Quantum process in probability representation of quantum mechanics

In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving of which with the initial tomogram set characterizing the system state gives the tomographic state of the transformed system. This kernel, in turn, is broken into the kernels of partial operations, each of them incorporating the symbol of the evolution operator related to the joint evolution of the system and an ancillary environment. Such a kernel decomposition for the projection to a certain basis state and a Gaussian-type projection is demonstrated as well as qubit flipping and amplitude damping processes.

Study on the Physical Properties and Joint Evolution Characteristics of Three-Dimensional Reconstructed Coal

There are various complex joints (fissures), laminae, and other soft structural surfaces in the roadway enclosure, and the existence of these soft structural surfaces seriously affects the stability of the roadway enclosure. In order to study the mechanical properties of the coal body and the development of joints during coal fracture, this paper establishes a three-dimensional model of the fracture structure of the coal body based on CT scanning and three-dimensional reconstruction technology. On this basis, a 3D numerical model of the equivalent nodal coal body is constructed, uniaxial compression simulation analysis is performed, and the joint evolution development law of the coal sample is studied by the built-in joint monitoring program of PFC3D. The results show that the larger the effective joint area and larger the joint size inside the coal sample, the smaller the compressive strength of the coal sample. The increase of joint size and joint surface area increased the ductility and stress-strain curve multipeak phenomenon of the coal sample to some extent. During the rupture of the coal sample, the changes of each phase of the statistical curve of joint number and the phases of the stress-strain curve of the coal sample are compatible.

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.

The joint evolution of movement and competition strategies

Competition typically takes place in a spatial context, but eco-evolutionary models rarely address the the joint evolution of movement and competition strategies. Here we investigate a spatially explicit producer-scrounger model where consumers can either forage on a heterogeneous resource landscape or steal prey from conspecifics (kleptoparasitism). We compare different scenarios for the interaction of movement and competition strategies. In all cases, movement strategies evolve rapidly and consistently across replicate simulations. At equilibrium, foragers do not match the prey input rate, contrary to 'ideal free' predictions. We show that this is related to the intrinsic difficulty of moving effectively on a depleted landscape with few reliable cues for movement. The evolved movement strategies of kleptoparasites differ markedly from those of foragers. Even within each competition strategy, polymorphisms emerge, corresponding to individual differences in movement rules. Our study emphasises the advantages of a mechanistic approach when studying competition in a spatial context.

Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates

We consider the model of Antonacci, Costantini, D’Ippoliti, Papi (arXiv:2010.05462 [q-fin.MF], 2020), which describes the joint evolution of inflation, the central bank interest rate, and the short-term interest rate. In the case when the diffusion coefficient does not depend on the central bank interest rate, we derive a semi-closed valuation formula for contingent derivatives, in particular for Zero Coupon Bonds (ZCBs). By using ZCB yields as observations, we implement the Kalman filter and obtain a dynamical estimate of the short-term interest rate. In turn, by this estimate, at each time step, we calibrate the model parameters under the risk-neutral measure and the coefficient of the risk premium. We compare the market values of German interest rate yields for several maturities with the corresponding values predicted by our model, from 2007 to 2015. The numerical results validate both our model and our numerical procedure.

Resource uptake and the evolution of moderately efficient enzymes

Enzymes speed up reactions that would otherwise be too slow to sustain the metabolism of self-replicators. Yet, most enzymes seem only moderately efficient, exhibiting kinetic parameters orders of magnitude lower than their expected physically achievable maxima. Here, we question how these parameters evolve using a mechanistic model where enzyme efficiency is a key component of individual competition for resources. We show that kinetic parameters are under strong directional selection only up to a point, above which enzymes appear to evolve under near-neutrality. A majority of kinetic parameters compiled elsewhere do spread onto this plateau. Nonetheless, using a population genetics model that includes genetic drift and mutational biases, we show that this is a very unlikely outcome of evolution on a common landscape, as even very moderate biases towards lower efficiency should prevent the occurrence of such a diversity. Instead, differences between species, and within a species between metabolic pathways and the reactions to perform, should be involved. Our results point to drift playing an important role, along with the kinetics of nutrient transporters, the tolerance to high concentrations of intermediate metabolites, and the reversibility of reactions. Enzyme concentration also shapes selection on kinetic parameters, suggesting that the joint evolution of concentration and efficiency, facilitated by the plateau, should matter. Interestingly, the position of an enzyme along the metabolic pathway is not key for its evolution, contrasting with the prediction of models assuming that fitness depends on a precise level of flux control, rather than on competitive abilities.

Economics and Epidemics: Evidence from an Estimated Spatial Econ-SIR Model

Economic analysis of effective policies for managing epidemics requires an integrated economic and epidemiological approach. We develop and estimate a spatial, micro-founded model of the joint evolution of economic variables and the spread of an epidemic. We empirically discipline the model using new U.S. county-level data on health, mobility, employment outcomes, and non-pharmaceutical interventions (NPIs) at a daily frequency. Absent policy or medical interventions, the model predicts an initial period of exponential growth in new cases, followed by a protracted period of roughly constant case levels and reduced economic activity. Nevertheless, if vaccine development proved impossible, and suppression cannot entirely eradicate the disease, a utilitarian policymaker cannot improve significantly over the laissez-faire equilibrium by using lockdowns. Conversely, if a vaccine will arrive within two years, NPIs can improve upon the laissez-faire outcome by dramatically decreasing the number of infectious agents and keeping infections low until vaccine arrival. Mitigation measures that reduce viral transmission (e.g., mask-wearing) both reduce the virus’s spread and increase economic activity.

Joint evolution of mycorrhizal type, pollination, and seed dispersal mode in trees

Mycorrhizal type, pollination, and seed dispersal mode are key drivers of tree diversity, but because they are usually studied in isolation, their evolutionary relationships are poorly understood. We investigated the evolutionary relationships among mycorrhizal type (arbuscular mycorrhizal [AM], ectomycorrhizal [EM], and AM + EM), seed dispersal mode (anemochorous, endozoochorous, and unspecialized), and pollination mode (biotic and wind) in 821 tree species. We found evidence of joint evolution of all three features. Most AM-associated trees had endozoochorous seed dispersal and biotic pollination, whereas most EM-associated trees had anemochorous seed dispersal and wind pollination. Overall, mycorrhizal type, seed dispersal mode, and pollination mode were linked, emphasizing the importance joint study of these traits for understand of tree diversity.