Cubic boron arsenide (BAs) is a promising semiconductor for next-generation electronics due to its outstanding ambipolar mobility and thermal conductivity, the latter of which is attributed to the suppression of three-phonon scattering. However, precisely accounting for different high-order anharmonic scattering processes is challenging from both theory and experiment, so that questions remain open regarding the ultimate limit of phonon lifetime and thermal conductivity in BAs. Here we show that this gap nearly eliminates three-phonon scattering for zone-center optical phonons in a wide temperature range, leading to a record-high, isotope purity-limited phonon coherence with a quality factor above $3.7\times 10^3$ for >98% enriched $^{11}$BAs below 100 K. We discriminate three decoherence mechanisms by their temperature-dependent contribution to the damping rate using high-resolution Raman and Fourier transform infrared spectroscopy. For the as-synthesized crystals, we find that defect scattering has negligible contributions to the linewidth of optical phonons in comparison to isotope scattering. These results provide critical insights into the intrinsic and extrinsic scattering mechanisms of optical phonons in BAs, motivating further studies to quantify anharmonic effects and realize superior phonon transport.

We study connectivity functions, that is, integer-valued symmetric submodular functions on a finite ground set attaining $0$ on the empty set. For a connectivity function $f$ on an $n$-element set $V$ and an integer $k\ge 0$, we show that the family of all sets $X\subseteq V$ with $f(X)=k$ admits a polynomial-size representation: it can be described by a list of at most $O(n^{4k})$ items, each consisting of a set to be included, another set to be excluded, and a partition of remaining elements, such that the union of some members of the partition and the set to be included are precisely all sets $X$ with $f(X)=k$. We also give an algorithm that constructs this representation in time $O(n^{2k+7}γ+n^{2k+8}+n^{4k+2})$, where $γ$ is the oracle time to evaluate $f$. This generalizes the low rank structure theorem of Bojańczyk, Pilipczuk, Przybyszewski, Sokołowski, and Stamoulis [Low rank MSO, arXiv, 2025] on cut-rank functions on graphs to general connectivity functions. As an application, for fixed $k$, we obtain a polynomial-time algorithm for finding a set $A$ with $f(A)=k$ and a prescribed cardinality constraint on $A$.

Let $R_h(k; \ell)$ be the smallest integer $n$ such that any edge coloring of a complete graph on $n$ vertices in $\ell$ colors results in a monochromatic $K_k$-minor, in other words, a graph with Hadwiger number $k$, i.e., a graph that could be transformed into a clique $K_k$ on $k$ vertices via a sequence of edge contractions and vertex deletions. More generally, for a graph $F$ and integer $\ell$ let $R_h(F;\ell)$ be the smallest integer $n$ such that any edge coloring of a complete graph on $n$ vertices in $\ell$ colors results in a monochromatic $F$-minor. In 2001 Thomason and in 2005 Myers and Thomason asymptotically determined the extremal numbers for clique minors and $F$-minors, respectively. They found the respective explicitly computable leading constants $β=0.265656...$ and $γ(F)\cdot β$ for these extremal numbers. We determine $R_h(F;2)$ for every graph $F$ as $$R_h(F;2)=(γ(F)+o(1))|V(F)|\sqrt{\log_2(|V(F)|)},$$ where the $o(1)$-term tends to zero as $|V(F)|\rightarrow \infty$. In particular, $$R_h(k;2)=(1+o(1))k\sqrt{\log_2 k}.$$ When $\ell\gg k \gg 1$, we show that $$ R_h(k; \ell) = (2β+o(1)) \ell k \sqrt{\log_2 k}.$$

We investigate the extent of the critical scaling region of the chiral phase transition at finite chemical potential within the quark-meson (QM) model using the functional renormalization group (fRG) approach. By analyzing the scaling behavior of the chiral order parameter and correlation length with respect to temperature and pion mass near the second-order phase transition, we extract critical exponents from the data and quantify the range over which the scaling relations remain valid. We find that both the leading order and the next-to-leading-order scaling regions systematically shrink as the chemical potential increases. This behavior is observed in both the local potential approximation (LPA) and its extension including anomalous dimensions (LPA'), with qualitatively consistent results, while the scaling region in LPA' is slightly smaller than that in LPA.

