We derive the quantum filter for a quantum open system undergoing quadrature measurements (homodyning) where the input field is in a general quasi-free state. This extends previous work for thermal input noise and allows for squeezed inputs. We introduce a convenient class of Bogoliubov transformations which we refer to as balanced and formulate the quantum stochastic model with squeezed noise as an Araki-Woods type representation. We make an essential use of the Tomita-Takesaki theory to construct the commutant of the C*-algebra describing the inputs and obtain the filtering equations using the quantum reference probability technique. The derived quantum filter must be independent of the choice of representation and this is achieved by fixing an independent quadrature in the commutant algebra.

Interacting with video games is challenging for people with upper-limb impairments, especially when multiple hand-based inputs are required in rapid succession. Human cooperation, where another person assists the player, has been proposed as a solution, but it is limited by copilot availability and co-location. An alternative is partial automation, where the player is assisted by a software agent. We present a study with 13 participants with upper-limb impairments, investigating how they collaborate with a copilot in both human cooperation and partial automation. The experiment is supported by GamePals, a configurable framework we developed to enable both human cooperation and partial automation in existing third-party video games.

Our objective is to illuminate the global structure of non-orientable manifolds with signature-changing metrics, with particular emphasis on global topological obstructions. Using explicit geometric constructions based on the topology of the Möbius strip, we produce examples of crosscap manifolds where the gluing junction coincides with the locus of signature change. Our main result shows that on non-orientable compact surfaces, the radical of such metrics cannot be everywhere transverse along the hypersurface of signature change. In particular, metrics arising from the transformation prescription $\tilde{g}=g+fV^{\flat}\otimes V^{\flat}$, with $g$ a Lorentzian metric and $f$ a smooth interpolation function, necessarily fail to satisfy the transversality condition. This obstruction is of purely global origin and is closely related to topological invariants such as the Euler characteristic and the non-existence of nowhere-vanishing vector fields. These results demonstrate that non-orientability imposes intrinsic limitations on the class of admissible signature-type changing metrics.

Analysis often splits change into components. For example, how much of the observed variance is caused by genes or environment? In many cases, the split is ultimately made by the logic of the chain rule, which divides the difference of a product into two terms. Each term quantifies the partial difference associated with change in one component while holding the other component constant. The chain rule is of course widely known. However, this article argues that its deep fundamental role often goes unrecognized. The article shows how simply the basic chain rule unifies Fisher's fundamental theorem of natural selection, the Price equation description of evolutionary change, the Oaxaca-Blinder decomposition of wage differences in economics, the Kitagawa decomposition of mortality differences in demography, many expressions of thermodynamics, and most strikingly back propagation, the core optimization method of modern machine learning and artificial intelligence. The success in creating good designs and finding good solutions in both natural selection and artificial intelligence depends on how the chain rule propagates causes from instances of success or failure back to the underlying genes or parameters of the system. The mathematical analysis presented here shows that, for finite differences, the product rule form of the chain rule yields a basic decomposition of change into two components of a regression equation. That regression decomposition is purely a description of change with no explicit causal meaning. However, simple additional assumptions lead naturally to the modern counterfactual analysis of causality. From that perspective, we can easily understand the causal interpretation that Fisher gave to his fundamental theorem, and we can see the same causal structure in the Oaxaca-Blinder decomposition of economics and in causal analyses across many disciplines.

Metamaterials with floppy modes called mechanisms are a burgeoning template for shape-morphing systems and structures across scales. Here, we present a design recipe that transforms an arbitrary plane tiling into a 2D kirigami pattern with a single degree-of-freedom mechanism motion, greatly expanding the known library of mechanism-based designs. We reveal that these kirigami patterns, when deformed along their mechanism, have a bulk shape change invariant to the underlying microstructure of the pattern. Experimental observations confirm this unusual kinematic prediction in illustrative classes of designs. We also exploit this invariance to elicit different elastic responses in patterns with identical bulk shape change. Finally, we discuss generalizations to compact and non-planar kirigami, as well as 3D metamaterials, highlighting the broad applicability of our new approach to design.

