The recently introduced quantum gravity-induced entanglement of masses (QGEM) protocol aims to test the quantum nature of gravity by witnessing the entanglement produced by the virtual exchange of a graviton between two spatially superposed masses. Shortly after the original proposal, further improvements upon the experiment were suggested, including the addition of a third mass, showing that three-qubit setups can be more resilient to higher rates of decoherence caused by the interaction of the system with the environment. In this work, we investigate the type of tripartite entanglement generated in these three-qubit QGEM experiments when considering the effects of decoherence. We show that the gravitational interaction between the qubits is able to generate genuine tripartite entanglement between them, studying the corresponding parameter spaces and comparing the performance of the possible experimental configurations of the three qubits at allowing for the detection of genuine entanglement via an entanglement witness.

Quantum geometry, characterized by the quantum metric and Berry curvature, is a powerful framework for understanding diverse physical phenomena in quantum materials, but its behavior in non-periodic systems remains largely uncharted. Here, we uncover a universal mechanism for the divergent enhancement of the quantum metric in one-dimensional quasiperiodic systems, governed by the interplay of wavefunction criticality and spectral fractality. Using the paradigmatic Fibonacci chain, we demonstrate that the quantum metric displays a hierarchical scaling structure that mirrors the fractal organization of the energy spectrum. A real-space renormalization-group analysis yields an analytic power-law scaling, $\mathcal{G} \propto (ΔE)^{-k}$, between the quantum metric $\mathcal{G}$ and spectral gap $ΔE$, with the exponent $k$ dictated by the system's self-similarity. This scaling persists in the critical Aubry-André-Harper model but disappears in both its localized and extended phases, confirming its universality across different quasiperiodic paradigms and its unique link to criticality. Our results show that the quantum metric provides a sensitive geometric indicator of quasiperiodic criticality, and highlight quasicrystals as promising platforms for realizing unconventional giant quantum geometric effects beyond the limits of periodic crystals.

We present a practical and effective method of planetary defense that allows for extremely short mitigation time scales if required as well as long time scale mitigation. This one system allows for virtually any required defense mode. In general, it uses much less launch mass with vastly shorter required response time than classical deflection techniques The method uses an array of small hypervelocity kinetic penetrators that pulverize and disassemble an asteroid or small comet. This approach works in both long warning time, as well as in short warning scenarios with intercepts of minutes to days before impact. In longer time intercept scenarios, the disassembled asteroid fragments largely miss the Earth. In short intercept scenarios, the asteroid fragments of maximum $\sim$10-meter diameter allow the Earth's atmosphere to act as a "beam dump" with fragment burn up and/or air burst, with the primary channel of energy going into spatially and temporally de-correlated shock waves. The effectiveness of the approach depends on the intercept time and size of the asteroid but allows for effective defense against asteroids in the 20-1000m diameter class and could virtually eliminate the threat. A 20m diameter asteroid ($\sim$0.5Mt, similar to Chelyabinsk) can be mitigated with a 100s prior to impact intercept with a 10m/s disruption. With ~1m/s internal disruption, a 5 hour prior to impact intercept of a 50m diameter asteroid ($\sim$10Mt yield, similar to Tunguska), a 1 day prior to impact intercept of 100m diameter asteroid ($\sim$100Mt yield), a 20 day prior to impact intercept of Apophis ($\sim$370m diameter, $\sim$4Gt yield). The use of active (explosive) penetrators including nuclear allows the same system to mitigate extremely large threats. A "single launcher" solution to planetary defense using existing launch vehicles that achieve positive C3 becomes a viable option.

We develop theory and examples of monoidal functors on tensor categories in positive characteristic that generalise the Frobenius functor from \cite{Os, EOf, Tann}. The latter has proved to be a powerful tool in the ongoing classification of tensor categories of moderate growth, and we demonstrate the similar potential of the generalisations. More explicitly, we describe a new construction of the generalised Verlinde categories $Ver_{p^n}$ in terms of representation categories of elementary abelian $p$-groups. This leads to families of functors relating to $Ver_{p^n}$ that we conjecture, and partially show, to exhibit the characteristic properties of the Frobenius functor relating to $Ver_p$. In particular, we conjecture some of these functors to detect categories that fibre over $Ver_{p^n}$.

