We perform a comparative Bayesian analysis of fermionic and bosonic dark matter admixed neutron stars (DMANS) by incorporating a comprehensive set of theoretical, experimental, and astrophysical constraints. The hadronic matter equation of state (EoS) is modeled using a relativistic mean-field approach, constrained by chiral effective field theory ($χ$EFT) calculations at low densities, finite nuclei and heavy-ion collision data at intermediate densities, and neutron star (NS) observations at high densities. For the dark sector, we consider fermionic dark matter (FDM) interacting via a dark vector meson, and two bosonic dark matter models (BDM1 and BDM2) characterized by self-interacting scalar fields. Bayesian inference is employed to constrain the model parameters, including the dark matter mass, coupling strength, and dark matter fraction within NSs. Our analysis finds that all models yield consistent nuclear matter parameters, allowing a small dark matter fraction under 10%. The presence of dark matter slightly softens the EoS, leading to a modest reduction in NS mass, radius, and tidal deformability, though all models remain compatible with NICER and GW170817 observations. The log-evidence and likelihood analyses reveal no statistical preference among the FDM and BDM models, indicating that current astrophysical data cannot decisively distinguish between fermionic and bosonic dark matter scenarios. This study provides a unified statistical framework to constrain dark matter properties using NS observables.

We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers. In conjunction with Grothendieck-Witt theoretic calculations, this determines a large part of the stable cohomology of the odd orthogonal groups $O_{\langle g,g \rangle}(\mathbb Z)$ in low degrees.

I review the physics of lattice fermions obeying the Ginsparg-Wilson relation. I describe their relation to domain wall fermions. I give a description of methodology for performing numerical simulations with overlap fermions. This is a chapter contributed to the on-line book ``Lattice QCD at 50 years,'' (LQCD@50), edited by Tanmoy Bhattacharya, Maarten Golterman, Rajan Gupta, Laurent Lellouch, and Steve Sharpe.

We propose a distributed accelerated primal-dual method with backtracking (D-APDB) for cooperative multi-agent constrained consensus optimization problems over an undirected network of agents, where only those agents connected by an edge can directly communicate to exchange large-volume data vectors using a high-speed, short-range communication protocol, e.g., WiFi, and we also assume that the network allows for one-hop simple information exchange beyond immediate neighbors as in LoRaWAN protocol. The objective is to minimize the sum of agent-specific composite convex functions over agent-specific private constraint sets. Unlike existing decentralized primal-dual methods that require knowledge of the Lipschitz constants, D-APDB automatically adapts to unknown smoothness constants by employing a distributed backtracking step-size search. Each agent relies only on first-order oracles associated with its own objective and constraint functions and on local communications with the neighboring agents, without any prior knowledge of Lipschitz constants. We establish $\mathcal{O}(1/K)$ convergence guarantees for sub-optimality, infeasibility and consensus violation, under standard assumptions on smoothness and on the connectivity of the communication graph. To our knowledge, when nodes have private constraints, especially when they are nonlinear convex constraints onto which projections are not cheap to compute, D-APDB is the first distributed method with backtracking that achieves the optimal convergence rate for the class of constrained composite convex optimization problems. We also provide numerical results for D-APDB on a distributed QCQP problem and distributed primal SVM training to illustrate the potential performance gains that can be achieved by D-APDB.

Metal-organic frameworks (MOFs) combine high porosity with structural fragility, raising important questions about their mechanical stability. We develop a rigidity-based framework in which spring networks parameterized by UFF4MOF are used to construct rigidity and dynamical matrices. Large-scale analysis of 5,682 MOFs from the CoRE 2019 database shows that most frameworks are formally over-constrained yet cluster sharply near the isostatic threshold, revealing accidental geometric modes and placing many MOFs near mechanical instability. In the representative case of UiO-66, we show that auxiliary long-range constraints introduced by tuning the neighbor cutoff lift these modes into soft, flat, finite-frequency bands. The results show that rigidity-matrix analysis can rapidly identify MOFs likely to remain mechanically stable. This near-criticality mirrors behavior known from topological mechanics and points to a deeper design principle in porous crystals.

The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are $\mathbb{P}$-almost surely continuous in time, Hölder in space, and satisfy the local energy inequality up to an arbitrarily large stopping time. Second, we prove several non-unique ergodicity results for the forced Euler equations with continuous-in-time external forcing. The solutions we construct are genuinely random and, almost surely, strictly dissipative and not steady states.

