In this paper we reexamine the definition of parafermions and parabosons by means of Green's triple relations, and extend these relations by including a parity operator $P$ which is also determined by means of triple relations. As a consequence, we are dealing with new algebraic structures. It is shown that the algebra underlying a set of $n$ parafermions together with $P$ is the orthogonal Lie algebra $so(2n+2)$. The Fock spaces correspond to particular irreducible representations of $so(2n+2)$, and the action of $P$ in these spaces leads to interesting observations. Next, we show that the algebra underlying a set of $n$ parabosons together with $P$ is the orthosymplectic Lie superalgebra $osp(2|2n)$. In this case, the Fock spaces correspond to certain irreducible infinite-dimensional representations of $osp(2|2n)$. Both for parafermions and parabosons the spectrum of $P$ is closely related to the so-called order of statistics $p$, introduced by Green.

Generative Recommendation (GR) reframes retrieval and ranking as autoregressive decoding over Semantic IDs (SIDs), unifying the multi-stage pipeline into a single model. Yet a fundamental expressive gap persists: discriminative models score items with direct feature access enabling explicit user-item crossing, whereas GR decodes over compact SID tokens without item-side signal. We formalize this via Bayes' theorem: ranking by p(y|f,u) is equivalent to ranking by p(f|y,u), which factorizes autoregressively over item features, showing that a generative model with full feature access matches its discriminative counterpart, with any practical gap stemming solely from incomplete feature coverage. We propose UniRec with Chain-of-Attribute (CoA) as its core mechanism. CoA prefixes each SID sequence with structured attribute tokens:category, seller, brand, before decoding the SID, recovering the item-side feature crossing that discriminative models exploit. Since items sharing identical attributes cluster in adjacent SID regions, attribute conditioning yields a measurable per-step entropy reduction H(s_k|s<k,a) < H(s_k|s<k), narrowing the search space and stabilizing beam search. We further address two deployment challenges: Capacity-constrained SID introduces exposure-weighted capacity penalties into residual quantization to suppress token collapse and the Matthew effect; Conditional Decoding Context (CDC) combines Task-Conditioned BOS with hash-based Content Summaries to inject scenario signals at each decoding step. A joint RFT and DPO framework aligns the model with business objectives beyond distribution matching. Experiments show UniRec outperforms the strongest baseline by +22.6% HR@50 overall and +15.5% on high-value orders. Deployed on Shopee's e-commerce platform, online A/B tests confirm significant gains in PVCTR (+5.37%), orders (+4.76%), and GMV (+5.60%).

We present Twisted Edges, a unified framework for designing Linked Knot (LK) structures using labeled non-manifold surface meshes. While the concept of edge twists, originating in topological graph theory, is foundational to these designs, prior approaches have been strictly limited to binary states. We identify this restriction as a critical barrier; binary twisting fails to capture the full spectrum of topological possibilities, rendering a vast class of structural and dynamic behaviors inaccessible. To overcome this limitation, we generalize the twist formulation to support arbitrary integer twist labels. This expansion reveals that while zero twists may introduce disconnections, applying even twists to 2-manifold meshes robustly preserves connectivity, transforming surfaces into fully connected, chainmail-like structures where faces form consistently linked cycles. Furthermore, we extend this framework to non-manifold meshes, where specific integer assignments prevent cycle merging. This capability, unattainable with binary methods, enables the design of partial connectivity and functional hinges, supporting dynamic folding and articulation. Theoretically, we show that these integer-twisted meshes correspond to knotted surfaces in four dimensions, with LK structures arising as their immersions into $\mathbb{R}^3$. By breaking the binary constraint, this work establishes a coherent paradigm for the systematic exploration of previously unstudied woven and articulated structures.

