We study the decomposition of real numbers into sums of Lüroth sets, which are defined by numbers whose Lüroth expansions have prescribed digit constraints. We establish several results on the congruence modulo 1 of sums of Lüroth sets, including summands with digits bounded above, below, and combinations of the two. We also analyse the Hausdorff dimension of Lüroth sets and their sums. The results extend classical findings on continued fractions to Lüroth expansions.

Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In this paper, we provide a systematic lattice model construction for all such gapped phases. Specifically, we consider "all-boson type" fusion 2-category symmetries, all of which are obtainable from 0-form symmetry groups $G$ (possibly with an 't Hooft anomaly) via generalized gauging--that is, by stacking with an $H$-symmetric TFT and gauging a subgroup $H$. The continuum classification directly informs the lattice data, such as the generalized gauging that determines the symmetry category, and the data that specifies the gapped phase. We construct commuting projector Hamiltonians and ground states applicable to any non-chiral gapped phase with such symmetries. We also describe the ground states in terms of tensor networks. In light of the length of the paper, we include a self-contained summary section presenting the main results and examples.

This work introduces a novel method to generate snapshot data for operator inference that guarantees the exact reconstruction of intrusive projection-based reduced-order models (ROMs). To ensure exact reconstruction, the operator inference least squares matrix must have full rank, without regularization. Existing works have achieved this full rank using heuristic strategies to generate snapshot data and a-posteriori checks on full rank, but without a guarantee of success. Our novel snapshot data generation method provides this guarantee thanks to two key ingredients: first we identify ROM states that induce full rank, then we generate snapshots corresponding to exactly these states by simulating multiple trajectories for only a single time step. This way, the number of required snapshots is minimal and orders of magnitude lower than typically reported with existing methods. The method avoids non-Markovian terms and does not require re-projection. Since the number of snapshots is minimal, the least squares problem simplifies to a linear system that is numerically more stable. In addition, because the inferred operators are exact, properties of the intrusive ROM operators such as symmetry or skew-symmetry are preserved. Numerical results for differential equations involving 2nd, 3rd and 8th order polynomials demonstrate that the novel snapshot data generation method leads to exact reconstruction of the intrusive reduced order models.

We introduce a theory of syntomic cohomology for ring spectra with involution, which we call Real syntomic cohomology. We show that our construction extends the theory of syntomic cohomology for rings with involution due to Park. Our construction also refines syntomic cohomology as developed by Bhatt--Morrow--Scholze, Morin, Bhatt--Lurie, and Hahn--Raksit--Wilson. We compute the Real syntomic cohomology of Real topological K-theory and topological modular forms with level structure.

We propose a revisited variational quantum solver for linear systems, designed to circumvent the barren plateau phenomenon by combining two key techniques: adiabatic evolution and warm starts. To this end, we define an initial Hamiltonian with a known ground state which is easily implemented on the quantum circuit, and then "adiabatically" evolve the Hamiltonian by tuning a control variable in such a way that the final ground state matches the solution to the given linear system. This evolution is carried out in incremental steps, and the ground state at each step is found by minimizing the energy using the parameter values corresponding to the previous minimum as a warm start to guide the search. As a first test case, the method is applied to several linear systems obtained by discretizing a one-dimensional heat flow equation with different physical assumptions and grid choices. Our method successfully and reliably improves upon the solution to the same problem as obtained by a conventional quantum solver, reaching very close to the global minimum also in the case of very shallow circuit implementations.

We investigate off-diagonal matrix elements of local operators in integrable spin chains, focusing on the isotropic spin-$1/2$ Heisenberg chain ($XXX$ chain). We employ state-of-the-art Algebraic Bethe Ansatz results, which allow us to efficiently compute matrix elements of operators with support up to two sites between generic energy eigenstates. We consider both matrix elements between eigenstates that are in the same thermodynamic macrostate, as well as eigenstates that belong to different macrostates. In the former case, focusing on thermal states we numerically show that matrix elements are compatible with the exponential decay as $\exp(-L |{M}^{\scriptscriptstyle{\mathcal{O}}}_{ij}|)$. The probability distribution functions of ${M}_{ij}^{\scriptscriptstyle{\mathcal{O}}}$ depend on the observable and on the macrostate, and are well described by Gumbel distributions. On the other hand, matrix elements between eigenstates in different macrostates decay faster as $\exp(-|{M'}_{ij}^{\scriptscriptstyle{\mathcal{O}}}|L^2)$, with ${M'}_{ij}^{\scriptscriptstyle \mathcal{O}}$, again, compatible with a Gumbel distribution.

