For a smooth algebraic curve defined over a number field, one can associate a bipartite graph known as a dessin d'enfant. In this paper, we investigate the regularity and automorphism groups of dessins d'enfants with uniform passports, that is, those for which the valencies of black vertices, white vertices, and faces are constant, and study how these properties depend on the genus. Although uniformity imposes a high degree of symmetry, such dessins are not necessarily regular. Our main results are as follows: (1) A passport of the form $[a^{p}, b^{q}, n]$ (the tree case) admits a regular dessin if and only if $\gcd(p,q)=1$. (2) Every passport of the form $[n, b^{q}, n]$ of genus at least 2 admits a dessin with a trivial automorphism group. In addition, we obtain several results on uniform passports of genus 0 and 1. We also establish two theorems on the enumeration of elements in symmetric groups, which are useful for the study of automorphism groups of dessins.

Spin-orbit coupling (SOC) is incorporated into the phaseless plane-wave-based auxiliary-field quantum Monte Carlo (pw-AFQMC) method. This integration is implemented using optimized multiple-projector norm-conserving pseudopotentials, which are derived from the fully-relativistic (FR) atomic all-electron Dirac-like equation. The inclusion of SOC enables accurate phaseless pw-AFQMC calculations that capture both electronic correlation and SOC effects concurrently, greatly improving the method's applicability for studying systems containing heavy atoms. We discuss the form of FR pseudopotentials and detail the corresponding formulations of phaseless pw-AFQMC with a two-component Hamiltonian in the spinor basis. The accuracy of our approach is demonstrated by computing the dissociation energy of molecule I2 and the cohesive energy of bulk Pb, highlighting the large influence of SOC in both. Subsequently, we determine the transition pressure of the III-V compound InP from its zinc-blende to rock-salt phase by constructing and analyzing their respective equations of state.

The Chinese Space Station Survey Telescope (CSST) will perform a decade-long high-precision wide-field imaging survey that relies on rigorous on-orbit calibration. This necessitates stable celestial benchmark fields to maintain photometric and astrometric consistency throughout the mission lifetime. We establish comprehensive selection criteria including observational visibility, stellar number density, bright-star contamination, and interstellar dust extinction. Using the CSST Observation Strategy Analysis Tool (COSAT) and all-sky dust maps from Planck and SFD, we constrain eligible regions to the ranges of ecliptic latitude $ |β| > 50^\circ$ and galactic latitude $|b| > 15^\circ$. From an initial sample of 29 candidate clusters meeting these spatial constraints, six globular clusters (M13, M92, NGC 104, NGC 362, NGC 1261, and NGC 1851) are identified as optimal calibration fields, fulfilling all the critical criteria. These selected clusters are recommended as optimal calibration field candidates for CSST's on-orbit calibration program, and are fundamental to achieving unprecedented photometric precision in CSST's space-based survey.

Starting from a subinvariant positive definite kernel under a branching pullback, we attach to the resulting kernel tower a canonical electrical network on the word tree whose edge weights are the diagonal increments. This converts diagonal growth into effective resistance and capacity, giving explicit criteria and quantitative bounds, together with a matching upper bound under a mild level regularity condition. When the diagonal tower has finite limit at a point, we prove convergence of the full kernels and obtain an invariant completion with a minimality property. We also describe the associated RKHS splitting and a boundary martingale construction leading to weighted invariant majorants.

We analyse several constructions of random point sets on the sphere $\mathbb{S}^{3}\subset\mathbb{R}^4$ evaluating and comparing them through their discrete logarithmic energy: \begin{equation*} E_0(ω_N) = \sum_{\substack{i, j=1\\ i \neq j}}^{N} \log\frac{1}{\|x_i - x_j\|}, \; \text{ where}\; ω_N=\{x_1,\ldots,x_N\} \subset \mathbb{S}^3. \end{equation*} Using the Hopf fibration, we lift a range of well-distributed families of points from the $2$-dimensional sphere - including uniformly random points, antipodally symmetric sets, determinantal point processes, and the Diamond ensemble - to $\mathbb{S}^{3}$, in order to assess their energy performance. In particular, we carry out this asymptotic analysis for the Spherical ensemble (a well known determinantal point process on $\mathbb{S}^2$), obtaining as a result a family of points on the $3$-dimensional sphere whose logarithmic energy is asymptotically the lowest achieved to date. This, in turn, provides a new upper bound for the minimal logarithmic energy on $\mathbb{S}^3$. Although an analytic treatment of the lifted Diamond ensemble remains elusive, extensive simulations presented here show that its empirical energies lie below all other deterministic and non-deterministic constructions considered. Together, these results sharpen the quantitative link between potential-theoretic optima on $\mathbb{S}^{2}$ and $\mathbb{S}^{3}$ and provide both theoretical and numerical benchmarks for future work.

