Trial-to-trial variability of neural responses has been linked to important aspects of neural computation and is essential for understanding how neuronal populations respond. While current overdispersion models treat each neuron's gain as independent of each other, this assumption fails to capture the network statistics of neuronal populations. As no existing model can capture overdispersed structured spiking gain-modulation across a neural population, network-level gain covariance remains largely unstudied. We thus present the Poisson matrix-normal latent variable (PMNLV) model, which extends single-neuron overdispersion to neural populations by placing a matrix-normal prior over the latent gain with a Kronecker-factored covariance. Spike counts are Poisson-distributed with a rate equal to the sum of a per-neuron stimulus tuning term and a matrix-normal gain, passed through a quadratic soft-rectifying link. We derive two complementary estimation algorithms: a variational EM (VEM) with a matrix-normal posterior that recovers dense Kronecker factors without structural assumptions, and a Kernel Tournament Method (KTM) that performs data-driven selection over a biologically motivated kernel dictionary and composite likelihood. On simulated data, both algorithms recover the inter-neuron and temporal covariance factors and accurate tuning curves. Applying VEM to Neuropixel recordings across four cortical regions of mouse visual hierarchy, we replicate a previous finding that single-neuron marginal variability changes little across cortical areas. We then show that shared population co-variability, invisible to scalar summaries e.g., the Fano factor, peaks in primary visual cortex and declines in higher visual areas. The PMNLV framework is applicable to any simultaneously recorded population where structured gain covariance is of scientific interest.

This paper details a novel indirect method for solving constrained optimal control problems (OCPs) directly in continuous-time function space. The KKT conditions are embedded in a non-smooth complementarity function, which enables their reformulation as a rootfinding problem in Banach space. This problem is then solved using a non-smooth Newton method. Finally, the paper shows that the Newton update can be obtained by solving a modified differential Riccati equation, where the cost terms are reweighted at every iteration based on the constraint multipliers. Numerical simulations show the effectiveness of the method, which converges superlinearly up to the tolerance of the ODE solver.

Let $T$ be a theory which is t-minimal, meaning that with respect to some definable topology, a unary definable set $D \subseteq M$ has non-empty interior iff it is infinite. If $K$ is a definable field in $T$, then $K$ is finite or "large" in the sense of Pop: any smooth algebraic curve $C$ over $K$ with at least one $K$-rational point has infinitely many $K$-rational points. We also assign a canonical topology to any abelian definable group $G$ in a t-minimal theory. In the case where the t-minimal theory is "visceral" in the sense of Dolich and Goodrick, meaning that the definable topology is induced by a definable uniformity, we can drop the assumption of abelianity of $G$, and the resulting topology on $G$ is a definable manifold in the style of Acosta López and Hasson.

We study the real time quantum dynamics of a matrix model consisting two bosonic fields on the fuzzy sphere using the Gaussian state approximation. Starting from the Hamiltonian formulation and using Wick's theorem, we derive a closed set of coupled nonlinear differential equations governing the time evolution of the one- and two-point correlation functions. Thermal equation of state is found by maximizing the von Neumann entropy over Gaussian states and solving algebraic self-consistency equation(s) leading to a complete determination of the symplectic spectrum of the covariance matrix. We identify near thermal initial conditions and use them to solve the equations of motion and employ our findings to probe chaos by calculating the largest Lyapunov exponent at various temperatures. Our results demonstrate that the latter tends to zero at a finite temperature indicating that the quantum dynamics respect the Maldacena,Shenker,Stanford bound across all temperatures, while approaching toward the classically chaotic regime at high temperatures. Finally, we examine the entanglement dynamics of the model in real-time by considering a sequence of bipartitions of the Hilbert space and computing the entanglement entropy and clearly exhibit the fast scrambling features that emerge in due detail.

We develop a nonadiabatic theory of phonon magnetic moments applicable to both insulators and metals. By relating the phonon magnetic moment to the force-velocity response of ions in a magnetic field, we derive a gauge-invariant expression using a gauge-covariant Wigner expansion. The formalism naturally separates Fermi-sea and Fermi-surface contributions and captures the full dependence on phonon frequency. In gapped systems, our theory reduces to previous adiabatic expressions in the low-frequency limit. Beyond this limit, it reveals additional contributions arising from resonant interband processes and the Fermi surface. Applying our theory to Pb$_{1-x}$Sn$_x$Te, we find that the Fermi-surface contribution substantially enhances the phonon magnetic moment, reproducing the same order of magnitude as the experimental observation. Our results provide a unified framework for describing phonon magnetic moments beyond the adiabatic regime.

