Daily Papers

Vacuum Kerr perturbations in general relativity have identical even- and odd-parity quasinormal frequencies. We establish this parity isospectrality for linear gravitoelectromagnetic perturbations of subextremal Kerr--Newman--de Sitter black holes, without a slow-rotation or small-charge expansion. We reconstruct the radiative metric and gauge-potential perturbations directly from gauge-invariant master variables in radiation gauge, without an intermediate complex potential.

We study linear perturbations of the Maldacena-Milekhin-Popov (MMP) wormhole in the parity sector that pairs axial metric perturbations with polar gauge perturbations. It contains the axial gravitational mode and the electric field along the magnetic field lines. The lowest Landau level (LLL) of the charged fermions responds through its charge. The gauge components a_τ, a_ρ form a two-dimensional gauge field on the worldsheet of each field line, and the fermions respond with the exact Schwinger current. Lifted over the sphere, it gives the electric field the MMP screening mass m_S^2=αq^2, which is not small and survives in the mouth. In the throat the perturbation tilts the worldsheets, and the Casimir stress tensor acquires mixed components. Force balance then requires a current across the field lines, and charge conservation fixes an accompanying polarisation current, the counterpart of the Hall current of the polar sector. These currents close the Bianchi identities at first order in the fermionic backreaction α. The system reduces to three coupled master equations, given in closed form and matched to the fermion-free mouth. Consistency alone does not select the fermionic constitutive relation, but locality, covariance and the index theorem do. At α=0 the throat reduces to Poschl-Teller problems with masses l(l-1) and (l+1)(l+2) at m_S^2=0. At finite m_S^2 one mode is screened, one tends to the mass l^2+l+2, and one neutral charge-density wave stays exactly massless. The O(α) shifts of the massive normal frequencies are real and negative. The two parity sectors are isospectral only without fermions. The neutral channel sees an attractive region in each mouth, and a numerical solution coupled to the gravitational channel in the exact mouth potential finds no bound state. The sector has no growing mode for lge2 at this order.

We study the pseudospectrum of the Kerr black hole for gravitational perturbations with spin weight s=2, the case of greatest interest in gravitational-wave astronomy. In the hyperboloidal framework with two-dimensional Chebyshev collocation, we formulate the quasinormal mode problem as a non-self-adjoint eigenvalue problem. For sneq0 the fields Ψ^{(s)} and Ψ^{(-s)} are independent, so the conserved current method yields no single-field energy norm. We overcome this with the Teukolsky--Starobinsky identities, which relate Ψ^{(-2)} to a fourth-order operator on Ψ^{(2)} and yield an H^2 energy norm after symmetrization. With the H^1 norm known for s=0, this suggests the pattern H^{|s|}, verified for s=0 and s=2. All results use an ω-independent two-field hierarchy. We find that the pseudospectrum tightens by 1.1 to 3.5 decades at each step of L^2to H^1to H^2, yet stays large in every norm. The s=+2 and s=-2 operators are isospectral but not isopseudospectral: at twelve of fourteen probes the ψ_0 resolvent exceeds the ψ_4 one by 0.19 to 0.82 decades in the H^2 norm, while at the two probes furthest along the QNM line the ordering reverses by 0.18 to 0.19 decades. The gravitational pseudospectrum exceeds the scalar one by 0.5 to 5.2 decades in the window minimum and by 5.9 decades in L^2 at ωM=0.47-0.17,i, while along the damping direction the s=2 resolvent is non-monotonic and the s=0 resolvent smooth. QNM spectral instability is therefore a universal feature of Kerr, and is stronger for gravitational perturbations.

If h is a ring-valued function on a simplicial complex G we can define two matrices L and g, where the matrix entries are the h energy of homoclinic intersections. We know that the sum over all h values on G is equal to the sum of the Green matrix entries g(x,y). We also have already seen that that the determinants of L or g are both the product of the h(x). In the case where h(x) is the parity of dimension, the sum of the energy values was the standard Euler characteristic and the determinant was a unit. If h(x) was the unit in the ring then L,g are integral quadratic forms which are isospectral and inverse matrices of each other. We prove here that the quadratic energy expression summing over all pairs h(x)^* h(y) of intersecting sets is a signed sum of squares of Green function entries. The quadratic energy expression is Wu characteristic in the case when h is dimension parity. For general h, the quadratic energy expression resembles an Ising Heisenberg type interaction. The conjugate of g is the inverse of L if h takes unit values in a normed ring or in the group of unitary operators in an operator algebra.

We show that pairs of widely separated interferometers are advantageous for measuring the Stokes parameter V of a stochastic background of gravitational waves. This parameter characterizes asymmetry of amplitudes of right- and left-handed waves and generation of the asymmetry is closely related to parity violation in the early universe. The advantageous pairs include LIGO(Livingston)-LCGT and AIGO-Virgo that are relatively insensitive to Omega_GW (the simple intensity of the background). Using at least three detectors, information of the intensity Omega_GW and the degree of asymmetry V can be separately measured.

An amplitude analysis of B^-rightarrow D^- D^0 K_S^0 decays is performed using proton-proton collision data, corresponding to an integrated luminosity of 9,fb^{-1}, collected with the LHCb detector at center-of-mass energies of 7, 8, and 13,Tekern -0.1em V. A resonant structure of spin-parity 0^+ is observed in the D^0 K_S^0 invariant-mass spectrum with a significance of 5.3,sigma. The mass and width of the state, modeled with a Breit-Wigner lineshape, are determined to be 2883pm11pm6,Mekern -0.1em V!/c^2 and 87_{-47}^{+22}pm6,Mekern -0.1em V respectively, where the first uncertainties are statistical and the second systematic. These properties and the quark content are consistent with those of the open-charm tetraquark state T_{cs 0}^{*}(2870)^0 observed previously in the D^+ K^- final state of the B^-rightarrow D^- D^+ K^- decay. This result confirms the existence of the T_{cs 0}^{*}(2870)^0 state in a new decay mode. The T_{cs1}^{*}(2900)^0 state, reported in the B^-rightarrow D^- D^+ K^- decay, is also searched for in the D^0 K_S^0 invariant-mass spectrum of the B^- rightarrow D^- D^0 K_S^0 decay, without finding evidence for it.

The eight-component relativistic wave equation for spin-1{2} particles of Robson and Staudte (FV1{2}), a Feshbach--Villars linearization of the Feynman--Gell-Mann equation, reproduces the Dirac hydrogenic spectrum with a doubled solution space and an indefinite inner product. Its exact Stark shifts must equal the Dirac ones; whether its indefinite-metric perturbation theory delivers them is not guaranteed. We compute the first- and second-order Stark shifts of the n=1--3 levels of hydrogenic ions from H to U^{91+} in the Schrödinger, Dirac and FV1{2} theories, evaluating all spectral sums, continuum included, by the Dalgarno--Lewis method. The FV1{2} and Dirac shifts coincide level by level, to working precision at first order (closed-form roots) and to 45 significant figures at second order. Both ingredients are needed: without the explicit spin--field coupling the first-order roots become complex, and without the negative-norm states the (Zα)^2 coefficient is wrong. Norm sign and parity are locked in the doubled space: a potential lifting the 2s_{1/2}--2p_{1/2} degeneracy needs its own spin--gradient term, and shifts placed by hand on the κ-labeled states give a spurious imaginary linear Stark shift. The relativistic linear Stark effect is smaller by finite factors, but a second-moment sum rule shows the non-relativistic linear Stark strength is conserved, the missing part reappearing in singular (Zα)^{-2} second-order terms. For levels with a fine-structure partner, an exact intra-shell/regular split of the second-order shift gives the (Zα)^0 coefficients analytically and relates the π^2 terms of the (Zα)^2 coefficients to the singular ones. The Dirac weak/strong-field crossover for n=2 of hydrogen lies near 2.8~kV cm^{-1}, and the perturbative window set by the fine structure grows as Z^5.

For a real quadratic field Q(d), we study the norm-form energy N = S_ζ^2 - d cdot S_L^2, where S_ζ and S_L are Lorentzian-weighted zero sums with w(ρ) = 2/(1/4 + γ^2). We prove three main results. (1) Spacelike spectral data: N < 0 unconditionally for all squarefree d > 1, as a consequence of a low-lying zero dominance theorem proved via explicit zero-counting. (2) Effective density bound: at each verified truncation level M, dens{N > 0} leq 2|f_{S_L^{(M)}}|_infty cdot (W_1(ζ)/d + ε_M), established unconditionally via Jacobi--Anger resonance analysis. (3) Exact asymptotic: under the computationally verified hypothesis that the infinite resonance lattice Λ_infty has finite rank (verified for M leq 20, where rank = 0), the sharp asymptotic dens{N > 0} = C(d)/d + o(1/d) holds. For d = 5, C(5) = 2,f_{S_L}(0)cdotE[|S_ζ|] = 0.1191; the constant depends on d through the zeros of L(s,χ_d), and C(d) = O(1/log d) as d to infty.

We compute Kerr-Newman quasinormal modes using a recently found exact separation of the gravitoelectric perturbation equations. For each spin-label ς=pm1, a matrix angular ordinary differential equation and a scalar second-order radial ordinary differential equation define a joint spectral problem for the complex frequency ω and separation constant λ. We solve this problem by imposing regularity at the angular poles, ingoing behavior at the event horizon, and outgoing behavior at infinity. We benchmark the numerical code built to solve the separated equations, and the resulting frequencies, against recently published spectral calculations of the coupled system. Comparisons with those results yield absolute differences of order 10^{-10} to 10^{-5}, depending on the BH parameters and overtone number. We also find numerical hints of spin-label isospectrality in both the electromagnetic-led and gravitational-led sectors of fundamental quasinormal modes, even at near-extremal Kerr-Newman configurations. These results provide numerical evidence that the separated equations reproduce Kerr-Newman quasinormal frequencies and offer a practical route to exploring the ringdown of rotating, charged black holes.

The Stokes V parameter characterizes asymmetry of amplitudes between right- and left-handed waves, and non-vanishing value of the V parameter yields a circularly polarized signal. Cosmologically, V parameter may be a direct probe for parity violation in the universe. In this paper, we theoretically investigate a measurement of this parameter, particularly focusing on the gravitational-wave backgrounds observed via ground-based interferometers. In contrast to the traditional analysis that only considers the total amplitude (or equivalently Omega_{GW}), the signal analysis including a circular-polarized mode has a rich structure due to the multi-dimensionality of target parameters. We show that, by using the network of next-generation detectors, separation between polarized and unpolarized modes can be performed with small statistical loss induced by their correlation.

Hyperspectral pansharpening has received much attention in recent years due to technological and methodological advances that open the door to new application scenarios. However, research on this topic is only now gaining momentum. The most popular methods are still borrowed from the more mature field of multispectral pansharpening and often overlook the unique challenges posed by hyperspectral data fusion, such as i) the very large number of bands, ii) the overwhelming noise in selected spectral ranges, iii) the significant spectral mismatch between panchromatic and hyperspectral components, iv) a typically high resolution ratio. Imprecise data modeling especially affects spectral fidelity. Even state-of-the-art methods perform well in certain spectral ranges and much worse in others, failing to ensure consistent quality across all bands, with the risk of generating unreliable results. Here, we propose a hyperspectral pansharpening method that explicitly addresses this problem and ensures uniform spectral quality. To this end, a single lightweight neural network is used, with weights that adapt on the fly to each band. During fine-tuning, the spatial loss is turned on and off to ensure a fast convergence of the spectral loss to the desired level, according to a hysteresis-like dynamic. Furthermore, the spatial loss itself is appropriately redefined to account for nonlinear dependencies between panchromatic and spectral bands. Overall, the proposed method is fully unsupervised, with no prior training on external data, flexible, and low-complexity. Experiments on a recently published benchmarking toolbox show that it ensures excellent sharpening quality, competitive with the state-of-the-art, consistently across all bands. The software code and the full set of results are shared online on https://github.com/giu-guarino/rho-PNN.

