The ambiguity of the active site, the empirical status of Brønsted-Evans-Polanyi relations, and the unpredictability of linear scaling relation breakdown are three symptoms of a single representational choice: treating chemical affinity as an attribute of discrete geometric sites. Here we show that all three are resolved when chemical affinity is represented as a continuous property of the interface: the covalent field. We present a framework, Covalent Field Theory (CFT), in which active sites emerge as regions where the field sustains a bias toward bond formation beyond the thermal threshold, removing the need for geometric classification. Linear scaling relations are correlation structure in the field across probe families; their breakdown is a topological bifurcation with a precise geometric signature. Brønsted-Evans-Polanyi correlations arise from the covalent field decomposition, providing a theoretical basis for what has previously been treated as an empirical regularity, demonstrated across ~120,000 candidate pathways. Applied to a high-entropy alloy nanoparticle and a partially reduced high-entropy oxide, CFT maps these properties onto surfaces of arbitrary compositional and structural complexity.

Whereas coil positioning in transcranial magnetic stimulation (TMS) to reach a specific cortical target with modern focal stimulation coils has been intensively studied, the alignment and contact of a coil with the head is often ignored. Focal figure-of-eight coils have a point on the surface, where they generate the largest induced electric field. This point should touch the head first, and the coil should be approximately tangential to the head in this point. Previous research has demonstrated the large impact if the coil does not touch the head with the right point and that many operators struggle with establishing or maintaining the correct coil-scalp alignment. This paper presents a technological support technology that can monitor the exact position of the contact point and also pressure to provide feedback to users. As the system uses exclusively components from consumer electronics, the sensor is low-cost and affordable. Through proper design, we achieved sufficient robustness so that the sensor does neither reset during TMS pulses and also not show any detectable degradation.

Cloning refers to producing identical copies of existing objects. Here, we experimentally show how to clone acoustic scattering objects. We acquire a digital twin and bring it back to life - a simple two-step process. First, we use broadband speakers to illuminate the scattering object within a closed receiver aperture. From these recorded reverberative data, we retrieve the object's scattering Green's functions using multidimensional deconvolution. In the second step, the acoustic scatterer is holographically reconstructed using the acquired scattering Green's functions. The hologram scatters any wavefield in real-time exactly like the original object would. Low-latency feedback reproduces all orders of interactions between the physical wavefield and the numerically defined hologram. This two-step process is demonstrated by cloning and modifying several rigid scatterers in a two-dimensional acoustic waveguide. Applications range from fully realistic digital scattering models to efficient metamaterial experimentation.

In this work we show that coulomb models, ones that obey a $\nabla\cdot\left\langle \mathbf{B}\right\rangle =0$ divergence free constraint - for $\left\langle \mathbf{B}\right\rangle $ being some coarse grained variables related to the microscopic degrees of freedom of the lattice system - are sick without the inclusion of defects with $\nabla\cdot\mathbf{B}\neq0$. We show that for generic boundaries (ones where the fluxes of the pseudo-magnetic fields on the boundary do not cancel: $\left(\left\langle \mathbf{B}_{R}\right\rangle -\left\langle \mathbf{B}_{L}\right\rangle \right)\cdot\mathbf{n}\neq0$ - here $\mathbf{n}$ is the unit normal and $\left\langle \mathbf{B}_{R/L}\right\rangle $ are the two ground state pseudo-magnetic fields on either side of the domain wall) without the inclusion of defects, sharp domain walls (on the order of the width of a unit cell) between different phases of the system cost energy proportional to system size (not boundary area). We present several different examples of this phenomena in the square lattice six vertex model, in quantum dimers and in classical spin ice in the presence of magnetic fields. We also show by example that the condition $\left(\left\langle \mathbf{B}_{R}\right\rangle -\left\langle \mathbf{B}_{L}\right\rangle \right)\cdot\mathbf{n}=0$ is a necessary but not sufficient condition for the boundaries to be compatible - that is domain wall energy to scale with domain wall area and not system size. To further present the importance of boundary conditions in Coulomb systems we show that system boundaries, even ones that satisfy $\int_{\partial V}\mathbf{B}\cdot\mathbf{n}=0$, have thermodynamic consequences - that is there is a cost, extensive in system size, to the Helmholtz free energy.

