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Two of the central concepts for the study of degree structures in computability theory are computably enumerable degrees and minimal degrees. For strong notions of reducibility, such as m-deducibility or truth table reducibility, it is possible for computably enumerable degrees to be minimal. For weaker notions of reducibility, such as weak truth table reducibility or Turing reducibility, it is not possible to combine these properties in a single degree. We consider how minimal weak truth table degrees interact with computably enumerable Turing degrees and obtain three main results. First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no \\Delta^0_2 set which Turing bounds a promptly simple set can have minimal weak truth table degree.

Deep learning (DL) is revolutionizing evidence-based decision-making techniques that can be applied across various sectors. Specifically, it possesses the ability to utilize two or more levels of non-linear feature transformation of the given data via representation learning in order to overcome limitations posed by large datasets. As a multidisciplinary field that is still in its nascent phase, articles that survey DL architectures encompassing the full scope of the field are rather limited. Thus, this paper comprehensively reviews the state-of-art DL modelling techniques and provides insights into their advantages and challenges. It was found that many of the models exhibit a highly domain-specific efficiency and could be trained by two or more methods. However, training DL models can be very time-consuming, expensive, and requires huge samples for better accuracy. Since DL is also susceptible to deception and misclassification and tends to get stuck on local minima, improved optimization of parameters is required to create more robust models. Regardless, DL has already been leading to groundbreaking results in the healthcare, education, security, commercial, industrial, as well as government sectors. Some models, like the convolutional neural network (CNN), generative adversarial networks (GAN), recurrent neural network (RNN), recursive neural networks, and autoencoders, are frequently used, while the potential of other models remains widely unexplored. Pertinently, hybrid conventional DL architectures have the capacity to overcome the challenges experienced by conventional models. Considering that capsule architectures may dominate future DL models, this work aimed to compile information for stakeholders involved in the development and use of DL models in the contemporary world.

We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite-sample properties. (ii) VAR-based structural identification—including short-run, long-run, or sign restrictions—can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs.

The increasing use of machine learning and Large Language Models (LLMs) opens up opportunities to use these artificially intelligent algorithms in novel ways. This article proposes a methodology using LLMs to support traditional deductive coding in qualitative research. We began our analysis with three different sample texts taken from existing interviews. Next, we created a codebook and inputted the sample text and codebook into an LLM. We asked the LLM to determine if the codes were present in a sample text provided and requested evidence to support the coding. The sample texts were inputted 160 times to record changes between iterations of the LLM response. Each iteration was analogous to a new coder deductively analyzing the text with the codebook information. In our results, we present the outputs for these recursive analyses, along with a comparison of the LLM coding to evaluations made by human coders using traditional coding methods. We argue that LLM analysis can aid qualitative researchers by deductively coding transcripts, providing a systematic and reliable platform for code identification, and offering a means of avoiding analysis misalignment. Implications of using LLM in research praxis are discussed, along with current limitations.

The effectiveness of machine learning models can be significantly averse to redundant and irrelevant features present in the large dataset which can cause drastic performance degradation. This paper proposes IGRF-RFE: a hybrid feature selection method tasked for multi-class network anomalies using a multilayer perceptron (MLP) network. IGRF-RFE exploits the qualities of both a filter method for its speed and a wrapper method for its relevance search. In the first phase of our approach, we use a combination of two filter methods, information gain (IG) and random forest (RF) respectively, to reduce the feature subset search space. By combining these two filter methods, the influence of less important features but with the high-frequency values selected by IG is more effectively managed by RF resulting in more relevant features to be included in the feature subset search space. In the second phase of our approach, we use a machine learning-based wrapper method that provides a recursive feature elimination (RFE) to further reduce feature dimensions while taking into account the relevance of similar features. Our experimental results obtained based on the UNSW-NB15 dataset confirmed that our proposed method can improve the accuracy of anomaly detection as it can select more relevant features while reducing the feature space. The results show that the feature is reduced from 42 to 23 while the multi-classification accuracy of MLP is improved from 82.25% to 84.24%.

We consider the random-design least-squares regression problem within the reproducing kernel Hubert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function within an RKHS ℋ, even if the optimal predictor (i.e., the conditional expectation) is not in ℋ. In a stochastic approximation framework where the estimator is updated after each observation, we show that the averaged unregularized least-mean-square algorithm (a form of stochastic gradient descent), given a sufficient large step-size, attains optimal rates of convergence for a variety of regimes for the smoothnesses of the optimal prediction function and the functions in ℋ. Our results apply as well in the usual finite-dimensional setting of parametric least-squares regression, showing adaptivity of our estimator to the spectral decay of the covariance matrix of the covariates.

Animals regularly return to locations such as foraging patches, nests, dens, watering holes, or movement corridors, and these revisited locations are often sites of ecological significance. Analyzing the temporal and spatial pattern of revisitation can lead to important insights into the life history and ecology of populations. We introduce the R package ‘recurse’ to calculate revisitations to locations in the movement trajectory or other locations for one or multiple individuals. The package also calculates metrics such as residence time and time between visits. It can be used to quantitatively identify frequently used sites (e.g. dens, nests, foraging locations), to examine patterns of revisitation and link them with covariates such as habitat features or climatic data, and to address conservation questions of interest about specific locations. We present an example application with movement trajectory data from a turkey vulture Cathartes aura during the breeding season and demonstrate analyzing recursions, specific locations, seasonal and daily temporal patterns, and visit timing. The ‘recurse’ package should be of interest both to ecologists looking to analyze their movement data and to conservationists needing site-specific information for management and conservation actions.