With the aim of testing massive gravity in the context of black hole physics, we investigate the gravitational radiation emitted by a massive particle plunging into a Schwarzschild black hole from slightly below the innermost stable circular orbit. To do so, we first construct the quasinormal and quasibound resonance spectra of the spin-2 massive field for odd and even parity. Then, we compute the waveforms produced by the plunging particle and study their spectral content. This allows us to highlight and interpret important phenomena in the plunge regime, including (i) the excitation of quasibound states, with particular emphasis on the amplification and slow decay of the post-ringdown phase of the even-parity dipolar mode due to harmonic resonance; (ii) during the adiabatic phase, the waveform emitted by the plunging particle is very well described by the waveform emitted by the particle living on the innermost stable circular orbit, and (iii) the regularized waveforms and their unregularized counterparts constructed from the quasinormal mode spectrum are in excellent agreement. Finally, we construct, for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle, the regularized multipolar waveforms, i.e., the waveforms constructed by summing over partial waveforms.

Informational completeness (IC) guarantees that an inverse exists, not that it is statistically well conditioned. For minimal rank-one Weyl--Heisenberg (WH) measurements, covariance makes the nonidentity projector-Gram spectrum proportional to the fiducial's ambiguity intensities, with eigenvalues \(d|χ_ϕ(u)|^2\), turning stability into an explicit worst-direction design problem; write \(λ\) for its smallest nonidentity eigenvalue. Haar fiducials are IC almost surely while \(\mathbb E[λ^{-1}]=\infty\), and an explicit geometric family used to establish balanced informationally complete measurements in every dimension has a normalized spectral floor bounded above by an exponentially decaying envelope. We then construct a hierarchy of minimal measurements. A cyclic family with exactly \(d^2\) outcomes in every integer dimension has floors \(Θ(d^{-3})\) for odd \(d\) and \(Θ(d^{-5})\) for even \(d\); a finite-field family for \(q=2^m\) obeys the uniform bound \(λ\ge4/9\). Our main result treats every prime-power dimension of characteristic \(p\ge5\). A balanced one-coordinate perturbation repairs the zero ambiguity axis of a cubic Alltop state, gives an attained floor uniformly bounded below by a positive constant, and confines the entire nonidentity spectrum to \([L_q,U_q]\) with \(U_q/L_q\to1\). Its SIC-normalized minimum tends to one, and \(λ(ϕ_q)/Λ_q^\star\to1\) for the global finite-field WH max--min optimum \(Λ_q^\star\), without assuming SIC existence. The complete spectrum determines the exact finite-sample Hilbert--Schmidt error of canonical linear inversion at \(I/d\), while its lower edge controls local Fisher efficiency and canonical-shadow bounds.

Enantiomers share atoms, bonds, and pairwise distances yet can behave differently in chiral environments, so molecular encoders must respect atom relabelings and proper rotations without becoming blind to reflection. We introduce GSF-χ, a graph transformer in which stereogenic units modulate all pairwise interactions rather than single out one atom as special. Each central or axial stereogenic unit creates a reflection-even phase field over all atoms, a handedness pseudoscalar χ sets the direction of a relative rotation on latent query--key blocks, giving a Chiral-RoPE that reflection inverts rather than leaves fixed. A C_2 projection separates mirror-even ECD peak counts and positions from mirror-odd peak signs. We prove the operator's even--odd decomposition and its annotation-inversion, permutation, and unit-order identities under explicit canonical-role conditions; property tests and a coordinate-reflection audit verify the laws end to end. GSF-χ leads every central-ECD output and improves axial Rotation and Symbol by 12.6% and 7.9% over the strongest baseline. Equal-budget controls attribute the Rotation advantage to global signed support rather than parameter or edge count; the C_2 projection yields exact enantiomer-pair consistency at a small raw-accuracy cost under complete supervision and becomes predictive when mirror supervision is scarce.

We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of estimation phase approaches Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cram\'er-Rao bound of the SU(1,1) interferometer.

Chirality plays an important role in many optical phenomena, and it is crucial to have efficient and accurate numerical algorithms to simulate solutions in this setting. In this paper, we discuss a High-Order Spectral method coupled to geometric regular perturbation theory, which results in just such a method. We view the chirality of the laterally periodic, constant permittivity/permeability structure as deviating from a background value, and demonstrate analyticity of the field scattered by a plane electromagnetic wave with respect to this deformation. This analyticity is not only with respect to chirality deformations of arbitrarily large real size, but also joint in the spatial variables. We also show how the High--Order Perturbation of Envelopes (HOPE) recursions, which we used to establish these results, can be implemented as a rapid, robust, and reliable numerical algorithm.

This paper presents the first numerical realization of Suzuki's Weil-Quadratic-Form operator, a candidate for the Hilbert--Pólya program linking spectral positivity to the Riemann Hypothesis (RH). Suzuki's 2026 construction was purely theoretical; here, the operator is instantiated via P1 finite-element discretization and Richardson extrapolation. Key results include: (R1) In the prime-free regime, the spectrum follows a closed Archimedean law A_k(a) = log(1/a) + log(k-2) + B_0 + O(a), with B_0 = log q - 2log 2, confirmed to 30-digit precision. (R2) A Mellin double-pole argument proves the head coefficient B(ν) and shows B_0 depends only on the conductor q, independent of the Archimedean parameter. (R2b) The degree d of an L-function appears directly as the logarithmic slope of the spectrum. (R3) Total spectral intensity follows the prime number theorem, S(a) sim (2a)^3/6. (R4) Nontrivial zeros are not eigenvalues but occur in the explicit-formula error term of the prime symbol. (R5) The best-match line σ^*(a) descends toward the critical line. (R6) Weil's positivity criterion is realized in operator form: bounded residual growth corresponds to all zeros on the line, while an injected off-line zero causes exponential blow-up. (R7) The lowest eigenvalue λ_1(a) is strictly positive, decays superexponentially, and passes smoothly through the first prime threshold. (R8) The characteristic function W(a,0;z) is computed for the first time, with all zeros confirmed real. (R9) Indirect traces of GUE statistics appear in the moment structure, even where direct detection is blocked. The authors emphasize that this work does not prove RH. All results are Archimedean and universal, with significance lying in the faithful numerical realization of classical identities rather than new arithmetic.

Hyperspectral pansharpening consists of fusing a high-resolution panchromatic band and a low-resolution hyperspectral image to obtain a new image with high resolution in both the spatial and spectral domains. These remote sensing products are valuable for a wide range of applications, driving ever growing research efforts. Nonetheless, results still do not meet application demands. In part, this comes from the technical complexity of the task: compared to multispectral pansharpening, many more bands are involved, in a spectral range only partially covered by the panchromatic component and with overwhelming noise. However, another major limiting factor is the absence of a comprehensive framework for the rapid development and accurate evaluation of new methods. This paper attempts to address this issue. We started by designing a dataset large and diverse enough to allow reliable training (for data-driven methods) and testing of new methods. Then, we selected a set of state-of-the-art methods, following different approaches, characterized by promising performance, and reimplemented them in a single PyTorch framework. Finally, we carried out a critical comparative analysis of all methods, using the most accredited quality indicators. The analysis highlights the main limitations of current solutions in terms of spectral/spatial quality and computational efficiency, and suggests promising research directions. To ensure full reproducibility of the results and support future research, the framework (including codes, evaluation procedures and links to the dataset) is shared on https://github.com/matciotola/hyperspectral_pansharpening_toolbox, as a single Python-based reference benchmark toolbox.

Hyperspectral unmixing (HU) is a very useful and increasingly popular preprocessing step for a wide range of hyperspectral applications. However, the HU research has been constrained a lot by three factors: (a) the number of hyperspectral images (especially the ones with ground truths) are very limited; (b) the ground truths of most hyperspectral images are not shared on the web, which may cause lots of unnecessary troubles for researchers to evaluate their algorithms; (c) the codes of most state-of-the-art methods are not shared, which may also delay the testing of new methods. Accordingly, this paper deals with the above issues from the following three perspectives: (1) as a profound contribution, we provide a general labeling method for the HU. With it, we labeled up to 15 hyperspectral images, providing 18 versions of ground truths. To the best of our knowledge, this is the first paper to summarize and share up to 15 hyperspectral images and their 18 versions of ground truths for the HU. Observing that the hyperspectral classification (HyC) has much more standard datasets (whose ground truths are generally publicly shared) than the HU, we propose an interesting method to transform the HyC datasets for the HU research. (2) To further facilitate the evaluation of HU methods under different conditions, we reviewed and implemented the algorithm to generate a complex synthetic hyperspectral image. By tuning the hyper-parameters in the code, we may verify the HU methods from four perspectives. The code would also be shared on the web. (3) To provide a standard comparison, we reviewed up to 10 state-of-the-art HU algorithms, then selected the 5 most benchmark HU algorithms, and compared them on the 15 real hyperspectral datasets. The experiment results are surely reproducible; the implemented codes would be shared on the web.

We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho{rmr}ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.

In this paper we construct the canonical harmonic coordinates of the Kerr metric within the multipolar post-Minkowskian (MPM) formalism to the fourth post-Minkowskian (4PM) order. Based on the well known Geroch--Hansen moments of Kerr metric and Gürsel's theorem, we derive the exact canonical MPM moments M_L,S_L, which are free of any gauge moments. With these moments, we iteratively compute the gothic metric perturbation h^{μν}_{can} up to 4PM order and compute the 4PM canonical metric g_{μν}^{can}. The resulting spatial and time components of these metrics are even functions of the spin parameter a while the mixed components are odd. This parity property distinguishes the canonical coordinates from other harmonic coordinates. To contrast this minimal-gauge construction, we also extract the 1PM source moments of the Kerr metric in the Jiang--Lin coordinates. We find that the Jiang--Lin representation possesses non-vanishing gauge moments starting from the 1PM order, whereas in the canonical representation gauge moments vanish to all orders. This comparison highlights the canonical coordinates as the most gauge-pure representation of the Kerr metric in the MPM framework. The complete canonical metric for the Schwarzschild case is also computed to all PM orders. A recent independent construction by Damgaard et al. using momentum-space recursion yields 4PM equivalent results expressed as a power series in a, providing a cross-validation of our closed-form 4PM canonical metric. The coordinate transformation linking the canonical Kerr coordinates to previously known harmonic Kerr coordinates remains an open problem.

Like general relativity, metric-affine gravity should be a viable effective quantum theory, otherwise it is a mathematical curiosity without physical application. Assuming a perturbative quantum field theory, the universal, flat limit of metric-affine gravity offers a good foundation for model-building only when symmetry constraints are themselves sufficient to get rid of ghosts and tachyons in the spectrum of propagating particle states, without requiring any further tuning of the couplings. Using this symmetry-first criterion, we find that for parity-preserving models with a totally symmetric distortion, only massless spin-one and spin-three modes are possible besides the graviton. Moreover, no viable models result from gauge symmetries generated by a scalar field.

In recent years, the demand for hyperspectral imaging devices has grown significantly, driven by their ability of capturing high-resolution spectral information. Among the several possible optical designs for acquiring hyperspectral images, there is a growing interest in interferometric spectral imaging systems based on division of aperture. These systems have the advantage of capturing snapshot acquisitions while maintaining a compact design. However, they require a careful calibration to operate properly. In this work, we present the interferometer response characterization algorithm (IRCA), a robust three-step procedure designed to characterize the transmittance response of multi-aperture imaging spectrometers based on the interferometry of Fabry-Perot. Additionally, we propose a formulation of the image formation model for such devices suitable to estimate the parameters of interest by considering the model under various regimes of finesse. The proposed algorithm processes the image output obtained from a set of monochromatic light sources and refines the results using nonlinear regression after an ad-hoc initialization. Through experimental analysis conducted on four different prototypes from the Image SPectrometer On Chip (ImSPOC) family, we validate the performance of our approach for characterization. The associated source code for this paper is available at https://github.com/danaroth83/irca.

We investigate the exceptional points (EPs) and their pseudospectra in black hole perturbation theory. By considering a Gaussian bump modification to the Regge-Wheeler potential with variable amplitude, position, and width parameters, (varepsilon,d,σ_0), a continuous line of EPs (exceptional line, EL) in this three-dimensional parameter space is revealed. We find that the vorticity ν=pm1/2 and the Berry phase γ=π for loops encircling the EL, while ν=0 and γ=0 for those do not encircle the EL. Through matrix perturbation theory, we prove that the ε-pseudospectrum contour size scales as ε^{1/q} at an EP, where q is the order of the largest Jordan block of the Hamiltonian-like operator, contrasting with the linear ε scaling at non-EPs. Numerical implements confirm this observation, demonstrating enhanced spectral instability at EPs for non-Hermitian systems including black holes.

