Disconnections, long recognized as the key mediators of grain boundary (GB) kinetics in polycrystalline materials, have traditionally been understood to nucleate through thermal or mechanical activation. In this work, using atomistic simulations, we reveal a distinct nucleation mechanism driven exclusively by solute interstitial segregation across multiple substitutional binary alloy systems (e.g., Al-Ni, Al-Fe). This process exhibits zero-nucleation energy barriers, contrasting sharply with the nucleation mechanisms in pure systems. We identify states that are activated through segregation-induced GB phase transitions: (i) isolated disconnections or phase junctions that promote GB migration and disappear with continuous segregation, and (ii) composite disconnections that are formed via two oppositely oriented isolated disconnections. The disconnections are mechanically robust, suppressing shear-coupled migration and instead resulting in GB amorphization and pure sliding under applied shear loading. The long-range stress fields associated with these composite disconnections further attract solute atoms and assist the nucleation of precipitates. These disconnections, absent in pure materials, follow unique nucleation pathways as confirmed through dichromatic pattern analysis and persist across different alloy chemistries and crystal structures. Our findings demonstrate that solute interstitial segregation provides a powerful and previously unrecognized pathway for barrier-free disconnection formation, thereby fundamentally extending current understanding of GB kinetics in alloy systems.

Machine learning interatomic potentials trained on first-principles reference data are becoming valuable tools for computational physics, biology, and chemistry. Equivariant message-passing neural networks, including transformers, achieve state-of-the-art accuracy but rely on cutoff-based graphs, limiting their ability to capture long-range effects such as electrostatics or dispersion, as well as electron delocalization. While long-range correction schemes based on inverse power laws of interatomic distances have been proposed, they are unable to communicate higher-order geometric information and are thus limited in applicability. To address this shortcoming, we propose the use of equivariant, rather than scalar, charges for long-range interactions, and design a graph neural network architecture, LOREM, around this long-range message passing mechanism. We consider several datasets specifically designed to highlight non-local physical effects, and compare short-range message passing with different receptive fields to invariant and equivariant long-range message passing. Even though most approaches work for careful dataset-specific choices of their model hyperparameters, LOREM works consistently without such changes, with excellent benchmark performance.

The modeling of genomic sequences presents unique challenges due to their length and structural complexity. Traditional sequence models struggle to capture long-range dependencies and biological features inherent in DNA. In this work, we propose TrinityDNA, a novel DNA foundational model designed to address these challenges. The model integrates biologically informed components, including Groove Fusion for capturing DNA's structural features and Gated Reverse Complement (GRC) to handle the inherent symmetry of DNA sequences. Additionally, we introduce a multi-scale attention mechanism that allows the model to attend to varying levels of sequence dependencies, and an evolutionary training strategy that progressively adapts the model to both prokaryotic and eukaryotic genomes. TrinityDNA provides a more accurate and efficient approach to genomic sequence modeling, offering significant improvements in gene function prediction, regulatory mechanism discovery, and other genomics applications. Our model bridges the gap between machine learning techniques and biological insights, paving the way for more effective analysis of genomic data. Additionally, we introduced a new DNA long-sequence CDS annotation benchmark to make evaluations more comprehensive and oriented toward practical applications.

In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of $p$-adic Galois representations attached to elliptic curves over $\mathbb{Q}$. Currently, the classification is only complete for $p \in \{2,3,13,17\}$. The main difficulty for other primes arises from the need to understand elliptic curves whose mod-$p^n$ Galois representations are contained in the normaliser of a non-split Cartan subgroup. Equivalently, this amounts to determining the rational points on the modular curves $X_{ns}^+(p^n)$. Here, we consider the case $p=7$ and show that the modular curve $X_{ns}^+(49)$, of genus 69, has no non-CM rational points. To achieve this, we establish a correspondence between the rational points on $X_{ns}^+(49)$ and the primitive integer solutions of the generalised Fermat equation $a^2 + 28b^3 = 27 c^7$, the resolution of which can be reduced to determining the rational points of several genus-three curves. Furthermore, we reduce the complete classification of $7$-adic images to the determination of the rational points of a single plane quartic.

Spin shuttling offers a promising approach for developing scalable silicon-based quantum processors by addressing the connectivity limitations of quantum dots. In this work, we demonstrate high-fidelity bucket-brigade spin shuttling in a silicon MOS device, utilizing Pauli-spin-blockade readout. We achieve an average shuttling fidelity of \SI{99.8}{\percent}. The residual shuttling error is highly sensitive to the ratio between interdot tunnel coupling and Zeeman splitting, with tuning of these parameters enabling up to a 20-fold variation in error rate. An appropriate four-level Hamiltonian model supports our findings. These results provide valuable insights for optimizing high-performance spin-shuttling systems in future quantum architectures.

