In this paper, we study vector valued de Branges spaces associated with a de Branges operator, defined as a pair of Fredholm operator valued analytic functions on a domain symmetric with respect to the unit circle. Using a suitable direct sum decomposition of a Hilbert space, we construct a class of vector valued reproducing kernel Hilbert spaces and show that under some assumptions these are vector valued de Branges spaces. We further demonstrate that these spaces provide functional models for certain class of completely non-unitary contraction operators. We also give a Fredholm-type criterion for verifying the hypotheses of the main construction and apply it to several concrete classes of completely non-unitary contractions. Next, we establish connections between the Sz.-Nagy-Foias characteristic function of the contraction operator, the projection operator valued function arising from the Hilbert space decomposition, and the reproducing kernel of the de Branges space. In particular, we show that the characteristic function coincides with the projection operator valued function on the unit disc. Enroute, we also obtain a characterization of unitary equivalence for a certain class of cnu contractions in terms of the corresponding de Branges operators. These results provide a new perspective on the role of vector valued de Branges spaces in operator model theory.

$SU(\infty)$ Quantum GRavity (QGR) is a recently proposed fundamentally quantum approach to gravity and cosmology. In this model the Hilbert space of the Universe represents $SU(\infty)$ symmetry. Its fragmentation generates approximately isolated subsystems (particles) representing, in addition to $SU(\infty)$, finite-rank local symmetries. The common $SU(\infty)$ is associated to quantum gravity, and at lowest quantum order the effective action for all symmetries is Yang-Mills on a 4D parameter space $Ξ$. Nonetheless, physical processes and measurables must be independent of the geometry of $Ξ$. In previous works we demonstrated that diffeomorphism of $Ξ$ can be neutralized by $SU(\infty)$ gauge transformation. In this work we show that the invariance of action under variation of $Ξ$'s metric leads to a constraint resembling Einstein equation. It consists of energy-momentum tensors for all components of the model, including the spin-1 gravitons. In addition, through calculation of quantum information measures we study the effect of Hilbert Space Fragmentation (HSF) on the emergent classical spacetime and different cosmological era, such as inflation, reheating, and late time accelerating expansion. The results of this preliminary and approximate investigation show that HSF may be classically interpreted as these phenomena. Consequently, inflaton, quintessence, and similar fields associated to these processes may be order parameters that phenomenologically present them.

We investigate whether the spinor field can be differential-algebraically eliminated from the Maxwell--Dirac equations in a particular gauge. To this end, we construct a generic truncated power-series solution and linearize the prolonged system of the Maxwell--Dirac equations about this solution. We then analyze the ranks of the coefficient matrices associated with the linearized system. Our results indicate that, generically, the spinor components are uniquely determined by the electromagnetic field and its derivatives. Furthermore, the fourth-order time derivatives of the components of the electromagnetic four-potential are uniquely determined by derivatives of the lower order with respect to time. These findings strongly suggest that the spinor field can be differential-algebraically eliminated, and the resulting equations describe independent evolution of the electromagnetic field, i.e., a Cauchy problem can be formulated in terms of the electromagnetic variables alone.

Conversational recommender systems (CRSs) operate under incremental preference revelation, requiring recommendation decisions under uncertainty. While recent LLM-based approaches achieve strong performance on proxy metrics such as Recall@K and BLEU, they often fail to deliver high-quality, user-aligned recommendations in practice, as they optimize intermediate objectives like retrieval accuracy or fluent generation rather than recommendation quality itself. We propose HARPO (Hierarchical Agentic Reasoning with Preference Optimization), an agentic framework that reframes conversational recommendation as a structured decision-making process optimized for multi-dimensional recommendation quality. HARPO integrates (i) hierarchical preference learning that decomposes recommendation quality into interpretable dimensions (relevance, diversity, satisfaction, and engagement) with context-dependent weighting; (ii) deliberative tree-search reasoning guided by a learned value network evaluating candidate paths on predicted quality; and (iii) domain-agnostic reasoning abstractions through Virtual Tool Operations and multi-agent refinement. We evaluate HARPO on ReDial, INSPIRED, and MUSE, demonstrating consistent improvements over strong baselines on recommendation-centric metrics while maintaining competitive response quality.

