Mobile spin qubit architectures promise flexible connectivity for efficient quantum error correction and relaxed device layout constraints, but their viability rests on preserving spin coherence during transport. While shuttling transforms spatial disorder into time-dependent noise, its net impact on spin coherence remains an open question. Here we demonstrate systematic noise mitigation during spin shuttling in a linear $^{28}$Si/SiGe quantum dot device. First, by passively reducing magnetic field gradients, we minimize charge-noise coupling to the spin and double the spatially averaged dephasing time $T_2^*(x_n)$ from $4.4$ to $8.5\,μ\text{s}$. Next, we exploit motional narrowing by periodically shuttling the qubit, achieving a further enhancement in coherence time up to $T_{2}^{*,sh} = 11.5\,μ\text{s}$. Finally, we incorporate dynamical decoupling techniques while periodically shuttling over distances exceeding $200\,\text{nm}$, reaching $T_\text{2}^{H,sh}= 32\,μ\text{s}$. For the same setup, we demonstrate that dressed-state shuttling provides robust protection against low-frequency noise with a decay time $T_R^{\text{sh}} = 21\,μ\text{s}$, without the overhead of pulsed control and allowing protection during one-way spin transport. By preserving coherence over timescales exceeding typical gate and readout operations, the demonstrated strategies establish mobile spin qubits as a viable solution for scalable silicon quantum processors.

Estimating quantum time-series such as the Loschmidt amplitude $f(t)=\langleψ|\mathrm{e}^{-\mathrm{i}Ht}|ψ\rangle$ is central to spectroscopy, Hamiltonian analysis, and many phase-estimation algorithms. Direct estimation via the Hadamard test requires controlled implementations of $\mathrm{e}^{-\mathrm{i}Ht}$, and the depth of these controlled circuits grows with $t$, making long-time estimation challenging on near-term hardware. We introduce Quantum Phaselift, a lifting-based framework that estimates the rank-one matrix $Z = f f^\dagger$ rather than estimating $f$ directly. We propose simple quantum circuits for estimating the entries of $Z$ and show that measuring only a narrow band of this matrix around the diagonal is sufficient to uniquely recover $f$. Crucially, this reformulation decouples the controlled circuit depth from the maximum evolution time to scale instead with the width of the measured band. We prove that a $O(1)$ bandwidth suffices for generic signals, leading to substantial savings in controlled operations compared to direct estimation methods. We develop three recovery algorithms with provable exact recovery in the noiseless setting and stability under measurement noise. Finally, we numerically demonstrate that high-quality recovery is possible for the 2D Fermi-Hubbard and 2D transverse-field Ising model signals of size exceeding 100 time points using only a few million measurement shots and reasonable post-processing time, making our time-series estimation techniques efficient and effective for near-term implementations.

Type Ia Supernovae (SNe Ia) are well known for their role as standardizable cosmological candles. Their uniformity is credited to their single origin as thermonuclear explosions of White dwarf (WD) stars. Nevertheless, some SNe Ia break this regularity. Prominently, the Iax subclass are less energetic and remarkably diverse, raising questions about their progenitor systems. While no progenitor system of a normal SN Ia has ever been detected, a luminous blue star was identified in pre-explosion images of the site of the bright SN Iax SN 2012Z, suggested to be a helium giant companion star acting as a mass donor to a WD SN progenitor. This is in line with models of weak mass accretion of a WD from a binary companion, producing an explosion that does not fully disrupt the star. However, these models fail to explain the properties of the faintest Type Iax explosions, suggesting either they originate from other WD binary systems, or even from massive progenitor stars. Here, we present the faint SN Iax SN 2024vjm - possibly the faintest supernova observed to date. Using a deep pre-explosion image taken by the recently launched Euclid space mission, we show that its progenitor system must be fainter than the helium giant SN Iax progenitor candidate of SN 2012Z, as well as that of the luminous red companion or remnant of the faint SN 2008ha, and may require a subdwarf helium star as a mass donor. The deep image also provides strong arguments against a massive star origin for this faint supernova. Our observations argue that SN 2024vjm is a WD explosion, but we find that remarkably faint SNe Iax fade more slowly than bright ones, i.e., they evolve in an opposite manner from the famous Phillips relation that makes regular SNe Ia cosmological candles.

Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving multistability and limit cycles unaddressed. We prove that Neural ODEs achieve $\varepsilon$-$δ$ closeness -- trajectories within error $\varepsilon$ except for initial conditions of measure $< δ$ -- over the \emph{infinite} time horizon $[0,\infty)$ for three target classes: (1) Morse-Smale systems (a structurally stable class) with hyperbolic fixed points, (2) Morse-Smale systems with hyperbolic limit cycles via exact period matching, and (3) systems with normally hyperbolic continuous attractors via discretization. We further establish a temporal generalization bound: $\varepsilon$-$δ$ closeness implies $L^p$ error $\leq \varepsilon^p + δ\cdot D^p$ for all $t \geq 0$, bridging topological guarantees to training metrics. These results provide the first universal approximation framework for multistable infinite-horizon dynamics.

Sound source tracking is commonly performed using classical array-processing algorithms, while machine-learning approaches typically rely on precise source position labels that are expensive or impractical to obtain. This paper introduces a physics-guided variational model capable of fully unsupervised single-source sound source tracking. The method combines a variational encoder with a physics-based decoder that injects geometric constraints into the latent space through analytically derived pairwise time-delay likelihoods. Without requiring ground-truth labels, the model learns to estimate source directions directly from microphone array signals. Experiments on real-world data demonstrate that the proposed approach outperforms traditional baselines and achieves accuracy and computational complexity comparable to state-of-the-art supervised models. We further show that the method generalizes well to mismatched array geometries and exhibits strong robustness to corrupted microphone position metadata. Finally, we outline a natural extension of the approach to multi-source tracking and present the theoretical modifications required to support it.

Let $G$ be a finite simple graph and $NI(G)$ be the closed neighborhood ideal of $G$ in the polynomial ring $S=K[V(G)]$. In this paper, we study the Castelnuovo-Mumford regularity, projective dimension and Cohen-Macaulayness of this ideal. For any chordal graph $G$, we show that $\text{reg}(S/NI(G))=τ(G)$, where $τ(G)$ denotes the vertex cover number of $G$. This generalizes the corresponding result for trees shown in [3], as in trees $τ(G)$ is the same as the matching number of $G$. When $G$ is a bipartite graph or a very well-covered graph, we notice that $\text{reg}(S/NI(G))\geq τ(G)$ and that this inequality can be strict in general. Moreover, we describe the projective dimension of $S/NI(G)$ for some families of graphs. Finally, we give a characterization of very well-covered graphs $G$ for which the ring $S/NI(G)$ is Cohen-Macaulay.

Boson peak dynamics in glasses produce a robust crossover in the terahertz (THz) dielectric response that standard Debye or Lorentz models do not capture. We develop a continuum description of this THz response, coupling an infrared-effective charge fluctuation spectrum to a frequency-dependent shear modulus, and apply it to glycerol glass. The model reproduces the measured complex dielectric function and the nearly linear infrared light-vibration coupling around the boson peak, and highlights the dominant role of transverse shear dynamics.

Teaching microservice architectures is challenging due to distributed complexity and the gap between academia and industry. Understanding the quality issues students introduce in MSAs is essential to improve education. This study analyzes student-developed microservices using an established anti-pattern taxonomy and derives lessons learned with actionable teaching recommendations. We conducted a longitudinal, project-based course (2023-2025) involving 216 Master's students (67 teams) who designed and deployed a realistic, containerized MSA for a gamified testing platform. The final systems revealed 23 out of 58 known MSA anti-patterns, spanning five categories. Security issues were most frequent, highlighting weaknesses in authentication, authorization, and data protection. Team Organization and Service Interaction problems followed, reflecting limited DevOps experience and difficulties in inter-service coordination. Fewer issues appeared in Intra-service Design and Inter-service Decomposition, suggesting students generally defined service boundaries well. Overall, students prioritized feature delivery over robustness and operational discipline. To address this, we recommend enforcing minimal standards (API contracts, gateways), providing labs on resilient communication, integrating security-by-design practices, and offering CI-CD templates. The paper contributes a realistic, full-scale educational experience and a replicable model for teaching industry-aligned microservice architecture.

