We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many previous investigations of the simplex method, which are restricted to Hilbert spaces or otherwise specially structured instances. Our generality is obtained by avoiding the ``algebraic'' machinery of pivoting via column operations, which has required stronger topological conditions in establishing a connection between basic feasible solutions and extreme point structure. We show that our definition of polytopes captures optimization over the Hilbert cube, a quintessential object in infinite-dimensional spaces known for its surprisingly complicated properties. Moreover, all polytopes (under our definition) have exposed extreme points connected by edge paths.

Mega-parsec giant radio sources (GRSs) have been known for decades. Their known population has soared from several hundred to more than $10^4$ in recent years. However, the formation mechanisms of GRSs remain elusive. In this work, we study the formation and properties of GRSs associated with dark matter halos of different masses and normal gas density environment. We use magnetohydrodynamic simulations to study the formation of GRSs from hosts residing in dark matter halos with masses of $10^{13}$, $10^{14}$ and $10^{15}$ solar masses, adopting normal hot baryonic gas fractions in ranges (0.02-0.1, 0.05-0.1, and 0.1-0.15) and varying density profiles. We inject jet energy of 0.06 percent of the central black hole's relativistic energy in their host galaxies with power of 0.05 percent of the Eddington luminosity in most runs. The successful formation of GRSs from hosts in dark matter halos with normal hot baryonic gas fractions indicates that an unusual low-density gas environment is not a prerequisite for their formation. The propagation of radio lobes can be slower in halos with sufficiently low or high central density and pressure, as a much lower central pressure cannot sufficiently collimate the jet and produces wider, less penetrating lobes, whereas an atmosphere with sufficiently high pressure enhances the interaction between the jet and the surrounding medium. Assuming equipartition between non-thermal electron and magnetic energy, the evolution of the simulated GRSs in the radio power--linear size diagram shows that the radio power of most simulated sources within halo masses of $\rm 10^{13}$ and $\rm 10^{14} M_\odot$ can reach values comparable to observational data at similar physical scales. The simulated sources with a shorter jet duration than other sources become faint remnant sources when they propagate to GRS scales.

We review the nearly complete classification project for finite distance-transitive graphs and compile a list of all known graphs. Interestingly, we find that those graphs with diameter larger than 4, apart from a small finite number of exceptions, are geodesic-transitive. Their geodesics exhibit a clear (often geometric) structure. On the other hand, we provide examples of graphs that are distance-transitive but not geodesic-transitive, including two infinite families with diameter 3 and a few sporadic ones with diameter 3, 4 or 7. In the last section, we extend our investigation to polar Grassmann graphs and provide an explicit description of their geodesics.

A hybrid framework is developed that highlights and unifies the most important aspects of the Noether correspondence between symmetries and conserved integrals in Lagrangian and Hamiltonian mechanics. Several main results are shown: (1) a modern form of Noether's theorem is presented that uses only the equations of motion, with no knowledge required of an explicit Lagrangian; (2) the Poisson bracket is formulated with Lagrangian variables and used to express the action of symmetries on conserved integrals; (3) features of point symmetries versus dynamical symmetries are clarified and explained; (4) both autonomous and non-autonomous systems are treated on an equal footing. These results are applied to dynamical systems that are locally Liouville integrable. In particular, they allow finding the complete Noether symmetry group of such systems.

Let $Z\subset{\bf P}^{n-1}$ be a hypersurface such that the associated reduced hypersurface $Z_{\rm red}$ has only weighted homogeneous isolated singularities. In the case $Z$ is a reduced curve or $Z_{\rm red}$ has only homogeneous isolated singularities with $n$ at least $4$, we show that the strong monodromy conjecture for a defining polynomial $f$ of $Z$ follows from arxiv:1609.04801v1 using in the reduced curve case a formula of Denef and Loeser for Newton-nondegenerate polynomials of three variables (which can be deduced in the applied case from the one for the two variable case) together with known results about the strong monodromy conjecture in the two variable case. Here an amazing cancellation occurs so that possible counterexamples fail. We also show the relation between the pole orders of topological zeta function and the root multiplicities of Bernstein-Sato polynomial in the case $Z$ has equimultiplicity and $Z_{\rm red}$ has only weighted homogeneous singularities with $n=3$ or $Z_{\rm red}$ has only homogeneous isolated singularities with $n>3$.

