In this paper, we study the Maximum Common Vertex Subgraph problem: Given two input graphs $G_1,G_2$ and a non-negative integer $h$, is there a common subgraph $H$ on at least $h$ vertices such that there is no isolated vertex in $H$. In other words, each connected component of $H$ has at least $2$ vertices. This problem naturally arises in graph theory along with other variants of the well-studied Maximum Common Subgraph problem and also has applications in computational social choice. We show that this problem is NP-hard and provide an FPT algorithm when parameterized by $h$. Next, we conduct a study of the problem on common structural parameters like vertex cover number, maximum degree, treedepth, pathwidth and treewidth of one or both input graphs. We derive a complete dichotomy of parameterized results for our problem with respect to individual parameterizations as well as combinations of parameterizations from the above structural parameters. This provides us with a deep insight into the complexity theoretic and parameterized landscape of this problem.

We investigate the interplay between genuine entanglement harvesting and communication mediated correlations for local particle detectors in expanding cosmological spacetimes. Focusing on a conformally coupled scalar field in de Sitter spacetime, we analyze how spacetime expansion induces interference between these two sources of entanglement when the detectors are in causal contact. We compare two physically distinct detector models: detectors whose spatial profile expands with the Universe, and detectors whose proper size remains fixed despite cosmological expansion. We find that the lack of time-reversal symmetry in cosmological settings generically leads to constructive or destructive interference between communication mediated correlations and harvested field correlations, dramatically affecting the entanglement that detectors can acquire. In particular, rapid expansion can suppress entanglement entirely for expanding detectors through destructive interference, even when both communication and field correlations are individually large, whereas detectors that maintain a fixed proper size remain capable of acquiring significant entanglement. Our results show that cosmological expansion qualitatively reshapes the balance between communication and harvesting, and that the detector internal cohesion (whether it expands with the Universe or not) plays a crucial role in determining whether detectors' entanglement can survive in rapidly expanding universes.

The rapid adoption of digital technologies has greatly increased the volume of real-world data (RWD) in education. While these data offer significant opportunities for advancing learning analytics (LA), secondary use for research is constrained by privacy concerns. Differentially private synthetic data generation is regarded as the gold-standard approach to sharing sensitive data, yet studies on the private synthesis of educational data remain very scarce and rely predominantly on large, low-dimensional open datasets. Educational RWD, however, are typically high-dimensional and small in sample size, leaving the potential of private synthesis underexplored. Moreover, because educational practice is inherently iterative, data sharing is continual rather than one-off, making a traditional one-shot synthesis approach suboptimal. To address these challenges, we propose the Cyclic Adaptive Private Synthesis (CAPS) framework and evaluate it on authentic RWD. By iteratively sharing RWD, CAPS not only fosters open science, but also offers rich opportunities of design-based research (DBR), thereby amplifying the impact of LA. Our case study using actual RWD demonstrates that CAPS outperforms a one-shot baseline while highlighting challenges that warrant further investigation. Overall, this work offers a crucial first step towards privacy-preserving sharing of educational RWD and expands the possibilities for open science and DBR in LA.

We reinterpret classic radiochemical solar-neutrino measurements as ``rate meters'' for additional, non-negative capture-like contributions induced by fermionic dark matter absorption. Using the chlorine and gallium production-rate data, we build a Bayesian likelihood that accounts for the dominant uncertainties in the solar-neutrino capture-rate prediction (solar fluxes, oscillation parameters, and capture cross sections). Solar-model metallicity systematics are made explicit by presenting results for both the B16--GS98 and B16--AGSS09met solar-model realizations. From the 1D marginalized posteriors of the joint $(R_{χ,\mathrm{Cl}},R_{χ,\mathrm{Ga}})$ analysis, we obtain 90\% upper limits on additional capture-like rate contributions, dominated by chlorine: $R_{χ,\mathrm{Cl},90}\simeq 0.388~\mathrm{SNU}$ (B16--GS98) and $0.588~\mathrm{SNU}$ (B16--AGSS09met). In the charged-current V--A benchmark, we map these constraints onto upper bounds on $y\equiv m_χ^2/(4πΛ^4)$ for $m_χ$ above the ${}^{71}$Ga and ${}^{37}$Cl capture thresholds, using a pep-normalized operator mapping anchored to solar-neutrino capture inputs, where $m_χ$ is the dark matter mass and $Λ$ is the effective scale suppressing the charged-current operator. At $m_χ\simeq 1~\mathrm{MeV}$, we find $y_{90}\simeq 4.88\times 10^{-49}~\mathrm{cm}^2$ (B16--GS98) and $7.08\times 10^{-49}~\mathrm{cm}^2$ (B16--AGSS09met). These radiochemical bounds are complementary to xenon-based absorption searches and collider interpretations by probing distinct nuclear targets with minimal reliance on spectral reconstruction.

