This is the first of two papers which together prove that the $12$-parameter family of parabolic $SU(2)$-Hitchin moduli spaces on the four-punctured sphere are all ALG gravitational instantons of type D4, and hence are asymptotic to $(\mathbb{C} \times T^2_τ)/\mathbb{Z}_2$ at infinity. The elliptic modulus $τ$ is determined by the cross-ratio of the four points. In this first paper, we consider each Hitchin moduli space corresponding to an allowable set of parabolic data and compute its Torelli parameters. There is a $12$-parameter family of Hitchin moduli spaces corresponding to different parabolic data, and we show that these realize all possible allowable Torelli parameters. In the companion paper, we we will show there that all of the Hitchin moduli spaces studied here are indeed ALG of type $D_4$, and consequently that every ALG-$D_4$ gravitational instanton can be realized as a Hitchin moduli space. Altogether, this will give the first verification of any case of the Modularity Conjecture: that all ALG gravitational instantons with tangent cone $\mathbb{C}/\mathbb{Z}_2$ can be realized as Hitchin moduli spaces with their natural associated $L^2$ metrics.

In this paper we study nearest-neighbour deformations of integrable models. After expanding in the deformation parameter, we identify four possible types of deformations. First there are deformations that simply break or preserve integrability. Then we find two different subtle cases. The first case is where the deformation is only integrable if all orders of the deformation parameter are taken into account. An example of these are the long-range deformations that appear in holographic models. The second case is when the deformation is perturbatively integrable to some order in the deformation parameter but can not be extended to an integrable model. In this paper we work this out for the XXZ spin chain and discuss the level statistics of each of these cases. We find numerical evidence that the onset of chaos occurs differently in each of these models. For the perturbatively integrable models, we find that the deformation strength at which chaos appears demonstrates a volume-scaling intermediate between strong and weak integrability breaking models.

Generalized Nash Equilibrium Problems (GNEPs) arise in many applications, including non-cooperative multi-agent control problems. Although many methods exist for finding generalized Nash equilibria, most of them rely on assuming knowledge of the objective functions or being able to query the best responses of the agents. We present a method for learning solutions of GNEPs only based on querying agents for their preference between two alternative decisions. We use the collected preference data to learn a GNEP whose equilibrium approximates a GNE of the underlying (unknown) problem. Preference queries are selected using an active-learning strategy that balances exploration of the decision space and exploitation of the learned GNEP. We present numerical results on game-theoretic linear quadratic regulation problems, as well as on other literature GNEP examples, showing the effectiveness of the proposed method.

The aim of this paper is to produce infinite exotic structures on smooth closed oriented $4-$manifolds with fundamental group isomorphic to the infinite dihedral group, assuming that $b_2^+$ and $b_2^-$ are at least $12$.

Ultrahigh-energy gamma rays ($E_γ>100 \, {\rm TeV}$) have been detected from a handful of astrophysical sources. Due to the Klein-Nishina suppression of inverse Compton scattering at such high energies, it has sometimes been argued that these sources must be accelerators of PeV-scale protons, making them the long-sought-after Galactic ''PeVatrons.'' Here, we challenge this conclusion, demonstrating that these sources can be straightforwardly explained by simple leptonic models. In this context, we consider the microquasar SS 433, the Galactic Center, and TeV halos, showing in each case that the observation of PeV-scale gamma rays from these sources does not indicate that they are accelerators of hadronic cosmic rays. We also note that the measured angular extension of SS 433 is in good agreement with the predictions of our model, favoring a leptonic origin for the gamma-ray emission from this source. A definitive identification of a PeVatron would require additional information, such as the combined observation of the pion bump and synchrotron peak, the spatial correlation of gamma-ray emission with gas, or the detection of neutrinos with $E_ν \gtrsim 100 \, {\rm TeV}$.