This paper is an introduction to Coxeter polyhedra in spherical, Euclidean, and hyperbolic geometries. It consists of essentially two parts that could be read independently. In the first we introduce non-obtuse polyhedra in the spherical, Euclidean, and hyperbolic spaces, and prove various fundamental theorems originated from Andreev, Coxeter, and Vinberg. In the second we introduce Coxeter polyhedra and use them to describe regular, semiregular, and uniform polyhedra and tessellations, mostly via the Wythoff construction.

Type-II hyperbolic lattices constitute a new class of hyperbolic structures that are projected onto the Poincaré ring and possess both an inner and an outer boundary. In this work, we reveal the higher-order topological phases in type-II hyperbolic lattices, characterized by the generalized quadrupole moment. Unlike the type-I hyperbolic lattices where zero-energy cornerlike states exist on a single boundary, the higher-order topological phases in type-II hyperbolic lattices possess zero-energy cornerlike states localized on both the inner and outer boundaries. These findings are verified within both the modified Bernevig-Hughes-Zhang model and the Benalcazar-Bernevig-Hughes model. Furthermore, we demonstrate that the higher-order topological phase remains robust against weak disorder in type-II hyperbolic lattices. Our work provides a route for realizing and controlling higher-order topological states in type-II hyperbolic lattices.

We present the longest-term optical analysis of the AM CVn system KL Dra using $\sim11$ years of monitoring from TESS and wide-field ground-based surveys. The continuous TESS coverage allows us to characterise its frequent outbursts with unprecedented detail, providing the first comprehensive study of an AM CVn during outbursts and enabling detailed modelling of these systems. The superoutbursts in KL Dra generally include a precursor, and are followed by a series of rebrightenings after which a sequence of 3-4 large amplitude normal outbursts is observed. We fit parametric profiles to each superoutburst component (precursor, rise to plateau, plateau, decay), to rebrightenings, and to normal outbursts, which let us quantify every high state feature and investigate correlations with the system's long term supercyle evolution. Our continuous coverage reveals an average value for the supercycles, superoutbursts and normal outbursts of $60.4 \pm 0.1$ d, $5.67\pm0.03$ d and $1.17 \pm0.01$ d, respectively. The supercycle duration may be correlated with the rebrightenings duration and superoutburst amplitude, and anticorrelated with the plateau length. Within a supercycle, normal outbursts grow in amplitude and duration, and the first normal outburst is usually highly asymmetric, while subsequent normal outbursts are more symmetric. We detected superhumps in TESS superoutbursts but not in the rebrightenings or normal outbursts. We interpret the results within the disk instability model, considering additional effects, such as changes in the donor mass transfer rate.

Reconfigurable intelligent surfaces (RISs) enable programmable control of the wireless propagation environment and are key enablers for future networks. Beyond-diagonal RIS (BD-RIS) architectures enhance conventional RIS by interconnecting elements through tunable impedance components, offering greater flexibility with higher circuit complexity. However, excessive interconnections between BD-RIS elements require multi-layer printed circuit board (PCB) designs, increasing fabrication difficulty. In this letter, we use graph theory to characterize the BD-RIS architectures that can be realized on double-layer PCBs, denoted as planar-connected RISs. Among the possible planar-connected RISs, we identify the ones with the most degrees of freedom, expected to achieve the best performance under practical constraints.

Van der Waals materials are offering intriguing opportunities as building blocks for advanced quantum information technologies and integrated quantum photonic systems. Critical to their development, is robust and high quality light-matter interactions which can be delivered through the fabrication of optical resonators. Here we demonstrate a robust fabrication of one dimensional photonic crystal cavities (1D PCC) and microdisk resonators from hexagonal boron nitride, exhibiting Quality factors of ~ 4300 and ~ 8300, respectively. With these two classes of devices we demonstrated cavity mode tuning via atomic layer deposition and gas condensation. Cavity resonances were shifted by and ~9 nm for the 1D PCCs and ~16 nm in the microdisk resonators, respectively. Our work opening a promising pathway for a realisation emitter cavity coupling in hBN and eventually to a fully integrated quantum photonic circuitry with hBN.