This work presents single-differential electron-neutrino charged-current cross sections on argon measured using the MicroBooNE detector at the Fermi National Accelerator Laboratory. The analysis uses data recorded when the Neutrinos at the Main Injector beam was operating in both neutrino and antineutrino modes, with exposures of $2 \times 10^{20}$ and $5 \times 10^{20}$ protons on target, respectively. A selection algorithm targeting electron-neutrino charged-current interactions with at least one proton, one electron, and no pions in the final topology is used to measure differential cross sections as a function of outgoing electron energy, total visible energy, and opening angle between the electron and the most energetic proton. The interaction rate as a function of proton multiplicity is also reported. The total cross section is measured as [4.1 $\pm$ 0.3 (stat.) $\pm$ 1.1 (syst.)]$ $$\times 10^{-39} \mathrm{cm}^{2}/ \mathrm{nucleon}$. The unfolded cross-section measurements are compared to predictions from neutrino event generators commonly employed in the field. Good agreement is seen across all variables within uncertainties.

Constraining the Epoch of Reionization (EoR) with physically motivated simulations is hampered by the high cost of conventional parameter inference. We present an efficient emulator-based framework that dramatically reduces this bottleneck for the photon-conserving semi-numerical code SCRIPT. Our approach combines (i) a reliable coarse-resolution MCMC to locate the high-likelihood region (exploiting the large-scale convergence of SCRIPT) with (ii) an adaptive, targeted sampling strategy to build a compact high-resolution training set for an artificial neural network based emulator of the model likelihood. With only $\approx 10^3$ high-resolution simulations, the trained emulators achieve excellent predictive accuracy ($R^2 \approx 0.97-0.99$) and, when embedded within an MCMC framework, reproduce posterior distributions from full high-resolution runs. Compared to conventional MCMC, our pipeline reduces the number of expensive simulations by a factor of $\sim 100$ and lowers total CPU cost by up to a factor of $\sim 70$, while retaining statistical fidelity. This computational speedup makes inference in much higher-dimensional models tractable (e.g., those needed to incorporate JWST and upcoming 21 cm datasets) and provides a general strategy for building efficient emulators for next generation of EoR constraints.

Two-dimensional turbulence with linear (Ekman) friction exhibits spectral properties that deviate from the classical Kraichnan prediction for the direct enstrophy cascade. In particular, for sufficiently small viscosity and large friction, the enstrophy flux is suppressed in the cascade and, as a consequence, the small-scale vorticity field becomes passively transported by the large-scale, chaotic flow. We numerically address this problem by investigating how the statistics of the Lagrangian Finite Time Lyapunov Exponent in 2D Ekman-Navier-Stokes simulations are affected by the friction coefficient and by the other parameters of the flow. We derive a simple phenomenological model that interpolates the dependence of the Lyapunov exponent on the flow statistics from the large friction limit, where analytical predictions are available, to the small friction region. We find that the distribution of the FTLE around this mean value is always close to a Gaussian, and this allows to make a simple prediction for the correction of the spectral slope of the direct cascade which is in very good agreement with the numerical results.

Transfer systems on finite posets have recently been gaining traction as a key ingredient in equivariant homotopy theory. Additionally, they also naturally occur in the data of a model structure. We give a complete characterization of all model category structures on a finite lattice, using transfer systems as our main tool, resulting in new connections between abstract homotopy theory and equivariant methods.

Backtesting risk measures is a central task in financial regulation. While standard backtests evaluate whether a forecasting model is statistically consistent with observed losses, regulatory practice often requires assessing the performance of an internal model relative to benchmark models. We develop a non-parametric sequential framework for comparative backtests of general elicitable risk measures using e-values and e-processes. The proposed methods provide anytime-valid inference and remain robust under dependence and model misspecification. In particular, we propose a modified three-zone approach based on weak dominance, which yields more informative conclusions in comparative backtesting. As a technical building block, we also construct general standard e-backtests for identifiable risk measures and characterize the associated e-values and e-processes. The resulting procedures apply to a broad class of commonly used risk measures, including the mean, variance, Value-at-Risk, Expected Shortfall, and expectiles. Simulation studies and empirical analyses illustrate the effectiveness of the proposed approach.

We study certain polarized degenerations of Calabi-Yau manifolds near an intermediate complex structure limit, and improve the potential $C^0$-convergence to a metric convergence result on the generic region for the corresponding collapsing Ricci-flat Kähler metrics.

We investigate how the notions of pairings of operads of May and compatible pairs of indexing systems of Blumberg--Hill relate via the correspondence between indexing systems and $N_{\infty}$-operads. We show that a pairing of operads induces a pairing on the associated indexing systems. Conversely, we show that in many cases, compatible pairs of indexing systems can be realized by a pairing of $N_{\infty}$-operads.

