Papers

Physical intelligence requires more than predicting how the world may evolve: predictions must remain actionable as the world continues to change. We introduce InternW0, the first instantiation of the InternW physical world model series from Shanghai AI Laboratory, built around omnimodal interfaces, asynchronous multi-frequency processing, and local physical modeling under partial observations and external influences. InternW0 jointly learns future visual dynamics and continuous robot control through an asymmetric video–action architecture with flow matching. A high-capacity video expert provides longer-horizon predictive context, while a lightweight action expert operates at a faster timescale. Instead of regenerating the future for every action update, InternW0 reuses layerwise K/V and adapts it to newly observed states through observation-conditioned context routing. Domain-specific interfaces and soft prompts support heterogeneous embodiments, while contact-aware post-training incorporates force and tactile signals for contact-rich manipulation. We train InternW0 on approximately 7,200 hours of heterogeneous robot and egocentric data, including EgoLab, a 275-hour real-laboratory egocentric dataset. Evaluation spans simulation benchmarks and real-world scientific tasks, including a 15-stage metal–organic framework synthesis workflow and 5-stage contact- and force-aware dexterous manipulation for general-purpose quantitative pipetting. These results advance scalable, asynchronous, and science-native physical world models for universal and efficient real-world interactions.

Self-organization of nonlinear waves underpins phenomena ranging from hydrodynamic pattern formation to optical frequency-comb generation. We introduce and numerically demonstrate a shift-register synchronization mechanism for pulse trains in quadratic nonlinear resonators. The synchronized state persists despite substantial group-velocity mismatch through continuous parametric energy exchange, resulting in deterministic discrete pulse shifts after each cavity round trip. Nonlinear parametric interaction modifies the effective walk-off, allowing the pulse trains to satisfy the shift-register synchronization conditions. The proposed mechanism reveals a previously unexplored synchronization regime in quadratic resonators and provides a route toward multicolour frequency combs, optical memories, and ultrafast photonic information processing.

Verified income is often unavailable in digital loan applications, forcing lenders to rely on reported income and potentially leading to over-lending, overly conservative offers, or rejection of creditworthy applicants. Cross-institutional data-sharing constraints make this problem especially difficult for smaller lenders with limited training data. We introduce FedIncome, a federated learning framework for income estimation that enables institutions to train a shared model without pooling raw borrower records. Using more than one million LendingClub loans partitioned into $50$ state-level clients, we simulate a heterogeneous lending consortium. The best federated model achieves out-of-time $R^2=0.608$, compared with $0.619$ for a pooled centralised benchmark. Small-sample clients obtain an average out-of-time $R^2$ improvement of $3.8$ percentage points relative to the pooled centralised benchmark, while the fitted client-level relationship places the empirical crossover at approximately $4,790$ training observations in this setting. When pooling is infeasible and the relevant alternative is local-only training, federation improves out-of-time performance across all sample-size groups, with the largest gains for data-scarce clients. We also combine federated income estimates with state- and income-specific debt-to-income thresholds. In a retrospective decision analysis, replacing reported income with the federated estimate increases simulated approval rates with only modest changes in observed default rates. FedIncome supports collaborative learning under data-locality constraints with little aggregate loss relative to pooled training and larger gains relative to local-only estimation.

We study finite-horizon distributionally robust linear-quadratic control with disturbances that can be arbitrarily correlated in time. The ambiguity set is modeled as a single 2-Wasserstein ball centered at a nominal elliptically contoured distribution of the disturbances. Despite the infinite-dimensionality of both the policy space and ambiguity set, we prove that the optimal policy is affine and that the worst-case distribution is an affine push-forward of the nominal distribution. These affine maps can be computed efficiently via a best-response algorithm based on the Frank–Wolfe algorithm. Experiments demonstrate improved out-of-sample performance over LQG and its distributionally robust extensions when the true disturbances are correlated, incurring only a small loss of performance under uncorrelated disturbances.

