Optimal Poisson Cognitive System with Markov Learning Model

The aim of the study is to develop a mathematical model of the trained Markov cognitive system in the presence of discrete training and interfering random stimuli arising at random times at its input. The research method consists in the application of the simplest Markov learning model of Estes with a stochastic matrix with two states, in which the transition probabilities are calculated in accordance with the optimal Neуman-Pearson algorithm for detecting stimuli affecting the system. The paper proposes a model of the random appearance of images at the input of the cognitive system (in terms of learning theory, these are stimuli to which the system reacts). The model assumes an exponential distribution of the system’s response time to stimuli that is widely used to describe intellectual work, while their number is distributed according to the Poisson law. It is assumed that the cognitive system makes a decision about the presence or absence of a stimulus at its input in accordance with the Neуman-Pearson optimality criterion, i.e. maximizes the probability of correct detection of the stimulus with a fixed probability of false detection. The probabilities calculated in this way are accepted as transition probabilities in the stochastic learning matrix of the system. Thus, the following assumptions are accepted in the work, apparently corresponding to the behavior of the system assuming human reactions, i.e. the cognitive system.The images analyzed by the system arise at random moments of time, while the duration of time between neighboring appearances of images is distributed exponentially.The system analyzes the resulting images and makes a decision about the presence or absence of an image at its input in accordance with the optimal Neуman-Pearson algorithm that maximizes the probability of correct identification of the image with a fixed probability of false identification.The system is trainable in the sense that decisions about the presence or absence of an image are made sequentially on a set of identical situations, and the probability of making a decision depends on the previous decision of the system.The new results of the study are analytical expressions for the probabilities of the system staying in each of the possible states, depending on the number of steps of the learning process and the intensities of useful and interfering stimuli at the input of the system. These probabilities are calculated for an interesting case in which the discreteness of the appearance of stimuli in time is clearly manifested and the corresponding graphs are given. Stationary probabilities are also calculated, i.e. for an infinite number of training steps, the probabilities of the system staying in each of the states and the corresponding graph is presented.In conclusion, it is noted that the presented graphs of the behavior of the trained system correspond to an intuitive idea of the reaction of the cognitive system to the appearance of stimuli. Some possible directions of further research on the topic mentioned in the paper are indicated.

Information flow in excerpts of two translations of Mme Bovary

This article explores how information is accumulated and collated in a cog-nitively realistic fashion in two very short excerpts of translations of Flaubert ’s ‘Mme Bovary’. The approach taken is a formal cognitive linguistic one using Discourse Information Grammar (DIG), a theory of grammar based on the intuitive idea that texts are understood by the reader incrementally, in a left-to-right fashion. Thus, a cognitive pragmatic approach is taken to the study of the excerpts, highlighting how much information is accumulated as the reader develops an understanding of the text in question. The analysis discusses the differences in the build-up of information in the source text and in its translations. The conclusion indicates that translation studies contribute much to the development of formal linear cognitive linguistic theories.

Ability, relevant possibilities, and the fixity of the past

In several writings, John Martin Fischer has argued that those who deny a principle about abilities that he calls ‘the Fixity of the Past’ are committed to absurd conclusions concerning practical reasoning. I argue that Fischer’s ‘practical rationality’ argument does not succeed. First, Fischer’s argument may be vulnerable to the charge that it relies on an equivocation concerning the notion of an ‘accessible’ possible world. Secondly, even if Fischer’s argument can be absolved of that charge, I maintain that it can be defeated by appeal to an independently plausible principle about practical reasoning that I call ‘the Knowledge Principle’. In addition, I point out that Fischer’s own presentation of his argument is flawed by the fact that the principle that he labels ‘the Fixity of the Past’ does not, in fact, succeed in representing the intuitive idea that it is intended to capture. Instead, the debate (including Fischer’s practical rationality argument) should be recast in terms of a different (and stronger) principle, which I call ‘the Principle of Past-Limited Abilities’. The principal contribution of my paper is thus twofold: to clarify the terms of the debate about the fixity of the past, and to undermine Fischer’s ‘practical rationality’ argument for the fixity of the past.

Deterministic policies based on maximum regrets in MDPs with imprecise rewards

Markov Decision Process Models (MDPs) are a powerful tool for planning tasks and sequential decision-making issues. In this work we deal with MDPs with imprecise rewards, often used when dealing with situations where the data is uncertain. In this context, we provide algorithms for finding the policy that minimizes the maximum regret. To the best of our knowledge, all the regret-based methods proposed in the literature focus on providing an optimal stochastic policy. We introduce for the first time a method to calculate an optimal deterministic policy using optimization approaches. Deterministic policies are easily interpretable for users because for a given state they provide a unique choice. To better motivate the use of an exact procedure for finding a deterministic policy, we show some (theoretical and experimental) cases where the intuitive idea of using a deterministic policy obtained after “determinizing” the optimal stochastic policy leads to a policy far from the exact deterministic policy.

