We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew-Gaussian process, thus obtaining a process with skew-t marginal distributions. For the proposed (skew) $t$ process we study the second-order and geometrical properties and in the $t$ case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the $t$ process. Moreover we compare the performance of the optimal linear predictor of the $t$ process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australia

We focus on a non-abelian gauge field coupled to a single (but general) representation of a family of Nf fermions. By using the same machinery that had allowed us to evaluate the sub-leading large-Nf term of the five-loop Beta function earlier, we here report on a confirmation of the all-Nf result that has in the meantime been published by another group. Furthermore, in order to push forward the 5-loop renormalization program regarding gauge parameter dependence, we present the linear terms of the complete set of anomalous dimensions, in an expansion in the covariant gauge parameter around the Feynman gauge.

We use the linear sigma model with quarks to study the magnetic-field-induced modifications on the longitudinal screening mass for the neutral pion at one-loop level. The effects of the magnetic field are introduced into the self-energy, which contains the contributions from all the model particles. We find that, to obtain a reasonable description for the behavior with the field strength, we need to account for the magnetic field dependence of the particle masses. We also find that the couplings need to decrease fast enough with the field strength to then reach constant and smaller values as compared to their vacuum ones. The results illustrate the need to treat the magnetic corrections to the particle masses and couplings in a self-consistent manner, accounting for the backreaction of the field effects for the magnetic field dependence of the rest of the particle species and couplings in the model.

Interpretation of resolved polarized images of black holes by the Event Horizon Telescope (EHT) requires predictions of the polarized emission observable by an Earth-based instrument for a particular model of the black hole accretion system. Such predictions are generated by general relativistic radiative transfer (GRRT) codes, which integrate the equations of polarized radiative transfer in curved spacetime. A selection of ray-tracing GRRT codes used within the EHT collaboration is evaluated for accuracy and consistency in producing a selection of test images, demonstrating that the various methods and implementations of radiative transfer calculations are highly consistent. When imaging an analytic accretion model, we find that all codes produce images similar within a pixel-wise normalized mean squared error (NMSE) of 0.012 in the worst case. When imaging a snapshot from a cell-based magnetohydrodynamic simulation, we find all test images to be similar within NMSEs of 0.02, 0.04, 0.04, and 0.12 in Stokes I, Q, U , and V respectively. We additionally find the values of several image metrics relevant to published EHT results to be in agreement to much better precision than measurement uncertainties.

In this study, we revisit the Schwinger-Dyson equation for the electron propagator in QED in three and four space-time dimensions. Our analysis addresses the non-perturbative phenomenon of dynamical chiral symmetry breaking, which requires a critical value of the coupling for the dynamical generation of electron masses, encoded in the infrared behavior of the corresponding Green function. With a minimalistic truncation of the infinite tower of equations and adopting standard assumptions, the resulting gap equation is linearized and transformed into a Schrödinger-like equation with an auxiliary potential barrier (or well) subjected to boundary conditions for both high and low momenta. The dynamical mass is then associated with the zero mode of the corresponding Schrödinger-like operator and follows the Miransky scaling law, as expected.

We present new analytical five-loop Feynman-gauge results for the anomalous dimensions of ghost field and -vertex, generalizing the known values for SU(3) to a general gauge group. Together with previously published results on the quark mass and -field anomalous dimensions and the Beta function, this completes the 5-loop renormalization program of gauge theories in that gauge.

We use the linear sigma model with quarks to study the magnetic-field-induced modifications on the longitudinal screening mass for the neutral pion at one-loop level. The effects of the magnetic field are introduced into the self-energy, which contains the contributions from all the model particles. We find that, to obtain a reasonable description for the behavior with the field strength, we need to account for the magnetic field dependence of the particle masses. We also find that the couplings need to decrease fast enough with the field strength to then reach constant and smaller values as compared to their vacuum ones. The results illustrate the need to treat the magnetic corrections to the particle masses and couplings in a self-consistent manner, accounting for the backreaction of the field effects for the magnetic field dependence of the rest of the particle species and couplings in the model.