Water-in-Salt-Electrolytes (WiSEs) are a promising class of next-generation electrolytes. Unlike classical dilute electrolytes or more conventional battery electrolytes, WiSEs are characterised by their super-concentrated salt concentration with only a small amount of water, which gives rise to their expanded electrochemical stability window (ESW). The expansion of the ESW is, in part, due to the formation of an inorganic solid electrolyte interphase (SEI) that passivates the anode; this principle is also important in graphite and Li-metal anodes, and beyond Li-ion technologies. The solvation and ionic associations are key descriptors in understanding the expansion of the ESW. Specifically, as reactions which lead to the SEI (or cathode electrolyte interphase, CEI) must occur at the electrode-electrolyte interface, the distribution of reactants and their various solvation environments are critical. This distribution near the interface is referred to as the electrical double layer (EDL), in the absence of reactions. Here we further develop and analyse a recently proposed thermodynamic theory of hydration and ionic associations in the EDL of WiSEs. We parameterize this theory from bulk molecular dynamics simulations and benchmark it against EDL simulations, finding good qualitative agreement. Using this thermodynamic theory, we rationalise changes in the ESW through: changes in the activity in the bulk electrolyte through the Nernst equation, which directly changes the stability of the electrolytes; and thermodynamic changes to the kinetics of these reactions, from the Butler-Volmer equation and coupled ion electron transfer kinetics, through the concentration of reactant species in the Helmholtz layer.

Taxation constitutes a fundamental component of modern national economic systems, exerting profound impacts on both societal functioning and governmental operations. In this paper, we employ an interdependent network approach to model the coevolution between citizens and regulators within a taxation system that fundamentally constitutes a public goods game framework with complex interactive dynamics. In a game layer, citizens engage in public goods games, facing the social dilemma of tax compliance (cooperation) versus evasion (defection). Tax compliance supports the sustainability of public finances while tax evasion presents markedly stronger short-term incentives. In a regulatory layer, fair regulators punish tax evaders, while corrupt regulators keep silent due to bribes. Governmental regulatory interventions introduce critical institutional constraints that alter the traditional equilibrium of the game. Importantly, there exists a strategy update not only among citizens but also among regulators. Our results indicate that strengthening penalties can effectively curb tax evasion, and the influence of bribery on both tax compliance rates and the proportion of fair regulators is nonlinear. Additionally, increasing regulators' salaries and intensifying the crackdown on corrupt regulators can foster the emergence of fair regulators, thereby reducing tax evasion among citizens. The results offer practical policy implications, suggesting that balanced deterrence and institutional fairness are essential to sustaining compliance, and point to the need for future empirical validation and model extensions.

The Richtmyer-Meshkov instability (RMI) poses a major challenge in inertial confinement fusion (ICF) due to its role in mixing and performance degradation. We report the first experimental observation of passive freeze-out of RMI in a low-pressure surrogate regime; an instability stagnation effect induced without modifying the driving pressure pulse or the target surface geometry. Using additively manufactured sub-surface voids in a sinusoidal target, we convert a single shock into a sequence of weaker shocks that suppress instability growth upstream of the surface by over 70%. High-speed X-ray imaging and hydrodynamic simulations suggest that this suppression arises primarily from temporal shaping, with lesser contributions from spatial curvature and shock weakening. Our results demonstrate a driver-independent pathway for controlling shock-driven hydrodynamic instabilities relevant to ICF and other high energy density systems.

