A search for pair-produced vector-like $T$-quarks in 139 fb$^{-1}$ of $pp$ collisions recorded by the ATLAS detector at a centre-of-mass energy $\sqrt{s}$=13 TeV is presented. The search targets signal events where at least one $T$-quark decays into a Higgs boson and a top quark, $T\rightarrow Ht$, with subsequent decays of the Higgs boson into a bottom quark-antiquark pair, $H\rightarrow b\bar{b}$, and the top quark into a light charged lepton, a neutrino and a bottom quark, $t\rightarrow\ell^+ν_\ell b$, where $\ell=e/μ$. The decay products of boosted heavy resonances are reconstructed using variable-radius, reclustered jets, and a neural network is employed to discriminate signal from Standard Model background processes. A profile-likelihood fit to the effective mass distribution is performed, and no excess above the Standard Model prediction is observed. Exclusion limits at 95% confidence level are set on the $T$-quark pair-production cross-section, corresponding to lower mass limits of 1.40 TeV in the SU(2) singlet representation, 1.56 TeV in the SU(2) doublet representation, and 1.66 TeV assuming the branching fraction of $T$-quarks to $Ht$ to be 100%.

For graphs $G, F_1$ and $F_2$, we say that $G$ is $(F_1,F_2)$-free if neither $F_1$ nor $F_2$ is an induced subgraph of $G$. We say that $G$ is $k$-vertex-critical if the chromatic number of $G$ is $k$, but every proper induced subgraph of $G$ has chromatic number at most $k-1$. The $\textit{chair}$ graph is a $5$-vertex graph obtained by adding a pendant vertex to one of the two central vertices of a path on $4$ vertices. The $\textit{cricket}$ graph is a $5$-vertex graph obtained by adding two pendant vertices to a common vertex of a triangle. The path on $5$ vertices is denoted by $P_5$. We prove that for every $k \geq 1$, there are only finitely many $(P_5,\text{chair})$-free $k$-vertex-critical graphs. We also prove that the same conclusion holds if $\text{chair}$ is replaced by $\text{cricket}$. We further characterize all $5$-vertex-critical $(P_5,\text{chair})$-free graphs, all $5$-vertex-critical $(P_5,\text{cricket})$-free graphs and all $6$-vertex-critical $(P_5,\text{cricket})$-free graphs. Our proofs rely on bounding the size of antichains and developing Ramsey-theoretic ideas. For any fixed integer $k \geq 1$, our results imply the existence of a polynomial time algorithm to decide whether a $(P_5,\text{chair})$-free (or $(P_5,\text{cricket})$-free) graph is $(k-1)$-colourable such that this algorithm can also present a negative constant-size certificate in case the graph is not $(k-1)$-colourable.

We construct a detailed microscopic noise model for multi-qubit (MQ) gate operations in the context of trapped ion architecture with all-to-all connectivity. We find that phonon heating and motional dephasing are well captured by effective single- and two-qubit error channels that can, in principle, act between arbitrary pairs of qubits. Nevertheless, the median magnitude of two-qubit errors between uncoupled qubits is substantially smaller than that of errors between gate-coupled qubits. Errors associated with photon scattering are shown to solely propagate to qubits participating in gate operations. Lastly, we combine all noise sources, assigned with experimentally relevant parameters, and explore the scalability of a quantum error correction (QEC) scheme based on the rotated surface code, as a function of error rates and code size. Our analysis bridges device-level physics and QEC performance for MQ gates in trapped-ion architectures.

