Gravitational waves (GWs) from the galactic double white dwarf (DWD) systems are one of the primary targets for upcoming space-based detectors. Due to their vast abundance and widespread distribution throughout the Galactic disk and bulge, these systems may provide a high-statistical population for probing GW microlensing effects induced by Galactic compact objects. To evaluate the detectability of such effects, in this work we simulate the four-year observation of DWD systems by Taiji, in the form of a second-generation Time Delay Interferometry (TDI) data stream. Within a Bayesian inference framework, we estimate parameters for lensed GWs from DWD systems for different values of the lens parameters, including the lens mass $M_\mathrm{L}\in [10, 10^6]$\,M$_\odot$, the effective velocity $v_\mathrm{eff}\in [50, 500]$\,km/s and the initial separation $L\in [R_\mathrm{E}, 3R_\mathrm{E}]$, and obtain the uncertainties of the corresponding parameters. These results characterize the capability of future Taiji observations to probe such systems. We further employ the Bayesian model selection framework to distinguish between lensed and unlensed scenarios, and investigate the impacts of three key physical parameters of the lens system: $M_\mathrm{L}$, $v_\mathrm{eff}$, and $L$ on distinguishing lensing events. Our results show that when $M_\mathrm{L}$ is below $10^5$\,M$_\odot$ or $L\geq3R_\mathrm{E}$, it is not possible to distinguish between lensed and unlensed models. For $v_\mathrm{eff}$, although the Bayes factor decreases as $v_\mathrm{eff}$ decreases, the lensed and unlensed models can still be distinguished within our parameter range.

Porous monolithic photocatalysts based on anatase TiO2 in silica aerogels are promising for air purification. Their bicontinuous spinodal architecture offers high surface area and strong light scattering. However, extracting intrinsic kinetic rates requires accurate optical models. Current methods replace the complex 3D pore network with a homogeneous 1D slab, an approximation whose error is unknown for spinodal geometries. We combine 3D spinodal masks from Cahn-Hilliard simulations with GPU Monte Carlo photon transport to quantify this. We introduce a solid-phase fluence estimator that accounts for catalytic site distribution, comparing it to volume averages and diffusion approximations. The solid phase receives 50% more photons than volume averages at porosity 0.70, rising to 70% at 0.90. This preferential illumination stems from quasi-ballistic paths through pore channels, termed photon channelling. The extracted kinetic descriptor differs by 34% between 3D Monte Carlo and diffusion models. Homogeneous controls show that roughly 50% of the total 73% discrepancy is intrinsic to the bicontinuous structure and cannot be fixed by effective medium theories. These results provide the first quantitative correction for kinetic extraction in such photocatalysts and establish design rules linking synthesis coarsening, pore size, and light efficiency.

Modern AI agents optimize programs by refactoring source code to trigger trusted compiler transformations. This preserves program semantics and reduces source code pollution, making the program easier to maintain and portable across architectures. However, this collaborative workflow is limited by legacy compiler interfaces, which obscure analysis behind unstructured, lossy optimization remarks that have been designed for human intuition rather than machine logic. Using the TSVC benchmark, we evaluate the efficacy of existing optimization feedback. We find that while precise remarks provide actionable feedback (3.3x success rate), ambiguous remarks are actively detrimental, triggering semantic-breaking hallucinations. By replacing ambiguous remarks with precise ones, we show that structured, precise analysis information unlocks the capabilities of small models, proving that the bottleneck is the interface, not the agent. We conclude that future compilers must expose structured, actionable feedback designed specifically for the future of autonomous performance engineering.