For a smooth projective surface $S$, Johnson--Oprea--Pandharipande defined cohomological descendent generating series for Quot schemes of rank-$0$ quotients of $\OO_S^{\oplus N}$. We prove rationality of these series in the remaining cohomological surface case \[ p_g(S)=0,\qquad β\neq 0,\qquad N>1. \] The wall-crossing part of the proof starts from Joyce-style generalized Donaldson--Thomas invariant classes of $H$-Gieseker semistable one-dimensional sheaves. We vary a single real parameter in the fixed-source Pairs stability condition and obtain the large-$c$ stable-pair chamber for maps $\OO_S^{\oplus N}\to F$. We then compare this pair chamber with the open pure Quot locus, meaning the locus inside the Quot scheme whose target quotient is pure one-dimensional, and then with the full Quot scheme, where zero-dimensional torsion in the target is allowed. The first comparison records the zero-dimensional cokernel of the image of a pair. After decomposing the pure Quot locus into locally-closed pieces on which the scheme-theoretic support curve is flat over the base, this comparison is identified with relative Quot theory on those support curves. The resulting curve-Quot contributions factor into smooth-normalization contributions and finitely many punctual factors at singular points of the support curve. The second comparison records the maximal zero-dimensional torsion subsheaf of a Quot target; locally it becomes a punctual Quot problem over the completed smooth surface ring $\C[[x,y]]$, and its contribution is the universal punctual smooth-surface factor.

Parkinsons disease (PD) alters cortical neural dynamics, yet reliable non-invasive electrophysiological biomarkers remain elusive. This study examined whether interpretable EEG features capturing complementary aspects of neural dynamics can discriminate Parkinsonian neural states. A comprehensive set of interpretable features was extracted and grouped into Standard descriptors (spectral power, phase synchronization, time-domain statistics) and Dynamical descriptors (aperiodic activity, cross-frequency coupling, scale-free dynamics, neuronal avalanche statistics, and instantaneous frequency measures). A multi-head attention transformer classifier was trained using strict LOSO validation. Group-level comparisons were performed to identify electrophysiological differences associated with disease and medication state. Standard feature sets achieved strongest performance in discriminating medication states (PDoff vs PDon), whereas Dynamical performed competitively in contrasts between PD patients and healthy controls. Random feature ablation analyses indicated that Dynamical descriptors provide complementary information distributed across features while correlation analysis revealed low redundancy within both feature sets. Group-level comparisons revealed medication-sensitive reductions in delta power and voltage variance, modulation of neuronal avalanche statistics, persistent increases in theta phase synchronization in PD patients, and disease-related alterations in cross-frequency interactions. Traditional spectral and synchronization features primarily reflect medication-related neural modulation, whereas dynamical descriptors reveal broader alterations in cortical network organization associated with disease but also with medication. These findings support multivariate EEG representations as a promising framework for developing non-invasive biomarkers of PD.

Market area models, such as the Huff model and its extensions, are widely used to estimate regional market shares and customer flows of retail and service locations. Another, now very common, area of application is the analysis of catchment areas, supply structures and the accessibility of healthcare locations. The huff Python package provides a complete workflow for market area analysis, including data import, construction of origin-destination interaction matrices, basic model analysis, parameter estimation from empirical data, calculation of distance or travel time indicators, and map visualization. Additionally, the package provides several methods of spatial accessibility analysis. The package is modular and object-oriented. It is intended for researchers in economic geography, regional economics, spatial planning, marketing, geoinformation science, and health geography. The software is openly available via the Python Package Index (PyPI) (https://pypi.org/project/huff/); its development and version history are managed in a public GitHub Repository (https://github.com/geowieland/huff_official) and archived at Zenodo (https://doi.org/10.5281/zenodo.18639559).