This paper presents EMSpice~3, a full-chip multiphysics framework for coupled electromigration (EM), thermomigration (TM), and IR-drop analysis of practical power-grid (P/G) networks. The framework is, to our knowledge, the first EM-IR analysis flow that jointly incorporates Joule heating and practical spatial thermal profiles for full-chip P/G network designs. It operates on extracted power-grid netlists and combines an immortality check, transient EM/TM stress evolution, void-induced resistance updates, repeated IR-drop recomputation, and optional Monte Carlo lifetime prediction. To make chip-level EM analysis tractable, the framework integrates an extended rational Krylov subspace method into the transient solver, achieving $1.18\times$--$1.50\times$ speedup with sub-0.05% reported TTF/final-IR metric error relative to the default non-Krylov FDTD analysis across six benchmark designs. The numerical results reveal that the specific spatial temperature profile can have a more significant impact on P/G network lifetime than the average temperature itself. In the RISC-V core, a higher-average-temperature profile can avoid the 10% IR-drop failure threshold when its hotspots are less aligned with critical current paths, while mapped temperature gradients can move the critical void location and change which resistor branches are degraded. Monte Carlo analysis further shows design-specific variation sensitivity: under 20% variation in EM diffusivity and critical stress, the RISC-V core exhibits about 15.8% TTF coefficient of variation, whereas the ARM Cortex-A logic core exhibits only 0.0058\%. These results show that practical thermal profiles, resistance feedback, and stochastic material variation must be considered jointly for predictive full-chip EM-IR analysis.

Rendering large-scale, unbounded scenes on AR/VR-class devices is constrained by the computation, bandwidth, and storage cost of 3D Gaussian Splatting (3DGS). We propose a low-power, low-cost 3DGS hardware accelerator that renders full-HD images in real time, together with a hardware-friendly compression pipeline that combines iterative Gaussian pruning and fine-tuning, progressive spherical harmonics (SH) degree reduction, and vector quantization of all SH coefficients and colors. The scheme achieves a $51.6\times$ model-size reduction with a 0.743 dB PSNR loss. The accelerator uses a frame-level pipeline that integrates point-based culling and projection with tile-based sorting and rasterization, skips zero-Jacobian matrix multiplications (reducing processing elements by 63\% and computation by 53\%), and adopts comparison-free tile-based sorting with deterministic latency. Implemented in a TSMC 28-nm process at 800 MHz, the design occupies $0.66~\text{mm}^2$ with 1.1438 M gates and 120 kB SRAM, consumes 0.219 W, and delivers 1219 Mpixels/J at 267.5 Mpixels/s, enabling 1080p at 129 FPS. Overall, it is $5.98\times$ smaller in area, $5.94\times$ higher throughput, and delivers $7.5\times$ higher energy efficiency than prior 3DGS accelerators.

Network segmentation is a foundational enterprise security control. Despite its recognized benefits, segmentation initiatives frequently fail in practice, and the field lacks a systematic empirical explanation for why these projects do not achieve their intended outcomes. This paper presents an empirical study of failed segmentation projects based on a survey of 400 U.S.-based\ network security practitioners. The survey was grounded in a two-part failure framework that separately measures general IT project failure factors and segmentation-specific technical and operational barriers. Clustering analysis of the responses reveals four distinct failure archetypes. Surprisingly, practitioners across all four archetypes propose general IT project management fixes over segmentation-specific fixes in the same ratio.

We address surface gradient flows which allow for energy dissipation by evolving the surface and a scalar quantity on it, simultaneously. A proper choice of the time derivative and the gauge of surface independence guarantees energy dissipation and ensures conservation of the scalar quantity. The resulting system of partial differential equations couples geometric evolution equations for the evolution of the surface in normal directions, equations for tangential movement and scalar-valued equations on the evolving surface. We discuss the general setting and the special case of surface tension flows and numerically demonstrate the importance of tangential movement on the evolution.

Token identity is semantic information for measurement-bearing expressions. Intervals, dimension tags, and token-erased syntax can say what values a measured leaf may take, but they cannot say whether two occurrences name the same observation or two fresh observations. We give a small formal semantics in which each measured leaf carries an interval of possible exact values and an opaque observation-event token. Here "token" means an identity for a measurement event, not a lexical token of the source syntax. The denotation of an expression is its warranted enclosure: the set of exact values still justified by hidden-value environments that assign one value to each observation token and respect the declared intervals. Over this semantics, e -> e' is a claim-tightening judgment, equivalently enclosure containment Encl(e') subseteq Encl(e), while interchangeability is equality of enclosures. The distinction is visible in cancellation, background subtraction, and self-division: reusing one token gives interchangeability with the expected simplified expression, while using distinct tokens gives only one-way containment. We prove that provenance-blind summaries of the kind studied here, preserving intervals, dimension tags, and token-erased syntax, are insufficient to recover the correct rewrite class. The formal results are mechanized in Lean 4 with no sorry or admit placeholders.