The cosmic dipole anomaly, currently detected at a significance exceeding 5$σ$ in several independent survey poses a significant challenge to the standard model of cosmology. The Ellis & Baldwin formula provides a theoretical link between the intrinsic dipole anisotropy in the sky distribution of extragalactic light sources and the observer's velocity relative to the cosmic rest frame, under the assumptions that the sources follow a power-law luminosity function and exhibit power-law spectral energy distributions. In this work, we demonstrate that this relation can be generalized to arbitrary luminosity distributions and spectral profiles. We derive the corresponding expression for the effective spectral index and apply it to a sample of quasars observed in the W1 band of the CatWISE survey. We show that the anomalous cosmic dipole persists beyond the power-law assumption. These results provide a more general and robust framework to interpret measurements of the cosmic dipole in future large-scale surveys.

Luminous blue variables (LBVs) exhibit unique variability features, characterized by episodic outbursts ($>$1 mag) accompanied by spectroscopic changes (S Dor variables). It is debated if all massive stars undergo an LBV-like phase during their evolution, or instead LBVs are exotic phenomena. We aim to quantify the incidence of LBV-like variability in the blue supergiant (BSgs) population of the Large Magellanic Cloud (LMC) using the OGLE survey. Here, we extend previous work in the Small Magellanic Cloud to the LMC, where we examine the light curves of 87 B Supergiants (BSgs) (out of 254 known BSgs) spanning timescales of twenty years, and 37 objects across a three year timescale for aperiodic variations resembling known S Dor variables. One blue supergiant, [ST92] 4-13 shows S Dor type photometric variations. New spectra of this object reveals a potential change in spectral type compared to the literature classification. However, based on its spectral characteristics and low luminosity and mass, we do not currently classify it as an LBV. Our study highlights the need to classify bona fide LBVs as stars undergoing both photometric and spectroscopic variations. Based on currently known stellar population of S Dor variables in the LMC, the lifetime of the S Dor phase is at most $\sim$10$^3$ yrs, in agreement with our duty cycle study based on OGLE data in the SMC. This is orders of magnitude shorter than assumed in literature. Our discovery of LBV-like variability at low luminosities may suggest that S Dor variations could arise from Eddington limit related physics over a wide range of stellar masses, rather than being linked to a unique evolutionary stage.

We analyse the net baryon (B) and net electric charge (Q) stopping in heavy-ion collisions using the statistical model. Focusing first on isobar collisions $\rm{Ru}+\rm{Ru}$ and $\rm{Zr}+\rm{Zr}$ at $\sqrt{s_{\rm NN}}=200$~GeV, we show that the excess baryon-stopping parameter $γ_B \equiv (N_B/N_Q)\,(Z/A)$ can be quantitatively extracted from forthcoming RHIC measurements of charge- and baryon-stopping ratios. We then generalize the approach to other collision systems at RHIC and LHC energies and introduce an oxygen-baseline observable, $r^{OX}$, whose central-to-peripheral ratio exhibits strong and systematic sensitivity to the neutron-skin thickness of the target nucleus $X$.

Circumstellar discs, and especially their inner regions, covering ranges from <1 au to a few astronomical units, are the birthplaces of terrestrial planets. The inner regions are thought to be similarly diverse in structure as the well-observed outer regions probed by ALMA. Combining data and results from previous studies of the VLTI/PIONIER and VLTI/GRAVITY instruments with new, multi-epoch VLTI/MATISSE observations, we aim to provide a comprehensive picture of the structure of the inner regions of the circumstellar disc around the F-type Herbig Ae/Be star HD 142527 A, the primary of a binary star system. We model the multi-wavelength interferometric data using a parametrised, geometrically thin disc model, allowing for azimuthal asymmetry, exploring a first-order disc modulation and an off-centre Gaussian component. We find time-variable structures in the N-band observables, which we reproduce with time-dependent models. This variability manifests as azimuthally asymmetric emission, evidenced by strong, non-zero closure phases in the N-band data. Fits to individual epochs of the N-band observations yield better $χ^2_\text{r}$ values than fits to all epochs simultaneously. This suggests substantial changes in the geometry of the inner disc emission from ~1 au up to a few astronomical-unit scales from one year to the next. Moreover, our models produce a very close-in inner disc rim $R_\text{rim}\approx0.1$ au. All together, we find a very complex, substantially non-point symmetric and temporally-variable disc ($r_\text{out}\lesssim6$ au) around the primary. The very close-in inner rim indicates the presence of material inside the typical wall-like sublimation radius $R_\text{rim,literature}\approx0.3$ au. The complex, temporally variable inner-disc geometry is likely affected or even caused by the close passing (~5 au) and short orbit ($P\approx24$ yr) of the companion HD 142527 B.

