Papers

Recent studies have revealed that not only does the correspondence between spectral winding numbers and skin modes break down in non-Hermitian systems, but the energy spectrum itself is highly sensitive to generic perturbations, system size, and boundary conditions. In amorphous non-Hermitian systems, where the positions of lattice sites are uncertain, the spectral instability becomes even more severe, making it difficult to identify stable topological edge states from the eigenvalue spectrum alone. To overcome this challenge, we introduce a correspondence between stable zero-mode singular states and mid-gap states of the energy spectrum in the thermodynamic limit. Because the singular value spectrum is highly robust against small perturbations and variation in size, topological edge states can be reliably probed via singular values even in finite-sized systems. Based on the singular-value decomposition of the Hamiltonian, we construct a topological invariant in real space to characterize the associated topologically protected edge states. Our approach provides a general strategy for exploring point-gap topology in real space and redefine the non-Hermitian skin effect from a new perspective.

Four-dimensional (4D) topological systems provide a promising platform for exploring topological phenomena beyond three dimensions. So far, extensive recent studies on 4D topological insulators have focused on the 4D Dirac model, while its second Chern number is restricted to a limited set of values. In this work, we demonstrate that introducing long-range hopping into the 4D Dirac model induces topological phases with high second Chern numbers. Furthermore, we show that the long-range hopping can transform a trivial insulator into a topological insulator with a nonzero second Chern number. Our work establishes long-range hopping as a powerful route for engineering 4D topological states and reveals new possibilities for realizing unconventional topological phases beyond minimal models.

(2,p) minimal Liouville gravity admits four algebraic descriptions interrelated by dualities. On the Frobenius manifold (FM) side the theory is built either on the $A_{1}$ manifold of $Q(y)=y^{2}+u_{1}$ ($y$-side) or on the $A_{p-1}$ manifold in the variable $x$ ($x$-side). On the spectral curve / topological recursion (SC) side the analogous choice is the Chebyshev curve and its $x\leftrightarrow y$ swap. FM-$y$, SC-$y$ require a resonance transformation between the KdV times and the Liouville couplings, while the other two do not. We work out the explicit correspondence between the four approaches at the level of the dispersionless tau-function. The normalisation-independent three-point ratios agree with conformal field theory in all four formulations, and matching the full amplitudes fixes a single per-insertion factor reproducing the signed Verlinde matrices. We use the Kharchev–Marshakov integral transform of the basis functions, whose determinant gives an explicit relation between the corresponding tau-functions and realises the $x\!\leftrightarrow\! y$ swap at genus zero. Once the independently fixed linear SC-$x$ normalisation is imposed, the Laurent deformation in the second coordinate gives an alternative genus-zero derivation of the known compact resonance transformation for the whole (2,p) series, including all mixed coefficients.

The Born-Oppenheimer (BO) and single-surface Born-Huang (BH) approximations replace the full molecular problem by nuclear motion associated with one clamped electronic state, whereas the full BH expansion and exact factorization (EF) are exact representations. We use two analytically transparent models to identify what controls one-surface error. For Fernández's bilinearly coupled oscillators, the Brattsev ground-state bracket was already known; we derive closed-form differences proving strictness for every positive nuclear mass and nonzero stable coupling. Using Hunter's conditional-amplitude construction, we place the closed-form ground-state EF potential alongside BO and single-surface BH. Exact excited-state calculations show that the bracket does not extend through the spectrum. The diagonal BH correction is the quantum-metric coefficient of the retained electronic state divided by twice the nuclear mass. Fernández's sixth-order expansion shows that the next omitted correction contains the same derivative couplings, an additional inverse electronic-energy separation, and a factor depending on the nuclear state. We therefore add a two-state model with a position-dependent gap. Decreasing its minimum separation makes the metric higher and narrower while leaving the total Fubini-Study length equal to pi/2. The exact EF, BO, and BH potentials can differ visibly even when their nuclear ground-state amplitudes are nearly identical. The two models show that one-surface accuracy depends on nuclear mass, electronic-state variation, energy separation from omitted states, and the nuclear wavefunction.

