sequence of processes is non-trivial because the particle system is non-monotone and interactions are non-local in type space. The uniqueness of the limit relies on a delicate coupling argument.

Equational reasoning about circuits is central in quantum software for validation, optimisation, and verification. For qubits, the CNOT-dihedral fragment supports efficient rewriting via phase polynomials and layered normal forms, yielding a complete and practically effective equational theory. In this work we generalise that CNOT-dihedral picture from qubits to prime-dimensional qudits. We present a compact PROP for reversible affine circuits over a prime field, with a strict symmetric monoidal semantics into the affine group and a Lafont-style affine normal form. We then adjoin finite-angle diagonal phase generators and organise them by polynomial degree, obtaining linear, quadratic (odd prime), and cubic (prime greater than 3) calculi. Using binomial-basis identities we derive uniform transport rules, establish unique phase-affine normal forms, and prove completeness: semantic equality coincides with derivable equality. This yields a prime-dimensional, phase-polynomial-aligned generalisation of the CNOT-dihedral equational theory.

Interacting binaries can produce a wide range of exotic systems, including X-ray binaries and merging neutron stars, through a mass transfer phase called Common Envelope (CE) evolution. A CE phase can occur during rapid expansion as a star as it moves off the main sequence. If the engulfed star is a compact object (e.g. neutron star), a CE phase can lead to hyperaccretion onto the neutron star. Previous work focused on systems in which the accreting material has low angular momentum, studying turbulent outflows. This study investigates the impact of angular momentum on accreting material leading to the formation of an accretion disk. Disk accretion systems lead to very different nuclear burning conditions. This paper presents the results of nucleosynthesis modelling of material ejected from an accretion disk surrounding a 1.5 M$_{\odot}$ neutron star in a CE with a 15 M$_{\odot}$ companion. As material is accreted towards the neutron star, sufficient heating will occur to eject a fracton of the material back into the surrounding envelope, producing a nucleosynthetic yield signature that differs from other explosions. We find that significant mass fractions of rp-process products are synthesised, thereby providing another mechanism for rp-process contribution to galactic chemical evolution, following ejection of the CE. Furthermore, later stages of the CE evolution the accrete helium leading to alpha-rich, supernova-like nucleosynthesis, producing $^{44}$Ti and $^{56}$Ni. Further work on modelling both the accretion disk wind, and the companion envelope ejection, is vital to understand the contributions of these scenarios to chemical evolution.

Distribution regression, where the goal is to predict a scalar response from a distribution-valued predictor, arises naturally in settings where observations are grouped and outcomes depend on group-level characteristics rather than on individual measurements. We introduce DistBART, a Bayesian nonparametric approach to distribution regression that models the regression function as a linear functional with the Riesz representer assigned a Bayesian additive regression trees (BART) prior. We argue that shallow decision tree ensembles encode reasonable inductive biases for tabular data, making them appropriate in settings where the functional depends primarily on low-dimensional marginals of the distributions. We show this both empirically on synthetic and real data and theoretically through an adaptive posterior concentration result. We also establish connections to kernel methods, and use this connection to motivate variants of DistBART that can learn nonlinear functionals. To enable scalability to large datasets, we develop a random-feature approximation that samples trees from the BART prior and reduces inference to sparse Bayesian linear regression, achieving computational efficiency while retaining uncertainty quantification.

Nanoscale molecular systems such as DNA require an atomistic quantum treatment to accurately capture their electrical properties, owing to their small dimensions. A central challenge in modeling transport through these systems is the inclusion of phase-breaking scattering. Decoherence-probe methods enable such modeling for large systems, but existing implementations have limitations. Energy-independent scattering rates tend to overly broaden energy levels, yielding an unphysically large density of states (DOS) within energy gaps. Conversely, energy-dependent models may introduce spurious energy levels and transmission peaks and require additional fitting parameters. To address these issues, we use a DOSweighted decoherence model in which the scattering rate and equivalently, the associated decoherence probe self-energy is proportional to the local DOS. The model iteratively updates the decoherence selfenergy and the DOS until self-consistency is achieved. This approach yields energy and spatially dependent scattering rates that avoid spurious energy levels without the excessive broadening of DOS in energy gaps. We also examine the impact of partitioning schemes that prevent artificial pathways for charge transport and discuss how they can be avoided. Overall, the DOS-weighted model provides an improved and more physically grounded framework for simulating charge transport in DNA and potentially other weakly coupled molecular systems.

We investigate the consequences of timelike sectional curvature bounds in Lorentzian length spaces for the existence and structure of the space of directions at a point. It is established that, under upper timelike sectional curvature bounds, the space of directions exists and is itself a metric space with curvature bounded above by $-1$. Furthermore, the metric cone over the space of directions, which canonically models the tangent space at a given point, is shown to constitute a Lorentzian length space with timelike sectional curvature bounded above by $0$. To do this, we introduce the notion of $ε$-$μ$ timelike sectional curvature bounds, which are compatible with pre-existing synthetic curvature conditions. These results extend the comparison-geometric framework to the Lorentzian setting, providing a synthetic characterization of geodesics, tangent cones, and curvature under causal constraints.