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Although it has long been known that politicians lie, Donald Trump’s entry to the political arena has seen lying been turned not just into an augmented political strategy unparalleled in the recent history of political falsehoods and manipulation, but one that has rapidly spread through the media and, helped by information and communication technologies, across public spaces to reach every domain of society. This example reveals the social dimension of new initiatives in organised lying (i.e. open lying) and upgraded versions of systemic deep manipulation (i.e. transparent manipulation). In the article, we reflect on what has recently happened to the social status of truth, and also to lying and manipulation, in this post-truth world. By conceptualising open lying and transparent manipulation, we try to answer what it means to “lie like Trump”.

We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.

People may repeatedly encounter the same misinformation when it “goes viral.” The results of four main experiments (two preregistered) and a pilot experiment (total N = 2,587) suggest that repeatedly encountering misinformation makes it seem less unethical to spread––regardless of whether one believes it. Seeing a fake-news headline one or four times reduced how unethical participants thought it was to publish and share that headline when they saw it again—even when it was clearly labeled as false and participants disbelieved it, and even after we statistically accounted for judgments of how likeable and popular it was. In turn, perceiving the headline as less unethical predicted stronger inclinations to express approval of it online. People were also more likely to actually share repeated headlines than to share new headlines in an experimental setting. We speculate that repeating blatant misinformation may reduce the moral condemnation it receives by making it feel intuitively true, and we discuss other potential mechanisms that might explain this effect.

With the rapid development of educational data mining and learning analytics, this study tries to make sense of education data and improve teachers’ competence and teaching experience. In recent years, massive open online courses (MOOCs) have become the first choice of online learning for tens of millions of people around the world. However, the dropout rates for MOOCs are high. The goal of dropout prediction is to predict whether learners will exhibit learning behavior in several consecutive days in the future. Therefore, in this study, we consider the correlation information of learners’ learning behaviors for several consecutive days. Through the in-depth statistical analysis of learners’ learning behavior, it is found that learners’ learning behavior on the next day is similar to that of the previous day. Based on this characteristic, we propose a Lie group region covariance matrix to represent the local correlation information of learning behavior and construct a convolutional neural network model with a multidilation pooling module to extract the local correlation high-level features of learning behavior for dropout prediction. In addition, extensive experiments show that the local correlation of learners’ learning behavior cannot be ignored, which is fully considered in our model. Compared with the existing methods, our method achieves the best experimental results in accuracy, F-measure, precision, and recall, which is better than the current methods.

It is widely assumed that people will share inaccurate gossip for their own selfish purposes. This assumption, if true, presents a challenge to the growing body of work positing that gossip is a ready source of accurate reputational information and therefore is welfare improving. We tested this inaccuracy assumption by examining the frequency and form of spontaneous lies shared between gossiping members of networks playing a series of one-shot trust games (N = 320). We manipulated whether gossipers were or were not competing with each other. We showed that lies make up a sizeable minority of messages and are twice as frequent under gossiper competition. However, this had no discernible effect on trust levels. We attribute this to the findings that (a) gossip targets are insensitive to lies and (b) some lies are welfare enhancing. These findings suggest that lies need not prevent—and may help—gossip to serve reputational functions.

Massive open online courses (MOOCs) represent an innovative online learning paradigm that has garnered considerable popularity in recent years, attracting a multitude of learners to MOOC platforms due to their accessible and adaptable instructional structure. However, the elevated dropout rate in current MOOCs limits their advancement. Current dropout prediction models predominantly employ fixed-size convolutional kernels for feature extraction, which insufficiently address temporal dependencies and consequently demonstrate specific limitations. We propose a Lie Group-based feature context-local fusion attention model for predicting dropout in MOOCs. This model initially extracts shallow features using Lie Group machine learning techniques and subsequently integrates multiple parallel dilated convolutional modules to acquire high-level semantic representations. We design an attention mechanism that integrates contextual and local features, effectively capturing the temporal dependencies in the study behaviors of learners. We performed multiple experiments on the XuetangX dataset to evaluate the model’s efficacy. The results show that our method attains a precision score of 0.910, exceeding the previous state-of-the-art approach by 3.3%.