The quark mass dependence of the pseudoscalar meson decay consntants, $f_π, f_K$ and $f_η$, are determined from three-flavor N$^2$LO ChPT till pion masses around $780$ MeV, near the SU(3) limit. This is done by conducting an analysis of recent LQCD data using the LASSO method, a machine-learning technique which allows to pin down the relevant low-energy-constants with high precision. Since the pion decay constant is a fundamental quantity which usually appears in relevant phenomenological lagrangians or Effective Field Theories based on QCD at low energies, this analysis can be used as input to evaluate the quark mass dependence of hadronic states. As an example, we predict the masses of the octect baryons in the SU(3) limit within covariant Baryon Chiral Perturbation Theory.

Ultrafast laser control of material properties hinges on understanding light-matter interactions. We use two experimentally accessible response functions, laser fluence induced phonon softening and the amplitude of coherent reflectance oscillations, to compare how strongly different materials respond to ultrafast photoexcitation. Comparing a diverse set of materials, we find that only a narrow class, including Sb, GeTe, and Bi2Te3, shows exceptional responses such as pronounced phonon softening and a giant increase of reflectance oscillations with increasing fluence. These response functions peak in an intermediate conductivity regime of about 102 - 104 S/cm, at the crossover between localized and delocalized electronic states. The corresponding class of solids also shows other unconventional properties including high dielectric constants, enhanced Born effective charges, coordination numbers exceeding the 8-N rule and uncommon bond rupture. This suggests that these materials employ a unique bonding mechanism, coined metavalent bonding. Frozen-phonon DFT calculations show that the strong fluence dependence arises from Peierls-like instabilities, leading to large deformation potentials and anharmonic double-well potentials. These findings identify metavalent bonding as a design principle for enhanced coherent phonon control and provide a quantitative framework for identifying materials with exceptional ultrafast responses.

We present 0.1" (~ 50 au) resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations of the HH 46/47 molecular outflow and its envelope-disk system. The 1.3 mm continuum emission reveals a compact central source surrounded by a circumbinary disk with substructures. The companion, identified in optical and infrared observations, is not detected in the millimeter continuum but coincides with a local intensity minimum. Two spur-like features extending from the primary source toward the companion are identified and are likely induced by gravitational perturbations from the companion. The envelope-disk system is traced by C18O, SO, H2CO, and CH3OH. C18O primarily traces the extended envelope, while SO probes the inner envelope, and H2CO and CH3OH trace compact, faster-rotating structures near the centrifugal barrier. The observations are well reproduced by a rotating-infalling envelope transitioning to an inner disk at a radius of ~30 au around a 0.3 Msun protostar. The 12CO emission, together with JWST NIRCam images, reveals multiple shell structures in the outflow. Using C18O and 13CO to correct for optical depth, we derive the spatial distributions of outflow mass, momentum, and kinetic energy, as well as their corresponding rates. A model-independent analysis of a well-defined redshifted shell yields its three-dimensional velocity field, showing that the shell expands radially rather than flowing along its surface. Although a transverse velocity gradient is detected, interpreting it as rotation implies an unphysically large magnetic lever arm, disfavoring a direct disk-wind origin. Instead, the shell kinematics support an entrainment scenario.

We study the finite-temperature stabilizer Rényi entropy of the open critical quantum spin chains. At Rényi index one half, this observable probes the distribution of thermal Pauli-string expectation values and can be written as a sum over absolute values of all square minors of a finite-temperature correlation matrix for the transverse-field Ising chain. We show that this exponentially large sum is exactly reducible to a single Pfaffian. The Pfaffian representation reveals a block Toeplitz--Hankel structure and allows us to extract the large-size scaling in several thermal regimes. In the crossover window where the inverse temperature is proportional to the system size, the stabilizer entropy factorizes into a saturated extensive contribution and a universal finite-size scaling function. We find that this scaling function is a level-eight eta quotient, rather than the ordinary free-boundary Majorana thermal factor. The deviation is exponentially hidden at low temperature but controls the high-temperature crossover, where it gives a Cardy-like asymptotic for the Pauli-string expectation-weight spectrum. These results show that finite-temperature stabilizer entropy reveals hidden defect-like conformal data invisible to ordinary thermodynamic probes.