The KM3NeT experiment has recently observed a neutrino with an energy around 100PeV, and IceCube has detected five neutrinos with energies above 1PeV. While there are no known astrophysical sources, exploding primordial black holes could have produced these high-energy neutrinos. For Schwarzschild black holes this interpretation results in tensions between the burst rates inferred from the KM3NeT and IceCube observations, with indirect constraints from the extragalactic gamma ray background and with the non-observation of an associated gamma ray signal at LHAASO. In this letter we show that if there is a population of primordial black holes charged under a new dark $u(1)$ symmetry which spend most of their time in a quasi-extremal state, the neutrino emission at 1PeV may be more suppressed than at 100PeV. The burst rates implied by the KM3NeT and IceCube observations and the indirect constraints can then all be consistent at $1σ$, and no associated gamma-ray signal was expected at LHAASO. Furthermore, these black holes could constitute all of the observed dark matter in the universe.

We revisit the phase diagram of an anisotropic Dicke model by revealing the non-analyticity induced by underlying exceptional points. We find that, from a dynamical perspective, the conventional superradiant phase can be further separated into three regions, in which the systems are characterized by different effective Hamiltonians, including the harmonic oscillator, the inverted harmonic oscillator, and their respective counterparts. We employ the Loschmidt echo to characterize different quantum phases by analyzing the quench dynamics of a trivial initial state. Numerical simulations for finite systems confirm our predictions about the existence of hierarchic superradiant phases.

Permissionless-consensus-based Decentralised Autonomous Organisations (DAOs) are the prevailing paradigm for participant-governed digital organisations. As participants have verified resources but no trusted identities, this ecosystem is necessarily plutocratic (one coin -- one vote). Here we offer, for the first time, a democratic (one person -- one vote) paradigm for the governance of digital communities and organisations, based on permissioned consensus and egalitarian decision processes. In line with Lamport's vision of consensus as a self-governing parliament, in the democratic paradigm a constitution specifies both a decision making protocol as well as a consensus protocol, combined to let participants amend the constitution through constitutionally-valid decisions that are ratified by consensus. To meaningfully instantiate this paradigm we integrate the disciplines of distributed computing and computational social choice, with the goal of providing a practical and efficient smartphone-based solution for the democratic self-governance of grassroots sovereign digital communities and organisations. The resulting Constitutional Consensus protocol employs (1) state-of-the-art Sybil-resilient democratic decision processes for amending the set of participants, supermajority threshold, and timeout; and (2) a novel Byzantine-fault tolerant consensus protocol that is DAG-based (following Cordial Miners) thus eschewing reliable broadcast, with dual-mode operation (following Morpheus) that is quiescent when idle, has spontaneous leaders for isolated transactions, and formal round-robin leadership during high throughput.

An automorphism of the free group $F_n$ is called pure symmetric if it sends each generator to a conjugate of itself. The group $\mathrm{PSA}_n$ of all pure symmetric automorphisms and its quotient $\mathrm{PSO}_n$ by the group of inner automorphisms are called the McCool groups. In this paper we prove that every BNSR-invariant $Σ^m$ of a McCool group is either dense or empty in the character sphere, and we characterize precisely when each situation occurs. Our techniques involve understanding higher generation properties of abelian subgroups of McCool groups, coming from the McCullough-Miller space. We also investigate further properties of the second invariant $Σ^2$ for McCool groups using a general criterion due to Meinert for a character to lie in $Σ^2$.