Nature exhibits a wide variety of nonlinear phenomena characterized by strong fluctuations that push the system away from equilibrium. Recent studies have shown that non-extensive statistics are more suitable for analyzing these phenomena, as they can capture long-range correlations and heavy-tailed distributions that conventional Boltzmann-Gibbs statistics cannot represent. However, estimating the non-extensiveness parameter ($q$) is not trivial, and methods vary significantly across disciplines. This paper presents a systematic and interdisciplinary comparison of three fitting methods: direct nonlinear fitting of the probability distribution function (PDF), linearization using the q-logarithm function, and numerical fitting of the cumulative distribution function (CDF). We applied this analysis to various phenomena, from areas such as geophysics, space weather and economics, analyzing the critical impact of discretization. The results show that $q$ estimates are highly sensitive to histogram binning, while the CDF-based method provides a bin-free alternative that yields more stable estimates for the datasets analyzed here. This contribution provides relevant information for the search for a method that allows the correct determination of the parameters of heavy-tailed distributions in various disciplines.

In the present paper, we derive a new charged black hole solution embedded in a quintessence field within a framework combining the Rastall and massive gravity in an asymptotically flat spacetime. We interpret the integration constant associated with the structural properties of the quintessence field as a thermodynamical variable. In this context, several limiting cases have been explored with the aim to shed light on the role of the model parameters. Then, we analyse the thermodynamic properties and stability of the charged black holes in flat spacetime, where the quintessence field is characterized by the state parameter \( \omega_q = -2/3 \). Detailed studies are perfomed to see how the various parameters affect phase transitions between small and large black holes. In particular, we establish a connection between the impact parameter and unstable circular photon orbits with the thermodynamic phase transitions. Our analysis suggest that the photon sphere observables could remarkably provide an indirect observational signature of black hole thermodynamic critical transitions. Generally, thanks to the effective contribution of the quintessence parameter, we found that the overall thermodynamic behavior basically resembles that of the charged RN–AdS black hole with thermal features analogous to of a Van der Waals fluid ones. Finally, we have checked these findings using thermodynamic geometry with the Quevedo metric. Our results showed that the critical behaviour derived from the standard thermodynamics is fully consistent with geothermodynamics description, where the phase structure and divergence points exactly coincide with those identified from heat capacity and Gibbs free energy analyses.

In this Brief Communication, we establish the notion of critical damping for generic two-degree-of-freedom system. For given set of masses and stiffnesses, the critical damping corresponds to the real eigenvalue with maximal multiplicity, equal to minus geometrical mean of the eigenfrequencies. This case corresponds to the fastest possible asymptotic decay rate for generic initial conditions. The damping matrix for the critical case is unique up to reflection of one modal coordinate and, generically, non-diagonal. Quite surprisingly, for large difference of the eigenfrequencies, it is also not positive definite. Therefore, physical realization of the critical case will require active elements that provide negative effective damping.

The dispersion relations of the helicon and Trivelpiece–Gould (TG) waves in a steady, fully developed magnetised plasma column are well established, but the discharge does not begin in that state. During ignition the electron density rises through five to seven orders of magnitude and the electron–neutral collision frequency falls by two to three, so the dispersion relation is itself a time-dependent object whose very existence must be justified. This paper develops a closed analytical theory of that transition for a cylindrical column in a uniform axial field, using a cold, collisional, two-species description that remains regular in the vacuum limit. Three structural results emerge. First, the vacuum limit is a degenerate double root of the quartic governing the perpendicular wavenumber; the helicon and TG branches are not independent modes that appear at some threshold but the two lobes of a single vacuum root, split by the gyrotropic and anisotropic parts of the dielectric tensor. The leading-order contribution to the discriminant cancels identically, so the branches separate linearly in density rather than with the square-root behaviour generic to a perturbed repeated root; the separation is correspondingly suppressed, and the helicon root remains pinned at its vacuum value until the electron density reaches about 10$^{15}$ m$^{-3}$ while the TG root departs immediately.

Optimization of next-generation materials synthesis and manufacturing processes can be accelerated by effective use of digital datasets. However, a majority of existing custom research infrastructure, including that for thin film deposition, is primarily manually operated and not compatible with this new research paradigm. Here, a template is provided for upgrading existing manual deposition chambers to enable automated and autonomous experimentation. As an example, the upgrade of an existing magnetron sputtering chamber dedicated to synthesis of wurtzite ferroelectrics is presented. Focus is placed on automation of instrumentation; system and deposition control; and synchronized and automated data collection strategies. An example use case of the system for semi-autonomous determination of process-property relationships is presented, specifically minimization of coercive field in wurtzite Al$_{1-x-y}$Sc$_x$B$_y$N thin films.