We study vector-valued incidence maps obtained from ordinary graph incidence maps by linear observation of the free vertex space. Let $\mathbb{F}$ be a field, $D = (X, E, s, t)$ a finite directed multigraph, $U$ an $\mathbb{F}$-vector space, and $ϕ: X \to U$ a vertex labeling with $\mathbb{F}$-linear extension $\hatϕ : \mathbb{F}^X \to U$. The vector-valued incidence map $\partial_ϕ: \mathbb{F}^E \to U$, $\partial_ϕ(\mathbf{1}_e) = ϕ(t(e)) - ϕ(s(e))$, factors as $\partial_ϕ= \hatϕ \circ B_D$, where $B_D$ is the classical incidence map of $D$. We prove the formula $\dim_{\mathbb{F}} \mathrm{Ker}(\partial_ϕ) = |E| - |X| + c(D) + δ_ϕ,$ where $c(D)$ is the number of weakly connected components of $D$ and $δ_ϕ:= \dim_{\mathbb{F}}(\mathrm{Im}(B_D) \cap \mathrm{Ker}(\hatϕ))$ is the defect invariant. We apply this framework to directed tensor-labeled hypergraphs $\mathcal{H} = (Q_0, Q_1, β)$, in which each hyperedge carries a pair of boundary tensors $(A_e, B_e)$ in the tensor algebra $T(\mathbb{F}^{Q_0})$, and prove that $δ(\mathcal{H}) = 0$ over any field for each of the six standard constructions, including symmetric encodings that degenerate in positive characteristic. Over $\mathbb{F} = \mathbb{R}$, the edge Gram operator $\mathcal{L} = \partial_β^* \partial_β$ has rank $|V_{\mathrm{macro}}| - c_{\mathrm{macro}} - δ(\mathcal{H})$, and its degree-truncated operators form a Loewner-monotone filtration whose rank increments equal the decrements of the defect filtration. We further realize the cycle space of every oriented hypergraph (in the sense of Reff--Rusnak) as $\mathrm{Ker}(\partial_β)$ within this framework, and exhibit a four-edge inclusion--exclusion example with $δ(\mathcal{H}) = 1$.

Motivated by the Engel and Pierce expansions, we introduce a signed Engel expansion. We expand each $x\in(0,1)\setminus\mathbb{Q}$ uniquely as $$x=\frac{ε_{1}(x)}{d_{1}(x)}+\frac{ε_{2}(x)}{d_{1}(x)d_{2}(x)}+\cdots+\frac{ε_{n}(x)}{d_{1}(x)d_{2}(x)\cdots d_{n}(x)}+\cdots,$$ where $ε_{1}(x)\coloneqq1$ and $ε_{n}(x)\in\left\{1,-1\right\}$ for $n\geq2$. The digit sequence $\left\{d_{n}(x)\right\}_{n\geq1}$ satisfying $d_{n+1}(x)\geq d_{n}(x)+2$ when $ε_{n+1}(x)=-ε_{n}(x)$ forms a non-decreasing sequence of even positive integers tending to infinity. On the one hand, we obtain the law of large numbers, the central limit theorem and the law of the iterated logarithm regarding $d_{n}(x)$ and $Δ_{n}(x)\coloneqq d_{n}(x)-d_{n-1}(x)\ (n\geq2)\ (Δ_{1}(x)\coloneqq d_{1}(x))$. On the other hand, we prove a Borel--Bernstein theorem on the zero-one law on the Lebesgue measure of the set $$\left\{x\in(0,1)\colon R_{n}(x)\geqϕ(n)\ \textnormal{ for infinity many } n\right\},$$ where $R_{n}(x)\coloneqq\frac{d_{n}(x)}{d_{n-1}(x)}\ (n\geq2)\ (R_{1}(x)\coloneqq d_{1}(x))$ and $ϕ$ is an arbitrary positive function defined on the set of positive integers.

This paper introduces the Myerson interaction index (MII), an extension of the Shapley interaction index to cooperative games with communication structures restricted by graphs. We establish a formal framework for interaction indices on graphs and provide an axiomatic characterization of the MII based on component efficiency, fairness, and veto partnership consistency. Furthermore, we analyse network-induced interaction to distinguish between effects arising from the graph topology and those stemming from the game's intrinsic synergies. This framework offers a robust tool for analysing coalitional behaviour in structured environments, with potential applications in social network analysis and explainable artificial intelligence.

In this note, we formulate the notions of the direct and inverse problems and contact points for the Feynman diagrams. For the electron-photon interaction case, the solutions of these direct and inverse problems are presented. The interrelations between Feynman diagrams and the classical colored graphs are discussed.