We have recently suggested that Nunki=Sigma Sagittarii is the closest core collapse progenitor candidate to the Sun based on a VLTI/GRAVITY observation that unveiled it as a $6.5+6.3 M_{\odot}$ binary at a projected separation of 0.60 au. Here we combine this observation with three VLTI/PIONIER archival and one previous MAPPIT observation to solve for the orbit of \textit{Nunki}, finding $a=1.26\pm0.05 \text{ au}$ ($P=134.779\pm0.025 \text{ days}$) and thereby confirming it as a close binary. The low orbital inclination $i=19.7\pm1.9^{\circ}$ coupled with the high projected rotational velocity $v \sin i \simeq 160 \text{ km}\text{ s}^{-1}$ and the absence of a decretion disk are a strong hint for spin-orbit misalignment. The significant eccentricity $e=0.492\pm0.003$ will cause the system to undergo eccentric Roche lobe overflow once the primary expands to $R\simeq50 R_{\odot}$, so that a merger into a $M \gtrsim 10 M_{\odot}$ star is a possible outcome. Therefore, we conclude that \textit{Nunki} at a distance $d \approx 69 \text{ pc}$ can indeed be considered the closest core collapse progenitor candidate to the Sun as it is closer than \textit{Spica} and \textit{Bellatrix} both at $d \approx 77 \text{ pc}$. Furthermore, we also report on a VLTI/GRAVITY observation of \textit{Bellatrix} that shows that it does not have any close companion with a K band flux ratio higher than 1\%; in particular, it is not a close equal mass binary as previously suspected. Two archival spectra of \textit{Nunki} illustrate how equal-mass binaries with rapidly rotating components can easily hide to become virtually spectroscopically undetectable when the radial velocity separation is several times smaller than the individual line widths.

Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of unitary evolutions. Characterizing channels that do not admit such a decomposition is in general a hard problem with significant implications for noise mitigation in quantum technologies and for fundamental problems in quantum information theory. Here we establish a link between mixed-unitarity of unital channels and the (quantum) nature of the memory effects in non-Markovian dynamics. Translating the problem into the language of process tensors, this connection yields a hierarchy of semidefinite programs that provides numerically efficient witnesses for non-mixed-unitary behavior, outperforming existing criteria. We demonstrate the power of this approach through illustrative examples of unital channels in dimensions three and four.

The recent gravitational-wave (GW) alert from a compact object merger involving at least one subsolar mass (SSM) object has prompted questions about their origins. S251112cm is reported by LIGO/Virgo with a false alarm rate of 1 per 6.2 years, nearby luminosity distance $93 \pm 27$ Mpc, probability of containing a SSM object of 100%, and probability of containing a $1-3~M_\odot$ object of just 8%. Such a system likely did not involve the supersolar neutron stars or black holes invoked to explain kilonovae. One must then also invoke hitherto unobserved and speculative models to produce SSM mergers and the resultant electromagnetic (EM) counterparts. We introduce a framework which vets and scores candidate counterparts to SSM GW events to inform follow-up in search of any among the zoo of potential EM transients: kilonovae, kilonovae-within-supernovae, super-kilonovae, or AGN flares from binary black hole mergers. We use a suite of telescopes to perform tiling, galaxy-targeted observations, and photometric/spectroscopic follow-up of promising candidates. In near-real time, we ingest candidates reported by the community, including some of the first observations reported by the Vera C. Rubin Observatory. We vet and score a total of 248 candidates, including 67 from Rubin, but find no likely counterpart. We nonetheless highlight candidates which demonstrate the ability of our framework to distinguish between different transient types and describe strategies to maximize the chances of detecting a counterpart to the next SSM event. Our framework will be implemented in the forthcoming Multimessenger Tool for Rapid Object Vetting and Examination (TROVE).

We study false vacuum decay catalyzed by black holes. We consider a scalar field model with unstable potential in the background of a dilaton black hole in two dimensions. The model reproduces many features of the Schwarzschild black hole background in four dimensions, including the centrifugal barrier for linearized field perturbations. We study decays from the non-equilibrium state describing the evaporating black hole immersed in the thermal bath with a different temperature. We analytically construct the tunneling solution relevant at small field excitations and evaluate the decay suppression. We show how they reduce to those for the Hartle-Hawking (equilibrium) and Unruh states in the corresponding limits. For large field excitations the decay proceeds via stochastic activation; we find the relevant non-thermal sphaleron configuration in a certain region of parameters of the model and construct the semiclassical solution describing tunneling onto this sphaleron. Our results provide insights into the vacuum decay induced by small primordial black holes in the radiation-dominated era of the universe.