We systematically investigate the nonlinear photogalvanic effect in few-layer graphene with various stacking orders, including AA- and AB-stacked bilayers, and AAA-, ABA-, and ABC-stacked trilayers. Using a tight-binding model to describe the electronic states, the shift current conductivity and jerk current conductivity are calculated over a broad spectral range from terahertz to visible frequencies. Our symmetry analysis reveals that a nonvanishing shift current emerges only in ABA-stacked trilayer graphene due to its broken inversion symmetry, with a peak conductivity reaching approximately $1.21 \times 10^{-13}$ A$\cdot$m/V$^2$ at optimal doping. In contrast, the jerk current, permitted in all structures, requires an in-plane static electric field and exhibits pronounced spectral tunability with chemical potential. These findings establish a comprehensive symmetry-band-field coupling paradigm for nonlinear photocurrents in layered graphene and provide design principles for tunable, polarization-sensitive photodetection and energy-harvesting devices based on van der Waals heterostructures.

Understanding how the composition of guest origin markets evolves over time is critical for destination marketing organizations, hospitality businesses, and tourism planners. We develop and apply Bayesian Dirichlet autoregressive moving average (BDARMA) models to forecast the compositional dynamics of guest origin market shares using proprietary Airbnb booking data spanning 2017--2025 across four major destination regions. Our analysis reveals substantial pandemic-induced structural breaks in origin composition, with heterogeneous recovery patterns across markets. In our analysis, the BDARMA framework achieves the lowest forecast error for EMEA and competitive performance across destination regions, outperforming standard benchmarks including naïve forecasts, exponential smoothing, and SARIMA on log-ratio transformed data in compositionally complex markets. For EMEA destinations, BDARMA achieves 27% lower forecast error than naïve methods ($p < 0.001$), with the greatest gains where multiple origin markets compete in the 5-25% share range. By modeling compositions directly on the simplex with a Dirichlet likelihood and incorporating seasonal variation in both mean and precision parameters, our approach produces coherent forecasts that respect the unit-sum constraint while capturing complex temporal dependencies. The methodology provides destination stakeholders with probabilistic forecasts of source market shares, enabling more informed strategic planning for marketing resource allocation, infrastructure investment, and crisis response.

Modern spectroscopic surveys obtain spectra for millions of stars. However, classical spectroscopic methods can often be computationally expensive, rendering them impractical for the analysis of large datasets. We introduce a novel simulation-based deep-learning approach for the efficient analysis of high-resolution stellar spectra to be obtained with the upcoming high-resolution 4MOST spectrograph. We used a suite of synthetic non-local thermodynamic equilibrium (NLTE) spectra generated with Turbospectrum to mimic 4MOST observations and trained a conditional invertible neural network (cINN) for the purpose of predicting self-consistently stellar surface parameters and chemical abundances. The cINN is a neural network architecture that estimates full posterior distributions for the target stellar properties, providing an intrinsic uncertainty estimate. We evaluated the predictive performance of the trained cINN model on both synthetic data and observed spectra of stars. We found that our new cINN trained on NLTE synthetic spectra is capable of recovering stellar parameters with average errors ($σ$) of $33$ K for $T_\mathrm{eff}$, $0.16$ dex for $\log(g)$, and $0.12$ dex for [Fe/H], $0.1$ dex for [Ca/Fe], $0.11$ for [Mg/Fe], and $0.51$ dex for [Li/Fe], respectively, at a signal to noise ratio of 250 per Angstrom. From the analysis of the observed spectra of Gaia-ESO / 4MOST / PLATO benchmark stars, we verified that our NLTE estimates for stellar parameters and abundances are consistent with results obtained with the independent code TSFitPy. We conclude that the NLTE cINN is robust and can, theoretically, evaluate 4 million high-resolution 4MOST spectra in less than a day, using GPU acceleration.