The spectral limited-memory preconditioner (sLMP) clusters leading eigenvalues of symmetric positive definite matrices to accelerate conjugate gradient (CG) convergence. In practice, the cluster point is often chosen to be unity. In some cases, however, this choice can fail to accelerate convergence relative to unpreconditioned CG, even when highly accurate spectral information is available. Alternative cluster points have been proposed based on exact-arithmetic convergence analysis, but such analysis does not explain this finite-precision behaviour. We study how the cluster point influences two sources of numerical error in sLMP-preconditioned CG. First, we analyse the propagation of floating-point rounding errors during application of the preconditioner and derive computable relative-error bounds. For the dominant subspace (spanned by the eigenvectors associated with the leading eigenvalues of the unpreconditioned system) and its orthogonal complement (spanned by the remaining eigenvectors), these bounds are minimized by a weighted median and a weighted arithmetic mean of the leading eigenvalues, respectively. Our analysis explains why small cluster points can strongly amplify errors in the dominant subspace. Second, we investigate sensitivity to perturbations in the dominant spectral information when constructing the preconditioner. The resulting perturbation bound is minimized by a weighted median of the perturbed dominant eigenvalues, with weights determined by the eigenvector perturbation magnitudes. Numerical experiments on synthetic problems illustrate the predicted rounding-error and sensitivity behaviour. Together, these results show that cluster-point selection in finite precision should account for exact-arithmetic convergence, rounding errors, and inaccuracies in the available spectral information.

Let $\Omega\subset\mathbb R^3$ be an unbounded domain with smooth boundary and let $\Sigma$ be a complete, noncompact, orientable, immersed free boundary minimal surface in $\Omega$, with compact boundary $\partial \Sigma\subset\partial \Omega$ and finite Morse index. We prove that if the mean curvature of $\partial \Omega$ satisfies $H_{\partial \Omega}\ge 0$ along $\partial \Sigma$ and $H_{\partial\Omega}>0$ at some point of $\partial\Sigma$, then \[ \textrm{Ind}(\Sigma)\ \ge\ \frac13\Bigl(2g+k+2\sum_{j=1}^r(d_j+1)-2\Bigr), \] where $g$ is the genus of $\Sigma$, $k$ is the number of connected components of $\partial\Sigma$, $r$ is the number of ends of $\Sigma$ and $d_1,\dots,d_r$ are their respective multiplicities. When $H_{\partial\Omega}$ is only assumed to be nonnegative we obtain $\textrm{Ind}(\Sigma)\ge(2g+k-2)/3$, with the sharp bound $(2g+k-1)/3$ under a mild condition on the ends. The proofs use the harmonic one-form method of Ros and Chodosh–Máximo, with weighted $L^2$ spaces, adapted to the free boundary setting in the spirit of Ambrozio–Carlotto–Sharp. The main new ingredient is the computation of the dimension of the space of harmonic one-forms on a punctured compact Riemann surface with boundary which are tangential along the boundary and square integrable with respect to a weight. For a class of admissible weights $\rho$, we prove that this dimension is $2g+k-1+2\sum_jN_j-\varepsilon$, where $N_j$ is the maximal order of pole allowed by $\rho$ at the $j$-th puncture and $\varepsilon\in\{0,1\}$. For the weight of Chodosh–Máximo one has $N_j=d_j+1$.

Brain-to-language decoding translates neural activity associated with language production, internal speech and perception into linguistic or expressive outputs. It offers a route to restoring communication after speech loss and a means of studying how the brain represents language. Advances in neural recording and representation learning have expanded the field from constrained recognition and acoustic reconstruction to text generation, streaming personalised speech and facial animation. This survey synthesises these developments across invasive and non-invasive measurements. We connect Articulated, Inner and Perceived paradigms to the neural populations they engage, the representations available to decoders and the outputs those representations can support. We examine model development, public resources and the evolution of evaluation, and compare published performance and communication costs within their reported protocols. The synthesis identifies complementary routes to progress: phonetic, acoustic and semantic targets preserve different aspects of a message; shared representations support reuse across recording conditions and tasks; and online communication increasingly depends on calibration, feedback and user control alongside decoding accuracy. Shared benchmarks enable algorithmic comparisons, while longitudinal studies reveal the demands of sustained use. We discuss these developments and their remaining limitations, then outline a prospective five-level trajectory from commands and language to meaning, scenarios and bidirectional cognitive exchange.