We present classical solutions for magnetic monopoles and dyons induced by global monopoles for string-inspired models, in the presence of gravity. Two distinct scenarios are analyzed. In the first, magnetic monopoles arise from the coupling of a non-trivial massless dilaton field to the electromagnetic (EM) sector. In the second, dyonic solutions emerge in the presence of a non-trivial Kalb-Ramond (KR) axion field and a massless dilaton field, which couples the KR and EM sectors. In both models, the monopole and dyon configurations originate from a global monopole associated with the spontaneous breaking of a global O(3) symmetry. The EM sector is described by Born-Infeld electrodynamics, ensuring regularity of the fields at the core of the monopole and a finite self-energy. The resulting solutions represent particle-like configurations with a well-defined core and positive ADM (Arnowitt-Deser-Misner) mass, and are shown to satisfy all standard energy conditions. We also demonstrate the existence of a minimum nonzero magnetic charge in the limiting case of a magnetic monopole with vanishing mass. We also discuss stability criteria for our magnetic-monopole and dyon solutions. We first demonstrate that the mechanical-stability criteria for these solutions are satisified. These require the finiteness of the total force components and also the outward-pointing nature of the radial component, which indicates the avoidance of collapse. Next we analyse the dynamical (linear perturbative) stability of the self-gravitating Born-Infeld monopole and dyon solutions within Einstein-Born--Infeld-dilaton-axion theory in the Gervalle-Volkov framework, and demonstrate that both monopole and dyonic configurations are linearly stable against electromagnetic perturbations in the exterior region, with dyons exhibiting a birefringent helicity structure due to axion-induced mixing.

This paper explores a version of the classical Cesàro integral operator for the Lebesgue space $L^p(0, 1)$ where we discuss its norm, spectral properties, cyclicity, and invariant subspaces. The spectrum of the Cesàro operator will be a crescent domain whose geometry depends on $p$. An important tool will be semigroups of weighted composition operators on $L^p(0, 1)$.

We study complex subvarieties in certain non-Kahler holomorphically symplectic manifolds $X$, called the Bogomolov-Guan manifolds. Let $E$ be an elliptic curve, $L$ an ample line bundle on $E$, $S\subset E^2$ a complex curve, and $p_1, p_2$ the corresponding projections of $S$ to $E$. The curve $S$ is called a quasi-diagonal if $p_1^*L\otimes p_2^* L^{-1}$ is a torsion line bundle. We show that there are at most countably many quasi-diagonals for any $(E,L)$. Using the quasi-diagonals, we classify the projective subvarieties in the Bogomolov-Guan manifold. The Bogomolov-Guan manifold is equipped with a Lagrangian fibration $π:\; X \to {\Bbb C} P^n$. We show that an irreducible complex subvariety $Z\subset X$ is Moishezon if and only if $π(Z)$ is a point or a certain complex curve which is described in terms of quasi-diagonals. This is used to prove that for a general Bogomolov-Guan manifold, any projective subvariety belongs to a fiber of $π$.

We present a broadband X-ray study of the transient hyperluminous X-ray source (HLX), 2SXPS J111416.1+481833, in the galaxy NGC 3583, using archival XMM-Newton, NuSTAR, Chandra data, and long-term Swift/XRT monitoring. The source episodically enters the hyperluminous regime with X-ray luminosities $L_X > 10^{41}$ erg s$^{-1}$ and drops by a factor of $>45$ from its peak into a deep low state. We detect a clear spectral cutoff at $\sim$5-6 keV in the broadband spectra, which are well modeled by a soft thermal component combined with optically thick thermal Comptonization or an inner advection-dominated disk. In the XMM-Newton spectra, we detect a statistically significant ($\gtrsim 3.9 σ$) absorption line centered at $E_{\rm line} \approx 1.97 \pm 0.04$ keV with a width of $σ_{\rm line} \approx 74 \pm 40$ eV. We primarily interpret the line as a candidate proton Cyclotron Resonance Scattering Feature (CRSF), implying a local magnetic field strength of $B \sim 4 \times 10^{14}$ G. Alternative interpretations, such as an origin in an ionized outflow, were explored and found to be less likely. We do not detect coherent X-ray pulsations, placing 90% confidence upper limits on the pulsed fraction of 19.3% in the 0.3-10 keV band and 36.3% in the 3-15 keV band. The combination of extreme luminosity, a hard spectral state, and the detection of a candidate cyclotron line provides strong evidence for a highly magnetized neutron star accretor.

