We provide a recursive construction of an acyclic matching (also known as a gradient vector field, an equivalent notion to a discrete Morse function) on the independence complex of a graph with a simplicial vertex using given acyclic matchings on the independence complexes of specific subgraphs. As an application, we determine the homotopy type of the independence complexes of the family of chordal graphs and of a class of graphs generalising the comparability graphs of grid posets in an algorithmic and combinatorial manner via discrete Morse theory, some of which were previously obtained by sophisticated homotopy theoretic techniques. Even when the homotopy type is not easily determinable, our construction may be applied to obtain a pre-processing framework for efficient homology computation.

A time-dependent theory for the interactions between spatially separated lossy cavities in a homogeneous background medium using quantized quasinormal modes (QNMs) is presented. The cavities interact via a bath of traveling photons, described by non-bosonic operators that are orthogonal to the open-cavity QNMs. The retarded (i.e., time-delayed) inter-cavity dynamics are fully described by system-bath correlation functions, in which the emission from one cavity appears as the input field for another. Coupling between quantum emitters (described as two-level systems), placed inside a cavity or embedded in an external medium, and the electromagnetic field (cavity modes and bath photons) is included in the theory, which gives rise to both bath-mediated and QNM-mediated interactions between the emitters.

The impact of open-flavor thresholds on the quarkonium spectrum has been a subject of study since the introduction of the Cornell potential and has been quantified through various phenomenological approaches, most notably the $^3P_0$ model. We revisit this problem using the Born--Oppenheimer effective field theory (BOEFT), an effective field theory systematically derived from QCD by exploiting hierarchies of energy scales and symmetries. Within the BOEFT, open-flavor threshold effects emerge from the mixing between quarkonium and tetraquark static potentials sharing the same Born--Oppenheimer quantum numbers. The shapes of the static potentials are constrained by lattice QCD calculations. Furthermore, we account for the distinctive behavior of the BOEFT tetraquark static potentials at short and large distances: at short distances they are repulsive, reflecting the color-octet configuration of the heavy quark-antiquark pair, while at large distances they asymptotically approach heavy-light meson-antimeson thresholds. To quantify threshold effects on the quarkonium spectrum below threshold, we solve a set of coupled Schrödinger equations dictated by the BOEFT, whose only free parameter, the adjoint meson mass, is fixed to the mass of the $χ_{c1}(3872)$ state. These coupled equations are solved both in the spin-isospin averaged threshold limit and, for the first time, including the spin splittings of the physical thresholds. We validate our results by computing the same threshold effects as self-energy corrections to the quarkonium propagator. We compare our predictions with existing experimental data and previous literature. Finally, we provide a field-theoretical interpretation of the pair-creation constant $γ$ appearing in the $^3P_0$ model.

The field of attosecond physics has expanded significantly in recent years, yet experimental facilities supporting attosecond pump attosecond probe spectroscopy remain rare. Here, we present a newly constructed beamline for the generation and application of energetic, isolated extreme ultraviolet (XUV) and soft X-ray attosecond pulses via upscaling of high-harmonic generation (HHG) in a gas medium. The fundamental properties of the HHG radiation energy, beam profile, spectrum, and divergence are characterized and optimized. The source delivers up to 55 nJ of pulse energy within the Zr window (65-150 eV) with high stability (~5-10) and a divergence of 0.1 mrad. Numerical simulations identify optimal operating conditions consistent with experimental results. Temporal super-resolution of the driving laser is applied, resulting in a broadened spectral continuum. Furthermore, the beamline includes a split-and-delay stage before focusing the HHG radiation to a <6 um spot for pump-probe experiments using two distinct focusing optics. Spatially resolved ion microscopy is employed to trace the generated ions at the focus. The presented beamline is designed for nonlinear XUV studies with attosecond isolated pulses.