Gravitational-wave observations have revealed an excess of binary black hole mergers with primary masses near $\sim 35\,M_\odot$. We show that if this feature originates from dynamical formation in dense stellar systems, and if the pair-instability supernova truncates the first-generation black hole mass spectrum, then second-generation mergers inevitably produce a second peak near $\sim 70\,M_\odot$. This structure reflects the suppression of first-generation black holes above a characteristic mass and the accumulation of merger remnants near twice that scale. Its location is robust, whereas its amplitude depends strongly on cluster initial conditions. Using a large suite of cluster population-synthesis models, we show that current gravitational-wave data already constrain the birth properties of globular clusters, irrespective of their overall contribution to the observed population. If clusters dominate mergers above the pair-instability scale, these constraints tighten further and imply a minimum first-generation merger rate of $\mathcal{R}(m_1 \leq 50\,M_\odot) \geq 0.099\,\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ ($99\%$ confidence). We further show that a drop or gap in the secondary black hole mass spectrum is not a robust signature of a cluster origin for high-mass mergers within the pair-instability mass gap. A confirmed excess near $\sim 70\,M_\odot$ would support a dynamical origin of the $\sim 35\,M_\odot$ feature and provide independent evidence for a pair-instability mass gap with a lower edge at $\lesssim 50M_\odot$.

We consider the $SU(2)$ Self-Dual Yang Mills Higgs Lagrangian in 3 dimension. By adding a ''Gauge Mass'' term to this YMH Lagrangian in the form of $L^2$ norm of the connection we break the gauge invariance and critical points are automatically fulfilling globally the Coulomb condition. We study the so called ``large mass asymptotic'', which has the effect of ''squeezing'' the monopoles. For any unit Higgs field data at the boundary we prove that minimizers of this Coulomb-Yang-Mills-Higgs Functional converge to harmonic maps into ${\mathbb S}^2$ extending this data. This asymptotic moreover is subject to concentration conpactness phenomena and the convergence is strong away from a 1 dimensional rectifiable closed concentration set. Then we prove that, having chosen a large enough coupling constant, the limiting minimal energy is converging towards the minimal Brezis-Coron-Lieb relaxed harmonic map energy for this boundary data. In the second part of the paper we examine a different asymptotic regime characterised by overloading monopoles. In this regime we prove that asymptotically, the magnetic field becomes exclusively longitudinal with a $U(1)$ abelian component along the Higgs Field while the Higgs field itself converges to a smooth absolute minimizer of a relaxation of the Faddeev-Skyrme functional of maps from ${\mathbb B}^3$ into ${\mathbb S}^2$. In the third part of the paper we study the behaviour of these configurations when the parameter in front of the Fadeev-Skyrme component respectively goes to zero and $+\infty$. In the first case one recovers the Brezis Coron Lieb relaxed energy at the limit while in the second case the minimal limiting energy is converging towards the minimal Dirichlet energy of maps into ${\mathbb S}^3$ whose projection by the Hopf fibration is equal to the fixed boundary data.

We put forward a proposal for topological quantum critical points (tQCPs) separating non-invertible chiral topological orders in $(2+1)$ dimensions. We conjecture that these tQCPs can be captured by a family of scale-invariant field theories forming a non-compact scale-invariant manifold. A central feature of our proposal is topological shadowing: the underlying critical theory is rigorously constrained by the global topological data of the two adjacent gapped phases. These theories can be further projected into quantum field theories with universal non-local structures. Specifically, we show that the quantum dynamics of the $U(1)$ symmetric critical point uniquely characterized by a topological angle $Θ_{\text{cft}}$ -- which is defined by a commutator between two Wilson loop operators on a torus -- is determined by the braiding angles $Θ_{1,2}$ of the adjacent gapped phases via the relation $Θ_{\text{cft}}^{-1} =\frac{1}{2}[Θ_1^{-1} + Θ_2^{-1}]$. Despite the non-locality, our renormalization group calculations (up to two-loop order) strongly suggest that the theory shall maintain exact scale invariance. This establishes, without supersymmetry, a continuous manifold of fixed points that naturally becomes a conformal manifold when the local structure is further enforced.