Determinations of the Hubble constant based on the local distance ladder remain in significant tension with early-Universe inferences from the cosmic microwave background. While this tension is often discussed in terms of new physics or unmodeled systematics, the role of the assumed priors on the model parameters has received comparatively little attention. Recently, Desmond et al. (2025) pointed out that the commonly adopted flat prior on distance moduli upweights smaller distances and systematically favors high inferred values of the Hubble constant. Motivated by this observation, we perform a comprehensive Bayesian recalibration of the distance ladder, applying physically motivated priors uniformly to all distances, including the Milky Way Cepheids, which are incorporated directly into the joint fit. Together with a conservative treatment of the Gaia EDR3 residual parallax offset, the Hubble constant shifts from $H_0 = 73.0 \pm 1.0 \, \mathrm{km/s/Mpc}$ to $H_0 = 70.6 \pm 1.0 \, \mathrm{km/s/Mpc}$, reducing the Hubble tension from $5 \, σ$ to $2 \, σ$. Our results show that the assumed priors -- often treated as innocuous defaults -- may play a central role in the Hubble tension. Because all local distance ladders rely on the calibration of distances, similar prior-driven effects are expected to arise across distance-ladder methods.

A very common task in data visualization is to plot many data points with some measured y-value as a function of fixed x-values. Uncertainties on the y-values are typically presented as vertical error bars that represent either a Frequentist confidence interval or Bayesian credible interval for each data point. Most of the time, these error bars represent a 68\% confidence/credibility level, which leads to the intuition that a model fits the data reasonably well if its prediction lies within the error bars of roughly two thirds of the data points. Unfortunately, this and other intuitions no longer work when the uncertainties of the data points are correlated. If the error bars only show the square root of diagonal elements of some covariance matrix with non-negligible off-diagonal elements, we simply do not have enough information in the plot to judge whether a drawn model line agrees well with the data or not. In this paper we will demonstrate this problem and discuss ways to add more information to the plots to make it easier to judge the agreement between the data and some model prediction in the plot, as well as glean some insight where the model might be deficient. This is done by explicitly showing the contribution of the first principal component of the uncertainties, and by displaying the conditional uncertainties of all data points.

We investigate the correspondence between the quasinormal modes and grey-body factors of Schwarzschild--Tangherlini black holes. The gravitational perturbations in higher-dimensional black holes can be classified into scalar, vector, and tensor types. Considering the dimension-dependent forms of their effective potentials, the correspondence was examined for each dimension and perturbation mode. The accurate quasinormal modes were computed by suitably adopting the continued fraction and integration-through-midpoints methods, depending on the structure of the singularity. The grey-body factor can be obtained through its correspondence with the quasinormal mode, and its accuracy was analyzed by calculating its difference from the numerically computed grey-body factor. The correspondence failed for $l=2$ scalar gravitational perturbations in $D\ge7$ because the form of the potential is markedly different from that in four dimensions. The vector and tensor perturbation types exhibited good correspondence accuracies in all cases. The breakdown of the correspondence was rigorously demonstrated to stem from multiple potential barriers, and its applicability to each mode in higher dimensions was assessed.