Recent advances in integrated photonics have enabled on-chip signal modulation and processing through localized photon-phonon interactions. For acousto-optic devices, compact footprint and high efficiency are essential for dense integration, while strong power handling is critical for stable operation in demanding applications. However, it remains challenging to achieve these features simultaneously on existing integrated platforms. Here, we propose and experimentally demonstrate, for the first time on a thin-film lithium tantalate platform, an ultra-compact acousto-optic modulator based on topological interface states. Benefiting from the strong optical confinement of the topological boundary state, the device achieves a footprint of 0.13 by 0.12 mm2 and a half-wave voltage-length product of 0.491 Vcm. We further demonstrate stable acousto-optic modulation at an on-chip optical power of up to 28 dBm (630.9 mW), highlighting the strong power-handling capability of the thin-film lithium tantalate topological structure. This work provides a compact and high-power solution for microwave-to-photonic transduction and shows the potential of the thin-film lithium tantalate for robust integrated photonic systems.

We present a Krylov space based theoretical framework for modeling inhomogeneous spin ensembles with arbitrary distributions of spin frequencies and couplings. The framework is then used to asymptotically large spin ensemble. In the single-excitation subspace, the Krylov construction allows for to derive exact expressions for the Lieb-Robinson velocity and quantum speed limit, and figure of merit such as Krylov complexity. Our work reveals a strong dependence of the speed of information flow on the statistical distribution of resonance frequencies in the spin ensemble with immediate implications for the design of components for quantum technologies, realized for example with nitrogen vacancy centers, nuclear spins or ultracold atoms.

We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and generalises a previously developed two-dimensional high-order formulation. The electric and magnetic fields are discretised on mutually dual barycentric grids using curl-conforming polynomial spaces constructed via tensor-product Gauss--Radau interpolation. The resulting semi-discrete formulation yields block-diagonal mass matrices and sparse discrete curl operators, enabling explicit time integration while preserving a discrete energy identity. Special attention is devoted to the construction of compatible approximation spaces on the three-dimensional primal and dual meshes, the reference-to-physical element mappings, and the preservation of tangential continuity. We show that the method achieves arbitrary-order convergence, avoids spurious modes, and maintains optimal sparsity properties. Numerical experiments confirm spectral correctness, high-order accuracy, and computational efficiency on unstructured tetrahedral meshes.

Nonlinear modal interactions in resonant systems govern a wide range of phenomena, with broad relevance across modern physics and engineering. Yet, experimentally determining the strength of nonlinear coupling in multimode resonators remains highly challenging. Here, we introduce a multi-tone spectroscopy method for identifying nonlinear coupling coefficients directly from experimental data. Our approach employs dual-tone excitation near selected resonances which, in combination with additional probing tones at higher-order modes, generates sideband responses associated with specific modal couplings. These spectral signatures are analyzed using an inverse reconstruction procedure to quantitatively determine the corresponding nonlinear coupling strengths in the frequency domain. Using this method, we determine ten pairwise nonlinear coupling parameters across five modes of highly tensioned nanostrings, enabling the reconstruction of fully experimental, device-specific nonlinear reduced-order models. Our experimentally derived models show excellent agreement with values obtained numerically using finite element based nonlinear reduced-order models. Our method is generic and can be used for the characterization of diverse modal and intermodal couplings in mechanical and hybrid resonant systems.

Future mobile networks must achieve substantial improvements in energy efficiency to offset the anticipated traffic growth. Despite this requirement, many discussions regarding physical layer design remain primarily focused on peak data rates and spectral efficiency, even though typical network operation is dominated by low-data-rate regimes. To address this mismatch, the Gearbox-PHY was proposed as an energy-efficient physical layer architecture that dynamically switches between modulation schemes and their associated analog front ends in order to adapt to varying operating requirements. This paper quantifies the achievable energy savings by jointly modeling front end power consumption and hardware-aware spectral efficiency to formulate an energy-per-bit minimization problem. To move beyond idealized assumptions, non-ideal hardware effects, including oscillator phase noise and limited quantizer resolution, are incorporated. These impairments simultaneously affect power consumption and achievable spectral efficiency, thereby introducing trade-offs between front end complexity, hardware non-linearities, spectral efficiency, and energy efficiency. Numerical results demonstrate that the Gearbox-PHY enables significant energy savings, particularly at low data rates. Evaluations with spatially distributed users confirm that gains of up to two orders of magnitude persist in a cellular deployment scenario.