Transversal Pauli $Z$ rotations provide a natural route to fault-tolerant logical diagonal gates in quantum CSS codes, but their capability is inherently constrained. We develop a homological framework that organizes transversal diagonal gates in terms of their logical action and physical implementation, revealing two layers of structure that govern their behavior. At a fixed level, we establish that their logical action admits a classification in terms of homological data of the underlying chain complex, extending the standard description of logical operators. We then formulate the refinement to finer angles as a lifting problem and derive two Bockstein-type obstruction maps, whose vanishing is a necessary and sufficient condition for the existence of a transversal logical diagonal gate at the next level. Within this framework, known algebraic conditions such as divisibility and triorthogonality are reinterpreted as necessary conditions for the existence of transversal logical diagonal gates with uniform rotation angles. Our results identify homological obstructions governing transversal implementability and provide a conceptual foundation for a formal theory of transversal structures in quantum error correction.

We construct a formulation of the Atiyah-Patodi-Singer index of Dirac operators in lattice gauge theory for domains with compact boundaries in a flat torus. The key idea is to exploit its equality to the spectral flow of the domain-wall fermion Dirac operators, which we generalize in this work to cases without product structure near the boundary. We prove that, for sufficiently small lattice spacings, this formulation correctly captures the continuum Atiyah-Patodi-Singer index.

We study information-theoretic phase transitions for the detectability of latent geometry in bipartite random geometric graphs RGGs with Gaussian d-dimensional latent vectors while only a subset of edges carries latent information determined by a random mask with i.i.d. Bern(q) entries. For any fixed edge density p in (0,1) we determine essentially tight thresholds for this problem as a function of d and q. Our results show that the detection problem is substantially easier if the mask is known upfront compared to the case where the mask is hidden. Our analysis is built upon a novel Fourier-analytic framework for bounding signed subgraph counts in Gaussian random geometric graphs that exploits cancellations which arise after approximating characteristic functions by an appropriate power series. The resulting bounds are applicable to much larger subgraphs than considered in previous work which enables tight information-theoretic bounds, while the bounds considered in previous works only lead to lower bounds from the lens of low-degree polynomials. As a consequence we identify the optimal information-theoretic thresholds and rule out computational-statistical gaps. Our bounds further improve upon the bounds on Fourier coefficients of random geometric graphs recently given by Bangachev and Bresler [STOC'24] in the dense, bipartite case. The techniques also extend to sparser and non-bipartite settings, at least if the considered subgraphs are sufficiently small. We furhter believe that they might help resolve open questions for related detection problems.

The James Webb Space Telescope has unveiled an abundant population of potential active galactic nuclei (AGN) at high redshift ($z\gtrsim4$) known as little red dots (LRDs), which are likely hosted in relatively low-mass galaxies. However, previous theoretical models have highlighted the difficulty in continuously feeding massive black holes in the central regions of bursty, high-redshift galaxies because of repeated gas evacuation by stellar feedback. We analyze galaxies in high-redshift FIRE-2 simulations to understand whether they are capable of hosting the observed abundant population of high-redshift AGN. We use a gravitational torque-driven accretion (GTDA) model and a simple free-fall accretion model to derive black hole accretion rates and construct predicted AGN bolometric luminosity functions for $z=5-7$. The GTDA model and the free-fall model with black holes accreting $\lesssim 1$ percent of their central gas supply ($<100 \rm \ pc$) per free-fall time predict AGN abundances that are more than sufficient to explain the most recent LRD observations. The fiducial models, in fact, overpredict the number of low-luminosity AGN as compared with observations. We explore possible resolutions of this tension. A plausible, though likely not unique, scenario for alleviating the AGN overpredictions and which also provides a good match to the host-galaxy UV luminosity distribution suggests that LRDs are super Eddington-accreting, Eddington luminosity-limited, $M_{\rm BH}\gtrsim 2\times10^5 \ \rm M_\odot$ black holes residing in $M_\star\gtrsim 2\times10^7 \ \rm M_\odot$ galaxies. We show that, under simple assumptions, mock observations of such sources can reproduce key observed LRD characteristics.

