Several numerical reconstruction algorithms for the inverse boundary value problem of the 1-dimensional wave equation exist. In this paper we revisit two of them, the Sondhi-Gopinath (SG) method from 1971 and the Korpela-Lassas-Oksanen (KLO) method from 2016. The former is stable enough that it was used in practical applications. The latter has a regularisation scheme with a theoretical proof, and is an evolution of the boundary control method. Both are based on the idea of constructing solutions that are characteristic functions of a set at a given time. This similarity has been pointed out before, but no systematic comparison has been published. We compare the performance of the two algorithms with noisy simulated data. The application in our minds is reconstructing the internal cross-sectional area of a pressurised fluid pipe which corresponds to the first order $\partial_x$ term of the wave equation. Instead of just observing the performance on a few test cases, we generate $n=1000$ random area profiles of various smoothness levels and measurement noise up to $10\%$ of the signal energy and perform statistical tests. SG and KLO have a difference of one time-derivative in their standard boundary data, which complicates the analysis. Our results show that SG performs better in the low noise regime, and KLO with high noise. SG is easier to implement and runs faster.

Neutrinoless double beta decay (0$νββ$) is a crucial for confirming neutrinos' Majorana characteristics. Previous searches for 0$νββ$ decay of $^{160}$Gd using GSO crystals was conducted, but the sensitivity was limited by background $α$-rays from radioactive impurities. To distinguish the backgrounds, PSD (Pulse Shape Discrimination) and energy resolution are essential. GAGG (Gd$_{3}$(Al, Ga)$_5$O$_{12}$) is a $^{160}$Gd-containing crystal that exhibits a higher light yield than GSO and excellent PSD capabilities. GYGAG (Gd$_{3-x}$Y$_x$(Al, Ga)$_5$O$_{12}$) is a variant crystal where a portion of Gd is substituted with Yttrium and can have enhanced light yield, motivating its investigation for 0$νββ$ decay searches. In this study, GYGAG crystals with different Yttrium concentrations were fabricated and their energy resolution, pulse shape discrimination capability between $α$ and $γ$ rays, and scintillation timing characteristics were evaluated for applications in 0$νββ$ decay searches. Y substitution enhanced the light yield, and the best energy resolution was achieved for Gd$_{2.5}$Y$_{0.5}$Al$_2$Ga$_3$O$_{12}$. GYGAG exhibited high pulse shape discrimination performance across various yttrium concentrations.

Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the arithmetics of binary relations, quasigroups, and automata theory, We present a general definition for an infinitary noncommutative partial semigroup; the definition extends and encompasses all the previous notions. In particular, we show that new phenomena occur in the noncommutative case, giving rise to a somewhat richer (and, by the way, more difficult) theory.

Neutron star (NS) radius measurements provide precious information to constrain the dense matter equation of state (EOS). Quiescent low-mass X-ray binaries (qLMXBs) have been used for this purpose, but a number of sources of systematic biases were uncovered, making other sources more favored for EOS studies. We aim to reintroduce qLMXBs as reliable sources of NS mass and radius measurements with a new method, free of systematic biases. We test our implementation on the qLMXB X7 in the globular cluster 47 Tucanae. We used X-PSI to perform the spectral analysis of the 47Tuc X7 observations. X-PSI accurately models the effects of the unknown NS rotation and possible surface anisotropies (two sources of biases in qLMXBs) on the NS spectra. The most significant source of bias on the radius is usually the chemical composition of the NS atmosphere, which, in the case of 47Tuc X7, is known to be hydrogen-rich. A broad range of masses and radii was explored. We obtain a NS radius at 1.4 $M_\odot$ of $R_{1.4} = 12.9\pm0.4$ km (68% credible interval). A shift of the radius by less than a % is measured compared to the model where these sources of systematic uncertainties are neglected. More importantly, including rotation and surface anisotropies in the modeling does not significantly broaden the radius posteriors. We also place strong constraints on the X-ray pulsed fraction (upper limit of 6.0% at a 99.97% credible level) caused by the possible presence of a hot spot. This suggests that, for 47Tuc X7, robust radius constraints can be obtained even without considering systematics, likely because of the deep exposures. We use the resulting M-R constraints from this NS to quantify the improvement on an EOS inference when combined with other measurements. We show that, using recently developed tools, qLMXBs can be exploited to infer reliable NS masses and radii, which can in turn constrain the EOS.