We show that the centralizer of a nonscalar element in the coproduct $k\langle X\rangle *k[Y]$ of a free associative algebra and a polynomial algebra over a given field is commutative. For $k\langle X \rangle$ this is part of Bergman's centralizer theorem. Our proof relies on a reduction given in Bergman's proof and is of combinatorial nature, employing a strict order structure of the coproduct monoid.

A rigid motion in $\mathbb{R}^d$ consists of a proper rotation and a translation, and it can be represented as a matrix in $\mathbb{R}^{(d+1)\times (d+1)}$. The problem of rigid motion synchronization aims to estimate a collection of rigid motions $G^*_1, \dots, G^*_n$ from noisy observations of their comparisons ${G^*_i}^{-1} G^*_j$. Such problems naturally arise in diverse applications across signal processing, robotics, and computer vision, and have thus attracted intense research attention in recent years. Motivated by geometric considerations, this paper develops a novel spectral approach for rigid motion synchronization, called the anchored spectral estimator (ASE). Theoretically, we establish uniform estimation error bounds for the estimators produced by ASE. Empirically, we show that ASE outperforms the widely used two-stage approach, which first estimates the rotations and then the translations. Further numerical experiments on the multiple point-set registration problem are presented to demonstrate the superiority of ASE over state-of-the-art methods.

This paper presents the primary research challenges and key findings from the 15th International Automated Negotiating Agents Competition (ANAC 2025), one of the official competitions of IJCAI 2025. We focus on two critical domains: multi-deal negotiations and the development of agents capable of concurrent negotiation within complex supply chain management environments. Furthermore, this work analyzes the results of the competition and outlines strategic directions for future iterations.

For any $β_0<1/3$ we construct divergence free vector fields in $ C_{x,t}^{β_0}$ and a sequence of diffusivities $κ_q \searrow 0$ such that, for an arbitrary initial datum from a low regularity class, the classical solution $ρ_q$ to the advection-diffusion equation exhibits anomalous dissipation along the sequence $κ_q$. At the same time $ρ_q$ remains uniformly bounded in $C_t^{0} C_x^{α_0}$, where $β_0 + 2α_0<1$. Our result confirms a conjecture of Armstrong and Vicol \cite{ArmstrongVicol} and shows sharpness of the Obukhov-Corrsin threshold within the context of iterated homogenization. Our construction confirms time-homogeneity of the dissipation anomaly, as required in turbulence theory, and as a consequence we also obtain better time regularity for the scalar $ρ_q$ than the classical prediction of Yaglom.

Distributed quantum computing (DQC) is a promising proposal for overcoming the scalability challenges of quantum computing. However, the evaluation of DQC hardware and software is difficult due to the relative dearth of classical simulation tools available for DQC devices. In this work, we introduce dqc_simulator, a novel simulation toolkit, written in Python, which automates many of the most challenging aspects of the DQC simulation workflow. dqc_simulator enables the easy simulation of both hardware and software, making it easy to create realistic and robust tests and benchmarks for the full DQC stack.

Twistoptics has recently emerged as a branch of nano-optics that explores light propagation in stacks of thin anisotropic layers rotated relative to one another. The concept is particularly relevant for polaritons -- hybrid light-matter quasiparticles -- in van der Waals (vdW) materials, where strong in-plane anisotropy and deep subwavelength confinement make the polaritonic dispersion highly sensitive to interlayer twist angles. This sensitivity enables exotic phenomena such as canalization, i.e., diffraction-free propagation, with potential applications ranging from thermal management to super-resolution imaging. Despite rapid progress, a general analytical framework to describe polariton propagation in twisted planar heterostructures has been missing. Here we present an analytical model for planar stacks comprising an arbitrary number of finite-thickness anisotropic (biaxial) layers and infinitesimally thin anisotropic conductive sheets. The formalism and its high-momentum and thin-film approximations predict key polaritonic observables, such as wavelength, propagation length, and electromagnetic field distributions. We also provide open-access numerical scripts implementing the model to support their practical use. Together, these results provide a general theoretical foundation for twistoptics and should facilitate the discovery and accelerate the implementation of twist-engineered polaritonic phenomena across the electromagnetic spectrum.