A rapidly rotating magnetar formed in the collapse of a massive star may release its spin-down power through both a collimated polar jet and a quasi-isotropic magnetar wind. With its long-lasting soft X-ray blackbody component and the double-peaked UV/optical light curves of SN 2006aj, GRB 060218-SN 2006aj provides a useful test case for such a two-component energy-injection scenario. We developed a magnetar-powered jet-wind model in which the two outflows interact with homologously expanding SN ejecta, driving forward shocks that produce shock-breakout emission and subsequent magnetar-powered thermal emission. We first used the jet component to fit the 0.3-10 keV blackbody flux and temperature evolution of GRB 060218 and subsequently added the wind component to model the UV/optical light curves of SN 2006aj. We find that the soft X-ray blackbody component can be reproduced mainly by shock-breakout emission from the polar ejecta driven by the jet. The double-peaked UV/optical light curves are instead produced by the interaction between the quasi-isotropic magnetar wind and a more massive ejecta component. The first optical peak is dominated by wind-driven shock-breakout emission, whereas the broader and later emission is powered mainly by the subsequent magnetar-powered thermal component. Our results suggest a two-component magnetar-engine picture for GRB 060218-SN 2006aj, in which the X-ray thermal emission and the UV/optical double-peaked evolution arise from different energy-injection channels of the same central engine.

We present a unified study of charge and spin qubits encoded in a single interacting quantum dot tunnel-coupled to Rashba fermionic leads. The dot is described by an Anderson impurity Hamiltonian with either repulsive or attractive local interactions and a magnetic field of arbitrary orientation. In the repulsive regime, a spin qubit is encoded in the singly occupied spin sector, whereas in the attractive regime, close to the degeneracy between the empty and doubly occupied configurations, these two states define a charge-qubit subspace. We combine a weak-coupling Lindblad master equation in the Markovian secular limit with numerically controlled matrix-product-state simulations of the full dot-reservoir system. In equilibrium, we identify magnetic pair breaking in the attractive regime and a weak Rashba-induced magnetic anisotropy when the magnetic field is rotated relative to the spin-orbit axis. In the dynamical regime, relaxation and decoherence are controlled by the energetic gap between the logical manifold and nearby leakage states, and are further enhanced by Rashba-dependent tunneling. These findings show that even a minimal Anderson-impurity description captures key ingredients for coherent spin and charge qubits: the energetic structure of leakage states and spin-orbit-dependent dot-lead hybridization.

We prove an upper bound on the homogenization length scale which is a fixed power of the coarse ellipticity ratio for coefficient fields that satisfy a finite range of dependence assumption.

We study graph hypersurfaces associated with higher-dimensional ($n>2$) Cobb–Douglas production functions with variable returns to scale. We prove a rigidity theorem showing that every flat model in this class is necessarily homogeneous. The proof relies on an affine dimension-reduction principle that transfers the higher-dimensional flatness condition to suitable two-dimensional restrictions. We then obtain a complete classification in the non-degree-one case: every such flat model is a power of a positive linear form. For degree one, we give a local structural description in terms of envelopes on the rank-one set, with linearity on open rank-zero regions. These results extend the two-input analysis recently developed in [8] to the higher-dimensional setting, where the degree-one case exhibits a genuinely different behavior.

We study a discrete-time auction model in which multiple sellers update their bids according to their performance in the preceding round. Bidders aim to maximize their profits and adjust their bids solely based on their most recent outcome (myopic behavior). In each round, the auctioneer purchases the lowest-priced $p$-fraction of the total quantity offered by the bidders. We find a system of differential equations governing the macroscopic dynamics and derive it as a scaling limit of the microscopic model. We find an explicit solution for the max-price evolution $q_t$ and show that, in the long run, bidders coordinate, i.e., their bids converge to a common value depending only on their initial distribution and the fraction $p$. For Poisson-distributed initial bids, we establish hydrodynamic limits for the empirical bid distribution and the max-price trajectory and conjecture the corresponding Gaussian fluctuations for $q_t$. Finally, we generalize the model to allow for heterogeneous bid-update velocities: in this case, the max-price velocity becomes proportional to the harmonic mean of the update velocities of bidders at the max-price.

We study a family of coupled geometric evolution equations describing the deformation of a Riemannian metric and a non-abelian gauge field on closed manifolds, which generalizes the Ricci–Yang–Mills flow. We derive interior curvature estimates, find a preserved integral curvature condition, and discover a scaling invariant monotone functional analogue to Perelman's entropy. In particular, we prove strong dominance of the Riemannian curvature over the gauge curvature at finite-time singularities in all dimensions. We also provide a non-trivial explicit example of a shrinking self-similar solution on a $SU(2)$ bundle over $S^4$.

