We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner automorphisms with a zero adjoined. We then describe this structure for completely simple semigroups, the full transformation monoid, and the endomorphism monoid of a finite $G$-set when $G$ is a finite abelian group. The paper ends with some open problems.

Revisiting a $50$-year-old estimate of Choi, Erdős and Szemerédi, we show that if $A \subseteq \{1, 2, \ldots, 2n\}$ satisfies $|A| \ge n + 1.2 \cdot 10^8$, then there exist five distinct integers whose pairwise sums are all contained in $A$. In order to guarantee pairwise sums of three or four integers instead, we show that one can replace the constant $1.2 \cdot 10^8$ by $1$ or $3$ respectively, which are both optimal.

In this study, we present a quantum-statistical analysis of H$_2$ and LiH diatomic molecules within the Frost--Musulin potential framework. By combining the analytical bound-state approach to the radial Schrödinger problem with the near-equilibrium Pekeris representation, we obtain a validated rotation-vibration spectrum that reproduces a physically consistent ordering of energy levels. These bound states are subsequently combined with standard translational and rotational ideal gas contributions to construct the total partition function and the corresponding thermodynamic observables of the ground state. The resulting formulation captures the Gibbs free energy deviation function for both molecules with high quantitative accuracy and provides chemically plausible trends for heat capacity and enthalpy increase over a wide temperature range. At the same time, residual errors become increasingly pronounced in derivative-sensitive quantities, particularly at high temperatures; this indicates that the dominant limitations now stem not from the local bound-state spectrum itself, but from the neglect of inelastic rotational, continuity contributions and dynamics close to dissociation. Consequently, the present results define the potential model as a compact and analytically tractable representation of the bound region, recovering a significant portion of the observed thermochemistry whilst also delineating the regime where more comprehensive molecular statistical mechanics is required.

To enable fault tolerance on millions of qubits in real time, scalable decoding is necessary, which motivates this paper. Existing decoding algorithms (decoders), such as clustering, matching, belief propagation (BP), and neural networks, suffer from one or more of inaccuracy, costliness, and incompatibility, upon a broad set of quantum error correction codes, such as surface code, toric code, and bivariate bicycle code. Therefore, there exists a gap between existing decoders and an ideal decoder that is accurate, fast, general, and scalable simultaneously. This paper contributes in three aspects, including decoder, decoder architecture, and decoding simulator. First, we propose Lottery BP, a decoder that introduces randomness during decoding. Lottery BP improves the decoding accuracy over BP by 2~8 orders of magnitude for topological codes. To efficiently decode multi-round measurement errors, we propose syndrome vote as a pre-processing step before Lottery BP, which compresses multiple rounds of syndromes into one. Syndrome voting increases the latency margin of decoding and mitigates the backlog problem. Second, we design a PolyQec architecture that implements Lottery BP as a local decoder and ordered statistics decoding (OSD) as a global decoder, and it is configurable for surface/toric code and X/Z check. Since Lottery BP boosts the local decoding accuracy, PolyQec invokes the costly global OSD decoder less frequently over BP+OSD to enhance the scalability, e.g., 3~5 orders of magnitude less for topological codes. Third, to evaluate decoders fairly, we develop a PyTorch-based decoding simulator, Syndrilla, that modularizes the simulation pipeline and allows to extend new decoders flexibly. We formulate multiple metrics to quantify the performance of decoders and integrate them in Syndrilla. Running on GPUs, Syndrilla is 1~2 orders of magnitude faster than CPUs.

Recent explorations of topological aspects in black hole thermodynamics have achieved unprecedented progress. By utilizing topological numbers, different black hole systems can be categorized into distinct universality classes. This universal classification is particularly evident in thermodynamic limits, offering valuable insights for developing a comprehensive quantum gravity framework. This review highlights the latest advancements in this field. Specifically, we outline fundamental topological frameworks underlying black hole solutions, critical points, Davies points, and the Hawking-Page phase transition. For each scenario, we calculate the associated topological numbers and analyze their physical significance. Furthermore, we explore the practical implications arising from this research.