We consider a class of Allen-Cahn equations associated with Ginzburg-Landau energies involving degenerate double-well potentials that vanish of order $m$ at the minima \begin{equation} J(v,Ω)=\int_Ω\Big\{|\nabla v|^{p}+(1-v^{2})^{m}\Big\}dx,\quad 1<p<m, \end{equation} and establish density estimates for the level sets of nontrivial minimizers $|v| \leq 1$. This extends a result of Dipierro-Farina-Valdinoci where the density estimates for such degenerate potentials were obtained for a bounded range of $m$'s. The original estimates for the classical case $p=m=2$ were established by Caffarelli-Córdoba.

A search for cosmological axions has been performed by scanning a frequency region of $38\,$MHz centered at about $10.2\,$GHz, corresponding to an axion mass $m_a \simeq 42\,μ$eV. The QUAX experimental apparatus, a haloscope comprised of a 1-liter volume tunable cavity immersed in an $8\,$T magnetic field and a quantum-limited detection chain, set limits on the axion-photon coupling at the $10^{-14}\,$GeV$^{-1}$ level. As no signal candidate has been observed, viable hadronic axion models are ruled out in a currently preferred post-inflationary region $m_a > 40\,μ$eV.

Mid-infrared spectroscopy enables biochemical sensing by identifying vibrational molecular fingerprints, but it faces limitations in instrumentation portability and analytical sensitivity. Optical metasurfaces with strong mid-IR photonic resonances provide an attractive solution towards on-chip spectrometry and sensitive molecular detection, yet their static nature hinders their anticipated impact. Here, we introduce and demonstrate dynamically tunable silicon membrane metasurfaces exhibiting high-Q transmissive resonances in the fingerprint region. By harnessing silicon's thermo-optical properties, we achieve continuous modulation of electromagnetically induced transparency (EIT)-like modes that emerge upon the interference of quasi-bound states in the continuum (q-BICs) and surface lattice modes. We measure a spectral tuning rate of 0.06 $cm^{-1}/K$ by continuously sweeping the sharp EIT resonances over a 23.5 $cm^{-1}$ spectral range across a temperature range of 300-700 K. This dynamic transmission control enables non-contact chemical analysis of polymer films by detecting characteristic absorption bands of polystyrene (1450 and 1492 $cm^{-1}$) and Poly(methyl methacrylate) (1730 $cm^{-1}$) without bulky spectrometers. When analyte molecules fill the metasurface-generated photonic cavities, we demonstrate vibrational strong coupling between the Poly(methyl methacrylate)'s carbonyl band and the EIT mode, manifested in the Rabi splitting of $\sim$ 43 $cm^{-1}$. Our results establish a new photonic platform that unites spectral precision, strong field enhancement, and reconfigurability, offering diverse potential for compact mid-IR spectroscopy, molecular sensing, and programmable polaritonic photonics.

In this work, we hope to expand the universe of security practitioners of open-source hardware by creating a bridge from hardware design languages (HDLs) to data science languages like Python and R through novel libraries that convert VCD (value change dump) files into data frames, the expected input type of the modern data science tools. We show how insights can be derived in high-level languages from register transfer level (RTL) trace data. Additionally, we show a promising future direction in hardware security research leveraging the parallelism of Spark to study transient execution CPU vulnerabilities, and provide reproducibility researchers via GitHub and Colab.

Addressing TedX, Amber Huffman made an impassioned case that "none of us is as smart as all of us" and that open-source hardware is the future. A major contribution to software quality, open source and otherwise, on the software side, is the systems design methodology of Continuous Integration and Delivery (CI/CD), which we propose to systematically bring to hardware designs and their specifications. To do so, we automatically generate specifications using specification mining, "a machine learning approach to discovering formal specifications" which dramatically impacted the ability of software engineers to achieve quality, verification, and security. Yet applying the same techniques to hardware is non-trivial. We present a technique for generalized, continuous integration (CI) of hardware specification designs that continually deploys (CD) a hardware specification. As a proof-of-concept, we demonstrate Myrtha, a cloud-based, specification generator based on established hardware and software quality tools.