We study bitstring measurements from the publicly available Aquila Rydberg-atom platform using a two-leg ladder that encodes a truncated lattice gauge model as a practical benchmark that can be directly implemented and simulated on current hardware. Our goal is diagnostic: we analyze how errors propagate into bitstring probability distributions and downstream information measures, focusing on ladders with 6, 8, and 10 rungs and $\mathcal{O}(10^3)$ shots. We introduce cumulative probability distributions as a compact way to compare Aquila data with high-accuracy density matrix renormalization group (DMRG) and exact references, and we use optimally filtered mutual information primarily as a robust device-data diagnostic rather than a direct entanglement estimator. By isolating finite sampling, sorting fidelity, adiabatic ramp-up, Rabi-frequency ramp-down, and readout errors, we find that readout mitigation performs well in controlled DMRG tests. Applying the same procedure on hardware shows accuracy limitations for the leading probabilities estimation, indicating that readout errors are not dominant and that residual error is instead driven by imperfect state preparation.

Many economic parameters are identified by ``thin sets'' (submanifolds with Lebesgue measure zero) and hence difficult to recover from data in an ambient space. This paper provides a unified theory for estimation and inference of such ``thin-set'' identified functionals. We show that thin sets are \emph{not} equally thin: their intrinsic dimensionality $m$ matters in a precise manner. For a nonparametric regression $h_0$ with Hölder smoothness $s$ and $d$-dimensional covariates in the ambient space, we show that $n^{-\frac{s}{2s+d-m}}$ is the minimax optimal rate of estimating linear and nonlinear (e.g., quadratic, upper contour) integrals of $h_0$ on an $m$-dimensional submanifold ($0\leq m < d$), which is the fastest possible attainable rate among all estimators. The minimax lower bound rate result is generalized to estimating submanifold integrals when $h_0$ is a nonparametric density and a nonparametric instrumental variable function. The asymptotic normality of t statistics is established via sieve Riesz representation, and the corresponding inference is computed using Sobol points.

Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It requires a formalism allowing \ creation and destruction of particles. This gets proper treatment only in a framework called quantum field theory. This article is a semi-historic account of the intriguing new features which emerge as a part of quantum field theory. Such a discussion is impossible without a basic presentation of the formalism itself. Hence some mathematics is included in finer print. The article is directed mostly to those familiar with essential classical mechanics and basic quantum mechanics, though I strive to provide a flavour of the subject to the keenly interested non-physics reader.

We considered a planar Josephson junction which is composed of two s-wave superconducting contacts deposited on the top of a thin antiferromagnetic (AFM) disordered metal film. In such a system noticeable Josephson currents may be observed, if contacts are just nanometers away from each other. It is shown that the excitation of AFM by magnons results in a strong enhancement of the stationary current through much longer junctions, whose length may be comparable to the coherence length of superconducting correlations in a nonmagnetic metal. Such a current is calculated at the weak tunneling amplitude of electrons between superconducting contacts and AFM. The problem is considered for nonequilibrium Green functions in the second-order perturbation theory with respect to the electron-magnon interaction. A spin-orbit torque oscillator was taken as a possible source of long-wavelength classic magnetic waves. This work predicts a strong effect of magnons on superconducting proximity effect in AFM, with promising applications in superconducting spintronics.

We study the Bergman determinantal point process from a theoretical point of view motivated by its simulation. We construct restricted and restricted-truncated variants of the Bergman kernel and show optimal transport inequalities involving the Kantorovitch-Rubinstein Wasserstein distance to show to what extent it is fair to truncate the restriction of this point process to a compact ball of radius $1 - \varepsilon $. We also investigate the deviation of the number of points of the restricted Bergman determinantal point process, indicate which number of points looks like an optimal choice, and provide upper bounds on its deviation, providing an answer to an open question asked in [5]. We also consider restrictions to other regions and investigate the choice of such regions for restriction. Finally, we provide general results as to the deviation of the number of points of any determinantal point process.