Large-scale pre-training of Foundational Models (FM) constitutes a computationally intensive first phase for enabling AI across diverse scientific and societal applications. This first phase has positioned High-Performance Computing (HPC) facilities as indispensable backbones of "Sovereign AI" initiatives. While the massive throughput requirements of FM pre-training align with the traditional capability-oriented mission of HPC, subsequent phases of the AI lifecycle, typically referred to as fine-tuning and inference, introduce operational paradigms that can conflict with established batch-processing environments. Moreover, these phases are not computationally trivial: they often require substantial high-end compute resources while exhibiting hardware utilization patterns that differ significantly from those of pre-training. This paper addresses the architectural and strategic challenges of operationalizing a complete AI lifecycle within a national supercomputing facility. We present a hybrid cloud-native platform being developed and deployed at the Swiss National Supercomputing Centre (CSCS) that combines diskless GPU-enabled HPE Cray EX compute nodes with virtualized commodity infrastructure. Orchestrated by Kubernetes, this novel service architecture bridges the gap between HPC batch processing and service-oriented workflows. We report our initial investigations into fine-tuning pipelines and highly available inference services, analyzing the associated trade-offs while improving user productivity. Our findings offer a blueprint for enabling supercomputers to integrate "AI Factories" services and workflows, supporting AI innovations into end-to-end scientific and industrial use cases.

Context. Be stars are presently viewed as B-type stars surrounded by a disc fueled by the star itself during episodicexcretion events. The origin of these events are poorly understood.Aims. This article aims to determine whether or not surface equatorial Kelvin waves can be unstable and therefore canplay a role in the triggering of the Be phenomenon.Methods. We first derive an analytical expression for gravito-inertial modes in the shallow-water framework. Then, weinvestigate numerically the evolution of equatorial Kelvin modes as system parameters vary. The study is extended tothick-layer configurations with a constant density fluid. We then analyze the stability of these modes under differentialrotation and viscous effects.Results. We show that equatorial Kelvin waves still exist in a spherical shell of finite thickness, but that their equatorialconfinement is weaker. At low azimuthal wavenumbers, Kelvin waves are in the inertial waves frequency band and thusget specificities of inertial waves like shear layers associated with singularities of the Poincaré equation. These shearlayers are new dissipative structures for Kelvin waves. When a radial (shellular) differential rotation is imposed, we showthat equatorial Kelvin waves can be destabilised provided that differential rotation and viscosity are in an appropriaterange. The non-monotonic behaviour of the growth rate of the instability is traced back to the rise of a critical layerwhere the fluid azimuthal velocity equals the phase speed of the surface waves.Conclusions. This study provides new insights into the behavior of equatorial Kelvin waves in astrophysics, particularlyin rapidly rotating stars. The results reinforce the idea that gravito-inertial waves, and more specifically the equatorialKelvin waves, can be unstable and thus be key parts in the mechanisms leading to the Be phenomenon.

Magnetic fields play a fundamental role in the formation of protostellar winds. In the magneto-centrifugal models, poloidal magnetic fields launch winds from accretion disks, and fast-rotating gas twists the fields into toroidal geometry that collimates and accelerates winds through magnetic hoop stress. However, toroidal fields in protostellar winds remain observationally unresolved. Here we report polarization observations of carbon monoxide emission toward the NGC1333 IRAS 4A protostellar outflow. The inferred magnetic fields are perpendicular to the outflow axis and aligned with the rotational structure of the outflow, indicating toroidal fields with strengths of a few milligauss, sufficient to collimate and accelerate the outflow at several hundred astronomical units from the protostar. A linear correlation is found between the curl of plane-of-the-sky magnetic field and the line-of-sight electric current density. Our analysis provides better constraints on ion-electron drift velocity in protostellar outflows and supports rotating outflows driven by the magneto-centrifugal mechanism.