We give an alternative proof of the existence of the anticanonical minimal model program for potentially klt pairs, assuming the anticanonical divisor admits a birational Zariski decomposition. Moreover, we establish a structure theorem showing that any partial anticanonical MMP starting from a potentially klt pair can be lifted to a compatible sequence of nonpositive maps between the $\mathbb{Q}$-factorial terminalizations of its successive steps.

Digital humans are lifelike virtual agents capable of natural conversation and are increasingly deployed in domains like retail and finance. However, most current digital humans operate in isolation from their surroundings and lack contextual awareness beyond the dialogue itself. We address this limitation by integrating ambient intelligence (AmI) - i.e., environmental sensors, IoT data, and contextual modeling - with digital human systems. This integration enables situational awareness of the user's environment, anticipatory and proactive assistance, seamless cross-device interactions, and personalized long-term user support. We present a conceptual framework defining key roles that AmI can play in shaping digital human behavior, a design space highlighting dimensions such as proactivity levels and privacy strategies, and application-driven patterns with case studies in financial and retail services. We also discuss an architecture for ambient-enabled digital humans and provide guidelines for responsible design regarding privacy and data governance. Together, our work positions ambient intelligent digital humans as a new class of interactive agents powered by AI that respond not only to users' queries but also to the context and situations in which the interaction occurs.

Dielectric screening plays a crucial role in shaping the electronic structure of two-dimensional (2D) materials. In 2D semiconductors, screened Coulomb interactions arising from the surrounding dielectric environment are known to induce band renormalization, which is typically understood as a rigid shift of the electronic bands. Here, we experimentally demonstrate that dielectric screening can also give rise to non-rigid, momentum-dependent band renormalization. Using temperature-dependent angle-resolved photoemission spectroscopy (ARPES), we observe pronounced changes in the electronic band structure of monolayer MoS2 on a highly oriented pyrolytic graphite (HOPG) substrate. The results indicate that temperature-driven variations in the effective interlayer separation modulate the dielectric screening experienced by monolayer MoS2. At room temperature, the screening behavior is well described by a momentum-independent monopole approximation, whereas at liquid-helium temperatures the screening evolves into a multipole-like regime, leading to momentum-dependent band shifts.

The smallest supermassive black holes (BHs), which provide constraints on BH seeds, reside in low-mass galaxies. Here, we present a systematic analysis of 990 low-mass galaxies in the SAMI Galaxy Survey to identify emission from accreting BHs using integral field spectroscopy (IFS). Employing a novel automated scoring algorithm based on spatially resolved narrow emission-line diagnostics, we find signatures of active galactic nuclei (AGNs) in 41 galaxies, as well as an additional 46 less secure candidates. The galaxies have stellar masses in the range $10^{9.4} \lesssim M_\star/M_\odot \lesssim 10^{10}$ (down to $10^{8.5}$ including less secure candidates), redshifts $z \lesssim 0.06$, and morphologies ranging from early-type ellipticals to late-type spirals. Our AGN fraction of 4% (9% including the less secure candidates) is significantly higher than those reported by studies using single-fiber spectroscopy ($\lesssim 1$--2%). Indeed, our additional analysis of single-fiber spectra of the objects in our sample demonstrates that many of our AGN candidates detected via IFS are missed. This work highlights the advantages of IFS, particularly its ability to capture extended or off-nuclear emission from accreting BHs.

