Generating stochastic trajectories with global dynamical constraints

We propose a method to exactly generate Brownian paths x c (t) that are constrained to return to the origin at some future time t f , with a given fixed area A f = ∫ 0 t f d t x c ( t ) under their trajectory. We derive an exact effective Langevin equation with an effective force that accounts for the constraint. In addition, we develop the corresponding approach for discrete-time random walks, with arbitrary jump distributions including Lévy flights, for which we obtain an effective jump distribution that encodes the constraint. Finally, we generalise our method to other types of dynamical constraints such as a fixed occupation time on the positive axis T f = ∫ 0 t f d t Θ x c ( t ) or a fixed generalised quadratic area A f = ∫ 0 t f d t x c 2 ( t ) .

Visual Features and Their Own Optical Flow

Symmetries, invariances and conservation equations have always been an invaluable guide in Science to model natural phenomena through simple yet effective relations. For instance, in computer vision, translation equivariance is typically a built-in property of neural architectures that are used to solve visual tasks; networks with computational layers implementing such a property are known as Convolutional Neural Networks (CNNs). This kind of mathematical symmetry, as well as many others that have been recently studied, are typically generated by some underlying group of transformations (translations in the case of CNNs, rotations, etc.) and are particularly suitable to process highly structured data such as molecules or chemical compounds which are known to possess those specific symmetries. When dealing with video streams, common built-in equivariances are able to handle only a small fraction of the broad spectrum of transformations encoded in the visual stimulus and, therefore, the corresponding neural architectures have to resort to a huge amount of supervision in order to achieve good generalization capabilities. In the paper we formulate a theory on the development of visual features that is based on the idea that movement itself provides trajectories on which to impose consistency. We introduce the principle of Material Point Invariance which states that each visual feature is invariant with respect to the associated optical flow, so that features and corresponding velocities are an indissoluble pair. Then, we discuss the interaction of features and velocities and show that certain motion invariance traits could be regarded as a generalization of the classical concept of affordance. These analyses of feature-velocity interactions and their invariance properties leads to a visual field theory which expresses the dynamical constraints of motion coherence and might lead to discover the joint evolution of the visual features along with the associated optical flows.

A Constrained Data Assimilation Algorithm Based on GSI Hybrid 3D-EnVar and Its Application

Data assimilation (DA) at mesoscales is important for severe weather forecasts, yet the techniques of data assimilation at this scale remain a challenge. This study introduces dynamical constraints in the Gridpoint Statistical Interpolation (GSI) three-dimensional ensemble variational (3D-EnVar) data assimilation algorithm to enable the use of high-resolution surface observations of precipitation to improve atmospheric analysis at mesoscales. The constraints use the conservations of mass and moisture. Mass constraint suppresses the unphysical high-frequency oscillation, while moisture conservation constrains the atmospheric states to conform with the observed high-resolution precipitation. We show that the constrained data assimilation (CDA) algorithm significantly reduced the spurious residuals of the mass and moisture budgets compared to the original data assimilation (ODA). A case study is presented for a squall line over the Southern Great Plains on 20 May 2011 during Midlatitude Continental Convective Clouds Experiment (MC3E) of the Atmospheric Radiation Measurement (ARM) program by using ODA or CDA analysis as initial condition of forecasts. The state variables, and the location and intensity of the squall line are better simulated in the CDA experiment. Results show how surface observation of precipitation can be used to improve atmospheric analysis through data assimilation by using the dynamical constraints of mass and moisture conservations.

Minisuperspace Quantization of f(T, B) Cosmology

We discuss the quantization in the minisuperspace for the generalized fourth-order teleparallel cosmological theory known as fT,B. Specifically we focus on the case where the theory is linear on the torsion scalar, in that consideration we are able to write the cosmological field equations with the use of a scalar field different from the scalar tensor theories, but with the same dynamical constraints as that of scalar tensor theories. We use the minisuperspace description to write for the first time the Wheeler-DeWitt equation. With the use of the theory of similarity transformations we are able to find exact solutions for the Wheeler-DeWitt equations as also to investigate the classical and semiclassical limit in the de Broglie -Bohm representation of quantum mechanics.

The evolving worldwide dynamic state of the COVID-19 outbreak

ABSTRACTThe dynamic characterization of the COVID-19 outbreak is critical to implement effective actions for its control and eradication but the information available at a global scale is not sufficiently reliable to be used directly. Here, we integrate multiple data sources through dynamical constraints to quantify its temporal evolution and controllability around the world and within the United States. Overall, the numbers of actively infectious individuals have remained high beyond targeted controllability, with worldwide estimates of 10.24 million on November 24, 2020, totaling in 266.1 million cumulative infections growing at a rate of 11.12 million new infections per week. The actively infectious population reached a local maximum of 7.33 million on July 16, 2020 and remained virtually stagnant at a global scale, with growth rates for most countries around zero that compensated each other, until reverting to net growth on September 22, 2020. We validated the approach, contrasting with prevalence data and the effects of nonpharmaceutical interventions, and we identified general patterns of recession, stabilization, and resurgence. The diversity of dynamic behaviors of the outbreak across countries is paralleled by those of states and territories in the United States, converging to remarkably similar global states in both cases. Our results offer precise insights into the dynamics of the outbreak and an efficient avenue for the estimation of the prevalence rates over time.

A search for transiting planets around FGKM dwarfs and subgiants in the TESS full frame images of the Southern ecliptic hemisphere

ABSTRACT In this work, we present the analysis of 976 814 FGKM dwarf and subgiant stars in the Transiting Exoplanet Survey Telescope (TESS) full frame images (FFIs) of the Southern ecliptic hemisphere. We present a new pipeline, DIAmante, developed to extract optimized, multisector photometry from TESS FFIs and a classifier, based on the Random Forest technique, trained to discriminate plausible transiting planetary candidates from common false positives. A new statistical model was developed to provide the probability of correct identification of the source of variability. We restricted the planet search to the stars located in the least crowded regions of the sky and identified 396 transiting planetary candidates among which 252 are new detections. The candidates’ radius distribution ranges between 1 R⊕ and 2.6 RJ with median value of 1 RJ and the period distribution ranges between 0.25 and 105 d with median value of 3.8 d. The sample contains four long period candidates (P > 50 d), one of which is new, and 64 candidates with periods between 10 and 50 d (42 new ones). In the small planet radius domain (4R < R⊕), we found 39 candidates among which 15 are new detections. Additionally, we present 15 single transit events (14 new ones), a new candidate multiplanetary system, and a novel candidate around a known TOI. By using Gaia dynamical constraints, we found that 70 objects show evidence of binarity. We release a catalogue of the objects we analysed and the corresponding light curves and diagnostic figures through the MAST and ExoFOP portals.