We consider the Diósi-Penrose problem but rather than postulating background gravitational fluctuations, we instead consider the quantum filter that arises from space-time homodyning the continuum of output quadrature described in the open quantum stochastic model presented here. This is described by a quantum Kushner-Stratonovich equation, typical of the form appearing in continuous-time collapse of the wave-function models in Quantum Decoherence Theory

We study current flow around a density inhomogeneity in a two-dimensional electron gas in the presence of a strong magnetic field. The inhomogeneity is parametrized by a power-law tail with an exponent $β> 2$. We show that current and electrochemical potential are exponentially suppressed inside a surrounding area much larger than the geometric size of the perturbation. The corresponding ``no-go'' radius grows as a certain power of the magnetic field. Residual current and potential exhibit spiraling patterns inside the no-go region. Outside of it, they acquire corrections inversely proportional to the distance, which is known as the Landauer resistivity dipole. The Landauer dipole is rotated by the angle $π(1 - 1 / β)$ with respect to the average electric field. The rotation direction depends on whether the local density is raised or lowered. We also consider the effect of electron viscosity and show that the variation of the no-go radius with magnetic field becomes more rapid if viscosity is large enough. The Landauer dipole size is set by the Gurzhi length, which is much larger than the no-go radius, which is in turn much larger than the geometric size of the perturbation. Our results may be useful for interpreting nanoimaging of current distribution in graphene and other two-dimensional systems.

We prove that the Weil representation over a non-archimedean local field can be realised with coefficients in a number field. We give an explicit descent argument to describe precisely which number field the Weil representation descends to. Our methods also apply over more general coefficient fields, such as $\ell$-modular coefficient fields, as well as coefficient rings such as rings of integers i.e. in families. We also prove that the theta correspondence over a perfect field is valid if and only if it is valid over the algebraic closure of this perfect field. These two results together show that the classical local theta correspondence is rational.

We present a comprehensive catalog of 251 potential counterparts for 250 unassociated hard X-ray sources detected in the Swift Burst Alert Telescope (BAT) 150-month hard X-ray survey. Over 150 months of observation, BAT has detected 2339 sources in the 15-150 keV energy range. Among these, 344 do not have a previously identified low-energy counterpart. Our study focuses on the analysis of soft X-ray observations at energies below 10 keV, spatially overlapping with these new Swift-BAT hard X-ray sources. Such observations were taken with Chandra, Swift-XRT, eROSITA, and XMM-Newton. Within the sample of 251 potential counterparts, 94 (37 percent) are identified as active galactic nuclei and 58 (23 percent) as galaxies. The remaining 99 sources (40 percent) include pulsars, cataclysmic variables, and unclassified soft X-ray counterparts in the 0.5-10 keV band. Redshift information is available for 139 out of the 251 sources, and its distribution is in close agreement with the redshift distribution of previous BAT catalogs. We also present the results of a small optical spectroscopy campaign of 9 out of 58 galaxies. The majority of these are classified as Seyfert 2 galaxies at redshifts slightly larger than the median of the BAT AGN sample.

We study temporal fair division, where agents receive goods over multiple rounds and cumulative fairness is required. We investigate Temporal Envy-Freeness Up to One Good (TEF1) and Up to Any Good (TEFX), its approximation $α$-TEFX, and Temporal Maximin Share (TMMS). Motivated by known impossibilities in standard settings, we consider the model in various restricted settings and extend it by introducing scheduling. Our main contributions draw the boundary between possibility and impossibility. First, regarding temporal fair division without scheduling, we prove that while constant-factor $α$-TEFX is impossible in general, a $1/2$-approximation is achievable for generalized binary valuations and identical days with two agents. Second, regarding temporal fair division with scheduling, we demonstrate that a scheduling buffer of size at least $n/2$ enables TEF1 for identical days. However, we establish that TEFX and TMMS remain largely impossible even with scheduling or restricted domains. These results highlight the inherent difficulty of strict temporal fairness and quantify the trade-offs required to achieve approximation guarantees.

Little Red Dots (LRDs) are enigmatic, compact, red galaxies at high redshift, $z\sim 4$-$7$, discovered by the James Webb Space Telescope. Broad emission lines in the absence of X-ray and radio counterparts suggest that they host accreting supermassive black holes embedded in dense gaseous envelopes. This black-hole-envelope configuration facilitates efficient photohadronic interactions and neutrino production. Remarkably, their observed source number density and luminosity are compatible with the energetics of the diffuse neutrino background. We consider that relativistic jets and outflows are launched from the black hole and propagate through low-density polar funnels within envelopes, where particle acceleration and neutrino emission occur. This leads to LRDs being effectively hidden sources. Our analytic and numerical calculations show that, in an optimistic scenario, LRDs can contribute $\sim 30\%$ of the observed diffuse background at TeV$-$sub-PeV energies, predominantly through photomeson production. At high neutrino energies, $\gtrsim 10^{5.5}~{\rm GeV}$, inverse-Compton cooling of muons modifies the resulting flavor ratio, providing a distinctive diagnostic for IceCube-Gen2 and other upcoming neutrino telescopes.