One of the main features of nonlinear electrodynamics (NED) is the existence of an effective geometry that describes the geodesic motion of photons. A detailed analysis of the properties of effective geometry is of utmost importance for a better understanding of NED theories and their possible imprints on physics, especially in the context of black holes (BHs). We consider a NED model that depends on the two electromagnetic scalar invariants and obtain that the motion of photons in NED exhibits \textit{vacuum birefringence}, i.e., photons can propagate along two distinct paths, depending on their polarization. As a consequence of this phenomenon, we show that static black hole solutions sourced by NED can admit two distinct unstable light rings, leading to the formation of two distinct shadows. Moreover, to explore the potential astrophysical relevance of our results, we also compare them with the astrophysical observations for the shadow radius of Sagittarius A*. We place upper limits on the charge-to-mass ratio of the NED-sourced black hole. We also show that the motion of photons in this context can be interpreted as nongeodesic curves subjected to a four-force term from the perspective of an observer in the spacetime metric, generalizing previous results in the literature for NED models that depend on a single electromagnetic scalar invariant.

Luttinger's theorem constrains the particle density of interacting fermions through global properties of the single-particle Green's function, and its violation signals a breakdown of the identification between the quantized Hall response and the Green-function-based Ishikawa-Matsuyama invariant. This phenomenon becomes especially compelling in strongly correlated topological phases, such as fractional Chern insulators, where fractionalized quasiparticles lack an adiabatic connection to electrons, raising the question of how Green's-function-based topological invariants manifest in such phases. Using exact diagonalization of the fermionic Harper-Hofstadter-Hubbard model, we compute bulk single-particle Green's functions deep inside a fractional Chern insulating phase and directly evaluate the Luttinger count, its possible correction (the Luttinger integral), and the Ishikawa-Matsuyama invariant $N_3[\mathrm{G}]$. We demonstrate a clear violation of Luttinger's theorem and show that the fractional nature of the many-body Chern number is encoded in the Středa response of the Luttinger integral, while the integer invariant $N_3[\mathrm{G}]$ arises from the Středa response of the Luttinger count. We also analytically prove that $N_3[\mathrm{G}]$ is fully determined by the Luttinger count together with the Chern number of the occupied Bloch band, upon neglecting Bloch-band mixing. Finally, we propose an experimental protocol to extract all Green-function-based topological invariants from local density-of-states measurements, experimentally accessible in fractional quantum Hall systems.

We study a doubly minimized variant of the lautum information - a reversed analogue of the mutual information - defined as the minimum relative entropy between any product state and a fixed bipartite quantum state; we refer to this measure as the tumula information. In addition, we introduce the corresponding Petz Renyi version, which we call the doubly minimized Petz Renyi lautum information (PRLI). We derive several general properties of these correlation measures and provide an operational interpretation in the context of hypothesis testing. Specifically, we show that the reverse direct exponent of certain binary quantum state discrimination problems is quantified by the doubly minimized PRLI of order $α\in (0,1/2)$, and that the Sanov exponent is determined by the tumula information. Furthermore, we investigate the extension of the tumula information to channels and compare its properties with previous results on the channel umlaut information [Girardi et al., arXiv:2503.21479].

Nature contains massless particles with linear dispersions, and massive particles whose energies depend quadratically on their momenta with finite mass gaps. Both have equivalents in condensed matter physics in the form of collective modes and quasiparticles, measurable excitations with well-defined energy-momentum relations. A hypothesised third particle type - the super-luminal tachyon - would have an undefined energy at low momentum. A similar collective mode - long hypothesised within the hydrodynamic theory of matter - would have a purely imaginary energy at low momentum, corresponding to a finite lifetime. This third possibility has never been directly observed in a quantum system. Through a careful comparison of hydrodynamics with microscopic models of metals, we establish that this previously unseen third dispersion occurs in correlated quantum matter whenever the electronic fluid undergoes momentum relaxation due to explicit breaking of translation by impurities. As a specific example of these momentum-relaxed modes we consider the recent discovery of an acoustic plasmon - dubbed Pines' demon - in Sr$_2$RuO$_4$. The observed dispersion of this neutral mode differed significantly from the massless linear behaviour predicted by the random phase approximation. We demonstrate that the observed dispersion corresponds, in fact, to a momentum-gapped quasiparticle.