High-frequency focused ultrasound is widely used in biomedical applications such as high-resolution imaging, neuromodulation, particle manipulation, and so on. However, dynamic tuning of the focal plane in conventional systems often relies on mechanically adjustable components or array-based control with complex system and high cost. In this work, an optically transparent, planar compact piezoelectric ultrasonic transducer was designed and fabricated by truncating an ideal spherical wavefront with a plane, enabling high-frequency focused ultrasound generation and convenient integration with microscopic platforms. The acoustic field was characterized experimentally at the focal plane under the design frequency and at propagation planes near the design frequency to evaluate the focal tuning. An approximate linear relation between the focal length and driving frequency near the design one is derived theoretically, and the finite-range tuning behavior is interpreted using the stationary-phase condition. Both theory and experiment show that the focal length varies approximately linearly with excitation frequency near the design frequency. Water-tank measurements agree well with the theoretical prediction, confirming the proposed model. This work provides a simple and cost-effective approach for focal tuning in compact high-frequency ultrasound devices.

Lithium Iron Phosphate (LFP) Battery Energy Storage Systems (BESSs) are a key enabler of the energy transition. However, they are known to exhibit significant inaccuracies in the estimation of their State of Charge (SOC). Such estimation errors can directly impact the participation of BESSs in electricity markets. In this work, we demonstrate that neglecting SOC uncertainty in battery bidding can lead to significant delivery failures, including the inability to meet promised frequency reserves. To address this risk, we investigate bidding strategies that account for SOC uncertainty. We propose three constraint-tightening optimization approaches of increasing complexity: (i) a fixed-margin formulation, (ii) an adaptive-margin optimizer, and (iii) an uncertainty-aware optimization model. The latter explicitly accounts for the decision-dependent nature of the uncertainty. Numerical results demonstrate that while all three approaches robustify against SOC uncertainty, the uncertainty-aware formulation outperforms the others in maximizing revenue while ensuring reliable frequency reserve provision. This highlights the significance of treating SOC uncertainty as an endogenous process within the operational strategy.

A precision measurement of the muon charge asymmetry from $W$-boson decays in proton-proton collisions at $\sqrt{s}$ = 13 TeV is presented. The analysis utilizes data corresponding to an integrated luminosity of 5.1 $fb^{-1}$, recorded by the LHCb detector during 2016, 2017 and 2018. The asymmetry is measured for muons with transverse momentum between 25 and 55 GeV and pseudorapidity between 2.0 and 4.5. This result represents the most precise determination of the muon charge asymmetry in the forward region to date, exhibiting excellent agreement with next-to-next-to-leading-order predictions in perturbative quantum chromodynamics.

In this paper we study existence and uniqueness of solutions for a very general class of doubly nonlinear diffusion equations on metric graphs, which provide the appropriate mathematical framework to describe complex tubular networks in which axial diffusion is the main focus. Some important particular cases covered in our study are the Porous Medium Equation and the evolution equation for the $p$-Laplacian, but we also consider the case in that diffusion changes from one edge to another, which takes into account the influence of the properties of the tubules forming the network on axial diffusion. Furthermore, the problem is studied under non-homogeneous Neumann-Kirchhoff conditions on the vertices of the graph.

Chiral phonon-polaritonic states are of interest for handedness-dependent light-matter interactions, yet their realization and magnetic control remain challenging, while direct magneto-optical tunability of phonon-polaritonic media is limited. Here, we propose a hybrid platform in which an hBN phonon polariton couples to a chiral bound state in the continuum supported by a magneto-optical photonic crystal, enabling strong and selective photonic coupling. The interaction gives rise to pronounced mode splitting and the formation of hybrid states, and their modal composition is quantified by phonon-proportion analysis and described by a coupling theory. Importantly, the hybridization can be controlled by magnetic bias through the magneto-optical response of the photonic component, providing control over the modal composition and spectral response. In addition, the hybrid states exhibit handedness-selective absorption under circularly polarized excitation. This work offers a feasible route toward magnetically tunable chiral phonon-polaritonic devices and hybrid polaritonic functionalities