A note on the stability of a modified Lotka-Volterra model using Hurwitz polynomials

In the analysis of the dynamics of the solutions of ordinary differential equations we can observe whether or not small variations or perturbations in the initial conditions produce small changes in the future; this intuitive idea of stability was formalized and studied by Lyapunov, who presented methods for the stable analysis of differential equations. For linear or nonlinear systems, we can also analyze the stability using criteria to obtain Hurwitz type polynomials, which provide conditions for the analysis of the dynamics of the system, studying the location of the roots of the associated characteristic polynomial. In this paper we present a stability study of a Lotka-Volterra type model which has been modified considering the carrying capacity or support in the prey and time delay in the predator, this stable analysis is performed using stability criteria to obtain Hurwitz-type polynomials.

A Comprehensive Survey of Neural Architecture Search

Deep learning has made substantial breakthroughs in many fields due to its powerful automatic representation capabilities. It has been proven that neural architecture design is crucial to the feature representation of data and the final performance. However, the design of the neural architecture heavily relies on the researchers’ prior knowledge and experience. And due to the limitations of humans’ inherent knowledge, it is difficult for people to jump out of their original thinking paradigm and design an optimal model. Therefore, an intuitive idea would be to reduce human intervention as much as possible and let the algorithm automatically design the neural architecture. Neural Architecture Search ( NAS ) is just such a revolutionary algorithm, and the related research work is complicated and rich. Therefore, a comprehensive and systematic survey on the NAS is essential. Previously related surveys have begun to classify existing work mainly based on the key components of NAS: search space, search strategy, and evaluation strategy. While this classification method is more intuitive, it is difficult for readers to grasp the challenges and the landmark work involved. Therefore, in this survey, we provide a new perspective: beginning with an overview of the characteristics of the earliest NAS algorithms, summarizing the problems in these early NAS algorithms, and then providing solutions for subsequent related research work. In addition, we conduct a detailed and comprehensive analysis, comparison, and summary of these works. Finally, we provide some possible future research directions.

Quantity, quality, equality: introducing a new measure of social welfare

In this essay I propose a new measure of social welfare. It captures the intuitive idea that quantity, quality, and equality of individual welfare all matter for social welfare. More precisely, it satisfies six conditions: Equivalence, Dominance, Quality, Strict Monotonicity, Equality and Asymmetry. These state that (i) populations equivalent in individual welfare are equal in social welfare; (ii) a population that dominates another in individual welfare is better; (iii) a population that has a higher average welfare than another population is better, other things being equal; (iv) the addition of a well-faring individual makes a population better, whereas the addition of an ill-faring individual makes a population worse; (v) a population that has a higher degree of equality than another population is better, other things being equal; and (vi) individual illfare matters more for social welfare than individual welfare. By satisfying the six conditions, the measure improves on previously proposed measures, such as the utilitarian Total and Average measures, as well as different kinds of Prioritarian measures.

Instilling the value of effort (Registered report stage 1)

People who take on challenges and persevere longer are more likely to succeed in life. But individuals often avoid exerting effort, and there is limited experimental research investigating whether we can learn to value effort. Because existing research focuses on enhancing cognitive performance rather than increasing the value of effort, it also remains unclear whether individuals can learn to care more about challenging themselves than performing well. We developed a paradigm to test an intuitive idea: that people can learn to value effort and will seek effortful challenges if directly incentivized to do so. Critically, we dissociate the effects of rewarding people for choosing effortful challenges and performing well. We predict that rewarding effortful choices will increase willingness to engage in challenging tasks. We also predict nearand far-transfer effects, as reflected in changes in preferences on unrewarded and unrelated tasks.

Idiosyncratic volatility, option-based measures of informed trading, and investor attention

We establish a direct link between sophisticated investors in the option market, private stock market investors, and the idiosyncratic volatility (IVol) puzzle. To do so, we employ three option-based volatility spreads and attention data from Google Trends. In line with the IVol puzzle, the volatility spreads indicate that sophisticated investors indeed consider high-IVol stocks as being overvalued. Moreover, the option measures help to distinguish overpriced from fairly priced high-IVol stocks. Thus, these measures are able to predict the IVol puzzle’s magnitude in the cross-section of stock returns. Further, we link the origin of the IVol puzzle to the trading activity of irrational private investors as the return predictability only exists among stocks that receive a high level of private investor attention. Overall, our joint examination of option and stock markets sheds light on the behavior of different investor groups and their contribution to the IVol puzzle. Thereby, our analyses support the intuitive idea that noise trading leads to mispricing, which is identified by sophisticated investors and exploited in the option market.

The Reputation Trap

Few want to do business with a partner who has a bad reputation. Consequently, once a bad reputation is established, it can be difficult to get rid of. This leads on the one hand to the intuitive idea that a good reputation is easy to lose and hard to gain. On the other hand, it can lead to a strong form of history dependence in which a single beneficial or adverse event can cast a shadow over a very long period of time. It gives rise to a reputational trap where an agent rationally chooses not to invest in a good reputation because the chances others will find out is too low. Nevertheless, the same agent with a good reputation will make every effort to maintain it. Here, a simple reputational model is constructed and the conditions for there to be a unique equilibrium that constitutes a reputation trap are characterized.