Triple descent and the two kinds of overfitting: where and why do they appear?*

A recent line of research has highlighted the existence of a ‘double descent’ phenomenon in deep learning, whereby increasing the number of training examples N causes the generalization error of neural networks (NNs) to peak when N is of the same order as the number of parameters P. In earlier works, a similar phenomenon was shown to exist in simpler models such as linear regression, where the peak instead occurs when N is equal to the input dimension D. Since both peaks coincide with the interpolation threshold, they are often conflated in the literature. In this paper, we show that despite their apparent similarity, these two scenarios are inherently different. In fact, both peaks can co-exist when NNs are applied to noisy regression tasks. The relative size of the peaks is then governed by the degree of nonlinearity of the activation function. Building on recent developments in the analysis of random feature models, we provide a theoretical ground for this sample-wise triple descent. As shown previously, the nonlinear peak at N = P is a true divergence caused by the extreme sensitivity of the output function to both the noise corrupting the labels and the initialization of the random features (or the weights in NNs). This peak survives in the absence of noise, but can be suppressed by regularization. In contrast, the linear peak at N = D is solely due to overfitting the noise in the labels, and forms earlier during training. We show that this peak is implicitly regularized by the nonlinearity, which is why it only becomes salient at high noise and is weakly affected by explicit regularization. Throughout the paper, we compare analytical results obtained in the random feature model with the outcomes of numerical experiments involving deep NNs.

Macroinvertebrate community responses to mammal control - Evidence for top-down trophic effects

<p>New Zealand’s invertebrates are characterised by extraordinary levels of endemism and a tendency toward gigantism, flightlessness and longevity. These characteristics have resulted in a high vulnerability to introduced mammals (i.e. possums, rats, mice, and stoats) which are not only a serious threat to these invertebrates, but have also altered food web interactions over the past two-hundred years. The establishment of fenced reserves and the aerial application of 1080 toxin are two methods of mammal control used in New Zealand to exclude and reduce introduced mammals, respectively. Responses of ground-dwelling invertebrates to mammal control, including a consideration of trophic cascades and their interactions, remain unclear. However, in this thesis, I aimed to investigate how changes in mammal communities inside and outside a fenced reserve (ZEALANDIA, Wellington) and before-and-after the application of 1080 in Aorangi Forest, influence the taxonomic and trophic abundance, body size and other traits of ground-dwelling invertebrates on the mainland of New Zealand. I also tested for effects of habitat variables (i.e. vegetation and elevation), fluctuations in predator populations (i.e. mice, rats and birds) and environmental variables (i.e. temperature). Additionally, I investigated how squid-bait suspended over pitfall traps influenced the sampling of ground weta and other invertebrates in Aorangi and Remutaka Forests. Contrary to my expectations, there were no differences in abundance or body size of invertebrates within ZEALANDIA (which excludes introduced mammals except mice) relative to the outside, except for Staphylinidae which were more abundant outside the fence. Differences in the agents of predation pressure from mainly mammals, outside the reserve, to mostly birds within ZEALANDIA, but potentially little change in net predation pressure, may explain this apparent similarity in ground-invertebrates. No differences in invertebrate communities were also recorded in the 1080-treated area (Aorangi Forest) after one year of the aerial application of 1080. It could imply that the use of this toxin does not produce any apparent detriment to invertebrates at a population level. The application of 1080 usually leads to changes in insectivorous predator (birds and introduced mammals) dynamics in the short-term mainly due to meso-predator release, which may affect invertebrate communities as a result. Temporal and spatial variation of different components of the ecosystem appear to be more significant drivers of invertebrate dynamics, than 1080 mammal control. For example, rats (Rattus spp.) limited the abundance and body size of large invertebrates (i.e. ground weta, cave weta and spiders) in Aorangi and Remutaka Forests. Smaller invertebrates such as gastropods, weevils and springtails were affected directly by spatial factors such as vegetation, while dung beetles responded to an increase in mouse density. Based on a comparison of pitfall trapping methods, I suggest the use of squid baiting as an effective method for sampling ground weta (Hemiandrus spp.) in New Zealand, as they responded positively to these baits. Finally, I propose ground weta and spiders as suitable indicators of rat predation, as they are abundant in forests and easily recognised by non-specialists, and they respond negatively to rat densities. This thesis underlines the importance of studying the effect of introduced mammal dynamics derived from mammal control in an ecosystem approach, to achieve conservation goals both in the short- and long-term, especially considering the New Zealand Government’s ambitious goal of eradicating three of the most prevalent mammal predators (rats, possums and stoats) by 2050.</p>