diffpy$.$morph addresses a need to gain scientific insights from 1D scientific spectra in model independent ways. A powerful approach for this is to take differences between pairs of spectra and look for meaningful changes that might indicate underlying chemical, structural, or other modifications. The challenge is that the difference curve may contain uninteresting differences such as experimental inconsistencies and benign physical changes such as the effects of thermal expansion. diffpy$.$morph allows researchers to apply simple transformations, or "morphs", to one of the datasets to remove the unwanted differences revealing, when they are present, non-trivial differences. diffpy$.$morph is an open-source Python package available on the Python Package Index and conda-forge. Here, we describe its functionality and apply it to solve a range of experimental challenges on diffraction and PDF data from x-rays and neutrons, though we note that it may be applied to any 1D function in principle.

Non-terrestrial networks (NTNs) have gained significant attention for their scalability and wide coverage in next-generation communication systems. A large number of NTN nodes, such as satellites, are required to establish a global NTN, but not all operators have the capability to deploy such a system. Therefore, cooperation among multiple operators, facilitated by an orchestrator, enables the construction of virtually large-scale constellations. In this paper, we propose a weak-control-based orchestration framework that coordinates multiple NTN operators while ensuring that operations align with the policies of both the orchestrator and the individual operators. Unlike centralized orchestration frameworks, where the orchestrator determines the entire route from source to destination, the proposed framework allows each operator to select preferred routes from multiple candidates provided by the orchestrator. To evaluate the effectiveness of our proposed framework, we conducted numerical simulations under various scenarios and network configurations including dynamic NTN environments with time-varying topologies, showing that inter-operator cooperation improves the availability of feasible end-to-end routes. Furthermore, we analyzed the iterative negotiation process to address policy conflicts and quantitatively demonstrated the "price of autonomy," where strict individual policies degrade global feasibility and performance. The results also demonstrate that outcomes of the proposed framework depend on the operators' policies and that hop count and latency increase as the number of operators grows. These findings validate the proposed framework's ability to deliver practical benefits of orchestrated multi-operator collaboration in future NTN environments.

Monitoring daily weather fields is critical for climate science, agriculture, and environmental planning, yet fully probabilistic spatio-temporal models become computationally prohibitive at continental scale. We present a case study on short-term forecasting of daily maximum temperature and precipitation across the conterminous United States using novel scalable spatio-temporal Gaussian process methodology. Building on three approximation families - inducing-point methods (FITC), Vecchia approximations, and a hybrid Vecchia-inducing-point full-scale approach (VIF) - we introduce three extensions that address key bottlenecks in large space-time settings: (i) a scalable correlation-based neighbor selection strategy for Vecchia approximations with point-referenced data, enabling accurate conditioning under complex dependence structures, (ii) a space-time kMeans++ inducing-point selection algorithm, and (iii) GPU-accelerated implementations of computationally expensive operations, including matrix operations and neighbor searches. Using both synthetic experiments and a large NOAA station dataset containing more than one million space-time observations, we analyze the models with respect to predictive performance, parameter estimation, and computational efficiency. Our results demonstrate that scalable Gaussian process models can yield accurate continental-scale forecasts while remaining computationally feasible, offering practical tools for weather applications.

The heterogeneity in nanoscale emitters hinders efforts to understand their basic photophysics and limits their use in practical applications. Existing methods have difficulty accurately characterizing single-emitter spectra and optical heterogeneity on a statistical scale. Here, we introduce SPICEE (SPectrally Imbalanced Correlations from Ensemble Emission), a spectrally filtered photon-correlation technique that recovers single-particle emission lineshapes from an ensemble sample. Analytical derivations, numerical modeling, and experiments on a solution ensemble of emitters validate the technique. We apply SPICEE to blue-emitting ZnSeTe semiconductor nanocrystals relevant to display applications and find that the low color purity in the ensemble spectrum is primarily caused by a small subpopulation of nanocrystals with a distinct emission mechanism. This work demonstrates that SPICEE is a powerful high-throughput tool for accurately characterizing the single-emitter properties of nanoscale systems.