The storage of quantum information in spin-ensembles is limited by practically unavoidable inhomogeneous broadening, and the macroscopic number of spins in such an ensemble makes the design of control solutions to increase the coherence time a challenging task. Together with a concurrently developed Krylov theory that allows us to treat the control problem efficiently, we design optimal cavity modulation for such spin ensembles that achieve an order of magnitude enhancement in qubit lifetime compared to the losses due to inhomogeneity and cavity decay.

Radio astronomy is uniquely coupled to exponential trends in computation because the optics (cross-correlation, beamforming, and imaging) and spectrometry (i.e. channelization) can now be done digitally. Inexpensive analog-to-digital converters (ADCs) can sample signals from large numbers of antennas and graphics processing units (GPUs) allow us to coherently process wide-field radio data in real time, motivating large-$N$ aperture arrays at moderate cost. We describe the 256-antenna Coherent All-Sky Monitor (CASM-256), a dense aperture array operating at 375-500\,MHz, currently being deployed at the Owens Valley Radio Observatory (OVRO) in Big Pine, California. The large field-of-view (FoV$\sim10^4$\,deg$^2$) and point-source sensitivity of CASM-256 will allow it to detect local Universe fast radio bursts (FRBs). The nearby sample is ideal for unveiling the physical origin of FRBs, measuring the baryonic content of nearby galaxy halos, and discovering prompt multi-wavelength and multi-messenger counterparts to FRBs. CASM will search for fast transients in the Milky Way such as FRB analogs, pulsar giant pulses, and the new source class known as long-period radio transients. We describe the instrument and present on-sky data from the first two dozen antennas, including an operational real-time GPU based FRB search pipeline. We emphasize the scalability of the concept and describe paths to a future CASM array with tens of thousands of antennas that could detect one million FRBs.

We study strong-field driven ultrafast dynamics and high-harmonic generation (HHG) in monolayer 2H-NbSe$_2$ and compare them with those of monolayer 2H-MoS$_2$ by solving the multiband reduced-density-matrix equations including time-dependent electron-electron interaction effects within the time-dependent Hartree + screened exchange (TD-HSEX). In MoS$_2$, these interactions strongly enhance the harmonic yield and modify the harmonic phases and angular emission patterns, wheras in NbSe$_2$ the yield enhancement is weaker but clear phase and angular changes remain. We trace these differences to the distinct optical resonances and to the different bands involved in the emission in each material. Finally, we show that carrier injection into empty bands of NbSe$_2$ differs qualitatively from interband excitation in MoS$_2$, and is well captured at a qualitative level by a Keldysh tunneling rate with a time-dependent band separation, allowing to control the timing and the region of injection of carriers to empty bands of the metal with the field parameters. Our work provides a framework to interpret ultrafast electron-hole interaction effects in experimental high harmonic generation spectra across semiconducting and metallic systems.

The Off-Resonant Cascaded Absorption (ORCA) protocol in warm atomic vapors offers a scalable platform for high-bandwidth, low noise quantum memories, but its coherence time is fundamentally limited by Doppler-induced dephasing. We introduce and experimentally demonstrate a dynamic rephasing protocol that counteracts Doppler dephasing in a telecom-band ORCA quantum memory. By transferring the stored excitation to an auxiliary shelving state, we effectively reverse the accumulated Doppler phase and extend the storage time by a factor of 50 while preserving the memory's GHz bandwidth and low noise. Using this protocol, we then demonstrate on-demand storage and retrieval of four independent time-bin modes within a single warm vapor memory -- showing that Doppler dephasing can alternatively be harnessed for high-dimensional temporal mode processing. Our results establish rephasing in warm atomic vapors as a viable route toward high-bandwidth, temporally multiplexed quantum memories operating at room temperature.