The detection of SO2 in both WASP-39 b and WASP-107 b recently brought more attention to the modeling of photochemistry in exoplanets. However, sulfur kinetics data is lacking in the literature for the full C/H/O/N/S system. The networks used to model this chemistry neglect the coupling between sulfur and other C/H/O/N species. We aimed to integrate sulfur kinetics to our previously developed C_0-C_2/H/O/N chemical network, with the inclusion of its coupling to carbon and nitrogen chemistry, for conditions between 500 - 2500 K and 100 - 10^-6 bar, and any atomic composition. To achieve this reliability, we used a dual approach, deriving the network from other available combustion networks and from original ab initio calculations where data was lacking. This was performed together with an extensive validation of the network on 1606 experimental measurements from the literature on the combustion and pyrolysis of multiple sulfur compounds such as H2S, CH3SH, CS2 and OCS. To examine the consequences of this new chemical network on exoplanets atmospheric studies, we generated abundance profiles for GJ 436 b, GJ 1214 b, HD 189733 b, HD 209458 b, WASP-39 b and WASP-107 b using the 1D kinetic model FRECKLL, calculated the corresponding transmission spectra using TauREx 3.1 and compared these results with other chemical networks used in exoplanet modeling with sulfur. The coupling between carbon and sulfur chemistry is found to be impactful on both abundance profiles and observables, with CH2S being its key species. CS2 abundance is found to be probably much higher than anticipated in current kinetic networks for exoplanets. The detection of CS2 in TOI-270 d highlights the importance of using validated chemical networks to improve the reliability of our models, particularly in the JWST era. Combustion and pyrolysis data are largely available tools that reveal to be very useful for this task.

Mass transfer (MT) in binary systems is a common evolutionary process that can significantly affect the structure, evolution, and final fate of both stars. In modeling MT hydrodynamics, it is usually assumed that the critical point of the flow, where the velocity exceeds the local sound speed, coincides with the inner Lagrange point (L1). However, in massive donors where radiative pressure dominates over gas pressure and the Eddington factor $Γ_\text{Edd}$ can approach or exceed unity, radiation-gas coupling can shift the critical point away from L1, altering the MT rate ($\dot{M}_\text{d}$). We investigate the effects of radiation on MT using time-steady radiative hydrodynamic equations and the von Zeipel theorem. We derive analytical expressions that closely approximate $\dot{M}_\text{d}$, algebraic solutions for simplified cases, and numerical results using a realistic equation of state. Two main differences emerge relative to traditional prescriptions for $\dot{M}_\text{d}$. First, for Roche-lobe-underfilling donors with $Γ_\text{Edd} \lesssim 1$, radiative momentum exchange leads to an exponential increase of $\dot{M}_\text{d}$ as a function of $1-Γ_\text{Edd}$. We provide a simple modification of existing prescriptions that captures this effect. Second, the photon tiring limit for super-Eddington outflows is much less restrictive near L1 than in spherical stars. We suggest that donors with super-Eddington, convectively inefficient subsurface layers can drive MT with $-\dot{M}_\text{d} \gtrsim 10^{-2}\,\text{M}_\odot\,\text{yr}^{-1}$ even before Roche-lobe overflow. We characterize the conditions for this new mode of super-Eddington-boosted MT and discuss its implications for binary evolution, including potential links to nonterminal outbursts of Luminous Blue Variables.

We demonstrate some very special features of the Dirac-Born-Infeld--like (DBI) gravitational counter-term in AdS$_4$ spacetime, in the context of holography with a sharp radial cut-off. We show that the three-sphere partition function is not only independent of a constant radial cut-off, but also remains unchanged under deformations of the cut-off surface. We also consider the renormalized holographic entanglement entropy for an equatorial Ryu-Takayanagi surface with a cut-off with an arbitrary shape and show that it can also be independent of the cut-off under a special condition. We also numerically study the behavior of the renormalized entropy with different counter-terms and relate the results to monotonicity properties under holographic renormalization group flow. The DBI counter-term is always seen to be associated with integrating out fewer degrees of freedom compared to other counter-terms.

Mass transfer in binary systems is the key process in the formation of various classes of objects, including merging binary black holes (BBHs) and neutron stars. Orbital evolution during mass transfer depends on how much mass is accreted and how much angular momentum is lost $-$ two of the main uncertainties in binary evolution. Here, we demonstrate that, despite these unknowns, a fundamental limit exists to how close binary systems can get via stable mass transfer (SMT), that is robust against uncertainties in orbital evolution. Based on detailed evolutionary models of interacting systems with a BH accretor and a massive star companion, we show that the post-interaction orbit is always wider than $\sim10R_{\odot}$, even with extreme shrinkage due to L2 outflows. Systems evolving towards tighter orbits become unstable and result in stellar mergers. This separation limit has direct implications for the properties of BBH mergers: long delay times ($\gtrsim1 \rm Gyr$), and no high BH spins from the tidal spin-up of helium stars. At high metallicity, the SMT channel may be severely quenched due to Wolf-Rayet winds. The reason for the separation limit lies in the stellar structure, not in binary physics. If the orbit gets too narrow during mass transfer, a dynamical instability is triggered by a rapid expansion of the remaining donor envelope due to its near-flat entropy profile. The closest separations can be achieved from core-He burning ($\sim8-15R_{\odot}$) and Main Sequence donors ($\sim15-30R_{\odot}$), while Hertzsprung Gap donors lead to wider orbits ($\gtrsim30-50R_{\odot}$) and non-merging BBHs. These outcomes and mass transfer stability are governed by the internal composition profiles of donor stars. Thus, the formation of compact binaries is a sensitive probe of chemical mixing in stars. We propose a simple treatment of mass transfer stability to reproduce the detailed results.