We solve the entropy-regularized mean-variance portfolio problem under Bayesian drift uncertainty. Combining continuous-time Bayesian filtering with stochastic policy optimization, the main finding is negative: the two mechanisms are orthogonal. Posterior dynamics are policy independent, so entropy regularization cannot accelerate learning about the unknown drift. The mean control is identical to the deterministic Bayesian Markowitz feedback, and entropy enters only through policy variance. On the technical side, the optimal policy is Gaussian, the value function is quadratic in wealth, and the belief-dependent coefficients close in exponential form. The framework recovers both parent models as limiting cases.

Autonomous electrolyte discovery demands a computational engine that satisfies a critical trilemma: it must be fast enough for high-throughput screening, accurate enough for quantitative property prediction, and calibratable enough for online refinement. Classical empirical force fields (FFs) are fast but rely on error cancellation, while standard machine learning interatomic potentials (MLIPs) are computationally expensive. In this Perspective, we highlight that differentiable hybrid FFs resolve this trilemma by fusing physically motivated functional forms with neural-network short-range corrections. Grounded in Energy Decomposition Analysis (EDA), state-of-the-art models such as PhyNEO-Electrolyte and ByteFF-Pol achieve zero-shot generalization to bulk phases, delivering throughputs on the order of tens of ns/day (up to $\sim$50 ns/day, depending on model complexity) for 10,000-atom systems. Crucially, their physical skeletons provide a well-conditioned parameter space for differentiable molecular dynamics (dMD). This enables a dual-calibration paradigm: bottom-up \textit{ab initio} parameterization combined with top-down fine-tuning from macroscopic experimental observables. We propose that this architecture meets the requirements of a ``ChemRobot-ready'' digital twin by integrating physics-grounded simulation with experimentally calibratable refinement, thereby enabling closed-loop autonomous electrolyte discovery.

We investigate the lift and drag corrections acting on a particle suspended in a planar viscoelastic shear flow when the particle is tuned to translate relative to the flow by an external mechanism. A cross-stream lift force arises when particle is driven in streamwise direction; we find that the nature of the driving mechanism dictates the lift direction: force-bearing mechanisms (such as gravity acting on non-neutrally buoyant particles) and force-free mechanisms (such as electrophoresis) generate lift forces of opposite sign. By explicitly deriving the first-order fields and stresses, we demonstrate that this reversal originates from distinct hydrodynamic disturbances induced by each mechanism, which produce qualitatively different polymeric stress distributions. This analytical result is further verified through an independent derivation using the reciprocal theorem. Further, we find that driving the particle in the gradient direction gives rise to a streamwise drag correction that is of the same sign for both mechanisms. Beyond microfluidic particle manipulation, these results have broader implications for understanding the locomotion of microswimmers in viscoelastic shear flows, where distinct force-free propulsion mechanisms are expected to generate unique force and torque modifications.

A matrix model on a D-dimensional Euclidean space is introduced as a generalization of random matrix models and as a non-perturbative definition of discretized closed string theory. The free energy of the matrix model is formally derived to all orders in string perturbation expansion and shown to be given in terms of invariant graph polynomials, whose coefficients enumerate ribbon graphs and are a refinement of the generalized Catalan numbers. The vacuum diagrams contributing to the free energy are found to be related to Gaussian molecules, known from the study of polymer structures. Coupling the matrix field to a curved background with Riemannian metric yields a non-perturbative definition of discretized string theory on this background. No on-shell condition for the metric is required to arrive at the free energy. Rather, it is shown that the free energy of the matrix model is the Einstein-Hilbert action with cosmological constant term. The gravitational and the cosmological constants are both formally determined to all orders in the string perturbation expansion. In fact, they are explicitly given by the expectation value of a particular graph invariant. Introducing a vector field, minimally coupled to a background gauge field, provides a discretized open-closed string theory, leading to the Yang-Mills action as well as intrinsic and extrinsic curvature terms.