In this study, we explore universal thermodynamic topological classes of charged dRGT black string within both the canonical ensemble and grand canonical ensemble frameworks, and further analyze its asymptotic behavior under limiting parameter regimes. We demonstrate that, while the outermost large black string branch remains thermodynamically stable in both ensembles, the innermost small black string branch exhibits distinctly different stability properties: it is stable in the canonical ensemble but becomes thermodynamically unstable in the grand canonical ensemble, corresponding to the $W^{1+}$ and $W^{0-}$ topological categories,respectively.These findings demonstrate that the selection of thermodynamic ensemble has a significant influence on the thermodynamic configuration of the charged dRGT black string. In the limit where gravitational effects are neglected, the charge contribution does not modify the underlying topological classification. This implies that the coupling between dRGT massive gravity and the electromagnetic sector is essential for the emergence of nontrivial thermodynamic topology.These results contribute to a deeper understanding of the black string thermodynamics and provide a novel theoretical basis for exploring the basic properties of quantum gravity.

Long-form Retrieval-Augmented Generation (RAG) brings the challenge of coverage-based ranking, because ranking methods must ensure the inclusion of comprehensive relevant nuggets (i.e., facts), which can thereby be synthesized into a comprehensive output. In this work, we propose CoveR (Our code is available at https://github.com/DylanJoo/CoveR ) a dense retrieval method optimized for coverage-aware retrieval scenarios. CoveR is a bi-encoder trained with the coverage-based contrastive and distillation objectives, which enables CoveR to capture diverse aspects of information needs. To train CoveR, we create the SCOPE dataset, (Our training data is available at https://huggingface.co/datasets/DylanJHJ/scope ) which comprises 90K training pairs from Researchy Questions with synthetic coverage signals augmented from sub-question answerability judgments generated by LLMs. Our empirical experiments show that CoveR enhances nugget coverage by 10\% over strong dense retrieval baselines without sacrificing its relevance-based retrieval capability. Further ablation studies validate the importance of our proposed learning method, showing that CoveR achieves a superior trade-off between relevance- and coverage-based ranking, which is essential for long-form RAG.

In this paper, we compute the leading-order and first-order radiative corrections to the Casimir energy of a massive Lorentz-violating scalar field governed by a $ϕ^4$ interaction on a network. For simplicity, the network is chosen to consist of three edges connected at a single central junction, with the scalar field defined in 1+1 dimensions on each edge. Dirichlet boundary conditions are imposed at the outer ends of the edges, thereby confining the field on the network. Beyond addressing the massive case of a Lorentz-violating scalar field, a key novelty of this work lies in the calculation of the radiative corrections to the Casimir energy using position-dependent counterterms. These counterterms emerge from a systematic renormalization program that consistently incorporates the effects of boundary conditions into the renormalization procedure. To eliminate divergences arising from vacuum energy contributions, we employ the box subtraction scheme in conjunction with cutoff regularization. Our results show that both the leading-order and first-order Casimir energies are negative, regardless of the presence or absence of Lorentz-violating effects, and are in agreement with general physical expectations.

In this paper, an outdoor channel measurement campaign at 330-360 GHz employing a 128 * 4 virtual antenna array (VAA)-based multiple-input multiple-output (MIMO) configuration is conducted. The transmitter (Tx) and receiver (Rx) location pairs are classified into line-of-sight (LoS) and obstructed-LoS (OLoS) scenarios to enable a detailed investigation of outdoor terahertz (THz) band channel characteristics. During the measurement process, the stationarity of the outdoor environment is carefully verified, and a linear phase drift (PD) effect is identified. Then, we propose a PD-aware Space-Alternating Generalized Expectation-Maximization (SAGE) algorithm, which significantly improves both delay resolution and channel parameter estimation accuracy. Based on the processed measurement data, we characterize key channel properties, including the power delay profile, path loss, shadow fading, delay spread, angular spread, Rician K-factor, as well as their cumulative distribution functions and correlation characteristics. In addition, near-field effects and MIMO-specific properties, including the spatial non-stationarity and the cluster birth-death property, are analyzed.

