This paper describes a fast direct boundary element method for elastodynamic transmission problems in two dimensions, which can be used for analyzing elastic wave scattering by an inclusion. We develop an efficient solver based on a discretization method that is broadly applicable regardless of the inclusion shape. From the smoothness of the solutions of the Navier--Cauchy equation, it is reasonable that the displacement is approximated by the piecewise linear bases and the traction is approximated by the piecewise constant bases. However, in this mixed bases strategy, Calderón preconditioning, that is, an analytical preconditioning with excellent performance, cannot be applied. To circumvent this issue, we developed a fast direct solver formulated using both Burton--Miller and Poggio--Miller--Chang--Harrington--Wu--Tsai (PMCHWT) boundary integral equations. Our method uses a technique based on the proxy method for low-rank approximation of the coefficient matrix's off-diagonal blocks. To handle transmission problems, the proposed fast direct solver uses separate binary tree partitions for nodes and elements. Numerical examples demonstrate that our solver achieves linear computational complexity at fixed low frequencies and can efficiently handle problems with multiple right-hand sides. Notably, the solver based on the Burton--Miller formulation is approximately 20\% faster than the one using the PMCHWT formulation. Our new method provides a versatile, fast solver, whose performance is relatively independent of the shape of inclusions and computational parameters, such as density, for elastodynamic transmission problems.

Quantum Annealing (QA) encounters limitations when the energy gap along the annealing path becomes exponentially small, leading to impractically long runtimes. In contrast, the success of hybrid digital methods like the Quantum Approximate Optimization Algorithm (QAOA), which operate via discrete unitary operations, relies on the optimization of the variational parameters appearing in the state. We analyze a class of transverse-field Ising models which includes problems with exponentially small spectral gaps, but whose dynamics is described in terms of fermionic Gaussian states after Jordan-Wigner mapping. We show that, for digital alternating QAOA-like states, the number of unitaries required to reach the exact ground state scales quadratically with system size and is independent of the annealing gap. This number can be exactly computed from the algebraic properties of the Ansatz, revealing a fundamental distinction between digital methods and their analog counterpart.

In the theory of hyperplane arrangements, M. Wakefield and S. Yuzvinsky utilized a square matrix in their research on the exponents of $2$-dimensional multiarrangements. Using such a matrix, they showed that the exponents of $2$-dimensional multiarrangements are as close as possible in general position for any fixed balanced multiplicity. In this article, we introduce a matrix similar to that of Wakefield and Yuzvinsky and explore further applications to the exponents. In fact, the exponents of $2$-dimensional multiarrangements are determined by whether the corresponding matrices have full rank. As one of our main results, we introduce a new class of $2$-dimensional arrangements for which the exponents are as close as possible for any balanced multiplicities, except for the constant one multiplicity. We also proceed with the classification of $B_2$-exponents, and we provide an alternative proof for some known results on the exponents.

We present a general theoretical framework for evaluating multi-photon processes in periodically driven quantum systems, which have been identified as a versatile tool for engineering and controlling nontrivial interactions in various quantum technology platforms. To achieve the accuracy required for such applications, the resulting effective coupling rates, as well as any drive-induced frequency shifts, must be determined with very high precision. Here, we employ degenerate Floquet perturbation theory together with a diagrammatic representation of multi-photon processes to develop a systematic and automatable approach for evaluating the effective dynamics of driven quantum systems to arbitrary orders in the drive strength. As a specific example, we demonstrate the effectiveness of this framework by applying it to the study of multi-photon Rabi oscillations in a superconducting fluxonium qubit, finding excellent agreement between our theoretical predictions and exact numerical simulations, even for large driving amplitude.

Goedgebeur and Schaudt [J. Graph Theory 87 (2018) 188-207] conjectured that all 4-vertex-critical $(P_7,C_3)$-free graphs belongs to the family $\cal G$, which consists of seven explicitly defined graphs. In this paper, we establish a structural decomposition for $(P_2\cup P_4,C_3)$-free graphs and show that the conjecture holds for this class. Consequently, we determine the chromatic number of $(P_2\cup P_4, C_3)$-free graphs. A graph $G$ is {\em perfectly divisible} if for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $ω(H[B])<ω(H)$. A {\em bull} is a graph consisting of a triangle with two disjoint pendant edges. Notice that the class of $(P_2\cup P_4, C_3)$-free graphs is a subclass of ($P_2\cup P_4$, bull)-free graphs. In this paper, we prove that a ($P_2\cup P_4$, bull)-free graph is perfectly divisible if and only if it contains no Mycielski-Grötzsch graph. This generalizes the main result of Deng and Chang [Graphs Combin. (2025) 41: 63].