The Spin Foam approach to quantum gravity aims at providing a covariant path-integral formulation of canonical Loop Quantum Gravity. Since spin foam amplitudes are defined through discretisations of spacetime, understanding the continuum limit of the theory remains a central open problem. In this work, we investigate the structural aspects of this limit in a model-independent manner. We begin by introducing an axiomatic framework for spin foam amplitudes inspired by Atiyah's formulation of Topological Quantum Field Theories (TQFTs). In this setting, Hilbert spaces and amplitudes are assigned to combinatorial and topological data associated with triangulated manifolds. By equipping the set of triangulations with suitable orders, this framework provides a precise notion of continuum limit and allows us to analyse its properties independently of any specific model. We proceed then to systematically investigate how the specifics of the limit procedure allow to go beyond TQFT in the continuum. Under natural assumptions on the convergence of spin foam amplitudes, we establish a no-go result: sufficiently strong notions of convergence necessarily lead to a topological theory. Motivated by this obstruction, we weaken the notion of convergence and consider the continuum limit of spin foam amplitudes in a distributional sense, in the spirit of Refined Algebraic Quantisation. Under this assumption, the amplitude associated with the cylinder defines a rigging map, yielding a canonical construction of the physical Hilbert space. The resulting continuum amplitudes act as well-defined distributions on this space of physical states, characterising this formulation of the gravitational path integral as physical in a precise sense.

Motivated by the DAMA/LIBRA annual modulation signal, the dark matter community has invested heavily in ultra-clean underground NaI detectors to search for light WIMPs. We point out a new target of opportunity for these detectors -- axions produced by the carbon-burning stars within our galaxy. These stars synthesize large quantities of $^{23}$Na, keeping it at temperatures $\sim 10^9$K for periods up to tens of thousands of years. Under these conditions, $^{23}$Na radiates 440 keV axions through repeated photo-excitation and axio-deexcitation of its first excited state. Upon reaching a NaI detector, the process is reversed: the axion is resonantly absorbed, producing a 440 keV deexcitation photon. NaI thus serves as both $γ$ source and $γ$ detector. We find that existing NaI detectors can probe axion-nucleon couplings $|g_{aNN}^\mathrm{eff~^{23}Na}| \approx g_{app} \sim 10^{-6}$--$10^{-2}$, including QCD axions with $m_a \gtrsim 10$ eV. While there are several astrophysical constraints on axions with these couplings, our re-examination of these bounds shows that substantial gaps remain, providing strong motivation for the proposed searches.

N-point energy correlators are powerful observables for studying strong interactions, with applications ranging from extractions of the strong coupling $α_s$ to probes of jet modification in heavy-ion collisions and determination of the top-quark mass. Their practical use has, however, been limited by the complicated phase space for large N. Using a recently introduced parametrization that simplifies this structure, we study projected N-point correlators in two regimes: factorization in the back-to-back limit and leading non-perturbative effects in the collinear limit. While results in the back-to-back regime were previously limited to the energy-energy correlator, our approach allows us to derive the factorization theorem for arbitrary N. We compute the new ingredient, a one-loop jet function, needed for the next-to-next-to-leading-logarithmic resummation, which enables future $α_s$ extractions with complementary systematics. We further determine the analytic structure of leading non-perturbative power corrections for arbitrary N, including their dependence on the center-of-mass energy Q, the value of N, and the angular scale $x$. We present the first results for non-integer N<1, finding that the classical scaling in $x$ acquires an N-dependent modification, and that a new non-perturbative matrix element $\tildeΩ^{[N]}$ appears. In a certain approximation, $\tildeΩ^{[N]}$ can be related to the standard parameter $Ω_1$ relevant for N>1. Our analytic predictions are tested against the hadronization model in Pythia, finding good agreement. The results presented in this paper demonstrate the significant advancements enabled through our new parametrization of energy correlators.