We present a theoretical investigation of coherent control over the orientation of an individual molecule strongly coupled with a cavity using chirped-pulse driving. Specifically, we explore the dynamics of carbonyl sulfide (OCS) molecules under the influence of two chirped pulses with different spectral phases. We compare two pulse configurations: one with equal chirp rates ($β_{+} = β_{-}$) and another with unequal chirp rates ($β_{+} \neq β_{-}$). Numerical simulations reveal that chirped pulses enable precise control of the molecular orientation, achieving a maximum orientation degree of 0.5773. By analyzing the distribution of molecular polariton states, we show that chirped pulses can activate multiphoton processes, leading to deviations from the predictions of first-order Magnus expansion methods. Additionally, we demonstrate the robustness of the maximum orientation with respect to chirp amplitude and detuning, providing insights into the role of pulse parameters in optimizing control. This work introduces a new strategy for controlling molecular orientation in cavity-based systems and offers valuable perspectives for future experimental applications.

Multimode fibers (MMFs) can transmit multiple guided modes simultaneously, making them a promising platform for high-resolution biomedical imaging, endoscopy and high-bandwidth optical communication. However, their complex modal behavior, influenced by environmental perturbations and mode coupling, presents a major challenge for accurate wavefront control. Conventional approaches for shaping the light at their output typically rely on the transmitted field as a source for iterative feedback, making it impractical for in-situ applications where direct access to the transmission is impossible. Here, we introduce a deep learning-based framework for predicting transmission through MMF by observing only the reflected signal. Harnessing the reflected signals that encode the fiber's internal configuration, our approach not only generalizes across varying fiber conditions but also enables focusing through the fiber without requiring transmission feedback. By training the system experimentally using a dataset of 4 million images across 1200 distinct fiber configurations, we demonstrate robust and precise wavefront reconstruction even under significant perturbations. Our results underscore the potential of learning-based techniques for real-time MMF-based imaging and optical communications, paving the way for efficient non-invasive focusing in practical applications.

We use the Stetson, HST, and Gaia DR3 data sets for 22 Galactic globular clusters to select their members and fit their CMDs with isochrones from DSED and BaSTI for $[α/$Fe$]=+0.4$ and an adopted helium mass fraction $Y$. As a result, we estimate the metallicity [Fe/H], age, distance from the Sun, and reddening E(B-V) for these clusters. Special attention is paid to identify variable stars among the cluster members. We combine these results with our earlier estimates for five other clusters into a homogeneous set of parameters for 27 clusters and investigate relationships among these parameters and their statistical properties. In particular, we count the giants on the red (RGB), horizontal (HB), and asymptotic branches using the clean data sets cross-identified to cover the entire cluster fields and count each giant only ones. This allows us to calculate the $R$-parameter, the ratio between the numbers of the HB and RGB, with unprecedented accuracy and to examine its relations with other parameters. These relations are much stronger for accreted clusters rejecting a constant $R$ value for them, possibly because of their heterogeneous origins and environments. For all in-situ clusters, a constant value of $R=1.31^{+0.06}_{-0.05}$ is consistent with the data. According to previous calculations, this value may imply anomalous energy losses in HB stars corresponding to an axion--photon coupling of $g_{aγ}=(0.66^{+0.11}_{-0.13})\times10^{-10}\,\mathrm{GeV}^{-1}$. However, the observed dependencies of $R$ on cluster parameters require improved statistics and a theoretical understanding of these dependencies. By comparing $R$-parameter estimates from HST and Gaia in cluster centres and peripheries, respectively, we suggest that the peripheral HB population is depleted by about half when the cluster crosses the Galactic disk, then the HB recovers over 60-80 Myr.