In this paper, we study the attractor mechanism for extremal, spherically symmetric black holes in pure, untruncated, N=4 Poincaré supergravity, which we demonstrate numerically. We further study the supersymmetries preserved by these attractor solutions by focussing specifically on the constant moduli solutions and show that they always preserve 1/4$^{th}$ of the total supersymmetries. We also give an argument that even the attractor solutions with a ``non-constant'' moduli would preserve 1/4$^{th}$ of the total supersymmetries. This would mean that in pure N=4 supergravity there exist no attractor solutions which are non-supersymmetric although they could in-principle exist in a matter coupled theory. We use the framework of conformal supergravity in our analysis, which is a manifestly off-shell framework and considerably simplifies the Killing spinor analysis.

We present a differential machine learning method for zero-days-to-expiry (0DTE) options under a stochastic-volatility jump-diffusion model. To handle the ultra-short-maturity regime, we express the option price in Black-Scholes form with a maturity-gated variance correction, combining supervision on prices and Greeks with a PIDE-residual penalty. Prices and Greeks are derived from a single trained pricing network, while jump-term identifiability is ensured by a jump-operator network fitted jointly in a three-stage procedure. The method improves jump-term approximation relative to one-stage baselines while maintaining comparable pricing errors. Furthermore, it reduces errors in Greeks, produces stable one-day delta hedges, and offers significant speedups over Fourier-based benchmarks. Calibration experiments demonstrate the network's efficiency as a pricer and incorporating jump-intensity price sensitivity into the learning process further improves the overall model fit. We also consider a jump rough Heston model.

The Friedmann cosmological solution of the standard Einstein gravitational field equation has a curvature singularity at a moment in time known as the Big Bang. It has been suggested that this Big Bang curvature singularity can be eliminated by use of a degenerate spacetime metric. This proposal was the main topic of our talk at the Workshop, but, here, we also discuss the possible appearance of CPT-conjugated worlds and the conjectured relevance of an extended version of Einstein's field equation.

The transition from 5G to 6G requires frequency-dependent, physically consistent radio channel models across the upper-FR1/FR3 transition region, particularly in the underexplored 4--8 GHz region targeted in the current WRC-27 studies, where outdoor urban channel measurements and characterizations remain scarce. This paper presents a 4.85 GHz measurement-anchored study of urban channels and a literature-referenced cross-band analysis. Double-directional measurements were conducted at 4.85 GHz in urban macrocell (UMa) and urban microcell (UMi) routes in Yokohama, Japan, from which path loss, delay spread (DS), azimuth spread of arrival/departure (ASA/ASD), K-factor, and route-dependent spatial-consistency statistics were extracted. To align these results in a broader cross-band context, the measured 4.85 GHz large-scale parameter (LSP) means were combined with scenario-matched literature anchors to derive log-log trends for DS, ASA, and ASD over an approximately 4--28 GHz range around the 7.125 GHz upper-FR1/FR3 cross-band boundary. The resulting trends were compared with 3GPP UMa/UMi reference parameterizations over the same interval, and the sensitivity of the UMi DS fit was examined via leave-one-out analysis. Because the cross-band analysis still relies on a single in-house measurement band alongside heterogeneous anchors from different campaigns, it is presented as measurement-informed and indicative rather than as a definitive multi-band model. The paper therefore contributes both a detailed, parameterized 4.85 GHz urban measurement reference and a bounded literature-referenced view of channel behavior near the upper-FR1/FR3 transition

Using the recent advances in the structure of algebraic groups over imperfect fields, we prove a generalization of Serre's Conjecture I and of results that revolve around it. In particular, we show that the first Galois cohomology set of any unirational algebraic group is trivial if the cohomological dimension of the field is at most 1 in Kato's sense.