$Q$-stars are a class of boson stars arising in scalar-field theories with interacting potentials, minimally coupled to gravity. We show that, in certain regions of parameter space, the angular velocity of stable timelike circular geodesics around $Q$-stars can attain a maximum at a nonzero radius. Notably, this behaviour may occur for stable configurations. This feature has been argued to produce effective shadows, but so far it has only been investigated for unstable solutions. We test this possibility by performing general relativistic magnetohydrodynamic evolutions for a representative stable $Q$-star model. A low-density, low-luminosity central region is indeed observed to form and persist -- at least until the evolution becomes affected by numerical viscosity. As a proof of principle, this suggests that families of stable bosonic stars can act as black hole mimickers. Moreover, for the model at hand, a heuristic analysis shows that the effective shadow has a comparable size to that of a Schwarzschild black hole with the same mass. Importantly, this mechanism for generating an effective shadow does not rely on the object being ultracompact, or an ad hoc chosen accretion disk.

Ram-pressure stripping is a key driver of galaxy morphological transformation in clusters, contributing to the formation of quenched, especially dwarf, populations. Ram-pressure compression can also induce a starburst prior to quenching and build up significant stellar mass in an initially gas-rich galaxy. The detailed physics of these processes remains poorly understood, especially in the low-mass regime. Here we demonstrate that the key factor for a ram-pressure induced starburst in a low-mass galaxy is its angular momentum within a host cluster. In this study, we select a sample of 41 post-starburst galaxies (PSGs) in the Coma cluster using the DESI EDR spectroscopic data, extending to low luminosities ($M_g < -14$). This sample is at least 90% complete down to $M_g \approx -14.8$, which enabled us a systematic analysis of their properties. For each galaxy, we use projected cluster-centric distances and line-of-sight velocities to constrain the normalized orbital angular momentum and a 3D radial coordinate to the cluster center, assuming zero orbital energy. The resulting probability distributions show that while star-forming galaxies are split into two populations favoring intermediate and high angular momentum, almost all PSGs prefer high angular momentum. Our analysis statistically demonstrates that ram-pressure-induced starbursts are more efficient on tangential orbits, where gas stripping proceeds slowly enough to allow substantial star formation before gas removal.

Many-body systems with strong interactions often exhibit macroscopic behavior markedly absent in single-particle or noninteracting limits. Such emergent phenomena are well exemplified in lattice Hubbard models, where the interplay between interactions, geometric frustration, and magnetic flux gives rise to rich physics. Superconducting qubits naturally enable analog quantum simulation of Bose-Hubbard models, while offering tunable parameters, site-resolved control, and rapid experimental repetition rates. Here, we study a superconducting-qubit device that realizes the Bose-Hubbard model on a triangular-ladder lattice. By tuning the magnitude and sign of couplings, we engineer a synthetic magnetic flux to characterize the resulting half-filling ground state for various parameter regimes. We measure observables analogous to current-current correlators and bond kinetic energies, finding signatures consistent with chiral superfluids, Meissner superfluids, and bond-ordered insulators. Our results establish superconducting circuits as a platform for robustly probing quantum phases of matter in frustrated Bose-Hubbard systems, even in strongly correlated and gapless regimes.

Measuring galaxy rotation curves is critical for inferring the properties of dark-matter haloes in the Lambda Cold Dark Matter ($Λ$CDM) paradigm. We present HI rotation curves and mass models for 20 galaxies from the MIGHTEE survey. Using extended HI kinematics, we construct resolved mass models that include stellar, gaseous, and dark-matter components. Stellar masses are derived using 3.6 $μ$m imaging under fixed mass-to-light ratio ($Υ_{*} = M/L$) assumptions and are complemented, for the first time for a HI-selected sample, by spatially resolved $M/L$, obtained from multi-wavelength SED fitting. We examine the ratio of baryonic to observed rotation velocity ($V_{\rm bar}/V_{\rm obs}$) at the characteristic radius $R_{2.2}$. Adopting a fixed $Υ_\star = 0.5\,M_\odot/L_\odot$ yields a clear dependence of $V_{2.2}/V_{\rm obs}$ on galaxy luminosity, while adopting $Υ_\star = 0.2\,M_\odot/L_\odot$ substantially weakens this trend. In contrast, the resolved $M/L$ analysis preserves the luminosity dependence while modifying the stellar contribution on a galaxy-by-galaxy basis, providing a more accurate representation of the underlying relation. We model the dark-matter haloes using Navarro-Frenk-White profiles and find that the different assumptions for a fixed a $M/L$ systematically shift galaxies relative to the theoretical stellar-to-halo mass and baryonic-to-halo mass relations, while the spatially varying $M/L$ yields the closest agreement with theoretical benchmarks within $Λ$CDM. We therefore demonstrate that future investigations of the dark matter properties of galaxies using rotation curves need to account for varying $M/L$ across individual galaxy profiles and between galaxies in order to obtain accurate measurements of the dark matter, and therefore test $Λ$CDM.