The first 6G standardization efforts are about to start, shaping the new generation of mobile networks. The IMT-2030 extends the IMT-2020 by expanding its usage scenarios to Immersive, Massive, and Hyper-Reliable and Low-Latency Communications. It also introduces novel scenarios by integrating Artificial Intelligence and Sensing with Communication and supporting Ubiquitous Connectivity. Compared to the previous generation, 6G is expected to improve not only throughput and latency, but also coverage and energy efficiency. A paradigm called Goal-Oriented (GO) communications has recently emerged as a promising solution to improve network efficiency. It relies on the fact that the goal of the communication network is to achieve a specific task with a defined accuracy, rather than creating perfect data delivery. Intelligent devices can pre-process data to send only what is relevant to achieve the task, thus saving precious network resources and energy. Recent works demonstrate that incorporating service- and application-level KPIs in the network allows to achieve higher communication efficiency for devices, but the consequence of using such techniques on the network itself has not yet been explored. This paper proposes a practical end-to-end framework to assess energy consumption, latency, and goal accuracy KPIs, which includes a Multi-Objective optimization model to evaluate the trade-offs between the multiple KPIs relevant to GO networking. We demonstrate, through simulation, that the network can benefit from the application of the GO paradigm, indicating its potential in future network architectures.

We study coherent electric manipulation of magnetic-field-induced localized states at a double kink of a helical edge in a HgTe/CdHgTe quantum well. An in-plane magnetic field opens a gap in the one-dimensional edge spectrum, while changes in the edge orientation generate localized in-gap states at the kinks. We show that, for suitable geometry and magnetic-field direction, two such states form an effective lithographically defined two-level subsystem. Using an edge-state model that includes both the localized levels and the continuum states outside the magnetic-field-induced gap, we calculate the electric-dipole matrix elements and solve the time-dependent problem under resonant driving. The resulting dynamics exhibits Rabi oscillations with linear frequencies of $20$--$40$~GHz for realistic parameters. We find that the continuum states provide a leakage channel whose strength is strongly controlled by the driving amplitude: reducing the electric field suppresses leakage below the percent level while preserving GHz-scale coherent oscillations. These results establish a route from magnetic-field-induced corner-state physics to electrically driven two-level dynamics in a realistic two-dimensional topological-insulator edge geometry.

RR Lyrae stars in the bulge have been reported to be associated with the spheroidal, relatively metal-poor component. They offer a way to trace this component with precise distances. While a few studies of RR Lyrae spectra with medium/high resolution are now available, none of them target stars in the Galactic bulge. We present here a spectroscopic determination of Fe and α-element abundances for RR Lyrae stars in the Galactic bulge, with the main goal of providing a benchmark to calibrate other metallicity indicators, appropriate for this specific stellar population. We analyzed FLAMES/GIRAFEE spectra of 78 RR Lyrae stars (60 ab-type and 18 c-type). We applied a full-spectrum fitting technique to obtain the spectroscopic metallicity and overall α-element abundance. Distances are derived by means of a period-luminosity-metallicity relation, and orbits are computed by combining the radial velocities derived here with the proper motions from DR3. Gaia The resulting metallicities peak at [Fe/H] _median = -1.34 +- 0.04 and -1.44 +- 0.08 dex for ab and c-types respectively. The majority of the bulge RR Lyrae are metal-poor stars with relatively high α-element abundances around [α/Fe] ~ 0.25 +- 0.03 dex. We used our spectroscopic measurements to test different methods for deriving metallicities based on photometry, which utilize Fourier parameters in the light curves of the RR Lyrae. The data suggest a possible correlation between the metallicity difference and the [α/Fe] ratio, which needs to be investigated further. There are some ab-type RR Lyrae that show metallicities higher than -1 dex and low [α/Fe] values. We studied these stars kinematically and found a difference between three stars with similar [α/Fe] values and the main group, indicating that they may be slightly younger and correspond to the disk population.

Sequential recommendation effectively models dynamic user interests but continues to face challenges related to data sparsity. While self-supervised learning has alleviated this issue to some extent, most existing methods focus exclusively on immediate next-item prediction during training, thereby neglecting the rich information embedded in longer-term future interactions. Although a few studies have explored the utilization of future data, existing attempts typically apply future supervision signals with uniform intensity across all samples, which may lead to suboptimal solutions. In this paper, we propose an adaptive future learning framework, UFRec, which encourages the model to look further ahead when it is confident in the current state, while focusing on the immediate task when it is uncertain. Specifically, UFRec incorporates an Uncertainty-Guided Future Supervision module that dynamically modulates the weight of multi-step future supervision based on the model's confidence in the primary next-item prediction task. Furthermore, we complement step-wise future supervision with a Future-Aware Contrastive Learning module that treats the future trajectory as a holistic entity. Notably, both auxiliary modules are utilized exclusively during training and incur no inference overhead. Extensive experiments on four benchmark datasets demonstrate that our method significantly outperforms state-of-the-art approaches by effectively leveraging future data.