We investigate how a thermodynamical first-order phase transition affects the dynamical chaotic behaviour of a given model. To this effect, we analyze the model of Berkooz, Brukner, Jia and Mamroud that interpolates between the double-scaled SYK model and an integrable chord Hamiltonian. This model exhibits a first-order transition, characterized by a kink in the free energy, between the chaotic and quasi-integrable phases, with the branch of subdominant saddles interpolating between them. We characterize the dynamical behavior across the phase diagram using the chord number, Krylov complexity, and operator size. The chord number, which is proportional to the Krylov state complexity in the classical limit, exhibits a discontinuous transition from linear to quadratic growth at the transition point. Similarly, the Krylov operator complexity and the operator size, as scrambling diagnostics, exhibit discontinuous transitions from exponential to quadratic growth. We also discuss a possible holographic interpretation of the model.

Recent work revealed a tension between the Gross-Mende analysis of the high-energy fixed-angle behavior of string amplitudes and the explicit numerical data. Motivated by this puzzle, we revisit the problem of classifying saddle-point geometries for the one-loop amplitude. We find an infinite family of complex saddles that dominate the high-energy regime. Using general constraints and matching to numerical data, we formulate a bootstrap problem that determines their multiplicities. This procedure yields a precise asymptotic expansion of the one-loop amplitude at high energies. The resulting oscillatory contributions lead to a much richer high-energy behavior than that predicted by the original Gross-Mende analysis.

Community detection is a fundamental task in data analysis, and block models provide an approach for identifying a wide variety of community structures while offering high interpretability. The degree-corrected block model (DCBM) is an established model that accounts for the heterogeneity of node degrees. However, inference methods are computationally costly and highly sensitive to initialization, while cheaper alternatives, such as spectral or modularity-based approaches, are restricted to detecting specific structures, typically assortative. In this work, we show that DCBM inference can be reformulated as a constrained nonnegative matrix factorization problem. Leveraging this insight, we propose a novel method for community detection and a theoretically well-grounded initialization strategy that provides an initial estimate of communities for inference algorithms. Our approach is agnostic to any specific network structure and applies to graphs with any structure representable by a DCBM. Experiments on synthetic and real benchmark networks show that our method detects communities comparable to those found by DCBM inference while being faster; for instance, it processes a graph with 100,000 nodes and 1,000,000 edges in approximately 4 minutes. Moreover, the proposed initialization strategy significantly improves solution quality and reduces the number of iterations required by all tested inference algorithms. Overall, this work provides a scalable and robust framework for community detection and highlights the benefits of a matrix-factorization perspective for the DCBM.

The Laser Interferometer Space Antenna (LISA) is expected to have a source rich data stream containing signals from large numbers of many different types of source. This will include both individually resolvable signals and overlapping stochastic backgrounds, a regime intermediate between current ground-based detectors and pulsar timing arrays. The resolved sources and backgrounds will be fitted together in a high dimensional Global Fit. To extract information about the astrophysical populations to which the sources belong, we need to decode the information in the Global Fit, which requires new methodology that has not been required for the analysis of current gravitational wave detectors. Here, we %start that development, presenting present a hierarchical Bayesian framework to infer the properties of astrophysical populations directly from the output of a LISA Global Fit, consistently accounting for information encoded in both the resolved sources and the unresolved background. Using a simplified model of the Global Fit, we illustrate how the interplay between resolved and unresolved components affects population inference and highlight the impact of data analysis choices, such as the signal-to-noise threshold for resolved sources, on the results. Our approach provides a practical foundation for population inference using LISA data.