Discovering technology opportunities (TOD) remains a critical challenge for innovation management, especially in early-stage development where consumer needs are often unclear. Existing methods frequently fail to systematically incorporate end-user perspectives, resulting in a misalignment between technological potentials and market relevance. This study proposes a novel decision support framework that bridges this gap by linking technological feasibility with fundamental human values. The framework integrates two distinct lenses: the engineering-based Technology Readiness Levels (TRL) and Schwartz's theory of basic human values. By combining these, the approach enables a structured exploration of how emerging technologies may satisfy diverse user motivations. To illustrate the framework's feasibility and insight potential, we conducted exploratory workshops with general consumers and internal experts at Sony Computer Science Laboratories, Inc., analyzing four real-world technologies (two commercial successes and two failures). Two consistent patterns emerged: (1) internal experts identified a wider value landscape than consumers (vision gap), and (2) successful technologies exhibited a broader range of associated human values (value breadth), suggesting strategic foresight may underpin market success. This study contributes both a practical tool for early-stage R\&D decision-making and a theoretical link between value theory and innovation outcomes. While exploratory in scope, the findings highlight the promise of value-centric evaluation as a foundation for more human-centered technology opportunity discovery.

We propose a unified framework that allows for the full mechanistic reconstruction of chemical reaction networks (CRNs) from concentration data. The framework utilizes an integral formulation of the differential equations governing the chemical reactions, followed by an automatic procedure to recover admissible mass-action mechanisms from the equations. We provide theoretical justification for the use of integral formulations using analytical and numerical error bounds. The integral formulation is demonstrated to offer superior robustness to noise and improved accuracy in both rate-law and graph recovery when compared to other commonly used formulations. Together, our developments advance the goal of fully automated, data-driven chemical mechanism discovery.

Here we show, in the second paper in a series of articles, methods to calculate propositional statements with algebraic polyno mials as symbols for the connectives, which here are named operators. In the first article, we explained this formulation of the Propositional Calculus. In short, we transform to a dual space, which we here refer to as a polynomial family, which is another shape of DBNF. We name the polynomial families as PBNF, which stands for Polynomial Boolean Normal Form. We just use the one law of inference, the rule of Substi tution. We can use different polynomial families in the House of PBNF, depending on the statement form, making it even simpler. It is also pos sible to find new theorems and generalize older ones, for example, those given by Church and Barkley Rosser (see follow-up article) concerning duality.

We study sequential quantum changepoint detection in settings where the pre- and post-change regimes are specified through constraints on the expectation values of a finite set of observables. We consider an architecture with separate measurement and detection modules, and assume that the observables relevant to the detector are unknown to the measurement device. For this scenario, we introduce shadow-based sequential changepoint e-detection (eSCD), a novel protocol that combines a universal measurement strategy based on classical shadows with a nonparametric sequential test built on e-detectors. Classical shadows provide universality with respect to the detector's choice of observables, while the e-detector framework enables explicit control of the average run length (ARL) to false alarm. Under an ARL constraint, we establish finite-sample guarantees on the worst-case expected detection delay of eSCD. Numerical experiments validate the theory and demonstrate that eSCD achieves performance competitive with observable-specific measurement strategies, while retaining full measurement universality.