Monolithic photonic integrated circuits (PICs) platforms exploiting III-V materials combine passive and active waveguide structures in multi-section optoelectronic device architectures. Their operation requires high electrical isolation between adjacent functional sections without compromising the optical signal. This fundamental requirement is addressed for GaSb-based waveguides, which are known to exhibit high conductivity of p-type layers reducing the electrical isolation capability. To this end, a co-designed electrical-optical isolation strategy based on using deeply etched strip waveguides combined with adiabatic ridge-to-strip waveguide tapers in GaSb-based multiple-quantum-well heterostructures is proposed. While deep etching alone enables isolation resistances of up to 40 k-ohm, it severely degrades optical propagation. By introducing optimized adiabatic tapers, we demonstrate good optical performance as single-mode continuous-wave lasing in a two-section device with integrated absorber, while maintaining an isolation resistance of 17.3 k-ohm; this corresponds to an approximately 17-fold improvement over previously reported GaSb two-section devices. The approach establishes a critical building block for the development of monolithic GaSb-based PICs operating above 2 um.

Four-wave mixing provides a simple setting in which dispersion, nonlinearity, and non-Hermiticity compete to select resonant energy-transfer channels. We study degenerate four-wave mixing in a Kerr dual-core coupler with balanced gain and loss and frequency-dependent intercore coupling. The dispersive coupling changes the symmetry from conventional $\mathcal{PT}$ symmetry to a combined $\mathcal{CPT}$ symmetry and reshapes the two-branch linear spectrum. We determine the unbroken-$\mathcal{CPT}$ domain and classify the branch configurations that can satisfy the degenerate phase-matching condition. In the parameter ranges examined, three resonant channels persist over broad regions, whereas a same-branch channel appears only close to the symmetry-breaking threshold. In this near-threshold regime, a single pump can simultaneously satisfy two distinct nonzero sideband resonances. Direct pulse simulations confirm the predicted resonances and reveal secondary-wave generation and multifrequency cascades near eigenmode coalescence. A reduced three-wave model captures the initial dynamics away from the exceptional point but loses accuracy as the modal basis becomes ill-conditioned. These results show how dispersive coupling reorganizes resonances, group-velocity mismatch, and nonlinear energy exchange in a non-Hermitian wave system, and they identify the exceptional-point region as a regime where a few-mode description can break down.

We present an asymptotic analysis of two diffusive capture problems in general smooth closed three-dimensional geometries with multiple small reactive boundary patches of arbitrary shapes. (i) The narrow escape problem seeks to determine the escape rate of Brownian particles from an enclosed region through small boundary windows. (ii) The related Berg-Purcell (or narrow entrance) problem seeks to resolve the capture rate for signaling molecules diffusing outside the cell and entering through localized reactions at membrane-bound receptors. We obtain matched asymptotic solutions of these two problems and thus address the long-standing challenge of describing the role that curvature and local reactivities play in modulating diffusive capture rates. Our explicit expansions quantify local effects on diffusive capture through the sizes, shapes, and reactivities of the patches together with the principal curvatures of the manifold at each patch. In turn, we examine global effects on diffusive capture such as the spatial configuration of patches on the manifold, as encloded by the associated surface Neumann Green's function and its regular part. The accuracy of our asymptotic formulas is validated against a full numerical solution for an ellipsoidal domain. Overall, our results yield new insights on how geometry and stochasticity combine to shape the dynamics of various biological processes.

The daily return of a stock is often restricted to an exchange-imposed band to curb extreme fluctuations. Any attempted price movement beyond this band is clipped, leaving an unobserved excess. We introduce a minimal stochastic latent-state model in which a fraction of this hidden excess is retained for the next day. This retention generates memory, even though the daily stochastic driving shocks are independent. For symmetric driving shocks with regularly varying tails, the stationary latent return preserves the tail index of the noise, but has an enhanced tail amplitude. In the wide-band limit, a close of the daily return at either limit of the band admits a single-dominant-shock description. We show that after such an event, the mean return on the following day has the same sign and grows proportionally to the band width, while the probability of reaching the same limit again approaches a finite value. Reaching the opposite band limit on the following day requires a second extreme shock of opposite sign and is power-law suppressed. Simulations support these analytical predictions. Empirical data from stocks subject to daily price limits are qualitatively consistent with the predicted same-sign response and its increase across wider price bands.