We prove that level-$\ell$ Kikuchi graphs of random $2r$-uniform hypergraphs spectrally approximate the Kikuchi graph of the complete $2r$-uniform hypergraph at a sampling rate that is sharp up to a logarithmic factor, in the regime $r\leq \ell \leq n/2$. Our proof is based on the matrix Bernstein inequality, but, unlike prior works, we apply it to an appropriate collection of blocks of Johnson eigenspaces. Our analysis relies on a new, simple band-locality property for arbitrary Kikuchi graphs. As an application, we prove that the natural degree-$2\ell$ sum-of-squares relaxation for the Max $2r$-XOR problem is ``integral'' when the input is a planted noisy $2r$-XOR instance on a random hypergraph with $\gtrsim n \cdot (n/\ell)^{r-1} \log n$ hyperedges.

Markovian open quantum theory assumes evolution with respect to an external classical time parameter, yet no preferred notion of time exists fundamentally in relativistic physics. We resolve this tension by formulating relativistic open quantum dynamics relationally through finite-resolution quantum clocks. Using the Schwinger-Tomonaga formalism, we derive a covariant master equation directly on spacetime hypersurfaces and show that the resulting reduced dynamics is generically non-Markovian even for local interactions. Environmental correlations and clock fluctuations jointly generate the memory kernel, while the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) structure emerges only after relational coarse-graining, implying that exact Markovian evolution is effective rather than fundamental. In the sharp-clock limit, the formalism reduces to the Anastopoulos-Hu gravitational decoherence equation.

We present a Bayesian reconstruction of the local density and velocity fields traced by the 2MASS Redshift Survey (2MRS) and test the inferred gravitational flow against independent Cosmicflows-4 (CF4) galaxy-group peculiar velocities. The fiducial reconstruction is the maximum-a-posteriori (MAP) solution of a Zel'dovich-approximation forward model, constrained by the 2MRS redshift-space distribution through an unbinned Poisson point-process likelihood. The model assumes Gaussian initial conditions and includes the 2MRS selection function, the Zone of Avoidance, redshift-space distortions, and a distance-dependent galaxy-bias prescription. Hamiltonian Monte Carlo provides posterior samples and constrained realizations within the same framework. The reconstructed velocity field agrees well with CF4 in object-by-object, density--velocity-correlation, and shell-by-shell reflex-dipole tests. These comparisons are made at the CF4 redshift-space positions and do not require smoothing the observed CF4 velocities to the MAP resolution. We also evolve constrained initial conditions with Gadget-4. The real-space density retains the large-scale Zel'dovich structure while developing additional nonlinear small-scale structure, and the redshift-space distribution develops nonlinear Fingers of God. The results show that the 2MRS field-level reconstruction captures the large-scale gravitational flow of the nearby Universe and provides initial conditions suitable for constrained simulations.

Let $N$ and $Q$ be a finite groups with $\gcd(|N|,|Q|) = 1$. In this paper we describe normal subgroups of $G = N \rtimes Q$ via normal subgroups of $N$ and $Q$. Let $p$ and $q$ be distinct primes. Let $\mathfrak{A}_p$ be the variety of elementary abelian $p$-groups. Let $\mathfrak{A}_p\mathfrak{A}_q$ be the variety of extensions of a group in $\mathfrak{A}_p$ by a group in $\mathfrak{A}_q$. We also provide a method of determining the normal subgroups of a group in the variety $\mathfrak{A}_p\mathfrak{A}_q$. We also provide the complete list of normal subgroups of a finite group with cyclic Sylow subgroups.

Large language models (LLMs) have shown considerable promise for automated unit test generation, yet their practical effectiveness relative to human-written tests remains poorly understood. Existing evaluations commonly rely on coverage-oriented benchmarks that do not assess fault-detection capability directly. We present an empirical comparison of LLM-generated and human-written unit tests across three complementary Python benchmarks: 29 real historical bugs from BugsInPy, a function-level benchmark drawn from python-slugify and packaging, and a controlled paired benchmark. Our generation pipeline couples Gemini 2.5 Flash with a lightweight lexical retrieval mechanism that supplies bug-relevant context at generation time. Across eight quality dimensions, LLM-generated tests with retrieval-augmented context detect faults in 69% of cases compared to 17.2% for general-purpose human-written tests (Fisher's exact, $p < 0.001$, Cohen's $h = 1.10$). Critically, line and branch coverage are nearly identical between the two approaches (84.8% vs. 88.5% and 75.2% vs. 82.1%), confirming that coverage is an insufficient proxy for fault-detection capability. We discuss the conditions under which each approach excels, characterize their complementary strengths, and identify the critical role of retrieval context and reproducible benchmark construction in meaningful test-quality evaluation.