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in order to resolve the solution accurately, resulting in increased computational cost. In order to accelerate the simulation of these ODEs we present a novel methodology that uses a pseudo-invertible neural network to map system states into a high-dimensional latent-space. The network is then trained so that the dynamics in this learned latent space are slow, and can be simulated with relatively few function calls. Unlike existing neural methods, the latent dynamic equations are not learned from trajectory data, but derived from the original system equations and the chain rule. This allows the method to generalize better than existing approaches because the derived equations are correct by construction. In this work, we derive latent state equations of motion for any general ODE, and describe the loss function used to enforce slow time evolution of the latent states. We then apply this technique to multiple example ODEs and show that these problems can be solved with $3$x to $20$x fewer function calls for the same accuracy when simulating in the learned latent space. This reduction in cost could decrease computational demands for scientific simulations across engineering and physics applications.

We present a set of new, efficient high-order symplectic methods designed for Hamiltonian systems with cubic or quartic potentials. By demonstrating that polynomial potentials require fewer order conditions, we develop schemes that outperform both standard symmetric compositions of second-order methods and existing RKN splitting methods. Numerical results confirm their improved efficiency over state-of-the-art alternatives found in the literature.

We consider an open quantum system governed $N$-body Lindblad equation and study mean-field limits in this setting. We prove that the $N$-particle dynamics converges, in the sense of quantum relative entropy, to the tensorized solution of the limiting nonlinear equation. More precisely, we establish explicit bounds of order $1/N$ on the relative entropy between the $N$-particle density operator and the corresponding product state, thereby providing a quantitative propagation of chaos.

Fully functional program verification is an undecidable$\unicode{x2014}$and, hence, inherently difficult$\unicode{x2014}$task, that is not automatically solvable but typically requires user interaction and guidance. Existing verifiers either work autoactively, requiring the user to write annotations in source code, without the possibility to inspect the proof state or intervene in case of an unsuccessful attempt, or allow interactions on a logical encoding that is on a lower level than the user-provided specifications. We present a novel interaction concept which allows the user to inspect and interact with the proof state on source code and specification level. This minimizes the mental gap between the representations. We provide an implementation of the concept as a plugin for the Java verification engine KeY, and show with a user study that this prototype can be beneficial for users to understand the proof state and find defects in source code or specifications.

As the current thermo-industrial civilization expands, its technological and societal complexities increase. We suggest that physical power, economic activity and societal complexity are linked. A simple, intuitive model based on Systems Dynamics is used as an illustration.

As high-performance computing (HPC) systems rapidly evolve, with increasing on-node parallelism and widespread use of accelerators, understanding how the code maps to hardware is essential for reaching optimal performance. Benchmarks are commonly used for early assessment of emerging architectures (as well as for informing the design of future hardware), but it is often unknown how well the benchmarks represent the performance characteristics of simulation codes. Existing methods for evaluating how well our benchmarks represent our HPC codes are manual, labor intensive, and challenging to scale to many benchmarks. In this paper, we propose performance similarity metrics based on how the code uses the compute hardware. We define and characterize two broad categories of kernels that exhibit similar performance characteristics. We evaluate the pairwise similarity metrics on kernels in the Kripke proxy application and the RAJA Performance Suite, using both a CPU-only system and a GPU-accelerated system. We validate that our similarity metrics correctly match a kernel in the Kripke proxy app to a kernel in the RAJA Performance Suite. Our proposed similarity metrics enable assessment of the similarity of computational kernels in our codes and the proxy applications we use to represent the codes.

We study flat metrics arising from right regular $n$-prisms by viewing them as $n$-differentials and analyzing their associated unfoldings. We show that the unfolding of a right regular $n$-prism is never a lattice surface unless $n=4$, in contrast with the case of Platonic solids. Despite this, we prove that these surfaces admit translation coverings to hyperelliptic surfaces, allowing us to determine their $\mathrm{GL}(2,\mathbb{R})$-orbit closures using the classification of hyperelliptic components of strata. As a consequence, we obtain exact quadratic asymptotics for a certain average of the number of saddle connections on the base surfaces, their unfoldings, and the original prisms, including their Siegel--Veech constants. This provides a natural infinite family of non-lattice surfaces for which orbit closures and counting problems can be computed explicitly.