We establish the extension of Milnor's inequality, relating total curvature with the bridge index, to the $C^1$-closure of a knot class, without any restriction on the self-intersections of the limit curve. Together with recent work of Reiter–von der Mosel, this resolves the circular elastic knot conjecture, first predicted by Gallotti–Pierre-Louis in 2007 and then formulated as a mathematical conjecture by Gerlach–Reiter–von der Mosel in 2017. More precisely, if the bridge and braid indices of a tame knot class coincide, then the multiply covered circle is the unique elastic knot.

The complex interplay between spin-orbit coupling, magnetism, and magnetic field at the interface of a heterostructure consisting of ferromagnet (FM) and heavy metal (HM), often exhibit extraordinary magnetic and electric phenomena where an in-plane Dzyaloshinskii-Moriya (DM) interaction plays a crucial role to stabilize local spin texture in FM layer. Here, we report detailed magnetic and magneto-transport behaviour on an epitaxially grown thin heterostructure with 3$d$ FM La$_{0.67}$Ca$_{0.33}$MnO$_3$ (LCMO) and 5$d$ HM SrIrO$_3$ (SIO). Magnetic measurements show an unusual development of magnetic ordering in SrIrO3 around 42 K, which further leads to a Mn/Ir magnetic coupling at the interface. The magnetoresistance (MR) measurements show an evolution of its value and shape with the magnetic state of this bilayer. While MR is negative at high temperature, it shows a positive to negative crossover with stable magnetic ordering of LCMO, and finally the positive MR exhibits an asymmetry at low temperature with the ordering of SIO. While we ascribe this unusual MR behaviour to interface-driven varying spin scattering between itinerant and localized electrons, our results shed a light to comprehend the complex but tunable interface behavior on charge transport in a particularly designed heterostructure, offering valuable insights for future functional material engineering.

We establish a sufficient condition for an additively idempotent semiring to be inherently nonfinitely based: if its generated variety is locally finite and every Zimin word is minimal in the additive order, then it is contained in no finitely based locally finite variety. We characterize Zimin minimality by the membership of a countable flat factor semiring $\Finf$ in the generated variety and prove that $\V(\Finf)$ is a minimal inherently nonfinitely based variety. We also obtain general restrictions on the additive order of finite inherently nonfinitely based ai-semirings. As applications, the six-element ai-semirings $\A$ and $\B$ are shown to be inherently nonfinitely based. Finally, we prove that the six-element ai semiring $\Abar$ is not inherently nonfinitely based and is finitely based. Its multiplicative reduct is inherently nonfinitely based; thus, to the best of our knowledge, $\Abar$ is the first finitely based ai-semiring with an inherently nonfinitely based multiplicative reduct.

Gottesman-Kitaev-Preskill (GKP) states are widely studied as a bosonic encoding for fault-tolerant quantum computing because small displacement errors can be identified and corrected through syndrome measurements. However, fault-tolerant operation requires substantially greater GKP squeezing than is currently available in optical platforms. It is therefore important to identify quantum-information tasks that can be realised with finite-squeezing GKP states. Here, we study Bell nonlocality in finite-energy GKP Bell states under experimentally motivated measurement constraints. Although finite-energy GKP Bell states support Bell nonlocality even at low squeezing, logical Pauli measurements alone cannot reveal it. Accessing the maximum CHSH violation supported by the state generally requires logical non-Clifford rotations. We instead show that the required non-Gaussian resource can reside in the measurement itself. Photon-number-resolving detection combined with Gaussian preprocessing and adaptive feed-forward closely approaches the maximum violation of the CHSH Bell inequality without implementing logical non-Clifford gates. The same measurement principle strongly enhances Bell violations for cat-code Bell pairs and entangled coherent states, demonstrating that its usefulness extends beyond the GKP lattice. Our results identify non-Gaussian measurements as a practical route to revealing Bell nonlocality in finite-energy bosonic states.

Online discussion of political and gender-related issues is often heated, and when opinions in a network draw closer, the convergence is readily taken as genuine consensus. Whether it carries a cost is a question existing methods cannot answer: coevolutionary opinion formation games measure the Price of Anarchy (PoA) of agents that update by numerical rules, while simulations with large language model (LLM) agents report only descriptive indices. We introduce the Hybrid Coevolutionary Opinion Game (H-COG), in which analytical and LLM-driven agents share one network, choose their neighbors by opinion similarity in every round, and hold stances drawn from real Reddit comments on gun control and abortion. To our knowledge, H-COG is the first framework to place Friedkin-Johnsen best-response agents and LLM agents in one coevolutionary game and to measure the social cost and PoA of LLM-driven populations. We prove that on any fixed network, given the LLM agents' opinions, the analytical agents' opinion stage has a unique equilibrium and the social optimum has a closed form, and that the convergence guarantee of Chen et al. for optimistic gradient ascent carries over to H-COG. All runs converge structurally. LLM-driven populations are less polarized yet have about five times the PoA of analytical ones; half of the gap comes from agents being pulled away from their own prior positions, a distance we prove must carry a cost whenever expressed opinions are more concentrated than intrinsic ones. Echo chambers form under every composition and grow out of the rewiring rule rather than the initial topology. Opinions in these populations draw closer largely because agents give up their own positions.