We analyse the 1/16-BPS superconformal index for BPS black holes at equal charge in $AdS_5 \times S_5$, uncovering evidence for a new instability in the microcanonical ensemble along the small black hole saddle. This is indicated by instanton condensation in the matrix model description of the index. This instability occurs for black holes of radius close to, but below, the scale at which black holes become `small', and implies a new dominant phase in this region. We propose a connection to the partially deconfined phase in the field theory dual description. This would resolve recent confusion about the location of the partially deconfined phase in the BPS phase diagram and promises new avenues for understanding confinement, partial deconfinement, and the encoding of colour degrees of freedom under the holographic map. We also motivate the importance of instantons in partial deconfinement from a matrix model perspective.

Differentiation in mathematical analysis is commonly built by using ε-δ-language. This approach also works similarly for defining continuity, Gateaux (directional) derivative and Frechet derivative in normed vector spaces, in particular, in Banach spaces, where Frechet derivatives are defined as limits of ratios with respect to the norms in the considered normed vector spaces. For general topological vector spaces, if the space is not equipped with a norm, then Frechet derivatives cannot be similarly defined as in normed vector spaces. The cornerstone of this paper is the fact that the topology of every topological vector space can be induced by a family of F-seminorms, which is used to develop an extended ε-δ-language with respect to the F-seminorms. By using the extended ε-δ-language in topological vector spaces, we first define the continuity of single-valued mappings. Then we define Gateaux and Frechet derivatives as a certain type of limits of ratios with respect to the F-seminorms equipped on the considered spaces, which are naturally generalized Gateaux and Frechet derivatives in normed vector spaces. We will prove some analytic properties of the generalized versions of Gateaux and Frechet derivatives, which are similar to the analytic properties in normed vector spaces. Then we apply them to some general topological vector spaces that are not normed, such as the Schwartz space and other two spaces that are not even locally convex. For some single-valued mappings defined on these three spaces, we will precisely calculate their Gateaux and Frechet derivatives. Finally, we apply the generalized Gateaux and Frechet derivatives to solve some vector optimization problems and investigate the order monotonic of single-valued mappings in general topological vector spaces.

Laser-induced lift-off of functional surface layers is a key process in micro- and nano-fabrication; however, optimization criteria for maximizing the lifted-off area remain insufficiently defined. In analogy to the well-established theory of efficient laser ablation, where the maximum ablated volume per pulse is achieved at a peak fluence of F_0^{\mathrm{opt}} = e^{2} F_{\mathrm{th}}, we develop a theoretical framework for efficient laser lift-off driven by Gaussian beams. By analytically describing the lift-off area as a function of peak fluence, beam radius, and focus position, we demonstrate that the maximum lifted-off area is achieved at a substantially lower optimal fluence, namely F_0^{\mathrm{opt}} = e^{1} F_{\mathrm{th}}. Closed-form expressions for the optimal beam radius, maximal lift-off area, and optimal focus position are derived and validated by numerical modeling. The theory is applied to picosecond laser lift-off of copper oxide from copper, showing excellent agreement between experimental observations and model predictions. The results reveal fundamental differences between ablation- and lift-off-dominated material removal and provide practical guidelines for maximizing process efficiency in laser-assisted delamination, selective coating removal, and surface functionalization.

Ga2O3 thin films were deposited by reactive magnetron sputtering from a liquid gallium target. The influence of deposition temperature, substrate type, and discharge parameters on the structural and electrical properties was systematically investigated. Films deposited on silicon and quartz glass exhibit polycrystalline growth, whereas sapphire substrates enable highly oriented growth of b-Ga2O3 with a preferred (-201) orientation. The lowest electrical resistivity of 7x10_3 ohm.cm was obtained for films deposited on sapphire at a temperature of 585C. At this temperature, the films reach sufficient crystalline quality to enable efficient charge carrier transport and thus the manifestation of unintentional conductivity. At higher deposition temperatures, pronounced crystallization occurs; however, it is not homogeneous throughout the entire film thickness, which leads to a deterioration of the electrical properties. These results demonstrate that, despite intrinsic limitations, reactive magnetron sputtering can be successfully employed for the preparation of Ga2O3 thin films with optimized electrical properties when appropriate substrates and deposition temperatures are selected.