Let $(a_n)_{n\ge 1}$ be the greedy self-generating sequence defined by $a_1=1$, $a_2=2$, and, for $k\ge 3$, by taking $a_k$ to be the least integer greater than $a_{k-1}$ that can be written as a sum of at least two consecutive earlier terms. Hofstadter asked about the asymptotic behavior of this sequence. In this paper we prove that $$ n+Ω(\log\log n)\le a_n \ll n^{4175/2506+o(1)}. $$ In particular, $(a_n)_{n\ge1}$ omits infinitely many positive integers, thereby settling a conjecture from the OEIS entry A005243.

We identify a universal structural principle underlying the smoothing of classical divergences: the optimizer of the smoothing problem is a clipped probability vector, independently of the specific divergence. This yields a divergence-independent characterization of all smoothed classical divergences and reveals a common geometric structure behind seemingly different quantities. Building on this structural insight, we derive optimal universal bounds for smoothed quantum divergences, including quantum R'enyi divergences of arbitrary order and the hypothesis testing divergence. Our inequalities relate divergences of different orders through bounds of the form $D_β^{\varepsilon} \le D_α+ \mathrm{correction}$ and $D_β^{\varepsilon} \ge D_α+ \mathrm{correction}$, and we prove that the correction terms are optimal among all universal, state-independent inequalities of this type. Consequently, our results strictly improve previously known bounds whenever those were suboptimal, and in cases where earlier bounds coincide with ours, our analysis establishes their optimality. In particular, we obtain optimal universal bounds for the hypothesis testing divergence.

We study the Ambrozio--Carlotto--Sharp (ACS) criterion on minimal isoparametric hypersurfaces $N^{n+1}\subset S^{n+2}$ with positive Ricci curvature, motivated by the Schoen--Marques--Neves conjecture on Morse index.For $g=4$ distinct principal curvatures with multiplicities $m_1,m_2$, we prove that the pointwise ACS inequality holds if and only if $\min\{m_1,m_2\}\ge 4$. Sufficiency is obtained via a moment-relaxation technique yielding the sharp bound $4a^2$ on the quadratic part of the integrand; necessity follows from an explicit extremal configuration in the top eigenspace of the shape operator. We also verify the ACS condition for $g=3$ with $m_1=m_2\in\{4,8\}$.As a consequence, for any closed embedded minimal hypersurface $M^n$ in such an ambient manifold, $\operatorname{index}(M)\ge \tfrac{2}{d(d-1)}\, b_1(M)$ with $d=n+3$.

This paper presents a detailed case study of the T2_BR_SPRACE storage frontend architecture and its observed performance in high-intensity data transfers. The architecture is composed of a heterogeneous cluster of XRootD [1] Virtual Machines (VMs) with 10 Gb/s and 40 Gb/s links, which aggregate data from a 77 Gb/s dCache [2] backend via pNFS to an external 100 Gb/s WAN link. We describe the system configuration, including the use of the BBR [3] congestion control algorithm and TCP extensions [4]. Under peak production conditions, we observed the system sustaining an aggregate throughput of 51.3 Gb/s. An analysis of a specific data flow to Fermilab (FNAL) showed peaks of 41.5 Gb/s, validated by external monitoring tools (CERN). This study documents the performance of a complex virtualized architecture under real load.