Anomaly detection methods in financial time series score statistically unusual observations in observable data, not topologically misexpected persistent deviations in the latent structure of co-movement. This study constructs a stock-level topological anomaly score jointly conditioned on market-level topological structure and cross-sectional peer context, and tests whether its history carries predictive content for return curves. Intraday data for ten liquid S&P 500 constituents (April 2025--March 2026) are embedded via Takens delay embedding, graphed by BallMapper, and scored by three decoder-conditional variational autoencoder variants. Predictive content is assessed by penalised function-on-function regression and confirmed across all assets, intraday bar frequencies, and scoring variants, revealing a consistent temporal fingerprint -- gradual accumulation of return impact, a frequent early reversal of its direction, and broadly distributed predictive content weighted toward recent anomaly history. When the reversal occurs depends on market regime; how evenly the anomaly history contributes to prediction depends on bar frequency.

In this work, we study the stochastic Schrödinger--KdV equation driven by additive noise from both analytical and numerical viewpoints. We first establish the evolution laws for the averaged plasmon number, momentum, and energy, together with the conservation of the averaged particle number. Motivated by these intrinsic structures, we develop two temporal discretizations. One is constructed based on the splitting strategy and Crank--Nicolson scheme, and is shown to preserve the discrete evolution laws of the averaged plasmon number and momentum, as well as the discrete conservation law of the averaged particle number. The other is proposed within the constant scalar auxiliary variable framework, in which the nonlinear energy functional is reformulated so that a modified averaged energy law can be preserved at the discrete level. Combining these temporal discretizations with a local discontinuous Galerkin approximation in space yields structure-preserving full discretizations inheriting the corresponding discrete physical laws. Numerical experiments are presented to validate the theoretical results and to demonstrate the accuracy, robustness, and effectiveness of the proposed methods.

Scattering amplitudes of $n$ particles in nonabelian gauge theories admit factorizations of the general form $\mathcal{A}_n \;=\; \mathcal{A}^{\rm soft}_n \times \mathcal{A}^{\rm hard}_n$, where $\mathcal{A}^{\rm soft}_n$ is IR divergent, while $\mathcal{A}^{\rm hard}_n$ is IR finite and encodes the higher loop corrections to scattering. We specify a particular all-orders definition of this factorization for planar ${\cal N}=4$ super Yang-Mills (SYM) and argue that the resulting $\mathcal{A}_n^{\rm hard}$ obeys an uncorrected tree-level soft theorem. Moreover it furnishes a representation of the undeformed tree-level $\cal S$-algebra generated by a tower of soft gluons. The results follow from several commonly invoked assumptions for ${\cal N}=4$ SYM, including BDS one-loop exponentiation of the splitting function and amplitude/Wilson-loop duality.

Consider a finite particle system in which, at each step, one particle from a vertex with a lower neighboring vertex moves to a neighboring vertex of minimum height. For the cycle C_n, started with n particles at one vertex and no particles elsewhere, we prove that the expected stabilization time is at most a constant multiple of n^3 The deterministic transportation lower bound is of order n^2. Simulations suggest that the true order should be near n^3. Chat GPT was used to reincarnate notes from 2007.

Multi-condition retrieval requires systems to identify documents that satisfy multiple distinct constraints, moving beyond mere topical relevance. While query decomposition is widely adopted as an intuitive remedy, its effectiveness across different retrieval pipeline stages remains underexplored. In this paper, we conduct a stage-aware empirical study and uncover a stark, stage-dependent effect: decomposition during initial retrieval frequently harms retrieval performance due to semantic dilution, yet substantially improves reranking by enabling more fine-grained constraint verification. Motivated by these insights, we propose a principled Stage-Aware Decomposition framework that retains the monolithic query during initial retrieval to preserve global semantic context, while employing sub-queries exclusively during reranking for fine-grained constraint matching. Extensive evaluations on the MultiConIR and SSRB benchmarks demonstrate that our framework consistently improves ranking performance for compositional queries across multiple retrieval and reranking models. We release our code at https://github.com/EIT-NLP/Query-Decompose.