In this work, we further develop the application of the topological diagram approach (TDA) to charmed baryon weak decays $\mathcal{B}_c \to \mathcal{B} V$ with a vector meson in the final state. By incorporating the Korner-Pati-Woo theorem, we show that only five independent sets of TDA parameters are required. Relations among different decay channels arising from isospin, U-spin, and V-spin symmetries are explicitly derived within the TDA framework. Partial wave contributions and form factors associated with different topological diagrams are extracted from global fits to the experimental data. It is found that the form factors $A_2$ and $B_2$ induced from the tensor interaction of the vector mreson with octet baryons are comparable in magnitude to $A_1$ and $B_1$, implying the importance of the tensor coupling in $\mathcal{B}_c \to \mathcal{B} V$ decays. Branching fractions for all $\mathcal{B}_c\to \mathcal{B} V$ channels are predicted, and most measured modes are found to be in good agreement with current data. More physical observables, including up-down asymmetries, longitudinal polarizations as well as observables in the subsequent decays are also predicted. Our results provide a systematic framework for understanding charmed baryon weak decays with vector mesons and can be further tested with future experiments.

We investigate Büchi Arithmetic $\mathsf{BA}_k$ -- the elementary theory of the natural numbers equipped with addition and the function mapping a number $x$ to the greatest power of $k$ dividing $x$. $\mathsf{BA}_k$ is known to be decidable and to enjoy a few important properties, in particular, a first-order structure is automatic iff it is interpretable in $\mathsf{BA}_k$. We propose a natural axiomatization of this theory based on a comprehension schema restricted to bounded formulas, interpreting natural numbers as finite (multi)sets of powers of $k$ via their base-$k$ expansions. The completeness proof for this axiomatization proceeds through a formalization of the Büchi-Bruyère Theorem on the equivalence of definability in Büchi Arithmetic and recognizability by finite automata.

Measurements of interplanetary magnetic fields have long relied on spacecraft measurements, which provide only in-situ sampling and therefore cannot capture the global magnetic structure. Faraday rotation of radio signals extends in-situ measurements to line-of-sight measurements, but it still depends on the number and spatial distribution of available radio sources. The Zeeman effect offers another route to remote sensing of magnetic fields, but it is generally too weak to diagnose the weak interplanetary magnetic fields. Here, we present a remote-sensing method to constrain weak magnetic field strength and orientation using spectral-line polarization induced by ground-state alignment (GSA) and Hanle effect, with collisional effects taken into account. This method is sensitive to weak magnetic fields in environments ranging from the high solar atmosphere and solar wind to the outer heliosphere, and we identify suitable spectral lines for different targets. We further perform forward modeling of Mercury's magnetosphere to demonstrate the feasibility of this imaging method. Spectral-polarization imaging therefore provides a new way toward remote imaging of dynamic heliospheric magnetic structures.

For models evaluated at a random set of independent variables, the variance-based Shapley effects range between Sobol' indices, and the corresponding total indices admit derivative-based upper-bounds. Such relationships fail when the inputs are non-independent. This study investigates a general inequality link between the variance-based dependent sensitivity indices, recently introduced by us, and the variance-based Shapley effects for models with dependent inpus. It turns out that Shapley effects range between the main and total dependent sensitivity indices, and such indices are computationally more attractive. Moreover, different upper-bounds of such indices are provided so as to ease the identification of non-relevant inputs in higher dimensions as well as to obtain sometimes practical estimates of total dependent indices. Some of such bounds rely on the traditional gradients, while others rely on generalized sensitivity indices using dependency models.