We prove that if a proper metric space is quasi-isometric to a finitely generated group and to a space with a horoball over a finitely generated group, then that space is quasi-isometric to a rank-one symmetric space or the real line.

Why do large gender inequalities in everyday life persist even as women strengthen their attachment to paid work? Existing evidence shows that women continue to do more unpaid work than men, but much of that evidence is based on individual diaries, says little about how inequality is jointly organized within couples, and rarely links daily time allocation to directly measured gender attitudes. This paper addresses that gap using the TIMES Observatory, an original survey of 1,928 co-resident couples with at least one child younger than 11 in Emilia-Romagna or Campania. The data combine matched partner diaries for one weekday and one weekend day with rich socio-economic information and direct measures of gender norms. We document three main findings. First, women do substantially more unpaid work and spend more time with children, while men do more paid work and enjoy more leisure without children. Second, these asymmetries remain sizeable even among dual full-time couples, implying that stronger female labor-market attachment does not by itself equalize daily life. Third, more traditional gender attitudes - especially among men - are descriptively associated with lower male participation in childcare and domestic work and with wider gaps in discretionary leisure. The analysis is descriptive rather than causal, but it shows that gender inequality within couples is visible not only in the amount of work performed, but also in the distribution of time that is genuinely discretionary.

We consider a shape optimization problem for a hybrid energy combining local confinement and nonlocal Coulomb repulsion. Specifically, for any open set $Ω\subseteq \mathbb{R}^3$ of prescribed volume, we consider the ground state energy of an $L^2$-normalized function supported in $Ω$, defined as a linear combination of its homogeneous $\dot{H}^1$ and $\dot{H}^{-1}$ seminorms. We show that in the small mass regime, volume-constrained minimizers of this geometric functional exist and are $C^{2,α}$ perturbations of a ball. The proof relies on a combination of surgery techniques, $Γ$-convergence, elliptic PDE theory, and one-phase free boundary regularity. A key novelty of this paper lies in the treatment of the Coulombic repulsive term: unlike standard competitive models, the lack of (a priori) sign constraints on the optimal functions forces the nonlocal term to exhibit two natures: it acts both as a scattering and an homogenizing force.

This paper introduces the concept of the wandering range of a robust symmetry $S$ of a Hamiltonian $H$. This quantity measures how the perturbed time evolution $\mathrm{e}^{\mathrm{i}t(H+\varepsilon V)} S \mathrm{e}^{-\mathrm{i} t(H+\varepsilon V)}$ deviates from its unperturbed counterpart $\mathrm{e}^{\mathrm{i} tH} S\mathrm{e}^{-\mathrm{i} tH} = S$. Although the wandering range does not necessarily scale linearly with the perturbation strength $\varepsilon$, we identify conditions under which this linear behavior is recovered and we obtain explicit nonperturbative bounds.

Quantum geometry, a quantum mechanical quantity comprised of Berry curvature and quantum metric, describes the geometric structure of the electronic bands in solids. The correlation between nontrivial quantum geometry and quantum materials leads to new findings in condensed matter systems. Here we demonstrate that altermagnets, with spontaneously broken time-reversal (T)- half-lattice-translation and parity-time symmetry, host both T-odd and T-even quantum geometric quantities that simultaneously manifest themselves despite the vanishing net magnetization. Consequently, giant room-temperature third-order electrical transport responses with sizable quantum geometric contributions are observed in (101)-oriented RuO2 thin films, an altermagnetic candidate; in particular, the third-order Hall effect is intimately correlated with altermagnetic order and can serve as a promising tool for detecting the Neel vector. Our work not only supports the existence of altermagnetism in 8-nm-thick RuO2 thin films, but also shows altermagnets as a versatile platform for exploring quantum geometry and constructing quantum electronic and spintronic devices.