Privacy-preserving utility mining (PPUM) aims to hide sensitive high-utility patterns while preserving the utility of the sanitized database. In practice, however, many datasets are associated with taxonomic information, which makes the identification and processing of generalized items more challenging. To address this, we investigate the cross-level privacy-preserving utility mining (CLPPUM) problem and propose a method for protecting generalized items. Based on different victim item selection strategies, we develop three CLPPUM algorithms: minimum RGISU first (Min-RF), maximum RGISU first (Max-RF), and best NSC first (Best-NSCF). Furthermore, to enable efficient victim item identification, a novel dictionary structure named GI-dic is designed to accelerate the computation of required utility metrics. Experimental results on multiple datasets demonstrate that the proposed algorithms successfully hide all sensitive cross-level high-utility itemsets without introducing artificial itemsets. The results also show that our method performs well on sparse datasets, and both Min-RF and Best-NSCF consistently outperform Max-RF. Overall, Min-RF achieves the best performance, particularly when the minimum utility threshold is low and the dataset is dense.

This paper presents a system combining symbolic execution (KLEE) with a 4-agent multi-LLM architecture for detecting memory vulnerabilities in Rust unsafe code. A central challenge we address is the incomplete-code problem: CVE database entries provide only isolated code snippets that lack struct definitions, imports, and Cargo manifests, causing all existing formal verification tools to fail at compilation with zero output. Our system resolves this through four specialized agents -- an Oracle/Validator for strategic planning, a Safety Checker for vulnerability analysis, a Code Specialist for FFI wrapper generation, and a Fast Filter for execution optimization -- that collaboratively synthesize KLEE-compatible harnesses from otherwise uncompilable fragments. KLEE's output is then ingested by graph_klee.py, which constructs a Graph Database linking CVE files, CWE categories, error types, and symbolic execution paths as typed nodes and labelled edges, enabling structured cross-CVE vulnerability queries. We evaluated our system on 31 real-world Rust CVEs spanning 11 CWE categories, achieving 90.3% wrapper compilation success where all state-of-the-art formal verification tools achieve 0%. Our system detected 1,206 critical errors across 26 files (83.9% detection rate), compared to 14 warnings across 11 files for Clippy (35.5%) and generic labels for Miri. The 4-agent architecture reduced wrapper compilation failures from 42% (single-agent baseline) to 9.7% and increased detected errors from 487 to 1,206, confirming that role specialization and structured context passing produce measurably better results than a single general-purpose model. Our replication package is publicly available at https://github.com/Zeyad-Ab/Symbolic-Execution-with-Multi-LLM-Architecture-for-Rust-Security

Let $G$ be a connected graph of order $n$. A $\{P_3,P_4,P_5\}$-factor is a spanning subgraph $H$ of $G$ such that every component of $H$ is isomorphic to an element of $\{P_3,P_4,P_5\}$. In this paper, we establish a sufficient condition on the size of the graph $G$ with minimum degree $δ$ to have a $\{P_3, P_4, P_5\}$-factor. Subsequently, we provide another sufficient condition on the adjacency spectral radius, ensuring that a connected graph $G$ with minimum degree $δ$ contains a $\{P_3, P_4, P_5\}$-factor.

Neuromorphic, or spiking, processors are increasingly being considered for use in harsh, radiation-prone environments such as space and avionics, where energy efficiency and graceful degradation are essential. In this study, we propose and experimentally validate a radiation-testing methodology specifically designed for neuromorphic processors that employ on-chip synaptic plasticity. We map the open-source ODIN SNN processor with Spike-Dependent Synaptic Plasticity (SDSP) onto the FPGA and expose it to a high-energy neutron beam while continuously monitoring MNIST classification accuracy and recording the synaptic state. From these measurements, we extract SEU cross-sections for ODIN's synaptic memory and develop a calibrated fault model to inform a complementary fault-injection campaign. By comparing inference-only and online-learning configurations, we demonstrate that enabling SDSP can significantly extend the time to application-level failure and enable partial recovery from accumulated bit flips, with modest hardware overhead.