Matrix product states (MPS) serve as a key tool for studying quantum systems from chemistry and condensed-matter physics, making their preparation on quantum computers an important task in interfacing classical and quantum simulation. Many systems of interest have $U(1)$-symmetries induced by particle number and spin projection conservation, allowing to restrict the MPS tensors to be of block-sparse form, a property widely used in the implementation of classical algorithms such as the density matrix renormalization group. We reduce the cost of fault-tolerantly preparing block-sparse MPS within the standard ancilla-assisted linear-depth approach by implementing row and column permutations that transform the block-sparse matrices into block-diagonal form. These block-diagonal unitaries are then implemented via unitary synthesis, with the cost being determined by the size of the largest block. In this context, we modify the unitary synthesis approach of Berry et al. in order to reduce the Toffoli cost for real-valued unitaries by a factor of $\sqrt{2}$. In numerical benchmarks, we achieve Toffoli cost improvement factors of $10 - 30$ compared to the state-of-the-art for MPS of various molecular systems.

We present a quantum mechanical approach to understanding the Hilbert space and the defect Hilbert spaces associated with line operators of BF theory combined with level-$k$ Chern-Simons theory. The defect Hilbert spaces are closely related to the category of $*$-representations of the $C^*$-algebra of the compactly supported sections of the Fell line bundle over the conjugation action groupoid $G//_{\mathrm Ad} G$, and the structure of this category and the groupoid action on the objects of this category is interpreted quantum mechanically. We show that the action of the line operators on the Hilbert space of the $BF+kCS$ TQFT is given concretely by a convolution between the kernels that represent the line operators, and that the codimension-$2$ twist and the codimension-$1$ prequantum line bundle arise as two transgressions of the same universal level $k\in H^4(BG,\mathbb{Z})$. For finite gauge group, the resulting convolution-eigenvalue formula is identified with the Verlinde formula for the (twisted) Drinfeld double $D^ω(G)$ via an explicit phase-by-phase match with the known finite modular data. For compact Lie group, the convolution-kernel eigenvalues coincide in the regular sector with the semiclassical Hopf-link $S$-kernel, identifying two complementary derivations of the same modular data.

Causal Inference offers a fundamental approach for advancing empirical software engineering (ESE) beyond traditional statistical association, enabling researchers to rigorously identify and quantify causal relationships in software experiments. This paper introduces CausalSE, a framework that operationalizes Judea Pearl's causal inference paradigm in ESE context. The paper focuses on Structural Causal Models (SCMs) to address the limitations of classical statistical methods in mitigating confounding bias. Through a case study using the Galeras dataset and propensity score matching, we demonstrate how CausalSE disentangles the effect of prompt engineering strategies on code generation outcomes in a popular LLM (i.e., GPT-3). The results reveal that while associational analyses can suggest improvements in certain interventions (e.g., more complex prompts), causal analysis often does not find a significant treatment effect, highlighting the risk of false positives when confounding is not addressed. By providing a tutorial-based methodology and a real-world case study, this work equips software researchers with practical tools to design, analyze, and interpret software experiments with methodological rigor, ultimately enabling more informed and actionable conclusions in both research and practice.