Time-resolved scanning near-field optical microscopy (tr-SNOM) enables the measurement of the dynamic optical response of functional surfaces beyond the diffraction limit. Experimental challenges are imposed both by the use of a pulsed light source, and by the need for interferometric signal modulation to isolate the near-field contribution. We present a novel experimental approach to retrieve the tr-SNOM signal using a 200 kHz laser system and pseudo-heterodyne modulation. We circumvent the Nyquist limit for spectral demodulation by sampling modulation phases, pump intensity and SNOM signal for every laser shot. A general time-resolved SNOM signal is derived, independent of detection scheme or physical assumptions about the near-field enhancement, and is successfully measured and isolated on WS$_2$ monolayer and multilayer regions. We confirm localization by signal-distance curves, spatial confinement at material boundaries, and by identifying signal contributions at individual modulation harmonics. Disentangling the dynamic contributions enables us to extract the dynamic dielectric function of the sample. Showing the capability of phase-domain sampling paves the way to integration of more diverse and specialized light sources, growing the potential of optical ultrafast near-field measurements.

In this paper, we propose an efficient two-level additive Schwarz method for solving large-scale eigenvalue problems arising from the finite element discretization of symmetric elliptic operators, which may compute efficiently more interior multiple and clustered eigenvalues other than only the first several smallest eigenvalues. The proposed method is parallel in two ways: one is to solve the preconditioned Jacobi-Davidson correction equations by the two-level additive Schwarz preconditioner, the other is to solve different clusters of eigenvalues (see Figure 1 in Introduction) simultaneously. It only requires computing a series of parallel subproblems and solving a small-dimensional eigenvalue problem per iteration for a cluster of eigenvalues. Based on some new estimates and tools, we provide a rigorous theoretical analysis to prove that convergence factor of the proposed method is bounded by $γ=c(H)ρ(\fracδ{H},d_{m}^{-},d_{M}^{+})$, where $H$ is the diameter of subdomains, $δ$ is the overlapping size and $d_{m}^{-},d_{M}^{+}$ are the distances from both ends of the targeted eigenvalues to others (see Figure 2 in Introduction). The positive number $ρ(\fracδ{H},d_{m}^{-},d_{M}^{+})<1$ is independent of the fine mesh size and the internal gaps among the targeted eigenvalues. The $H$-dependent constant $c(H)$ decreases monotonically to 1, as $H\to 0$, which means the more subdomains lead to the better convergence. Numerical results supporting our theory are given.

The orbit dimension $σ(G)$ (also called the separation number or rigidity index) of a permutation group $G$ with domain $Ω$ is the minimum cardinality of a subset $S \subseteq Ω$ such that, for any two distinct elements $ω,ω'\in Ω$, there exists $α\in S$ for which $ω$ and $ω'$ lie in distinct orbits of the stabilizer $G_α$. In this paper, we first observe that if $G$ is transitive, then $σ(G)\le |Ω|-r+1$, where $r$ is the rank of $G$, and we obtain strong structural information on the groups for which equality holds. Next, we investigate the orbit dimension in the case where $G$ is the symmetric group of degree $n$, acting on the set of $k$-subsets of $\{1,\ldots,n\}$. In this case, this invariant equals the metric dimension of Johnson graphs.

Synchronized radio telescope-based experiments conducted since 2017, together with subsequent interferometer experiments, provide evidence of an anomalous source of 3.7 Hz bandwidth pulses, sourced from near the direction of the star Rigel. The current experiment, reported here, uses a two-element phase-measuring interferometer to monitor the hypothetical pulse source across azimuths within the beam-widths of the elements of a south-facing interferometer. 123 days of phase measurements of 3.7 Hz bandwidth pulse pairs, adds to the prior evidence that the pulsing signal source has celestial origin. Associated measurements of noise power in 954 Hz and 50 MHz bandwidths, made simultaneous with the 0.27 second duration pulse pair measurements, are presented. Measurement results are presented to aid in the development of independent experimental replication, and alternate and auxiliary explanatory hypotheses.