We consider the transfer of continuous-variable entangled states in coupled oscillator chains embedded in a generic environment. We demonstrate high-fidelity transfer via optimal control in two configurations-a linear chain and an X-shaped chain. More specifically, we use the Krotov optimization algorithm to design control fields that achieve the desired state transfer. Under environmental memory effects, the Krotov algorithm needs to be modified, since the dissipative terms in non-Markovian dynamics are generally governed by the time-dependent system Hamiltonian. Remarkably, we can achieve high-fidelity transfer by simply tuning the frequencies of the oscillators while keeping the coupling strength constant, even in the presence of open-system effects. For the system under consideration, we find that quantum memory effects can aid in the transfer of entanglement and show improvement over the memoryless case. In addition, it is possible to target a range of entangled states, making it unnecessary to know the parameters of the initial state beforehand.

The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action. A novel symplectic thermodynamics and information geometry known as “Lie group thermodynamics” then explains foliation structures of thermodynamics. We then infer a geometric structure for heat equation from this archetypal model, and we have discovered a pure geometric structure of entropy, which characterizes entropy in coadjoint representation as an invariant Casimir function. The coadjoint orbits form the level sets on the entropy. By using the KKS 2-form in the affine case via Souriau’s cocycle, the method also enables the Fisher metric from information geometry for Lie groups. The fact that transverse dynamics to these symplectic leaves is dissipative, whilst dynamics along these symplectic leaves characterize non-dissipative phenomenon, can be used to interpret this Lie group thermodynamics within the context of an open system out of thermodynamics equilibrium. In the following section, we will discuss the dissipative symplectic model of heat and information through the Poisson transverse structure to the symplectic leaf of coadjoint orbits, which is based on the metriplectic bracket, which guarantees conservation of energy and non-decrease of entropy. Baptiste Coquinot recently developed a new foundation theory for dissipative brackets by taking a broad perspective from non-equilibrium thermodynamics. He did this by first considering more natural variables for building the bracket used in metriplectic flow and then by presenting a methodical approach to the development of the theory. By deriving a generic dissipative bracket from fundamental thermodynamic first principles, Baptiste Coquinot demonstrates that brackets for the dissipative part are entirely natural, just as Poisson brackets for the non-dissipative part are canonical for Hamiltonian dynamics. We shall investigate how the theory of dissipative brackets introduced by Paul Dirac for limited Hamiltonian systems relates to transverse structure. We shall investigate an alternative method to the metriplectic method based on Michel Saint Germain’s PhD research on the transverse Poisson structure. We will examine an alternative method to the metriplectic method based on the transverse Poisson structure, which Michel Saint-Germain studied for his PhD and was motivated by the key works of Fokko du Cloux. In continuation of Saint-Germain’s works, Hervé Sabourin highlights the, for transverse Poisson structures, polynomial nature to nilpotent adjoint orbits and demonstrated that the Casimir functions of the transverse Poisson structure that result from restriction to the Lie–Poisson structure transverse slice are Casimir functions independent of the transverse Poisson structure. He also demonstrated that, on the transverse slice, two polynomial Poisson structures to the symplectic leaf appear that have Casimir functions. The dissipative equation introduced by Lindblad, from the Hamiltonian Liouville equation operating on the quantum density matrix, will be applied to illustrate these previous models. For the Lindblad operator, the dissipative component has been described as the relative entropy gradient and the maximum entropy principle by Öttinger. It has been observed then that the Lindblad equation is a linear approximation of the metriplectic equation.

We discuss basic properties and some applications of a generalized notion of differential for set-valued maps, called Quasi Differential Quotient. The latter was proved to be extremely useful to deal with several open questions in Optimal Control, such as the so called “Infimum Gap” problem. Furthermore, it recently revealed to be a valuable tool to prove second order necessary conditions expressed in terms of non-smooth Lie-brackets when the vector field is merely Lipschitz continuous. In this paper, we present a first step towards a more systematic theory of Quasi Differential Quotients and we study the relation between Quasi Differential Quotients and other generalized differentials such as the Sussmann’s Generalized Differential Quotient and Sussman’s Approximate Generalized Differential Quotient, the Clarke’s Generalized Jacobian and the Warga’s Derivative Container.

Given smooth manifolds M1,…,Mn (which may have a boundary or corners), a smooth manifold N modeled on locally convex spaces and α∈(N0∪{∞})n, we consider the set Cα(M1×⋯×Mn,N) of all mappings f:M1×⋯×Mn→N which are Cα in the sense of Alzaareer. Such mappings admit, simultaneously, continuous iterated directional derivatives of orders ≤αj in the jth variable for j∈{1,…,n}, in local charts. We show that Cα(M1×⋯×Mn,N) admits a canonical smooth manifold structure whenever each Mj is compact and N admits a local addition. The case of non-compact domains is also considered.