Search

Plastic waste entering the riverine harms local ecosystems leading to negative ecological and economic impacts. Large parcels of plastic waste are transported from inland to oceans leading to a global scale problem of floating debris fields. In this context, efficient and automatized monitoring of mismanaged plastic waste is paramount. To address this problem, we analyze the feasibility of macro-plastic litter detection using computational imaging approaches in river-like scenarios. We enable near-real-time tracking of partially submerged plastics by using snapshot Visible-Shortwave Infrared hyperspectral imaging. Our experiments indicate that imaging strategies associated with machine learning classification approaches can lead to high detection accuracy even in challenging scenarios, especially when leveraging hyperspectral data and nonlinear classifiers. All code, data, and models are available online: https://github.com/RIVeR-Lab/hyperspectral_macro_plastic_detection.

Purpose: To develop a deep learning model that predicts active inflammation from sacroiliac joint radiographs and to compare the success with radiologists. Materials and Methods: A total of 1,537 (augmented 1752) grade 0 SIJs of 768 patients were retrospectively analyzed. Gold-standard MRI exams showed active inflammation in 330 joints according to ASAS criteria. A convolutional neural network model (JointNET) was developed to detect MRI-based active inflammation labels solely based on radiographs. Two radiologists blindly evaluated the radiographs for comparison. Python, PyTorch, and SPSS were used for analyses. P<0.05 was considered statistically significant. Results: JointNET differentiated active inflammation from radiographs with a mean AUROC of 89.2 (95% CI:86.8%, 91.7%). The sensitivity was 69.0% (95% CI:65.3%, 72.7%) and specificity 90.4% (95% CI:87.8 % 92.9%). The mean accuracy was 90.2% (95% CI: 87.6%, 92.8%). The positive predictive value was 74.6% (95% CI: 72.5%, 76.7%) and negative predictive value was 87.9% (95% CI: 85.4%, 90.5%) when prevalence was considered 1%. Statistical analyses showed a significant difference between active inflammation and healthy groups (p<0.05). Radiologists accuracies were less than 65% to discriminate active inflammation from sacroiliac joint radiographs. Conclusion: JointNET successfully predicts active inflammation from sacroiliac joint radiographs, with superior performance to human observers.

In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schr{\"o}dinger type bearing cubic nonlinearity. We present the first 6 families of multikink solutions and explore their bifurcations as the strength of the quadratic dispersion is varied. We reveal a rich bifurcation structure for the system, connecting two-kink states with states involving 4-, as well as 6-kinks. The stability of all of these states is explored. For each family, we discuss a ``lower branch'' adhering to the energy landscape of the 2-kink states. We also, however, study in detail the ``upper branches'' bearing higher numbers of kinks. In addition to computing the stationary states and analyzing their stability within the partial differential equation model, we develop an effective particle ordinary differential equation theory that is shown to be surprisingly efficient in capturing the kink equilibria and normal (as well as unstable) modes. Finally, the results of the bifurcation analysis are corroborated by means of direct numerical simulations involving the excitation of the states in a targeted way in order to explore their instability-induced dynamics.

In this paper we present a hybrid neural network augmented physics-based modeling (APBM) framework for Bayesian nonlinear latent space estimation. The proposed APBM strategy allows for model adaptation when new operation conditions come into play or the physics-based model is insufficient (or incomplete) to properly describe the latent phenomenon. One advantage of the APBMs and our estimation procedure is the capability of maintaining the physical interpretability of estimated states. Furthermore, we propose a constraint filtering approach to control the neural network contributions to the overall model. We also exploit assumed density filtering techniques and cubature integration rules to present a flexible estimation strategy that can easily deal with nonlinear models and high-dimensional latent spaces. Finally, we demonstrate the efficacy of our methodology by leveraging a target tracking scenario with nonlinear and incomplete measurement and acceleration models, respectively.

We show theoretically that dark solitons can exist in the presence of pure quartic dispersion, and also in the presence of both quadratic and quartic dispersive effects, displaying a much greater variety of possible solutions and dynamics than for pure quadratic dispersion. The interplay of the two dispersion orders may lead to oscillatory non-vanishing tails, which enables the possibility of bound, potentially stable, multi-soliton states. Dark soliton-like states which connect to low amplitude oscillations are also shown to be possible. Dynamical evolution results corroborate the stability picture obtained, and possible avenues for dark soliton generation are explored., Comment: 4 pages, 5 figures

Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physics-based models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework. Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.