We calculate the electromagnetic dipole transition cross sections for the $np \rightarrow dγ$ and $ dγ\rightarrow np$ reactions over a broad range of energies. We use the LENPIC nucleon-nucleon interaction obtained from chiral effective field theory ($χ$EFT) up to next-to-next-to-next-to-next-to-leading order (N4LO) and effective electromagnetic dipole transition operators obtained from the same $χ$EFT up to N2LO. Our results agree with existing experiments. We get results at energies for which experimental data and/or modern theoretical calculations have not been reported. In this study, we utilize a new approach, namely, our adaptation of the Efros [V. D. Efros, Phys. Rev. C 99, 034620 (2019)] method that is prospective for future many-body applications in calculations of bound and continuum state wave functions.

We investigate an intrinsic step-jamming phenomenon at the nanometer scale on Kardar-Parisi-Zhang (KPZ)-like kinetically roughened crystal surfaces that arises during interface-limited steady crystal growth or retreat. Monte Carlo simulations using the Metropolis algorithm on a restricted solid-on-solid (RSOS) lattice model demonstrate that intrinsic step jamming persists on surfaces below 20 nm. In the present model, transport processes such as surface and volume diffusion are excluded, as are elastic interactions, step-step repulsion or attraction, and stoichiometric effects. We show that intrinsic step jamming arises from asymmetric fluctuations in atomic attachment and detachment driven by biased transition probabilities under the SOS restriction, leading to collective step congestion. Asymmetric fluctuations also determine whether adatom or hole clusters grow or recede. This mechanism bears close similarity to jamming phenomena in the asymmetric simple exclusion process (ASEP), including multi-lane variants. In contrast, symmetric thermal fluctuations generate adatom or hole clusters on terraces, thereby suppressing intrinsic step jamming. Possible routes to suppress intrinsic step jamming, including experimentally accessible strategies, are also discussed.

Automatically determining the number of intrinsic mode functions (IMFs) and their center frequencies in Variational Mode Decomposition (VMD) remains an open mathematical challenge. Existing methods rely on heuristic settings, trial-and-error, or recursive extraction lacking theoretical convergence guarantees. We propose a variational framework that endogenously determines the number of modes. Any curve below the spectral amplitude divides the area under the spectrum into 2 parts and generate the connected intervals where spectrum locates above it, whose count defines the modal number K[g] -- a topological functional induced by the cutting curve. Since K[g] is discontinuous and intractable for direct optimization, we seek the optimal cutting curve as a continuous variational surrogate: it separates distinct spectral peaks into individual regions above it while merging noise-induced fragments below. This surrogate adversarially maximizes the integral of g while penalizing its curvature, transforming the problem into iteratively solving a fourth-order boundary value problem via Lagrangian duality. We establish a rigorous proof of global convergence for the dual ascent algorithm in function space. Comprehensive numerical experiments on artificial and real-world signals including ECG data show accurate estimates of IMFs and center frequencies, avoiding redundant modes while ensuring recovery of necessary components, providing a robust, theoretically grounded initialization routine for VMD.

During inflation long wavelength gravitational waves are produced, which form stochastic background in the present universe with very wide range of frequencies. Higher frequency gravitational waves never experience super-Hubble-radius regime, but they are also amplified after inflation due to the inflaton oscillation. Taking account of the inflaton dynamics after inflation, the spectrum of such quantum-mechanically produced gravitational waves may extend to much higher frequencies than previously thought. In this paper we calculate the spectrum of high frequency gravitational waves produced during and after inflation in detail, in particular focusing on the connection between the low and high frequency regime, and show that the detailed spectrum can distinguish inflation models.