Macroinvertebrate community responses to mammal control - Evidence for top-down trophic effects

<p>New Zealand’s invertebrates are characterised by extraordinary levels of endemism and a tendency toward gigantism, flightlessness and longevity. These characteristics have resulted in a high vulnerability to introduced mammals (i.e. possums, rats, mice, and stoats) which are not only a serious threat to these invertebrates, but have also altered food web interactions over the past two-hundred years. The establishment of fenced reserves and the aerial application of 1080 toxin are two methods of mammal control used in New Zealand to exclude and reduce introduced mammals, respectively. Responses of ground-dwelling invertebrates to mammal control, including a consideration of trophic cascades and their interactions, remain unclear. However, in this thesis, I aimed to investigate how changes in mammal communities inside and outside a fenced reserve (ZEALANDIA, Wellington) and before-and-after the application of 1080 in Aorangi Forest, influence the taxonomic and trophic abundance, body size and other traits of ground-dwelling invertebrates on the mainland of New Zealand. I also tested for effects of habitat variables (i.e. vegetation and elevation), fluctuations in predator populations (i.e. mice, rats and birds) and environmental variables (i.e. temperature). Additionally, I investigated how squid-bait suspended over pitfall traps influenced the sampling of ground weta and other invertebrates in Aorangi and Remutaka Forests. Contrary to my expectations, there were no differences in abundance or body size of invertebrates within ZEALANDIA (which excludes introduced mammals except mice) relative to the outside, except for Staphylinidae which were more abundant outside the fence. Differences in the agents of predation pressure from mainly mammals, outside the reserve, to mostly birds within ZEALANDIA, but potentially little change in net predation pressure, may explain this apparent similarity in ground-invertebrates. No differences in invertebrate communities were also recorded in the 1080-treated area (Aorangi Forest) after one year of the aerial application of 1080. It could imply that the use of this toxin does not produce any apparent detriment to invertebrates at a population level. The application of 1080 usually leads to changes in insectivorous predator (birds and introduced mammals) dynamics in the short-term mainly due to meso-predator release, which may affect invertebrate communities as a result. Temporal and spatial variation of different components of the ecosystem appear to be more significant drivers of invertebrate dynamics, than 1080 mammal control. For example, rats (Rattus spp.) limited the abundance and body size of large invertebrates (i.e. ground weta, cave weta and spiders) in Aorangi and Remutaka Forests. Smaller invertebrates such as gastropods, weevils and springtails were affected directly by spatial factors such as vegetation, while dung beetles responded to an increase in mouse density. Based on a comparison of pitfall trapping methods, I suggest the use of squid baiting as an effective method for sampling ground weta (Hemiandrus spp.) in New Zealand, as they responded positively to these baits. Finally, I propose ground weta and spiders as suitable indicators of rat predation, as they are abundant in forests and easily recognised by non-specialists, and they respond negatively to rat densities. This thesis underlines the importance of studying the effect of introduced mammal dynamics derived from mammal control in an ecosystem approach, to achieve conservation goals both in the short- and long-term, especially considering the New Zealand Government’s ambitious goal of eradicating three of the most prevalent mammal predators (rats, possums and stoats) by 2050.</p>

ABOUT THE FEATURES OF FORMATION OF AVAR PERSONAL NAMES (in comparison with Russian and English names)

The article deals with the peculiarities of the formation of Avar personal names in comparison with Russian and English names. The general and national-specific conditions for the formation of names in different linguistic cultures under the influence of historical and cultural phenomena are revealed. It is shown that despite the apparent similarity of modern anthroponymic systems, each nation has its own special traditions of naming people, reflecting the ethnic view of the world.

Marxism-Leninism and Christianity: dictatorship of the “proletariat” and terror

This article carries out a historical-theological analysis of compatibility of the theory and practice of Marxism-Leninism with Christianity. The relevance of this topic is substantiate by the ongoing polemic, which is directly pertains to the social structure. The author reviews the historical-theological aspects of this question based on the critical study of historical-philosophical research, as well as historical documents on the matter. In order to conduct comprehensive analysis on this topic, the article explores the dictatorship of the &ldquo;proletariat&rdquo; and terror views of opposing sides, as well as describes contrary opinions, texts of Holy Scripture, and views of the Orthodox Church Fathers. The novelty of this research lies in introduction of certain documents in the context of articulated problem for the first time. The author gives a detailed historical-theological overview on the comparison of Marxism-Leninism with Orthodox Christianity. The goal of this work lies in examination of the historical documents and historical-theological writings on the topic at hand. The conclusion is made that despite apparent similarity of certain provisions, Marxism-Leninism and Christianity are by no means compatible. In theoretical terms, socialism could exist in symbiosis with Christianity if the existing contradictions are eliminated. However, such socialism would be no longer based on Marxism-Leninism.