Debugging distributed systems in-production is inevitable and hard. Myriad interactions between concurrent components in modern, complex and large-scale systems cause non-deterministic bugs that offline testing and verification fail to capture. When bugs surface at runtime, their root causes may be far removed from their symptoms. To identify a root cause, developers often need evidence scattered across multiple components and traces. Unfortunately, existing tools fail to quickly and automatically record useful provenance information at low overheads, leaving developers to manually perform the onerous evidence collection task. Lumos is an online debugging framework that exposes application-level bug provenances--the computational history linking symptoms of an incident to their root causes. Lumos leverages dependency-guided instrumentation powered by static analysis to identify program state related to a bug's provenance, and exposes them via lightweight on-demand recording. Lumos provides developers with enough evidence to identify a bug's root cause, while incurring low runtime overhead, and given only a few occurrences of a bug.

The deployment of Large Language Models (LLMs) has ignited concerns about technological unemployment. Existing task-based evaluations predominantly measure theoretical "exposure" to AI capabilities, ignoring critical frictions of real-world commercial adoption: liability, compliance, and physical safety. We argue occupations are not eradicated instantaneously, but gradually encroached upon via atomic actions. We introduce a Tech-Risk Dual-Factor Model to re-evaluate this. By deconstructing 923 occupations into 2,087 Detailed Work Activities (DWAs), we utilize a multi-agent LLM ensemble to score both technical feasibility and business risk. Through variance-based Human-in-the-Loop (HITL) validation with an expert panel, we demonstrate a profound cognitive gap: isolated algorithmic probabilities fail to encapsulate the "institutional premium" imposed by experts bounded by professional liability. Applying a strictly algorithmic baseline via mathematical bottleneck aggregation, we calculate Relative Occupational Automation Indices ($OAI$) for the U.S. labor market. Our findings challenge the traditional Routine-Biased Technological Change (RBTC) hypothesis. Non-routine cognitive roles highly dependent on symbolic manipulation (e.g., Data Scientists) face unprecedented exposure ($OAI \approx 0.70$). Conversely, unstructured physical trades and high-stakes caretaking roles exhibit absolute resilience, quantifying a profound "Cognitive Risk Asymmetry." We hypothesize the emergent necessity of a "Compliance Premium," indicating wage resilience increasingly tied to risk-absorption capacity. We frame these findings as a cross-sectional diagnostic of systemic vulnerability, establishing a foundation for subsequent Computable General Equilibrium (CGE) econometric modeling involving dynamic wage elasticity and structural labor reallocation.

The interplay between interlayer coupling and quantum fluctuations governs charge ordering and defect dynamics in Kagome systems, yet these parameters are intrinsically entangled in existing Kagome metals and artificial spin-ice platforms, preventing their independent control. Here we realize a bilayer Kagome frustrated-magnet simulator comprising 1,536 connected spins on D-Wave quantum annealer, in which the effective quantum drive, $Γ_{\rm eff}$, and interlayer exchange, $J_{\perp}$, are independently programmable. We observe an interlayer-driven transition from ferroelectric to antiferroelectric Ice-II charge order at a critical coupling $(J_\perp/J_1)^*\approx0.04$, a phenomenon absent in single-layer geometries. Monte Carlo calculations show the transition persists in the classical limit, allowing the experimentally observed critical coupling to quantify the quantum renormalization induced by fluctuations. Applying resulting phase diagram to Kagome charge-density-wave materials places KV$_3$Sb$_5$ and RbV$_3$Sb$_5$ deep within the ordered antiferroelectric regime, while locating CsV$_3$Sb$_5$ near the phase boundary, providing a natural explanation for its metastable $2\times2\times4$ stacking order. We further show that restricting charge-correlation measurements to ice-rule configurations resolves a systematic underestimation of ordering in conventional analyses, enabling direct reinterpretation of resonant X-ray, XMCD, STM and anomalous Hall experiments. Finally, we demonstrate that the same charge-sector reorganization framework explains near-degenerate plateau states in the metallic Kagome spin-ice HoAgGe and yields experimentally testable predictions for nanomagnetic, Kagome-metal and van der Waals frustrated systems. These results establish programmable quantum annealers as scalable simulators of emergent charge order and monopole physics in frustrated quantum matter.