We present the first spectroscopic characterization of an interstellar object at mid-infrared wavelengths. Post-perihelion observations of 3I/ATLAS using the JWST/MIRI medium-resolution spectrometer were obtained on 2025 December 15--16 and 27 when the object was at heliocentric distances of 2.20 and 2.54 au, respectively. Our 5--28 micron spectra exhibit fluorescence features from several gaseous species, including the $ν_2$ band of water at 5.8--7.0 microns. the primary $ν_2$ and associated hot bands of carbon dioxide around 15 microns, and a forbidden transition of atomic nickel at 7.507 microns. We also report the first direct detection of methane in an interstellar object. The delayed onset of methane production relative to water suggests past depletion from the outermost layers, with the observed methane emerging from unprocessed subsurface material. Comparison of the volatile production rates measured during the two epochs indicate a significant reduction in overall outgassing over 12 days, with the measured water activity level dropping more steeply than other species. As shown through near-nucleus coma mapping, 3I continues to display an extended source of water production from icy grains entrained within the coma. Our production rate measurements confirm that 3I exhibits a strongly enhanced CO$_2$:H$_2$O mixing ratio relative to typical solar system comets, as well as a somewhat enriched CH$_4$:H$_2$O value.

Metropolis algorithms are classical tools for sampling from target distributions, with broad applications in statistics and scientific computing. Their convergence speed is governed by the spectral gap of the associated Markov operator. Recently, Andrieu et al. (2024) derived the first explicit bounds for the spectral gap of Random--Walk Metropolis when the target distribution is smooth and strongly log-concave. However, existing literature rarely discusses non-smooth targets. In this work, we derive explicit spectral gap bounds for the random-walk Metropolis and Metropolis--adjusted Langevin algorithms over a broad class of non-smooth distributions. Moreover, combining our analysis with a recent result in Goyal et al. (2025), we extend these bounds to targets satisfying a Poincare or log-Sobolev inequality, beyond the strongly log-concave setting. Our theoretical results are further supported by numerical experiments.

In the experiment to study the e+e->n+anti n process at the VEPP-2000 $e^+e^-$ collider, the ratio |GE|/|GM| of the neutron timelike electric and magnetic form factors has been measured. The experiment was carried out with the SND detector in the center-of-mass energy range 1890-2000 MeV in eight energy points with an integrated luminosity of 83 inv.pb. The |GE|/|GM| ratio is determined by the analyzing the distribution of the polar angle of the produced antineutron. The measured |GE|/|GM| value in the energy range under study is between 1.0 and 1.5 with an average value of 1.21+-0.13.

Hybrid reconfigurable intelligent surfaces (HRIS) enhance wireless systems by combining passive reflection with active signal amplification. However, jointly optimizing the transmit beamforming with the HRIS reflection and amplification coefficients to maximize spectral efficiency (SE) is a non-convex problem, and conventional iterative solutions are computationally intensive. To address this, we propose a deep reinforcement learning (DRL) framework that learns a direct mapping from channel state information to the near-optimal transmit beamforming and HRIS configurations. The DRL model is trained offline, after which it can compute the beamforming and HRIS configurations with low complexity and latency. Simulation results demonstrate that our DRL-based method achieves 95% of the SE obtained by the alternating optimization benchmark, while significantly lowering the computational complexity.

Octupole excitations of atomic nuclei can be viewed as fluctuations around an equilibrium shape. These fluctuations in turn can be seen as probes of nuclear matter properties to the extent that the shape changes explore changes in compression, surface to volume ratio, or isospin overlap. In the present work we use a series of Skyrme interactions, which were fitted to provide a systematic range of surface energies, to explore the surface energy dependence of octupole excitations in $^{208}$Pb. We find a strong positive linear corelation between the surface energy of a Skyrme interaction and its prediction of the first $3^-$ octupole excitation energy.