The values of the Hubble constant ($\rm{H_0}$) inferred from the cosmic microwave background (CMB) and local measurements via the distance ladder exhibit a $\sim5σ$ tension. In this work we propose that the tension might be partially alleviated if a subcomponent of the dark matter undergoes decays triggered by spontaneous symmetry breaking in the dark sector, so that the equation of state parameter of the subcomponent shifts from $w \approx 0$ at early times to $w \approx -1/3$ at late times. We provide an effective field theory whose structure is partially motivated by the desire for a plausible UV completion. We find that such a construction naturally produces a possible self-interacting dark matter candidate with a velocity-dependent scattering cross section as a by-product of gauge invariance. This is relevant for addressing tensions between the predictions of $Λ$CDM and observations of small-scale structure, such as the core-cusp problem.

This study examines electrostatic screening effects in graphene using tight binding calculations based on the Binding energy and Bond Charge model and a modified version of it. The results indicate that the modified BBC potential decays in an exponential manner with distance, which suppresses electron electron interactions. The hopping integrals exhibit a pronounced decrease over distance and shift with parameter variation. A band gap opens once the parameter exceeds a certain threshold. The density of states shows a prominent peak near the Fermi level, whereas the low-energy region remains largely unchanged. The low energy helical wave functions in graphene display topological characteristics, including pseudospin momentum locking and a π Berry phase, resulting in distinctive transport properties. By avoiding the Coulomb singularity, the model offers valuable insights for the engineering of screening in two-dimensional systems and the design of topological devices.

In crystallography, a structure is typically represented by the arrangement of atoms in the direct space. Furthermore, space group symmetry and Wyckoff site notations are applied to characterize crystal structures with only a few variables. While this representation is effective for data records and human learning, it lacks one-to-one correspondence between the crystal structure and its representation. This is problematic for many applications, such as crystal structure determination, comparison, and more recently, generative model learning. To address this issue, we propose to represent crystals in a four-dimensional (4D) reciprocal space featured by their Cartesian coordinates and scattering factors, which can naturally handle translation invariance and space group symmetry with the help of structure factors. In order to achieve rotational invariance, the 4D coordinates are then transformed into a power spectrum representation under the orthogonal spherical harmonic and radial basis. Hence, this representation captures both periodicity and symmetry of the crystal structure while also providing a continuous representation of the atomic positions and cell parameters in the direct space. Its effectiveness is demonstrated by applying it to several crystal structure matching and reconstruction tasks.

This letter reports statistically significant changes in the equivalent widths of MgII and CaII lines in the dusty and polluted white dwarf WD 0106-328, based on six epochs of spectroscopy using the VLT and Keck spanning 25 yr. Furthermore, the ratio of these two equivalent widths may also vary, with a 7% probability of being constant. Between 2000 and 2025, both Mg and Ca have experienced decreases in accretion rates, of approximately 20 and 60%, respectively, but with individual variation during the interim. These metal abundance decreases are the first empirical corroboration of diffusion theory in white dwarfs, which predict sinking timescales on the order of days for this star. However, the persistent atmospheric metals require a more gradual, circumstellar process, where one possibility is viscous spreading in an ionized disk of metals, consistent with $α\approx0.1$ within that formalism. The combination of optical and ultraviolet spectroscopy with the Hubble Space Telescope detects all the major rock-forming elements (O, Mg, Si, Fe), and demonstrates that Fe dominates the accreted material by mass, and that it is delivered mostly as pure metal from within a differentiated parent body. This inference is consistent with the possibility that chemically-segregated accretion may result from a combination of planetary assembly, fragmentation, disk evolution, and be observed on relatively short timescales.