This paper describes a measurement of the $Λ_b^0\to J/ψΛ$ branching fraction using data collected with the LHCb experiment in proton-proton collisions from 2016 to 2018. The dataset corresponds to an integrated luminosity of 5.4$\,\text{fb}^{-1}$. The branching fraction is determined relative to that of $B^0\to J/ψK^0_\text{S}$ decays, $\frac{\mathcal{B}(Λ_b^0\to J/ψΛ)}{\mathcal{B}(B^0\to J/ψK^0_\text{S}} = 0.750 \pm 0.005 \pm 0.022 \pm 0.005 \pm 0.062\,,$ yielding $\mathcal{B}(Λ_b^0\to J/ψΛ) = (3.34 \pm 0.02 \pm 0.10 \pm 0.08 \pm 0.28)\times 10^{-4}$, where the first uncertainty is statistical, the second systematic, the third due to external inputs on branching fractions and the fourth due to the ratio of $Λ_b^0$ baryon and $B^0$ meson hadronisation fractions. In addition, the isospin asymmetry between the rates of $B^0\to J/ψK^0_\text{S}$ and $B^+\to J/ψK^+$ decays is measured to be $A_{\rm I} = -0.0135 \pm 0.0004 \pm 0.0133$, where the first uncertainty is statistical and the second systematic.

Black holes are believed to possess vanishing Love numbers, which implies that they do not deform in the presence of external tides. This fact has been verified in a number of scenarios, that involve tides of bosonic fields of various natures (e.g. scalar, electromagnetic and gravitational), and has triggered active research in trying to identify the underlying reason. Surprisingly, two counterexamples have been found recently. The first, concerns charged-field tides on electrically-charged black holes. In that case, however, the response cannot be disentangled from dissipative effects, and might thus be argued to not consist of a truly conservative deformation. The second concerns fermionic tides on neutral holes. While these yield a purely conservative response, they lack a classical interpretation, which is the physical regime where black hole deformability is understood. Here, we consider magnetic Reissner-Nordstrom black holes and show that electrically-charged, scalar-field tides induce non-vanishing tidal Love numbers. We prove that this is a purely non-dissipative effect, in contrast to the cases of rotating or electrically-charged black holes, and hence consists of a genuine deformation. In addition, the magnetic charge resolves common ambiguities in defining Love numbers, so our result does not rely on any regularisation scheme. This constitutes a clear realisation of how new physics can influence black hole tidal deformability, and offers new perspectives on the study of black hole Love numbers.

The Busy Beaver value $S(n)$ is the maximum number of steps that an $n$-state 2-symbol Turing machine can perform from the all-zero tape before halting. $S$ was historically introduced by Tibor Radó in 1962 as one of the simplest examples of an uncomputable function. We prove that $S(5) = 47,176,870$ using the Coq proof assistant. The proof enumerates $181,385,789$ Turing machines with 5 states and, for each machine, decides whether it halts or not. Our result marks the first determination of a new Busy Beaver value in over 40 years and the first Busy Beaver value ever to be formally verified, attesting to the effectiveness of massively collaborative online research (bbchallenge$.$org).

We demonstrate that the non-Hermitian quantum geometric tensor (QGT) governs nonlinear electrical responses in systems with a spectral line gap. The quantum metric, which is the symmetric component of the QGT and takes complex values in non-Hermitian systems, generates an intrinsic nonlinear conductivity independent of the scattering time. In contrast, the full complex-valued QGT induces a distinct conductivity that depends explicitly on the wavepacket width. Using one- and two-dimensional non-Hermitian models, we establish a direct link between nonlinear dynamics and the QGT, thereby connecting quantum state geometry to observable transport phenomena. Crucially, we reveal that the finite wavepacket width fundamentally alters non-Hermitian transport -- a mechanism strictly absent in Hermitian systems. This framework elucidates non-Hermitian response theory by revealing how the complex geometry of quantum states, captured by the QGT, and the wavepacket width jointly encode transport in open and synthetic quantum matter.