Government transparency, widely recognized as a cornerstone of open government, depends on robust information management practices. Yet effective assessment of information management remains challenging, as existing methods fail to consider the actual working behavior of civil servants and are resource-intensive. Using a design science research approach, we present the Transparency Anti-Pattern Assessment System (TAPAS) -- a novel, data-driven methodology designed to evaluate government transparency through the identification of behavioral patterns that impede transparency. We demonstrate TAPAS's real-world applicability at a Dutch ministry, analyzing their electronic document management system data from the past two decades. We identify eight transparency anti-patterns grouped into four categories: Incomplete Documentation, Limited Accessibility, Unclear Information, and Delayed Documentation. We show that TAPAS enables continuous monitoring and provides actionable insights without requiring significant resource investments.

We consider the spectrum of the Laplace operator on 3D rod structures, with a small cross section depending on a small parameter $\varepsilon$. The boundary conditions are of Dirichlet type on the basis of this structure and Neumann on the lateral boundary. We focus on the low frequencies. We study the asymptotic behavior of the eigenvalues and associated eigenfunctions, which are approached as $\varepsilon\to 0$ by those of a 1D model with Dirichlet boundary conditions, but which takes into account the geometry of the domain. Explicit and numerical computations enlighten the interest of this study, when the parameter becomes smaller. At the same time they show that in order to capture oscillations in the transverse direction we need to deal with the high frequencies. For prism like domains, we show the different asymptotic behavior of the spectrum depending on the boundary conditions.

Hexagonal boron nitride (hBN), a two-dimensional (2D) material, garners interest for hosting bright quantum emitters at room temperature. A great variety of fabrication processes have been proposed with various yields of quantum emitters. In this work, we study the influence of several parameters, such as irradiation energy, annealing environment, and the type of hBN, on the emitter density in hBN. Our results show (i) high emitter density with oxygen irradiation at 204 eV, (ii) post-annealing in carbon-rich atmospheres significantly increases emitter density, reinforcing carbon's potential role, (iii) no significant effect of oxygen pre-annealing, and (iv) a slightly increased emitter density from hBN crystals with lower structural quality. Although the precise origin of the emitters remains unclear, our study shows that oxygen irradiation and subsequent inert annealing in a carbon-rich environment play a crucial role in emitter generation, while the other processing parameters have a smaller influence. As such, our systematic study and findings show relevant advances towards the reproducible formation of visible-frequency quantum emitters in hBN.

Accurate estimation of meal macronutrient composition is a pre-perquisite for precision nutrition, metabolic health monitoring, and glycemic management. Traditional dietary assessment methods, such as self-reported food logs or diet recalls are time-intensive and prone to inaccuracies and biases. Several existing AI-driven frameworks are data intensive. In this study, we propose MealMeter, a machine learning driven method that leverages multimodal sensor data of wearable and mobile devices. Data are collected from 12 participants to estimate macronutrient intake. Our approach integrates physiological signals (e.g., continuous glucose, heart rate variability), inertial motion data, and environmental cues to model the relationship between meal intake and metabolic responses. Using lightweight machine learning models trained on a diverse dataset of labeled meal events, MealMeter predicts the composition of carbohydrates, proteins, and fats with high accuracy. Our results demonstrate that multimodal sensing combined with machine learning significantly improves meal macronutrient estimation compared to the baselines including foundation model and achieves average mean absolute errors (MAE) and average root mean squared relative errors (RMSRE) as low as 13.2 grams and 0.37, respectively, for carbohydrates. Therefore, our developed system has the potential to automate meal tracking, enhance dietary interventions, and support personalized nutrition strategies for individuals managing metabolic disorders such as diabetes and obesity.

The Immersion GRating INfrared Spectrometer (IGRINS) is a compact, high-resolution (R~45,000) near-infrared spectrograph spanning 1.45 to 2.45 um in a single exposure. We introduce the Raw and Reduced IGRINS Spectral Archive (RRISA), which provides public data access for all non-proprietary IGRINS data taken at McDonald Observatory's Harlan J. Smith Telescope, the Lowell Discovery Telescope (formerly Discovery Channel Telescope), and Gemini South. RRISA provides access to raw files, reduced data products, and cross-matched IGRINS targets with the SIMBAD, 2MASS, Gaia DR3, APOGEE2 DR17, and PASTEL catalogs. We also introduce version 3 of the IGRINS data reduction pipeline, IGRINS PLP v3, which implements an improved cosmic ray correction, pattern noise removal, and a new flexure correction that reduces telluric residuals. RRISA and supporting information can be found at http://igrinscontact.github.io.