We introduce a single dimensionless landscape function $\Jchem(ρ) = \cosh(ρ\ln \phig) - 1$, $\phig = (1+\sqrt{5})/2$, on the noble-gas-centred coordinate $ρ= d/L_p \in [0,1)$, and show that it organizes four central atomic observables: first ionization energy $\IEone$, electron affinity $\EA$, Mulliken electronegativity $χ_M$, and Pearson chemical hardness $η$, on one periodic-table axis. The outward step $Δ\Jchem^{+}$ delivers $\IEone$; the inward gap $Δ\Jchem^{-} = \Jchem(1) - \Jchem(ρ)$ delivers $\EA$ and $η$; $χ_M$ follows by Mulliken's identity. Three results establish the empirical content. (i) The within-period $\IEone$ envelope reproduces the full noble-gas-to-alkali ordering across periods 2--6: of 34 atoms compiled across periods 2--4, 26 lie on the predicted monotone descent and the 8 upward deviations occur exactly at the textbook anomaly sites $\{p^3, d^5, f^7, s^2, d^{10}\}$. (ii) Two golden-ratio identities, $\IEone(G_p)/\IEone(G_{p+1}) \approx \phig^{1/4}$ on three heavy noble-gas pairs and $\IEone(\text{halogen})/\IEone(\text{alkali}) \approx \phig^2$ on four within-period pairs, agree with NIST data to MAD $\approx 1\%$ and $\approx 5\%$, respectively. (iii) The shared kernel $Δ\Jchem^{-}$ provides single-parameter analytical fits to $\EA$ across periods 4--6 (MAE $0.3$--$0.4$~eV), to Pearson hardness $η$ across periods 2--4 (MAE $\sim 1$~eV on noble-gas maxima up to $10.8$~eV), and to Mulliken $χ_M$ across a 15-atom four-class benchmark ($R^2 = 0.73$). \edit{At the period-averaged scale level, the shared-kernel relation $\EA/η\approx C^{(p)}_{\mathrm{EA}}/C^{(p)}_η$ is supported on period-4 NIST data: the empirical nine-atom mean $\overline{\EA/η} = 0.180$ agrees with the predicted constant $0.182$ to better than $1\%$, although individual-atom scatter ($σ\approx 0.13$) is much larger.}

We quantify the excitonic coupling in the homodimer of dimeric Venus fluorescent protein using a quantum-classical hybrid workflow. Employing a transition-density coupling formalism, we calculate $J = 74.38~\mathrm{cm^{-1}}$, which is 5.6 times stronger than the far-field point-dipole estimate of $13.31~\mathrm{cm^{-1}}$. This disparity highlights the critical role of near-field multipolar effects at the 27.6~Å chromophore centroid separation. Furthermore, we argue that a separation of timescales resolves the apparent theoretical tension between robust experimental excitonic couplings and the highly decoherent biological environment. While it has been hypothesised that the fluorescent protein $β$-barrel scaffold sustains coupling by attenuating thermal fluctuations, we emphasise that the separation of timescales fundamentally applies irrespective of the exact degree of environmental noise suppression. Collective photoexcitation imprints the Davydov splitting under optical-limit dielectric screening upon absorption, preceding bulk solvent relaxation and sub-picosecond environmental dephasing. To characterise the subsequent post-absorption evolution, we employ stochastic simulations for quantum parts to model the transition from a delocalised exciton superposition to incoherent hopping between localised chromophore states.

After the Planck mission's launch in 2009, bolometers of its High Frequency Instrument (HFI) were considerably affected by cosmic rays, which necessitated several years of post-treatment to clean the data. To study the susceptibility of high sensitivity cryogenic detectors to particle impacts, IAS has developed the DRACuLA facility. We present the results of the latest two test campaigns performed on new generation of detectors.

This manuscript introduces a novel method to assess tissue oxygen concentration via the quantum entanglement (QE) of photons originating from positronium which is produced within the patient's body during positron emission tomography. We also investigate the possibility of assessing hypoxia by simultaneously detecting positronium lifetime and the positronium decay rate ratio. We introduce two distinct quantum sensing approaches. Method 1 utilizes the correlation between oxygen concentration and ortho-positronium (o-Ps) decay rates, relying on the simultaneous measurement of the mean o-Ps lifetime ($τ_{\mathrm{oPs}}$) and the $3γ$-to-$2γ$ annihilation rate ratio of o-Ps ($R_{\mathrm{oPs-3γ/2γ}}$). Method 2 introduces a novel hypothesis: that the degree of QE is sensitive to the relative contribution of annihilation mechanisms (pick-off vs. conversion), which in turn depends on oxygen concentration. We derive a formula for partial pressure of oxygen ($p\mathrm{O}_2$) as a function of $R_{\mathrm{oPs-3γ/2γ}}$ and $τ_{\mathrm{oPs}}$ and estimate the measurement accuracy required for these parameters - and for the degree of QE - to sense in-vivo oxygen pressure in the range between hypoxic and physoxic conditions. Theoretical models and quantitative estimates for $R_{\mathrm{oPs-3γ/2γ}}$, $τ_{\mathrm{oPs}}$ and for the degree of QE ($C_{\mathrm{QE}}$ ) as a function of $p\mathrm{O}_2$ are provided for water, isopropanol, cyclohexane, isooctane, and adipose tissue. In particular, applying the formulas derived under the working hypothesis that in pick-off process the photons are not entangled, we estimated that for $p\mathrm{O}_2 = 0$, the degree of quantum entanglement $C_{\mathrm{QE}}$ is equal to 0.890 for adipose, 0.886 for isopropanol, 0.867 for water, 0.818 for cyclohexane, and 0.784 for isooctane.