JWST observations have suggested that some high-redshift galaxies may be ultra-massive, thereby challenging standard models of early galaxy formation and cosmology. We analyse the stellar masses using different modelling assumptions and with new data of three galaxies (S1, S2 and S3), whose NIRCam/grism redshifts were consistent with $z>5$. These three optically dark galaxies have previously been reported to host exceptionally high stellar masses and star-formation rates, implying extremely high star-formation efficiencies. Recent NIRSpec/IFU observations for S1 indicate a spectroscopic redshift of $z_{\rm spec}=3.2439\pm0.0002$, which is lower than previously reported. Using the Bayesian spectral energy distribution (SED) modelling tool \texttt{Prospector}, we investigate the impact of key model assumptions on stellar mass estimates, such as the choice of star-formation history (SFH) priors (constant versus rising SFH base for the non-parametric prior), the dust attenuation law, and the treatment of emission line fluxes. Our analysis yields revised stellar masses of $\log(M_{\star}/M_{\odot}) \approx 10.36^{+0.47}_{-0.32}, 10.95^{+0.11}_{-0.10}$ and $10.31^{+0.24}_{-0.19}$ for S1, S2, and S3, respectively. We find that adopting a rising SFH base prior results in lower inferred stellar masses compared to a constant SFH base prior. We identify a significant degeneracy between the dust attenuation curve slope, the amount of dust attenuation, and stellar mass. Our results highlight various systematics in SED modelling due to SFH priors and dust attenuation that can influence stellar mass estimates of heavily dust obscured sources. Nevertheless, even with these revised stellar mass estimates, two of the three galaxies remain among the most massive and actively star-forming systems at their respective redshifts, implying high star-formation efficiencies.

In arXiv:2211.09069, significant progress was made in decomposing simple products of fermion correlation functions, and in summing over spin structures of superstring amplitudes in genus two under cyclic constraints. In this manuscript we consider part of the same subject using a framework in which one of the branch points of the genus two curve is fixed at infinity. This framework is a direct generalization of the popular one in the case of genus one. We address some of the issues that remained unresolved in our previous paper arXiv:2209.14633. We show that the spin structures of the simple products of fermion correlation functions with cyclic conditions depend only on the Pe-function values at the half-periods of the genus two surface, for any number of factors in the products. Similar to the genus one case, we can provide basis functions to decompose the product. Consequently, the trilinear relations found in arXiv:2211.09069 can be derived from the known set of differential equations of genus two Pe-functions by simply setting the variables equal to the half-periods of the non-singular and even spin structures, as is the case for genus one. The focus of this manuscript is on the procedures for expressing the results of decomposed formulae in terms of the unique genus two theta function. At present we cannot provide a procedure for deriving the general form of the decomposed formula totally expressed in terms of the theta functions for an arbitrary number of the fermion correlation functions in the product, by the reason described in the text. We present some general results and demonstrate that concrete expressions of both the spin structure dependent and independent parts will be derived and simplified to analyze using the logic of the derivations of the classical solutions to Jacobi inversion problem and their modifications which will be given in this manuscript.

It was conjectured for a long time that the tectonic plates are in a self-organized state of criticality and that the Gutenberg-Richter law is a manifestation of that. It was recently shown that for a system near criticality, the inequality of their responses due to external driving would sharply rise and show universal behavior that could indicate proximity of the system to a critical point. As a result, measures such as the Gini and Kolkata indices that quantify inequality, can also serve as indicators of imminent criticallity and that of diverging (system spanning) responses. In the context of earthquakes, such a large response would correspond to events of high magnitudes. In this work, we show with numerical simulations and seismic data analysis that large earthquake events have a tendency to follow events that are highly unequal, similar to the case of a system near a critical point. Therefore, a continuous monitoring of the inequality indices of the earthquake time series could be useful for hazard estimates. We have applied this framework to models of earthquakes as well as to the earthquake time series from various tectonically active regions, such as North America, Southern Japan, parts of South-East Asia and Indonesia. The findings also indicate a quantitative estimate of the distance from criticality, when the tectonic plates are viewed as a self-organized critical system.

A paradefinite logic is a logic that can serve as the underlying logic for theories that are inconsistent or incomplete. A well-known paradefinite logic is Belnap-Dunn logic. Various expansions of Belnap-Dunn logic have been studied in the literature. In this note, it is argued that the most natural paradefinite logic relative to classical logic is the expansion of Belnap-Dunn logic with a falsity connective and an implication connective for which the standard deduction theorem holds.

We prove that the Gorenstein locus of the Hilbert scheme of points on $\mathbb A^n$ is non-reduced for $n\geq 12$; we construct examples of non-reduced points that come from apolar algebras of the sum of general cubics. As a corollary, we get a non-reducedness result for the cactus scheme. We generalise the Białynicki-Birula decomposition to abstract deformation functors, providing a new method of studying deformation theory. Our construction gives us fractal structures on the nested Hilbert scheme.