We compute static ($ω\to0$) tilde Love numbers for scalar ($s=0$) and Dirac ($s=1/2$) perturbations of static acoustic black holes (ABHs) in (3+1) and (2+1) dimensions respectively. By imposing horizon regularity condition and matching to the large-radius expansion, we extract the ratio between decaying and growing modes. It turns out that in (3+1) dimensions the scalar Love number is generically nonzero for ABHs, while the Fermionic Love numbers follow a universal power-law form $F^{\pm1/2}_{\ell m}=\pm 4^{-(\ell+1/2)}$. In (2+1) dimensions the scalar field exhibits a strange logarithmic structure, causing the Bosonic Love number to vanish for even $m$ but remain nontrivial for odd $m$; In contrast, the Fermionic Love number in this case retains a simple power-law form $F_m=4^{-m}$ and is generically nonzero. These results provide insights into tidal response in analogue gravity systems and highlight qualitative differences between integer- and half-integer-spin fields.

We aim to answer the following question: is the complexity of numerically solving the Poisson equation increasing or decreasing for very large simulations of incompressible flows? Physical and numerical arguments are combined to derive power-law scalings at very high Reynolds numbers. A theoretical convergence analysis for both Jacobi and multigrid solvers defines a two-dimensional phase space divided into two regions depending on whether the number of solver iterations tends to decrease or increase with the Reynolds number. Numerical results indicate that, for Navier-Stokes turbulence, the complexity decreases with increasing Reynolds number, whereas for the one-dimensional Burgers equation it follows the opposite trend. The proposed theoretical framework thus provides a unified perspective on how solver convergence scales with the Reynolds number and offers valuable guidance for the development of next-generation preconditioning and multigrid strategies for extreme-scale simulations.

Recent advancements in large-scale position-reconfigurable antennas have opened up new dimensions to effectively utilize the spatial degrees of freedom (DoFs) of wireless channels. However, the deployment of existing antenna placement schemes is primarily hindered by their limited scalability and frequently overlooked near-field effects in large-scale antenna systems. In this paper, we propose a novel antenna placement approach tailored for near-field massive multiple-input multiple-output systems, which effectively exploits the spatial DoFs to enhance spectral efficiency. For that purpose, we first reformulate the antenna placement problem in the angular domain, resulting in a weighted Fekete problem. We then derive the optimality condition and reveal that the {optimal} antenna placement is in principle an electrostatic equilibrium problem. To further reduce the computational complexity of numerical optimization, we propose an ordinary differential equation (ODE)-based framework to efficiently solve the equilibrium problem. In particular, the optimal antenna positions are characterized by the roots of the polynomial solutions to specific ODEs in the normalized angular domain. By simply adopting a two-step eigenvalue decomposition (EVD) approach, the optimal antenna positions can be efficiently obtained. Furthermore, we perform an asymptotic analysis when the antenna size tends to infinity, which yields a closed-form solution. Simulation results demonstrate that the proposed scheme efficiently harnesses the spatial DoFs of near-field channels with prominent gains in spectral efficiency and maintains robustness against system parameter mismatches. In addition, the derived asymptotic closed-form {solution} closely approaches the theoretical optimum across a wide range of practical scenarios.

This paper establishes the existence of infinitely many solutions for nonlinear problems without any symmetry, achieving three major advances. First, in the setting of semilinear elliptic PDEs, we introduce a refined variational truncation method that yields infinite sequences of positive as well as negative solutions. Second and most notably, we resolve a long-standing and difficult problem for nonvariational elliptic PDEs with gradient dependence. By combining our truncation method with an iterative scheme, we prove, for the first time, the existence of infinitely many solutions for this class of PDEs. Third, we overcome a central difficulty for periodic Hamiltonian systems on the real line: we show that the multiplicity of solutions, constructed on a sequence of finite intervals, survives in the limit; in other words, no collapse occurs, and we obtain multiple distinct solutions on the whole real line. The core novelty lies in a carefully designed truncation methodology that systematically separates solutions and remains effective across variational and non-variational PDEs as well as infinite dimensional dynamical systems. This unified perspective provides a robust and versatile tool for addressing multiplicity problems in the absence of symmetry.