It has recently been proved that the category of N-manifolds of degree $n$, that is, $\mathbb N$-graded supermanifolds of degree $n$ for which the parity agrees with the gradation, is equivalent to the category of purely even $n$-tuple vector superbundles equipped with a suitable action of the symmetric group $S_n$ permuting the vector bundle structures. This equivalence may be interpreted as a `desuperization' of N-manifolds. In the present paper, we place this result within a broader framework of graded structures on supermanifolds and explicitly describe several canonical equivalences between the corresponding categories in a purely geometric, constructive manner. The desuperization equivalence functor appears as a composition of some of these canonical equivalences. Our constructions are entirely canonical and rely on standard tools of supergeometry, including iterated tangent functors, parity reversion in vector superbundles, and the interpretation of $n$-tuple vector bundles in terms of commuting Euler vector fields associated with the underlying vector bundle structures.

We perform a high-statistics lattice QCD calculation of the low-energy two-nucleon scattering amplitudes. In order to address discrepancies in the literature, the calculation is performed at a heavy pion mass in the limit that the light quark masses are equal to the physical strange quark mass, $m_π= m_K \simeq 714 $ MeV. Using a state-of-the-art momentum space method, we rule out the presence of a bound di-nucleon in both the isospin 0 (deuteron) and 1 (di-neutron) channels, in contrast with many previous results that made use of compact hexaquark creation operators. In order to diagnose the discrepancy, we add such hexaquark interpolating operators to our basis and find that they do not affect the determination of the two-nucleon finite volume spectrum, and thus they do not couple to deeply bound di-nucleons that are missed by the momentum-space operators. Further, we perform a high-statistics calculation of the HAL QCD potential on the same gauge ensembles and find qualitative agreement with our main results. We conclude that di-nucleons do not form bound states at heavy pion masses and that previous identification of deeply bound di-nucleons must have arisen from a misidentification of the spectrum from off-diagonal elements of a correlation function.

We report on Chandra X-ray observations of four narrow-line quasar candidates at z~6, selected from the SHELLQs project, based on the Subaru Hyper Suprime-Cam survey. These objects are characterised by narrow (FWHM<310 km/s), luminous (>1e44 erg/s) Lya and faint UV continuum (M_1450 = -22 - -21), prompting us to examine whether they are obscured luminous AGN at the epoch of reionization. However, none of these objects were detected by Chandra, giving an upper limit to their rest-frame 2-10 keV luminosity (Lx) of 2e44 erg/s (2 sigma), assuming a spectral slope Gamma=2. Subsequent rest-frame optical spectroscopy of these objects by the JWST-NIRSpec, presented in a companion paper, show weak broad Balmer emission at the base of narrow cores. With the scaling relation for low-redshift AGN, the observed strong [OIII]5007 flux of these sources would predict Lx to be around 1e45 erg/s, which is well above the Chandra upper limits. These optical spectra and X-ray quietness are reminiscent of JWST-selected broad-line AGN. We attribute the weak broad Balmer emission to the broad-line regions hidden partially by optically-thick obscuring matter which also hides the optical and X-ray continuum emission from the accretion disc. Compton-thick obscuration, which would strongly suppress X-ray emission, could be due to a dense inter-stellar medium that is often present in galaxies at high redshifts. Alternatively, the same effect could be obtained from an inflated disc at the innermost radii in a supercritical accretion flow, when the disc is viewed at inclined angles.