This paper develops the logical extension of the JFR-rg framework introduced in Part I within the same observables-centered and regime-conditional architecture. Six extensions are formalized: the Virtuous Ratchet (E1), the corrected Repression Dividend Multiplier (E2), the Debt Reduction Paradox (E3), the Multi-Country Repression Equilibrium (E4), the Demographic-$ϕ$ Clock (E5), and the Institutional Control Rights Index (E6). Together, these clarify the dynamic implications of a JFR-rg regime for path dependence, institutional erosion, growth-enhancing investment, and regime transition in high-debt, low-growth economies. The paper's claim of logical completion is architectural rather than universal. It does not claim a full welfare-theoretic or political-economy microfoundation. Rather, it shows that the principal dynamic implications internal to Part I can be stated in closed form, and that two natural excluded generalizations -- bounded stochastic perturbations and endogenous fiscal responses -- preserve the regime logic. A Minimal Equilibrium Closure is then introduced to endogenize the sovereign risk premium through a two-layer domestic demand structure and a complementarity condition. The paper also formulates the statistical problem of inferring a latent regime boundary under one-sided regime dominance. The inferential contribution is conservative by design: it constructs outer statistical summaries of the relevant boundary objects rather than forcing point classification when the observables remain compatible with multiple nearby regime readings. Comparison with Blanchard (2019), Hoshi-Ito (2014), and Mehrotra-Sergeyev (2021) shows where JFR-rg adds explanatory value in the Japanese case: not by replacing standard debt-sustainability analysis, but by endogenizing the institutional conditions under which low sovereign rates are sustained, weakened, or lost.

Waste heat recovery improves energy efficiency and reduces greenhouse gas emissions; however, much industrial and environmental heat is wasted at low temperature. Thermomagnetic recovery of waste heat has a high potential for sustainable production of electric energy, especially for low-grade waste heat where conventional technology is inefficient or infeasible. Of particular interest are thermomagnetic generators (TMG) as they require almost no mechanically moving parts, which is beneficial for high reliability. However, all existing prototypes have two remaining challenges: low efficiency and low cycle frequency. In this work, we develop a digital twin of a recent TMG with genus 3 by using multi-physics simulations. We identify shortcomings of previous simulation approaches, and describe why simulations in three dimensions are necessary, which consider coupling between magnetic, thermal, fluid flow, and electrical physics domains. We validate our model, which only uses known geometry and material parameters, by experimental data of the TMG with highest power density today, and attain 96% accuracy in open-circuit voltage and 95% accuracy in power output. This high accuracy allows us to identify the origin of both challenges for TMGs, which are not accessible by experiments. First, we uncover inefficiencies by analyzing the energy flow within a Sankey diagram. Second, we trace the transient heat flow through the generator, which identifies the factors limiting frequency. This paves the way for more efficient and faster TMGs, and their development will be accelerated by our validated digital twin.

This study examines the disposition effect in both long and short exposure positions in FTSE MIB tracking ETFs using a unique dataset of almost 9 million individual transactions. Building on the integrated framing approach, we extend the analysis to explicitly incorporate leverage and long short exposures, allowing us to assess how portfolio context and systematic risk exposure jointly are associated to investors realization behavior. Methodologically, we generalize Odean canonical Count and Total measures to wide and integrated framing, introduce a novel Value metric that captures the return thresholds required to realize gains versus losses, and implement these measures in dispositionEffect, an open-source R package for large-scale intraday data. We show that short positions exhibit a weaker disposition effect than long positions under narrow framing, but that this asymmetry reverses in positively performing portfolios under integrated framing. Systematic risk further amplifies these behavioral asymmetries across positions. Overall, our findings demonstrate that the disposition effect is not solely asset-specific, but is critically shaped by the interaction between portfolio context, position type, and systematic risk exposure. More broadly, the results are consistent with the joint predictions of Prospect Theory and Regret Theory, highlighting the central role of framing in investor decision-making.