This paper incorporates fixed capital into a multi-sectoral input-output model to reassess the Okishio Theorem. We establish the existence of a critical wage elasticity strictly less than unity, beyond which cost-reducing technical progress leads to a declining equilibrium rate of profit. This implies that profit rates may fall even under Kaldor's Stylized Facts or a moderately declining labour share, significantly extending the theorem's domain of validity. Game-theoretic analysis reveals a strict Prisoner's Dilemma structure underlying technical adoption. Empirical evidence from Chinese industrial data confirms that fixed capital intensity exerts a significant dampening effect on the profit-enhancing impact of productivity growth.

We show that mean curvature flow translators may exhibit non-removable singularities at infinity, due to jump discontinuities in their asymptotic profiles, and that oscillation can persist so as to yield a continuum of subsequential limit tangent planes. Nonetheless, we prove that as time $t\to\pm \infty$, any finite entropy, finite genus, embedded, collapsed translating soliton in $\mathbb{R}^3$ converges to a uniquely determined collection of planes. This requires global analysis of quasilinear soliton equations with non-perturbative drifts, which we analyze via sharp non-standard elliptic decay estimates for the drift Laplacian, implying improvements on the Evans-Spruck and Ecker-Huisken estimates in the soliton setting, and exploiting a link from potential theory of the Yukawa equation to heat flows with $L^\infty$-data on non-compact slice curves of these solitons. The structure theorem follows: such solitons decompose at infinity into standard regions asymptotic to planes or grim reaper cylinders. As one application, we classify collapsed translators of entropy two with empty limits as $t\to +\infty$.

We construct good GKP (Gottesman-Kitaev-Preskill) codes (in the sense of Conrad, Eisert and Seifert proposed) from standard short integer solution lattices (SIS) as well as from ring SIS and module SIS lattices, R-SIS and M-SIS lattices, respectively. These lattice are crucial for lattice-based cryptography. Our construction yields GKP codes with distance $\sqrt{n/πe}$. This compares favorably with the NTRU-based construction by Conrad et al. that achieves distance $Ω(\sqrt{n/q}),$ with $n\le q^2/0.28$. Unlike their codes, our codes do not have secret keys that can be used to speed-up the decoding. However, we present a simple decoding algorithm that, for many parameter choices, experimentally yields decoding results similar to the ones for NTRU-based codes. Using the R-SIS and M-SIS construction, our simple decoding algorithm runs in nearly linear time. Following Conrad, Eisert and Seifert's work, our construction of GKP codes follows directly from an explicit, randomized construction of symplectic lattices with (up to constants $\approx 1$) minimal distance $(1/σ_{2n})^{1/2n}\approx \sqrt{\frac{n}{πe}}$, where $σ_{2n}$ is the volume of the 2n-dimensional unit ball. Before this result, Buser and Sarnak gave a non-constructive proof for the existence of such symplectic lattices.

Medicine is evolving beyond therapy largely predicated on anatomical information and towards incorporating patient-specific molecular biomarkers of disease for more accurate diagnosis and effective treatment. The complementary combination of hyperpolarization by spin-lock induced crossing signal amplification by reversible exchange (SLIC SABRE) and low field magnetic resonance imaging (MRI) can enable accessible metabolic imaging to advance personalized medicine. Hyperpolarized 13C-enriched pyruvate has demonstrated utility for MRI of metabolism in cancer, heart disease and neurodegenerative disorders but has been restricted from widespread clinical adoption by a lack of access to affordable technology. Parahydrogen-based polarization techniques, paired with low-cost high-performance MRI at millitesla fields, offer a means of broadening the reach of metabolic imaging. Here we show results demonstrating in situ hyperpolarization of pyruvate at 6.5 mT by SLIC SABRE, followed by immediate readout without field cycling or sample shuttling. We achieve 13C signal enhancements several million times above thermal equilibrium at 6.5 mT, corresponding to polarization levels of approximately 3%. Leveraging this enhancement, we perform 13C MRI and acquire NMR spectra with resolution sufficient to distinguish chemical shifts between pyruvate isotopomers. These results show a viable pathway towards accessible metabolic imaging with hyperpolarized 13C MRI at ultra-low field.