We explicitly demonstrate the importance of a new thermal resonant channel in the context of low-scale leptogenesis, which goes beyond the well-known mixing and oscillation of massive singlet neutrinos. This new channel is always present when considering the thermally-induced Higgs decay to leptons and relativistic singlet neutrinos, and can become dominant thanks to thermally-generated resonant lepton-doublet flavour coherences. This mechanism, which we call Thermal Resonant Leptogenesis (TRL), can yield the observed baryon asymmetry in our universe, even if there is no resonant enhancement from quasi-degenerate sterile neutrinos. The required active-to-sterile neutrino mixing for TRL differs from other known low-scale leptogenesis scenarios and can be probed in fixed-target and long-lived particle experiments, and by displaced vertex searches at high-energy colliders.

We construct four-dimensional de Sitter space as an excited state, rather than as a vacuum configuration, in type IIB, heterotic SO(32), and heterotic E_8 \times E_8 string theories. This framework provides a mechanism to evade vacuum-based no-go theorems for de Sitter solutions in string theory. Starting from a generic M-theory configuration, we obtain de Sitter isometry in the dual string theories through appropriate dynamical duality sequences in the late-time limit. The excited state, identified as a Glauber-Sudarshan state, is constructed as the expectation value of the metric operator in M-theory using path-integral techniques. We further analyze the conditions required for the existence of a well-defined effective field theory description and show that these conditions are equivalent to the null energy condition for a (3+1)-dimensional FLRW cosmology. Finally, we investigate constraints arising from axionic cosmology and demonstrate how the time-dependent solutions are modified when experimental bounds on the axionic coupling constant are taken into account. This article serves as a computational companion to sections 3 and 4 of the paper arXiv:2511.03798 [hep-th].

In this paper, we consider power allocation and antenna activation of cell-free massive multiple-input multiple-output (CFmMIMO) systems. We first derive closed-form expressions for the system spectral efficiency (SE) and energy efficiency (EE) as functions of the power allocation coefficients and the number of active antennas at the access points (APs). Then, we aim to enhance the EE through jointly optimizing antenna activation and power control. This task leads to a non-convex and mixed-integer design problem with high-dimensional design variables. To address this, we propose a novel DRL-based framework, in which the agent learns to map large-scale fading coefficients to AP activation ratio, antenna coefficient, and power coefficient. These coefficients are then employed to determine the number of active antennas per AP and the power factors assigned to users based on closed-form expressions. By optimizing these parameters instead of directly controlling antenna selection and power allocation, the proposed method transforms the intractable optimization into a low-dimensional learning task. Our extensive simulations demonstrate the efficiency and scalability of the proposed scheme. Specifically, in a CFmMIMO system with 40 APs and 20 users, it achieves a 50% EE improvement and 3350 times run time reduction compared to the conventional sequential convex approximation method.

We evaluate the misclustering probability of a spectral clustering algorithm under a Gaussian mixture model with a general covariance structure. The algorithm partitions the data into two groups based on the sign of the first principal component score. As a corollary of the main result, the clustering procedure is shown to be consistent in a high-dimensional regime.

In this work, we investigate the performance of polar codes with the assistance of feedback in communication systems. Although it is well known that feedback does not improve the capacity of memoryless channels, we show that the finite length performance of polar codes can be significantly improved as feedback enables genie-aided decoding and allows more flexible thresholds for the polar coding construction. To analyze the performance under the new construction, we then propose an accurate characterization of the distribution of the error event under the genie-aided successive cancellation (SC) decoding. This characterization can be also used to predict the performance of the standard SC decoding of polar codes with rates close to capacity.