This paper presents a version of the HEXTOR energy balance model that has been configured for the study of habitable terrestrial planets orbiting low-mass stars. The model is validated for rapidly-rotating Earth-like planets using latitudinal coordinates, which shows expected patterns of bistability. A tidally-locked coordinate transformation is then applied to the model, which is calibrated to match mean values of the minimum, average, and maximum surface temperatures from a general circulation model ensemble of TRAPPIST-1 e. This calibrated energy balance model is used to characterize the possible climate states of such a synchronously rotating planet across a parameter space of instellation and carbon dioxide partial pressure. These calculations suggest a state of partial ice cover for TRAPPIST-1 e and complete ice cover for TRAPPIST-1 f, unless carbon dioxide partial pressure is ~1 bar or greater. This approach demonstrates the capability of a simplified one-dimensional model to study the climates of terrestrial planets in synchronous rotation, which can help guide more complex models and observations toward the most promising targets of interest.

In this paper, we discuss expanding maps on a class of invariant sets called flowers. We show that any set contained in a flower has at most linear complexity, and we present a relationship between flowers and a special class of interval exchange transformations. This extends work of Bullett and Sentenac, who showed that any Sturmian system may be embedded into the circle as a doubling-invariant subset that is contained in a half circle. Flowers were first introduced in the context of ergodic optimization, as candidate sets for supporting maximizing measures. We discuss the relationship to ergodic optimization, and present numerical results that support the conjecture that trigonometric polynomials are maximized on flowers.

We develop the second-order quantum perturbation theory of gravity in the Null Surface Formulation (NSF) of asymptotically flat spacetimes. In this framework all dynamical degrees of freedom are radiative data defined at null infinity; no bulk fields or off-shell propagators enter the construction. Working directly at null infinity, we derive the helicity-resolved Bondi shear and the corresponding out-operators governing nonlinear graviton processes. The formalism naturally generates a gravitational tail amplitude requiring opposite incoming helicities, and a graviton scattering amplitude that factorizes into two tail vertices connected by an on-shell intermediate graviton. Imposing the Poincare limit reproduces the s-channel contribution of the Weinberg tree-level amplitude, while the crossed channels are shown to arise at higher perturbative order. The theory is perturbatively finite for two independent reasons: all intermediate gravitons are strictly on-shell, so no loop integrals over virtual bulk momenta are generated; and the perturbative regime requires Gaussian-smeared graviton states (small Bondi mass relative to the Planck scale), whose suppression propagates recursively through the hierarchy, rendering all energy integrals absolutely convergent at every order without renormalization or counterterms. This finiteness is structurally distinct from the ultraviolet problem of covariant perturbative gravity, where divergences originate in off-shell bulk propagators and asymptotic states are defined only indirectly via an iε bulk prescription. The natural observables of the NSF are spectral-angular distributions on the celestial sphere, which encode BMS supermomentum flux rather than ordinary Poincare momentum conservation. Gravitational memory, MHV helicity selection rules, and the coherent-state classical limit arise naturally within the same framework.

The rapid proliferation of distributed energy resources (DERs) and the electrification of residential loads offer significant potential for grid flexibility but pose stability challenges under static pricing regimes. Specifically, high levels of automation under static Time-of-Use (TOU) tariffs often induce ``device synchronization,'' where simultaneous responses from home energy management systems (HEMS) create artificial demand peaks that threaten grid stability. This paper proposes a privacy-preserving, one-way dynamic signaling framework to unlock deep demand flexibility from HEMS. We utilize a feedback-based learning algorithm that updates day-ahead price profiles based on aggregate substation demand and environmental contexts, effectively closing the loop between utility objectives and aggregated edge behaviors. The framework is rigorously validated using high-fidelity simulations on an 84-bus distribution network populated with hundreds of HEMS controlling diverse devices, including HVAC, PV, batteries, and flexible loads. Results demonstrate that the proposed mechanism achieves substantial reductions in both peak demand and total load variation. Extensive analyses across diverse climates and scalable deployments confirm the framework's robustness, indicating that dynamic pricing acts as a force multiplier for DERs, with peak shaving potential increasing significantly under high renewable penetration scenarios.