We investigate the spectral statistics of an interacting fermionic system derived by projecting the Hubbard interaction onto the two lowest-energy, degenerate flat bands of the dice lattice subjected to a $π$-flux. Surprisingly, the distributions of level spacings and gap ratios correspond to distinct Gaussian ensembles, depending on the parity of the particle number. For an even number of particles, the spectra conform to the Gaussian Orthogonal Ensemble, as expected for a time-reversal-symmetric Hamiltonian. In stark contrast, the odd-parity sector exhibits exact double degeneracy of all eigenstates even after resolving all known symmetries, and the Gaussian Unitary Ensemble accurately describes the spacing distribution between these doublets. The simultaneous emergence of two different random-matrix ensembles within a single physical system constitutes an unprecedented finding, opening new avenues for both random matrix theory and flat-band physics.

Truncated Neumann series $S_k(A)=I+A+\cdots+A^{k-1}$ are used in approximate matrix inversion and polynomial preconditioning. In dense settings, matrix-matrix products dominate the cost of evaluating $S_k$. Naive evaluation needs $k-1$ products, while splitting methods reduce this to $O(\log k)$. Repeated squaring, for example, uses $2\log_2 k$ products, so further gains require higher-radix kernels that extend the series by $m$ terms per update. Beyond the known radix-5 kernel, explicit higher-radix constructions were not available, and the existence of exact rational kernels was unclear. We construct radix kernels for $T_m(B)=I+B+\cdots+B^{m-1}$ and use them to build faster series algorithms. For radix 9, we derive an exact 3-product kernel with rational coefficients, which is the first exact construction beyond radix 5. This kernel yields $5\log_9 k=1.58\log_2 k$ products, a 21% reduction from repeated squaring. For radix 15, numerical optimization yields a 4-product kernel that matches the target through degree 14 but has nonzero spillover (extra terms) at degrees $\ge 15$. Because spillover breaks the standard telescoping update, we introduce a residual-based radix-kernel framework that accommodates approximate kernels and retains coefficient $(μ_m+2)/\log_2 m$. Within this framework, radix 15 attains $6/\log_2 15\approx 1.54$, the best known asymptotic rate. Numerical experiments support the predicted product-count savings and associated runtime trends.

We propose a practical recipe to transform any depth-$L$ block of CNOTs that prepares $n$-qubit GHZ states into an $n$-qubit fanout gate (multitarget-CNOT) of depth $2L-1$, without the need for ancilla qubits. Considering known logarithmic-depth circuits to prepare GHZ-states, this allows us to construct an $n$-qubit fanout gate with depth $2\log_2(n)-1$, reproducing previous ancillaless constructions. We employ our recipe to construct $n$-qubit fanout gates under heavy-hex connectivity restrictions, obtaining a depth of $O(n^{1/2})$, again reproducing previous complexity theory constructions. Using this recipe on the \textit{ibm\_fez} architecture yields a $156$-qubit fanout construction with depth $33$. Additionally, we show how to employ these $n$-qubit fanout constructions to measure complete sets of commuting observables from the $n$-body Pauli group with the same depth, allowing for efficient single-shot characterization of any GHZ-like state in a given known basis, e.g. fully characterizing a single copy of a $156$-qubit GHZ state using circuit depth $33$ in $\textit{ibm\_fez}$ (its preparation requires an additional depth of $17$).

The celebrated Antezana-Pujals-Stojanoff Theorem states that the iterated Aluthge transforms of an arbitrary matrix converge to a normal matrix. We introduce a family of matrix flows that share this convergence property by defining them through ordinary differential equations. The family includes a continuous analogue of the Aluthge transform, as well as a differential equation discussed by Haagerup in the context of II$_1$ factors. We also examine the same type of flows in the setting of Hilbert space operators equipped with unitarily invariant norms.

We consider the problem of finding a Nash equilibrium (NE) in a general-sum game, where player $i$'s objective is $f_i(x)=f_i(x_1,...,x_n)$, with $x_j\in\mathbb{R}^{d_j}$ denoting the strategy variables of player $j$. Our focus is on investigating first-order gradient-based algorithms and their variations, such as the block coordinate descent (BCD) algorithm, for tackling this problem. We introduce a set of conditions, called the $n$-sided PL condition, which extends the well-established gradient dominance condition a.k.a Polyak-Łojasiewicz (PL) condition and the concept of multi-convexity. This condition, satisfied by various classes of non-convex functions, allows us to analyze the convergence of various gradient descent (GD) algorithms. Moreover, our study delves into scenarios where the standard gradient descent methods fail to converge to NE. In such cases, we propose adapted variants of GD that converge towards NE and analyze their convergence rates. Finally, we evaluate the performance of the proposed algorithms through several experiments.