Strong coupling in the conventional sense requires that the Rabi cycling process between two interacting states is faster than other dissipation rates. Some recent experimental findings show intriguing properties that were attributed to polaritonic states (e.g., plexcitons) even though the above criterion is not satisfied. Here, we theoretically predict and provide experimental evidence of polariton-like behavior in a system that does not show Rabi splitting. The photoluminescence of an exciton-cavity system consisting of a two-dimensional exciton monolayer (tungsten disulfide, WS2) coupled to a planar, open, one-mirror optical cavity configuration is studied. We experimentally observed a transition from the weak coupling regime crossing an exceptional point to form polariton-like states by varying the coupling strength and the cavity loss. Our observations are fully in agreement with a theoretical quasi-normal mode analysis, which predicts this transition and confirms the presence of exceptional points in the system. These results provide evidence that polaritonic effects can be experimentally observed even when the conventional strong coupling condition is not satisfied.

The clockwork framework can realize TeV-scale $U(1)_{PQ}$ symmetry breaking while generating a large axion decay constant \(f_a\). We propose a minimal clockwork axion model with three scalar fields, in which two domain walls (DWs) have non-zero tension. The DW associated with one of the fields is formed following the Peccei-Quinn (PQ) symmetry breaking and subsequently collapses due to the potential bias induced by the QCD instanton. The nano-hertz stochastic gravitational waves (GWs) generated from this DW annihilation can be probed by Pulsar Timing Arrays experiments. In addition, the DW related to the other field is annihilated by a bias potential originating from higher-dimensional operators, producing a significant GW signal with a peak frequency around \(9.41\times10^{-5}\) Hz, which can be detected by the LISA, Taiji, and TianQin experiments. Constraints on the model from SN1987, dark matter overproduction, Big Bang Nucleosynthesis, cosmic microwave background, and primordial black holes have been considered. The relic density of QCD axion dark matter can be explained through the misalignment mechanism.

We analytically and numerically investigate an Aharonov-Bohm interferometer with two superconducting terminals and a strongly correlated quantum dot in one arm. Through a rigorous derivation, we prove that this double-path interferometer is spectrally equivalent to a simpler system: an interacting quantum dot coupled to a non-interacting side-coupled proximitized mode and a semiconductor lead. This equivalence reveals a simple interpretation of the interferometer's behavior through the competition of a geometric factor $χ$, a key parameter characterizing the anomalous part of the hybridization function, with the properties of the side-coupled mode. We identify the conditions for the formation of doublet chimney in the phase diagrams in more general setting. Moreover, we show how the obtained Andreev bound state spectra clearly indicate the presence of Josephson diode effect generated by interferometric phenomena.

Electronically-driven nematic order breaks the rotational symmetry of a system, e.g., through a Pomeranchuk instability of the Fermi surface, with a concomitant distortion of the lattice. As a result, in a metal, the nematic collective mode interacts with two different sets of gapless excitations: the particle-hole excitations of the metal and the lattice fluctuations that become soft at the induced structural transition, namely, the transverse acoustic phonons. However, the \textit{dynamics} of these hybridized collective modes formed by the transverse acoustic phonons and the metallic electronic-nematic fluctuations has remained largely unexplored. Here we address this problem by developing a formalism in which the nemato-elastic coupling is obtained microscopically from the direct coupling between electrons and transverse acoustic phonons enabled by impurities present in the crystal. We then demonstrate the emergence of hybrid nemato-elastic modes that mix the characteristics of the transverse phonons and of the nematic fluctuations. Near the nematic quantum critical point in a metal, two massless modes emerge with intertwined dynamic behaviors, implying that neither mode dominates the response of the system. We systematically study the non-trivial dependence of these collective modes on the longitudinal and transverse momenta, revealing a rich landscape of underdamped and overdamped modes as the proximity to the quantum critical point and the strength of the electron-phonon coupling are changed. Since dynamics play an important role for determining superconducting instabilities, our results have implications for the study of pairing mediated by electronic nematic fluctuations.

We introduce magic-augmented Clifford circuits -- architectures in which Clifford circuits are preceded and/or followed by constant-depth circuits of non-Clifford (``magic") gates -- as a resource-efficient way to realize approximate $k$-designs, with reduced circuit depth and usage of magic. We prove that shallow Clifford circuits, when augmented with constant-depth circuits of magic gates, can generate approximate unitary and state $k$-designs with $ε$ relative error. The total circuit depth for these constructions on $N$ qubits is $O(\log (N/ε)) +2^{O(k\log k)}$ in one dimension and $O(\log\log(N/ε))+2^{O(k\log k)}$ in all-to-all circuits using ancillas, which improves upon previous results for small $k \geq 4$. Furthermore, our construction of relative-error state $k$-designs only involves states with strictly local magic. The required number of magic gates is parametrically reduced when considering $k$-designs with bounded additive error. As an example, we show that shallow Clifford circuits followed by $O(k^2)$ single-qubit magic gates, independent of system size, can generate an additive-error state $k$-design. We develop a classical statistical mechanics description of our random circuit architectures, which provides a quantitative understanding of the required depth and number of magic gates for additive-error state $k$-designs. We also prove no-go theorems for various architectures to generate designs with bounded relative error.