The Bourbaki degree of a plane projective curve $F$, denoted by $\mathrm{Bour}(F)$, was introduced in \cite{Marcos} by Jardim, Nejad and Simis. It is defined as the degree of $R/I_ε$, where $R = k[x,y,z]$ is the graded polynomial ring, with $k$ algebraically closed, and $I_ε\subseteq R$ is the Bourbaki ideal associated with a minimal generator $ε$ of the module of first syzygies of the Jacobian ideal $J_F$. In this work, we propose the definition of the local Bourbaki degree at a point $P \in \mathbb{P}^2$, denoted by $\mathrm{Bour}_P(F)$, and prove that $\mathrm{Bour}(F) = \sum_{P \in \mathbb{P}^2}\mathrm{Bour}_P(F).$ Furthermore, we present results that follow from this local definition, which are instrumental in determining the Bourbaki degree and in establishing whether a curve is (nearly) free. In addition, we provide examples of computing the Bourbaki degree via the local formula - an approach that is computationally advantageous, as it, generically, demands fewer calculations.

Usage-based insurance (UBI) uses telematics to align premiums with risk and encourage safe driving. However, deploying these programs is challenging due to heavy-tailed claim costs, nonstationary driver behavior, and limited incentive budgets. While existing research focuses on profiling drivers, prescriptive pricing remains underexplored. We propose an optimal control framework that integrates telematics directly into dynamic pricing. Our approach (i) learns claim frequency and severity, (ii) models multi-period behavioral evolution in response to discounts, and (iii) optimizes portfolio-wide discount allocation using a Lagrangian relaxation. This decomposes the non-convex centralized problem into independent dynamical systems. We theoretically prove this relaxation's duality gap vanishes as the portfolio scales, guaranteeing asymptotic optimality. We validate our approach computationally on a simulated industry-scale portfolio. Our results demonstrate not only the computational tractability of our approach but also that it outperforms static baselines, reducing both expected losses and claim probabilities to benefit insurers and policyholders alike.

The article explores the asymptotic behavior of the expected number of drawings in the Coupon Collector's Problem with group-drawing under the uniform distribution. In this variant, each draw consists of a package of $s$ distinct coupons selected uniformly at random from a set of $n$ coupons. We focus on three regimes of the package size $s$: (i) constant $s$, (ii) $s$ proportional to $n$, and (iii) $s$ "very close" to $n$. For each case, we provide precise asymptotic expressions for the expected collection time. Keywords: Coupon Collector's Problem, Group Drawings, Uniform Distribution, Asymptotic Analysis, Expected Collection Time

The continuous scaling of CMOS technology has significantly increased the complexity of very large-scale integrated circuits, driving interest in applying machine learning (ML) to electronic design automation (EDA). However, the limited availability of open and standardized datasets limits interoperability, comparability, and reproducibility in ML-based research. This paper introduces EDA-Schema-V2, an open multimodal schema that provides a structured framework for representing and analyzing datasets in digital physical design. The schema includes representations of physical attributes and quality-of-results metrics across multiple stages of the design flow, including logic synthesis, floorplanning, placement, clock network synthesis, and routing. Utilizing the SkyWater 130nm, Nangate 45nm, IHP SG13G2 130nm, and ASAP 7nm open-source process design kits with the OpenROAD tool flow, datasets of physical circuit designs from the IWLS'05 benchmark suite are generated and analyzed. The dataset comprises 7,776 design instances spanning 18 benchmark circuits and includes stage-resolved representations from synthesis through detailed routing, generated through parameter sweeps over clock period, core utilization, and aspect ratio. The dataset contains over 275 million gates, 75 million nets, and more than 36 million extracted timing paths. In addition, twelve representative prediction tasks spanning timing, power, area, and routing metrics are identified, along with baseline analyses that characterize stage-to-stage predictability across the design flow. The resulting datasets and baselines are publicly released to support reproducible ML research and establish standardized benchmarks for evaluating ML-based approaches in digital physical design.

Many important systems across biology, engineering, physics, and economics are characterized by polynomial ordinary differential equations (ODEs), yet analytical solutions are rare. We develop a framework for identifying and solving a broad class of two-dimensional quadratic ODEs using linear rational Koopman eigenfunctions. By imposing a linear rational form on the eigenfunctions, we convert the Koopman eigenfunction PDE into a large algebraic system of polynomials. We then study the solutions of this polynomial system that satisfy the ODE restrictions; we call the solution set the rational eigenfunction variety of an ODE system. The nonlinear algebra method uses formal algebraic geometry theory to analyze and solve systems otherwise intractable and to discover relationships between ODE and eigenfunction parameters that must hold to extract eigenfunctions. We identify families of quadratic ODEs that can be solved analytically, characterize their eigenfunction parameters, and use the resulting eigenfunctions to produce closed-form analytical solutions.