We report a real-time first-principles study of ultrafast spin injection in a WSe$_2$-graphene heterobilayer under circularly polarized laser irradiation, using time-dependent density functional theory. Contrary to conventional expectations, spin transfer into graphene is not a passive process but is actively driven by spin-selective carrier filtering at the interface. Spin-polarized carriers generated in the WSe$_2$ layer induce a preferential migration of opposite-spin carriers from graphene, which results in net spin magnetization in graphene. This process is governed by interlayer band offsets, density-of-state asymmetry, and Pauli blocking. These findings indicate a microscopic mechanism of spin injection in non-magnetic systems and identify a guiding principle for the design of ultrafast opto-spintronic functionalities in van der Waals heterostructures.

A model-independent measurement of the differential production cross section of the Higgs boson decaying into a pair of W bosons, with a final state including two jets produced in association, is presented. In the analysis, events are selected in which the decay products of the two W bosons consist of an electron, a muon, and missing transverse momentum. The model independence of the measurement is maximized by making use of a discriminating variable, developed through machine learning, that is agnostic to the signal hypothesis. The analysis is based on proton-proton collision data at $\sqrt{s}$ = 13 TeV collected with the CMS detector from 2016$-$2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. The production cross section is measured as a function of the difference in azimuthal angle between the two jets. The differential cross section measurements are used to constrain Higgs boson couplings within the standard model effective field theory framework.

A swimming microorganism stirs the surrounding fluid, creating a flow field that governs not only its locomotion and nutrient uptake, but also its interactions with other microorganisms and the environment. Despite its fundamental importance, capturing this flow field and unraveling its biological implications remains a challenge. Here, we report the first direct, time-resolved measurements of the three-dimensional (3D) flow field generated by a single, free-swimming microalga, Chlamydomonas reinhardtii, a model organism for microbial locomotion and flagellar dynamics. Supported by hydrodynamic modeling and simulations, our measurements resolve how established two-dimensional (2D) flow features such as in-plane vortices and the stagnation point emerge from and shape the full algal flow in 3D. Moreover, we reveal unexpected low-Reynolds-number flow phenomena including micron-sized vortex rings and periodically recurring translating vortices and uncover topological changes in the underlying flow structure associated with the puller-to-pusher transition of an alga. Biologically, access to the 3D flow field enables rigorous quantification of the alga's energy expenditure, as well as its swimming and feeding efficiency, improving the precision of these physiological metrics. Taken together, our study demonstrates rich vortex dynamics in inertialess flows and shows their influence on microbial motility. The work also introduces a new experimental method for mapping the fluid environment sculpted by beating flagella.

Primordial non-Gaussianities (PNGs) are imprints in the initial density field sourced by the dynamics of inflation. These dynamics can induce scale dependence, oscillations, and other features in the primordial bispectrum. We analyze a suite of over thirty PNG templates, including those used in the _Planck_ analyses of the Cosmic Microwave Background (CMB), and resolve their signatures in the deeply nonlinear regime of the late-time density field. Using simulations, we forecast results from a lensing analysis of the Year-10 data from the Rubin Observatory Legacy Survey of Space and Time (LSST). We find that lensing achieves sensitivity comparable to the CMB for many models, and even surpasses it for templates whose features peak on smaller scales, $k \gtrsim 0.2 h/{\rm Mpc}$. Many templates generate non-monotonic behaviors in mass and length scales, providing a distinct phenomenology in the resulting late-time structure. We simulate, for the first time, resonant signatures consistently in both the primordial power spectrum and bispectrum. The constraints on their amplitudes $(A_{\rm pk}, f_{\rm NL})$ are essentially independent, as each affects structure formation in distinct ways. Overall, we find that lensing data can provide competitive and complementary constraints on these models, and can deliver leading constraints when the primordial features are predominantly on smaller scales. The data products are publicly released as part of the Ulagam simulation suite. Our initial conditions generator is publicly available at https://github.com/DhayaaAnbajagane/Aarambam.

Infrared-blocking, aerogel-based scattering filters have a broad range of potential applications in astrophysics and planetary science instruments in the far-infrared, sub-millimeter, and microwave regimes. This paper demonstrates the ability of conductively-loaded, polyimide aerogel filters to meet the mechanical and science instrument requirements for several experiments, including the Cosmology Large Angular Scale Surveyor (CLASS), the Experiment for Cryogenic Large-Aperture Intensity Mapping (EXCLAIM), and the Sub-millimeter Solar Observation Lunar Volatiles Experiment (SSOLVE). Thermal multi-physics simulations of the filters predict their performance when integrated into a cryogenic receiver. Prototype filters have survived cryogenic cycling to 4\,K with no degradation in mechanical properties. Measurement of total hemispherical reflectance and transmittance, as well as cryogenic tests of the aerogel filters in a full receiver context, allow estimates of the integrated infrared emissivity of the filters. Knowledge of the emissivity will help instrument designers incorporate the filters into future experiments in planetary science, astrophysics, and cosmology.