Genuine multipartite entanglement and full inseparability are two inequivalent quantum resources. Even though all genuinely multipartite entangled states are also fully inseparable, not all fully inseparable states are genuinely multipartite entangled. There exist fully inseparable states that can be prepared as convex mixtures of states separable with respect to different bipartite splits. Here, we are interested in examples of Gaussian states that possess this type of entanglement, so-called fully inseparable biseparable states. We show for several archetypical families of multimode Gaussian states that fully inseparable biseparable candidate states are actually genuinely multipartite entangled. Using projections to finite-dimensional subspaces and fully decomposable witnesses, we observe a shrinking of the regions of potentially fully inseparable biseparable Gaussian states with growing dimension of the projection subspaces. We therefore conjecture that all fully inseparable Gaussian states are genuinely multipartite entangled.

We propose a decentralized, frequency-domain identification algorithm that estimates the grid-equivalent model from the perspective of local converters. Since local electric signals in a multi-converter setup are affected by voltage inputs from other converters, considered as the grid, estimating a single apparent impedance yields biased and inaccurate results. To overcome this, we design a framework that decouples the effect of the equivalent impedance (passive) from that of the equivalent voltage (active). The parameters and equivalent grid voltages are then estimated using a constrained least squares and a Kalman filter algorithm, respectively, applied across frequency samples. We then demonstrate the accuracy and performance of our algorithm on an interconnected 5-converter system in grid-forming mode, with minimal voltage excitations and non-ideal operating conditions.

The smallest eigenvalues of (distance-j) Hamming graphs with distance parameter j at least half the length were completely determined by Brouwer et al. (2018). In the present work, we address the complementary regime, namely distances j strictly less than half the length, and derive asymptotic lower bounds on the smallest eigenvalue of binary Hamming graphs. For certain natural generalizations, specifically Cayley graphs defined over quaternary vector spaces, we asymptotically determine the smallest eigenvalue as well. As an application, we obtain lower bounds on the quantum chromatic number of these graphs. In particular, for the aforementioned Cayley graphs over quaternary vectors, our lower bounds for the quantum chromatic number coincide with known upper bounds.

State-of-the-art multiple sequence alignment (MSA) algorithms are based on progressive approaches that rely on pairwise sequence alignment (PSA) to generate guide trees to align all sequences. Given an evidenced explosion in genomic data availability, research efforts have focused on accelerating PSA on massively-parallel architectures (e.g., GPUs) and specialized hardware (e.g., FPGAs). However, there is increasing evidence that starting from exact 3-way alignments could provide more robust, accurate MSAs, and improve genomic analysis. While the current literature has shown that PSA algorithms can be extended to align sequence triplets, the existent state-of-the-art on hardware acceleration of exact 3-way alignments is still scarce. In particular, current GPU methods are still inefficient due to lacking support for novel hardware features (e.g., cross-thread intrinsics), while being closed-source and vendor-specific. In this paper, TrioSeq is proposed as a fine-grained strategy to efficiently implement 3-way alignments on GPUs, leveraging novel levels of GPU parallelism and synchronization to achieve high throughput in aligning sequence triplets. Evaluation on NVIDIA and AMD GPUs shows that TrioSeq outperforms state-of-the-art GPU progressive methods on 3-way alignment by at least 20% on simulated genomic datasets.

We investigate the trade-off between controllability, channel access, and age-related performance in a wireless network of control systems. Controllers share a random-access channel to transmit control inputs to actuators over slotted blocks. We measure reliable control via block controllability, where a block is controllable if it contains a required number of consecutive successful transmissions. In parallel, we capture information freshness via the age of information. To enable efficient allocation of channel resources over time, we introduce adaptive access probabilities at the block level, prioritizing controllers that have not yet achieved controllability. We then derive closed-form expressions for block controllability probability, the peak latency between inter-block consecutive successes, and peak age of information. We further characterize the peak control latency, defined as the time between consecutive controllable blocks. Finally, we optimize access probabilities to jointly balance controllability and age-related metrics. Numerical results illustrate the effectiveness of the proposed adaptive access policies in managing this trade-off in interference-limited wireless control networks.