We consider an Asymmetric Exclusion Process evolving on parallel mutually interacting lanes with neighbouring nearest hoppings of hardcore particles. Number of particles on each lane is conserved. We find a choice of the hopping rates, for which the process has Bernouilli stationary product measure, and calculate the stationary particle currents as a function of average particle densities.

This paper studies the estimation of ranked-list discrete choice models with single and multiple purchases. In this setting, each consumer type is characterized by a ranking over a subset of products and a desired number of purchases, and the estimation task is to identify the set of consumer types and their probabilities that best explain the observed transactional data. This problem is computationally challenging due to the exponential number of possible consumer types and becomes more difficult when multiple purchases are allowed. We propose a column generation framework for this problem. Our main contribution is a dynamic programming algorithm for the column generation subproblem. This subproblem generalizes the linear ordering problem and incorporates acceleration techniques to improve computational efficiency. To the best of our knowledge, this is the first dynamic programming-based approach for generating consumer types in non-parametric models. The proposed framework supports multiple model variants with minor modifications. Computational experiments on synthetic and real data show substantial speedups over existing methods while maintaining high solution quality, and demonstrate effectiveness in both estimation and assortment optimization.

An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model training. The purpose of the auxiliary loss is to provide a mechanism for creating a low-order Hessian-type approximation for the original loss. The proposed algorithm employs the resulting low-order second-derivative approximation terms in place of the second-order momentum terms (i.e., squared elements of the gradient of the loss function) in an overall scheme that has computational cost on par with an Adam-type approach. Whereas the squared elements of a gradient vector do not necessarily approximate second-order derivatives well, by careful construction of the auxiliary loss, second-order derivative-type approximations for the original loss can be computed and employed by the algorithm in an efficient manner. A convergence guarantee is provided for the proposed algorithm that is on par with guarantees available for similar stochastic diagonal-scaling methods. The results of numerical experiments show situations when the proposed algorithm outperforms Adam and other popular modern optimizers.

Let $\mathcal{F}=\{f_1,\ldots,f_R\}$ be a family of forms of odd degrees at most $d$ in $s$ variables. We study the solutions to the system $f_1(\mathbf{x})=\ldots=f_R(\mathbf{x})=0$ of the form $x_i=y_ip_i$ with $|y_i|\leq Y_\mathcal{F}$ and $p_i$ being a prime for all $i\in [s]$ inside the box $[-N,N]^s$, for large $N$. We show that if the number of variables $s$ is sufficiently large with respect to the parameters $R$ and $d$, then there are at least $C_\mathcal{F} N^{s-D}/(\log\,N)^s$ such solutions for some constants $C_\mathcal{F}>0$ and $D\in\mathbb{N}$, with $D$ depending only on the initial parameters $R$ and $d$.

Faculty mobility is often understood as a mechanism through which universities redistribute scientific talent and potentially improve research performance. Yet the system-level structure of mobility and its association with individual research trajectories have rarely been examined together. We link longitudinal faculty rosters from U.S. research universities to OpenAlex publication records and study 11,535 tenure-system faculty members who changed institutions between 2011 and 2020, with a comparison group of more than 200,000 non-moving faculty members. A directed network of faculty moves reveals a strongly hierarchical market: high-prestige institutions are net importers, lower-prestige institutions are net exporters, and the mobility hierarchy closely parallels the hierarchy observed in faculty hiring. However, event-study models that account for pre-move trajectories show little evidence of sustained post-move gains in publication volume, citation impact, or top-cited publication rates, including among upward moves to more prestigious institutions. The most consistent post-move change is collaborative: movers form new coauthor ties. We also observe modest increases in the share of papers with positive CD-index values. These patterns suggest that faculty mobility primarily reallocates existing research capacity within a persistent institutional hierarchy rather than systematically altering individual research trajectories.