Due to their exceptional isolation from the environment, magnetically levitated particles are explored as extremely sensitive mechanical sensors. For future gravity experiments on quantum superpositions, such systems need to be cooled close to their ground state. To demonstrate the combination of state of the art vibration isolation, milligram levitated high Q mechanical resonators and position detection with low noise, we present linear feedback cooling of a magnetically levitated gravity sensor to below 2 picometer amplitude and below 10 millikelvin mode temperature for two translational modes (the x- and y-mode) simultaneously. The sensor is a levitating permanent magnet in a type I superconducting trap, where its six resonance frequencies are measured with a superconducting coil coupled to a DC SQUID. This signal is measured with a lock-in amplifier and a feedback signal is sent to a piezoelectric actuator, allowing the cooling of resonant modes at 50.6 and 68.0 Hz simultaneously. These two translational modes have Q factors of $3.8 \cdot 10^6$ and $5.5 \cdot 10^6$ respectively. The experiment is mounted inside a dry dilution refrigerator where it is vibrationally attenuated with 110-130 dB at these frequencies. In this work, we discuss future improvements on the setup which may enable quantum ground state cooling on a magnetically levitated particle, that has previously been shown to be a gravitational sensor.

The commissioning of industrial electric drives still relies heavily on manual tuning of cascaded control loops, requiring expert knowledge and significant time. In this paper, we propose a fully automated approach for tuning the current control loop of industrial drives using Bayesian Optimization (BO) directly on real hardware, without requiring a system model or firmware modifications. The drive is treated as a black-box system, and the controller parameters are iteratively updated through closed-loop experiments. The tuning problem is formulated as a multi-objective optimization task that directly minimizes tracking error, time-weighted error, overshoot, and oscillatory behavior, enabling the identification of Pareto-optimal controller configurations. To address discrete parameters, noisy evaluations, and limited budgets, we adopt a multivariate Tree-structured Parzen Estimator (TPE) as the underlying BO strategy. The proposed method operates under practical industrial constraints, including communication latency and limited evaluation budgets. The experimental validation on a real motor drive system under no-load conditions shows that the method achieves performance comparable to expert tuning within a few minutes and without human intervention. Results show that Gaussian Process (GP)-based BO can yield highly competitive final solutions, but TPE-based BO is better aligned with this setting due to faster convergence, richer Pareto-front approximation, and lower computational overhead.

Digital forensic relies on validated tools and established procedures, yet the underlying operating systems, applications, and analysis tools evolve rapidly. This evolution can cause artifact behavior and tool outputs to drift, silently degrading repeatability and confidence in long-lived forensic interpretations. We present test-driven forensics, a practical approach that treats forensic expectations as executable specifications: expected artifacts and expected tool outputs are encoded as tests that can be rerun across versions to detect regressions. Crucially, our approach also enables State Transition Testing, validating the system's expected state after each user action rather than only performing post-mortem checks on a final disk image; this supports causal attribution and makes transient behavior testable. We implement the methodology in ADARE, an open-source framework that runs controlled experiments in virtual machines and simulates realistic user activity via computer-vision-guided GUI automation. ADARE includes a companion web platform for sharing experiments, environments, and results to facilitate independent reruns and peer verification. We evaluate ADARE in five case studies spanning artifact research and tool validation. In particular, a 25-version regression study of Autopsy reveals substantial, largely undocumented changes in exported report outputs, demonstrating how executable tests make drift measurable and reproducible at scale.

We reduce the eight-dimensional weak form of the bilinear Boltzmann collision operator to a five-dimensional kinematic core by rigidly rotating the laboratory frame to align with the colliding pair and integrating over the $\mathrm{SO}(3)$ rotation group. This reduction yields an exact Wigner--Eckart factorization within a spectral Galerkin framework of associated Laguerre polynomials and spherical harmonics. The decomposition decouples the angular geometry from the scattering physics. The former, represented by Clebsch--Gordan coefficients, is evaluated exactly, while the latter is evaluated to machine precision by a spectrally convergent singular quadrature strategy. By explicitly zeroing specific entries, the macroscopic collision invariants are embedded without approximation. Cache-optimized contractions deliver up to a 37-fold single-core speedup and a 1000-fold memory reduction over standard dense Cartesian formulations. The approach is validated against analytical solutions for Maxwell molecules and infinite-order Chapman--Enskog viscosity coefficients for hard spheres.