Suppressing coherent energy backflow while maintaining extractable energy in a stable nonequilibrium state remains a central challenge for quantum energy storage. Here, we introduce a reservoir-engineered dual-charger quantum battery architecture, in which nonequilibrium dissipation is exploited as a control resource to stabilize useful stored energy. A hot-reservoir-coupled driver supplies excitations, while a cold-reservoir-coupled cache biases the resonant three-body transition toward charging and suppresses the dressed-state coherences responsible for energy backflow. This mechanism establishes a population-inverted steady state with finite ergotropy and converts reversible charger–battery exchange into persistent energy storage. For uniformly spaced multilevel batteries, we show that the stored energy and ergotropy scale approximately linearly with the number of accessible levels, while the stored-energy utilization approaches unity. The accompanying stationary heat current provides a thermodynamic signature of the charging regime. Our results demonstrate dissipation engineering as a strategy for achieving stable and scalable quantum energy storage beyond transient coherent charging protocols.

In this contribution, we present thermal photon production mechanisms within a magnetized quark-gluon plasma, utilizing the framework of Landau-level quantization. We examine the specific influences of the magnetic field, chemical potential, and chiral chemical potential on photon yield and polarization. By providing a more comprehensive theoretical description of photon production across the full evolution of heavy-ion collisions, our study offers a promising new avenue for resolving the photon $v_2$ puzzle and potentially detecting the signature of magnetic fields in heavy-ion collision experiments.

We investigate two parity-time-symmetric ring resonators coupled over a finite angular region described by a super-Gaussian profile. In the linear regime, analytical spectra are obtained in the homogeneous-coupling and fixed-amplitude narrow-contact limits, while the finite-width problem is treated numerically. Local coupling introduces nonzero spatial Fourier components that mix angular harmonics and lift the degeneracy of counterpropagating modes, resolving each excited doublet into parity-dependent branches. Collisions among these branches generate multiple exceptional-point boundaries and disconnected broken-PT domains. The resulting phase diagrams exhibit re-entrant unbroken-broken-unbroken transitions when the gain-loss strength, coupling width, or peak coupling amplitude is varied. The numerical spectra continuously recover both analytical limits. In the nonlinear regime, selected ground and excited linear modes are used as seeds for adiabatic propagation into finite-amplitude Kerr waveforms that remain dynamically persistent over the simulated observation interval for finite ranges of nonlinear strength. These results show that the spatial profile of inter-resonator coupling provides a geometric means of controlling multimode PT transitions and selecting dynamically accessible nonlinear waveforms in coupled-ring systems.

Nonseparability among multiple degrees of freedom has enabled fundamental advances in structured light and related applications. Here we unveil a previously overlooked form of nonseparability in phase space, which we term geometric phase-space nonseparability. The latter arises solely from the wavefront curvature of a conventional wave packet, such as a fundamental Gaussian beam. This phase-space structure manifests as a position-dependent transverse-momentum distribution across the beam profile leading to the giant spatial and angular beam shifts upon reflection at a planar interface that we predict analytically and observe experimentally. Remarkably, the curvature-induced phase-space correlation remains robust against spatial-coherence degradation, allowing the giant shifts to persist even in the nearly incoherent regime. Our results establish wavefront curvature as a general mechanism for engineering beam shifts across optical, acoustic, and matter-wave systems.

In this paper, we study the impact of different cross-section models in the measurement of the neutrino oscillation parameters in DUNE. In particular, for the quasi-elastic (QEL) region, we considered the Llewellyn-Smith formalism (LS) and the Hartree-Fock Continuum Random Phase Approximation (HF-CRPA) and for the resonance (RES) region, we consider the Rein-Sehgal (RS) and the Berger-Sehgal (BS) models, and compare our results with the DUNE cross-section tune (Valencia model for QEL and RS model for RES), which was considered in their technical design report. Our results show that while the DUNE tune is best for QEL, the best model for RES is BS. As the DUNE energy region is mainly dominated by RES, for the total cross-section, the HF-CRPA+BS model provides the best strength in the cross-section, whereas the DUNE tune is the weakest among all the configurations considered in our work. Regarding the neutrino mass ordering, CP violation and octant sensitivity, the HF-CRPA+BS model provides $(25- 30)$% improvement, and regarding the precision of the $\theta_{23}$ and $\Delta m^2_{32}$, the same model provides $(15 - 20)$% improvement as compared to the DUNE tune.