We investigate the numerical range $W(T)$ and numerical radius $w(T)$ of operators of the form $T = \begin{pmatrix} A & B \\ 0 & 0 \end{pmatrix}$. We show that $W(T)$ is the union of the numerical ranges of a family of $2\times 2$ matrices, $T_x$, leading to several consequences, including improved inequalities for $w(T)$. For cases where $A$ is a self-adjoint involution, we characterize the conditions under which $W(T)$ is an elliptical disk and determine the minimum numerical radius of $T_U = \begin{pmatrix} U^*AU & B \\ 0 & 0 \end{pmatrix}$ over all unitary operators $U$. Finally, we study matrices $T \in M_n$ satisfying $\|T^m x\| = \|T^m\| = \|T\|$ for a unit vector $x$ and all positive integers $m$. This analysis connects these matrices to the aforementioned block form and provides a counterexample to the conjecture that if $\|T^k\| = \|T\|$ for all $k \ge 1$, then some power of the matrix has a direct summand that is a scalar multiple of an idempotent.

The dynamics of buoyant droplets rising freely in a large body of an immiscible liquid is investigated numerically for a moderate drop-to-fluid viscosity ratio $μ^\ast$. We focus on toluene droplets rising in clean water, for which $μ^\ast=0.62$, and vary the radius over $0.5\,\text{mm}\leq R\leq3.0\,\text{mm}$. Direct numerical simulations are performed in imposed axisymmetric and fully three-dimensional configurations. As $R$ increases, the system displays a rich sequence of rise regimes. Starting from steady vertical rise with an axisymmetric disturbance flow, it first undergoes an internal flow instability associated with an azimuthal mode $m=2$, leading to a biplanar-symmetric wake and reduced terminal speed. This state is followed by a steady oblique regime, in which the $m=1$ mode also becomes unstable and coexists with the $m=2$ mode. At larger radii, the path becomes nearly vertical again before the flow enters an $m=2$ rotating-wave regime, where the wake drifts azimuthally at an approximately constant angular velocity. For still larger droplets, persistent shape oscillations and vortex shedding lead to fully three-dimensional chaotic paths. Simulations initialised from finite-amplitude asymmetric states further reveal several multistable size ranges, in which distinct terminal states coexist depending on the initial condition. Taken together, these findings show that the path instability of moderate-viscosity-ratio droplets differs fundamentally from that of bubbles and solid particles: in most regimes encountered here, axisymmetry breaking is initiated within the droplet, highlighting the central role of the internal flow instability in shaping the subsequent wake structure, rise speed and droplet dynamics.

We construct Newton--Okounkov polytopes of Schubert varieties in partial flag varieties of arbitrary type using the cluster structure on a unipotent cell. When the governing cluster algebra is of infinite type, we prove that for any very ample homogeneous line bundle over a simply laced partial flag variety, the resulting family of Newton--Okounkov polytopes contains infinitely many pairwise nonequivalent polytopes up to integral affine transformation. As an application to symplectic geometry, we construct infinitely many distinct monotone Lagrangian tori in a broad class of simply laced partial flag varieties.

This paper has used European put option to construct the p-index risk measure to evaluate the performance of different investment strategies in China's SSE 50 index and the US SP500 index during 2018-2023. The p-index measures the insurance fee for each insured dollar to guarantee that the asset achieves at least a delta rate of return on a specified future date. It is found that with the fair price strategy, one-week and one-month holding periods can earn more, and among seven economic sectors, materials sector stocks generated highest annualized rates of return: 11.04% (one-week period), 11.93% (two-week period) and 10.18% (one-month period). With momentum and contrarian strategies of one-week holding period, the p-ratio-efficient-contrarian strategy produced the highest annualized rate of return (9.97%), followed by the p-index-inefficient-momentum strategy (9.01%) and the p-index-efficient-contrarian strategy (6.48%), the MCIRS method employing the p-index consistently delivered higher returns than its beta-based approach, and efficient (outperforming) stocks failed to sustain their momentum while inefficient (underperforming) stocks exhibited no mean reversion. It is also found that the p-index-efficient-contrarian strategy outperformed in low-sentiment (low-volume) regimes, while the p-index-inefficient-momentum strategy outperformed during high-sentiment (high-volume) periods. For the five hundred stocks of the US S&P 500 index during 2018-2023, it is found that efficient stocks sustained their momentum while inefficient stocks exhibited mean reversion. The p-index-efficient-momentum strategy produced the highest annualized rate of return (3.69%), followed by the p-ratio-inefficient-contrarian strategy (3.67%) and the beta-efficient-momentum strategy (3.48%).