We formulate a geometric framework for quasistatic thermodynamics in open quantum systems by parameterizing the dynamics on a control manifold. In the quasistatic limit, the system follows a manifold of stationary states, and the work performed over a cycle is given by the flux of a curvature two-form, $W \sim \int Ω$, defined by the parametric response of the stationary state, establishing an open-system analog of classical thermodynamic area laws. \erbedit{For thermal stationary states at fixed temperature, the curvature vanishes, reflecting the integrability of the work one-form.} Beyond this limit, nonequilibrium stationary states can retain coherence in the energy representation; using a fixed-basis Lindblad model, we show that this coherence reshapes the curvature, making it anisotropic and sign-changing, so that work depends sensitively on the placement and orientation of the cycle. Quantum coherence, therefore, partitions the control manifold into regions of opposite curvature, producing geometric cancellation of work and allowing the net work over a cycle to be reduced or reversed despite dissipative dynamics. Thermodynamic work thus emerges as a curvature flux whose structure is set by thermodynamic response in classical systems and by basis misalignment between the Hamiltonian eigenbasis and the environment-selected pointer basis in open quantum systems.

The abundance discrepancy problem refers to the systematic differences observed between chemical abundances derived from collisionally excited lines (CELs) and recombination lines (RLs) of heavy ions. It remains a major unsolved problem in the study of ionized nebulae and is quantified by the abundance discrepancy factor (ADF). In this work, we present a deep integral field spectroscopic dataset covering the entire Lagoon Nebula (M 8), obtained by the SDSS-V Local Volume Mapper project, at a spatial resolution of 0.21 pc per spaxel. This unique dataset allows us, for the first time, to investigate spatially resolved maps of oxygen RL intensities (O II V1), together with maps of H I RLs, heavy-ion CELs, and dust attenuation across a whole H II region. We map the electron temperature using CELs and RLs of $O^{2+}$, CELs of $N^{+}$, and the electron density using CELs of $S^{+}$. We derive CEL-based ionic and elemental oxygen abundances and, for the first time, a spatially resolved map of the RL-based $O^{2+}$ abundance in an H II region. These measurements enable the construction of the first spatially resolved ADF($O^{2+}$) map of an H II region and yield a global mean ADF of ~0.47 +/- 0.02 dex. Focusing on the central region of M 8, where ionization is dominated by the O-type star Her 36, we find radial variations in the ADF ranging between ~0.35-0.50 dex. Our findings provide novel constraints on the spatial behavior and origin of the abundance discrepancy in H II regions.

In March 2025, Meta announced a new AI system to rank the order of the comments shown to Instagram users. With existing research showing how feed personalization systems can lead to increased polarization, the introduction of this new system raises similar questions. This paper presents a small-scale exploratory study examining whether the ranking system produces systematic differences in visible comments shown to different users, particularly for news-related content. Using four sock-puppet accounts varying in gender and political leaning, we collect visible comments on posts from ten news and ten non-news accounts. This collection is repeated twice from two VPN locations to assess location effects. We ask 1) how many visible comments vary across different users, 2) is this variation higher for news accounts than non-news accounts, and 3) can user-attributes like gender, political leaning, and location systematically explain the observed variation. Contrary to our expectations, we find that visible comments on news posts are less likely to vary across users than those on non-news posts. Variation is better explained by account metrics like comment and follower counts than by user attributes. These findings provide an initial glimpse into personalized comment ranking on Instagram and motivate larger, more systematic audits of how comment personalization may shape online discourse. To support further research, we provide the code to collect comments and the data upon request.