Ultra-high-energy cosmic rays (UHECR) scattering off the cosmic relic neutrino background have recently gained renewed interest in the literature. Current data suggest that (UHECR) are predominantly made of heavy nuclei. Similar to the coherent elastic neutrino-nucleus scattering (CE$ν$NS) observed at low-energy neutrino experiments, the cross section of heavy nucleus scattering off relic neutrinos will be coherently enhanced since the energy of relic neutrinos can reach $\sim O(10)$ MeV in the rest frame of the UHECR. We calculate the diffuse flux of relic neutrinos boosted by UHECR after taking into account the contributions from both coherent and incoherent scatterings. Using current data from IceCube and Pierre Auger Observatory, we place constraints on the overdensity of relic neutrinos down to $\sim 10^8$. Since the flux of boosted relic neutrinos peaks at an energy of $\sim 200\, \text{PeV}$, we also entertain the possibility to explain the recently observed KM3NeT event with boosted relic neutrinos from UHECR.

We explore the impact of finite-temperature quantum gravity effects on cosmological parameters, particularly the cosmological constant $Λ$, by incorporating temperature-dependent quantum corrections into the Hubble parameter. For that purpose, we modify the Cosmic Linear Anisotropy Solving System. We introduce new density parameters, $Ω_{Λ_2}$ and $Ω_{Λ_3}$, arising from finite-temperature quantum gravity contributions, and analyze their influence on the cosmic microwave background power spectrum using advanced machine learning techniques, including artificial neural networks and stochastic optimization. Our results reveal that $Ω_{Λ_2}$ assumes a negative value, consistent with dimensional regularization in renormalization and that the presence of $Ω_{Λ_2}$ as well as $Ω_{Λ_3}$ enhances model accuracy. Numerical analyses demonstrate that the inclusion of these parameters improves the fit to 2018 Planck data. Although further work is required, our results suggest that finite-temperature quantum gravity effects may play a non-negligible role in cosmological evolution. Although the Hubble tension persists, our findings highlight the potential of quantum gravitational corrections in refining cosmological models and motivate further investigation into higher-order thermal effects and polarization data constraints.

Detecting genuine multipartite entanglement (GME) is a state-characterization task that benchmarks coherence and experimental control in quantum systems. Existing GME tests often require joint measurements on many qubits, posing challenges for systems like time-bin encoded qubits and microwave photons from superconducting circuits, where qubit connectivity is limited or measurement noise grows with the number of jointly measured qubits. Here we introduce versatile GME and $k$-inseparability criteria applicable to any state, which only require measuring $O(n^2)$ out of $2^n$ (at most) $m$-body stabilizers of $n$-qubit target graph states, with $m$ upper-bounded by twice the graph's maximum degree. For cluster or ring-graph states, only constant-weight stabilizers are needed. Using semidefinite programming (and sometimes graph-local complementations), we can reduce the number or weight of required stabilizers. Analytical and numerical results show that our criteria are noise-robust and may infer state infidelity from certified $k$-inseparability in microwave photonic graph states generated under realistic conditions.

In this paper, we propose a multi-user downlink system for two users based on the orthogonal time frequency space (OTFS) modulation scheme. The design leverages the generalized singular value decomposition (GSVD) of the channels between the base station and the two users, applying precoding and detection matrices based on the right and left singular vectors, respectively. We derive the analytical expressions for three scenarios and present the corresponding simulation results. These results demonstrate that, in terms of bit error rate (BER), the proposed system outperforms the conventional multi-user OTFS system in two scenarios when using minimum mean square error (MMSE) equalizers or precoder, both for perfect channel state information and for a scenario with channel estimation errors. In the third scenario, the design is equivalent to zero-forcing (ZF) precoding at the transmitter.

We consider a mobile impurity coupled to an ideal Fermi gas in one spatial dimension through an attractive contact interaction. We calculate the quasi-particle residue $Z$ exactly, based on Bethe Ansatz and diagrammatic Monte Carlo methods, and with varational Ansatz up to one particle-hole excitation of the Fermi sea. We find that the exact quasi-particle residue vanishes in the thermodynamic limit as a power law in the number of particles, consistent with the Luttinger-liquid paradigm and the breakdown of Fermi-liquid theory. The variational Ansatz, however, predicts a finite value of $Z$, even in the thermodynamic limit. We also study how the presence of the impurity affects the density of the spin-up sea by calculating the pair correlation function. Subtracting the homogeneous background and integrating over all distances gives the charge $Q$. This charge turns out to grow continuously from 0 at zero coupling to 1 in the strong-coupling limit. The varational Ansatz predicts $Q=0$ at all couplings. So, although the variational Ansatz has been shown to be remarkably accurate for the energy and the effective mass, it fails even qualitatively when predicting $Z$ and the pair correlation function in the thermodynamic limit.