The analyses presented herein demonstrate that neuronal electrical activity can be consistently interpreted as a manifestation of murburn redox-mediated electronic dynamics rather than as a process fundamentally driven by transmembrane ionic flux. By integrating comparison with established models, quantitative predictions, and diverse experimental observations, the murburn framework emerges as a unified and chemically grounded description of excitability. A key strength of the model lies in its predictive structure. Unlike phenomenological frameworks that rely on parameter fitting, the murburn formulation links measurable electrophysiological outputs: such as conduction velocity, waveform morphology, and threshold behavior; to physically interpretable variables including redox kinetics, transport efficiency, and environmental conditions. This enables direct experimental validation through perturbations in oxygen availability, redox balance, solvent properties, ionic strength, and external fields. Importantly, the framework extends beyond neurons to a broader class of excitable systems, including cardiac tissue, photoreceptors, and artificial redox-active materials, suggesting that excitability is a general physicochemical phenomenon rooted in reaction-transport dynamics. While the present work establishes the mid-scale dynamics of neuronal electricality, further developments are required to connect quantum-level electron transfer processes with macroscopic electrophysiological signals such as EEG and EMG. These extensions, along with targeted experimental tests, will determine the ultimate scope and applicability of the murburn paradigm.

The spin representation $(\mathbb C^2)^{\otimes n}$ has a dual canonical basis introduced by Lusztig that is important in many areas of algebra, geometry, and physics. Khovanov observed that a portion of the dual canonical basis can be viewed diagrammatically through the Temperley-Lieb algebra. We provide a simpler construction that we generalize to the entire dual canonical basis, and write explicit formulas to compute the dual canonical basis, and thus the canonical basis of the spherical module, as a byproduct. We reprove some of Khovanov's results using our new perspective. Furthermore, we use the Hecke algebra to reprove the fact that the canonical basis is indeed dual to the dual canonical basis, leading to similar results about the canonical basis in $\mathcal M^*$ and $\mathcal N^*$, the dual spaces to the spherical and aspherical modules, as a byproduct. Finally, we present an alternative axiomatic definition of the canonical basis using diagrams.

We address a fundamental challenge in space mission design and space logistics: planning interplanetary trajectories for missions that must rendezvous with multiple bodies. Such mission occur, for instance, in active debris removal, in-orbit servicing, or asteroid belt exploration. We model these problems as a variant of the Traveling salesperson problem (TSP), which we term the Keplerian TSP (KTSP). Unlike the well-studied TSP, the KTSP accounts for the motion of orbital targets, leading to time-dependent and asymmetric transfer costs that capture key real-world effects in astrodynamics. We provide a rigorous formalization of the KTSP and release a benchmark suite to support its study. Central to our approach is a time-unfolding technique that reformulates the continuous problem as a discrete optimization task in a time-expanded network. This representation makes the benchmark accessible to researchers in discrete optimization even without prior knowledge of celestial mechanics. We also develop an alternative encoding as an integer linear program using Interval-based Dynamic Discretization Discovery to handle the time-dependent nature of transfers. We leverage state-of-the-art ILP solvers to solve the KTSP instances, accompanied by a detailed computational study that highlights their strengths and limitations. We complement these exact methods with an initial solution heuristic, an improvement heuristic, and preprocessing routines that preserve optimality.

In the current work, we propose a generalization of angles and orthogonality from $L^2$ to generic Banach spaces, starting from a $L^p$ version of the Pythagorean theorem, $p\in [1,\infty)$. The starting point is conservation of energy measured in $L^1$ norm, as it occurs when considering the intrinsic mode functions decomposition in signal processing. This conservation of energy measure in $L^1$ norm is exactly the $L^1$ Pythagorean theorem. Besides the theoretical analysis, we apply the new notions in the context of preconditioning for structured large linear systems, by obtaining new classes of preconditioners. The present work contains numerical experiments and various remarks on the possible use of the given framework.