AI-generated software changes make it increasingly important to determine what a change preserves, where local consistency fails to extend globally, and which alternatives remain. We develop the foundations of Algebraic Architecture Theory (AAT) from Atoms, typed primitive facts, and Laws, equations that objects must satisfy. A reading specifies what counts as structure and which operations and laws to preserve. The main reconstruction theorem identifies the category of full geometries and all their structure-preserving morphisms with an independently defined category of local models, up to equivalence. Objects are recovered up to isomorphism and morphisms between fixed endpoints uniquely. The theory addresses gluing, diagnosis, transport, classification of changes, and reconstruction. From finite Atom families we construct cores closed under operations and geometries with sites and coefficients. We give conditions under which a Cech obstruction detects the existence of a global state and, through comparison with repair semantics, a global repair. We compare diagnoses and give a finite criterion for uniform invariance given computable finite data. Transport along exact changes has a universal property and commutes with base change on exact pointed pullback squares. Comparisons of routes generated from the same square, finite comparison diagram, and geometry factor into an invertible comparison and an idempotent normalization. We characterize when observations determine comparison preservation and classify compatible lifts. Encodings of lens and protocol semantics preserve and reflect laws and recover semantics-preserving morphisms. Applications classify and count operation-preserving changes and extend morphisms uniquely from finite tables. Corresponding Lean declarations are listed in the appendix.

Traffic flow forecasting is essential to intelligent transportation systems. Large-scale traffic forecasting requires jointly modeling local spatial dependencies and cross-region context.Spatial dependencies between geographically neighboring nodes are heterogeneous due to differences in road identity and travel direction, while acquiring global information through allpairs node interactions incurs substantial computational costs. Therefore, capturing local heterogeneity while efficiently acquiring long-range context remains an important challenge in largescale traffic forecasting. To address these challenges, we propose LoReST, a Local-Region Spatial Temporal network that models spatial dependencies at two complementary granularities: node neighborhoods and road network regions. Specifically, relation-aware local aggregation captures heterogeneous dependencies within geographic neighborhoods through road and direction specific feature transformations. Cross-region interaction constructs region representations through mean pooling, exchanges long range context via inter-region attention, and broadcasts it back to nodes. By integrating local information aggregation with crossregion interaction, LoReST is able to effectively achieve spatial dependency learning in large-scale road networks. Experiments on four datasets of the LargeST benchmark show average relative reductions of 4.78%, 3.60%, and 5.75% in MAE, RMSE, and MAPE, respectively.

This paper proposes a formal multi-agent architecture for implementing enterprise AI in regulated insurance firms, integrating economic theory with institutional design. The framework synthesises three core theoretical perspectives: Arrow's risk pooling theory to formalise risk transformation under uncertainty, Nash equilibrium to model strategic interactions between decision agents, and Principal-Agent theory to address incentive alignment under information asymmetry. The insurer is modelled as a constrained optimisation entity operating under solvency, legal, ESG, and operational boundaries, with specific focus on the regulatory contexts of Austria and Germany. The architecture decomposes the firm into multiple specialised agents, each representing distinct functional domains such as capital management, underwriting, claims processing, compliance, fraud detection, and client interaction. Human-in-the-loop agents are integrated through a tiered access control system, ensuring differentiated data visibility and decision influence based on user roles. An orchestrator agent supervises inter-agent coordination, enforcing regulatory admissibility and institutional coherence under frameworks such as Solvency II, the AI Act, and the Insurance Distribution Directive. Protocol integration is based on asynchronous execution and dual-layer communication infrastructures, specifically the Model Context Protocol (MCP) and Agent-to-Agent (A2A) messaging. This structure enables the systematic design of compliant, auditable multi-agent systems aligned with the institutional logic of financial firms in Austria and Germany.