We consider two scalar fields interacting through a $\chi^*\chi\phi^*\phi$ term in the presence of a Reissner-Nordstrom black hole. Initially, only $\chi$ particles are present. We find that the produced $\phi$ particles are localized in a region around the black hole and have a tendency towards condensation provided that $\phi$ particles are much heavier than the $\chi$ particles. We also find that such a configuration is phenomenologically viable only if the scalars and the black hole have dark electric charges., Comment: The submitted version of the paper. The revised form of the paper is published in European Physical Journal Plus 136 (2021) 972

We consider the interaction of solitary waves in a model involving the well-known $\phi^4$ Klein-Gordon theory, but now bearing both Laplacian and biharmonic terms with different prefactors. As a result of the competition of the respective linear operators, we obtain three distinct cases as we vary the model parameters. In the first the biharmonic effect dominates, yielding an oscillatory inter-wave interaction; in the third the harmonic effect prevails yielding exponential interactions, while we find an intriguing linearly modulated exponential effect in the critical second case, separating the above two regimes. For each case, we calculate the force between the kink and antikink when initially separated with sufficient distance. Being able to write the acceleration as a function of the separation distance, and its corresponding ordinary differential equation, we test the corresponding predictions, finding very good agreement, where appropriate, with the corresponding partial differential equation results. Where the two findings differ, we explain the source of disparities. Finally, we offer a first glimpse of the interplay of harmonic and biharmonic effects on the results of kink-antikink collisions and the corresponding single- and multi-bounce windows.

We consider the problem of gravitational collapse of a fluid under the effect of a Schwarzschild black hole (e.g. a primordial one) that suddenly forms inside the fluid. We assume the fluid initially be a uniform dust. Starting from this configuration we obtain a class of metrics under some assumptions. We find that the metric we obtain includes the dust collapse as a subcase. After discussing some basic properties of the solution, we discuss the case of dust collapse in more detail. We find that the radial and tangential pressures outside the horizon may take positive or negative values depending on the values of the parameters., Comment: Major revisions in the abstract and the text

We consider the interaction of solitons in a biharmonic, beam model analogue of the well-studied $\phi^4$ Klein-Gordon theory. Specifically, we calculate the force between a well separated kink and antikink. Knowing their accelerations as a function of separation, we can determine their motion using a simple ODE. There is good agreement between this asymptotic analysis and numerical computation. Importantly, we find the force has an exponentially-decaying oscillatory behaviour (unlike the monotonically attractive interaction in the Klein-Gordon case). Corresponding to the zeros of the force, we predict the existence of an infinite set of field theory equilibria, i.e., kink-antikink bound states. We confirm the first few of these at the PDE level, and verify their anticipated stability or instability. We also explore the implications of this interaction force in the collision between a kink and an oppositely moving antikink.

We study collisions of coherent structures in higher-order field-theoretic models, such as the $\phi^8$, $\phi^{10}$ and $\phi^{12}$ ones. The main distinguishing feature, of the example models considered herein, is that the collision arises due to the long-range interacting algebraic tails of these solitary waves. We extend the approach to suitably initialize the relevant kinks, in the additional presence of finite initial speed, in order to minimize the dispersive wave radiation potentially created by their slow spatial decay. We find that, when suitably initialized, these models still feature the multi-bounce resonance windows earlier found in models in which the kinks bear exponential tails, such as the $\phi^4$ and $\phi^6$ field theories among others. Also present is the self-similar structure of the associated windows with three- and more-bounce windows at the edges of two- and lower-bounce ones. Moreover, phenomenological, but highly accurate (and predictive) scaling relations are derived for the dependence of the time between consecutive collisions and, e.g., the difference in kinetic energy between the incoming one and the critical one for one-bounces. Such scalings are traced extensively over two-bounce collision windows throughout the three models, hinting at the possibility of an analytical theory in this direction.

In this paper, we study the single kink and the kink-antikink collisions of a nonlinear beam equation bearing a fourth-derivative term. We numerically explore some of the key characteristics of the single kink both in its standing wave and in its traveling wave form. A point of emphasis is the study of kink-antikink collisions, exploring the critical velocity for single-bounce (and separation) and infinite-bounce (where the kink and antikink trap each other) windows. The relevant phenomenology turns out to be dramatically different than that of the corresponding nonlinear Klein-Gordon (i.e., $\phi^4$) model. Our computations show that for small initial velocities, the kink and antikink reflect nearly elastically without colliding. For an intermediate interval of velocities, the two waves trap each other, while for large speeds a single inelastic collision between them takes place. Lastly, we briefly touch upon the use of collective coordinates (CC) method and their predictions of the relevant phenomenology. When one degree of freedom is used in the CC approach, the results match well the numerical ones for small values of initial velocity. However, for bigger values of initial velocity, it is inferred that more degrees of freedom need to be self-consistently included in order to capture the collision phenomenology.