Generative AI (GenAI) tools are now common learning companions for adolescents, yet how they regulate their use during authentic learning tasks remains poorly understood. Self-regulated learning (SRL) and high-level help-seeking (HS) are commonly proposed as safeguards against passive or shortcut-oriented use, but most empirical studies focus on aggregate learning outcomes rather than these moment-to-moment processes during AI-supported learning. This work-in-progress examines open-ended conversational data from 98 Grade-9 students across three German Gymnasium schools, who used a web-based Mistral-Large tutor to prepare a curriculum-aligned mathematics skill before an exam. Alongside chat logs (1,616 turns; 808 student turns), we collected pre-post domain knowledge, pre-chat learning needs, and self-reported cognitive load. We propose a turn-level codebook combining theory-driven SRL and HS constructs with two LLM-specific inductive codes (agency over the AI; epistemic vigilance), and report preliminary AI-coded results. Although students overwhelmingly selected scaffolded support before the chat, their interactions were dominated by instrumental requests with almost no explicit monitoring or evaluation. Post-test performance was significantly lower than pre-test, and higher extraneous cognitive load predicted lower post-test scores after controlling for prior knowledge. We discuss how these patterns can support hybrid human-AI analysis of interaction patterns and inform scaffolds for more agentic and epistemically proactive GenAI use.

V-doped [Ca$_{2}$Nb$_{3-x}$V$_{x}$O$_{10}$]$^{-}$ (x = 0, 0.15, 0.3, 0.6, 0.75) nanosheets were produced by solid state reaction followed by protonation and exfoliation by tetrabutylammonium ions. 2D nanosheets have improved photocatalytic activity due to their small thickness that reduces electron-hole recombination, larger surface area that increases photocatalytic sites, and decreased band gap from added V. V-doping has caused the wide band gap of 3.54 eV of undoped nanosheets to decrease to 2.60-2.88 eV range. 10 vol% methanol was used as a hole scavenger in the hydrogen evolution reactions, and 3 wt% Pt was deposited on nanosheets as a co-catalyst. Under a full-spectrum Xe light, [Ca$_{2}$Nb$_{2.7}$V$_{0.3}$O$_{10}$]$^{-}$ has produced 4.7 times the H$_{2}$ yield as undoped nanosheets with a 11.3 mmol/g/h production rate, [Ca$_{2}$Nb$_{2.7}$V$_{0.3}$O$_{10}$]$^{-}$ with Pt co-catalyst has produced 2.9 times the H$_{2}$ yield as undoped Pt-loaded nanosheets.

We study particle-loss resistant entanglement within the framework of stabilizer and graph states. A pure state is \(m\)-resistant if it remains entangled after the loss of any \(m\) particles and becomes fully separable after the loss of any \(m+1\) particles. The smallest previously unresolved qubit case was the existence of a five-qubit \(1\)-resistant pure state, which is resolved here by the five-cycle graph state \(\ket{C_5}\). A stabilizer-subgroup method is also developed for verifying \(m\)-resistance in graph states, using local stabilizers to certify full separability and exact negative partial transpose~(NPT) witnesses to certify entanglement. Applying this to all graph states associated with non-isomorphic graphs on five, six, and seven vertices, we obtain a graph state classification up to local Clifford equivalence, which also classifies stabilizer states up to local Clifford equivalence. Thus, the five-qubit \(1\)-resistant stabilizer states are exactly the local Clifford class of \(C_5\). Six-qubit \(2\)-resistant stabilizer states exist in three distinct local Clifford classes, whereas no seven-qubit stabilizer state is \(m\)-resistant for any nonzero admissible \(m\). Finally, we prove that the cycle graph states \(\ket{C_N}\) with \(N\ge 7\) are not \(m\)-resistant for any \(0\le m\le N-2\).

We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors are linearly independent, allowing the factors to be correlated and the factor loading vectors to be not nearly orthogonal. The procedure adapts to the sparsity of the factor loading vectors, accommodates weak factors, and demonstrates strong performance across a wide range of scenarios. To further reduce estimation errors, we also introduce an iterative algorithm based on a novel double projection approach. We theoretically justify the improved convergence rate of the iterative estimator, and derive the associated limiting distribution. A consistent estimator of the asymptotic variance is also provided, which plays a key role in the related inference problems. All results are validated through extensive simulations and two real data applications.