Space-based distribution of quantum entanglement will be essential for global quantum networking and secure communications. Modelling and analysis of the performance of satellite entanglement pair distribution is important for the architecture and design of constellations and space systems. Entanglement-based quantum key distribution, in the absence of quantum repeaters, is especially prone to finite key effects due to low coincident count rates compared to trusted node single-path links. Therefore, there is a need for a comprehensive study of finite-key effects in the context of direct dual downlink quantum key distribution taking into account the characteristics of the overpass geometries. We develop a high-fidelity model of pair distribution from a low Earth orbit satellite that captures orbital dynamics, elevation-dependent loss, background noise, and extraneous detector effects. We integrate this with a rigorous finite-key security framework for the BBM92 protocol to optimise secret key length across different overpass geometries, orbital altitudes, and optical ground station (OGS) separations. These results provide quantitative performance bounds and design guidelines for near-term SatQKD missions, enabling informed trade-offs between satellite payload complexity, ground infrastructure, and achievable secure key throughput.

Assessing an individual's contribution within a team remains a fundamental challenge across many domains, particularly when recognition for collective achievements is limited to only a few members. This issue is especially important in professional road cycling, where personal success depends on both individual talent and group effort. Existing points-based ranking systems tend to disproportionately reward high-scoring team leaders while undervaluing domestiques - riders who sacrifice personal success to support group performance. To better capture a rider's impact on the team, we propose a weighted measure of cycling productivity that factors in race points, a redistribution metric, and an adapted version of the CoScore formula. This formula assesses an individual's productivity relative to their teammates' performance. Using data from the 2023 season, we show that our approach offers a comprehensive evaluation of professional cyclists, addressing key limitations of existing ranking systems.

In this paper, we prove that the property of being a grape (in any of its variants) is invariant under Alexander duality. The explicitly determined (simple-)homotopy type of a grape can be transferred to its Alexander dual via Combinatorial Alexander Duality in (co)homology. We also provide several applications.

Emergent modified gravity provides a covariant framework for holonomy effects in models of loop quantum gravity with consistent black hole solutions coupled to a scalar field. Several independent studies of the Hawking thermal distribution are shown here to lead to the same final result. This internal consistency is a direct consequence of general covariance, which is analogous to the situation in classical general relativity but highly nontrivial in the context of modified canonical gravity. Holonomy corrections to the evaporation rate enter through the greybody factor, slowing down the evaporation process when the holonomy modification function decreases monotonically. Accounting for backreaction, corrected covariant semi-classical stress-energy tensors are computed in various vacuum states. Thanks to these results, the new concept of a net stress-energy tensor makes it possible to compute evaporation rates directly from energy conservation laws.

We present correct proof of G. Chung, Y.-J. Tsay result on partial gossip problem.

This paper investigates the non-trivial consensus problem on directed signed matrix-weighted networks\textemdash a novel convergence state that has remained largely unexplored despite prior studies on bipartite consensus and trivial consensus. Notably, we first prove that for directed signed matrix-weighted networks, every eigenvalue of the grounded Laplacians has positive real part under certain conditions. This key finding ensures the global asymptotic convergence of systems states to the null spaces of signed matrix-weighted Laplacians, providing a foundational tool for analyzing dynamics on rooted signed matrix-weighted networks. To achieve non-trivial consensus, we propose a systematic approach involving the strategic selection of informed agents, careful design of external signals, and precise determination of coupling terms. Crucially, we derive the lower bounds of the coupling coefficients. Our consensus algorithm operates under milder connectivity conditions, and does not impose restrictions on whether the network is structurally balanced or unbalanced. Moreover, the non-trivial consensus state can be preset arbitrarily as needed. We also carry out the above analysis for undirected networks, with more relaxed conditions on the coupling coefficients comparing to the directed case. This paper further studies non-trivial consensus with switching topologies, and propose the necessary condition for the convergence of switching networks. The work in this paper demonstrates that groups with both cooperative and antagonistic multi-dimensional interactions can achieve consensus, which was previously deemed exclusive to fully cooperative groups.