We present a systematic benchmark of MACE potentials for iron-nickel alloys, focusing on structural, elastic, magnetic, and finite-temperature properties relevant to phase stability. The reference dataset comprises spin-polarized PBE density functional theory (DFT) calculations for chemically disordered special quasirandom structures (SQS), spanning compositions, bcc and fcc crystal structures, and volumetric and shear deformations. A system-specific MACE-sqs model trained on this dataset achieves validation errors of 2.0 meV/atom for energies and 24.3 meV/Angstrom for forces. Compared with several MACE foundation models, including models trained with Hubbard U corrections, MACE-sqs gives the most consistent agreement with DFT and experiment for equations of state, equilibrium volumes, elastic constants, and thermal expansion trends in bcc and fcc Fe-Ni alloys. For the bcc-to-hcp transition, MACE-sqs predicts a pure-Fe transition pressure closer to experiment than the tested foundation models, but all models predict an incorrect increase of transition pressure with Ni content. This failure indicates that high-pressure magnetic collapse and composition-dependent magnetoelastic effects are not yet fully captured. Overall, targeted SQS-based training substantially improves the accuracy of MACE potentials for Fe-Ni alloys, while phase stability under magnetic collapse remains a key limitation for future model development.

NiAs-type compounds such as CrSb and MnTe host $g$-wave altermagnet (AM) state. In order to search other possible unconventional magnets in this system, we present a global magnetic phase diagram based on a classical $J_1$-$J_2$-$J_3$ Heisenberg model and density functional theory (DFT) calculations. We find another $g$-wave AM state and two $f$-wave OPMs in the phase diagram. Intriguingly, we show that a mixed-parity of the $f$-wave OPM and $g$-wave AM state can naturally emerge in an umbrella-like noncollinear magnetic structure. Our DFT calculations show that CrSe and CrTe$_{1-x}$Se$_x$ are generally in such mixing state with dominated $f$-wave component. The interlayer next-nearest-neighbor coupling $J_3$ is shown to be crucial in determining the phase diagram and in inducing strong competition between conventional and unconventional magnets. Inspired by this, we demonstrate that AM or OPM could be realized by applying chemical doping or strain to conventional magnets. Our results provide a guidance for design of both even- and odd-parity as well as mixed-parity unconventional magnets in NiAs-type compounds.

Active matter sustains emergent flows at the expense of preserving structural order. The feedback between structure and viscous flows typically disrupts crystalline and liquid-crystalline organization by amplifying the very deformations they generate. Yet this destabilizing paradigm has recently been challenged by experiments showing that inertial fluid flows can stabilize few-body bound states of active spinners. Whether inertial active matter can sustain genuine cohesion and order at the many-body level, however, remains elusive. Here we investigate two-dimensional assemblies of macroscopic spinners operating at high Reynolds number and uncover two phase transitions leading to the emergence of a dilute percolating fluid and a dense spin-textured crystal. At low density, inertial flows generate two competing interactions: anisotropic attractions and transverse Magnus forces that continuously break and reconfigure bonds. Together they drive a percolation transition toward a dynamically rearranging holey liquid reminiscent of the empty-liquid states observed in equilibrium patchy colloids. At high density, the feedback between spin alignment and particle positions suppresses transverse rearrangements and yields a first-order transition toward a spin-ordered crystal. Our results demonstrate that, beyond the overdamped limit, hydrodynamic feedback can promote rather than destroy collective order, revealing a distinct regime of many-body active matter governed by inertial flows.