General matrix multiplication (GEMM) on spatial accelerators is highly sensitive to mapping choices in both execution efficiency and energy consumption. However, the mapping space exhibits combinatorial explosion, which makes it extremely challenging to obtain optimal mappings within an acceptable time budget. Existing approaches typically face challenges: They often lack global-optimality guarantees and become prohibitively slow as the mapping space grows. To address these limitations, we propose \textsc{GOMA}, a geometric-abstraction-based, globally optimal GEMM mapping framework via analytical modeling, which achieves efficient solving while guaranteeing optimality. \textsc{GOMA} introduces, from first principles, a geometric abstraction for GEMM mapping, yielding an exact analytical energy objective with $O(1)$ evaluation for any given mapping. The objective is highly accurate. \textsc{GOMA} then formulates mapping selection as an integer optimization problem under hardware and mapping constraints, using the analytical energy model as the objective to automate mapping search. \textsc{GOMA} can quickly compute a global-optimal mapping for any (GEMM workload, target hardware) pair, achieving this for the first time in mapping space exploration. Experiments confirm that across representative accelerators and large language model prefill workloads, \textsc{GOMA} improves the energy--delay product (EDP) by $2.24$--$4.24\times$ over SOTA mappers, while accelerating time-to-solution by $3.83$--$73.6\times$.

A ring polymer in a confining space may exhibit at least two phases, namely an expanded (or solvent-rich phase) if its concentration is small, or a collapsed (or polymer-rich phase) when it is concentrated and compressed. These phases are discussed in reference \cite{deG79}, and have been modelled, traditionally, in the mean field using Flory-Huggins theory \cite{Flory42,Huggins42}. In three dimensions the ring polymer may also be knotted, or linked, and have its conformational degrees of freedom constrained by its topology. In a lattice model of confined knotted ring polymers there are indications that the thermodynamic properties of the ring polymer (for example, the osmotic pressure \cite{GJvR18,JvR19}) is a function of its topology. In this paper we explore a lattice knot model of a confined ring polymer as a function of its chemical potential. We show that a well-defined phase transition occurs between solvent-rich and polymer-rich phases when the lattice knot exhibits either the unknot topology or any other fixed knot type. Furthermore, we observe small yet significant variations in the free energy near the critical point when comparing trefoil knots with other non-trivial knot types. These findings indicate that the thermodynamic properties of confined ring polymers depend on their topological entanglement characteristics (namely, their knot type).

We investigate how diversity in the core-halo mass relation affects constraints on the fuzzy dark matter particle mass $m_ψ$ inferred from the internal kinematics of dwarf galaxies, and how these constraints are impacted by the inclusion of higher-order stellar velocity moments. Using stellar line-of-sight velocities and projected positions for eight Milky Way dwarf spheroidal galaxies, we model their dark matter halos as solitonic cores embedded within outer NFW envelopes. We apply both second- and fourth-order Jeans analyses to derive the posterior distribution of $m_ψ$. Our results show that there are two ranges of $m_ψ$ consistent with the observed kinematics: $\log_{10}(m_ψ/\mathrm{eV}) = -19.79^{+0.60}_{-0.53}$, and a narrower small-mass window $\log_{10}(m_ψ/\mathrm{eV}) = -21.82^{+0.35}_{-0.26}$, both within the 68% credible intervals. The latter becomes prominent only when core-halo diversity is taken into account, which highlights the sensitivity of the inferred fuzzy dark matter particle mass constraints to our understanding of the core-halo relation. Future observations, providing larger stellar samples and more precise kinematic measurements, will be essential for clarifying the allowed parameter space of fuzzy dark matter.

We examine whether the Schwarzschild black hole can emerge as the continuous end state of gravitational collapse from a non-singular configuration. Employing a time dependent extension of the regular Schwarzschild metric, we track the evolution of the geometry during collapse and find that the process cannot remain continuous. The metric function develops a discontinuity at the origin, marking a breakdown of spacetime smoothness, an effect identified as ``Minkowski breaking.'' Before the Schwarzschild point source can form at $r=0$, curvature singularities appear and the Cauchy horizon disappears. These results strongly suggest that spacetime may not evolve smoothly toward the Schwarzschild geometry. Instead, the formation of a Schwarzschild black hole appears to entail a discrete change in the structure of spacetime, pointing to the need for a noncontinuous, possibly quantized, framework to describe the emergence or regularization of gravitational singularities.