Understanding the contact dynamics of nonspherical particles beyond the microscale is crucial for accurately modeling colloidal and granular systems, where shape anisotropy dictates structural organization and transport properties. In this paper, we introduce an energy-conserving contact dynamics framework for arbitrary convex rigid-body particles, integrating vertex-boundary interactions in 2D with vertex-surface and edge-edge detection in 3D. This formulation enables continuous force evaluation and strictly prevents particle overlap while conserving total energy during translational and rotational motion. Simulations of polygonal and polyhedral particles confirm the framework's stability and demonstrate its capability to capture packing behavior, anisotropic diffusion, and equations of state. The framework establishes a robust and extensible foundation for investigating the nonequilibrium dynamics of complex nonspherical particle systems, with potential applications in colloidal self-assembly, granular flow, and hydrodynamics.

We present a simple and broadly applicable extension of the Casas-Ibarra parametrisation that captures the structure of all Majorana neutrino mass models. Building directly on the original formulation, our approach naturally accommodates additional degrees of freedom and provides a unified, minimal framework for parametrising the Yukawa sector. It significantly simplifies both analytical treatments and numerical scans, and can be universally applied to any Majorana neutrino mass model, regardless of the underlying dynamics. The approach also offers a unified framework for classifying neutrino mass models according to the structure of the neutrino mass matrix, which naturally motivates the proposal of an extended version of the Scotogenic Model. This classification scheme yields tree-level (loop-level) representative models: the seesaw (Scotogenic Model), the linear seesaw (the Generalised Scotogenic Model), and the linear plus inverse seesaw (the Extended Scotogenic Model). We provide ready-to-use explicit expressions for several well-known scenarios, including the Zee model where one of the Yukawa matrices is antisymmetric.

An outline is given of how Jackson may have obtained the inhomogeneous wave equations for the auxiliary functions $Ψ$ and $\bf V$ in his influential 2002 AJP paper on the transformation from the Lorenz gauge to other electromagnetic gauges. It clarifies the roles of these functions in the calculation of the Coulomb-gauge vector potential ${\bf A}_C$ by showing that while ${\bf A}_C$ is given directly $\nabla\times{\bf V}$, only the subtraction of $\nablaΨ$ from the Lorenz-gauge vector potential ${\bf A}_L$ yields ${\bf A}_C$.

The BUTTON-30 detector is a 30-tonne technology demonstrator designed to evaluate the potential of hybrid event detection, simultaneously exploiting both Cherenkov and scintillation light to detect particles produced in neutrino interactions. The detector is installed at a depth of 1.1 km in the Boulby Underground Laboratory allowing to test the performance of this new technology underground in a low background environment. This paper describes the design and construction of the experiment.

Entanglement underpins the power of quantum technologies, yet it is fragile and typically destroyed by dissipation. Paradoxically, the same dissipation, when carefully engineered, can drive a system toward robust entangled steady states. However, this engineering task is nontrivial, as dissipative many-body systems are complex, particularly when they support multiple steady states. Here, we derive analytic expressions that predict how the steady state of a system evolving under a Lindblad equation depends on the initial state, without requiring integration of the dynamics. These results extend the frameworks developed in Refs. [Phys. Rev. A 89, 022118 (2014) and Phys. Rev. X 6, 041031 (2016)], showing that while the steady-state manifold is determined by the Liouvillian kernel, the weights within it depend on both the Liouvillian and the initial state. We identify a special class of Liouvillians for which the steady state depends only on the initial overlap with the kernel. Our framework provides analytical insight and a computationally efficient tool for predicting steady states in open quantum systems. As an application, we propose schemes to generate metrologically useful entangled steady states in spin ensembles via balanced collective decay.

We consider fluctuating Sabra models of turbulence, which exhibit the phenomenon of spontaneous stochasticity: their solutions converge to a stochastic process in the ideal limit, when both viscosity and small-scale noise vanish. In this paper, we develop a renormalization group (RG) approach to explain this phenomenon. Here, RG is understood as an exact relation between the stochastic properties of systems with different dissipative and noise terms, in contrast to the Kadanoff-Wilson coarse-graining procedure, which involves small-scale integration. We argue that the stochastic process in the ideal limit is represented as a fixed point of the RG operator. The existence of such a fixed point confirms not only the convergence in the ideal limit, but also the universality of the spontaneously stochastic process, i.e. its independence from the type of dissipation and noise. The dominant eigenmode of the linearized RG operator determines the leading correction in the convergence process. The RG eigenvalue $ρ\approx 0.84 \exp(2.28i)$ is universal and it turns out to be complex, which explains the rather slow and oscillatory convergence in the ideal limit. These universality predictions are accurately confirmed by numerical data.