Galactic haloes host a complex, multiphase circumgalactic medium (CGM), and at high redshift are fed by cold, filamentary inflows. In contrast, mature galaxy clusters are dominated by a hot, enriched, X-ray emitting intracluster medium (ICM), with cold gas largely confined to member galaxies. However, the transition between these regimes remains poorly constrained. We present a cosmological zoom-in simulation of a massive cluster progenitor evolved to $z=2.7$, with enhanced CGM resolution to better trace the accretion, mergers and feedback events that precede the birth of the ICM. We connect this evolution to mock MgII and OVII absorption, tracing low and high ionisation gas phases. We also study Lyman-$α$ (Ly$α$) and Balmer-$α$ (H$α$) haloes in emission, using radiative transfer in post-processing. Between $z\sim4.4$ and $2.7$, a major merger and AGN feedback drive an inside-out transformation, redistributing gas to larger radii and flattening density, temperature and metallicity profiles. Intermediate column MgII absorbers are rapidly destroyed, leaving a clumpier cold gas distribution associated with satellites, while gas is ionised beyond OVII as the inner halo enters the X-ray regime. An extended Ly$α$ halo remains detectable even without AGN photoionisation, and evolves from filamentary to more spherical as inflowing gas is disrupted. Our fiducial model underpredicts observed central Ly$α$ emission - we likely require more efficient Ly$α$ production in the nuclear region, either through more effective escape of stellar Ly$α$ photons or through enhanced conversion of AGN-powered ionisation into Ly$α$ emission. H$α$ haloes are dimmer and smaller than Ly$α$, but with JWST may provide a complementary probe of the evolving CGM at this critical epoch.

In J. Chem. Phys. 152, 144105 (2020) Lehtola et al introduced the efficient Gaussian-basis representation of Superposition of Atomic Potentials (SAP) which "can be easily implemented in any Gaussian-basis quantum chemistry code in terms of two-electron integrals". Here we demonstrate that it is possible to evaluate Gaussian AO representation of SAP by nearly trivial modification of one-electron nuclear attraction integrals.

We consider the Gabor system $\mathcal{G}(g,a\mathbb{Z}\times b\mathbb{Z})$ generated by a continuous, compactly supported function $g$ over the time-frequency lattice generated by the parameters $a$ and $b$. We show that, under an appropriate ordering of the Gabor elements, certain submatrices of the Gram matrix of $\mathcal{G}(g,a\mathbb{Z}\times b\mathbb{Z})$ exhibit a block-Toeplitz structure. This structural property enables us to derive spectral results for finite sub-blocks of the Gram matrix by appealing to the spectral theory of Toeplitz matrices. In particular, we apply our results to the Gram matrix of Gabor systems generated by the $N$th-order B-spline.

Many diatoms follow a size diminuation - size restoration cycle in their vegetative phase, leading to daughter cells that differ in size. For the diatom Seminavis robusta, we investigated by cell tracking over several generations whether the size difference reflects also in different intermitotic times or in the mobility of the cells. A tracking setup and machine-learning based detection algorithm was developed that revealed no significant difference in intermitotic times, a weak coupling to the day- night cycle, and a higher motility of the hypothecal, smaller daughter cell.