We investigate the redistribution of continuous-variable quantum discord within the framework of an expanding universe. We find that quantum discord exhibits stronger sensitivity to the spacetime expansion rate than to the expansion volume. As both the expansion rate and expansion volume increase, the initial quantum discord shared by the two bosonic modes decays, while quantum discord is induced in additional mode pairs by the underlying spacetime expansion, signaling a global redistribution of quantum correlations across the system. Specifically, the induced discord is largest for cross-observer bosonic-antibosonic pairs, followed by same-observer bosonic-antibosonic pairs, and smallest for the pair of antibosonic modes. Furthermore, our quantum discord analysis demonstrates that particles with lower momentum and optimal mass serve as more favorable candidates for extracting information about the expanding universe. This work substantially enriches the theoretical framework of quantum discord in expanding spacetimes, and provides new perspectives as well as a solid theoretical foundation for further investigations.

We investigate small-instanton contributions to the axion potential across a range of KSVZ models containing vector-like quarks~(VQs), using naive dimensional analysis. We consider scenarios containing a single VQ, multiple identical copies, and sets of distinct VQs, requiring in each case that the gauge couplings remain perturbative up to the Planck scale under the two-loop gauge running. The associated fermion zero-mode content varies between these cases, requiring different combinations of mass insertions and scalar–Yukawa contractions for its saturation. Increasing the copies of VQs can render the instanton-size integral dominated by instantons of the smallest size, corresponding to the scale near the ultraviolet~(UV) cut-off. The resulting contribution then becomes sensitive to the UV completion and the induced potential can compete with, or dominate over, the ordinary QCD contribution. Assuming that the QCD and small-instanton potentials are aligned, we determine the resulting axion-mass shift and its consequences for the axion–photon coupling. When the small-instanton induced susceptibility becomes comparable to or larger than the QCD susceptibility, the physical axion mass of $m_a$ is enhanced at fixed decay constant~$f_a$, while the axion-photon of $g_{a\gamma\gamma}$ coupling remains controlled by $f_a$ and the anomaly ratio of $E/N$. The standard QCD relation among $m_a$, $f_a$ and $g_{a\gamma\gamma}$ is consequently modified, opening new regions of the $(m_a,g_{a\gamma\gamma})$ plane for axion searches.

We study two conformal images of the HKLL reconstruction problem for a conformally coupled scalar on AdS$_3$. The first mapping is to a Dirichlet problem on one half of the Einstein static universe. A further conformal transformation maps this half-ESU problem to a massless scalar in a region of $(2+1)$-dimensional Minkowski space bounded by an uniformly accelerated circular Dirichlet mirror. However, the global HKLL problem, the resulting flat-space problem is not a generic local mirror problem with arbitrary boundary data. Rather, the mirror response data must belong to a restricted spectral class inherited from normalizable global AdS modes. We formulate and solve this restricted mirror problem intrinsically in flat space. In the process, we find an example of a valid smearing function which itself does not satisfy the equations of motion. We further consider AdS-Rindler wedge reconstruction. By conformal mapping to an appropriate coordinate system in flat space, we find a simple way to see the blow-up of the smearing function.

Expanding the operational boundaries of radiation detection is imperative for contemporary particle physics, astrophysics, and cosmology. At this frontier, the direct detection of the Cosmic Neutrino Background (C$\nu$B), the determination of the absolute neutrino mass scale, and the search for sub-GeV Light Dark Matter (LDM) necessitate detector architectures capable of sub-millielectronvolt (sub-meV) energy thresholds, exceptional absolute energy resolution, fast time response, and massive scalability. Current technologies confront an intrinsic limit—the “impossible triangle”—wherein optimizing for sub-meV thresholds inherently compromises either macroscopic timing response or spatial scalability. Here, we introduce the Superconductor-Coupled Semiconductor Electron-Multiplying (SuperEM) detector, a fundamentally novel structural paradigm designed to bypass this limitation. The architecture couples the ultra-low energy threshold of a superconducting absorber with the intrinsic high-gain digitization of a strongly biased, high-density semiconductor P-N junction. Incident energy yields a proliferation of non-equilibrium quasiparticles, which are subsequently extracted via quantum tunneling across an ultra-thin Atomic Layer Deposition (ALD) insulating barrier. Building upon our prior empirical validation of deep-cryogenic avalanche mechanics, this manuscript establishes the fundamental theoretical feasibility and structural foundation of the complete device. Signal transport simulations confirm that an undoped interface coupled with a strong drift field enables highly efficient, nanosecond-scale transient electron drift, resolving completely within 35 ns. The SuperEM architecture thus constitutes a scalable, high-resolution, and fast time-response framework for next-generation C$\nu$B and LDM observatories.