In this paper, we first study the consequence of spacetime translations and Lorentz transformations on Celestial CFT OPEs. Working with the light transforms of the operators belonging to the modified Mellin basis, we found that the leading order singularity in the OPE of such operators could be fixed purely using Poincaré symmetries owing to the non-trivial action of the translations on these operators. The OPE coefficient is then fixed using the soft limit of the correlation functions. We check that this singular structure obtained from symmetries is consistent with the OPE limit of three-point functions. This approach could potentially be useful for studying Celestial CFT without adverting to bulk physics. As another goal, we explore the significance of light transformation in Carrollian CFTs. In the special cases we considered, we show that light transformation equips us with a map between two branches of Carroll CFT in d=3 dimension at the level of correlation functions in the near coincident limit.

In the applications of proxy-SU(3) model in the context of determining (beta,gamma) values for nuclei across the periodic table, for understanding the preponderance of triaxial shapes in nuclei with Z ge 30, it is seen that one needs not only the highest weight (hw) or leading SU(3) irreducible representation (irrep) (lambda_H, mu_H) but also the lower SU(3) irreps (lambda ,mu) such that 2lambda + mu =2lambda_H + mu_H-3r with r=0,1 and 2 [Bonatsos et al., Symmetry {\bf 16}, 1625 (2024)]. These give the next highest weight (nhw) irrep, next-to-next highest irrep (nnhw) and so on. Recently, it is shown that for nuclei with 32 le Z,N le 46, there will be not only proxy-SU(3) but also proxy-SU(4) symmetry [Kota and Sahu, Physica Scripta {\bf 99}, 065306 (2024)]. Following these developments, presented in this paper are the SU(3) irreps (lambda ,mu) with 2lambda + mu =2lambda_H + mu_H-3r, r=0,1,2 for various isotopes of Ge, Se, Kr, Sr, Zr, Mo, Ru and Pd (with 32 le N le 46) assuming good proxy-SU(4) symmetry. A simple method for obtaining the SU(3) irreps is described and applied. The tabulations for proxy-SU(3) irreps provided in this paper will be useful in further investigations of triaxial shapes in these nuclei.

We study a variant of quantum hypothesis testing wherein an additional 'inconclusive' measurement outcome is added, allowing one to abstain from attempting to discriminate the hypotheses. The error probabilities are then conditioned on a successful attempt, with inconclusive trials disregarded. We completely characterise this task in both the single-shot and asymptotic regimes, providing exact formulas for the optimal error probabilities. In particular, we prove that the asymptotic error exponent of discriminating any two quantum states ρ and σ is given by the Hilbert projective metric D_{max}(ρ|σ) + D_{max}(σ| ρ) in asymmetric hypothesis testing, and by the Thompson metric max { D_{max}(ρ|σ), D_{max}(σ| ρ) } in symmetric hypothesis testing. This endows these two quantities with fundamental operational interpretations in quantum state discrimination. Our findings extend to composite hypothesis testing, where we show that the asymmetric error exponent with respect to any convex set of density matrices is given by a regularisation of the Hilbert projective metric. We apply our results also to quantum channels, showing that no advantage is gained by employing adaptive or even more general discrimination schemes over parallel ones, in both the asymmetric and symmetric settings. Our state discrimination results make use of no properties specific to quantum mechanics and are also valid in general probabilistic theories.

Risk parity, also known as equal risk contribution, has recently gained increasing attention as a portfolio allocation method. However, solving portfolio weights must resort to numerical methods as the analytic solution is not available. This study improves two existing iterative methods: the cyclical coordinate descent (CCD) and Newton methods. We enhance the CCD method by simplifying the formulation using a correlation matrix and imposing an additional rescaling step. We also suggest an improved initial guess inspired by the CCD method for the Newton method. Numerical experiments show that the improved CCD method performs the best and is approximately three times faster than the original CCD method, saving more than 40% of the iterations.

We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of {\pi}/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincar\'e sphere, showing that the number of near-optimal solutions behaves according to a power law with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vector-like optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.

We consider the possibility that gravity breaks parity, with left and right handed gravitons coupling to matter with a different Newton's constant and show that this would affect their zero-point vacuum fluctuations during inflation. Should there be a cosmic background of gravity waves, the effect would translate into anomalous CMB polarization. Non-vanishing TB (and EB) polarization components emerge, revealing interesting experimental targets. Indeed if reasonable chirality is present a TB measurement would provide the easiest way to detect a gravitational wave background. We speculate on the theoretical implications of such an observation.

Single hyperspectral image super-resolution (single-HSI-SR) aims to restore a high-resolution hyperspectral image from a low-resolution observation. However, the prevailing CNN-based approaches have shown limitations in building long-range dependencies and capturing interaction information between spectral features. This results in inadequate utilization of spectral information and artifacts after upsampling. To address this issue, we propose ESSAformer, an ESSA attention-embedded Transformer network for single-HSI-SR with an iterative refining structure. Specifically, we first introduce a robust and spectral-friendly similarity metric, \ie, the spectral correlation coefficient of the spectrum (SCC), to replace the original attention matrix and incorporates inductive biases into the model to facilitate training. Built upon it, we further utilize the kernelizable attention technique with theoretical support to form a novel efficient SCC-kernel-based self-attention (ESSA) and reduce attention computation to linear complexity. ESSA enlarges the receptive field for features after upsampling without bringing much computation and allows the model to effectively utilize spatial-spectral information from different scales, resulting in the generation of more natural high-resolution images. Without the need for pretraining on large-scale datasets, our experiments demonstrate ESSA's effectiveness in both visual quality and quantitative results.

The charmonium-like exotic states Y(4230) and the less known Y(4320), produced in e^+e^- collisions, are sources of positive parity exotic hadrons in association with photons or pseudoscalar mesons. We analyze the radiative and pion decay channels in the compact tetraquark scheme, with a method that proves to work equally well in the most studied D^*to γ/π+D decays. The decay of the vector Y into a pion and a Z_c state requires a flip of charge conjugation and isospin that is described appropriately in the formalism used. Rates however are found to depend on the fifth power of pion momentum which would make the final states πZ_c(4020) strongly suppressed with respect to πZ_c(3900). The agreement with BES III data would be improved considering the πZ_c(4020) events to be fed by the tail of the Y(4320) resonance under the Y(4230). These results should renovate the interest in further clarifying the emerging experimental picture in this mass region.

We use the extrapolate dictionary to revisit the spectrum of operators in Celestial CFT. Under the Celestial CFT map, each state in the 4D Hilbert space should map to one in the 2D Hilbert space. This implies that, beyond the familiar single particle states/operators, there should be multiparticle operators appearing in the celestial OPE. We extend the existing flat-space dictionary by constructing composite primaries from both Carrollian and Celestial perspectives. In the process, we demonstrate some subtleties in deriving the Poincaré primary condition from the Carrollian limit, clarify the compatibility of principal series representations with highest weight representations and unitarity in Celestial CFT, and discuss how the celestial OPE block expansion emerges from a 2D CFT standpoint.

The Kramers-Kronig relations are a pivotal foundation of linear optics and atomic physics, embedding a physical connection between the real and imaginary components of any causal response function. A mathematically equivalent, but simpler, approach instead utilises the Hilbert transform. In a previous study, the Hilbert transform was applied to absorption spectra in order to infer the sole refractive index of an atomic medium in the absence of an external magnetic field. The presence of a magnetic field causes the medium to become birefringent and dichroic, and therefore it is instead characterised by two refractive indices. In this study, we apply the same Hilbert transform technique to independently measure both refractive indices of a birefringent atomic medium, leading to an indirect measurement of atomic magneto-optical rotation. Key to this measurement is the insight that inputting specific light polarisations into an atomic medium induces absorption associated with only one of the refractive indices. We show this is true in two configurations, commonly referred to in literature as the Faraday and Voigt geometries, which differ by the magnetic field orientation with respect to the light wavevector. For both cases, we measure the two refractive indices independently for a Rb thermal vapour in a 0.6 T magnetic field, finding excellent agreement with theory. This study further emphasises the application of the Hilbert transform to the field of quantum and atomic optics in the linear regime.

Recently, Hastings & Haah introduced a quantum memory defined on the honeycomb lattice. Remarkably, this honeycomb code assembles weight-six parity checks using only two-local measurements. The sparse connectivity and two-local measurements are desirable features for certain hardware, while the weight-six parity checks enable robust performance in the circuit model. In this work, we quantify the robustness of logical qubits preserved by the honeycomb code using a correlated minimum-weight perfect-matching decoder. Using Monte Carlo sampling, we estimate the honeycomb code's threshold in different error models, and project how efficiently it can reach the "teraquop regime" where trillions of quantum logical operations can be executed reliably. We perform the same estimates for the rotated surface code, and find a threshold of 0.2%-0.3% for the honeycomb code compared to a threshold of 0.5%-0.7% for the surface code in a controlled-not circuit model. In a circuit model with native two-body measurements, the honeycomb code achieves a threshold of 1.5% < p <2.0%, where p is the collective error rate of the two-body measurement gate - including both measurement and correlated data depolarization error processes. With such gates at a physical error rate of 10^{-3}, we project that the honeycomb code can reach the teraquop regime with only 600 physical qubits.

Polarization analysis in x-ray spectroscopy provides an orientation dependent sensitivity to local bonding environments. For a cluster of atoms, polarization sensitivity is most often discussed through the lens of point group symmetries. However, this is a discrete, qualitative method of classifying clusters, and it does little to indicate the degree of spectral anisotropy. Here we adopt a random forest model for quantitative prediction of spectral anisotropy. Its input relies on simplified local geometric and chemical information that can be obtained from any crystal structure file. The model is trained on over 10,000 experimentally realized transition metal structures from the Materials Project, with the target being VtC-XES calculated using the real space Green's function code FEFF. We find that the model can strongly predict the degree of spectral anisotropy, with the primary factors being derived from the spatial moments of ligands in a cluster.

For a vertex v of a graph G, the triangle-degree td_G(v) is the number of triangles containing v. A graph is triangle-distinct, or K_3-irregular, if its vertex triangle-degrees are pairwise distinct. Chartrand, Erdős, and Oellermann asked whether a regular K_3-irregular graph exists. We prove that such graphs exist for every regularity rge 9. More precisely, for every integer kge 15 we construct a 2k-regular triangle-distinct graph on 4k+2 vertices; complementation gives a (2k+1)-regular example of the same order. The construction uses two antiregular threshold blocks joined by a zero-one matrix with prescribed margins, followed by matrix 2-switches that preserve those margins. After a uniform reference perturbation, exactly three triangle-degree collisions remain. Switches chosen according to parity remove two of them, and the last possible collision is controlled by a short quadratic discriminant argument. Odd kge 17 and even kge 62 are handled symbolically, while the remaining 24 values are settled by exact finite verification. Together with the known examples for 9le rle 29, this closes the positive existence problem for every rge 9.

External potentials break the translational invariance of nonlinear Schrödinger (NLS) equations and generally convert a continuous family of standing wave solutions into isolated pinned states. We study this mechanism for the prototypical case of a kink in the NLS equation with competing focusing cubic and defocusing quintic nonlinearities. The Lyapunov--Schmidt reduction method is used to prove that the location s_0 of the pinned kinks is selected near roots of an effective potential V_{rm eff}(s). We then determine how the translational zero eigenvalue of the Jacobian operator splits under the perturbation and prove that the sign of V_{rm eff}'(s_0) distinguishes eigendirections of positive and negative energy. We further show that if the Jacobian operator admits a negative eigenvalue, then the stability problem contains a real unstable eigenvalue. The derivation of the asymptotic expansion for the unstable eigenvalue is nonstandard because the zero eigenvalue is embedded in the continuous spectrum of the linearized operator. Finally, we show that the persistence of kinks lacks parity symmetry even if the external potential is odd. Numerical continuation, spectral computations with domains adapted to the slowly decaying eigenfunctions, and direct dynamical simulations of the time evolution corroborate the analytical predictions for different representative examples.