Determination of sexual dimorphism using morphometric techniques in Rachycentron canadum (Perciformes: Rachycentridae) cultivated in captivity

Rachycentron canadum is an economically important fish in aquaculture due to its resistance to environmental variations, the feasibility of culture in confinement, high growth rates, and good acceptance by consumers. The profitability of their cage culture is negatively affected by the difficulty of implementing monosex cultures due to the apparent similarity between sexes. In this study, morphometric techniques were used to determine sexual dimorphism by analyzing measurements and the fish’s shape. Differences were found between the sexes in the position of the eyes, lips, pectoral fin and ventral fin, and the body’s general shape. The sexing precision of the individuals was 75.4 % with distances and 82.7 % with geometric morphometry.

Trap Seeker and Digger: The Dual Identity of the Solvated Electron in Methanol

<div> <div> <div> <p>The structure of the solvated electron in methanol is less studied but more complicated than the one of the hydrated electron. In this condensed-phase first principles molecular dynamics study we reveal the nature of the recently discovered shallow and deep trap states of the excess electron and suggest a more complex picture including four bound cavity states classified by the number of the hydroxy-groups coordinated to the electron, their binding energy gradually increasing with the OH-coordination. The initial shallow bound states are formed via a transient diffusion mechanism, in a trap-seeking fashion, whereas, deeper bound states are formed via a slower methanol molecules reorientation. Despite apparent similarity of the absorption spectrum of the solvated electron in methanol to that in water, the origin of the absorption maximum is drastically different. The previously assumed model of hydrogenic transitions (s-p etc.) as is the case in water does not hold for methanol. Instead, the main bands arise due to the charge-transfer states, promoting the excess electron to the nearby cavity, naturally abundant in this solvent. We propose an alternative simple model to describe electronic states of the solvated electron in methanol: the double square well.</p> </div> </div> </div>

Trap Seeker and Digger: The Dual Identity of the Solvated Electron in Methanol

<div> <div> <div> <p>The structure of the solvated electron in methanol is less studied but more complicated than the one of the hydrated electron. In this condensed-phase first principles molecular dynamics study we reveal the nature of the recently discovered shallow and deep trap states of the excess electron and suggest a more complex picture including four bound cavity states classified by the number of the hydroxy-groups coordinated to the electron, their binding energy gradually increasing with the OH-coordination. The initial shallow bound states are formed via a transient diffusion mechanism, in a trap-seeking fashion, whereas, deeper bound states are formed via a slower methanol molecules reorientation. Despite apparent similarity of the absorption spectrum of the solvated electron in methanol to that in water, the origin of the absorption maximum is drastically different. The previously assumed model of hydrogenic transitions (s-p etc.) as is the case in water does not hold for methanol. Instead, the main bands arise due to the charge-transfer states, promoting the excess electron to the nearby cavity, naturally abundant in this solvent. We propose an alternative simple model to describe electronic states of the solvated electron in methanol: the double square well.</p> </div> </div> </div>

Opposition behaviour against the third wave of autocratisation: Hungary and Poland compared

Hungary and Poland are often placed in the same analytical framework from the period of their ‘negotiated revolutions’ to their autocratic turn. This article aims to look behind this apparent similarity focusing on opposition behaviour. The analysis demonstrates that the executive–parliament power structure, the vigour of the extra-parliamentary actors, and the opposition party frame have the strongest influence on opposition behaviour, and they provide the sources of difference between the two country cases: in Hungary an enforced power game and in Poland a political game constrain opposition opportunities and opposition strategic behaviour.

The features of solutions of dynamical systems with an external exciting load and non-conservative dynamical systems with pairwise interaction of degrees of freedom

When mathematical models are developed, as a rule, a number of assumptions is done, which makes it possible to simplify the model, reduce its dimension and simulation time, or use the dimension reduction method. When modeling non-conservative systems with pairwise interaction of degrees of freedom, e.g. mechatronic systems, an elastic aircraft in a flow, an aeroelastic aircraft with an automated control system, etc., there is a desire to reduce the problem to a conservative dynamic system with harmonic action. The study shows that despite the apparent similarity of the tasks, they have significant differences that cannot be ignored. Differences in the behavior of conservative dynamical systems and non-conservative dynamical systems with pair interaction of degrees of freedom are considered. The results are demonstrated on the simplest example with an analytical solution, and in the finite element software package MSC.Nastran. The results of the solution in MSC.Nastran are compared with the results of the analytical solution.