We develop operator-theoretic and cohomological tools for quaternionic quasi-Lie structures, with sliding mode control as a motivating application. Three main results are established. First, an exact operator-norm transfer under the quaternionic anti-isomorphism $a \mapsto \bar{a}$, which enables quantitative bounds from~\cite{Athmouni2026} to transfer between left- and right-module conventions with no constant factor. Second, a transcription of the cohomological rigidity result of~\cite{Athmouni2026} into a form usable here: in the homogeneous case, under a local cohomological non-obstruction hypothesis, an explicit bilinear correction $Ω$ produces a bracket satisfying the Jacobi identity exactly on a ball of admissible radius, with all quantitative constants expressed through $C_{2}$ and the admissible radius. Third, the projected Jacobi defect is shown to satisfy a generalized one-sided Lipschitz condition with computable constants, obtained via a uniform-selection argument handling state-dependence of the measurable selection. As an application, we develop a robust control framework with a cohomological matching condition replacing pointwise verification: an integral sliding surface yields $β$-exponential stability via an iterative linear matrix inequality (LMI) scheme. The work is purely analytical; closed-loop numerical simulations for multidimensional systems are deferred to a companion paper. The framework is restricted to the homogeneous quasi-Lie case; the Sobolev extension is conjectural, and algorithm termination is established conditionally on sufficient continuity assumptions on the LMI solution map.

Electron beams enable highly localized near-field excitation of waveguided optical modes, yet their coupling is typically limited by short interaction times along straight-line trajectories with fixed impact parameters. Here, we theoretically demonstrate that electrostatic steering overcomes this limitation by introducing a tunable turning point in grazing electron trajectories, thus controlling the minimum electron--waveguide separation and producing strong coupling to waveguided modes. Specifically, we consider a biased rectangular silicon waveguide, where a repulsive static field deflects a grazing electron. In this configuration, the electron turning point governs both the coupling strength and the modal selectivity, which can be dynamically tuned through the electron incidence angle and the applied bias. In addition, the aloof electron--waveguide interaction suppresses lossy high-energy channels (e.g., above the silicon band gap) while preserving substantial excitation of the targeted waveguided modes. Using a practical biasing configuration and 100~keV electrons, we predict an average yield exceeding ten photons per electron, with voltage-tunable control of the interaction. Our results establish electrostatic steering as a practical route for engineering and enhancing free-electron coupling to waveguided photonic modes.

Asymptotic methods are used to derive a geometrically nonlinear beam model for thermoelastic solids with a spatially localised heat source. The asymptotic reduction is based on collapsing the heated region to a point. Away from the point of heating, the governing equations reduce to a pair of beam equations with nonlinear von Kármán strains. The effects of the localised heat source are captured through asymptotically consistent jump conditions that hold at the point of heating. The model accounts for changes in beam length due to longitudinal thermal expansion and bending moments produced by transverse thermal gradients. The model is used to study light-induced actuation of photoresponsive hydrogel beams with localised heating arising from laser irradiation. Two loading scenarios are considered. In the first, the ends of the beam are assumed to be free, resulting in a V-shaped deformation upon heating. An analytical expression for the fold angle of the V is provided. In the second, the beam is assumed to be in a pre-buckled configuration due to clamped end conditions. The critical conditions leading to light-driven snap-through are calculated. Offsetting the laser from the mid-point of the beam is found to inhibit the onset of snap through.

Molecular rectifiers, as prototypical components of molecular electronics, present unique opportunities for pushing device miniaturization to its ultimate limits. Nevertheless, challenges including limited rectification ratios (RR), insufficient robustness, and poor reproducibility impede their practical deployment. To make molecular rectifiers competitive with silicon-based devices, it is important to fully understand the design principles and fabrication methods from both mechanistic and experimental perspectives. By holistically considering the transport mechanisms, modulation strategies, fabrication, characterization techniques, and theoretical simulations, this review provides a comprehensive overview of molecular rectifiers. Representative examples of conceptually significant and high-performance molecular rectifier systems are highlighted to illustrate the relationships between rectification mechanisms, molecular design strategies, and device realization. Building on these discussions, we present an outlook for current bottlenecks and future directions to guide the development of molecular rectifiers. This review aims to serve as both a conceptual framework and a technical reference for researchers working at the intersection of molecular electronics and nanoscale device engineering in the post-CMOS era.