A heliocentric dust ring on Venus orbit was discovered following observations by the Helios spacecraft, and then confirmed thanks to observations by STEREO and the Parker Solar Probe. The impact risk it poses needs to be evaluated for any spacecraft crossing the ring. This study aims to provide a first model of the dust ring, in terms of distribution of particles (including size distribution), velocity, density of the ring, and deduce a first estimation of the impact risk to spacecrafts crossing the ring. We seek to describe the orbits of dust particles in the ring. We explore a first simple model, that leads us to propose a second, more elaborate, model. This model is then populated by particles that we integrate for 2000 years. We demonstrate that the dust ring will persist over the next 2000 years, only slightly extending radially and perpendicularly to the Venus orbital plane. We show that particles tend to accumulate at Venus orbit, but that along it the differences in density is negligible. We compute the number of particles we can expect to find in the ring. Finally, as an example, we apply this model to Bepi-Colombo to obtain a first estimate of the impact flux in function of radius and mass, for radii between 2 $μ$m and 2 cm (i.e. for masses between 10^-2 kg and 10^-14 kg). We also present the impact velocity and direction of impacts with respect to Bepi-Colombo. We are able to conclude that the ring seems to present a low risk for spacecrafts using Venus as a gravity assist.

We examine four dimensional, near-extremal black hole solutions in the presence of a finite boundary obeying conformal boundary conditions, where the conformal class of the induced metric and the trace of the extrinsic curvature are fixed. Working in Euclidean signature and at fixed charge, we find the near-extremal regime is dominated by a double-scaling limit which reveals new scaling laws for the quasi-local conformal entropy at low temperatures. Upon spherical dimensional reduction, we obtain the effective two-dimensional dilaton-gravity theory that describes the near-extremal regime. In contrast to Dirichlet boundaries, for conformal boundaries a linear dilaton potential is not sufficient to capture the leading correction away from extremality and higher orders are needed. We also examine near-Nariai solutions and the spherical reduction of pure three-dimensional gravity in (Anti-) de Sitter space. In the latter, provided the boundary is placed near the conformal boundary of three-dimensional Anti-de Sitter space, the dynamics of the spherically symmetric boundary mode is governed by a Liouville equation that descends from a (minus) Schwarzian effective action.

We present a modified simulated annealing method with a dynamical choice of the cooling temperature. The latter is determined via a closed-loop control and is proven to yield exponential decay of the entropy of the particle system. The analysis is carried out through kinetic equations for interacting particle systems describing the simulated annealing method in an extended phase space. Decay estimates are derived under the quasi-invariant scaling of the resulting system of Boltzmann-type equations to assess the consistency with their mean-field limit. Numerical results are provided to illustrate and support the theoretical findings.

We present the first three-dimensional theoretical model of microparticle-assisted super-resolution imaging, enabling accurate simulation of virtual image formation. The model reveals that accounting for partial spatial coherence of illumination is a fundamental prerequisite for achieving super-resolution. We also propose a novel illumination strategy based on suppressing the normal component of incident light, which enhances image contrast and resolution. It is shown that as the size of the investigated objects increases, the optical resolution of the microsphere improves. An analytical estimate for the resolution criterion in microsphere-assisted imaging is presented. The results establish a consistent wave-optical framework that reproduces experimentally observed subwavelength imaging and clarifies the underlying physical mechanisms.

Keratin composites enable animals to hike with hooves, fly with feathers, and sense with skin. These distinct functions arise from variations in the underlying properties and microscale arrangement of this natural polymer. One well-studied example is mammalian whiskers, elongated keratin rods attached to tactile skin structures that extend the animal's sensory volume. Here, we investigate the non-actuated whiskers that cover Asian elephant (Elephas maximus) trunks and find they are geometrically and mechanically tailored to facilitate tactile perception by encoding contact location in vibrotactile signal amplitude and frequency. Elephant whiskers emerge from armored trunk skin and shift from a thick, circular, porous, stiff root to a thin, ovular, dense, soft point. This smooth transition enables interaction with widely varying substrates, reduces wear, and increases the vibrotactile signal information generated during contact. The functionally graded geometry, porosity, and stiffness of elephant whiskers tune the neuromechanics of trunk touch, facilitating highly dexterous manipulation.