We resolve the longstanding geometric ideal triangulation conjecture arising from Thurston's theory of hyperbolic 3-manifolds: every finite-volume cusped hyperbolic 3-manifold admits a finite geometric ideal triangulation realizing its complete hyperbolic structure.

Blest's rank correlation $\nu$ is a variant of Spearman's rho $\rho$ that weights the leading ranks of one variable more heavily, at the price that $\nu$ is not symmetric in its arguments. We quantify both features by determining the exact region of $(\rho,\nu)$ over all bivariate copulas, as well as that of $(\eta,\nu)$, where $\eta$ is the symmetrized Blest coefficient of Genest and Plante. The latter region is a linear image of the set of all pairs $(\nu(C),\nu(C^\top))$ formed by a copula $C$ and its transpose. Consequently, Blest's coefficient differs from Spearman's rho by at most $1/4$, and interchanging the two variables changes it by at most $27/64$, improving on the bound $1/2$ implied by the first inequality. For every given value of $\rho$ or $\eta$, each corresponding extreme value of $\nu$ is attained by exactly one copula, given in closed form and supported on finitely many line segments. Near countermonotonicity, the upper extremizers of the $(\eta,\nu)$-region are supported on the graph of a function of the second coordinate, yet their conditional laws given the first coordinate carry two atoms. The proofs rest on a rearrangement inequality with equality case and on explicit Kantorovich potentials.

High-throughput single-cell data is now collected across large patient cohorts. Understanding patient-level heterogeneity from cellular-level data motivates phenoscaping: embedding each single-cell distribution as a "datapoint," with distances given by optimal transport (OT). Computing geometry-aware OT at this scale, between all pairs of patient datasets, remains an open challenge, since existing methods either rely on Euclidean ground metrics that distort manifold structure or fail under sparse, unevenly sampled, or large-scale data. We present Pheno-GS (Phenoscape-scale Geodesic Sinkhorn), which computes accurate, scalable geodesic transport distances under noisy, unbalanced, large-scale settings via three components: ($1$) graph connectivity regularization for well-defined geodesics on sparse/disconnected manifolds; ($2$) an unbalanced OT formulation via KL marginal penalties; and ($3$) a batched matrix algorithm computing all pairwise distances in one heat diffusion (over $200 \times$ faster than Geodesic Sinkhorn for $500$ distributions). We validate Pheno-GS on synthetic benchmarks and a CyTOF perturbation dataset.

We present a compliance-first architecture for AI in regulated finance that treats regulation as an orientation layer rather than a deterministic ruleset. A matrix of regulatory intent and exposure provides a compact classification handle, which a governed policy compiler then maps into concrete prohibitions, obligations and runtime budgets. Prohibitions constrain feasibility and block externalisation, while obligations extend tasks with artefacts that must meet explicit admissibility criteria. Committee activation remains policy-driven and proportionate, preserving efficiency while ensuring supervisory oversight. Evidence, decisions and reason codes are bound to a permissioned DAG with deterministic timestamping, enabling replay, provenance checks and clear attribution of failure. Clause-level legal indexing with effective dates and capability-based agent routing ensure portability across DACH and the wider EU. The result is assurance by construction: compliance is embedded in execution and verifiable by auditors without sacrificing proportionality or transparency.

An all-dielectric leaky-wave antenna, radiating unidirectionally at broadside without the use of a metallic ground plane, is designed and manufactured. It operates in the 70-90 GHz frequency range with a design broadside frequency of 77 GHz. The design process makes use of the theory of photonic bandgaps to position a -1 harmonic at the broadside frequency on the second Bragg-condition point. The structure is then modified to close the bandgap and to simultaneously guarantee maximum total field coupling to the relevant radiating harmonic, ensuring radiation unidirectionality. The antenna is manufactured with an Al2O3 ceramic printing process, demonstrating its manufacturing potential for complex low-loss high-frequency structures. Simulations agree well with measurements, with the main deviation being a 1 GHz frequency shift that could be reproduced in simulation. The antenna prototype shows a scanning range of -18{\deg}-22{\deg} and gain values above 23 dBi. More than 85 % of the radiation power is radiated unidirectionally at broadside, with simulations showing potential to attain 98 %.