Inter-satellite-link-enabled low-Earth-orbit (LEO) satellite constellations are evolving toward networked architectures that support constellation-level cooperation, enabling multiple satellites to jointly serve user terminals through cooperative beamforming. While such cooperation can substantially enhance link budgets and achievable rates, its practical realization is challenged by the scalability limitations of centralized beamforming designs and the stringent computational and signaling constraints of large LEO constellations. This paper develops a fully decentralized cooperative beamforming framework for networked LEO satellite downlinks. Using an ergodic-rate-based formulation, we first derive a centralized weighted minimum mean squared error (WMMSE) solution as a performance benchmark. Building on this formulation, we propose a topology-agnostic decentralized beamforming algorithm by localizing the benchmark and exchanging a set of globally coupled variables whose dimensions are independent of the antenna number and enforcing consensus over arbitrary connected inter-satellite networks. The resulting algorithm admits fully parallel execution across satellites. To further enhance scalability, we eliminate the consensus-related auxiliary variables in closed form and derive a low-complexity per-satellite update rule that is optimal to local iteration and admits a quasi-closed-form solution via scalar line search. Simulation results show that the proposed decentralized schemes closely approach centralized performance under practical inter-satellite topologies, while significantly reducing computational complexity and signaling overhead, enabling scalable cooperative beamforming for large LEO constellations.

We develop an effective description of the local cosmic environment, namely, for redshift $z \lesssim 0.1$, to quantify the bias induced by local structure on cosmological observables. Our approach models the metric of the nearby Universe as a superposition of multi-structured $Λ$-Szekeres patches, calibrated against the HAMLET peculiar velocity and density field reconstructions of Cosmicflows-4. From this framework we compute the fully inhomogeneous and anisotropic quasilocal expansion field predicted by our model, and use it to assess the impact of local structure on estimates of $H_0$. For this purpose we analyse low-redshift Type Ia supernovae from the Pantheon+ catalogue. We find that accounting for the local structure increases the Hubble tension, yielding a shift in the best-fit value of the Hubble constant of order $ΔH_0 \approx 0.5\ \mathrm{km\,s^{-1}Mpc^{-1}}$.

In this paper, we propose a new method for calculating integrals for a special class of integrands. As an application, we show how this method can be used to derive optimal pointwise temporal estimates for a class of nonlocal evolution equations. Compared with other methods, our approach can obtain both upper bound and lower bound simultaneously.

Mesoscopic fluctuations reveal stochastic dynamics of molecules in both inanimate and living matter. We investigate how small-number fluctuations shape the collective dynamics of molecular motors using motile cilia as model system. We theoretically show that fluctuations in the number of bound motors are sufficient to explain experimentally observed fluctuations in the cilia beat, including a quality factor $Q$ that measures oscillation precision and phase defects of intra-cilium synchronization. Our findings constrain theories of motor control and establish a link between microscopic motor noise and mesoscopic non-equilibrium dynamics.

The square-kagome lattice, composed of two-dimensional corner-sharing triangles, provides a novel platform for studying frustrated magnetism. However, material realizations of the square-kagome lattice remain scarce. Here, we report the single-crystal growth, structural characterization, magnetic and electric properties of KCu$_7$TeO$_4$(SO$_4$)$_5$Cl, a nabokoite compound featuring a distorted and decorated square-kagome lattice. Weak anomalies near 4 K are observed in both magnetization and specific heat, indicating the onset of a magnetic transition.The formation of a long-range antiferromagnetic state below 4.5 K is further confirmed by $^{35}$Cl nuclear magnetic resonance (NMR) measurements. Magnetic susceptibility data reveal nearly isotropic Curie-Weiss temperatures ($\sim-145$ K) and $g$-factors ($\sim2.4$) for both in-plane and out-of-plane magnetic fields. Moreover, we observe two successive ferroelectric transitions at $T_\mathrm{FE1}\sim30$ K and $T_\mathrm{FE2}\sim27$ K, driven by inversion-symmetry breaking, most likely associated with distortions in the Cu2O$_4$Cl$_1$ pyramids and the adjacent SO$_4$ tetrahedra. These results suggest that a three-dimensional model incorporating interlayer couplings via decorating Cu2 sites is essential for capturing the magnetic and electric behaviors in KCu$_7$TeO$_4$(SO$_4$)$_5$Cl.