We investigate the impact of a late-time transition in the standardized absolute magnitude $M$ on the best-fit values of cosmological parameters using the Pantheon+ dataset. Extending previous analyses which focused on flat $Λ$CDM, we examine this transition within flat $Λ$CDM, wCDM, and CPL cosmologies, as well as a model-independent cosmographic expansion, employing both frequentist ($χ^2$ minimization with \textit{AIC}/\textit{BIC}) and Bayesian (MCMC and Nested Sampling) inference frameworks. We confirm that the data consistently favor a step in absolute magnitude of $ΔM \simeq 0.19~\mathrm{mag}$ at a characteristic distance of $d_{\mathrm{crit}} \approx 20~\mathrm{Mpc}$. The inclusion of this transition leads to a statistically significant improvement in the quality of fit and has a distinct impact on parameter estimation: it induces a systematic increase in the inferred Hubble constant of approximately $2\%$ across all tested models. In contrast, we find that the dynamical parameters governing the background expansion, including the matter density $Ω_m$ and the dark energy equation of state ($w_0, w_a$), remain stable and largely unaffected. These results indicate that the $20~\mathrm{Mpc}$ feature acts primarily as a low-redshift calibration shift rather than a modification of the late-time expansion history.

We prove conditions under which the total space of the pullback of a sphere fibration over a connected sum is homotopy equivalent to a connected sum with a gyration. Existing results of this type often depend on geometric methods. We develop new methods based only on homotopy theory, allowing for generalisations from manifolds to Poincaré Duality complexes and from integral settings to local ones. Several applications are given.

The sine-Gordon model serves as a foundational $1+1$-dimensional quantum field theory with numerous applications in condensed matter physics. Despite its integrability, characterizing its finite-temperature behavior remains a significant theoretical challenge. Here we use the previously developed Method of Random Surfaces (MRS) to evaluate two-point and higher-order correlation functions. We cross-check these results with known analytical limits, demonstrating that the MRS provides reliable, non-perturbative data in intermediate regimes where traditional form-factor expansions and semiclassical methods are inapplicable. Furthermore, we derive an exact result for arbitrary $N$-point functions satisfying an appropriate selection rule, providing a direct computational method for complex multi-point observables at finite temperature. We also characterize the non-Gaussianity of correlations and demonstrate that the results align with intuitive theoretical expectations.

We present an additive $\varepsilon n^{2}$-approximation algorithm for the Graph Edit Distance problem (GED) on graphs of VC dimension $d$ running in time $n^{O(d/\varepsilon^{2})}$. In particular, this recovers a previous result by Arora, Frieze, and Kaplan [Math. Program. 2002] who gave an $\varepsilon n^{2}$-approximation running in time $n^{O(\log n/\varepsilon^{2})}$. Similar to the work of Arora et al., we extend our results to arbitrary Quadratic Assignment problems (QAPs) by introducing a notion of VC dimension for QAP instances, and giving an $\varepsilon n^{2}$-approximation for QAPs with bounded weights running in time $n^{O(\varepsilon^{-2}(d + \log\varepsilon^{-1}))}$. As a particularly interesting special case, we further study the problem $\varepsilon$-$\mathsf{GI}$, which entails determining if two graphs $G,H$ over $n$ vertices are isomorphic, when promised that if they are not, their graph edit distance is at least $\varepsilon n^{2}$. We show that the standard Weisfeiler--Leman algorithm of dimension $O(\varepsilon^{-1}d\log(\varepsilon^{-1}))$ solves this problem on graphs of VC dimension $d$. We also show that dimension $O(\varepsilon^{-1}\log n)$ suffices on arbitrary $n$-vertex graphs, while $k$-WL fails on instances at distance $Ω(n^{2}/k)$.

We review the role of primordial black holes (PBHs) for illuminating the dark ages of the cosmological evolution and as dark matter (DM) candidates. We elucidate the role of phase transitions for primordial black hole formation in the early Universe and focus our attention on the cosmological QCD phase transition within a recent microscopical model. We explore the impact of physics beyond the Standard Model (SM) on the cosmic equation of state and the probability distribution for the formation of PBHs which serve as candidates for DM and contribute to present-day binary black-hole merger events.