We introduce a monoidal analogue of Jantzen filtrations in the framework of monoidal abelian categories with generic braidings. It leads to a deformation of the multiplication of the Grothendieck ring. We conjecture, and we prove in many remarkable situations, that this deformation is associative so that our construction yields a quantization of the Grothendieck ring as well as analogs of Kazhdan-Lusztig polynomials. As a first main example, for finite-dimensional representations of simply-laced quantum loop algebras, we prove the associativity and we establish that the resulting quantization coincides with the quantum Grothendieck ring constructed by Nakajima and Varagnolo-Vasserot in a geometric manner. Hence, it yields a unified representation-theoretic interpretation of the quantum Grothendieck ring. As a second main example, we establish an analogous result for a monoidal category of finite-dimensional modules over symmetric quiver Hecke algebras categorifying the coordinate ring of a unipotent group associated with a Weyl group element. We obtain various applications, in particular on the homological structure of representations.

This thesis explores the evolution of liquid-state theories based on the Ornstein-Zernike (OZ) equation, summarizing the foundational methods developed by Baxter, Lebowitz, Wertheim, and others. A unifying feature of these approaches is their shared analytical strategy: by introducing an intermediate function with specific mathematical properties, they effectively decouple the total correlation function and the direct correlation function. This allows the OZ equation to be solved within specific spatial intervals by exploiting regions where either the total or direct correlation function is known. Furthermore, this work presents a comprehensive derivation of analytical solutions to the OZ integral equation under the hard-sphere model. This includes applications of the Percus-Yevick (PY) approximation for both single- and multi-component systems, as well as the Mean Spherical Approximation (MSA) for systems of charged hard spheres. Building upon these analytical solutions, explicit expressions for macroscopic thermodynamic properties, such as the equation of state and activity coefficients, are rigorously derived. These derivations extensively employ advanced mathematical techniques, including Fourier transforms, complex analysis, and integral equation theory. Notably, many of the intermediate analytical steps and thermodynamic derivations presented herein offer a level of clarity and completeness previously absent from the existing literature.

We investigate the dynamical and thermodynamic evolution of a Schwarzschild black hole in Modified Gravity (MOG) perturbed by a scalar gravitational wave breathing mode. By evaluating the linearized modified Einstein equations at the near-horizon boundary, we reduce the spatial wave operator to a closed-form temporal ordinary differential equation, thereby explicitly deriving the damped-oscillatory kinematics of the scalar strain. Using a quasi-adiabatic approximation, we show that the effective surface gravity and dynamical temperature are linearly modulated by the perturbation amplitude and velocity. These rapid geometric fluctuations break the semiclassical adiabatic regime, triggering explicitly non-thermal particle creation analogous to the dynamical Casimir effect. Furthermore, we resolve a local thermodynamic paradox concerning apparent horizon area fluctuations. We prove that first-order geometric perturbations $\mathcal{O}(h_b)$ are fully reversible kinematic artifacts, whereas irreversible entropy generation is a strictly second-order $\mathcal{O}(h_b^2)$ effect driven by the Raychaudhuri expansion, thereby preserving the Generalized Second Law. Finally, we apply these mechanisms to the black hole information paradox. We show that treating the MOG deformation parameter as a quantum-scale running coupling, $α(M)$, mathematically decouples the effective gravitational charge from linear mass scaling. This dynamically forces the evaporating black hole toward the extremal limit ($M_G \to Q_G$), smoothly quenching the Hawking temperature to zero and yielding a thermodynamically stable, information-preserving remnant.

