Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle

Causality describes the process and consequences from an action: a cause has an effect. Causality is preserved in classical physics as well as in special and general theories of relativity. Surprisingly, causality as a relationship between the cause and its effect is in neither of these theories considered a law or a principle. Its existence in physics has even been challenged by prominent opponents in part due to the time symmetric nature of the physical laws. With the use of the reduced action and the least action principle of Maupertuis along with a discrete dynamical time physics yielding an arrow of time, causality is defined as the partial spatial derivative of the reduced action and as such is position- and momentum-dependent and requests the presence of space. With this definition the system evolves from one step to the next without the need of time, while (discrete) time can be reconstructed.

Efficient and stochastic mouse action switching during probabilistic decision making

To gain insight into the process by which animals choose between actions, we trained mice in a two-armed bandit task with time-varying reward probabilities. Whereas past work has modeled the selection of the higher rewarding port in such tasks, we sought to also model the trial-to-trial changes in port selection − i.e. the action switching behavior. We find that mouse behavior deviates from the theoretically optimal agent performing Bayesian inference in a hidden Markov model (HMM). Instead the strategy of mice can be well-described by a set of models that we demonstrate are mathematically equivalent: a logistic regression, drift diffusion model, and ′sticky′ Bayesian model. Here we show that switching behavior of mice is characterized by several components that are conserved across models, namely a stochastic action policy, a representation of action value, and a tendency to repeat actions despite incoming evidence. When fit to mouse behavior, the expected reward under these models lies near a plateau of the value landscape even in changing reward probability contexts. These results indicate that mouse behavior reaches near-maximal performance with reduced action switching and can be described by models with a small number of relatively fixed-parameters.

O(n, n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in α′

We perform the toroidal compactification of the full Bergshoeff-de Roo version of the Heterotic Superstring effective action to first order in α′. The dimensionally-reduced action is given in a manifestly-O(n, n)-invariant form which we use to derive a manifestly-O(n, n)-invariant Wald entropy formula which we then use to compute the entropy of α′-corrected, 4-dimensional, 4-charge, static, extremal, supersymmetric black holes.

Action predictability is reflected in beta power attenuation and predictive eye movements in adolescents with and without autism

Most theoretical accounts of autism posit difficulties in predicting others’ actions, and this difficulty has been proposed to be at the root of autistic individuals’ social communication differences. Empirical results are mixed, however, with autistic individuals showing reduced action prediction in some studies but not in others. It has recently been proposed that this effect might be observed primarily when observed actions are less predictable, but this idea has yet to be tested. To assess the influence of predictability on neural and behavioural action prediction, the current study employed an action observation paradigm with multi-step actions that become gradually more predictable. Autistic and non-autistic adolescents showed similar patterns of motor system activation during observation, as seen in attenuated mu and beta power compared to baseline, with beta power further modulated by predictability in both groups. Bayesian statistics confirmed that action predictability influenced beta power similarly in both groups. The groups also made similar behavioural predictions, as seen in three eye-movement measures. We found no evidence that autistic adolescents responded differently than non-autistic adolescents to the predictability of an observed action. These findings show that autistic adolescents do spontaneously predict others’ actions, both neurally and behaviourally, which calls into question the role of action prediction as a key mechanism underlying autism.

T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in α′

We consider the compactification on a circle of the Heterotic Superstring effective action to first order in the Regge slope parameter α′ and re-derive the α′-corrected Buscher rules first found in ref. [42], proving the T duality invariance of the dimensionally-reduced action to that order in α′. We use Iyer and Wald’s prescription to derive an entropy formula that can be applied to black-hole solutions which can be obtained by a single non-trivial compactification on a circle and discuss its invariance under the α′-corrected T duality transformations. This formula has been successfully applied to α′-corrected 4-dimensional non-extremal Reissner-Nordström black holes in ref. [21] and we apply it here to a heterotic version of the Strominger-Vafa 5-dimensional extremal black hole.

Alternative self-dual gravity in eight dimensions

We develop an alternative Ashtekar formalism in eight dimensions. In fact, using a MacDowell–Mansouri physical framework and a self-dual curvature symmetry, we propose an action in eight dimensions in which the Levi-Civita tenor with eight indices plays a key role. We explicitly show that such an action contains number of linear, quadratic and cubic terms in the Riemann tensor, Ricci tensor and scalar curvature. In particular, the linear term is reduced to the Einstein–Hilbert action with cosmological constant in eight dimensions. We prove that such a reduced action is equivalent to the Lovelock action in eight dimensions.