We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system for metrology applications without complete knowledge of the quantum state. We implement the algorithm to study quantum spin ensembles. We first focus on Dicke states, where our findings challenge and complement previous results in the literature. We then investigate states generated during the one-axis twisting dynamics, where in particular we find that the metrological power of the so-called multi-headed cat states can be certified using simple collective spin observables, such as fourth-order moments for small systems, and parity measurements for arbitrary system sizes.

We present a new method for generating emission spectra from polycyclic aromatic hydrocarbons (PAHs) in arbitrary radiation fields. We utilize the single-photon limit for PAH heating and emission to treat individual photon absorptions as independent events. This allows the construction of a set of single-photon emission "basis spectra" that can be scaled to produce an output emission spectrum given any input heating spectrum. We find that this method produces agreement with PAH emission spectra computed accounting for multi-photon effects to within simeq10% in the 3-20~{rm mu m} wavelength range for radiation fields with intensity U<100. We use this framework to explore the dependence of PAH band ratios on the radiation field spectrum across grain sizes, finding in particular a strong dependence of the 3.3 to 11.2~mum band ratio on radiation field hardness. A Python-based tool and a set of basis spectra that can be used to generate these emission spectra are made publicly available.

Transformers, with their attention mechanisms, have emerged as the state-of-the-art architectures of sequential modeling and empirically outperform feed-forward neural networks (FFNNs) across many fields, such as natural language processing and computer vision. However, their generalization ability, particularly for low-sensitivity functions, remains less studied. We bridge this gap by analyzing transformers on the k-parity problem. Daniely and Malach (NeurIPS 2020) show that FFNNs with one hidden layer and O(nk^7 log k) parameters can learn k-parity, where the input length n is typically much larger than k. In this paper, we prove that FFNNs require at least Omega(n) parameters to learn k-parity, while transformers require only O(k) parameters, surpassing the theoretical lower bound needed by FFNNs. We further prove that this parameter efficiency cannot be achieved with fixed attention heads. Our work establishes transformers as theoretically superior to FFNNs in learning parity function, showing how their attention mechanisms enable parameter-efficient generalization in functions with low sensitivity.

We report on an extraction of the polarized photoproduction cross-section for the proton, deuteron, neutron and ^3He, obtained by extrapolating electron scattering data to the real photon point. The data are from the Jefferson Lab E97-110 (^3He) and CLAS EG4 (proton and deuteron) experiments. Information on the neutron is extracted from the deuteron or ^3He data using the weak binding approximation. Comparing with data obtained with real photons, we find that while the proton results agree, our results on the deuteron and the neutron exhibit a larger strength in the Δ(1232) region, and are more consistent with isospin symmetry when compared with the proton results.

We study superspace concentration as a quantum resource, formalized through the focus measure F(ho) = λ_max(ho_super) - the largest eigenvalue of the reduced superspace state - which quantifies the capacity of a quantum system to concentrate informational weight into a preferred subspace of an extended degree-of-freedom space. We develop a complete resource-theoretic framework around this measure and validate its properties through GPU-accelerated numerical simulation. Analytic decoherence predictions are confirmed to machine precision (1.11 x 10^{-16}) for superspace dimensions dS in {2,4,8,16,32}. Focus monotonicity holds across 10,000 random states with zero violations under four focus-non-generating channels across six system configurations. Focused quantum states resist coherent unitary attacks with significantly greater resilience than standard fidelity predicts, with focus remaining above 0.9 at attack strength ε = 0.302 versus ε = 0.174 for fidelity. We further demonstrate that the focus measure and the U(dS)-asymmetry measure are operationally distinct: asymmetry remains near zero and provides no robustness signal under coherent and targeted attacks while focus tracks spectral concentration and remains robust until ε > 0.3. The connection between Grover's algorithm and superspace concentration is made explicit via the identity F(|ψ_k><ψ_k|) = P(marked), providing a resource-theoretic interpretation of oracle query complexity. Finally, we provide the first numerical characterization of the focus capacity gap ΔF, identifying a log_2(dS) scaling law confirmed for both product and correlated noise channels.

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U(1) gauge transformations that asymptotically approach an arbitrary function varepsilon(z,z) on the conformal sphere at future null infinity (mathscr I^+) but are independent of the retarded time. The value of varepsilon at past null infinity (mathscr I^-) is determined from that on mathscr I^+ by the condition that it take the same value at either end of any light ray crossing Minkowski space. The varepsilonneq constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U(1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.

Machine-learning models trained directly on electronic spectra can predict spin--orbit-driven properties, yet models with comparable predictive accuracy may learn different electronic dependencies. We examine this problem using magnetic anisotropy in atomic-scale magnets and a validation strategy designed to assess the physical relevance of learned spectral relationships. We compare a bidirectional gated recurrent unit and a one-dimensional convolutional neural network, both trained to predict magnetic anisotropy energy (MAE) from spin- and orbital-resolved scalar-relativistic densities of states (SR-DOS). Despite comparable in-domain (ID) accuracy, the architectures learn only partly overlapping spectral dependencies. Shapley additive explanations identify spectral features shared between the two architectures that can be associated with plausible spin--orbit-coupling pathways consistent with second-order perturbation theory (PT2). Adding PT2-derived MAE contributions to the model inputs has little effect on ID performance but can improve transfer beyond the training domain, with gains differing between architectures. Controlled spectral perturbations further demonstrate that similar attribution patterns do not imply the same functional dependence of the predicted MAE on spectral weight. The contrasting responses provide a functional context for architecture-dependent out-of-domain transfer. End-to-end learning can identify candidate electronic signatures of magnetic anisotropy. Their credible microscopic interpretation, however, rests on convergent evidence from predictive performance, model comparison, physical theory, controlled spectral interventions, and evaluation under distribution shift.

We present an initial analysis of the properties of the all-sky image obtained by the Far-Infrared Surveyor (FIS) onboard the AKARI satellite, at 65~μm (N60), 90~μm (WIDE-S), 140~μm (WIDE-L),and 160~μm (N160). Absolute flux calibration was determined by comparing the data with the COBE/DIRBE data sets, and the intensity range was as wide as from a few MJy~sr^{-1} to >1~GJy~sr^{-1}. The uncertainties are considered to be the standard deviations with respect to the DIRBE data, and they are less than 10\% for intensities above 10, 3, 25, and 26~MJy~sr^{-1} at the N60, WIDE-S, WIDE-L, and N160 bands, respectively. The characteristics of point sources in the image were also determined by stacking maps centred on photometric standard stars. The full width at half maxima of the point spread functions (PSFs) were 63", 78", and 88" at the N60, WIDE-S, and WIDE-L bands, respectively. The PSF at the N160 band was not obtained due to the sensitivity, but it is thought to be the same as that of the WIDE-L one.

The polycyclic aromatic hydrocarbon (PAH) hypothesis proposes that the aromatic infrared bands (AIBs) observed at 3.3, 6.2, 7.7, 8.6, 11.3, and 12.7 mic originate from gas-phase PAH molecules. These bands exhibit consistent peak wavelengths and profiles in diverse sources, and ISO SWS and JWST spectra show a nearly identical red wing of the 3.3 mic AIB and blue wing of the 11.2 mic AIB in the dominant Class A sources. This spectral uniformity suggests that the AIBs arise from a small, well-defined set of gas phase PAH species, regardless of the excitation conditions or the nature of the source such as HII regions, reflection nebulae, planetary nebula, young stellar objects, or the diffuse interstellar medium. However, a small number of gas phase PAH species is inconsistent with current modeling of the AIBs that require a wide range of PAH types and sizes. It is also inconsistent with the lack of observed UV and optical absorption bands from gas phase PAH molecules. Furthermore, there is no plausible formation pathway to produce only a small number of specific PAH molecules in the interstellar medium. These issues require quantitative investigation in order to definitively establish gas-phase PAH molecules as the carrier of the AIBs.

Photon loss and dephasing rapidly degrade the sensitivity of quantum sensors, yet systematic methods for designing error-correcting codes whose geometry is simultaneously adapted to the sensing task and the noise channel do not exist. Here we establish that orbital-angular-momentum (OAM) encoding and Gottesman-Kitaev-Preskill (GKP) lattice geometry are structurally coupled: an OAM mode of topological charge ell induces a phase-space rotation θ_ell=ellπ/ell_{max}, corresponding to a family of twisted GKP stabilizer lattices. Using an end-to-end differentiable Strawberry Fields--TensorFlow circuit, we jointly optimise ell, the lattice aspect ratio r, and the finite-energy envelope ε to maximise quantum Fisher information subject to P_{rm err}leq10^{-3}. The optimum occurs at the fractional charge ell=1.5 (θ=67.5^circ), implementable with a half-integer spiral phase plate, which reduces P_{rm err} by 23.9times relative to the square-lattice baseline while leaving F_Q unchanged to within 0.2%. This surpasses the best integer value (ell=2, 15.7times) and arises from an exact 180^circ periodicity of the P_{rm err}(θ) landscape, confirmed analytically and numerically. We derive a transcendental balance equation for the optimal angle θ^*(η,γ,r) and prove that it decreases with both γ and η. A Shannon-inspired metrological capacity C=F_Qcdot(-ln P_{rm err}), maximised at ell=1.5 with a 41% gain over the square lattice, quantifies the joint sensitivity--fault-tolerance resource. These results establish a geometric design principle for noise-adaptive quantum sensors and a fully open-source differentiable template extensible to other bosonic code families.

We provide the first method allowing to retrieve spaceborne SIF maps at 30 m ground resolution with a strong correlation (r^2=0.6) to high-quality airborne estimates of sun-induced fluorescence (SIF). SIF estimates can provide explanatory information for many tasks related to agricultural management and physiological studies. While SIF products from airborne platforms are accurate and spatially well resolved, the data acquisition of such products remains science-oriented and limited to temporally constrained campaigns. Spaceborne SIF products on the other hand are available globally with often sufficient revisit times. However, the spatial resolution of spaceborne SIF products is too small for agricultural applications. In view of ESA's upcoming FLEX mission we develop a method for SIF retrieval in the O_2-A band of hyperspectral DESIS imagery to provide first insights for spaceborne SIF retrieval at high spatial resolution. To this end, we train a simulation-based self-supervised network with a novel perturbation based regularizer and test performance improvements under additional supervised regularization of atmospheric variable prediction. In a validation study with corresponding HyPlant derived SIF estimates at 740 nm we find that our model reaches a mean absolute difference of 0.78 mW / nm / sr / m^2.

Common sense suggests that a particle must have a definite origin if its full path information is available. In quantum mechanics, the knowledge of path information is captured through the well-established duality relation between path distinguishability and interference visibility. If visibility is zero, high path distinguishability can be achieved, which enables one to determine with high predictive power where the particle originates. We investigate the complementarity between path information and interference visibility through an experiment involving three sources emitting into identical modes. Our findings challenge the classical intuition that a particle can be traced back to its origin through its trajectory when full path information is available. By grouping the crystals in different ways, we demonstrate that it is impossible to ascribe a definite physical origin to the photon pair, even if the emission probability of one individual source is zero and full path information is available. Our results shed new light on the physical interpretation of probability assignment and path information beyond its mathematical meaning and show that the interpretation of path information in quantum mechanics is subjective.

Gradient descent on a factored model W = UV^top is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not. We trace the difference to the gauge symmetry of the loss, its invariance under (U, V) mapsto (UQ, VQ). Gradient flow's low-rank mechanism is available to an optimizer only if that optimizer is gauge-equivariant, a condition necessary for the transfer but not sufficient for low-rank recovery. Gradient descent, momentum, "shared-scalar" Adam, Muon, and Shampoo satisfy it. Adam, RMSProp, and the other coordinate-wise methods do not. A structure theorem characterizes the memoryless equivariant rules as exactly the Gram-determined left preconditioners, and a transfer theorem carries gradient flow's pathwise properties to common-scalar flows. We then sort nine update rules on underdetermined matrix sensing by recovery error against the planted ground truth. A one-parameter family from coordinate-wise to shared-scalar preconditioning restores the bias monotonically, isolating anisotropy as the cause. A "spectral schedule" reconciles two opposing reports about Muon: equal-rate updates recover exactly low-rank targets but lose their edge as the spectral tail grows. In transformers, Adam separates two gauge-equivalent initializations at the first step, where the equivariant optimizers stay at float precision, and ends with the per-head invariants W_Q^top W_K 56% apart in relative Frobenius distance, a gap no per-head rotation can close. On two hyperspectral datasets at matched training loss, gradient descent cuts held-out error by 43-44% at the lowest sampling density, and at lower effective rank. Basis choice is therefore not a tuning detail but a decision about which interpolant the optimizer selects.