We present the Parallel Application of Slitless Spectroscopy to Analyze Galaxy Evolution (PASSAGE) spectroscopic redshift catalog in the COSMOS field. PASSAGE is a JWST Cycle 1 Near Infrared Imager and Slitless Spectrograph (NIRISS) wide-field slitless spectroscopy (WFSS) pure-parallel survey, obtaining near-infrared spectra of thousands of extragalactic sources. 15 out of 63 PASSAGE fields fall within the Hubble Space Telescope (HST) COSMOS footprint, of which 11 overlap with COSMOS-Web, a JWST treasury survey providing additional space-based photometry. We present our custom line-finding algorithm and visual inspection effort used to identify emission lines and derive the spectroscopic redshifts for line-emitting sources in PASSAGE. The line-finding algorithm identifies between ~200 and 950 line-emitting candidates per field, of which typically 47% were identified as true emission lines post visual inspection. We identify 2183 emission line sources at 0.08<z<4.7, 1896 of which have available COSMOS photometric redshifts. We find excellent redshift agreement between the COSMOS photometric redshifts and the PASSAGE spectroscopic redshifts for strong (S/N>5), multi-line emitting sources. This agreement weakens for PASSAGE single-line emitters with ambiguous identities. These single-line emitters are likely mis-identified around 18% of the time based on comparisons to photometric redshifts. We derive stellar masses using PASSAGE photometry and spectroscopic redshifts, in broad agreement with existing COSMOS-Web stellar masses, but with some discrepancy driven by redshift disagreements. We publicly release this spectroscopic redshift catalog, which will enable community-led science in prime extragalactic fields and serve as a crucial dataset for validating Euclid and Roman spectroscopy.

The double-exponential Sinc-collocation method is known as a super-accurate method for solving initial value problems of ordinary differential equations, for which the error decreases almost exponentially as a function of the number of sample points in the temporal direction, $N$. However, this method requires solving nonlinear simultaneous equations in $nN$ variables when the problem dimension is $n$. Recently, Ogata pointed out that Gauss-Seidel type fixed-point iteration works surprisingly well for solving these equations, typically reducing the error by one or two orders of magnitude at each iteration. In this paper, we analyze the convergence of this iteration and give a sufficient condition for its global convergence. We also provide an upper bound on its convergence factor, which explains the efficiency of this iteration. Some numerical examples that illustrate the validity of our analysis are also provided.

We develop a systematic Hamiltonian formulation of minimally doubled lattice fermions in (3+1) dimensions, derive their nodal structures (structures of zeros), and classify their symmetry patterns for both four-component Dirac and two-component Weyl constructions. Motivated by recent single-Weyl proposals based on Bogoliubov-de Gennes (BdG) representation, we argue that the corresponding single-Weyl Hamiltonians are obtained from the minimal-doubling Hamiltonians supplemented by an appropriate species-splitting mass term, and we re-examine the non-onsite symmetry protecting the physical Weyl node in terms of a Ginsparg-Wilson-type relation. We then construct a one-parameter family of deformations that preserves all the symmetries and demonstrate that, once the parameter exceeds a critical value, additional Weyl nodes emerge and the system exits the single-node regime. This indicates that in interacting theories radiative corrections can generate symmetry-allowed counterterms, so maintaining the desired single-Weyl phase generically requires "moderate" parameter tuning.

Accurate channel state information (CSI) acquisition under tight pilot and training-energy constraints is essential for next-generation wireless networks. In this work, we model the wireless channel as a proper complex Gaussian process over the transmit and receive antenna arrays, reducing pilot overhead and training energy by estimating the CSI from partial observations. We formulate the CSI acquisition problem as a highly underdetermined Bayesian linear inverse problem. We develop a Gaussian process regression (GPR) framework that reconstructs the full CSI from sparse and noisy observations by extrapolating to the unknown entries. To incorporate propagation information into the GPR prior, we introduce a novel array-geometry-based kernel and prove that it is Hermitian positive semidefinite. The proposed kernel better captures the channel spatial correlations through richer hyperparameters. Our GPR-based CSI extrapolation approach learns the channel hyperparameters online from sparse, noisy pilot measurements within each coherence block. Numerical results show that the proposed estimator reduces pilot overhead by up to 75 percent and total training energy by up to 93.75 percent, while maintaining lower normalized mean-square error and higher spectral efficiency in the low-to-moderate signal-to-noise-ratio regime.