We introduce and study dual Chow functions associated to kernels in incidence algebras of weakly ranked posets. Given a kernel, its dual Chow function is defined as the Chow function associated to the sign-twisted reverse kernel. For kernels satisfying a natural skew-symmetry condition, such as the Eulerian kernel of an Eulerian poset or the kernel given by R-polynomials on Bruhat intervals, this construction recovers the ordinary Chow function. In contrast, when this skew-symmetry fails, the dual Chow function gives a genuinely different invariant. The main example considered in this paper is the dual Chow function associated to the characteristic function. We develop the basic theory of these dual Chow functions, with particular emphasis on posets arising from matroids. We prove chain formulas, unimodality and gamma-positivity results, formulas under standard poset operations, and deletion formulas for matroids. Along the way, we also obtain a general deletion formula for the ab-index of matroids, which leads to new formulas for extended ab-indices and, in turn, specializes to several deletion formulas appearing in the literature.

Under the duality between the two-dimensional XY model and an integer-valued height function, the BKT transition is expected to correspond to the disappearance of a corner in the surface tension; in the delocalised phase, its zero-slope curvature should determine the Gaussian free field prefactor. We prove that the XY mass equals the right derivative at zero slope of the dual height function's free energy, with a uniform quadratic error bound near the origin. Thus the massive phase is exactly the corner regime, while in the BKT phase the surface tension is quadratically bounded at zero slope. The proof combines Kadanoff--Ceva duality, Ginibre's inequality, and a pushing lemma (an estimate of Russo--Seymour--Welsh type) for the cable height function.

Let $r,s,t\geq2$ be integers. For $r$-graphs $G$ and $F_1,\dots,F_s$, we write $G\to(F_1,\dots,F_s)$ if every $s$-edge-coloring of $G$ yields a monochromatic copy of $F_i$ in the $i$-th color for some $1\leq i\leq s$. Let $\mathcal{R}(F_1,\dots,F_s)$ denote the family of all $r$-graphs $G$ with $G\to(F_1,\dots,F_s)$. When $F_1=\dots=F_s=F$, we write $\mathcal{R}(F;s)=\mathcal{R}(F_1,\dots,F_s)$. In this paper, we investigate when $\mathcal{R}(H;s)\subseteq\mathcal{R}(Q_1,\dots,Q_t)$ holds, where $H=H^{(r)}(n,p)$ is a random $r$-graph and $Q_1,\dots,Q_t$ are fixed $r$-graphs. Our main result determines the threshold for a large class of such $Q_1,\dots,Q_t$, including complete $r$-graphs. The key ingredient in our proof is a generalization of a result of Graham, Łuczak, Rödl, and Ruciński, which provides a necessary and sufficient condition for $\mathcal{R}(F_1,\dots,F_s)\subseteq\mathcal{R}(Q_1,\dots,Q_t)$, where $Q_1,\dots,Q_t$ are highly connected. As a byproduct, we characterize when two tuples of highly connected $r$-graphs are Ramsey equivalent.

The Egger intercept (EI) test is a widely used tool to detect horizontal pleiotropy in two-sample summary-data Mendelian randomization. A significant EI test suggests that either the average pleiotropic effect differs from zero (i.e., directional pleiotropy) or the InSIDE (Instrument Strength Independent of Direct Effect) assumption is violated (i.e., correlated pleiotropy) or both. As such, the EI test provides an assessment of the validity of the instrumental variable assumptions, with a non-zero EI indicating that the commonly used inverse-variance weighted (IVW) estimator will be biased. However, the EI test may exhibit inaccurate type one error rates due to biased estimation in Egger regression caused by the measurement error and winner's curse. In this article, we propose a modified EI (MEI) test based on a bias-corrected EI estimator under the null hypothesis of no directional or correlated pleiotropy, leveraging the recently developed rerandomized IVW estimator. We then prove the asymptotic properties of the MEI test under realistic conditions. Like the EI test, we find that the power of the MEI test is also affected by the orientation of SNPs. To enhance the robustness of power, we further combine the MEI test statistics obtained under two specific allele coding schemes. Both simulation and real data studies show that the combined test outperforms the EI test in terms of type one error control and power.

Dobbs proved that the second iterate of almost every line in the complex plane under the exponential function is dense in the plane. In this paper, we prove an analogous result for the second iterate of the Zorich map in $\mathbb{R}^3$.