The dense amalgam is an operation (introduced in arXiv:1410.4989) which to any finite collection of metrizable compacta associates canonically some new highly disconnected compact metrisable space in which embedded copies of the initial spaces are appropriately uniformly and disjointly distributed. We show that in the very general framework of $E\mathcal{Z}$-boundaries (unifying many frameworks such as Gromov boundaries, CAT(0)-boundaries, systolic boundaries, etc.), any boundary $Z$ of an infinitely ended group $Γ$ equipped with an appropriate splitting along finite subgroups has a form of the dense amalgam of the limit sets in $Z$ of the factor subgroups of this splitting.

Nickelate superconductors provide a valuable new platform for the study of unconventional superconductivity that is complementary to the cuprates. One of the central puzzles about high-temperature superconductors is what factors determine the scale of their superconducting transition temperature ($T_\mathrm{c}$). To address this question for infinite-layer nickelates, we present a systematic mutual inductance study of the superfluid density across the doping-dependent superconducting dome of $\mathrm{Nd}_{1-x}\mathrm{Sr}_x\mathrm{NiO}_2$. We observe a weak superfluid stiffness that exhibits an approximately square-root correlation with $T_\mathrm{c}$. We also find a strong interplay between Nd magnetism and the superconducting phase, manifested as a substantial low-temperature suppression of superfluid density. These observations highlight the importance of superconducting phase fluctuations in limiting $T_\mathrm{c}$ and unexpectedly strong coupling between the Nd 4$f$ moments and the superfluid.

Odd-parity-wave magnets are noncollinear compensated magnets with spin-split band structure in the absence of spin-orbit coupling and dipolar interactions. In contrast to altermagnets, their spin-polarized band structure breaks inversion symmetry, but preserves time-reversal symmetry rendering their spin texture odd in momentum space. Here, we study the spin dynamics of the magnetic texture and compute the band structure and spin polarization of magnons. We present minimal spin models of noncoplanar odd-parity-wave magnets purely stabilized by exchange interactions that host p- and f-wave spin textures for the magnetic excitations. We demonstrate that two of these models exhibit collinear spin textures, i.e., the magnon spin polarization is restricted to a global (quantization) axis independent of the momentum giving rise to single-component odd-parity-wave magnetism, previously associated primarily with coplanar ground states. Finally, the nonrelativistic magnonic thermal Edelstein effect -- a nonequilibrium magnetization induced by a temperature gradient -- is shown to exist for p-wave magnets in linear response and inherits its anisotropic angular dependence from the partial-wave character of the spin-polarized band structure. Our findings suggest that insulating odd-parity-wave magnets are promising candidates for magnon spintronics applications.

We have generalised an all-optical telecorrection protocol for the higher orders of the cat code, and show that with these higher orders we can achieve target performance at substantially reduced iteration counts at the cost of a higher mean photon-number. We also introduce a probabilistic scheme for correcting deformation of the state, which highlights two interesting abilities of telecorrection: to encode new sets of transformations, and to change the basis of the code. We find that for a target channel fidelity of $99.9\%$ over a channel with $1\text{ dB}$ of loss, a third-order cat code requires $70$ times fewer telecorrection iterations than a first-order one, at a cost of a $3.6$-fold increase in mean photon-number.

Our main result is a robust generalisation of the Cockayne-Lorimer theorem on the multicolour Ramsey number of matchings. It is moreover a generalisation of the transference generalisation of Cockayne-Lorimer, which (informally) says that the random graph $G \sim G(n,p)$ with $np \to \infty$ has, with high probability, essentially the same Ramsey matching properties as the complete graph $K_n$. We show, somewhat surprisingly, that the same is true under the rather weak robustness assumption that $G$ is an $s$-connector (i.e. $\overline{G}$ is $K_{s,s}$-free) with $s=o(n)$. Moreover, we show that such $G$ has only an additive $O(s)$ loss with respect to $K_n$ for monochromatic matchings, which is essentially sharp. Our proof adapts a compression algorithm based on Gallai-Edmonds decompositions that we developed previously for generalised Ramsey-Turán problems.