We investigate the quantum dynamics generated by quantum quenches (QQs) of the Hamiltonian parameters in many-body systems, focusing on protocols that cross first-order and continuous quantum transitions, both in finite-size systems and in the thermodynamic limit. As a paradigmatic example, we consider the quantum Ising chain in the presence of homogeneous transverse ($g$) and longitudinal ($h$) magnetic fields. This model exhibits a continuous quantum transition (CQT) at $g=g_c$ and $h=0$, and first-order quantum transitions (FOQTs) driven by $h$ along the line $h=0$ ($g<g_c$). In the integrable limit $h=0$, the system can be mapped onto a quadratic fermionic theory; however, any nonvanishing longitudinal field breaks integrability and the spectrum of the resulting Hamiltonian is generally expected to enter a chaotic regime. We analyze QQs in which the longitudinal field is suddenly changed from a negative value $h_i < 0$ to a positive value $h_f>0$. We focus on values of $h_f$ such that the spectrum of the post-QQ Hamiltonian $H(g,h_f)$ lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of $g$, finding qualitatively distinct behaviors for $g > g_c$ (where the chain is in the disordered phase), for $g = g_c$ (QQ across the CQT), and for $g<g_c$ (QQ across the FOQT line).

We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper then focuses on working out the implications of this in the case of the canonical exponential family. The results are simple exact filters, predictors and smoothers with linear recursions. A theory for these models is developed and the models are illustrated on simulated and real data.

Coarse-grained continuous descriptions for lipid bilayers are typically based on minimizing the Helfrich energy. Such models consider the fluid properties of these structures only implicitly and have been shown to nicely reproduce equilibrium properties. Model extensions that also address the dynamics of these structures are surface (Navier--)Stokes--Helfrich models. They explicitly account for membrane viscosity. However, these models also usually treat the lipid bilayer as a homogeneous continuum, neglecting the molecular degrees of freedom of the lipids. Here, we derive refined models which consider in addition a scalar order parameter representing the molecular alignment of the lipids along the surface normal. Starting from hydrodynamic surface liquid crystal models, we obtain a hydrodynamic surface Landau--Helfrich model for asymmetric lipid bilayers and a surface Beris--Edwards model for symmetric lipid bilayers. The fully ordered case for both models leads to the known surface (Navier--)Stokes--Helfrich models. Besides more detailed continuous models for lipid bilayers, we therefore also provide an alternative derivation of surface (Navier--)Stokes--Helfrich models.

Using only retrospective data, we study the problem of predicting treatment effects for the same treatment/policy implemented in a different location or time period. We propose a distributionally robust estimator that minimizes the worst-case mean squared error for the prediction of treatment effect over a class of distributions defined by a Wasserstein neighborhood around the source distribution. Because the joint distribution of potential outcomes is unidentified, the problem is inherently one of partial identification. We characterize the sharp upper and lower bounds of the minimax optimizer by exploiting the Fréchet class of distributions consistent with the marginal distributions of potential outcomes. The resulting predictor preserves the sign of the average treatment effect under the source distribution but is shrunk toward zero, with the degree of shrinkage depending on the extent of treatment effect heterogeneity. We establish consistency and asymptotic normality of the bound estimators, develop a two-step inference procedure, and discuss the choice of the robustness parameter.

We select seventy tidal disruption event (TDE) candidates among X-ray transients discovered during the eROSITA all-sky surveys in the Eastern Galactic hemisphere between December 2020 and February 2022 (eRASS1--5). We cross-match each X-ray source to a host galaxy in archival optical surveys using Bayesian likelihood-ratio techniques and obtain Keck/LRIS spectroscopy for all 70 host galaxies. Host properties are inferred through SED fitting with Prospector and emission line analysis with pPXF. We develop a robust classification scheme using X-ray and broad line luminosities, narrow-line ionization diagnostics, and optical variability to identify high-confidence TDEs, for which we analyze optical spectral features, light curve properties, and host galaxy demographics. Our final sample contains 52 TDEs with redshifts of $0.018 \leq z\leq0.714$, comprising 41 gold (high-confidence) and 11 silver (lower-confidence) events. The vast majority (93\%) of gold TDEs are intrinsically brighter in the X-ray band, with $L_{\rm X,peak} > L_{\rm opt,peak}$. Among 23 events with detected optical flares, delayed X-ray peak is commonly observed. We identify transient spectral features in eight events, including six with prominent broad \ion{He}{II} $λ$4686 and/or H$α$ emission and two coronal-line TDEs. Host galaxy demographics reveal modest over-representation in green valley ($\times1.8$) and quiescent Balmer-strong ($\times5.3$) galaxies, significantly weaker than previous TDE samples, demonstrating greater diversity in star formation histories than previously recognized. Most TDE hosts exhibit suppressed star formation relative to the main sequence, consistent with X-ray selection biases against dusty star-forming galaxies.