The excitation spectrum of an anisotropic magnet provides a direct link between its microscopic Hamiltonian and interaction-driven quasiparticles. Here we use high-resolution time-domain terahertz spectroscopy to map the magnetic excitations of the three-dimensional kagome-staircase compound Co$_{3}$V$_{2}$O$_{8}$ as functions of temperature and magnetic field. At low energies, polarization-resolved spectra identify magnetic-dipole-active one-magnon modes and track their evolution across the ferromagnetic and spin-density-wave phases. Combining their field dependence with previously reported inelastic-neutron-scattering dispersions, we determine an effective spin-$\frac{1}{2}$ Hamiltonian with strongly anisotropic exchange that quantitatively reproduces the one-magnon spectrum. This model provides a noninteracting benchmark for the high-energy response, where we observe sharp branches with field slopes that are two to four times those of the one-magnon modes, together with anticrossings between branches of different magnon numbers. Their sharpness, polarization dependence, and departure from the calculated multi-magnon continua identify them as interacting multi-magnon quasiparticles that can be stabilized by strong exchange anisotropy.

Femtosecond relativistic electron beams are key probes of ultrafast dynamics, and their pulse duration directly limits the achievable temporal resolution. Laser wakefield acceleration (LWFA) provides a compact source of such beams, but the injection-induced energy spread makes bunch compression sensitive to nonlinear longitudinal transport, motivating direct longitudinal phase space (LPS) measurements. Here, a terahertz transverse-deflecting cavity (THz-TDC) combined with a dipole magnet is used to reconstruct the nonlinear LPS of LWFA electron bunches compressed in a double-bend achromat (DBA), resolving a characteristic C-shaped distribution associated with higher-order longitudinal transport. At an average energy of approximately 4.55 MeV, the diagnostic achieves a temporal resolving power of 1.8 fs and an energy resolution of 6.0 keV, corresponding to a relative energy resolution of 0.13%. For comparable energy spreads of approximately 2.9%, shifting the transmitted energy-window center from 4.574 MeV to 4.532 MeV moves the selected beam away from a low-slope region of the nonlinear LPS and increases the root-mean-square bunch length from 26 fs to 42 fs; with the window center held near 4.553 MeV, increasing the energy spread from 2.0% to 4.4% lengthens the bunch from 27 fs to 44 fs. These results show that the final bunch duration is governed by both the position and width of the transmitted energy window within the nonlinear LPS, establishing an LPS-guided strategy for optimizing DBA-compressed LWFA electron bunches and providing a basis for future higher-order phase-space correction.

We present the commissioning and first results of the Thirty and Forty Gigahertz Instrument (TFGI), which observes the sky at 31 and 41 GHz with angular resolutions of 21' and 18' from the second QUIJOTE telescope at the Teide Observatory. Its primary goal is to conduct a deep cosmological survey in selected regions of the Northern sky with high-sensitivity polarization measurements. The commissioning phase covered Nov2021-Oct2022, during which the instrument operated with a configuration of 7 receivers, 4 at 31 GHz and 3 at 41 GHz. Over this period, approximately 1200 h of data were acquired. Of these, 380 h were dedicated to calibration sources, used to characterize the instrumental properties of TFGI, including the pointing model, beam response, gain stability, polarimetric performance, and instantaneous sensitivity. We provide a detailed characterization of these properties and describe how they are being improved for future observing runs. We use 230 h of observations from bright Galactic regions (Cygnus, W43, W44, and W47) to further validate the instrument performance. As an illustrative example, we present the intensity and polarization spectral energy distributions of W44, finding good agreement with existing measurements. From the noise map of these observations, we measure a polarization sensitivity of ~8.3 $\mu$K deg$^{-1}$ after an effective observing depth of 0.57 h deg$^{-2}$. This performance, achieved considering only 2 detectors at 31 GHz, is already comparable to that achieved by WMAP (with almost 3 times the integration time per unit area, 1.61 h deg$^{-2}$). Extrapolating these results to the full TFGI array, with up to 29 detectors, we show that the instrument is expected to reach the target sensitivity of ~ 1 $\mu$K deg$^{-1}$ at both 31 and 41 GHz over three cosmological fields covering a total area of 3600 deg$^2$ after an effective integration time of 5.7 years.