The alloying elements introduced into carbon steel to enhance its mechanical properties also diffuse into cementite (Fe$_3$C) particles, modifying their characteristics and thereby influencing the overall performance of the steel. This study employs density functional theory (DFT) calculations to investigate cementite doped with Ni and Cr which exhibit contrasting effects. The preferred lattice sites of impurity atoms were determined through a comparison of calculated and experimental structural parameters. The formation mechanism of the hyperfine magnetic field (HFF) and its correlation with atomic magnetic moments were systematically investigated. The validity of common approximations in Mössbauer spectroscopy analysis was evaluated for the cementite system. HFF distribution functions were modeled using calculated values and compared with experiments.

We show how entangled steady states can be prepared by purely dissipative dynamics in a system coupled to a thermal environment. While entanglement is hindered by thermalization when the system and environment exchange a conserved quantity, we demonstrate that breaking this conservation law through the system-environment interaction drives the system to a nonequilibrium steady state. Such an interaction will generate multiple competing equilibration channels, effectively mimicking baths at distinct chemical potentials. When the environment also supports long-range correlations, these channels mediate nonlocal dissipation capable of generating entanglement. We illustrate the scheme in a model of two nitrogen-vacancy (NV) centers weakly coupled to a spin-pumped magnet, where tuneable magnon excitations enable steady-state entanglement over finite distances. Our results identifies a general mechanism for dissipative entanglement generation, rooted in the conservation structure and environmental correlations rather than fine-tuned coherent control or active driving.

The stochastic-$δ\mathcal{N}$ formalism is widely used to study inflation models in which the quantum diffusion of inflatons dominates the background dynamics, leading to interesting phenomena such as the production of primordial black holes. Among numerical approaches to calculate the curvature perturbation spectrum $\mathcal{P}_ζ(k)$ in this formalism, the Monte Carlo simulation-based approach has been proposed as a promising choice, especially in multifield cases. In this approach, we generate many paths of inflatons from the initial points to the end of inflation, obtain statistics of $δN$ from the paths, and then estimate $\mathcal{P}_ζ(k)$. However, this method involves a nested Monte Carlo simulation, which requires generating many branch paths from each trunk path at the point corresponding to the scale $k$ of interest, resulting in a high computational cost. In this paper, we propose a new Monte Carlo-based approach that utilizes least squares fitting, introducing two novel features for reducing computational cost. First, we devise a simple estimator of a key statistic $\langle δ\mathcal{N}_{\mathbf{X}}^2\rangle$, the variance of $δ\mathcal{N}$ conditioned on the branching point, to avoid nesting path generation. Second, via least squares fitting of a parametric function to the sampled values of the estimator, we obtain not just an estimate of $\mathcal{P}_ζ(k)$ for a single value of $k$ but an approximating function of $\mathcal{P}_ζ(k)$ over a range of $k$ of interest. We also conduct numerical demonstrations for concrete inflation models, which show the usefulness of our method.

This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp spectral density estimates--establishing both lower and upper bounds--to demonstrate that a significant proportion of transmission eigenfunctions manifest this surface-localizing behavior. Our analysis elucidates the connection between the geometric rigidity of eigenfunctions and their spectral properties. Though primarily explored within a radially symmetric framework, this study provides rigorous theoretical insights, advances new perspectives in this emerging field, and offers meaningful implications for inverse scattering theory.