Last-mile logistics (LML) is characterized by high fragmentation, yet existing research treats this as an exogenous constraint rather than a quantifiable and optimizable system property. This paper introduces a framework for measuring LML complexity using structural entropy, derived from Boltzmann's statistical mechanics. Unlike traditional KPIs such as distance or cost, structural entropy quantifies the cardinality of the configuration space, providing a diagnostic of inherent system disorder. We establish a formal duality with Shannon entropy, linking absolute complexity burden to distributional balance. We apply our entropy framework to 6,112 Amazon last-mile routes across five U.S. cities. Current operations exhibit persistently high normalized entropy, indicating near-maximal fragmentation. A stable non-linear scaling relationship between entropy and route distance validates the metric as a predictive indicator of operational difficulty. To evaluate spatial consolidation, we develop a system-wide entropy measure accounting for all movements by both carriers and customers. We establish a theoretical conservation principle: under idealized conditions, spatial consolidation merely redistributes entropy from carrier to customer. Both idealizing conditions are violated in practice, thereby increasing total system entropy. Our system-wide measure reveals that spatial consolidation reduces carrier entropy by up to 40% under aggressive adoption but increases total system entropy by activating customer collection trips, though trip chaining can diminish this effect. Temporal consolidation, by contrast, genuinely reduces entropy by decreasing delivery events without creating new movements. By formalizing fragmentation as a measurable structural property, this research provides a new lens for network design, consolidation policy, and evaluation last-mile system performance.

We present an analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric, focusing on highly symmetric configurations on the unit sphere $\mathbb S^2$. Three discrete uniform models are analyzed and closed-form expressions for optimal quantizers and mean-square errors are derived. (I) For $N$ equally spaced points on the equator, exact error formulas are obtained for both divisible and non-divisible cases, showing that optimal Voronoi cells form contiguous arcs with midpoint representatives. (II) For two antipodally symmetric small circles at latitudes $\pmϕ_0$, each with $M$ longitudes, we establish a no-cross-circle Voronoi phenomenon, symmetry-preserving optimality, and finite-sum error formulas with curvature-dependent bounds and asymptotics. (III) For a single small circle at latitude $ϕ_0$, analogous formulas are proved and curvature is shown to reduce distortion by a factor $\cos^2ϕ_0$ while preserving the $n^{-2}$ decay rate. Across all models we rigorously formulate the block-midpoint principle: optimal Voronoi cells are contiguous azimuthal blocks whose representatives are azimuthal midpoints. These explicit benchmark models clarify curvature effects and support further developments in quantization on curved manifolds.

In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of controllers to stabilize the system to a desired state via Lyapunov functionals, and to ensure forward invariance of a desired subset via boundary control barrier functionals. The control input is then selected from the intersection of those sets via a convex optimization problem. We determine sufficient conditions to ensure the existence of an optimal boundary control problem achieving both stability and invariance for a generic traffic flux function. Simulation results showcase the behavior of the proposed optimization-based controller applied to conservation laws with several traffic flow functions.

We develop a homotopy-based framework for computing Karush-Kuhn-Tucker (KKT) points of multiobjective optimization problems. The proposed homotopy map continuously deforms an easily solvable system into the KKT conditions associated with the multiobjective problem, yielding a deterministic and structure-preserving continuation path. Under mild regularity assumptions, we establish global convergence of the homotopy trajectory to a Pareto-stationary solution for any initial point chosen in the interior of the feasible region. In numerical experiments, the method exhibits robust convergence even when initialized from nonfeasible points, indicating stability beyond the theoretical guarantees. Efficient predictor-corrector continuation strategies are employed to trace the homotopy path. Numerical results on benchmark problems compare the proposed approach with classical scalarization methods and the evolutionary algorithm NSGA-II, demonstrating competitive computational efficiency and consistent solution quality. These results highlight the effectiveness of the homotopy framework for constrained multiobjective optimization and motivate extensions to more general problem settings and adaptive parameter strategies.

This paper proposes novel fixed-time (FXT) convergent neurodynamic approaches for solving mixed variational inequality problems (MVIs). A class of first-order proximal neurodynamic models (PNMs), including time-varying proximal neurodynamic models (TVPNMs), is developed to guarantee FXT convergence to the solution of MVIs from arbitrary initial conditions. Rigorous convergence and stability analyses are established under the assumptions of strong pseudomonotonicity and Lipschitz continuity, using Lyapunov stability theory. The proposed methods exhibit FXT convergence from any initial point, with convergence speed significantly enhanced through the strategic design of time-varying coefficients. Explicit upper bounds on the settling time are derived for the time-varying neurodynamic models. In addition, the robustness of the proposed approaches against bounded noise disturbances is analyzed. The applicability of the proposed framework is further demonstrated for composite optimization problems and minimax optimization problems. Also, numerical examples are presented to demonstrate the effectiveness and convergence behavior of the proposed methods.