This paper considers a new secure gradient coding problem with uncoded groupwise keys, formalized as a (K, N, N_r, M, S) secure gradient coding model, where a user aims to compute the sum of the gradients from K datasets with the assistance of N distributed servers. We consider arbitrary heterogeneous data assignment, where each dataset is assigned to at least M servers. The user should recover the sum of gradients from the transmissions of any N_r servers. The security constraint guarantees that even if the user receives the transmitted messages from all servers, it cannot obtain any other information about the datasets except the sum of gradients. Compared to existing secure gradient coding works, we introduce a practical constraint on secret keys, namely uncoded groupwise keys, where the keys are mutually independent and each key is shared by precisely S servers. An achievable secure gradient coding scheme with uncoded groupwise keys is proposed, which is then proven to be optimal if S > M and to be order optimal within a factor of 2 otherwise.

The RELICS (REactor neutrino LIquid xenon Coherent elastic Scattering) experiment employs a dual-phase liquid xenon time projection chamber to search for Coherent Elastic Neutrino-Nucleus Scattering (CE$ν$NS) induced by reactor neutrinos. To detect these sub-keV nuclear recoils and minimize signal attenuation, it is critical to maintain a sufficiently low impurity concentration in the detector. This work presents a comprehensive purity evolution model developed to describe impurity migration inside the detector. Utilizing measured material outgassing rates as input parameters, the model incorporates non-uniform transport mechanisms of the impurities, including circulation, vaporization, and condensation. The model is validated using data from a dedicated prototype detector. Based on this validated model, projections for the purification performance of the upcoming RELICS-10 and RELICS-50 detectors are provided.

The shaping of planetary nebulae on their evolution from asymptotic giant branch circumstellar envelopes to their final, most often axisymmetrical, form is still a process with many unknown details. The key to understanding the whole shaping process is the study of the transition objects called pre-planetary nebulae (pPNe). In this context, modelling tools must be kept to the standard of radio telescope capabilities, so we can make the most of the data they collect. In this work we first present the newest update of the SHAPE and SHAPEMOL modelling tools, adding ten new molecular species to be reproduced together with other general improvements. Later, we put this new update into practice to study M1-92, a pPN with a rich chemistry that can provide valuable information on its origin and shaping. We created a 3D morpho-kinematical model of the nebula in SHAPE that is able to reproduce 23 line profiles from the IRAM 30m telescope and HIFI/HSO and five maps from IRAM NOEMA. The observational dataset is reproduced simultaneously under the same physical conditions, adjusting only the relative abundance of the different species. We obtained a full description of the nebula's physical and chemical properties, and we provide the total estimates for mass (0.79 $M_\odot$), linear momentum (4.10$\times10^{39}$ g cm s$^{-1}$), and kinetic energy (6.48$\times10^{45}$ erg) as well as their detailed distribution across the nebula. We also analysed the isotopic ratios, finding robust discrepancies (values of 10 versus 30) in the $^{12}$C/$^{13}$C ratio across structures depending on their age.

Micro-Doppler signatures are a proven modality for discriminating between drones and birds, but their reliability degrades in low-SNR, data-constrained settings where deep learning models often fail. This paper presents a systematic study of ten statistical and physics-motivated handcrafted features for micro-Doppler classification under controlled signal degradation, using a publicly available 77 GHz FMCW radar dataset. Spectrograms are corrupted with additive white Gaussian noise, phase noise, and their combination across SNRs from -10 dB to 10 dB and phase noise levels from 1 to 10 degrees. Features are evaluated using stratified 5-fold cross-validation with Support Vector Machine and Random Forest classifiers, using fixed hyperparameters across all noise conditions. On clean data, both models achieve mean accuracy of 0.916, with F1 scores of 0.909 (SVM) and 0.892 (Random Forest). Under severe noise, entropy-based and side-lobe features remain robust, yielding F1 scores up to 0.773 and 0.831, respectively. Permutation-based importance analysis shows that some features retain complementary discriminative power even when their individual importance is low. These results highlight the value of principled feature design and provide insight into feature robustness for interpretable radar classification systems.