In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally proposed in [Li et al. SIAM J. Sci. Comput. 42(2), 2020], in which an arbitrarily high-order approximation space with one degree of freedom per element is constructed by solving local least squares fitting problems. The space can be applied within the cut discontinuous Galerkin framework, where the jump conditions across the interface are weakly enforced by the Nitsche's penalty method. In this work, the local least squares problem is modified by introducing appropriate constraints, which allows us to naturally ensure the stability near the interface by the reconstructed space, and further enables us to establish a norm equivalence between the high-order space and the lowest-order space. This equivalence property motivates us to construct a preconditioner from the piecewise constant space, and this preconditioning method is shown to be optimal in the sense that the upper bound of the condition number of the preconditioned system is independent of the mesh size, the coefficient and the interface location relative to the unfitted mesh. We also present the multigrid algorithms that serve as the inverse of the lowest-order system matrix. Numerical experiments in both two and three dimensions confirm the optimal convergence rates under error measurements and illustrate the efficiency and the robustness of the preconditioning method.

In this short note, we establish an upper bound for the conjugate radius of an open $n$-dimensional Riemannian manifold under a scalar curvature lower bound and a bottom-of-spectrum upper bound. As a consequence, if $λ_{0}(M)=0$ and scalar curvature $\ge n(n-1)$, then the conjugate radius $\le π$.

In recent years, light detection and ranging (LIDAR) has seen a steep rise in the sensitivity of measuring the distances of remote objects. Here, we propose to enhance the sensitivity of LIDAR even further by exploiting Dicke's concept of superradiance, i.e., the collective light emission of statistically independent light sources. By using $N$ thermal light sources (TLS) and measuring intensity correlations of order $m \geq 2$ instead of $m=1$, i.e., the intensity, we show that the Cramér-Rao bound on the measurement of the distance of a remote object undercuts that of traditional LIDAR by a factor of $N$, and can be reduced further with increasing correlation order $m$. Our numerical calculations are supported by analytical expressions for the special cases of two and three TLS and a general approximate expression for any number of TLS.

We study Brownian motion on Hermitian symmetric spaces of non-compact type in their bounded-domain realization. Using Jordan triple systems, we identify the spectral values after an appropriate change of variables as a Heckman-Opdam diffusion of type $BC_r$. We then analyze two Brownian functionals: the symplectic area associated with the canonical Kähler form, and, in the tube-type case, the winding defined by the Jordan determinant. For the area process we prove a martingale representation, a central limit theorem, and an exact conditional characteristic function expressed as a ratio of Heckman-Opdam heat kernels. For the determinant winding process we obtain analogous heat kernel formulas and prove convergence to a Cauchy law with scale determined by the initial determinant. These results extend classical formulas of Paul Lévy and Marc Yor from the Euclidean setting to the full class of Hermitian symmetric spaces of non-compact type.

We investigate thin-disk imaging of Kerr black holes with synchronized scalar hair, focusing on backreacted parity-odd excited states of a complex scalar field minimally coupled to Einstein gravity. The spacetime displays a core-double-torus lensing structure, with a central black hole surrounded by two scalar clouds. We study the dependence of the images on hair strength and viewing angle, identifying a weak-hair regime close to Kerr. With increasing hair, the photon ring and shadow region shrink and become more distorted. In the strong-hair regime, gravitational lensing produces new features, including multiple disconnected shadow components, crescent-shaped structures, and signatures of chaotic lensing. For nearly edge-on viewing angles, repeated equatorial crossings generate nested ring-like patterns. These results highlight possible geometric signatures of black holes with excited scalar hair.

Quantum Cramér--Rao theory is intrinsically local: it bounds precision near a specified parameter value, and its saturating measurement generally depends on that value. Barankin-type bounds use finite parameter displacements, but remain anchored to a chosen reference value. This leaves open a basic global-estimation problem: when the parameter is known only within a broad domain, what precision can be guaranteed by a single estimator and a single measurement strategy fixed before the true value is localized? We answer this question by introducing global score functions tied to a weighted variance over the whole parameter domain. Their correlations generate a hierarchy of precision bounds: global Cramér--Rao and Barankin-type bounds arise as restricted levels, whereas unrestricted score correlations yield a fully global bound for the prescribed weighted variance. The hierarchy recovers local Cramér--Rao theory in the many-repetition limit and reveals genuinely global precision limits for finite data over broad domains. In the quantum setting, the construction identifies when this fully global bound can be realized by a single parameter-independent measurement. The same framework extends to Bayesian estimation, recovering the Van Trees bound in the local limit while yielding stronger finite-width lower bounds on the Bayesian mean-square error beyond this limit.