Previous pandemics, including influenza pandemics and Covid-19, have disproportionately impacted Māori and Pacific populations in Aotearoa New Zealand. The reasons for this are multi-faceted, including differences in socioeconomic deprivation, housing conditions and household size, vaccination rates, access to healthcare, and prevalence of pre-existing health conditions. Many mathematical models that were used to inform the response to the Covid-19 pandemic did not explicitly include ethnicity or other socioeconomic variables. This limited their ability to predict, understand and mitigate inequitable impacts of the pandemic. Here, we extend a model that was developed during the Covid-19 pandemic to support the public health response by stratifying the population into four ethnicity groups: Māori, Pacific, Asian and European/other. We include three ethnicity-specific components in the model: vaccination rates, clinical severity parameters, and contact patterns. We compare model results to ethnicity-specific data on Covid-19 cases, hospital admissions and deaths between 1 January 2022 and 30 June 2023, under different model scenarios in which these ethnicity-specific components are present or absent. We find that differences in vaccination rates explain only part of the observed disparities in outcomes. While no model scenario is able to fully capture the heterogeneous temporal dynamics, our results suggest that differences between ethnicities in the per-infection risk of clinical severe disease is an important factor. Our work is an important step towards models that are better able to predict inequitable impacts of future pandemic and emerging disease threats, and investigate the ability of interventions to mitigate these.

Vibrational sum- and difference-frequency generation (SFG and DFG) spectroscopy probes the nonlinear response of interfaces at mid-infrared (MIR) wavelengths while detecting upconverted signals in the visible. Recent work has moved from large-area films and colloids to nanoscale structures using dual-resonant plasmonic nanocavities that co-confine light and matter in deep-subwavelength volumes. Here we implement high-resolution ($<1$~cm$^{-1}$), continuous-wave ultrabroadband vSFG, vDFG, and four-wave mixing (FWM) coherent spectroscopy from 860 to 1670~cm$^{-1}$ on dual-resonant antennas under ambient conditions. Using a commercial, broadly tunable quantum-cascade laser and eliminating geometric phase matching simplify acquisition and expand spectral reach. The resulting spectra exhibit coherent interference between resonant (vibrational) and nonresonant (electronic) contributions to the effective $χ^{(2)}$, previously accessible only under fs/ps excitation. Simultaneous measurement of SFG and DFG enables a {ratiometric} analysis that suppresses common-mode drifts and helps reveal vibrational resonances. We demonstrate versatility and reproducibility across several analytes that span distinct relative strengths of vibrational vs. electronic nonlinearities. Together, these capabilities position our approach as a scalable route to multiplexed, high-resolution MIR sensing and a practical basis for chip-level, label-free coherent spectroscopy. It opens a feasible path toward single- and few-molecule optomechanical studies using nanoscale trapping strategies.

Tree walks are a class of closed walks on a complete graph constrained to span trees. In this work, we focus on a special subclass called $k$-tours, which were recently introduced by Gunnells and are enumerated by the hypergraph Catalan numbers $ c_n^{(k)}$. Gunnells conjectured an asymptotic formula for $c_n^{(k)}$ which we confirm through an alternative approach to their enumeration. As it turns out, the asymptotic growth is governed by the number of $k$-tours on star-like trees.

Speciation is often associated with geographical barriers that limit gene flow. However, species can also emerge in continuous homogeneous environments through isolation by distance. When the environment is not homogeneous, natural selection contributes to differentiation by local adaptation and tends to facilitate speciation. To explore how isolation by distance and adaptation combine to determine species diversity, we implemented a model regulated by these two components. The first is implemented via mating restrictions on spatial proximity and genetic similarity. The second is realized by an ecological phenotype subjected to adaptation by natural selection. We consider scenarios where the environment is either homogeneous, with a single ecological optimum, or heterogeneous with two distinct optima. We show that the interplay between selection and isolation by distance affect not only species formation but also phenotypic distributions and speed of speciation. In homogeneous environment, speciation occurs only under restrictive mating, but it takes longer if selection is weak. In contrast, in heterogeneous environments with two local optima and strong selection, species well adapted to each of the optima emerge along the spatial structure, leading to the formation of groups with distinct phenotypes. Permissive mating leads to the formation of only two species, each occupying one of the optima; restrictive mating leads to several species per optimum, in a much faster speciation process. Interestingly, when selection is weak and mating is restrictive, several species form, but the process is slow. Moreover, species average phenotypes do not remain constant over generations, causing the phenotypic distribution to oscillate, never reaching a stationary pattern.

The entanglement swapping protocol (ESP) is a fundamental primitive for distributing quantum correlations across distant nodes in a quantum network. Recent studies have demonstrated that even when the involved qubit pairs are only partially entangled, it is still possible to concentrate and transmit entanglement via Bell-basis measurements. In this work, we extend these ideas to quantum networks with various topologies--including linear, star, and hybrid configurations--by analysing the application of the ESP to initially partially entangled pure states. We investigate how entanglement evolves under such protocols by considering the transformations of the initial states and evaluating the success probabilities for generating maximally entangled states at the output. Our results offer new insights into the dynamics of the entanglement distribution in quantum networks.