Modern computing workloads demand energy-efficient, high-bandwidth interconnects, motivating photonic interposers as an alternative to electrical links. Here we demonstrate a compact 3D silicon nitride (SiN) photonic interposer prototype comprising two routing layers, with the 3D routing scheme optimized by a global optimization algorithm. The 3D interposer realizes a fully connected 12-node optical network that reduces the total number of intralayer crossings from 495 for all-planar routing to merely 150 (69.7% reduction), below the theoretical lower bound of 153 for all-planar interconnects. Comparing the two schemes, our 3D design achieves a 45.8% reduction experimentally in the average loss per waveguide. The proposed 3D routing architecture also features inherent symmetry and is scalable to higher node counts, flexible node placements, additional routing layers, and other operating wavelengths, enabling denser, lower-loss photonic interposers for next-generation scale-up and high-performance computing (HPC) systems.

Precise on-chip dispersion control is essential for advanced integrated photonic technologies, enabling applications ranging from high-speed communications and sensing to signal processing and biomedical imaging. However, existing on-chip dispersion control methods still suffer from substantial loss and a limited dispersion-bandwidth product (DBP) far from application needs. As a result, on-chip systems continue to rely exclusively on off-chip dispersion control solutions provided by optical fiber or bulky free-space optics. To overcome these limitations, we design and fabricate meter-long chirped spiral Bragg gratings (CSBGs) on the ultra-low-loss silicon nitride (SiN) photonic platform for advanced dispersion control. Our device achieves a 10-nanosecond group delay with customizable bandwidths exceeding 10 nanometers within a compact footprint of only 30 $\text {mm} ^2$, surpassing the physical limits of fiber-based grating devices. More importantly, CSBGs can simultaneously possess the characteristics of high stability, low latency, and a large DBP, thanks to the ultra-low-loss SiN platform with a loss of only 0.3 dB/m. Leveraging the precise and stable dispersion profile, we demonstrate high-fidelity pulse shaping and compression of electro-optic frequency combs (EOCs) with a 1-GHz repetition rate centered across the entire reflection bandwidth. The compressed pulse has an on-chip peak (average) power of 21.6 watts (580 milliwatts). Furthermore, we showcase for the first time the application of on-chip pulse-compressed EOC in wavelength-swept coherent anti-Stokes Raman scattering (CARS) microscopy. Our work provides integrated photonics with a long-sought, scalable, and robust solution for high-performance on-chip dispersion control, empowering a new generation of on-chip functionalities.

This paper proposes a dynamic network framework for uncovering latent community paths in high-dimensional VAR-type models. By embedding a degree-corrected stochastic co-blockmodel (ScBM) into the transition matrices of VAR-type systems, we separate sending and receiving roles at the node level and summarize complex directional dependence in an interpretable low-dimensional form. Our method integrates directed spectral co-clustering with eigenvector smoothing to track how directional groups split, merge, or persist over time. This framework accommodates both periodic VAR (PVAR) models for cyclical seasonal evolution and generalized VHAR models for structural transitions across ordered dependence horizons. We establish non-asymptotic misclassification bounds for both procedures and provide supporting evidence through Monte Carlo experiments. Applications to U.S.\ nonfarm payrolls distinguish a recurrent business-centered core from more mobile, seasonally sensitive sectors. In global stock volatilities, the results reveal a compact U.S.-centered long-horizon block, a Europe-heavy developed core, and a more dynamic short-horizon reallocation of peripheral and bridge markets.

In 2006 and 2014, the Antarctic Impulsive Transient Antenna (ANITA), a balloon-borne radio observatory flying over Antarctica, detected two strange upward-going radio pulse events that have not yet been explained by our current understanding of physics. These were not signals reflected by the ice and therefore it must have been an air shower originating from a cosmic ray coming from under the Antarctic ice, but this hypothesis was also ruled out by various data analyses. The CPT gravity theory and its associated cosmological model, the lattice Universe, can instead explain those events in a completely natural and spontaneous way, without any additional assumptions beyond general relativity and the expected matter-antimatter symmetry of the Universe on which they are based. Together with the antihelium candidate events from AMS-02, the anomalous ANITA events can thus lend further validity to a cosmological model that has already achieved considerable success in explaining the accelerated expansion of the Universe, without the need for dark energy. These events thus add to a series of problems unsolved by standard cosmology and physics, but whose solution is straightforward, spontaneous and natural within the framework of CPT gravity, without the need for ad hoc hypotheses and unknown ingredients.