Let $C$ be an $[n,k]$ linear code chosen uniformly at random over a finite field $\mathbb{F}_q$ of size $q$. The following asymptotic probability of $C$ being maximum distance separable (MDS) as $q,n,k\to\infty$ is known: If $\frac{1}{q}\binom{n}{k} \to 0$, then $P(C\ \text{is MDS}) \to 1$. We demonstrate that this growth rate is in fact a threshold by proving: If $\frac{1}{q}\binom{n}{k} \to \infty$, then $P(C\ \text{is MDS}) \to 0$. A matrix is ($\textit{contiguous}$) $\textit{super-regular}$ if all of its (contiguous) square submatrices are nonsingular. The above results imply that for any $k \times k$ matrix $A$ chosen uniformly at random over $\mathbb{F}_q$, the following hold: If $\frac{4^k/\sqrt{k}}{q} \to 0$, then $P(A \text{ is super-regular}) \to 1$. If $\frac{4^k/\sqrt{k}}{q}\to \infty$, then $P(A \text{ is super-regular}) \to 0$. We also obtain the following asymptotic probabilities for two variations of the above questions: If $\frac{1}{q}\binom{n}{k} \to λ\in (0,\infty)$ and $k/n\to 0$, then $P(C\ \text{is MDS}) \to e^{-λ}$. If $\frac{k^3/3}{q} \to λ\in [0,\infty]$, then $P(A \text{ is contiguous super-regular}) \to e^{-λ}$. The number of super-regular $3\times 3$ matrices is known to be a polynomial in $q$. We show that the number of contiguous super-regular $3\times 3$ matrices is also a polynomial. Finally, for $4\times 4$ matrices, we show that the number of super-regular matrices is not a polynomial, nor even a quasi-polynomial of period less than $7$, whereas our experimental evidence suggests that the number of contiguous super-regular matrices is a polynomial.

Let $\|n\|$ stand for the integer complexity of the number $n$, i.e. for the least number of $1$'s needed to write $n$ using arbitrary many additions, multiplications, and parentheses. The two-sided inequality $3\log_3 n\leq\|n\|\leq 3\log_2 n$ for all $n$ is well known and reveals the logarithmic behaviour of the complexity function $\|n\|$. While the lower bound $3\log_3 n$ is attained infinitely many times at powers of $3$, the best upper estimate is still unknown, although there are some improvements of the trivial bound $3\log_2 n$. Besides, for $``$typical$"$ numbers, i.e. for almost all numbers $n$, the better inequality $\|n\|\leq C_{avg}\log n$ holds, where, importantly, $C_{avg}\approx 3.236<\sup_{n} \frac{\|n\|}{\log n}$. We show that in fact $\|n\|\leq C_{avg}\log n+o(\log n)$ as $n\to\infty$, which, in particular, yields that $\limsup\limits_{n\to\infty}\frac{\|n\|}{\log n}\leq C_{avg}$. We also obtain the first nontrivial lower bound $\|n\|\geq 3.06\log_3 n$ for almost all numbers $n$.

Although the deuterium fraction is known to be a powerful evolutionary tracer, its variation within individual molecular cloud cores is still poorly understood. The northern $\int$-shaped filament and 20 individual starless cores in the Orion A and B clouds were mapped in the deuterated molecules of DNC and DCO$^+$ with the Receiver 7BEE installed on the Nobeyama 45~m radio telescope. In a ~ 5' X 30' map of the northern $\int$-shaped filament in the Orion A cloud, the DNC emission is detected over the filament, whereas the DCO$^+$ emission is localized toward OMC-3, the northernmost region of the filament. The difference in distribution between DNC and DCO$^+$ can be attributed to that between N- and C-bearing molecules as previously suggested by Tatematsu et al. High DNC/HN$^{13}$C column density ratios were observed in OMC-2 and OMC-3, and low ratios in OMC-1. It seems that OMC-2 and OMC-3 still contain molecular gas close to the onset of star formation. In 3' X 3' maps of the individual starless cores in Orion, the column density ratios of DNC/HN$^{13}$C and DCO$^+$/H$^{13}$CO$^+$ are found to be rather constant locally within each core, although the core-to-core variation is not small. Similar timescales of deuterization, depletion, and dynamical evolution might explain the locally constant ratio.

Modified gravity theories (MGTs) have long been studied as alternatives to general relativity (GR) and the standard Lambda CDM cosmological model. For example, exponential f(R) models often yield better fits to observational data, suggesting that Lambda CDM may be inadequate. In this work, we argue that the gravitational and accelerating cosmology paradigm can remain close to GR and Lambda CDM if one considers broader classes of off-diagonal cosmological solutions of the Einstein equations. These solutions are constructed using the anholonomic frame and connection deformation method (AFCDM), which enables the decoupling and integration of nonlinear systems of partial differential equations in nonholonomic dyadic variables with connection distortions. The resulting off-diagonal Einstein manifolds and cosmological models are characterized by nonholonomic constraints, nonlinear symmetries, and effective cosmological constants. Such structures allow one to approximate cosmological effects, mimic features of MGTs, and describe gravitational polarization, local anisotropies, and dark energy and dark matter phenomena within GR.