We call a foliation $\mathcal{F}$ on a compact manifold infinitesimally rigid if its deformation cohomology $H^{1}(\mathcal{F},N\mathcal{F})$ vanishes. This paper studies infinitesimal rigidity for a distinguished class of Riemannian foliations, namely Lie foliations with dense leaves. We construct infinitesimally rigid Lie foliations with dense leaves, modeled on any compact semisimple Lie algebra with simple ideals different from $\mathfrak{so}(3)$. To our knowledge, these are the first examples of infinitesimally rigid Riemannian foliations that are not Hausdorff.

Metasurface research has shown significant potential for controlling the polarization, amplitude, phase and propagation direction of light. Nevertheless, control over the angular response of incident light still remains a long-standing problem. In this work, we show the potential of diffractive systems for obtaining a step function in momentum space where the mirror symmetry of the angular transmittance is broken. By engineering the scattering response of an asymmetric particles in a metagrating, we could obtain such a step function in a passive, reciprocal, and lossless fashion. More specifically, the metagrating performs filtering in the momentum space with an abrupt switching from reflection to transmission for an incident electromagnetic wave with an arbitrary spatial profile. This metagrating may find diverse applications in the context of optical spatial analog computing. Moreover, it paves the way for exploring the capabilities of diffractive systems for gaining full control over the angular response of light using arbitrary momentum transfer functions.

This article is devoted to calculating the form factors of $B_c \to D^{*}$, $B_c \to D$, $B_c \to D_s^{*}$ and $B_c \to D_s$ transitions in the framework of three-point QCD sum rules. At the QCD side, the contributions of $\langle\overline{q}q\rangle$, $\langle\overline{q}g_{s}σGq\rangle$, $\langle g_{s}^{2}G^{2}\rangle$, $\langle f^{3}G^{3}\rangle$ and $\langle\overline{q}q\rangle \langle g_{s}^{2}G^{2}\rangle$ are taken into account. With the obtained form factors, the decay widths and branching ratios of several two-body nonleptonic decay processes $B_c \to η_c D^{*}$, $η_c D$, $ J/ψD^{*}$, $ J/ψD$, $η_c D_s^{*}$, $η_c D_s$, $J/ψD_s^{*}$ and $J/ψD_s$ are predicted. These results about the form factors and decay properties of $B_c$ meson provide useful information for us to study the heavy-quark dynamics.

Recently, it has been revealed that a variety of novel phenomena emerge in hyperbolic spaces, while non-Hermitian physics has significantly enriched the landscape of condensed matter physics. Building on these developments, we construct a geodesic-based method to study the non-Hermitian skin effect (NHSE) in non-reciprocal hyperbolic lattices. Additionally, we develop a geodesic-periodic boundary condition (geodesic-PBC), akin to the Euclidean periodic boundary condition (PBC), that complements its open boundary condition. Importantly, we find that the non-reciprocal directionality within a hyperbolic regular polygon and the geodesic-based boundary determine the spectral sensitivity, and hence, the NHSE. Unlike in Euclidean models, however, we must utilize boundary localization to distinguish non-trivial skin modes from their trivial boundary counterpart due to the extensive boundary volume of hyperbolic lattices. We also relate the spatial density profile with the finite-size scaling of hyperbolic lattices. These aspects highlight the profound impact of hyperbolic geometry on non-Hermitian systems and offer new perspectives on the intricate relationship between the geometric characteristics of hyperbolic lattices and non-Hermitian physics.

Quantifying the entanglement generation of a multipartite unitary operation is a key problem in quantum information processing. We introduce the definition of multipartite entangling, assisted entangling, and disentangling power, which is a natural generalization of the bipartite ones. We show that they are assumed at a specified quantum state. We analytically derive the entangling power of Schmidt-rank-two multi-qubit unitary operations by the minimal convex sum of modulo-one complex numbers. Besides we show the necessary and sufficient condition that the assisted entangling power of Schmidt-rank-two unitary operations reaches the maximum. We further investigate the widely-used multi-qubit gates, for example, the entangling and assisted entangling power of the $n$-qubit Toffoli gate is one ebit. The entangling power of the three-qubit Fredkin gate is two ebits, and that of the four-qubit Fredkin gate is in two to $\log_25$ ebits.