We develop the parabolic weak porosity to characterize the parabolic Muckenhoupt $A_1$ weights with time-lag. Our main result shows that a nonempty closed set is parabolic weakly porous if and only if the parabolic distance function of the set to a negative power is in the parabolic Muckenhoupt $A_1$ class. We apply a novel stopping time argument in combination with the translation and doubling results for the parabolic weakly porous sets.

Fault-tolerant quantum computers (FTQCs) based on surface codes and lattice surgery have been widely studied, and there is strong demand for a framework that can identify logical operations with low space-time cost, verify their functionality and fault tolerance, and demonstrate their optimality within a given search space, much like electronic design automation (EDA) in classical circuit design. In this paper, we propose KOVAL-Q, an EDA kernel that verifies and optimizes surface-code logical operations by formulating them as a satisfiability (SAT) problem. Compared with existing SAT-based frameworks such as LaSsynth, our method can handle logical qubits with more flexible surface-code encodings, both as target configurations and as intermediate states. This extension enables the optimization of advanced layouts, such as fast blocks, and broadens the search space for logical operations. We demonstrate that KOVAL-Q can determine the minimum execution time of fundamental logical operations in given spatial layouts, such as $d$-cycle logical CNOTs and $2d$-cycle patch rotations. Their use reduces the execution time of widely studied FTQC applications by about 10% under a simplified scheduling model. KOVAL-Q consists of three subkernels corresponding to different types of constraints, which facilitates its integration as a submodule into scalable heuristic frameworks. Thus, our proposal provides an essential framework for optimizing and validating core FTQC subroutines.

Nash equilibrium is a fundamental solution concept in extensive-form games, while its efficient computation is still far from straightforward. This paper considers finite $n$-player extensive-form games with perfect recall under the sequence-form representation. Unlike existing approaches, which mainly treat the sequence form as a compact computational reformulation, we develop a direct sequence-form definition of Nash equilibrium. Building on this, we rigorously establish the associated sequence-form Nash equilibrium system through an equivalence proof with mixed-strategy Nash equilibrium. On this basis, we propose a single-stage interior-point differentiable path-following method for equilibrium computation. The method uses logarithmic-barrier regularization to generate a differentiable equilibrium path in the interior of the realization-plan space, leading to favorable numerical stability and convergence properties. Numerical results show that the proposed method is effective and computationally efficient.

In the preceding decade, Andrews and Newman resurrected the concept of a `minimal excludant' of a partition ($mex$, for short), namely, the least positive missing integer in a partition. Subsequently, several authors have not only studied its generalizations, analogues and the like but also connected the mex to several important partition statistics. In the present paper, we study the set of missing positive integers as a whole, in two different classes of partitions, namely, unrestricted partitions and overpartitions. To be precise, a $missing \ integer$ is a positive integer that is less than the largest part of a partition and which does not occur as a part. In particular, we examine the number of partitions with a given number of missing integers, determine congruences for two pairs of functions associated to them, and propose three bias type inequality conjectures for these functions.

Continuous contactless respiration monitoring of co-sleeping subjects faces a dilemma: conventional single-site multiple-input multiple-output (MIMO) radars struggle with limited angular resolution for closely spaced individuals, while distributed radar networks typically require complex hardware synchronization. To address these limitations, this paper proposes non-coherent multi-site single-input-single-output (SISO) radar systems that completely eliminate the need for physical synchronization cables or common reference clocks. The fundamental challenge of ghost target ambiguity in such non-coherent multilateration is resolved through a novel physiological-feature-assisted suppression technique. By exploiting the inherent statistical independence of individual respiratory rhythms, true target locations are robustly distinguished from ghosts via cross-correlation analysis. Experimental validation demonstrates that the proposed system can accurately resolve two subjects spaced less than 20 cm apart, surpassing the resolution limits of traditional compact MIMO arrays, while achieving a respiration rate estimation accuracy of 0.7 bpm root mean square error (RMSE) compared to contact-based ground truth.