The nature of the so-called G objects orbiting the Galactic Center remains unresolved. These sources exhibit compact Br$γ$ emission, extreme infrared colors, and remarkable dynamical stability through close passages to the central supermassive black hole, challenging conventional interpretations as stars or unbound gas clouds. We investigate the hypothesis that G objects are the remnants of neutron stars that have been converted into low-mass black holes through the capture of primordial black holes, a viable dark-matter candidate. We construct a population-level framework linking the abundance and spatial distribution of these remnants to the neutron-star population, the inner dark-matter density profile, and the primordial black-hole mass and abundance. Within this framework, the observed G-object population and the long-standing deficit of ordinary radio pulsars in the Galactic Center emerge as complementary consequences of the same conversion process. We further identify a suite of observational signatures-across infrared, radio, X-ray, and microlensing channels-that render this scenario empirically testable and distinguishable from stellar-envelope models. Our results show that G objects can act as sensitive probes of compact-object capture physics and of dark matter on sub-galactic scales.

Located at the BEPCII $e^{+}e^{-}$ collider, the BESIII experiment provides a robust platform for investigating (anti)hyperon-nucleon ($YN$) and antineutron-nucleon ($\bar{n}N$) interactions. This is made possible by the high production cross-sections of $J/ψ$ and $ψ(3686)$ resonances and their substantial decay branches into these baryons. Although previous studies using the beam pipe as a target demonstrated feasibility, statistical precision remains constrained by the limited material budget. To address this, we propose installing a dedicated liquid hydrogen or liquid deuterium target between the beam pipe and the Cylindrical Gas Electron Multiplier Inner Tracker. Monte Carlo simulations confirm that the added material has a negligible effect on charged particle tracking. This upgrade is expected to enhance the effective luminosity for scattering on free protons by a factor of 10--30 for $Λ$, $Σ^{+}$, $Ξ$, and $\bar{n}$ beams, enabling high-precision measurements of $YN$ and $\bar{n}N$ interactions that will significantly advance our knowledge of non-perturbative strong interactions.

As argued by Hone in the paper [Commun. Pure Appl. Math., 74(11):2310--2347, 2021], a ``mismatch" problem remained unsolved while he was investigating continued fraction expansions and Hankel determinants from hyperelliptic curves. In this paper, by introducing a new notion called quadratic orthogonal pairs for hyperelliptic functions, we resolve the corresponding problem. As further applications, we give a thorough treatment of the initial value problems for two discrete integrable systems, i.e. the bilateral Somos-4 and Somos-5 recurrences.

We develop a framework for the formation of exotic muonic kaon atoms ($Kμ$) in semileptonic $D^{0}$ decays, using the effective weak Hamiltonian, a helicity-based treatment of the leptonic current, and a nonrelativistic bound-state projection. The resulting branching ratio, $\mathrm{BR}(D^{0} \to (Kμ)ν_μ)=2.29\times10^{-10}$, is implemented in a ROOT-based code to estimate yields at RHIC, LHC, and STCF. We show quantitatively that $Kμ$ atoms-also produced through coalescence in the quark-gluon plasma (QGP)-provide a sensitive probe of low-momentum primordial muons and early time electromagnetic radiation, offering complementary constraints in an otherwise unexplored phase space for thermal dilepton and photon emission. Newly estimated dissociation cross sections in detector material indicate that secondary-vertex reconstruction should be experimentally feasible, allowing clean experimental identification of the atoms. Projected yields from QGP coalescence in LHC and RHIC heavy-ion collisions, and from $D^{0}$ decays in LHC high luminosity $p+p$ collisions indicate that the first observation of $Kμ$ atoms is within reach.