The newsvendor model is a well-known stochastic model for inventory management; however, it was originally developed for a single-period context and focuses on trading companies. This paper proposes an extension of the newsvendor model into a mutli-period setting, aiming to develop a decision-making tool for manufacturing firms to determine the optimal production batch size. The objective function is to maximize operating profit in accordance with generally accepted accounting principles. The model can also incorporate overhead costs, such as warehousing, shrinkage, cost of capital, and lead time between the production decision and output. Monte Carlo simulations demonstrate that the proposed model results in higher profitability compared to other newsvendor models used in our analysis, as well as the safety stock buffer approach. The key feature explaining its outperformance is better adaptability of the production batch size, that leads to fewer stock-outs relative to other newsvendor models and lower inventory levels compared to the safety stock buffer approach. The robustness analysis shows that the proposed model is quite tolerant of mismatches between the "model" and the "true" demand distributions. Finally, we provide some recommendations on selecting the appropriate "model" distribution for different SKUs.

The Open Radio Access Network (O-RAN) offers flexibility and innovation but introduces unique security vulnerabilities, particularly from cryptographically relevant quantum computers. While Post-Quantum Cryptography (PQC) is the primary scalable defence, its computationally intensive handshakes create a significant bottleneck for the RAN control plane, posing sustainability challenges. This paper proposes an energy-aware framework to solve this PQC bottleneck, ensuring quantum resilience without sacrificing operational energy efficiency. The system employs an O-RAN aligned split: a Crypto Policy rApp residing in the Non-Real-Time (Non-RT) RIC defines the strategic security envelope (including PQC suites), while a Security Operations Scheduling (SOS) xApp in the Near-RT RIC converts these into tactical timing and placement intents. Cryptographic enforcement remains at standards-compliant endpoints: the Open Fronthaul utilizes Media Access Control Security (MACsec) at the O-DU/O-RU, while the xhaul (midhaul and backhaul) utilizes IP Security (IPsec) at tunnel terminators. The SOS xApp reduces PQC overhead by batching non-urgent handshakes, prioritizing session resumption, and selecting parameters that meet slice SLAs while minimizing joules per secure connection. We evaluate the architecture via a Discrete-Event Simulation (DES) using 3GPP-aligned traffic profiles and verified hardware benchmarks from literature. Results show that intelligent scheduling can reduce per-handshake energy by approximately 60 percent without violating slice latency targets.

We construct a finitely generated residually finite group $G$ with the property that every finite index subgroup of $G$ contains a subgroup isomorphic to Promislow's group. Hence $G$ does not have a finite index subgroup with the unique product property.

In this paper, we propose and analyze a third-order dynamical system for solving a generalized inverse mixed variational inequality problem in a Hilbert space H. We establish the existence and uniqueness of the trajectories generated by the system under suitable continuity assumptions, and prove their exponential convergence to the unique solution under strong monotonicity and Lipschitz continuity conditions. Furthermore, we derive an explicit discretization of the proposed dynamical system, leading to a forward -backward algorithm with double inertial effects. We then establish the linear convergence of the generated iterates to the unique solution.

Let $R$ be a commutative ring with unity 1, and $ G(V,E)$ be a simple, connected, nontrivial graph. Let $d(a,c)$ be the distance between the vertices $a$ and $c $ in $G$. An undirected zero divisor graph of a ring $R$ is denoted by $Γ(R) = (V(Γ(R)), E(Γ(R)))$, where the vertex set $V(Γ(R))$ consists of all the non-zero zero-divisors of $R$, and the edge set $E(Γ(R))$ is defined as follows: $E(Γ(R)) = $ $\{e = a_1a_2$ $ |$ $ a_1 \cdot a_2 = 0$ $\&$ $ a_1, a_2 \in V(Γ(R))\}$. In this article, we consider the zero divisor graph of a group of integers modulo \(n\), denoted as \(Γ(\mathbb{Z}_n)\), where \(n=pq\). Here, \(p\) and \(q\) are distinct primes, with \(q > p\). We aim to determine the metric dimension of the barycentric subdivision of the zero divisor graph \(Γ(\mathbb{Z}_n)\), denoted by \(dim(BS(Γ(\mathbb{Z}_n)))\), and we also prove that \(dim(BS(Γ(\mathbb{Z}_n)))\geq q-2\) for every \(n=pq\), where \(p\) and \(q\) are distinct primes and $q>p$.