The recently discovered "hat" aperiodic monotile mixes unreflected and reflected tiles in every tiling it admits, leaving open the question of whether a single shape can tile aperiodically using translations and rotations alone. We show that a close relative of the hat -- the equilateral member of the continuum to which it belongs -- is a weakly chiral aperiodic monotile: it admits only non-periodic tilings if we forbid reflections by fiat. Furthermore, by modifying this polygon's edges we obtain a family of shapes called Spectres that are strictly chiral aperiodic monotiles: they admit only chiral non-periodic tilings based on a hierarchical substitution system.

We describe an analysis comparing the pp elastic cross section as measured by the D0 Collaboration at a center-of-mass energy of 1.96 TeV to that in pp collisions as measured by the TOTEM Collaboration at 2.76, 7, 8, and 13 TeV using a model-independent approach. The TOTEM cross sections extrapolated to a center-of-mass energy of s = 1.96 TeV are compared with the D0 measurement in the region of the diffractive minimum and the second maximum of the pp cross section. The two data sets disagree at the 3.4σ level and thus provide evidence for the t-channel exchange of a colorless, C-odd gluonic compound, also known as the odderon. We combine these results with a TOTEM analysis of the same C-odd exchange based on the total cross section and the ratio of the real to imaginary parts of the forward elastic scattering amplitude in pp scattering. The combined significance of these results is larger than 5σ and is interpreted as the first observation of the exchange of a colorless, C-odd gluonic compound.

To study the onset of scalarization, we investigate linear scalar perturbations around Kerr--Newman black holes in the Einstein-Chern-Simons-Maxwell-scalar theory with quadratic Chern--Simons (CS) coupling γ (hatγ=γ/M^2) and Maxwell coupling η. For this purpose, we employ hyperboloidal Rácz--Tóth evolution and a stationary axisymmetric zero-mode computation. The resulting thresholds are compared with the time-domain response at representative points. For hatγ=0, we find two asymmetric threshold branches in η, while for hatγ=η, the two branches have opposite signs and unequal magnitudes. For unequal CS and Maxwell couplings, the two real threshold branches merge as the spin or CS coupling increases.

In this study, we propose a simple method for fault-tolerant Strassen-like matrix multiplications. The proposed method is based on using two distinct Strassen-like algorithms instead of replicating a given one. We have realized that using two different algorithms, new check relations arise resulting in more local computations. These local computations are found using computer aided search. To improve performance, special parity (extra) sub-matrix multiplications (PSMMs) are generated (two of them) at the expense of increasing communication/computation cost of the system. Our preliminary results demonstrate that the proposed method outperforms a Strassen-like algorithm with two copies and secures a very close performance to three copy version using only 2 PSMMs, reducing the total number of compute nodes by around 24\% i.e., from 21 to 16.

Image datasets are essential not only in validating existing methods in computer vision but also in developing new methods. Most existing image datasets focus on trichromatic intensity images to mimic human vision. However, polarization and spectrum, the wave properties of light that animals in harsh environments and with limited brain capacity often rely on, remain underrepresented in existing datasets. Although spectro-polarimetric datasets exist, these datasets have insufficient object diversity, limited illumination conditions, linear-only polarization data, and inadequate image count. Here, we introduce two spectro-polarimetric datasets: trichromatic Stokes images and hyperspectral Stokes images. These novel datasets encompass both linear and circular polarization; they introduce multiple spectral channels; and they feature a broad selection of real-world scenes. With our dataset in hand, we analyze the spectro-polarimetric image statistics, develop efficient representations of such high-dimensional data, and evaluate spectral dependency of shape-from-polarization methods. As such, the proposed dataset promises a foundation for data-driven spectro-polarimetric imaging and vision research. Dataset and code will be publicly available.

We study the parity-perturbed Hofstadter Q-recursion $ widetilde Q(1)=widetilde Q(2)=1,qquad widetilde Q(n)=widetilde Q(n-widetilde Q(n-1)) +widetilde Q(n-widetilde Q(n-2))+(-1)^n, and the associated two-variable Dirichlet series Z_{widetilde Q}(s,t)=sum_{nge1}n^{-s}widetilde Q(n)^{-t}. The estimate \widetilde Q(n)=n/2+O(n/\log n) gives the exact domain of absolute convergence Re(s+t)>1. With w=s+t, we separate the universal term 2^tζ(w) and derive exact transport, frequency-position, and dyadic renormalization identities. The main result concerns t=-1. For E(n)=2\widetilde Q(n)-n and A(X)=\sum_{n\le X}E(n), the binary-arch clock yields A(X)=Xlog_2X+XΩ!left(log_23X{32}right) +O!left(X{log X}right), where Ω is an explicit continuous periodic function. This continues the normalized correction to Rew>0 and yields a boundary resonance lattice: a double resonance at w=0 and simple resonances at 2πi m/\log2. After subtracting the full-slice order-X skeleton, we analyze the negative-even arch channel. Its companion-forest layers have a weak Gaussian limit, and a canonical subsequence realizes the optimal n/\log n pointwise scale with an explicit signed constant. The negative-arch mass satisfies A_r=512{92π}16^r{sqrt r} left(1-13{16r}+O(r^{-2})right). We do not claim a full-slice continuation across Rew=0$.

In recent years, there has been a growing interest in deep learning-based pansharpening. Thus far, research has mainly focused on architectures. Nonetheless, model training is an equally important issue. A first problem is the absence of ground truths, unavoidable in pansharpening. This is often addressed by training networks in a reduced resolution domain and using the original data as ground truth, relying on an implicit scale invariance assumption. However, on full resolution images results are often disappointing, suggesting such invariance not to hold. A further problem is the scarcity of training data, which causes a limited generalization ability and a poor performance on off-training test images. In this paper, we propose a full-resolution training framework for deep learning-based pansharpening. The framework is fully general and can be used for any deep learning-based pansharpening model. Training takes place in the high-resolution domain, relying only on the original data, thus avoiding any loss of information. To ensure spectral and spatial fidelity, a suitable two-component loss is defined. The spectral component enforces consistency between the pansharpened output and the low-resolution multispectral input. The spatial component, computed at high-resolution, maximizes the local correlation between each pansharpened band and the panchromatic input. At testing time, the target-adaptive operating modality is adopted, achieving good generalization with a limited computational overhead. Experiments carried out on WorldView-3, WorldView-2, and GeoEye-1 images show that methods trained with the proposed framework guarantee a pretty good performance in terms of both full-resolution numerical indexes and visual quality.

This paper presents several notable properties of the matrix U shown to be related to the isomorphism between H_4 and E_8. The most significant of these properties is that U.U is to rank 8 matrices what the golden ratio is to numbers. That is to say, the difference between it and its inverse is the identity element, albeit with a twist. Specifically, U.U- (U.U)^{-1} is the reverse identity matrix or standard involutory permutation matrix of rank 8. It has the same palindromic characteristic polynomial coefficients as the normalized 3-qubit Hadamard matrix with 8-bit binary basis states, which is known to be isomorphic to E8 through its (8,4) Hamming code.

Bound states in the continuum (BIC) metasurfaces are typically described by geometry-specific parameters, hindering cross-geometry comparison, while ultranarrow qBIC features are easily diluted in full-spectrum learning. Here, 2015 samples from seven dielectric metasurface families are mapped to a shared reciprocal-lattice grid, where two frozen low-order Fourier channels capture resonance shifts with mean within-branch R^2 values of 0.871-0.999. Field-level analysis of two representative branches further confirms that these shifts are consistent with the Maxwell-Fourier perturbation picture. A five-channel K-space backbone models the broadband spectrum, while a local complex K-space expert parameterizes the qBIC resonance through a differentiable Fano layer. The expert reduces resonance-position mean absolute error (MAE) from 3.2 to 0.95 nm and the resonance-depth error by 14-fold on a geometry-blocked test set. The same coordinate supports spectrum-to-structure reconstruction.

Hyperspectral unmixing is one of the crucial steps for many hyperspectral applications. The problem of hyperspectral unmixing has proven to be a difficult task in unsupervised work settings where the endmembers and abundances are both unknown. What is more, this task becomes more challenging in the case that the spectral bands are degraded with noise. This paper presents a robust model for unsupervised hyperspectral unmixing. Specifically, our model is developed with the correntropy based metric where the non-negative constraints on both endmembers and abundances are imposed to keep physical significance. In addition, a sparsity prior is explicitly formulated to constrain the distribution of the abundances of each endmember. To solve our model, a half-quadratic optimization technique is developed to convert the original complex optimization problem into an iteratively re-weighted NMF with sparsity constraints. As a result, the optimization of our model can adaptively assign small weights to noisy bands and give more emphasis on noise-free bands. In addition, with sparsity constraints, our model can naturally generate sparse abundances. Experiments on synthetic and real data demonstrate the effectiveness of our model in comparison to the related state-of-the-art unmixing models.

The Minimum-Weight Perfect Matching (MWPM) decoder is widely used in Quantum Error Correction (QEC) decoding. Despite its high accuracy, existing implementations of the MWPM decoder cannot catch up with quantum hardware, e.g., 1 million measurements per second for superconducting qubits. They suffer from a backlog of measurements that grows exponentially and as a result, cannot realize the power of quantum computation. We design and implement a fast MWPM decoder, called Parity Blossom, which reaches a time complexity almost proportional to the number of defect measurements. We further design and implement a parallel version of Parity Blossom called Fusion Blossom. Given a practical circuit-level noise of 0.1%, Fusion Blossom can decode a million measurement rounds per second up to a code distance of 33. Fusion Blossom also supports stream decoding mode that reaches a 0.7 ms decoding latency at code distance 21 regardless of the measurement rounds.

Isogenies occur throughout the theory of elliptic curves. Recently, the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic protocols. Given two elliptic curves E_1, E_2 defined over a finite field k with the same trace, there is a nonconstant isogeny beta from E_2 to E_1 defined over k. This study gives out the index of Hom_{it k}(it E_{rm 1},E_{rm 2})beta as a left ideal in End_{it k}(it E_{rm 2}) and figures out the correspondence between isogenies and kernel ideals. In addition, some results about the non-trivial minimal degree of isogenies between the two elliptic curves are also provided.

Hyperspectral pansharpening is receiving a growing interest since the last few years as testified by a large number of research papers and challenges. It consists in a pixel-level fusion between a lower-resolution hyperspectral datacube and a higher-resolution single-band image, the panchromatic image, with the goal of providing a hyperspectral datacube at panchromatic resolution. Thanks to their powerful representational capabilities, deep learning models have succeeded to provide unprecedented results on many general purpose image processing tasks. However, when moving to domain specific problems, as in this case, the advantages with respect to traditional model-based approaches are much lesser clear-cut due to several contextual reasons. Scarcity of training data, lack of ground-truth, data shape variability, are some such factors that limit the generalization capacity of the state-of-the-art deep learning networks for hyperspectral pansharpening. To cope with these limitations, in this work we propose a new deep learning method which inherits a simple single-band unsupervised pansharpening model nested in a sequential band-wise adaptive scheme, where each band is pansharpened refining the model tuned on the preceding one. By doing so, a simple model is propagated along the wavelength dimension, adaptively and flexibly, with no need to have a fixed number of spectral bands, and, with no need to dispose of large, expensive and labeled training datasets. The proposed method achieves very good results on our datasets, outperforming both traditional and deep learning reference methods. The implementation of the proposed method can be found on https://github.com/giu-guarino/R-PNN

We investigate the entanglement properties in the symmetric subspace of N-partite d-dimensional systems (qudits). For diagonal symmetric states, we show that there is no bound entanglement for d = 3,4 and N = 3. Further, we present a constructive algorithm to map multipartite diagonal symmetric states of qudits onto bipartite symmetric states of larger local dimension. This technique greatly simplifies the analysis of multipartite states and allows to infer entanglement properties for any even N geq 4 due to the fact that the PPT conditions that arise from the bipartite symmetric state correspond to the same PPT conditions that appear in the multipartite diagonal symmetric state.