We present an experimental protocol for the fabrication and characterization of scalable microarchitected elastic waveguides. Using silicon microfabrication techniques, we develop free-standing 2D truss-based architected waveguides with a maximum diameter of 80 mm, unit cells size of 100 micrometer, and minimum beam width of 5 micrometer, thus achieving scale separation. To characterize elastic wave propagation, we introduce a custom-built scanning optical pump-probe experiment that enables contactless excitation of elastic wave modes and full spatio-temporal reconstruction of wave propagation across hundreds of unit cells with sub-unit cell resolution. Results on periodic architectures show excellent agreement with finite element simulations and equivalent experimental data at larger length scales. Motivated by scalable computational inverse design, we fabricate a specific example of a spatially graded waveguide and demonstrate its ability to guide elastic waves along an arbitrary pre-designed path.

Gravitational lensing serves as a powerful probe of compact astrophysical objects and dark matter distributions. As relativistic counterparts to photons, neutrinos experiencing lensing offer a complementary means to investigate the properties of curved spacetimes. This paper studies neutrino oscillations within the spacetime geometry described by the Hu-Sawicki f(R) gravity model, focusing on the modifications induced by gravitational lensing. We calculate the oscillation phases for both radial and non-radial neutrino propagation and derive the corresponding flavor transition probabilities for 2-flavor and 3-flavor scenarios under the weak-field approximation. Our analysis demonstrates that the lensing-affected oscillation probabilities exhibit a clear dependence on the Hu-Sawicki model parameter $λ$ , the neutrino mass hierarchy, and the absolute value of the lightest neutrino mass. Furthermore, extending the analysis beyond the weak-field regime reveals that strong-field gravitational lensing amplifies these effects. These results suggest that measurements of lensed neutrino signals could provide a novel avenue for testing modified gravity models and constraining fundamental neutrino parameters.

The phenomenon of quantum many-body scars (QMBS) has been studied both theoretically and experimentally, due to its unusual violation of the eigenstate thermalization hypothesis (ETH). In this paper, we extend the ETH to a new description based on the grand canonical ensemble to depict the thermal properties of QMBS models. For this purpose, we embed the dynamics of kinetically constrained systems within the Lindblad-like master equation, and demonstrate that the violation of the ETH by scar eigenstates is related to their slow decay in the corresponding dissipative process. Within this open system description, we reformulate the ETH to demonstrate that both scar eigenstates and thermal ones exhibit thermalization governed by grand canonical statistics. Consequently, our revised ETH unifies scars and thermal states under a cohesive thermodynamic rule. Our work resolves the fundamental tension between constraint-induced non-ergodicity and thermalization paradigms, establishing a unified route to generalized thermalization for quantum many-body systems.

The main result of this paper is an explicit description of the stratification of the phase space of Calogero--Moser--Sutherland (CMS) integrable systems corresponding to Lie groups $SU(n)$. The phase space decomposes into symplectic strata of dimensions $2s$, where $s = 0, 1, \ldots, n - 1$. On each stratum of the positive dimension, we construct natural action-angle coordinates and compute the symplectic form explicitly, showing that every stratum is symplectomorphic to $\mathbb{R}_{> 0}^s \times \mathbb{T}^s$. The zero-dimensional stratum corresponds to the equilibrium point of the multi-time CMS dynamics.

We have assessed accuracy of estimates of Earth orientation parameters (EOP) determined from several very long baseline interferometry (VLBI) observing programs that ran concurrently at different networks. We consider that the root mean square of differences in EOP estimates derived from concurrent observations is a reliable measure of accuracy. We confirmed that formal errors based on the assumption that the noise in observables is uncorrelated have a limited use. We found no evidence that advanced scheduling strategies with special considerations regarding the ability to better solve for atmospheric path in zenith direction applied for 1-hr single-baseline sessions have any measurable impact on the accuracy of EOP estimates. From this, we conclude that there is a certain limit in our ability to solve for the atmospheric path delay using microwave observations themselves and a scheduling strategy is not the factor that impairs accuracy of EOP determination. We determined that EOP errors vary with season, being smaller in winter and greater in summer. We got the quantitative estimate of the impact of unmodeled source structure on EOP estimates and we found that the seasonal extra variance is one order of magnitude greater than the impact of source structure. We have established that the EOP errors are scaled with an increase in duration of an observing session as a broken power law with the power of -0.3 at durations longer than 2-4 hours, which we explain as a manifestation of the presence of correlations in the atmospheric noise.