In context of Brans-Dicke scalar-tensor theories of gravity, it has recently been obtained that the post-Newtonian parameters should be generalized in the context of strongly gravitating bodies, and that its generalization -- the so-called $\textit{exact parameters}$ -- actually depends on the pressure and energy density of a considered celestial body. Here we develop two new methods to numerically obtain the $\textit{exact parameters}$ by means of usual Tolman-Oppenheimer-Volkoff computation, and find that the difference with the value of standard post-Newtonian parameters can be more than 80% in some situations. We also provide the connection with the Damour-Esposito Farèse non-pertubative parameter $α_{DEF}$. We then apply the methodology to the case of Entangled Relativity, and derive these exact parameters for the Sun and the Earth, as well as for neutron stars. We argue that current and foreseeable experiments are likely able to constrain the theory under the assumption that $\mathcal{L}_m=-ρ$, where $ρ$ is the total energy density. If $\mathcal{L}_m=T$ instead, as often advocated in the literature, then there is no deviation with respect to General Relativity and the prospects of testing Entangled Relativity become much more remote in time, as only compact objects with extreme electric or magnetic fields could lead to some deviation from General Relativity.

In this article, we establish Hineva inequality for different types of submanifolds of Quaternionic Space forms

Next-generation communication networks are characterized by integrated ultra-high reliability, ultra-low latency, massive connectivity, and ubiquitous coverage. However, this paradigm faces significant structural challenges of liquidity and security. Liquidity issues arise from prohibitive upfront costs of network resources, which strain the limited capital and financial flexibility. This also limits the deployment of the resource- and investment-intensive security solutions, bringing security issues. Security vulnerabilities arise from the decentralized architecture as well, particularly threats posed by Byzantine nodes. To address these dual challenges, we propose a novel framework utilizing Real-World Asset (RWA) tokenization for tokenizing network resources. RWA tokenization uses blockchain to convert ownership rights of real-world assets into digital tokens that can be programmed, divided, and traded. We then analyze the criteria for identifying suitable assets. Through a case study on dynamic spectrum allocation, we demonstrate the superior performance of this RWA approach. Particularly under conditions of resource scarcity, it can exhibit strong resilience against collusion and default attacks. Finally, we delineate fruitful avenues for future research in this nascent field.

Distributed architectures are gaining prominence in quantum machine learning as a means to overcome hardware limitations and enable scalable quantum information processing. In this context, we analyze the design and performance of distributed Quantum Extreme Learning Machine (QELM) architectures for learning functions of quantum states directly from data, restricting measurements to easily implementable projective measurements in the computational basis. The aim is to determine which schemes can effectively recover specific properties of input quantum states, including both linear and nonlinear features, while also quantifying the resource requirements in terms of measurements and reservoir dimensionality. We compare standard three-layer QELM with a spatially multiplexed architecture composed of multiple independent three-layer units for linear (quantum) tasks, showing a linear reduction in resource requirements per unit. For nonlinear properties, the study examines the multiple-injection architecture and introduces a novel distributed design that incorporates entanglement between subsystems within a spatially multiplexed framework, evaluating its performance through the reconstruction of complex nonlinear quantities such as polynomial targets, Rényi entropy, and entanglement measures. Our results demonstrate that the distributed design enables the reconstruction of higher-order nonlinearities by increasing the number of interacting subsystems with reduced resources, rather than increasing the size of an individual reservoir, providing a scalable and hardware-efficient route to quantum property learning.

In 1987, Frankl proved an influential stability result for the Erd\H os--Ko--Rado theorem, which bounds the size of an intersecting family in terms of its distance from the nearest (subset of) star or trivial intersecting family. It is a far-reaching extension of the Hilton--Milner theorem. In this paper, we prove its analogue for permutations on $\{1,\ldots, n\}$, provided $n$ is large. This provides a similar extension of a Hilton--Milner type result for permutations proved by Ellis.