This paper is a sequel to arXiv:2511.01024 (Base 1), where an axiomatic framework for angles and the foundations of difference-angle geometry were introduced. In difference-angle geometry, where the difference of slopes of lines is treated as a primary angular quantity (the difference angle), we reconstruct the focal structure of parabolas from a difference-angle-theoretic viewpoint and develop the associated algebraic and analytic structures. First, we introduce the difference-angle focal function and define the focus of a parabola constructively as its zero set. This approach yields a formulation of the parabolic power that differs from that presented in Base 1. Next, by interpreting the power as a classical representation of an inner product, we derive a difference-angle version of the parallelogram theorem via a polarization identity, and thereby define the difference-angle inner product as a pseudo-inner product. The robustness of this structure is substantiated by deriving a difference-angle version of Stewart's theorem based solely on computations involving the difference-angle inner product. Furthermore, we define the parabolic trigonometric functions cosp(theta) and sinp(theta) (together with related functions) associated with a difference angle (theta), and show that they satisfy identities corresponding to the first and second cosine laws in Euclidean geometry. Finally, we reexamine the Cayley-Klein angle and distance derived from Laguerre's formula, and in particular verify that the existing Cayley-Klein angle satisfies the axiomatic system for angles introduced in Base 1. We then show that, in the parabolic limit of the absolute conic, the difference angle and the difference-angle norm arise naturally as the linear degeneration of the logarithmic cross ratio.

We advance Matkovič ideas, originally applied to complete the classification of tight structures on small Seifert fibred $L$-spaces, to show the existence of contact structures on Brieskorn spheres which are tight and zero-twisting. This uncovers a phenomenon that has never appeared in literature before: namely, that a contact structure $ξ$ on a 3-manifold can be such that $\widehat c(ξ)$ is non-vanishing, but $c^+(ξ)$ is zero.

We adapt the Ozsváth-Szabó full path algorithm to every star-shaped graph and establish a correspondence between negative-twisting tight contact structures on any Seifert fibred space over $S^2$, and its Heegaard Floer homology groups equipped with the Alexander filtration induced by the regular fibre. This provides the complete classification of negative-twisting structures on these manifolds; in particular, we distinguish them by their contact invariant $c^+$. We prove that every such structure is symplectically fillable and extend a known obstruction to Stein fillability. In addition, we show that the number of negative-twisting structures can be expressed combinatorially in terms of the Seifert coefficients of the star-shaped graph, while their $d_3$-invariant and homotopy type are determined explicitly through our correspondence. Our results also complete the classification of fillable structures on any small Seifert fibred space.

We numerically study a formation of near extremal horizons from a gravitational collapse of radially symmetric gravitational waves in $4+1$ dimensions within the framework of pure Einstein gravity with positive cosmological constant. Evolution of a regular initial data with cosmological horizon leads to a formation of a black hole with mass exceeding $99\%$ of the extremal value corresponding to the black hole and cosmological horizons coinciding. We demonstrate how our results fit within the framework of characteristic gluing, and present some evidence that the third law of black hole thermodynamics may not hold in the cosmological context, where the extremality corresponds to the maximal mass of the Schwarzschild black hole in de--Sitter space.

A search is presented for a light charged Higgs boson H$^\pm$ in top quark pair production ($\mathrm{t\bar{t}}$), where one of the top quarks decays to an H$^\pm$ and a bottom quark, while the other decays to a W$^\mp$ boson and a bottom quark. The H$^\pm$ is assumed to decay into a charm and a strange quark, whereas the W$^\mp$ boson decays into a charged lepton (electron or muon) and a neutrino. Results are reported based on proton-proton collision data at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The analysis probes H$^\pm$ masses in the range 40 to 160 GeV using the invariant mass spectrum of the two light jets, where light jets are defined as jets that do not satisfy the bottom quark tagging requirement. The observed yield is found to be consistent with standard model predictions. Upper limits are set on the branching fraction $\mathcal{B}$(t $\to$ H$^\pm$ b), with values in the range of 0.07$-$1.12% at 95% confidence level, under the assumption that $\mathcal{B}$(H$^\pm$ $\to$ cs) = 100%. These are the first direct limits on charged Higgs bosons produced in top quark decays for masses between 40 and 50 GeV, and the most stringent limits to date in the 70$-$110 GeV range.