Within the general framework of $f(R)$ gravity, we introduce a function of the electromagnetic curvature invariant $f(\mathbb{F})$ that couples minimally to gravitation to ensure a consistent treatment of curvature functions in these theories. We show that one of the solutions leads to field equations that are a generalization of the Klein-Gordon equation while the other leads to a typically non-linear massless solution. Focusing on flat spacetime, our formalism recovers the Plebanski family of models and Bopp-Podolsky electrodynamics as specific limits. These extensions may have phenomenological consequences in extreme environments, such as the early universe or near charged compact objects, where deviations from classical electrodynamics might be probed.

There is a recent interest in studying odd elasticity in soft solids. Current focus has been on simple solids. However, many soft solids are structured and can exhibit nematic elasticity or viscoelasticity. Here we generalize the concept of odd elasticity to nematic elasticity. By rewriting the governing equation for two-dimensional nematic liquid crystals (LCs) in terms of complex Ginzburg--Landau equation, we propose an odd nematic elastic term and its stress term in the hydrodynamic model of nematic LCs. The odd nematic elasticity can be physically interpreted as non-reciprocal interactions between neighboring directors. In odd nematics we find that domain walls become self-propelled and are accompanied by a bidirectional flow, and point defects can self-spin, develop a spiral pattern, and induce a vortical flow. Interactions of a pair of defects show rich dynamics that are distinct from those in active nematics. As such, we have developed an odd general elasticity, which can be further generalized to other viscoelastic materials, and proposed a novel way to manipulate topological defects in nematic LCs.

We define a deterministic family of permutations generated by an alternating center-edge extraction process on the ordered set [n] = {1,2,...,n}. Starting from the ordered list (1,2,...,n), one repeatedly removes the median element or elements of the current list, then removes its extreme elements, alternating these two operations until the list is exhausted. The resulting output is a permutation pi_n in S_n, which we call the Median-Extremes Alternation (MEA) permutation. Although the construction is elementary, the resulting permutations exhibit unexpectedly rigid combinatorial structure. We prove that pi_n is always an alternating permutation, with parity-dependent alternating type. As a consequence, its descent set is completely determined by the parity of n. We also prove an exact formula for the inversion number, inv(pi_n) = floor((n-1)^2/4), which immediately yields a characterization of the sign of pi_n. In addition, we give an exact recursive description of the family and a recursive formula for the inverse permutation.

In this paper, we study the concept of complex fuzzy soft matrices. The application of complex fuzzy soft matrices in signals and systems via the cross product of complex fuzzy soft matrices and Fourier transform was carried out. In this application, an algorithm for the identification of a reference signal out of large interest signals detected by a digital receiver was presented. It was recorded that, the Fourier transform is better because it gave a higher optimal value and as a result, there was a better reference signal $R.$

The resource theory for nonnegativity of quantum amplitudes distinguishes completely positive completely positive (CPCP) quantum channels from the larger and more tractable class of completely positive doubly nonnegative (CPDNN) quantum channels. It was left open whether there exists a qutrit-to-qubit quantum channel \(Φ:M_3\to M_2\) that is CPDNN but not CPCP. We answer this question in the negative and prove the stronger statement that every CPDNN quantum channel \(Φ:M_n\to M_2\) is CPCP for every \(n\in\mathbb N\). Equivalently, for qubit-output quantum channels the doubly nonnegative relaxation is exact.

Raman spectroscopy is a promising tool for microbial identification, yet its implementation in microbiology and clinical workflow is still restricted due to the accompanying additional preparation required to focus on microbial signals. Here, we demonstrate Raman-based bacterial identification directly from unopened, inverted agar plates, the same conditions used during incubation. Our approach enabled identification with single gene-level sensitivity using two Escherichia coli variants, differing only in green fluorescent protein (GFP) expression, across diverse media and substrate material conditions, despite the interrogation path traversing 3-4 mm thick background material. We integrated traditional density functional theory (DFT)-based material computation with machine learning analysis, achieving over 97.7% classification accuracy, surpassing the performance of standard measurements from opened plates by 10.8% higher mean accuracy and 0.76% less variance. We further demonstrated Raman mapping-based colony identification via Raman peaks characteristic to GFPmut3 chromophore structure generated by DFT. Our approach is robust to changes in algorithms or substrate materials and promises real-time, non-perturbative monitoring of bacterial growth, biofilm formation, and antimicrobial resistance development.