Quantum processors based on integrated nanoscale silicon spin qubits are a promising platform for highly scalable quantum computation. Current CMOS spin qubit processors consist of dense gate arrays to define the quantum dots, making them susceptible to crosstalk from capacitive coupling between a dot and its neighbouring gates. Small but sizeable spin-orbit interactions can transfer this electrostatic crosstalk to the spin g-factors, creating a dependence of the Larmor frequency on the electric field created by gate electrodes positioned even tens of nanometers apart. By studying the Stark shift from tens of spin qubits measured in nine different CMOS devices, we developed a theoretical frawework that explains how electric fields couple to the spin of the electrons in increasingly complex arrays, including those electric fluctuations that limit qubit dephasing times $T_2^*$. The results will aid in the design of robust strategies to scale CMOS quantum technology.

Aims. We aim to study chemically peculiar Am and Fm stars, distinguished by their unique abundance patterns, which are crucial for studying mixing processes in intermediate-mass stars. These stars provide a window into the atomic diffusion in their stellar envelopes, the evolution-dependent changes in mixing, and the resulting effects on pulsation mechanisms. Methods. This study examines the pulsation characteristics of the Am/Fm star group. Our analysis encompasses 1276 stars (available as catalogues on GitHub), utilising data from TESS and Gaia and focusing on stars from the Renson catalogue. Results. In our sample, 51% (649 stars) display no variability, thus categorised as constant stars. Among the remaining, 25% (318 stars) are pulsating Am/Fm and ρ Puppis stars, including 20% (261 stars) that are exclusively Am/Fm stars. Additionally, 17% (210 stars) show variability indicative of binarity and/or rotational modulation and 7% (93 stars) are eclipsing binaries. Of the pulsating stars, 10% (32 stars) are γ Doradus type, 54% (172 stars) δ Scuti type, and 36% (114 stars) are hybrids, underlining a diverse pulsational behaviour of Am/Fm stars. Conclusions. Our findings indicate that pulsating stars predominantly occupy positions near the red edge of the classical instability strip, allowing us to ascertain the incidence of pulsations in this stellar population.

Charge diffusion through desoxyribonucleic acid (DNA) is a physico-chemical phenomenon that on the one hand is being explored for technological purposes, on the other hand is applied by nature for various informational processes in life. With regard to the latter, increasing experimental and theoretical evidence indicates that charge diffusion through DNA is involved in basic steps of DNA replication and repair, as well as regulation of gene expression via epigenetic mechanisms such as DNA methylation or DNA binding of proteins. From the physics point of view, DNA supports a metallic-like behavior with long-range charge mobility. Nevertheless, particularly considering a living environment, charge mobility in DNA needs to take into account omnipresent noise and disorder. Here, we analyze quantum diffusion of single charges along DNA-inspired two-dimensional tight-binding lattices in presence of different sources of intrinsic and environmental fluctuations. It is shown that double-strand lattices, parametrized according to atomistic calculations of DNA sequences, offer a complex network of pathways between sites and may give rise to long-distance coherence phenomena. These effects strongly depend on carrier type (electrons, holes), the energetic profile of the lattice (composition) as well as the type of noise and disorder. Of particular interest are spatially correlated low-frequency fluctuations which may support coherent charge transfer over distances of a few sites. Our results may trigger further experimental activities aiming at investigating charge mobility in DNA both in the native in-vivo context as well as on artificial platforms.

This review paper examines state-of-the-art algorithms and techniques in quantum machine learning with potential applications in finance. We discuss QML techniques in supervised learning tasks, such as Quantum Variational Classifiers, Quantum Kernel Estimation, and Quantum Neural Networks (QNNs), along with quantum generative AI techniques like Quantum Transformers and Quantum Graph Neural Networks (QGNNs). The financial applications considered include risk management, credit scoring, fraud detection, and stock price prediction. We also provide an overview of the challenges, potential, and limitations of QML, both in these specific areas and more broadly across the field. We hope that this can serve as a quick guide for data scientists, professionals in the financial sector, and enthusiasts in this area to understand why quantum computing and QML in particular could be interesting to explore in their field of expertise.