We present a multi-band optical variability study of the $\gamma$-ray emitting high-synchrotron-peaked blazar 1ES~0647+250 during its enhanced optical activity in 2020. The analysis utilizes 107 epochs of high-precision $B$, $V$, and $R$-band photometry obtained with the 75 cm telescope at the Vainu Bappu Observatory, combined with high-cadence $z_g$ and $z_r$ survey data from the Zwicky Transient Facility. The combined light curves reveal coherent variability across all optical filters, with the source reaching a peak $R$-band magnitude of 15.74 mag. We calculated the variability amplitude, finding the highest intrinsic variability in the B- band. Spectral analysis using color–magnitude diagrams reveals a statistically significant “Bluer-When-Brighter” trend, supported by a Pearson correlation coefficient of $r = 0.68$ ($p < 0.001$) for the (V$-$R) index. Furthermore, the discrete correlation function analysis indicates a near-zero time lag between the $V$ and $R$ bands, suggesting simultaneous emission within the observational cadence. The observed spectral hardening is consistent with synchrotron-dominated optical emission, likely associated with enhanced particle acceleration within the jet during the active phase of 1ES~0647+250.

Accurate measurement of an intended conditional phase does not by itself place a multiqubit phase gate in its declared generalized-gate equivalence class. We cast the diagnosis as structured Hamiltonian learning of the diagonal successful block in a known basis: Ramsey measurements on a connected graph reconstruct a target-relative eigenphase map; a Walsh transform then yields the per-cycle stroboscopic error generator in a selected logarithm branch, whose branch-dependent coefficients alone cannot decide global equivalence. For diagonal Pauli-Z dressing of weight at most m we derive an exact branch-independent criterion from multiplicative Boolean-Mobius invariants, converted at finite shot counts into a pass/fail/unresolved decision under prespecified tolerances and simultaneous confidence, separate from model rejection. For shared-control C^mZ gates a circular target-face contrast isolates each intended conditional phase, yet a support theorem exhibits forbidden interactions invisible to every target face once multiple targets or external spectators are present. We derive a Cramer-Rao bound for arbitrary integer phase contrasts, recovering the 4^m attempted-circuit scaling of a uniform (m+1)-body face, and quantify degradation from visibility loss, heralded survival, readout confusion, and correlated noise, while systematic bias triggers model rejection. Seeded simulations implement the 4M-setting multiplexed acquisition end to end: for M=3,4,5 at a common budget its mean phase-map RMSE is 0.689-0.794 times a separately compiled statewise scan, and a blind-interaction test yields 300/300 global-audit rejections versus 1/300 for target faces. These results estimate the error generator of a diagonal successful block under a specified acquisition model; they are not unknown-basis Hamiltonian identification, arbitrary-channel tomography, or hardware certification.

Duke's interpolation theorem states that the orientable genera of a connected graph form an integer interval, and Stahl established the corresponding result for nonorientable embeddings. In 1991, Širáň showed that this interpolation property fails for signed graph embeddings: the Euler-genus spectrum of a signed graph may contain gaps. He subsequently asked whether all such gaps must occur at the lower end of the spectrum. In this paper, we establish a characterization of the Euler-genus spectrum of a connected signed graph. We prove that, for each parity class, the Euler genera form a step-two interval. Moreover, whenever both parity classes are nonempty, their maximum elements differ by one. As an consequence, if two consecutive integers $k$ and $k+1$ belong to the Euler-genus spectrum, then every integer from $k$ to the maximum Euler-genus also belongs to the spectrum, thereby answering Širáň's question affirmatively. Our proof uses the pre-signed graph representation of signed embeddings together with ordered adjacent-exchange operations and a matching interpretation of face numbers.

This work presents the development of an automatic refactoring tool for Java code built on top of the Eclipse JDT API. The proposed approach transforms control structures containing break and continue statements within different types of loops into semantically equivalent constructs that avoid their explicit use. To achieve this, auxiliary boolean variables are introduced to restructure the control flow while preserving the original program behavior. The main objective of this transformation is to improve code structure and enable the application of subsequent automated refactorings, particularly those based on the Extract Method operation, which are typically restricted by the presence of jump statements. The implementation relies on the analysis and rewriting of the Abstract Syntax Tree (AST), ensuring semantic equivalence in all addressed scenarios. The tool was validated through 54 manually designed test cases and 151 units tests, all of which produced satisfactory results. In addition, it was applied to 139 methods from seven open-source projects, generating code without compilation errors and preserving the original behavior as verified by the projects' test suites. The results demonstrate that the proposed approach safely automates the restructuring of code containing break and continue statements, facilitating further evolution and structural analysis.