For many fundamental physics applications, transformers, as the state of the art in learning complex correlations, benefit from pretraining on quasi-out-of-domain data. The obvious question is whether we can exploit Large Language Models, requiring proper out-of-domain transfer learning. We show how the Qwen2.5 LLM can be used to analyze and generate SKA data, specifically 3D maps of the cosmological large-scale structure for a large part of the observable Universe. We combine the LLM with connector networks and show, for cosmological parameter regression and lightcone generation, that this Lightcone LLM (L3M) with Qwen2.5 weights outperforms standard initialization and compares favorably with dedicated networks of matching size.

We study light-hadron production in Au+Au collisions at $\sqrt{s_{NN}} = 7.7-39$ GeV using an extended Integrated HydroKinetic Model (iHKMe). Focusing on transverse momentum spectra, we investigate the sensitivity to key model parameters, particularly the thermalization timescale. We consider two distinct equations of state: one featuring a crossover and the other a first-order phase transition. In both cases, thermalization begins shortly before full nuclear overlap and lasts approximately 1~fm/$c$ across all energies. Both equations of state provide a similarly good description of the soft particle momentum spectra once the other parameters are slightly adjusted. The most pronounced differences arise at the lower RHIC BES energy of $\sqrt{s_{NN}} = 7.7$~GeV, particularly in proton and kaon yields, reflecting their sensitivity to the freeze-out parameters.

Trying to export ab initio polaritonic chemistry onto emerging quantum computers raises fundamental questions. A central one is how to efficiently represent both fermionic and bosonic degrees of freedom on the same platform, in order to develop computational strategies that can accurately capture strong electron-photon correlations at a reasonable cost for implementation on near-term hardware. Given the hybrid fermion-boson nature of polaritonic problem, one may legitimately ask: should we rely exclusively on conventional qubit-based platforms, or consider alternative computational paradigms? To explore this, we investigate in this work three strategies: qubit-based, qudit-based, and hybrid qubit-qumode approaches. For each platform, we design compact, physically motivated quantum circuit ansätze and integrate them within the state-averaged variational quantum eigensolver to compute multiple polaritonic eigenstates simultaneously. A key element of our approach is the development of compact electron-photon entangling circuits, tailored to the native capabilities and limitations of each hardware architecture. We benchmark all three strategies on a cavity-embedded H$_{2}$ molecule, reproducing characteristic phenomena such as light-induced avoided crossings. Our results show that each platform achieves comparable accuracy in predicting polaritonic eigen-energies and eigenstates. However, with respect to quantum resources required the hybrid qubit-qumode approach offers the most favorable tradeoff between resource efficiency and accuracy, followed closely by the qudit-based method. Both of which outperform the conventional qubit-based strategy. Our work presents a hardware-conscious comparison of quantum encoding strategies for polaritonic systems and highlights the potential of higher-dimensional quantum platforms to simulate complex light-matter systems.

The Einstein Telescope (ET), a planned third-generation gravitational-wave (GW) observatory, will offer significantly improved sensitivity, introducing new challenges for data analysis and computing. To prepare for these demands, the ET community has initiated a series of Mock Data Challenges (MDCs) aimed at developing and testing analysis pipelines under realistic conditions. This paper presents the first ET MDC, providing an overview of the simulated dataset and the properties of the injected GW signals, with a focus on populations of compact binary coalescences and Gaussian noise. A tutorial is also included to guide users in accessing the data and performing basic analyses. This initial challenge establishes a baseline for future MDCs and supports collaborative efforts toward the successful scientific operation of the ET.

The Bisognano-Wichmann and Haag duality properties for algebraic quantum field theories are often studied using the powerful tools of Tomita-Takesaki modular theory for nets of operator algebras. In this article, we study analogous properties of nets of algebras generated by smeared Wightman fields, for potentially non-unitary theories. In light of recent work constructing Wightman field theories for (non-unitary) Möbius vertex algebras, we obtain a broadly applicable non-unitary version of the Bisognano-Wichmann property. In this setting we do not have access to the traditional tools of Hilbert space functional analysis, like functional calculus. Instead, results analogous to those of Tomita-Takesaki theory are derived `by hand' from the Wightman axioms. As an application, we demonstrate Haag duality for nets of smeared Wightman fields.