The growing proliferation of unmanned aerial vehicles (UAVs) poses major challenges for reliable airspace surveillance, as drones are typically small, have low radar cross-sections, and often move slowly in cluttered environments. These characteristics make the joint tasks of detecting, localizing, and tracking multiple objects difficult for conventional detect-then-track (DTT) approaches, which rely on pre-processed measurements and may discard informative low-signal-to-noise ratio (SNR) signal components. To overcome these limitations, we propose a variational message passing (VMP)-based direct multiobject tracking (MOT) method that operates directly on raw radar signals and explicitly accounts for an unknown and time-varying number of objects. The proposed method is formulated for MIMO multi-radar systems and performs data fusion by jointly processing the signals of all radar sensors using a probabilistic model. A superimposed signal model is employed to capture correlations in the raw sensor data caused by closely spaced objects, and a hierarchical Bernoulli-Gamma model is introduced to jointly model object existence, reflectivities, and the reliability of individual radar-object links. Using a mean-field approximation, we derive message updates, yielding a computationally efficient VMP algorithm that simultaneously performs object detection, track formation, state estimation, and nuisance parameter learning directly from the radar signal. Simulation results in synthetic scenarios with weak and closely-spaced objects show that the proposed direct-MOT method outperforms a conventional pipeline based on super-resolution estimation followed by belief propagation (BP)-based tracking, particularly in low-SNR and clutter-rich conditions, demonstrating the advantages of direct signal-level inference and coherent multi-radar fusion.

Quantum-limited parametric amplifiers are essential components for many quantum technologies operating in the microwave domain. Achieving both high gain and broad bandwidth, however, remains challenging due to trade-offs between gain and bandwidth, pump efficiency, and dynamic range. Moreover, high-gain broadband amplifiers become increasingly sensitive to their external electromagnetic environment, which can distort their gain spectra and hinder reliable operation. Here, we present an accurate theoretical model and a systematic design methodology for a flux-driven, lumped-element Josephson parametric amplifier based on a SQUID array. Our device achieves near-quantum-limited, phase-preserving amplification with a net gain of 20 (maximally 44) dB and a 3-dB bandwidth of $\sim$50 ($\lesssim$0.2) MHz. We further show that the gain spectra exhibit pronounced sensitivity to weak reflections in the input-output waveguide caused by impedance mismatches in the microwave environment. By incorporating Fabry-Pérot-type interference into a quantum input-output model, we analytically reproduce these complex spectral features and identify how they depend on the physical parameters of the environment. More generally, our results provide a practical framework for separating the intrinsic dynamics of parametric amplifiers from environmental effects. This approach enables reliable characterization and optimization of amplifier performance while providing a systematic strategy for diagnosing microwave reflections and engineering environmental interference to shape amplifier gain spectra, thereby offering a pathway toward robust, reproducible, and truly quantum-limited microwave amplification.

Cartograms are a technique for visually representing geographically distributed statistical data, where values of a numerical attribute are mapped to the size of geographic regions. Contiguous cartograms preserve the adjacencies of the original regions during the mapping. To be useful, contiguous cartograms also require approximate preservation of shapes and relative positions. Due to these desirable properties, contiguous cartograms are among the most popular ones. Most methods for constructing contiguous cartograms exploit a deformation of the original map. Aiming at the preservation of geographical properties, existing approaches are often algorithmically cumbersome and computationally intensive. We propose a novel deformation technique for computing time-varying contiguous cartograms based on integral images evaluated for a series of discrete density distributions. The density textures represent the given dynamic statistical data. The iterative application of the proposed mapping smoothly transforms the domain to gradually equalize the temporal density, i.e., region areas grow or shrink following their evolutionary statistical data. Global shape preservation at each time step is controlled by a single parameter that can be interactively adjusted by the user. Our efficient GPU implementation of the proposed algorithm is significantly faster than existing state-of-the-art methods while achieving comparable quality for cartographic accuracy, shape preservation, and topological error. We investigate strategies for transitioning between adjacent time steps and discuss the parameter choice. Our approach applies to comparative cartograms' morphing and interactive cartogram exploration.