We prove a local Brunn-Minkowski inequality for a functional corresponding to p-harmonic measures for 2 < p < n+1.

Previously, we have investigated a natural smooth map onto the region surrounded by the graphs of two smooth real-valued functions in the plane converging to a same value or diverges to $+\infty$ or $-\infty$ simultaneously, at each infinity, and topological properties and combinatorial ones of its composition with the canonical projection. Here, we consider smooth functions with congruent or globally similar graphs instead. Here, the Reeb space of a smooth function on a manifold with no boundary is fundamental and important. This is the naturally topologized quotient space of the manifold, consisting of all connected components (contours) of the function and is a graph under a certain nice situation. Related studies also related to the present study were started due to interest of the author in theory of Reeb spaces of non-proper functions. For proper functions, in 2020s related studies have developed mainly due to Gelbukh and Saeki.

We investigate Extended Geometric Trinity of Gravity at both classical and quantum cosmological levels using the minisuperspace approach. Adopting Noether symmetries to select viable models, we examine metric-affine theories of gravity, in particular the extensions of General Relativity, Teleparallel Equivalent General Relativity and Symmetric Teleparallel Equivalent General Relativity, and show that the equivalence among these different formulations can be restored by including in the Lagrangian the divergence terms that relate their respective geometric invariants to the Ricci scalar. Exact cosmological solutions are derived and compared in the different models.

Incidence theorems concern configurations of points, lines, and, more generally, higher-dimensional subspaces in projective space. Broadly speaking, such theorems fall into two classes: those that hold over an arbitrary division ring, such as Desargues' theorem, and those that hold only over fields, such as Pappus' theorem. In this paper, we explain the topological origin of this distinction. To this end, we extend to the noncommutative setting the surface-graph approach to incidence theorems developed by Richter-Gebert, Fomin, and Pylyavskyy. We then show that theorems associated with graphs embedded on the sphere, such as Desargues' theorem, hold over any division ring, whereas theorems corresponding to graphs embedded on surfaces of positive genus, such as Pappus' theorem, typically hold if and only if the ground ring is a field. We also extend these results to the setting of arbitrary rings, not necessarily admitting division.

Sex chromosomes have evolved repeatedly across the Tree of Life, yet their evolutionary fates differ strikingly. In sharp contrast to mammals and birds with degenerated, stable Y/W chromosomes, in most amphibians, teleosts, non avian reptiles and flowering plants, sex chromosomes remain largely homomorphic and undergo frequently turnover. Explanations such as the evolutionary trap hypothesis, sexually antagonistic selection, mutation load, genetic drift and selfish genetic elements, focus on population genetic processes and do not fully explain this pattern. Here we propose the developmental gene regulatory network (GRN) lock in hypothesis. We compile case studies of turnover across vertebrates, synthesise comparative developmental data on sex determination and dosage regulation (DC). In mammals and birds, sex is determined by an early, initiation by somatic cells, fully penetrant master signal acting within a narrow, thermally buffered embryonic window. This signal operates within highly canalised GRNs, coupled to chromosome scale dosage compensation, with alternative splicing events playing little or no causal role in primary sex determination. This configuration makes it difficult for new master sex determining loci to invade without generating deleterious intermediate states. By contrast, many ectothermic vertebrates possess flexible, integrative threshold GRNs in which genetic, germ cells and environmental inputs interact over a prolonged sensitive embryonic period, with absent or largely gene-by-gene based DC and environmentally responsive splicing near key regulatory nodes, providing many entry points for sex determining loci to evolve. We outline empirical predictions and highlight how integrating developmental biology, molecular mechanisms and population genetics can yield testable models for when sex chromosomes become evolutionarily locked-in versus repeated turnover.