Exciton-polaritons are light-matter hybrid quasi-particles that have emerged as a flexible platform for developing quantum technologies and engineering material properties. However, the fundamental mechanistic principles that govern their dynamics and relaxation remain elusive. In this work, we provide the microscopic mechanistic understanding of the exciton-polariton relaxation process that follows from an excitation in the upper polariton. Using both mixed quantum-classical simulations and analytical analysis, we reveal that phonon-induced upper-to-lower polariton relaxation proceeds via two steps: the first step is a vertical inter-band transition from the upper to the lower polariton, which is followed by a second step that is a phonon-induced Fröhlich scattering within the lower polariton. We find that in materials of finite thickness (which include filled cavities), phonon-induced polaritonic intraband Fröhlich scattering is significantly suppressed. We show that the microscopic origin of this suppression is phonon-fluctuations synchronization (or self-averaging) due to the polaritonic spatial delocalization in the quantization direction. Finally, we show that the same phonon fluctuation-synchronization effect plays a central role across polaritonic relaxation pathways, and we derive simple analytical expressions that relate a material's finite thickness to the corresponding relaxation rate constants.

Testing the unimodular equivalence of two full-dimensional integral simplices can be reduced to testing unimodular permutation (UP) equivalence of two nonsingular matrices. We conduct a systematic study of UP-equivalence, which leads to the first average-case quasi-polynomial time algorithm, called \texttt{HEM}, for deciding the unimodular equivalence of $d$-dimensional integral simplices, as well as achieving a polynomial-time complexity with a failure probability less than $2.5 \times 10^{-7}$. A key ingredient is the introduction of the \emph{permuted Hermite normal form} and its associated \emph{pattern group}, which streamlines the UP-equivalence test by comparing canonical forms derived from induced coset representatives. We also present an acceleration strategy based on Smith normal forms. As a theoretical by-product, we prove that two full-dimensional integral simplices are unimodularly equivalent if and only if their $n$-dimensional pyramids are unimodularly equivalent. This resolves an open question posed by Abney-McPeek et al.

Guided by the flipping principle, we propose a novel extension of the Standard Model based on a double right-handed $U(1)$ gauge symmetry. In this framework, all left-handed fermions are neutral, while right-handed fermions of the third generation carry charges distinct from those of the first two generations. This structure naturally explains the observed Standard Model fermion mass hierarchy: the heavy masses of the third generation are generated at tree level, while the lighter masses of the first and second generations arise radiatively at the one-loop level. For the active neutrino sector, the tiny masses are generated through a combination of tree-level and two-loop seesaw mechanisms. Crucially, this approach successfully reproduces the observed neutrino mass hierarchy, with the atmospheric mass-squared difference generated at tree level and the solar neutrino mass squared difference emerging at the two-loop level. These hierarchical patterns stem from the interplay between gauge invariance and a residual parity symmetry that survives the spontaneous breaking of the extended gauge group. The same residual symmetry stabilizes a viable scalar singlet dark matter candidate, which we show can reproduce the observed relic abundance while remaining consistent with current direct detection bounds. After addressing constraints from electroweak precision tests and flavor-changing neutral currents, we explore the discovery prospects for the new neutral bosons at existing and future colliders, including the LEP, LHC, and a future ILC.

High-dimensional dense embeddings have become central to modern Information Retrieval, but many dimensions are noisy or redundant. Recently proposed DIME (Dimension IMportance Estimation), provides query-dependent scores to identify informative components of embeddings. DIME relies on a costly grid search to select a priori a dimensionality for all the query corpus's embeddings. Our work provides a statistically grounded criterion that directly identifies the optimal set of dimensions for each query at inference time. Experiments confirm achieving parity of effectiveness and reduces embedding size by an average of $\sim50\%$ across different models and datasets at inference time.

We construct a position-space cosmological perturbation theory around spatially flat Friedmann-Lemaître-Robertson-Walker geometries that allows to model localized primordial sources of gravitational waves. The equations of motion are decoupled using a generalized harmonic gauge, which avoids the use of a scalar-vector-tensor decomposition. We point out that sources cannot generically be defined in a compact domain due to fluctuations of the cosmic perfect fluid. For power law cosmologies, we obtain the exact Green's function necessary to solve for all metric perturbations in terms of a hypergeometric function, which matches with a Green's function derived earlier by Chu. This allows us to derive the closed form expression of the linearized metric perturbation generated by sources up to quadrupolar order in the multipolar expansion.