The multi-word-representation number $μ(G)$ of a graph $G$ is the minimum number of word-representable graphs whose union is $G$. We study the behavior of $μ$ under six standard graph products: the lexicographic, Cartesian, rooted, corona, tensor, and strong products. For the Cartesian and rooted products, we show that $μ(G_1 \square G_2)=μ(G_1 \diamond G_2)=\max\{μ(G_1),μ(G_2)\}$. For the corona product, we prove that $μ(G_1 \odot G_2)\le \max\{μ(G_1),μ(G_2)\}+1$, and we identify a condition under which equality holds. For the lexicographic product, we establish $μ(G_1 \circ G_2)\le μ(G_1)+μ(G_2)$, which reduces to $\max\{μ(G_1),μ(G_2)\}$ under a comparability cover condition on $G_2$, and we characterize the case when the lexicographic product of two minimal non-word-representable graphs has $μ=2$. For the tensor product $G_1 \times G_2$, we show $μ(G_1 \times G_2)\le \log_3(\min\{χ(G_1),χ(G_2)\})$. For the strong product $G_1 \boxtimes G_2$, we establish $\max\{μ(G_1),μ(G_2)\}\le μ(G_1 \boxtimes G_2)\le \max\{μ(G_1),μ(G_2)\}+\log_3(\min\{χ(G_1),χ(G_2)\})$. For lexicographic powers $G^{[k]}$, we prove that $μ(G^{[k]})\le k$ when $G$ is word-representable but not a comparability graph, and in general $μ(G^{[k]})$ is bounded by the comparability cover number of $G$. We further show that $G^{[k]}$ is word-representable if and only if $G$ is a comparability graph. As an application, we obtain a sublinear upper bound on the extremal function $τ(n)$, defined as the largest integer such that every $n$-vertex graph contains a word-representable induced subgraph of that size; in particular, $τ(8^k)\le 6^k$, implying $τ(n)\le n^{\log_8 6+ε}$ for large $n$.

Symmetric mass generation (SMG) has attracted growing interest in both condensed matter theory and lattice-QCD communities. Here we formulate general criteria for SMG and examine their compatibility with lattice-QCD. We propose possible RG-flow scenarios near the SMG transition, and argue that meson mass ratio can serve as a probe of the SMG transition viewed as a UV fixed point. We further identify Goldstone tetraquark meson states as phenomenological signatures of the "type-II'' SMG phase.

We present an X-ray characterization of a fully depleted, 725 $μ$m thick p-channel SiSeRO-CCD. Measurements with a $^{55}$Fe source yield an energy resolution of $54 \pm 0.9$ eV ($14.6 \pm 0.25 e^{-}$) at 5.9 keV for single-pixel events, indicating that the SiSeRO amplifier preserves the intrinsic charge resolution of the CCD under multi-sample non-destructive readout. Characterization with a $^{241}$Am source extends the response to higher-energy photons, with reconstructed spectral features observed between 9-26 keV and the 59.5 keV $γ$ emission. These measurements, together with a muon-derived diffusion calibration, show that charge transport and diffusion are consistent with interactions spanning the full sensor depth. These results demonstrate that the SiSeRO-CCD simultaneously achieves sub-electron noise performance and efficient charge collection in a thick, fully depleted silicon detector. This combination enables X-ray spectroscopy across a broad energy range while maintaining sensitivity to faint signals.

Data-driven approximations of the infinite-dimensional Koopman operator rely on finite-dimensional projections, where the predictive accuracy of the resulting models hinges heavily on the invariance of the chosen subspace. Subspace pruning systematically discards geometrically misaligned directions to enhance this invariance proximity, which formally corresponds to the largest principal angle between the subspace and its image under the operator. Yet, existing techniques are largely restricted to Euclidean settings. To bridge this gap, this paper presents an approach for computing principal angles and vectors to enable Koopman subspace pruning within a Reproducing Kernel Hilbert Space (RKHS) geometry. We first outline an exact computational routine, which is subsequently scaled for large datasets using randomized Nystrom approximations. Based on these foundations, we introduce the Kernel-SPV and Approximate Kernel-SPV algorithms for targeted subspace refinement via principal vectors. Simulation results validate our approach.