Hyperspectral remote sensing has advanced across diverse deep learning paradigms, including spectral spatial CNNs, Vision Transformers, Mamba, graph neural networks, Kolmogorov Arnold networks, and self supervised masked autoencoding. Yet progress remains hindered by fragmented repositories, incompatible tensor conventions, and non standardized evaluation. Hyperspectral Image Models addresses these challenges through a modular framework unifying 55 representative models across six paradigms with a common registry, automatic 4D/5D tensor adaptation, and standardized constructors. It integrates 24 benchmark scenes from Airborne, Spaceborne, UAV, and Mars CRISM sensors, with caching, label remapping, PCA, explicit band selection or raw spectra, optional spatial max pooling, and arbitrary PxP patch extraction. To prevent inflated accuracy from overlapping windows, it supports class balanced random partitioning and spatially disjoint regional blocking with Chebyshev guard bands that eliminate train test pixel overlap. Experiments use a single config.yaml with deterministic seeds and complete provenance, generating LaTeX benchmark tables and classification maps. Across 1,320 model scene evaluations and 6,600 seeded runs, scene difficulty dominates architecture, with mean accuracy ranging from 96.40% on Botswana to 56.70% on Houston 2018, versus a 15 point spread across paradigm means. No paradigm universally dominates, while sub 1 M parameter models can match architectures two orders of magnitude larger. Code is publicly available at https://github.com/Tanishq251/Hyperspectral-Image-Models.

In hyperspectral image classification (HSIC), most deep learning models rely on opaque spectral-spatial feature mixing, limiting their interpretability and hindering understanding of internal decision mechanisms. We present physical spectrum-aware white-box mHC, named ES-mHC, a hyper-connection framework that explicitly models interactions among different electromagnetic spectrum groupings (residual stream in mHC) interactions using structured, directional matrices. By separating feature representation from interaction structure, ES-mHC promotes electromagnetic spectrum grouping specialization, reduces redundancy, and exposes internal information flow that can be directly visualized and spatially analyzed. Using hyperspectral image classification as a representative testbed, we demonstrate that the learned hyper-connection matrices exhibit coherent spatial patterns and asymmetric interaction behaviors, providing mechanistic insight into the model internal dynamics. Furthermore, we find that increasing the expansion rate accelerates the emergence of structured interaction patterns. These results suggest that ES-mHC transforms HSIC from a purely black-box prediction task into a structurally transparent, partially white-box learning process.

The reciprocal distance Laplacian matrix of a connected graph G is defined as RD^L(G)=RT(G)-RD(G), where RT(G) is the diagonal matrix of reciprocal distance degrees and RD(G) is the Harary matrix. Since RD^L(G) is a real symmetric matrix, we denote its eigenvalues as λ_1(RD^L(G))geq λ_2(RD^L(G))geq dots geq λ_n(RD^L(G)). The largest eigenvalue λ_1(RD^L(G)) of RD^L(G) is called the reciprocal distance Laplacian spectral radius. In this article, we prove that the multiplicity of n as a reciprocal distance Laplacian eigenvalue of RD^L(G) is exactly one less than the number of components in the complement graph G of G. We show that the class of the complete bipartite graphs maximize the reciprocal distance Laplacian spectral radius among all the bipartite graphs with n vertices. Also, we show that the star graph S_n is the unique graph having the maximum reciprocal distance Laplacian spectral radius in the class of trees with n vertices. We determine the reciprocal distance Laplacian spectrum of several well known graphs. We prove that the complete graph K_n, K_n-e, the star S_n, the complete balanced bipartite graph K_{n{2},n{2}} and the complete split graph CS(n,α) are all determined from the RD^L-spectrum.

We update predictions for observables in the "delicate" D3/anti-D3 inflationary model on the conifold. We use a full CMB likelihood calculation to assess goodness-of-fit, which is necessary because in this model the zeta power spectrum often cannot be modelled as a power-law over observable scales. For the first time we are able to provide accurate forecasts for the amplitude of three-point correlations. In a significant portion of its parameter space the model follows Maldacena's single-field prediction fNL ~ -(5/12)(ns-1) if nt << 1. Therefore |fNL| is usually small when the power spectrum satisfies observational constraints. In a small number of cases the bispectrum is instead dominated by effects from rapid switching between angular minima. The resulting amplitudes are larger, but mostly with unacceptable spectral behaviour. In the most extreme case we obtain |fNLeq| ~ 75 at kt/3 = 0.002/Mpc. It has been suggested that the quasi-single field inflation ("QSFI") mechanism could produce significant 3-point correlations in this model. We do observe rare shifts in amplitude between equilateral and squeezed configurations that could possibly be associated with QSFI effects, but more investigation is needed to establish the full bispectrum shape. There is evidence of "shape" running between equilateral and squeezed configurations that may be inherited from the scale dependence of the spectrum. We explore the dependence of observables on discrete choices such as the truncation point of the potential. Our analysis illustrates the advantages of a standard format for information exchange within the inflationary model-building and testing community.

Large-amplitude molecular motions which occur during isomerization can cause significant changes in electronic structure. These variations in electronic properties can be used to identify vibrationally-excited eigenstates which are localized along the potential energy surface. This work demonstrates that nuclear quadrupole hyperfine interactions can be used as a diagnostic marker of progress along the isomerization path in both the HC14N/H14NC and DC15N/D15NC chemical systems. Ab initio calculations at the CCSD(T)/cc-pCVQZ level indicate that the hyperfine interaction is extremely sensitive to the chemical bonding of the quadrupolar 14N nucleus and can therefore be used to determine in which potential well the vibrational wavefunction is localized. A natural bonding orbital analysis along the isomerization path further demonstrates that hyperfine interactions arise from the asphericity of the electron density at the quadrupolar nucleus. Using the CCSD(T) potential surface, the quadrupole coupling constants of highly-excited vibrational states are computed from a one-dimensional internal coordinate path Hamiltonian. The excellent agreement between ab initio calculations and recent measurements demonstrates that nuclear quadrupole hyperfine structure can be used as a diagnostic tool for characterizing localized HCN and HNC vibrational states.

For a signing σ of a d-regular graph, the spectrum of A_σ depends only on the signs of cycles. We study the affine mathbb F_2 family of signings making every short even cycle unbalanced, and show that averaging over it converts the sign problem of the Bilu-Linial conjecture into a counting problem: a master identity expresses the family-averaged trace as a parity-weighted sum over wrap classes confined to the span W of the constraint cycles, and the family-averaged Ihara L-function diagonalizes so that every prime whose parity escapes W contributes the Ramanujan rate d-1 automatically. Uniform averaging over all signings, by contrast, provably cannot certify a spectral radius below the Kesten profile. We prove matched upper and lower bounds for the confined walk counts, a doubling injection from below, and from above an ear-decomposition encoding in which the number of fresh runs of a non-backtracking walk equals the cycle rank of its support, combined with a window lemma for bicycle-free graphs and a rank bound via the Moore bound for irregular graphs. Consequences include varepsilon-versions of the Bilu-Linial conjecture: every d-regular graph that is subcritical at scale log n, and every d-regular graph bicycle-free at radius Cloglog n/δ, admits a signing in the parity family with ρ(A_σ)le2d-1(1+Cδlog(1/δ))(1+o(1)). We further identify the necessary hypotheses exactly (K_d-trapping; tree-burst gadgets), give an exact certificate on the hypercube, and record a decisive obstruction to two-sided interlacing: mathbb E_σdet(xI-A_σ^2) is not real-rooted, already for the quadrilateral, where it equals (x^2-4x+2)^2+4.

The Karhunen--Loève transform (KLT) of the stationary AR(1) source is the classical optimality benchmark of transform coding. Its frequencies are roots of the transcendental equations of Ray and Driver, and the transform has therefore long been treated as an unstructured dense matrix. Rather than compute the exact KLT, the field turned to fast approximations of it, most famously the discrete cosine transform (DCT). This paper shows that the retreat was premature. The exact AR(1) KLT admits direct recursive factorizations, at every order Nge2 and every correlation coefficient ρin(0,1): at even orders, the transform reduces to a butterfly stage, two half-order copies of itself, and orthogonal corrections generated by rank-one boundary perturbations of the covariance; at odd orders, to two copies of the KLT of the one-sided prediction residual and an arrowhead stage absorbing the center sample. The residual KLT recurses through half order as well. All correction stages are Cauchy-structured, and applying them by the fast multipole method yields exact-KLT algorithms of O(Nlog N) complexity---the same order as the FFT and the fast sinusoidal transforms. The factorizations follow from the covariance matrix by the Sherman--Morrison identity and the classical secular eigenvalue updates, and degenerate, as ρto1, to the known parity splittings of the DCT-II. As secondary results, the factorization constants are shown to be algebraic functions of ρ---in radicals for all Nle8---and complete exact KLT modules for N=2,dots,8 are given.

This paper presents a systematic cataloging of the generators of celestial symmetries on phase space. Starting from the celestial OPEs, we first show how to extract a representation of the general-spin analog of the wedge subalgebra of w_{1+infty} on the phase space of massless matter fields of arbitrary helicity. These generators can be expressed as light-sheet operators that are quadratic in the matter fields at future or past null infinity. We next show how to extend these symmetries beyond the wedge. Doing so requires us to augment the quadratic operators with: 1) linear terms corresponding to primary descendants of the negative helicity gauge fields the matter modes couple to, and 2) a tower of higher-particle composite operator contributions. These modes can be realized as light-ray operators supported on generators of null infinity, but local on the celestial sphere. Finally, we construct a representation of the celestial symmetries that captures how the positive helicity gauge fields transform. We close by discussing how these celestial symmetries inform our choice of detector operators.

The planned space-based gravitational wave detector, LISA, will provide a fundamentally new means of studying the orbital alignment of close white dwarf binaries. However, due to the inherent symmetry of their gravitational wave signals, a fourfold degeneracy arises in the transverse projections of their angular momentum vectors. In this paper, we demonstrate that by incorporating timing information from electromagnetic observations, such as radial velocity modulations and light curves, this degeneracy can be reduced to twofold.

We show that the Turing complete rule 110 in elementary cellular automata can be emulated by alternating three simple symmetric rules in space. As the constituent rules themselves are trivial, this shows that diversity alone can generate emergent phenomena. The rules cannot distinguish left from right, and the chirality of rule 110 is created by their arrangement. Random initial conditions lock on to rule 110 over 90% of the time, explained through the motion of domain walls between desynchronized regions. Adding random noise creates errors that seed domain walls, whose fraction scales with the square root of noise strength, explained through a simple rate equation. This points to a route to complexity through repeated, perturbed units, common in biology, and shows that in cellular automaton models of quantum field theory, broken symmetries such as parity need not be present in the local rules.

We study Krasner quotient hyperfields arising from finite fields, F_q/G_r, where G_rle F_q^times has index r. Building on the structure theorem of Baker--Jin, we determine the characteristic and C-characteristic of all sufficiently large such quotients: they depend only on the parity of r and, when r is even, on the residue class of q modulo 2r. In particular, the two Baker--Jin stable classes for even r are separated by characteristic 2 versus 3, while the C-characteristic is always 1. We complement this structural result with a computational laboratory: sharp Weil thresholds for Baker--Jin large-q isomorphism, empirical minimal stabilization bounds N_r^{emp}, complete finite-field quotient atlases for hyperfield orders nle 7, and comparisons with the enumerations of Ameri--Eyvazi--Hošková-Mayerová (orders le 6) and Massouros--Massouros (order 7). Among other findings, exactly 15 isomorphism types of order 7 arise as finite-field quotients, out of 277 hyperfields of that order -- a concrete data point toward the Baker--Jin rarity conjecture for quotients. All algorithms and tables are available in an open-source package suitable for independent verification and arXiv ancillary material.