Quantum states in complex aggregates are unavoidably affected by environmental effects, which typically cannot be accurately modeled by simple Markovian processes. As system sizes scale up, nonperturbative simulation become thus unavoidable but they are extremely challenging due to the intimate interplay of intrinsic many-body interaction and time-retarded feedback from environmental degrees of freedom. In this work, we utilize the recently developed Quantum Dissipation with Minimally Extended State Space (QD-MESS) approach to address reservoir induced long-ranged temporal correlations in finite size Ising-type spin chains. For thermal reservoirs with ohmic and subohmic spectral density we simulate the quantum time evolution from finite to zero temperature. The competition between thermal fluctuations, quantum fluctuations, and anti-/ferromagnetic interactions reveal a rich pattern of dynamical phases including dissipative induced phase transitions and spatiotemporal correlations.

In the search for axionic Dark Matter, the high frequency part of the QCD axion parameter space is favored, as indicated by both cosmological and astrophysical arguments and recent indications from lattice QCD calculations. To extend the probing range of cavity haloscopes, solutions addressing the unfavorable scaling of cavity volume with frequency must be developed. Here, we present a novel type of high-volume thin shell resonator for high frequency haloscope dark matter searches. The cavity is formed by two nested and coaxial right angle polygonal prisms enclosed within two flat endcaps. For the axion-sensitive (pseudo-)TM010 mode, finite element simulations yield form factor of the order of 0.8 and Q factor of the order of 60000 for a copper cavity at 4$\,$K. High tunability of up to $\sim 5\%$ is achieved by reciprocal rotation of the two prisms, without significant changes in haloscope sensitivity. A prototype aluminium hexagonal cavity was built and tested, confirming the main characteristics of the design.

The study delves into 425 industrial incidents documented on Kaggle [1], all of which occurred in 12 separate plants in the South American region. By meticulously examining this extensive dataset, we aim to uncover valuable insights into the occurrence of accidents, identify recurring trends, and illuminate underlying causes. The implications of this analysis extend beyond mere statistical observation, offering organizations an opportunity to enhance safety and health management practices. Our findings underscore the importance of addressing specific areas for improvement, empowering organizations to fortify safety measures, mitigate risks, and cultivate a secure working environment. We advocate for strategically applying statistical analysis and data visualization techniques to leverage this wealth of information effectively. This approach facilitates the extraction of meaningful insights and empowers decision-makers to implement targeted improvements, fostering a preventive mindset, and promoting a safety culture within organizations. This research is a crucial resource for organizations committed to transforming data into actionable strategies for accident prevention and creating a safer workplace.

Given a monoidal adjunction, we show that the right adjoint induces a braided lax monoidal functor between the corresponding Drinfeld centers provided that certain natural transformations, called projection formula morphisms, are invertible. We investigate these induced functors on Drinfeld centers in more detail for the monoidal adjunction of restriction and (co-)induction along morphisms of Hopf algebras. The resulting functors are applied to examples related to affine algebraic groups, quantum groups at roots of unity, and Radford--Majid biproducts of Hopf algebras. Moreover, we use the projection formula morphisms to prove a characterization theorem for monoidal Kleisli adjunctions and a crude monoidal monadicity theorem. The functor on Drinfeld centers induced by the Eilenberg--Moore adjunction is given in terms of local modules over commutative central monoids.

Quantum state discrimination depicts the general progress of extracting classical information from quantum systems. We show that quantum state discrimination can be realized in a device-independent scenario using tools of self-testing results. That is, the states can be discriminated credibly with the untrusted experiment devices by the correspondence between quantum correlations and states. In detail, we show that two arbitrary states can be discriminated in a device-independent manner when they are not conjugate with each other, while other states can be discriminated measurement-device-independently. To fulfill the device-independent requirement, the measurements are restricted on Pauli observables. The influence of this restriction is acceptable based on the guessing probability analysis for minimum error discrimination.

A traveling wave parametric amplifier has been integrated in the haloscope of the QUAX experiment. A search for dark matter axions has been performed with a high Q dielectric cavity immersed in a 8 T magnetic field and read by a detection chain having a system noise temperature of about 2.1 K at the frequency of 10.353 GHz. Scanning has been conducted by varying the cavity frequency using sapphire rods immersed into the cavity. At multiple operating frequencies, the sensitivity of the instrument was at the level of viable axion models.

This note reports some advances in the Equivariant Minimal Model Program (EMMP) for non-isomorphic surjective endomorphisms and their applications in complex and arithmetic dynamics.