The harvest-now, decrypt-later (HNDL) threat--adversaries intercepting and archiving ciphertext today for retrospective decryption once quantum computers mature--turns the future quantum threat into a present liability for the public-key primitives (RSA, Diffie-Hellman, ECC) that anchor modern session-key exchange. We present Aquaman, a transparent-proxy architecture for quantum-resilient session-key establishment. A transparent proxy intercepts session-key requests at the edge of a trusted network without requiring client-side configuration, deploying quantum-resistant capability at the network boundary on behalf of clients that may themselves lack post-quantum cryptography (PQC). Aquaman supports four operating modes: PQC offloaded to the proxy for clients without trusted PQC stacks; classical multi-path key fragmentation over heterogeneous media (with an optional anonymous proxy-pool variant); QKD with the SKIP/ETSI GS QKD 014 key-delivery interface; and classical/PQC hybrid handshakes. We implement and evaluate the first two modes; the latter two are well-trodden in the PQC literature and we discuss but do not implement them. The implemented multi-path mode splits the session key into ciphertext fragments distributed across diverse media (Wi-Fi, Bluetooth, NFC, cellular, Ethernet); reconstruction requires all fragments. We formalize the security argument and prove that recovery probability decays as (B/d)^n in the diversity dimension. A 1,000-run prototype evaluation on AWS EC2 shows that latency is dominated by network transmission, not by multi-path overhead.

Recently, true-time-delay (TTD) arrays, also referred to as joint phase-time arrays (JPTA), have been investigated for low-cost frequency-dependent beamforming capabilities to enable various applications, including beam-squint correction, fast beam training, and serving multiple user equipment (UE)s by frequency band to direction mapping, termed as split beampatterns. Several heuristics and optimization-based solutions have been proposed to determine TTD array parameters settings. However, they have practical limitations due to either computationally demanding optimization procedures, requirements for extremely large memory look-up tables, or degradations due to the beam-squint effect. In this article, we propose a novel split-beampattern generation algorithm based on the observed homomorphism between TTD array configuration matrices and corresponding beampatterns. First, we rigorously analyze the beampattern synthesis process and demonstrate the observed homomorphism and mathematical structure. Then, we propose the Homomorphic Directional Beamforming (HDB) algorithm to approximate the desired split beampatterns by utilizing a generator beampattern dictionary that requires a dictionary size orders of magnitude lower than existing approaches without ignoring the beam squint. With extensive simulations, we show that the proposed algorithm can provide a practical implementation with low memory and low computational cost requirements. In addition, HDB design provides close to uniform beamforming gains among UEs in different subbands, enabling fairness in power allocation.

Quantum repeaters are essential for scalable long-distance quantum networking. As quantum information processing moves toward fault-tolerant and error-corrected operations, it becomes increasingly important to study quantum repeaters that also move beyond raw physical entanglement and towards logical entanglement. In this paper, we implement and simulate the quantum repeater with encoding and classical error correction (QRE-CEC) protocol in SeQUeNCe, a discrete-event simulator of quantum networks. The protocol distributes logical Bell pairs, performs encoded entanglement swapping, and uses classical error correction for the decoding of entanglement swapping measurement outcomes to determine Pauli-frame corrections. For this study, we extend SeQUeNCe with a stabilizer-based backend, add support for CSS code-based encoded operations, and integrate gate, measurement, idle decoherence, and state-initialization noise models. Our simulation results show that QRE-CEC suppresses all modeled errors to the second order. Also, QRE-CEC can distribute logical Bell pairs with 0.91 fidelity over a distance of 2000 km under the parameter regimes we study. Beyond protocol-level performance evaluation, our implementation exposes practical simulator and control-plane challenges that are typically abstracted away in theoretical studies.

Positron binding energies and Dyson orbitals for five-membered heterocycles with N, O, S and NH substituents are predicted \emph{ab initio} via many-body theory. The positron-molecule correlation potential (self energy) is calculated via solution of Bethe-Salpeter equations that describe the positron-induced polarization of the target and screening of the electron-positron Coulomb interaction at the $GW$@BSE level, the infinite electron-positron ladder series that describes the crucially important process of virtual positronium formation, and the analogous positron-hole ladder series. The all-order calculations employ Gaussian-orbital bases and are implemented in the {\tt EXCITON+} code. The effect of substituting combinations of N, O and S atoms, and the NH group in the molecule's ring is studied, and the role of individual molecular orbitals, many of which are found to significantly contribute to the correlation potential, quantified. Analysis of the positron bound-state Dyson orbitals shows that the positron is typically localized next to one or two of the substituents in the ring, with the order of preference N, S, O, then NH, and is also influenced by aromaticity and the presence of double ($π$) bonds in the ring.