In this work, we use the matrix formulation of the Permutation Flowshop Scheduling Problem with makespan minimization to derive an upper bound and a general framework for obtaining lower bounds. The proposed framework involves solving a min-max or max-min expression over a set of paths. We introduce a family of such path sets for which the min-max expression can be solved in polynomial time under certain bounded parameters. To validate the proposed approach, we test it on the Taillard and VRF benchmark instances, the two most widely used datasets in PFSP research. Our method improves the bounds in $112$ out of the $120$ Taillard instances and $430$ out of the $480$ VRF instances. These improvements include both small and large instances, highlighting the scalability of the proposed methodology. Additionally, the upper bound is used to give a more accurate estimate of the number of possible makespan values for a given instance and to present asymptotic results which provide advances in a conjecture given by Taillard related to the quality of one of the most popular lower bounds, as well as the asymptotic approximation ratio of any algorithm.

Study of nanoscale hafnia-zirconia physical properties is the key topic in fundamental and applied science. However, charge transport mechanisms and magnetic properties of hafnia-zirconia nanoparticles are very poorly studied both theoretically and experimentally. In this work we observed a superparamagnetic-like and superparaelectric-like response of ultra-small hafnia-zirconia nanoparticles prepared by the solid-state organonitrate synthesis. The EPR spectra of hafnia-zirconia nanopowders reveal the presence of paramagnetic defect centers, which may be hafnium and/or zirconium ions, which trapped an electron near an oxygen vacancy and changed their valence state from the non-paramagnetic +4 to the paramagnetic +3 state. The Raman spectra indicate the decisive role of surface defects, presumably oxygen vacancies, for all studied Zr compositions.At the same time the EELS analysis does not reveal any noticeable concentration of magnetic impurities in the hafnia-zirconia nanopowders, and the X-ray diffraction analysis reveals the dominant presence of the orthorhombic phase. We observed that the quasi-static relative dielectric permittivity of the hafnia-zirconia nanopowders overcomes 10^6 - 10^7 and related the colossal values with the superparaelectric state of the nanoparticles cores induced by the flexo-electro-chemical strains. It has been found that ultra-small hafnia-zirconia nanoparticles reveal posistor effect and relatively large values of accumulated charge. Thus, obtained results open the way for creation of silicon-compatible ferroics oxygen-deficient hafnia-zirconia nanoparticles with superparamagnetic and superparaelectric properties, which may be used in advanced FETs and electronic logic elements.

We report nuclear magnetic resonance (NMR) Knight shift measurements of the In(1) and In(2) sites in CeRhIn$_5$ as a function of pressure. In contrast to the $c$ axis, the in-plane components of the In(1) Knight shift tensor exhibit little to no pressure dependence. These results indicate that the dipolar component of the tensor is strongly suppressed at the In(1) site, while it remains constant with pressure at the In(2) site. We analyze the hyperfine coupling in terms of a tight binding model for the electronic structure, and determine that the pressure dependence of the In(1) shift cannot be explained in terms of changes to the crystal field parameters, but rather can be understood in terms of an increase in the 4f electron content at the Fermi surface. Our results indicate that the hyperfine coupling reflects changes in the electronic structure near a Kondo breakdown quantum critical point.

The divergence of curvature invariants at a given point signals the impossibility of extending the spacetime to that point, with the derivative order of these diverging invariants determining the differentiability class of the considered spacetime. We hereby focus on a general static and spherically symmetric geometry and determine, in the full non-linear regime and in a model-independent way, the conditions that the metric functions must satisfy in order to achieve finiteness of all curvature invariants at the origin. Our findings have direct implications regarding the extendibility of such spacetimes, which we illustrate by making explicit examples of various black hole geometries. This work is structured around a central theorem, which relates the finiteness of curvature invariants at the origin to the leading order behavior and parity properties of the metric functions. The detailed proof of this theorem constitutes the main result of the paper.

