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Scalar field ϕCDM models provide an alternative to the standard ΛCDM paradigm, while being physically better motivated. Dynamical scalar field ϕCDM models are divided into two classes: the quintessence (minimally and non-minimally interacting with gravity) and phantom models. These models explain the phenomenology of late-time dark energy. In these models, energy density and pressure are time-dependent functions under the assumption that the scalar field is described by the ideal barotropic fluid model. As a consequence of this, the equation of state parameter of the ϕCDM models is also a time-dependent function. The interaction between dark energy and dark matter, namely their transformation into each other, is considered in the interacting dark energy models. The evolution of the universe from the inflationary epoch to the present dark energy epoch is investigated in quintessential inflation models, in which a single scalar field plays a role of both the inflaton field at the inflationary epoch and of the quintessence scalar field at the present epoch. We start with an overview of the motivation behind these classes of models, the basic mathematical formalism, and the different classes of models. We then present a compilation of recent results of applying different observational probes to constraining ϕCDM model parameters. Over the last two decades, the precision of observational data has increased immensely, leading to ever tighter constraints. A combination of the recent measurements favors the spatially flat ΛCDM model but a large class of ϕCDM models is still not ruled out. 

Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in the purely topological persistence diagrams (also termed as barcodes). In our earlier work, we showed that computing minimal 1-dimensional persistent cycles (persistent 1-cycles) for finite intervals is NP-hard while the same for infinite intervals is polynomially tractable. In this paper, we address this problem for general dimensions with Z2 coefficients. In addition to proving that it is NP-hard to compute minimal persistent d-cycles (d>1) for both types of intervals given arbitrary simplicial complexes, we identify two interesting cases which are polynomially tractable. These two cases assume the complex to be a certain generalization of manifolds which we term as weak pseudomanifolds. For finite intervals from the d-th persistence diagram of a weak (d+1)-pseudomanifold, we utilize the fact that persistent cycles of such intervals are null-homologous and reduce the problem to a minimal cut problem. Since the same problem for infinite intervals is NP-hard, we further assume the weak (d+1)-pseudomanifold to be embedded in R^{d+1}Rd+1 so that the complex has a natural dual graph structure and the problem reduces to a minimal cut problem. Experiments with both algorithms on scientific data indicate that the minimal persistent cycles capture various significant features of the data. 

With the rise in popularity of drones, their use in anti-social activities has also proliferated. Nationwide police increasingly report the appearance of drones in unauthorized settings such as public gatherings and also in the delivery of contraband to prisons. Detection and classification of drones in such environments is very challenging from both visual and acoustic perspective. Visual detection of drones is challenging due to their small size. There may be cases where views are obstructed, lighting conditions are poor, the field of view is narrow, etc. In contrast, acoustic-based detection methods are omnidirectional, however, they are prone to errors due to possible noise in the signal. This paper presents a method of predicting the presence (detection and classification) of a drone using a single microphone and other inexpensive computational devices. A Support Vector Machine classified the spectral and temporal features of pre-segments generated using a sliding window for the audio signal. Additionally, spectral subtraction was used to reconstruct the magnitude spectrum of drone sounds to reduce false alarms. To increase the accuracy of predictions, an added confidence script is proposed based on a queue-and-dump approach to make the system more robust. The proposed system was tested in real time in a realistic environment with various drone models and flight characteristics. Performance is satisfactory in a quiet setting but the system generates excessive false alarms when exposed to lawn equipment.