We use a new formula for the symplectic structure on the phase space of open string field theory to evaluate the energy of a D-brane carrying a constant electric flux. This is shown to be consistent with the energy computed using the Dirac-Born-Infeld action through a generalization of the Ellwood invariant to nonpolynomial open string field theories.

We investigate the total scattering cross section($σ$), the differential cross section$\left(\frac{dσ}{dQ^2}\right)$, the longitudinal($A_L(E_e,Q^2)$) and perpendicular($A_P(E_e,Q^2)$) spin asymmetries of the polarized target proton, as well as the longitudinal($P_L(E_e,Q^2)$), perpendicular($P_P(E_e,Q^2)$), and transverse($P_T(E_e,Q^2)$) polarization components of the final neutron, in the weak charged current induced electron-proton scattering relevant to the future experiments at the Thomas Jefferson National Accelerator Facility(JLab) and Mainz Microtron(MAMI). The analysis is performed assuming time-reversal(T) invariance as well as without assuming T invariance, allowing for a nonvanishing transverse polarization component of the final nucleon, perpendicular to the production plane. Numerical results are presented for the above mentioned observables, and their sensitivities to the various parameterizations of the axial vector form factor $g_1(Q^2)$ and a nonzero weak electric form factor $g_2(Q^2)$ are examined. We find that the cross section depends strongly on the parameterizations used for the axial vector form factor. Moreover, the dipole parameterization of $g_1(Q^2)$ with a higher value of the axial dipole mass $M_A$ simulates the apparent enhancement in $σ$ obtained using the non-dipole parameterizations like the $z$-expansion and Faddeev equation form. The cross sections are found to depend only weakly on the weak electric form factor $g_2(Q^2)$, which is associated with the violation of G-invariance. On the contrary, the spin observables both $A_{L,P}(E_e, Q^2)$ and $P_{L,P}(E_e, Q^2)$ are found to be strongly dependent on $g_2(Q^2)$. This study may be useful in the analysis of the neutrino oscillation experiments to provide an alternative constrain on the parameterization of axial vector form factor, which currently has large uncertainties.

Transition-metal perovskite oxides exhibit moderately correlated metallic phases, several of which exhibit a $T^2$ resistivity scaling up to temperatures far exceeding the regime where Fermi-liquid electron-electron scattering is expected to dominate. Some of these materials, such as SrMoO$_3$, also exhibit unexplained ultra-low room-temperature resistivity. We demonstrate that in SrMoO$_3$, SrWO$_3$, SrTaO$_3$, SrNbO$_3$, and SrVO$_3$ electron-phonon scattering results in quadratic-scaling resistivity due to the shape of the Fermi surface and the thermal activation of optical phonons. We also reveal that the origin of the low resistivity of SrMoO$_3$ is an overall low electron-phonon coupling strength, and identify SrWO$_3$ and SrTaO$_3$ as other possible low-resistivity oxides. Additionally, we find that the strength of electron-phonon coupling is sensitive to structural distortions, energies of optical phonons, and the treatment of electronic correlations. This suggests design principles for finding other ultra-high conductivity transition-metal oxides, and has significant implications for theoretical interpretation of direct-current resistivity in transition-metal oxides and beyond.

By employing the classical tools from the theory of $q$-series and theta functions, new fascinating identities on different continued fractions can be achieved. In this article, we use the product expansion of Jacobi's theta function to establish identities that connect Ramanujan-Göllnitz-Gordon continued fraction with Ramanujan's continued fraction of order four. Also, we obtain Lambert series identities using Ramanujan's $_1 ψ_1$ summation formula.