Many works have been done on salient object detection using supervised or unsupervised approaches on colour images. Recently, a few studies demonstrated that efficient salient object detection can also be implemented by using spectral features in visible spectrum of hyperspectral images from natural scenes. However, these models on hyperspectral salient object detection were tested with a very few number of data selected from various online public dataset, which are not specifically created for object detection purposes. Therefore, here, we aim to contribute to the field by releasing a hyperspectral salient object detection dataset with a collection of 60 hyperspectral images with their respective ground-truth binary images and representative rendered colour images (sRGB). We took several aspects in consideration during the data collection such as variation in object size, number of objects, foreground-background contrast, object position on the image, and etc. Then, we prepared ground truth binary images for each hyperspectral data, where salient objects are labelled on the images. Finally, we did performance evaluation using Area Under Curve (AUC) metric on some existing hyperspectral saliency detection models in literature.

For a locally linear graph G, which is a graph built out of triangles, it is possible to construct another graph G^* that would consist of triangles of G as vertices, while sharing (or not sharing) a common vertex between a pair of triangles would define a binary relation for edges of G^*. In this paper we show that the spectrum of G^* is uniquely defined by G. We will also show some structural similarities of these graphs; in particular, that the number of quadrilaterals and pentagons in both graphs are the same; that G^* does not contain K_4-e and K_{1,4}; and that G can be reconstructed from G^*.

We provide a geometric description of Lee-Yang tensors, building upon several recent results of Bravyi, Gosset, Liu, and Wong. By applying tools from complex Perron-Frobenius theory, we generalize one of their key lemmas to bound the spectral ratio of non-normal operators with Lee-Yang radius greater than one. As a direct consequence, we provide a local-to-global principle for bounding spectral gaps of Suzuki-Fisher Hamiltonians, a family of 2-local Hamiltonians, using only the Lee-Yang radius of each local operator to bound the gap from below. On the other hand, we develop a simple perturbative technique to show that the Gibbs states of k-local Hamiltonians, k geq 3, cannot have Lee-Yang radius at least one for all inverse temperatures βgeq 0. We apply this same method to conclude that Suzuki-Fisher Hamiltonians are precisely those Hamiltonians whose Gibbs states are Lee-Yang at all inverse temperatures βgeq 0.

Passive long-wave infrared (LWIR) hyperspectral imaging under a standoff geometry depends on atmospheric absorption and emission, as well as reflected radiance, thus making atmospheric compensation essential to get knowledge of a target of interest. Despite its importance, this compensation has been largely overlooked due to its practical and modeling difficulty. In this paper, we present a lightweight set-based deep learning framework that takes multiple radiance measurements, collected at different standoff ranges, as input and jointly estimates transmittance, atmospheric path radiance, and a shared downwelling spectrum. We analyze the learned representation with a sparse autoencoder and observe that several latent features do activate on geographically coherent subsets of the test data despite the absence of location supervision. Experiments on a MODTRAN generated standoff LWIR dataset demonstrate low spectral distortion across all estimated products. The dataset and code is publicly available at: https://factral.co/SAE-LWIR/

We propose a quark flavor model based on modular S'_4 with a general CP symmetry. CP violation in the quark sector is entirely realized by the modulus langle τrangle. We show that the canonical normalization induced by the Kähler metric plays a crucial role in reproducing the observed hierarchies, while maintaining coupling constants of order O(1). The minimal model achieves a great fit to the quark sector data, which we take as the PDG 2024 data extrapolated to the GUT scale.

Detecting a stochastic gravitational wave background, particularly radiation from individually unresolvable super-massive black hole binary systems, is one of the primary targets for Pulsar Timing Arrays. Increasingly more stringent upper limits are being set on these signals under the assumption that the background radiation is isotropic. However, some level of anisotropy may be present and the characterisation of the power at different angular scales carries important information. We show that the standard analysis for isotropic backgrounds can be generalised in a conceptually straightforward way to the case of generic anisotropic background radiation by decomposing the angular distribution of the gravitational wave power on the sky into multipole moments. We introduce the concept of generalised overlap reduction functions which characterise the effect of the anisotropy multipoles on the correlation of the timing residuals from the pulsars timed by a Pulsar Timing Array. In a search for a signal characterised by a generic anisotropy, the generalised overlap reduction functions play the role of the so-called Hellings and Downs curve used for isotropic radiation. We compute the generalised overlap reduction functions for a generic level of anisotropy and Pulsar Timing Array configuration. We also provide an order of magnitude estimate of the level of anisotropy that can be expected in the background generated by super-massive black hole binary systems.

This paper gives an explicit isomorphic mapping from the 240 real R^{8} roots of the E_8 Gosset 4_{21} 8-polytope to two golden ratio scaled copies of the 120 root H_4 600-cell quaternion 4-polytope using a traceless 8times8 rotation matrix U with palindromic characteristic polynomial coefficients and a unitary form e^{i\mathbb{U}}. It also shows the inverse map from a single H_4 600-cell to E_8 using a 4Dhookrightarrow8D chiral leftleftrightarrowright mapping function, φ scaling, and U^{-1}. This approach shows that there are actually four copies of each 600-cell living within E_8 in the form of chiral H_{4L}oplusφH_{4L}oplusH_{4R}oplusφH_{4R} roots. In addition, it demonstrates a quaternion Weyl orbit construction of H_4-based 4-polytopes that provides an explicit mapping between E_8 and four copies of the tri-rectified Coxeter-Dynkin diagram of H_4, namely the 120-cell of order 600. Taking advantage of this property promises to open the door to as yet unexplored E_8-based Grand Unified Theories or GUTs.

Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to implement. We study a challenging problem called self-calibration, i.e., the task of designing an algorithm for devices so that the algorithm is able to perform calibration automatically. More precisely, we consider the setup y = A(d) x + epsilon where only partial information about the sensing matrix A(d) is known and where A(d) linearly depends on d. The goal is to estimate the calibration parameter d (resolve the uncertainty in the sensing process) and the signal/object of interests x simultaneously. For three different models of practical relevance, we show how such a bilinear inverse problem, including blind deconvolution as an important example, can be solved via a simple linear least squares approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus potentially allowing for real-time deployment. We also present a variation of the least squares approach, which leads to a~spectral method, where the solution to the bilinear inverse problem can be found by computing the singular vector associated with the smallest singular value of a certain matrix derived from the bilinear system. Explicit theoretical guarantees and stability theory are derived for both techniques; and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

We study photon conversion into light particles, such as dilatons, axions, and gravitons, induced by background magnetic fields, and formulate the resulting evolution in terms of the Stokes parameters. We show that photon conversion reduces to an effective non-unitary evolution of the photon sector. In the perturbative regime, the Hermitian and anti-Hermitian parts of the effective photon Hamiltonian are related through Kramers--Kronig relations, revealing that the changes in the Stokes parameters are not independent. We apply this general framework to photon evolution in Gaussian stochastic magnetic fields with possible helicity, and derive the ensemble-averaged evolution of the Stokes parameters. We find that two nonzero contributions arise even in the absence of magnetic helicity, which respectively correspond to the overall attenuation of all the Stokes parameters and to an irrelevant overall phase. We also find that magnetic helicity gives rise to two additional contributions, one of which changes the circular polarization while the other induces a rotation of linear polarization. These contributions form two Kramers--Kronig pairs. In particular, photon conversion induced by magnetic helicity is accompanied by both circular-polarization and birefringent responses. The same structure appears in dilaton-photon, axion-photon, and graviton-photon systems, revealing universality of photon conversion in magnetic fields.

We point out that, when the Unruh-DeWitt detector couples to a scalar primary operator of d-dimensional conformal field theory, the detector's power spectrum generally obeys the thermal distribution for (1+1)-dimensional anyons.

We study two-step recurrences with positive step sizes and nonnegative momentum coefficients whose terminal residual is the Chebyshev minimax polynomial on a prescribed spectral interval [μ,L]. These recurrences have the same terminal error on a fixed quadratic, but their first-order responses to stepwise Hessian perturbations can differ. We prove that the sine-Jacobi recurrence of Part I is asymptotically optimal for this response norm within a factor of 1.000004, uniformly over 0<μ<L. Every terminal-exact recurrence satisfies A_Nge(2c_{cert}-o(1))N^{3/2}ε_N^star/(L-μ) with c_{cert}>1.14268353624, whereas the sine-Jacobi recurrence attains the constant 2c_{sin} with c_{sin}<1.14269218. The proof reduces the gain to the diagonal energy of a Jacobi Green matrix. A centering lift represents this matrix by an exponential kernel; packing its diagonal into a density on the line preserves the energy and controls the change in the Birman-Schwinger spectrum. A calibrated identity gives a lower bound using the ground parameter and one Fredholm determinant. Two further determinants and a trace observation improve the bound through a pointwise inequality on an explicit compact state region. One rational certificate verifies this inequality by interval arithmetic. A second certificate constructs a density satisfying the selected observations and both normalizations with energy below the sine value. Finally, no C^1 function of finitely many observations of the specified kinds gives a locally sharp lower bound at the sine density.

A fundamental problem in quantum information is to understand the operational significance of quantum resources. Quantum resource theories (QRTs) provide a powerful theoretical framework that aids in analyzing and comprehending the operational meaning of these resources. Early resource theories primarily focused on analyzing static quantum resources. Recently, there has been growing interest in the study of dynamic quantum resources. In this paper, we utilize superchannel theory to describe the dynamic resource theory of quantum coherence. In this dynamic resource theory, we treat classical channels as free channels and consider two classes of free superchannels that preserve channel incoherence (maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC)) as free resources. We regard the quantum Fourier transform as the golden unit of dynamic coherence resources. We first establish the one-shot theory of dynamic coherence cost and dynamic coherence distillation, which involves converting the quantum Fourier transform into an arbitrary quantum channel using MISC and DISC. Next, we introduce a class of free superchannels known as δ-MISC, which asymptotically generate negligible dynamic coherence. Finally, we provide upper and lower bounds for the one-shot catalytic dynamic coherence cost of quantum channels under the action of these δ-MISC superchannels.

Sagnac interferometers are important tools for precision measurements. Cancellation of common-path noise ensures a high degree of stability against external perturbations, while their sensitivity to rotations provides the basis of laser gyroscopes. Here we highlight another, less explored feature of Sagnac interferometers: the fact that optical elements are traversed in reverse order for clockwise and counterclockwise propagating light components. This provides the opportunity to explore a classical realization of indefinite causal order, where the order of events within a sequence is not fixed. We explore this concept to identify the geometric phase associated with two non-commuting polarization operations with a single measurement. This idea may have applications for the rapid determination of polarization manipulations or optical activity within chiral media, but foremost it provides a geometric illustration of indefinite causal order.

We present a rigorous analysis of the algebraic and geometric structure of the quantum complexity resource of a system of bosonic modes in Gaussian boson sampling. This resource underlies the quantum advantage of the system: its photon-counting statistics require the evaluation of a hafnian of the resource covariance matrix, and that computation is #P-hard. The resource covariance matrix is the solution of a semidefinite program that extracts the minimum-trace physical quantum part of the total covariance matrix; the complementary part is positive semidefinite and can therefore be simulated classically. Earlier work characterized this resource only through the trace of the quantum part, equal to its photon number. We characterize the optimizer itself, as a quantum state and as a geometric object, beyond the scalar given by its trace. We prove that it is a unique pure Gaussian state and construct an explicit oracle map, obeying an algebraic Riccati identity, that reconstructs the resource. We prove that the full problem compresses exactly onto the active symplectic sector that the dual program support generates. The passive-diagonalizable states are solved in closed form, the first explicit solvable class, and the whole program is shown to be equivalent to a minimization over the symplectic group, that is, over the Siegel upper half-space. Together these results establish that the program determines a canonical localized pure Gaussian component of the resource, and they provide the structural foundation for its detailed analysis.