We present an exhaustive BRST lagrangian description of partially massless bosonic fields in four-dimensional space. The basic fields are formulated in terms of two-component spin-tensors in (A)dS space where the tracelessness conditions are automatically fulfilled. The mass shell of partially massless fields is reformulated in terms of constraints on Fock space vectors including the second-class constraints. A conversion procedure for transforming second-class constraints into first-class ones is developed, allowing one to construct a Hermitian and nilpotent BRST charge in the Fock space under consideration. It is proven that the hermiticity and nilpotency restrict the conditions on the theory parameters, which are fulfilled only in dS space. The hermiticity of the BRST charge is incompatible with AdS space. The gauge invariant Lagrangian is constructed on the basis of the BRST charge, and for spin $s$ and depth $t$ the allowed states in the Lagrangian include only $(s-t-1)$ Stückelberg fields. Their exclusion leads to gauge transformations of degree $(s-t)$ for the physical fields. The Lagrangian equations of motion exactly reproduce the mass shell conditions. The Lagrangian in terms of conventional spin-tensor fields is also presented.

This paper introduces the notion of an $(ι,q)$-critical graph. The isolation number of a graph $G$, denoted by $ι(G)$ and also known as the vertex-edge domination number of $G$, is the size of a smallest subset $D$ of the vertex set of $G$ such that the subgraph induced by the set of vertices that are not in the closed neighbourhood of $D$ has no edges. A graph $G$ is $(ι,q)$-critical if every subdivision of $q$ edges of $G$ gives a graph whose isolation number is greater than $ι(G)$, and $G$ has $q-1$ edges such that subdividing them gives a graph whose isolation number is $ι(G)$. We show that an $(ι,q)$-critical graph exists for every integer $q \ge 1$. We prove that if $G$ is a connected $m$-edge non-star graph, then $G$ is $(ι,q)$-critical for some $q \le m - 1$. We show that this bound is best possible. We provide a general characterization of $(ι,1)$-critical graphs as well as a constructive characterization of $(ι,1)$-critical trees, demonstrating that $(ι,1)$-criticality can be checked in linear time for trees.

Based on a data sample corresponding to an integrated luminosity of 6.4~fb$^{-1}$ of $e^+e^-$ annihilation and collected with the BESIII detector at 13 center-of-mass energy points ranging between 4.600~GeV and 4.950~GeV, we report the first observation of the singly Cabibbo-suppressed decay $Λ_c^+ \to Σ^0 K_S^0 π^+$ with a statistical significance of 5.9$σ$. The branching fraction is determined to be $\mathcal{B}(Λ_c^+ \to Σ^0 K_S^0 π^+) = (0.58 \pm 0.14_{\rm stat.} \pm 0.04_{\rm syst.}) \times 10^{-3}$. In addition, the decay $Λ_c^+\toΣ^0K_{S}^{0} K^+$ has also been investigated, and the first evidence for this decay is obtained with a statistical significance of 3.7$σ$.

We define \emph{engineered simultaneity}: the construction of a system that requires temporal comparison of events at spacelike-separated locations, implements this comparison via an implicit simultaneity convention, and represents the result as an objective measurement rather than a conventional choice. We show that the National Best Bid and Offer (NBBO) -- the regulatory cornerstone of U.S. equity markets -- is an instance of engineered simultaneity. The NBBO requires determining ``current'' prices across exchanges whose spatial separation places their price events outside each other's light cones. Special relativity proves that the temporal ordering of such events is frame-dependent: there exist inertial reference frames in which the NBBO differs from the value reported by the Securities Information Processor. The impossibility is not approximate; it is exact and unavoidable within the causal structure of Minkowski spacetime. General relativity compounds the impossibility: gravitational time dilation introduces frame-rate discrepancies between exchanges at different altitudes, and recent work on indefinite causal order in quantum information theory undermines the premise of a fixed causal structure altogether. We formalize the special-relativistic argument using the causal precedence relation, connect it to Lamport's theorem on distributed ordering, and note that approximately \$5~billion per year in latency arbitrage profits are extracted from the gap between the NBBO's implicit simultaneity convention and physical reality.