We study the matter power spectrum constraint on primordial black holes (PBH) by the dark matter (DM) emitted through Hawking radiation. We particularly focus on the scenario where PBH, with mass ranges between 1g and $10^9$g, evaporates before big-bang nucleosynthesis (BBN). Addition to that, we consider the case where PBH abundance is scarce and there is no early PBH domination taking place. On the DM side, we assume a fraction of the population is produced from PBH evaporation, while the remaining part is the regular cold dark matters (CDMs) which is produced by some genesis processes that decouples later on. Therefore, in the rest of the cosmological history, DM interacts solely through gravity. Under this condition, there is no thermal equilibrium ever established between DM and SM plasma. An important feature in our analysis is that, for the light PBH we consider, its temperature is much larger than the mass of DM which is consequently produced ultra-relativistically and require a protracted time to become matter-like. In this context, even though PBH evaporates in the very early Universe, PBH-produced DM could still be energetic and smooth out the small scale structure at much later time. By the precision measurement on the matter power spectrum from cosmic surveys, we are able to set joint constraint on light PBHs and the non-cold DMs it produced.

In this paper, we study two types of inverse problems for space semi-discrete stochastic parabolic equations in arbitrary dimensions. The first problem concerns a semi-discrete inverse source problem, which involves determining the random source term of the white noise in the semi-discrete stochastic parabolic equation using observation data of the solution at the terminal time and on an arbitrary open spatial subdomain over a time interval. The second problem addresses a semi-discrete Cauchy inverse problem, which involves determining the solution of the stochastic parabolic equation in a space-time subdomain, from measurements of the solution and the trace of its discrete spatial derivative on an arbitrary open subset of the lateral boundary over a time interval. The key tools are three new global Carleman estimates for the semi-discrete stochastic parabolic operator, one for interior observations and two for boundary observations (homogeneous and nonhomogeneous Dirichlet conditions). Applying these Carleman estimates, we obtain Lipschitz and Hölder stability for the first and second inverse problems, respectively.

A subparsec supermassive black hole binary (SMBHB) at the center of the galaxy 3C 66B is a promising candidate for continuous gravitational-wave searches with pulsar timing arrays (PTAs). In this work, we search for such a signal in the third data release of the Parkes Pulsar Timing Array. Matching our priors to estimates of binary parameters from electromagnetic observations, we find a log Bayes factor $\ln B = - 0.0027(7)$, highlighting that the source can be neither confirmed nor ruled out. We place upper limits at $95\%$ credibility on the chirp mass $M < 6.90 \times 10^{8}\ M_{\odot}$, and on the characteristic strain amplitude $\textrm{log}_{10}(h_0)< -14.44$. This partially rules out the parameter space suggested by electromagnetic (EM) observations of 3C 66B. We also independently reproduce the calculation of the chirp mass with the 3 mm flux monitor data from the unresolved core of 3C 66B. Based on this, we outline a new methodology for constructing a joint likelihood of EM and gravitational-wave data from SMBHBs. Finally, we suggest that targeted searches may allow firmly established SMBHB candidates to be treated as standard sirens, for complementary constraints on the Universe expansion rate.

Driving non-topological materials out of equilibrium using time-periodic perturbations, such as circularly-polarized laser light, is a compelling way to engineer topological phases. At the same time, topology has traditionally only been considered for crystalline materials. Here we propose an experimentally feasible way of driving monolayer amorphous carbon topological.We show that circularly polarized laser light induces both regular and anomalous edge modes at quasienergies $0$ and $\pm π$, respectively. We also obtain a complete topological characterization using an energy- and space-resolved topological marker based on the spectral localizer. Additionally, by introducing atomic coordination defects in the amorphous carbon, we establish the importance of the local atomic coordination in topological amorphous materials. Our work establishes amorphous systems, including carbon, as a versatile and abundant playground to engineer topological phases.

In this paper, we obtain upper and lower bounds for the partition function $p(n)$ by using an elementary geometric inequality in Euclidean space, and we extend the method to generalizations of the partition function.

We prove a standard Central Limit Theorem for the (normalized) number of triangles in a class of Exponential Random Graphs derived from a slight modification of the edge-triangle model. Our main theorem covers the whole analyticity region of the free energy, and is based on a polynomial representation of the partition function.

While the spectral properties and invariant subspaces of compressed shifts on model spaces are well understood, their behaviour on nearly $S^*$-invariant subspaces, a natural generalization with weaker structural constraints, remains largely unexplored. These operators are closely related to the Clark-type unitary operators, yet differ from them in several ways. In this paper, we completely characterize the point spectrum, whole spectrum and invariant subspace structure for such compressed shifts by unitary equivalence, using the Frostman shift, Crofoot transform, and Sz.-Nagy--Foias theory. Our results reveal how the relaxation of $S^*$-invariance impacts spectral structure and invariant subspaces, bridging a gap between classical model space theory and broader function-theoretic settings.