We develop a novel way to probe subgalactic-scale matter distribution with diffractive lensing on gravitational waves. Five-year observations from Einstein Telescope and DECIGO are expected to probe k= 10^5sim 10^8 ,{rm Mpc}^{-1} down to P(k) = 10^{-16} sim 10^{-14} ,{rm Mpc}^3 level. These results can be interpreted in terms of primordial black holes in the range M_{rm PBH} gtrsim 10^{-3}M_odot down to f_{rm PBH} = 10^{-6} level, or QCD axion minihalos in the range m_a = 10^{-3} sim 10^{-12} ,{rm eV}. A key result of the paper is the approximate relation between the scale k and the gravitational wave frequency f, derived in an ensemble of `multi-lensing' events. This relation enables direct measurement of the power spectrum at specific scales, with sensitivities characterized by model-independent kernels delta P(k). Additionally, we delineate the statistical properties of `multi-lensing' based on the `Fresnel number' N_F. When N_F cal O(1), the statistical significance can be approximately calculated by Variance of lensing effects, which is directly related to the power spectrum among other moments of matter distribution.

Hyperspectral sensors have enjoyed widespread use in the realm of remote sensing; however, they must be adapted to a format in which they can be operated onboard mobile robots. In this work, we introduce a first-of-its-kind system architecture with snapshot hyperspectral cameras and point spectrometers to efficiently generate composite datacubes from a robotic base. Our system collects and registers datacubes spanning the visible to shortwave infrared (660-1700 nm) spectrum while simultaneously capturing the ambient solar spectrum reflected off a white reference tile. We collect and disseminate a large dataset of more than 500 labeled datacubes from on-road and off-road terrain compliant with the ATLAS ontology to further the integration and demonstration of hyperspectral imaging (HSI) as beneficial in terrain class separability. Our analysis of this data demonstrates that HSI is a significant opportunity to increase understanding of scene composition from a robot-centric context. All code and data are open source online: https://river-lab.github.io/hyper_drive_data

The singlet-doublet vector-like fermion dark matter model has been extensively studied in the literature over the past decade. An important parameter in this model is the singlet-doublet mixing angle (sintheta). All the previous studies have primarily focused on annihilation and co-annihilation processes for obtaining the correct dark matter relic density, assuming that the singlet and doublet components decouple at the same epoch. In this work, we demonstrate that this assumption holds only for larger mixing angles with a dependency on the mass of the dark matter. However, it badly fails for the mixing angle sintheta<0.05. We present a systematic study of the parameter space of the singlet-doublet dark matter relic, incorporating annihilation, co-annihilation, and, for the first time, co-scattering processes. Additionally, the freeze-in parameter space is also explored. We found that due to the inclusion of co-scattering processes, the correct relic density parameter space is shifted towards the detection sensitivity range of the LHC and MATHUSLA via displaced vertex signatures.

The strong intervening absorption system at redshift 1.15 towards the very bright quasar HE 0515-4414 is the most studied absorber for measuring possible cosmological variations in the fine-structure constant, α. We observed HE 0515-4414 for 16.1,h with the Very Large Telescope and present here the first constraint on relative variations in α with parts-per-million (ppm) precision from the new ESPRESSO spectrograph: Δα/α= 1.3 pm 1.3_{rm stat} pm 0.4_{rm sys},{rm ppm}. The statistical uncertainty (1σ) is similar to the ensemble precision of previous large samples of absorbers, and derives from the high S/N achieved (approx105 per 0.4,km,s^{-1} pixel). ESPRESSO's design, and calibration of our observations with its laser frequency comb, effectively removed wavelength calibration errors from our measurement. The high resolving power of our ESPRESSO spectrum (R=145000) enabled the identification of very narrow components within the absorption profile, allowing a more robust analysis of Δα/α. The evidence for the narrow components is corroborated by their correspondence with previously detected molecular hydrogen and neutral carbon. The main remaining systematic errors arise from ambiguities in the absorption profile modelling, effects from redispersing the individual quasar exposures, and convergence of the parameter estimation algorithm. All analyses of the spectrum, including systematic error estimates, were initially blinded to avoid human biases. We make our reduced ESPRESSO spectrum of HE 0515-4414 publicly available for further analysis. Combining our ESPRESSO result with 28 measurements, from other spectrographs, in which wavelength calibration errors have been mitigated, yields a weighted mean Δα/α= -0.5 pm 0.5_{rm stat} pm 0.4_{rm sys},ppm at redshifts 0.6-2.4.

We present synthetic light curves and spectra from three-dimensional (3D) Monte Carlo radiative transfer simulations based on a 3D core-collapse supernova explosion model of an ultra-stripped 3.5,M_{odot} progenitor. Our calculations predict a fast and faint transient with Delta m_{15} sim 1- 2,mag and peak bolometric luminosity between -15.3,mag and -16.4,mag. Due to a large-scale unipolar asymmetry in the distribution of ^{56}Ni, there is a pronounced viewing-angle dependence with about 1,mag difference between the directions of highest and lowest luminosity. The predicted spectra for this rare class of explosions do not yet match any observed counterpart. They are dominated by prominent Mg~II lines, but features from O, C, Si, and Ca are also found. In particular, the O~I line at 7{774} appears as a blended feature together with Mg~II emission. Our model is not only faster and fainter than the observed Ib/c supernova population, but also shows a correlation between higher peak luminosity and larger Delta m_{15} that is not present in observational samples. A possible explanation is that the unusually small ejecta mass of our model accentuates the viewing-angle dependence of the photometry. We suggest that the viewing-angle dependence of the photometry may be used to constrain asymmetries in explosion models of more typical stripped-envelope supernova progenitors in future.

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or unitarily invariant, i.e., they depend only on the eigenvalues or singular values of the matrix. This paper investigates how spectral matrix cones -- cones defined from epigraphs and perspectives of spectral or unitarily invariant functions -- can be used to enhance first-order conic solvers for semidefinite programs. Our main result shows that projecting a matrix can be reduced to projecting its eigenvalues or singular values, which we demonstrate can be done at a negligible cost compared to the eigenvalue or singular value decomposition itself. We have integrated support for spectral matrix cone projections into the Splitting Conic Solver (SCS). Numerical experiments show that SCS with this enhancement can achieve speedups of up to an order of magnitude for solving semidefinite programs arising in experimental design, robust principal component analysis, and graph partitioning.

Foundation models have triggered a paradigm shift in computer vision and are increasingly being adopted in remote sensing, particularly for multispectral imagery. Yet, their potential in hyperspectral imaging (HSI) remains untapped due to the absence of comprehensive and globally representative hyperspectral datasets. To close this gap, we introduce SpectralEarth, a large-scale multi-temporal dataset designed to pretrain hyperspectral foundation models leveraging data from the Environmental Mapping and Analysis Program (EnMAP). SpectralEarth comprises 538,974 image patches covering 415,153 unique locations from more than 11,636 globally distributed EnMAP scenes spanning two years of archive. Additionally, 17.5% of these locations include multiple timestamps, enabling multi-temporal HSI analysis. Utilizing state-of-the-art self-supervised learning (SSL) algorithms, we pretrain a series of foundation models on SpectralEarth. We integrate a spectral adapter into classical vision backbones to accommodate the unique characteristics of HSI. In tandem, we construct four downstream datasets for land-cover and crop-type mapping, providing benchmarks for model evaluation. Experimental results support the versatility of our models, showcasing their generalizability across different tasks and sensors. We also highlight computational efficiency during model fine-tuning. The dataset, models, and source code will be made publicly available.

Stochastic bubble nucleation makes the local completion time of a first-order phase transition a random spatial field. We study its power spectrum and equilateral bispectrum in Minkowski and de Sitter backgrounds, with particular emphasis on the infrared consequences of a finite transition duration. In an eternally extended de Sitter history, rare bubbles nucleated in the remote past generate an ancient-bubble tail that produces a hierarchy of infrared-sensitive spatial moments. For the two-point function, the first finite-k correction becomes tail sensitive at H/β=1/5, while the leading moment becomes singular at H/β=1/3. The corresponding three-point thresholds are H/β=1/8 and 1/6, showing that the bispectrum is more infrared sensitive than the power spectrum. For any finite starting time, however, the ancient-bubble tail is cut off, all spatial moments remain finite, and the strict infrared spectra recover the analytic white-noise limits {cal P}_τpropto k^3 and {cal B}^{rm eq}_τpropto k^6. The eternal-background thresholds instead control the duration dependence of the moment coefficients and the crossover into an intermediate tail-sensitive regime, in agreement with our numerical calculations. We further show that temporal localization of the nucleation history provides a smooth regulator of the ancient-bubble tail and restores the same analytic infrared limits. These results establish a general first-arrival framework for completion-time fluctuations and clarify how de Sitter expansion can generate distinct power-spectrum and bispectrum infrared hierarchies relevant to curvature perturbations and non-Gaussianity.

We study quantum state tomography when the unknown state lies in a trace-distance ball of radius R around a known reference state ρ. For arbitrary collective measurements, we determine the minimax expected risk and confidence radius up to universal constants, uniformly over the dimension, center spectrum, radius, and sample size. Write Γ=d(Trsqrtρ)^2+d^2R. For dge2, 0<Rle1, and nge1 copies, the expected risk is Θ(min{R,Γ/n}). At failure probability 0<δle1/3, the minimax confidence radius is \[ Θ\!\left(\min\left\{R,\frac{Γ+\log(1/δ){n}}\right\}\right). \] For varepsilonle c_0R with a universal c_0>0, the copy complexity is Θ((Γ+log(1/δ))/varepsilon^2). For the lower bound we use a weighted trace-norm witness to retain all spectral scales in a square-root perturbation family. For the upper bound, we give a direct spectral and concentration analysis of a modified existing purification-based procedure.

Fix a strip width \(ρ>0\), a Diophantine frequency \(α\), an integer \(N\ge2\), and \(λ>1\). For the family \[ V_{\varepsilon,δ}(x) =2λ\cos(2πN x)+\varepsilonδ(x), \] we prove that there is an open prevalent set \(\mathcal P_{\rm strat}\) of real-analytic strip-\(ρ\) perturbations such that every \(δ\in\mathcal P_{\rm strat}\) admits \(\varepsilon_0(δ)>0\) for which \[ gathered Leb\left\{ E\inΣ(V_{\varepsilon,δ},α): ω(α,E;V_{\varepsilon,δ})=s \right\}>0, 0<\varepsilon<\varepsilon_0(δ), \qquad s=1,\ldots,N. gathered \] The proof relates acceleration to the total multiplicity of real zeros of analytic overlap coefficients for first-return cocycles. Under quantitative control of the return products, Poisson integration and Kac normalization identify acceleration with half this multiplicity. A positive analytic dual state gives the finite-volume spectral gaps and Schur curvature needed at the upper spectral edge. Schur variations separate the perturbed maxima, and parameter exclusion preserves \(s\) pairs of simple zeros on a positive-measure spectral set.

The sufficiently scattered condition (SSC) is a key condition in the study of identifiability of various matrix factorization problems, including nonnegative, minimum-volume, symmetric, simplex-structured, and polytopic matrix factorizations. The SSC allows one to guarantee that the computed matrix factorization is unique/identifiable, up to trivial ambiguities. However, this condition is NP-hard to check in general. In this paper, we show that it can however be checked in a reasonable amount of time in realistic scenarios, when the factorization rank is not too large. This is achieved by formulating the problem as a non-convex quadratic optimization problem over a bounded set. We use the global non-convex optimization software Gurobi, and showcase the usefulness of this code on synthetic data sets and on real-world hyperspectral images.

We develop a novel systematic method for constructing exact, static, and asymptotically flat black-hole solutions in shift-symmetric and Z_2-symmetric beyond Horndeski theories. In contrast to previous studies, our approach does not rely on the restrictive reciprocal condition g_{tt}g_{rr}=-1, allowing for more general geometries characterized by two independent metric functions. The resulting solution space contains two qualitatively distinct types of hair originating from different branches of the theory. One branch is characterized by khronometric hair, while the other by genuine scalar hair. In both, the scalar profile defines a nontrivial preferred foliation, but the shift-symmetry Noether current and the associated propagating degree of freedom are trivial for the former and nonvanishing for the latter. Focusing mainly on the second branch, we derive several distinct families of exact black-hole solutions. In general, these solutions are singular and exhibit primary scalar hair associated with an independent scalar charge. Nevertheless, we demonstrate that they can be regularized to yield regular black-hole or solitonic configurations, for which the scalar hair becomes secondary. We further investigate the stability properties of these solutions under linear perturbations by analyzing the axial sector and the monopole (ell=0) mode of the even-parity sector. For representative solutions with scalar hair, the perturbative analysis provides evidence for linear stability under the modes considered.