Quantum universal invariants of general N-beam Gaussian fields are investigated from the point of view of fields' intensity moments. A method that uniquely links these invariants, including the global and marginal fields' purities, to intensity moments is suggested. Determination of these invariants identifies the Gaussian states including their quantum correlations. In particular, the Peres-Horodecki separability criterion is reformulated in terms of quantum universal invariants, and consequently in terms of experimental intensity moments, offering a practical tool for determining the entanglement or separability of these states. The approach is experimentally demonstrated by determining the invariants of noisy symmetric 3-beam Gaussian states using photon-number-resolved measurements. Furthermore, their entanglement properties are analyzed and characterized.

We investigate the asymptotic symmetry structure of two--dimensional dilaton gravity in its $\mathcal{N}=1$ supersymmetric extension based on the $\mathfrak{osp}(1|2)$ Lie superalgebra. Within the BF theoretical framework, we analyze affine and superconformal boundary conditions and systematically derive the corresponding asymptotic symmetry algebra(ASA). While the bosonic theory reproduces the Virasoro algebra and its affine enhancement, the supersymmetric extension yields a classical $\mathcal{N}=1$ superconformal algebra whose realization is dynamically restricted by the dilaton supermultiplet. We show that the boundary behavior of the dilaton induces a controlled dynamical reduction of the full affine $\mathfrak{osp}(1|2)_k$ symmetry to its $\tt{O}\tt{S}p(1|2)$ stabilizer subalgebra, while simultaneously generating an abelian ideal composed of mutually commuting modes. This establishes a coherent interplay between asymptotic symmetry breaking and symmetry extension in low--dimensional supergravity.Our construction generalizes previous analyses of $\mathfrak{sl}(2,\mathbb{R})$ dilaton gravity to the supersymmetric setting and provides a consistent bulk--based framework for investigating boundary dynamics beyond the Schwarzian regime.

This article focuses on the occurrence of 3-point configurations in subsets of $\mathbb{R}^d$ of sufficient thickness. We prove that a compact set $A\subset \mathbb{R}^d$ contains a similar copy of any linear $3$-point configuration (such as a $3$-point arithmetic progression) provided $A$ satisfies a mild Yavicoli-thickness condition and an $r$-uniformity condition for $d\geq 2$; or, when $d=1$, the result holds provided the Newhouse thickness of $A$ is at least $1$. Moreover, we prove that compact sets $A\subset \mathbb{R}^2$ contain the vertices of an equilateral triangle (and more generally, the vertices of a similar copy of any given triangle) provided $A$ satisfies a mild Yavicoli-thickness condition and an $r$-uniformity condition. Further, $C\times C$ contains the vertices of an equilateral triangle (and more generally the vertices of a similar copy of any given 3-point configuration) provided the Newhouse thickness of $C$ is at least $1$. These are among the first results in the literature to give explicit criteria for the occurrence of 3-point configurations in the plane.These are among the first results in the literature to give explicit criteria for the occurrence of three-point configurations in the plane.

With technological advancements, the quantity and quality of animal movement data have increased greatly. Currently, no movement model can be used to describe full-year data from migratory species by leveraging both individual movement and species distribution data. Herein we propose a full-year stochastic differential equation model for jointly modeling both individual movement and species distribution data. We show that this joint model, under certain assumptions, results in efficient computation of the spatio-temporal dynamics of the entire population, and thus provides straightforward inference on the species distribution data. We illustrate this model by analyzing 215 bird-years of golden eagle movement in western North America jointly with relative abundance data from eBird. We use the results to estimate wind project risk for these eagles and predict where they came from earlier in the year based on a single telemetry observation from later in the year. Our joint model enables additional inference and greater predictive power than afforded by sole use of eBird relative abundance.

Analyzing and modeling the mobility process with tour behavior is fundamental to understanding a wide range of complex systems, including animal foraging, human mobility and freight transportation. However, despite their importance, the distribution of tour length has long been neglected in individual human mobility models. To fill this gap, we analyze Foursquare users' check-in data and find that the distribution of urban tour length follows a truncated power-law distribution. To reproduce the universal scaling law for human mobility in urban areas, we introduce a tour terminate-continue model. Our model reproduces not only the urban tour length distribution but also Heaps' law, Zipf's lawand the distribution of the radius of gyration, providing a new perspective for characterizing individual human mobility.