Approximate nearest neighbor (ANN) search on SSD-backed indexes is increasingly I/O-bound (I/O accounts for 70--90\% of query latency). We present an I/O-first framework for disk-based ANN that organizes techniques along three dimensions: memory layout, disk layout, and search algorithm. We introduce a page-level complexity model that explains how page locality and path length jointly determine page reads, and we validate the model empirically. Using consistent implementations across four public datasets, we quantify both single-factor effects and cross-dimensional synergies. We find that (i) memory-resident navigation and dynamic width provide the strongest standalone gains; (ii) page shuffle and page search are weak alone but complementary together; and (iii) a principled composition, OctopusANN, substantially reduces I/O and achieves 4.1--37.9\% higher throughput than the state-of-the-art system Starling and 87.5--149.5\% higher throughput than DiskANN at matched Recall@10=90\%. Finally, we distill actionable guidelines for selecting storage-centric or hybrid designs across diverse concurrency levels and accuracy constraints, advocating systematic composition rather than isolated tweaks when pushing the performance frontier of disk-based ANN.

We start studying the character variety of the algebraic supergroup OSp(1|2) from the algebraic perspective. We do this by first investigating the specific case of the character variety of the free group on two letters and try to describe the ring of invariants with respect to the conjugation action. The explicit description of the corresponding character variety for SL(2) was done by Fricke and Klein, so this can be seen as a variant of this theorem for its supergeometric counterpart OSp(1|2) and briefly touch upon the character stack for OSp(1|2)

Underwater Acoustic (UWA) networks are vital for remote sensing and ocean exploration but face inherent challenges such as limited bandwidth, long propagation delays, and highly dynamic channels. These constraints hinder real-time communication and degrade overall system performance. To address these challenges, this paper proposes a bilevel Multi-Armed Bandit (MAB) framework. At the fast inner level, a Contextual Delayed MAB (CD-MAB) jointly optimizes adaptive modulation and transmission power based on both channel state feedback and its Age of Information (AoI), thereby maximizing throughput. At the slower outer level, a Feedback Scheduling MAB dynamically adjusts the channel-state feedback interval according to throughput dynamics: stable throughput allows longer update intervals, while throughput drops trigger more frequent updates. This adaptive mechanism reduces feedback overhead and enhances responsiveness to varying network conditions. The proposed bilevel framework is computationally efficient and well-suited to resource-constrained UWA networks. Simulation results using the DESERT Underwater Network Simulator demonstrate throughput gains of up to 20.61% and energy savings of up to 36.60% compared with Deep Reinforcement Learning (DRL) baselines reported in the existing literature.

We introduce a functor $Ψ$ that associates to a dioperad $P$ acting on a vector space $V$ a two-colored operad $Ψ(P)$ acting on the pair $(V, V^*)$. The construction is based on a simple pictorial idea: by selecting one input or output and dualizing, if necessary, the remaining ones, any dioperadic tree can be ``rerooted'' as a colored operadic tree. This transformation allows one to apply the standard operadic machinery -- such as Gröbner bases and Hilbert series -- to the study of dioperads. We illustrate the method with several examples and applications. (1) We compute the dimensions of the spaces of operations for the dioperad of Lie bialgebras. (2) We describe a Gröbner basis and construct a minimal resolution for the dioperad of triangular Lie bialgebras. (3) We perform explicit computations for the dioperad of ``algebraic string operations''. (4) We give a pictorial construction proving the existence of quadratic Gröbner bases and establishing the Koszul property for a broad class of dioperads arising from cyclic operads.