In this work we study thermodynamics of 2+1-dimensional static black holes with a nonlinear electric field. Besides employing the standard thermodynamic approach, we investigate the black hole thermodynamics by studying its thermodynamic geometry. We compute the Weinhold and Ruppeiner metrics and compare the thermodynamic geometry with the standard description on the black hole thermodynamics. We further consider the cosmological constant as an additional extensive thermodynamic variable. In the thermodynamic equilibrium three dimensional space, we compute the efficiency of the heat engine and show that it is possible to be built with this black hole.

We propose a model for the coupling of flow and transport equations with porous membrane-type conditions on part of the boundary. The governing equations consist of the incompressible Navier--Stokes equations coupled with an advection-diffusion equation, and we employ a Lagrange multiplier to enforce the coupling between penetration velocity and transport on the membrane, while mixed boundary conditions are considered in the remainder of the boundary. We show existence and uniqueness of the continuous problem using a fixed-point argument. Next, an H(div)-conforming finite element formulation is proposed, and we address its a priori error analysis. The method uses an upwind approach that provides stability in the convection-dominated regime. We showcase a set of numerical examples validating the theory and illustrating the use of the new methods in the simulation of reverse osmosis processes.

We perform a Bayesian model selection analysis for interacting scenarios of dark matter and modified holographic Ricci dark energy (MHRDE) with linear interacting terms. We use a combination of some of the latest cosmological data such as type Ia supernovae, cosmic chronometers, cosmic microwave background and baryon acoustic oscillations measurements. We find strong evidence against all the MHRDE interacting scenarios studied with respect to $\Lambda$CDM when the full joint analysis is considered.

In this work, we propose a framework to store and manage spatial data, which includes new efficient algorithms to perform operations accepting as input a raster dataset and a vector dataset. More concretely, we present algorithms for solving a spatial join between a raster and a vector dataset imposing a restriction on the values of the cells of the raster; and an algorithm for retrieving K objects of a vector dataset that overlap cells of a raster dataset, such that the K objects are those overlapping the highest (or lowest) cell values among all objects. The raster data is stored using a compact data structure, which can directly manipulate compressed data without the need for prior decompression. This leads to better running times and lower memory consumption. In our experimental evaluation comparing our solution to other baselines, we obtain the best space/time trade-offs.

We show that statistics is crucial for the instability problem derived from higher time derivatives. In fact, and contrary to previous statements, we check that when dealing with Fermi systems, the Hamiltonian is well bounded and the quantum states are normalizable. Although, ghost states are still present, they do not affect unitarity under certain conditions. We first analyze a quantum oscillator involving Grassman variables and then we generalize it to a Dirac field. Finally, we discuss some physical implications

A well-established result in quantum field theory in four-dimensional de Sitter space is that the vacuum state of a massless scalar field breaks the de Sitter isometry group, leading to time-dependent (secular) growth in correlation functions computed in inflationary coordinates. This behavior is widely believed to extend to more general theories involving light scalar fields with weak non-derivative interactions. In such cases, secular growth is thought to be further amplified by loop corrections, and the stochastic formalism is often regarded as the appropriate framework to resum these infrared effects. In this article we challenge this prevailing view. A crucial distinction must be made between two cases: a massless scalar field protected by a shift symmetry, and a light scalar without such a symmetry. In the former, the shift symmetry enforces derivative interactions, yielding observables in which secular growth plays no physical role. In the latter, although correlation functions develop infrared divergences in the massless limit, they remain fully invariant under the de Sitter isometry group. We analyze the structure of these divergences arising from loop integrals and show that, in the soft-momentum limit, they do not alter the time dependence of tree-level correlators. In fact, using a de Sitter-invariant renormalization scheme based on Wilson's axioms for integration, these divergences can be systematically removed order by order. We therefore conclude that neither massless nor light scalar fields in de Sitter space exhibit genuine secular growth. We further discuss the implications of these findings for the validity and scope of the stochastic approach to inflation.