We study feedback control of twisted states in the Kuramoto model (KM) of identical oscillators defined on deterministic nearest neighbor graphs containing complete simple ones when it may have phase-lag. Bifurcations of such twisted solutions in the continuum limit (CL) for the uncontrolled KM defined on nearest neighbor graphs that may be deterministic dense, random dense or random sparse were discussed very recently by using the center manifold reduction, which is a standard technique in dynamical systems theory. In this paper we analyze the stability and bifurcations of twisted solutions in the CL for the KM subjected to feedback control. In particular, it is shown that the twisted solutions exist and can be stabilized not only for nearest neighbor graphs but also for complete simple graphs. Moreover, the CL is shown to suffer bifurcations at which the twisted solution becomes unstable and a stable one-parameter family of modulated or oscillating twisted solutions is born, depending on whether the phase-lag is zero or not. We demonstrate the theoretical results by numerical simulations for the feedback controlled KM on deterministic nearest neighbor and complete simple graphs.

We study the contact Lefschetz condition on compact contact solvmanifolds, as introduced by B.\ Cappelletti-Montano, A.\ De Nicola and I.\ Yudin. We seek to fill the gap in the literature concerning Benson-Gordon type results, characterizing $1$-Lefschetz contact solvmanifolds. We prove that the $1$-Lefschetz condition on Lie algebras is preserved via $1$-dimensional central extensions by a symplectic cocycle, thereby establishing that a unimodular symplectic Lie algebra $(\mathfrak{h}, ω)$ is $1$-Lefschetz if and only if its contactization $(\mathfrak{g}, η)$ is $1$-Lefschetz. We achieve this by showing an explicit relation for the relevant cohomology degrees of $\mathfrak{h}$ and $\mathfrak{g}$. Using this, we show how the commutators $[\mathfrak{h},\mathfrak{h}]$ and $[\mathfrak{g},\mathfrak{g}]$ are related, especially when the $1$-Lefschetz condition holds. By specializing to the nilpotent setting, we prove that $1$-Lefschetz contact nilmanifolds equipped with an invariant contact form are quotients of a Heisenberg group, and deduce that there are many examples of compact $K$-contact solvmanifolds not admitting compatible Sasakian structures. We also construct examples of completely solvable $1$-Lefschetz solvmanifolds, some having the $2$-Lefschetz property and some failing it.

We investigate gravitational wave emission from periodic timelike orbits of a test particle around a loop quantum gravity-inspired Schwarzschild black hole. The spacetime is characterised by a holonomy-correction parameter that modifies the radial metric component while preserving asymptotic flatness and the classical location of the horizon. The bound geodesics are systematically classified using the zoom--whirl representation labelled by three integers $(z,w,v)$. Gravitational waveforms are computed within a numerical framework that combines exact geodesic motion with the quadrupole approximation, which is suitable for extreme mass ratio inspirals. We demonstrate that the quantum corrections lead to distinct phase shifts, amplitude variations, and modifications to the harmonic structure of the waveforms, with increasingly complex features for orbits with larger zoom numbers. The corresponding frequency spectra and characteristic strain peak, which fall within the millihertz band, are within the sensitivity ranges of space-based detectors such as LISA, Taiji, and TianQin. For specific orbital configurations and values of the quantum-correction parameter, the characteristic strain exceeds the projected detector noise, indicating potential observability. Our results demonstrate that gravitational waves from periodic orbits provide a sensitive probe of quantum-corrected black hole spacetimes in the strong-field regime.

Population-scale pangenome analysis increasingly requires representations that unify single-nucleotide and structural variation while remaining scalable across large cohorts. Existing formats are typically sequence-centric, path-centric, or sample-centric, and often obscure population structure or fail to exploit carrier sparsity. We introduce the H1 pan-graph-matrix, an allele-centric representation that encodes exact haplotype membership using adaptive per-allele compression. By treating alleles as first-class objects and selecting optimal encodings based on carrier distribution, H1 achieves near-optimal storage across both common and rare variants. We further introduce H2, a path-centric dual representation derived from the same underlying allele-haplotype incidence information that restores explicit haplotype ordering while remaining exactly equivalent in information content. Using real human genome data, we show that this representation yields substantial compression gains, particularly for structural variants, while remaining equivalent in information content to pangenome graphs. H1 provides a unified, population-aware foundation for scalable pangenome analysis and downstream applications such as rare-variant interpretation and drug discovery.