The main motivation of this work is the quantitative prediction and description of particle manipulation (displacement across streamlines) in microfluidic flow. Much attention has been paid recently to placing particles in fast oscillatory flow fields, usually driven by microbubbles actuated by low-frequency ultrasound, where particle inertia leads to deterministic displacements. However, such devices invariably set up simultaneous streaming flows that are interpretable as driven Stokes flows. The potential role of these flows in not just passively transporting but likewise manipulating the particles has not been appreciated. Therefore, we investigate whether a Stokes flow by itself can meaningfully affect the displacement of a single particle or a rigid dumbbell, given the properties and symmetries of the flow. To manipulate a single particle, its hydrodynamic interaction with a nearby boundary is crucial for obtaining non-trivial results. To irreversibly displace a particle using this effect, we find that the flow symmetry must be broken in specified ways. Controlling the flow geometry, one can drive particles to fixed points, cycles, or towards boundaries, with the possibility of controlling eventual attachment (sticking) of the particle. For rigid dumbbell particles, we show that such controlled displacement in Stokes flow is possible even without the presence of nearby boundaries, but again with requirements on the broken symmetry of the chosen flow. In practical microfluidic devices, these effects could be set up in manifold ways, by themselves or in combination with inertial forces for more versatile particle manipulation.

We develop a strategy for computing the $B\to K\ell^+\ell^-$ and $\bar{B}_s\toγ\ell^+\ell^-$ decay amplitudes using lattice QCD (where $\ell^\pm$ are charged leptons). We focus on those terms which contain complex contributions to the amplitude, due to on-shell intermediate states propagating between the weak operator and electromagnetic current(s). Such terms, which are generally estimated using model calculations and represent significant uncertainties in the phenomenological predictions for these decays, cannot be computed using standard lattice QCD techniques. It has recently been shown that such contributions can be computed using spectral-density methods and our proposed strategy, which we discuss in detail, is built on this approach. The complex contributions include the ``charming penguins" (matrix elements of the current-current operators $O_1^{(c)}$ and $O_2^{(c)}$ defined in Eq. (6) below), in which the charm-quark loop can propagate long distances, particularly close to the region of charmonium resonances. They also include the contributions from the chromomagnetic operator ($O_8$ in standard notation, defined in Eq. (8) below). We discuss the renormalization of the ultra-violet divergences, and in particular those which arise due to ``contact" terms, and explain how those which appear as inverse powers of the lattice spacing can be subtracted non-perturbatively. We apply the spectral density methods in an instructive exploratory computation of the charming penguin diagram in $B\to K\ell^+\ell^-$ decays in which the virtual photon is emitted from the charm-quark loop (the diagram in Fig. 1(a) below) and discuss the prospects and strategies for the reliable determination of the amplitudes in future dedicated computations; computations which are however, beyond the scope of the present paper.

Quantum materials with bands of narrow bandwidth near the Fermi level represent a promising platform for exploring a diverse range of fascinating physical phenomena, as the high density of states within the small energy window often enables the emergence of many-body physics. On one hand, flat bands can arise from strong Coulomb interactions that localize atomic orbitals. On the other hand, quantum destructive interference can quench the electronic kinetic energy. Although both have a narrow bandwidth, the two types of flat bands should exhibit very distinct spectral properties arising from their distinctive origins. So far, the two types of flat bands have only been realized in very different material settings and chemical environments, preventing a direct comparison. Here, we report the observation of the two types of flat bands within the same material system--an above-room-temperature van der Waals ferromagnet, Fe$_{5-x}$GeTe$_2$, distinguishable by a switchable iron site order. The contrasting nature of the flat bands is also identified by the remarkably distinctive temperature-evolution of the spectral features, indicating that one arises from electron correlations in the Fe(1) site-disordered phase, while the other geometrical frustration in the Fe(1) site-ordered phase. Our results therefore provide a direct juxtaposition of the distinct formation mechanism of flat bands in quantum materials, and an avenue for understanding the distinctive roles flat bands play in the presence of magnetism, topology, and lattice geometrical frustration, utilizing sublattice ordering as a key control parameter.