Knowledge distillation transfers more than task competence: it also transmits response propensities, refusal policies, error boundaries, and latent safety biases. We formulate this behavioral inheritance as a coarse-graining model grounded in statistical mechanics, in which the student's answer and refusal decisions define two macrostates, while the teacher induces an effective field that reshapes the student's free-energy landscape. The model yields a reliability-safety trade-off relation controlled by a single parameter K, which we term the hazard discrimination capability. The predicted trade-off is consistent with refusal-token data [arXiv: 2412.06748]. In knowledge distillation, a teacher with strong hazard discrimination improves the student's attainable reliability and safety, whereas poor discrimination limits the attainable trade-off. Repeated distillation acts as an iterated renormalization-group-like transformation, under which K follows a flow across generations. The flow exhibits a tricritical structure separating regimes of K loss, stable transmission, and threshold-dependent inheritance, and yields testable scaling predictions for multigenerational distillation.

Biological recognition rarely rests on one strong bond. It works by forming many weak ones at once, between crowded, deformable surfaces in water. This review develops that process as a problem in statistical mechanics. Counting the ways two multivalent objects can bind proves to be the classical monomer-dimer problem on a graph, with a rigorous consequence: the apparent switching of multivalent binding is always a smooth crossover, never a phase transition. Three constraints follow. A repulsive surface layer is obligatory rather than a design choice; bonds do not act independently; and since free energies enter rates exponentially, small changes in receptor number shift binding lifetimes by orders of magnitude. One set of equations then covers antibodies, lipoproteins, and T cell recognition. In each, what decides the outcome is not the strength of any single bond but how a fixed total is spread over many: affinity is a property of a molecule, selectivity a property of an assembly.

Fluids with nonvanishing antisymmetric components of the transport coefficient tensor are named odd fluids. In our previous works, we proposed a mesoscale simulation model for isotropic two-dimensional odd fluids and then extended it to the three-dimensional case to model an anisotropic odd fluid with cylindrical symmetry. The Navier-Stokes equation and the viscosity tensor of this three-dimensional mesoscale odd fluid were derived previously via a kinetic theory. Herein, we derive the heat conduction and self-diffusion equations, along with the corresponding thermal conductivity and self-diffusivity tensors. These theoretical results are validated by simulations. We further investigate heat and mass transport behaviors of three-dimensional odd fluids in a confined geometry through our mesoscale model. In striking contrast to normal isotropic fluids, the steady-state temperature and density distributions of confined odd fluids are significantly deformed by the odd transport coefficients.

The random-cluster model with cluster weight $0<q<1$ is expected to exhibit negative dependence, but without FKG even pairwise negative correlation remains open on general graphs. We study the model on the infinite $\Delta$-regular tree with wired boundary conditions. Write $\widehat p:=p/(p+q(1-p))$ and $p_{\mathsf c}:=q/(\Delta+q-2)$. Classical results identify the product wired state for $p\le p_{\mathsf c}$ and construct a percolative all-wired limit for $p>p_{\mathsf c}$. We prove that the supercritical wired DLR specification has a unique Gibbs measure, namely this all-wired limit. Consequently, the wired DLR phase diagram is complete: the unique measure is Bernoulli bond percolation with parameter $\widehat p$ for $p\le p_{\mathsf c}$, while it percolates for $p>p_{\mathsf c}$. We also establish negative dependence across wired branches. On a finite wired tree, the vector of branch-connectivity indicators satisfies conditional negative association under positive external fields (CNA+). Hence bounded increasing observables supported on disjoint collections of branches incident to a common vertex have nonpositive covariance. The same inequality holds in the unique infinite-volume wired measure for every $p$, with equality for $p\le p_{\mathsf c}$.

Extreme monsoon rainfall over Kerala presents a major operational forecasting challenge because of the interaction of Arabian Sea moisture transport, mesoscale convection, coastal convergence, and strong orographic forcing along the Western Ghats. Spatial analysis showed that WFS reproduced the principal Western-Ghats-aligned rainfall corridor and represented localized high-intensity rainfall structures more distinctly than the smoother global-model guidance examined for the event. The results demonstrate the complementary roles of operational regional guidance and higher-resolution diagnostic forecasts and highlight the importance of region-specific calibration, spatial verification, and continued evaluation across multiple monsoon events and forecast lead times.