Hybrid systems play a crucial role in modeling real-world applications where discrete and continuous dynamics interact, including autonomous vehicles, power systems, and traffic networks. Safety verification for these systems requires determining whether system states can enter unsafe regions under given initial conditions and uncertainties, a question directly addressed by reachability analysis. However, hybrid systems present unique difficulties because their state space is divided into multiple regions with distinct dynamic models, causing traditional data-driven methods to produce inadequate over-approximations of reachable sets at region boundaries where dynamics change abruptly. This paper introduces a novel approach using hybrid zonotopes for data-driven reachability analysis of piecewise affine systems. Our method addresses the boundary transition problem by developing computational algorithms that calculate the family of set models guaranteed to contain the true system trajectories. Additionally, we extend and evaluate three methods for set-based estimation that account for input-output data with measurement noise.

The depth and coverage of the first years of JWST observations have revealed low luminosity active galactic nuclei (AGN) across a wide redshift range, shedding light on black hole (BH) assembly and feedback. We present our spectroscopic sample of 34 Type 1 AGN obtained from JADES survey data and spanning $1.5 < z < 9$. Our sample of AGN probes a BH mass range of $10^{6-9}$~M$_{\odot}$ at bolometric luminosities down to $10^{43}$~erg~s$^{-1}$, implying generally sub-Eddington ratios of $<0.5L_{\rm Edd}$. Most of these AGN are hosted in low mass ($M_{\star}\sim10^8$~M$_{\odot}$) galaxies and are overmassive relative to the local $M_{BH}-M_{\star}$ relation, while remaining consistent with the local $M_{BH}$-$σ_*$ relation. The wide redshift range provided by our sample allows us to trace the emergence of local $M_{BH}$-$M_*$ scaling relation across the cosmic epoch. Additionally, we explore the capability of narrow-line diagnostics in identifying Type 2 AGN and find that a significant fraction of our AGN would be missed by them due to low metallicity or lack of high energy ionizing photons (potentially due to dust absorption, dense gas blanketing the broad and narrow line regions, or intrinsically soft ionizing spectra). We explore the UV luminosity function of AGN and their hosts and find that it is subject to significant cosmic variance and is also dependent on the AGN bolometric luminosity. Finally, we show that the electron and Balmer scattering scenarios recently proposed to explain the broad components of the Balmer lines are untenable on multiple grounds. There is no evidence that the black hole masses have been overestimated by orders of magnitude as proposed in those scenarios.

Void galaxies are located in the most underdense environments of the Universe, where the number density of galaxies is extremely low. They are, hence, good targets for studying the secular evolution of galaxies and the slow buildup of stellar mass through star formation. To date, very little is known about their cold gas content, both molecular (H$_2$) gas and atomic hydrogen (HI) gas. We present CO (1--0) observations of the H$_2$ gas disk in CG 910, which lies in the Boötes void, one of the largest nearby voids at relatively low redshifts (z$\sim$0.04-0.05). We used the Combined Array for Research in Research in Millimeter Astronomy (CARMA) to study the CO(1-0) distribution and gas kinematics in CG 910. We also carried out atomic hydrogen observations of the galaxy using the Robert C. Byrd Green Bank Telescope (GBT). The CARMA CO(1-0) observations reveal a molecular gas disk of mass, M(H$_{2}$) $\sim$12.0$\pm$1.1$\times$10$^{9}$M$_{\odot}$ and diameter 7 kpc. The CO velocity field shows a regularly rotating disk with a flat rotation velocity of 256 kms$^{-1}$ with no clear signatures of interaction or gas accretion. This is possibly the first CO (1-0) map of a void galaxy, and hence, important for understanding the molecular gas distribution and kinematics in void galaxies. The GBT observations reveal a HI disk of mass, M(HI) $\sim$3.1$\pm$0.8$\times$10$^{9}$M$_{\odot}$, which is relatively small compared to its stellar mass of M$_{\star}\sim$21.5$\times$10$^{9}M_{\odot}$. The total gas mass fraction, (M(H$_2$)+M(HI))/$M_{\star}$ and the atomic gas mass fraction, M(HI)/M$_{\star}$ for CG 910 are 0.70 and 0.14, respectively. We conclude that CG 910 has a regularly rotating but massive molecular gas disk. The lower atomic gas mass fraction and star formation rate indicate a longer gas depletion timescale, confirming that CG 910 is slowly evolving compared to normal disk galaxies.