This article discusses the incorporation of dark matter and dark energy into a new physics model called the Three-Higgs Doublet Model. Dark matter and dark energy are accommodated as CP-even and $Z_2$-odd scalars in their respective inert doublets. By leveraging a $Z_2$ symmetry to suppress certain interactions, we model the behavior of dark matter. Similarly, by imposing a shift symmetry, dark energy can be mimicked within the same framework for the current cosmic epoch. The dark matter relic density is calculated for our model using \texttt{micrOMEGAs}. It is shown that despite the inclusion of dark energy, dark matter relic density can be brought within observational bounds and match existing literature. Furthermore, the one-loop and two-loop Renormalization Group Equations (RGEs) were computed using \texttt{SARAH} to ensure radiative stability over a large range of energies. This study lays the groundwork for a future study of dark matter-dark energy interactions in the early universe and the exploration of different early universe dynamics.

We investigate stellar mass and central dark matter density profiles of photometric luminous red galaxies with stellar masses of $\sim10^{10}-10^{12}M_\odot$ using weak gravitational lensing measurements from the Hyper Suprime-Cam Subaru Strategic Program data obtained with the Subaru Telescope. By stacking weak lensing signals from a large number of galaxies, we obtain average tangential shear profiles down to $\sim 10\,\mathrm{kpc}/h$, which are fitted assuming a two-component model consisting of stellar and dark matter components to constrain their central dark matter distribution. We find a preference for non-zero core radii of dark matter distributions in galaxies with stellar masses of $\sim 10^{11}M_\odot$. Our results imply a stronger feedback effect than that typically predicted by current hydrodynamical simulations. In addition, we provide a new constraint on the stellar-to-halo mass relation, where both stellar and halo masses are, for the first time, directly constrained by weak gravitational lensing. Our results prefer the stellar initial mass function (IMF) that is more bottom-heavy than the Salpeter IMF.

A deep learning model is proposed for reconstructing 2D dielectric breast images from time-domain signals. Unlike existing learning models that employ a fixed antenna array, where input data consists solely of measurements, the proposed system integrates antenna positioning into the processing pipeline. This allows for a conformal antenna array that adapts to different breast sizes for optimal data collection across various patients, which eliminates undesired signal attenuation in coupling liquid when implemented for the fixed array. By leveraging antenna positions, the breast surface can be pre-estimated, enabling the neural network to focus on image reconstruction within the region of interest. Numerical results demonstrate that the proposed model may reconstruct breast images with good quality.

We investigated the occurrence rate of the sustained gamma ray emission (SGRE) events from the Sun using data obtained by Fermi Large Area Telescope (LAT) since its launch in 2008. Only 16 SGRE events were observed during the first 61 months of solar cycle (SC) 25, likely due to the solar array drive assembly's malfunction in 2018; 27 SGRE events were observed in SC 24 over the corresponding epoch. The average sunspot number (SSN) increased from 56.9 in SC 24 to 79.0 in SC 25. Fast and wide (FW) CMEs and decameter-hectometric (DH) type II bursts increased significantly in SC 25 by 29% and 33%, respectively when normalized to SSN. Therefore, we expect a higher number of SGREs in SC 25. We estimated the number of SGREs in SC 25 using three methods. (i) If the SGRE number varies commensurate with SSN, we should have 38 SGRE events in SC 25. However, FW CMEs and DH type II bursts in SC 25 were overabundant by 29% and 33%, so the number SGRE events should be 48 or 50. (ii) In SC 24, ~18% of FW CMEs and 27% of DH type II bursts were associated with SGRE events. At this rate SC 25 should have 48 and 49 SGRE events. (iii) Since SGRE events are invariably associated with >100 keV hard X-ray (HXR) bursts, we identified DH type II bursts associated with >100 keV HXR bursts from Fermi's Gamma ray Burst Monitor (GBM) during LAT data gaps. Almost all SGRE events in SCs 24 and 25, and 27 of the 79 LAT-gap type IIs were associated with HXR bursts of duration > ~5 min. These DH type II bursts are indicative of SGRE, bringing the total number of SGRE events to 43 (16 + 27). Thus, the three methods provide similar estimates of the number of SGRE events in SC 25. We, therefore, conclude that SC 25 is stronger than SC 24 based on the estimated number SGRE events.