The beta regression model is a useful framework to model response variables that are rates or proportions, that is to say, response variables which are continuous and restricted to the interval (0,1). As with any other regression model, parameter estimates may be affected by collinearity or even perfect collinearity among the explanatory variables. To handle these situations shrinkage estimators are proposed. In particular we develop ridge regression and LASSO estimators from a penalized likelihood perspective with a logit link function. The properties of the resulting estimators are evaluated through a simulation study and a real data application

Quasispecies theory provides the conceptual and theoretical bases for describing the dynamics of biological information of replicators subject to large mutation rates. This theory, initially conceived within the framework of prebiotic evolution, is also being used to investigate the evolutionary dynamics of RNA viruses and heterogeneous cancer cells populations. In this sense, efforts to approximate the initial quasispecies theory to more realistic scenarios have been made in recent decades. Despite this, how time lags in RNA synthesis and periodic fluctuations impact quasispecies dynamics remains poorly studied. In this article, we combine the theory of delayed ordinary differential equations and topological Leray-Schauder degree to investigate the classical quasispecies model in the single-peak fitness landscape considering time lags and periodic fluctuations in replication. First, we prove that the dynamics with time lags under the constant population constraint remains in the simplex in both forward and backward times. With backward mutation and periodic fluctuations, we prove the existence of periodic orbits regardless of time lags. Nevertheless, without backward mutation, neither periodic fluctuation nor the introduction of time lags leads to periodic orbits. However, in the case of periodic fluctuations, solutions converge exponentially to a periodic oscillation around the equilibria associated with a constant replication rate. We check the validity of the error catastrophe hypothesis assuming no backward mutation; we determine that the error threshold remains sound for the case of time of periodic fitness and time lags with constant fitness. Finally, our results show that the error threshold is not found with backward mutations.

We present analytical five-loop results for the quark mass and quark field anomalous dimensions, for a general gauge group and in the MSbar scheme. We confirm the values known for the gauge group SU(3) from an independent calculation, and find full agreement with results available from large-Nf studies.

We consider background fields within the gravitational sector of the Standard-Model Extension (SME) in a cosmological setting. Our analysis is divided into two parts. The first part addresses the consistency of nondynamical backgrounds in scenarios where diffeomorphism invariance is explicitly broken. Focusing on gravitational systems that admit Killing vector fields and possess a priori symmetries, we demonstrate that potential discrepancies between Riemannian geometry and dynamical equations can be avoided. The second part presents a direct application of various techniques developed by decomposing the modified Einstein equations along normal and tangential directions of the (3+1) decomposition. We show that nondynamical backgrounds can lead to accelerated cosmological expansion without requiring a cosmological constant, thereby opening new avenues for interpreting dark energy.

The United States, a leading global producer and consumer of beef, continues to face substantial challenges in achieving price harmonization across its regional markets. This paper evaluates the validity of the Law of One Price (LOP) in the U.S. beef industry and investigates causal relationships among regional price dynamics. Through a series of econometric tests, we establish that regional price series are integrated of order one, displaying non-stationarity in levels and stationarity in first differences. The analysis reveals partial LOP compliance in the Northeast and West, while full convergence remains elusive at the national level. Although no region demonstrates persistent price leadership, Southern prices appear particularly sensitive to exogenous shocks. These findings reflect asymmetrical integration across U.S. beef markets and suggest the presence of structural frictions that hinder complete market unification.

DGLAP integro-differential equation can be solved by applying certain map in the complex plane of Mellin moments. It may be re-written as Schrödinger equation for $n$ particles. By applying another map in the complex plane of Mellin moment we may re-write the DGLAP equation as a dual DGLAP equation. Regge limit of the dual DGLAP equation coincides with BFKL integro-differential equation which in turn is the Regge limit of optic theorem in quantum field theory and may be re-written as another Schrödinger equation. This means that the BFKL equation and the corresponding Schrödinger equation may be solved by the proposed method of complex mapping in the complex plane of Mellin moments. This approach may be useful in solving tasks related to quantum communication processes.