We characterize smooth irreducible curves $C$ on a smooth hyperquadric $Y$ of $\mathbb{P}^4$ such that the blowup of $Y$ along $C$ is a weak Fano threefold. These are precisely the smooth irreducible curves $C$ of degree $d$ and genus $g$ lying on a smooth hypercubic section of $Y$ such that (i) $C$ has no 4-secant line and no 7-secant conic; (ii) $d< 18$ and $(g,d)\not \in \{(4,7),\:(10, 11)\}$; (iii) either $3d-26<g\leq\frac{d^2-1}{12}$ or $(g,d)\in \{(4,6),\:(13,12)\}$. We prove the geometric realizability of each case, thereby proving the existence of weak Fano threefolds and Sarkisov links constructed from them, which were previously known only as numerical possibilities.

We investigate the detection of composite dark matter that disassembles into a cascade while crossing the Earth. This occurs for loosely bound composite dark matter, where the binding energy per constituent is small, such that scattering with Standard Model nuclei typically imparts enough energy to dissociate a constituent from its composite. Trajectories and cascade profiles are found for dissociated constituents that are further diverted by scattering through the Earth. Such scattering cascades are a common feature of TeV-scale weakly-interacting dark matter loosely bound in composites. We identify underground detector signatures of constituent cascades that depend on composite characteristics; these signatures include non-collinear multiple scatters in detectors, parameter-dependent timing separation of multiscatter events, and regions of parameter space where a dark matter cascade would leave a coincident signature in different underground laboratories.

We show how interval-based temporal separation on the extension of Moszkowski's discrete time interval temporal logic (Moszkowski, 1986) by the neighbourhood modalities (ITL-NL) and a lemma which is key in establishing this form of separation in (Guelev and Moszkowski, 2022) can be used to obtain concise proofs of an interval-based form of the reactivity normal form as known from (Manna and Pnueli, 1990), a new normal form for ITL formulas which, given a state formula w, features the conditions that the maximal w- and non w-subintervals of an interval satisfying the given formula need to satisfy, the expressibility of the inverse of the temporal projection operator from (Halpern, Manna and Moszkowski, 1983), the elimination of propositional quantification in ITL-NL and, consequently, uniform Craig interpolation and Beth definability for ITL-NL.

The Kepler problem in classical mechanics exhibits a rich structure of conserved quantities, highlighted by the Laplace--Runge--Lenz (LRL) vector. Through Noether's theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which is well known in the literature. However, the physically relevant part of the LRL vector is its direction angle in the plane of motion (since its magnitude is just a function of energy and angular momentum). The present work derives the infinitesimal dynamical symmetry corresponding to the direction part of the LRL vector, and obtains the explicit form of the symmetry transformations that it generates. When combined with the rotation symmetries,the resulting symmetry group is shown to be the semi-direct product of $SO(3)$ and $R^3$. This stands in contrast to the $SO(4)$ symmetry group generated by the LRL symmetries and the rotations. As a by-product, the action of the new infinitesimal symmetries on all of the conserved quanties is obtained. The results are given in terms of the physical kinematical variables in the Kepler problem, rather than in an enlarged auxiliary space in which the LRL symmetries are usually stated.

This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We first show some properties of optimal solutions, which are then used to decompose the problem into instances of the multidimensional knapsack cover problem with a single continuous variable per dimension. The proposed decomposition is used to design a polynomial-time approximation scheme for the problem with a fixed number of constraints. To the best of our knowledge, this is the first approximation scheme for such a general class of covering mixed-integer linear programs. Moreover, we design a fully polynomial-time approximation scheme and an approximate linear programming formulation for the case with a single constraint. These results improve upon the previously best-known 2-approximation algorithm for the knapsack cover problem with a single continuous variable. Finally, we show a perfect compact formulation for the case where all variables have the same lower and upper bounds. Analogous results are derived for the packing and more general variants of the problem.