We use the FLAMINGO galaxy formation model to quantify the impact of baryon-CDM isocurvature perturbations on galaxy formation in $Λ$CDM. In linear theory, these perturbations represent local, compensated variations in the ratio between the baryon and CDM densities; they freeze in amplitude at late times, with an RMS amplitude of $1.5\%$ on the Lagrangian scale of a $10^{11}\,\rm M_\odot$ halo ($0.85\, \rm{Mpc}$). Although such perturbations arise naturally within $Λ$CDM, most cosmological simulations and semi-analytic models to date omit them. These perturbations are strongly anti-correlated with the matter overdensity field such that halos form with baryon fractions below the cosmic mean, with earlier-collapsing halos exhibiting stronger baryonic suppression. To isolate the galaxy response, we analyse three hydrodynamical simulations with identical initial matter overdensity fields that: i) include isocurvature modes, ii) omit them, or iii) invert their amplitude. At $z=8$, isocurvature perturbations reduce the mean baryon fraction and star formation rates of resolved halos by $ 5\%$ and $ 12\%$, respectively, relative to the null-isocurvature case. These effects are almost independent of halo mass and diminish steadily with time, reaching $ 0.1\%$ and $ 1\%$ by $z=0$. We develop a model based on spherical collapse that accurately reproduces the mean baryon fraction suppression. As high-redshift observations become increasingly routine, incorporating isocurvature perturbations into simulations and semi-analytic models will be important for robust predictions of early galaxy and black hole formation in the JWST era.

Accurate determination of ground-state energies for molecules remains a challenge in quantum chemistry and a cornerstone for progress in fields such as drug discovery and materials design. The Variational Quantum Eigensolver (VQE) represents a leading hybrid quantum-classical paradigm for addressing this challenge; however, its widespread realization is limited by noise and the restricted scalability of current quantum hardware. Achieving efficient simulations on Noisy Intermediate-Scale Quantum (NISQ) devices and forthcoming Fault-Tolerant Application-Scalable Quantum (FASQ) systems demands a detailed understanding of how computational resources scale with molecular complexity and fermion-to-qubit encodings. In this study, resource requirements for VQE implementations employing the Unitary Coupled Cluster Singles and Doubles (UCCSD) ansatz are systematically analyzed. The molecular Hamiltonian is formulated in second quantization and mapped to qubit operators through the Jordan-Wigner (JW), Bravyi-Kitaev (BK), and Parity (Pa) transformations. Hamiltonian reduction strategies, including $\mathbb{Z}_2$ tapering and frozen-core approximations, are examined to assess their effect on quantum resource scaling. The analysis reveals that appropriate transformations, when combined with symmetry-based reductions, can substantially reduce qubit counts by up to $\approx 50\%$ and quantum gate counts by up to $\approx 27.5\times$ and Hamiltonian Pauli string counts by up to $\approx 2.75\times$, relative to the corresponding unreduced Hamiltonian representations within the same active-space configuration for the representative set of molecular systems under study. These findings provide practical circuit-level insights for executing chemically relevant simulations on NISQ hardware, while establishing physical-resource baselines that may inform future logical-level analyses targeting FASQ systems.

Bound states in the continuum (BICs) have attracted intense interest, yet their many-particle counterparts remain largely unexplored in waveguide quantum electrodynamics. We identify and characterize a bound state embedded in the doublon continuum (BIDC) that emerges when four atoms couple to a coupled-resonator waveguide with strong on-site interaction. Exploiting this interaction-enabled BIDC, we show that (i) a distant, four-atom entangled state can be prepared with high fidelity, and (ii) quantum entangled states can be coherently transferred between spatially separated nodes. Our results establish a scalable mechanism for multi-particle state generation and routing in waveguide platforms, opening a route to interaction-protected quantum communication with many-particle BICs.