We develop an analytical theory of coherent (scaled quadratically with the number of particles) radiation and coherent radiation friction in a head-on collision of a dense charged particle bunch with an intense laser pulse. We demonstrate that the low-frequency coherent radiation in the forward and backward directions dominates the energy-momentum losses of a mildly relativistic bunch and can result in a substantial enhancement of the overall radiation friction as compared to the incoherent case. We derive the scaling laws for the average momentum losses of the bunch over the collision with respect to laser intensity, pulse duration, and particle bunch parameters, and show their robustness with respect to laser polarization and the shape of the particle distribution in the bunch.

We consider a question of Edjvet and Vdovina concerning which groups defined by special presentations are large. For each integer $n \ge 3$, we construct an $n$-generator one-relator presentation whose star graph is the complete bipartite graph $K_{n,n}$; the resulting groups are large and hyperbolic. We also classify concise special presentations with star graph $K_{3,3}$, showing that they are one-relator presentations and that, up to Tietze equivalence, there are exactly twelve that define torsion-free groups. The torsion cases arise precisely as positive powers of the relators in the torsion-free cases, and define pairwise non-isomorphic groups that remain large and hyperbolic.

For multi-signal detection and direction-of-arrival (DoA) estimation, conventional Capon beamforming degrades when there are more transmitters than receive antennas minus one. This paper proposes a lightweight method using adaptive notch filters (ANFs) with only two receive antennas for simultaneous DoA of two or more narrowband signals. Cascaded ANF stages form isolated channels per signal, and Capon estimates direction on each. The method has very low computational cost, and in simulation, for transmitters separable in time, frequency, and angle, performance approaches that of an oracle with prior signal knowledge. As with ANFs themselves, multiple components at closely spaced frequencies are poorly resolved, forming the main limitation of the proposed method. Simulations are complemented by an experimental implementation on a low-cost software-defined radio (ADALM-Pluto).

Laminar--turbulent transition remains a major uncertainty in the aerothermal design of entry, descent, and landing (EDL) vehicles. We show that, under high-enthalpy Mars-entry conditions, the detached bow shock and shock-generated shear--entropy layer can become unstable under freestream disturbances, leading to nonlinear breakdown and enhanced wall heating. The analysis spans freestream Mach numbers ($M_\infty$) up to 30 for both Earth and Mars at high altitude, with Mars being more susceptible. The receptivity analysis shows that disturbance amplification occurs through a three-step mechanism: (i) transmission and amplification of acoustic and entropic freestream components across the bow shock; (ii) further convective amplification within the post-shock shear--entropy layer; and (iii) bow-shock corrugation driven by the downstream pressure field, which reinforces the instability. The dominant response is localized in the shock layer, with no classical boundary-layer mode required. The total optimal energy gain scales as $\overline{G}_T^{\rm opt}\sim γ_2^*M_\infty^2 \exp[(ρ_2/ρ_1)/C-B/\sqrt{Re_\infty}]$, where $γ_2^*$ is an effective specific-heat ratio, $ρ_1$ and $ρ_2$ the pre- and post-shock densities, $Re_\infty$ the freestream Reynolds number, and $B$, $C$ geometry-dependent constants. For a representative EDL vehicle during Mars entry, amplification factors reach order $10^6$. Flight measurements from the Mars Science Laboratory (MSL) and Mars 2020/Perseverance capsules are consistent with these results, as are wall-modeled large-eddy simulations of MSL under representative Mars-entry conditions. These results suggest that bow-shock instabilities may constitute a transition mechanism for blunt hypersonic entry vehicles, either alone or combined with others.