Related papers: Non-Commutation Chains in Pre- and Post-Selection …

This paper is composed of two main results concerning chains of infinite order which are not necessarily continuous. The first one is a decomposition of the transition probability kernel as a countable mixture of unbounded probabilistic…

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…

Uncertainties in the real world mean that is impossible for system designers to anticipate and explicitly design for all scenarios that a robot might encounter. Thus, robots designed like this are fragile and fail outside of…

The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…

A new paradox in superluminal signaling is presented. In contrast to the Tolman paradox with tachyon exchange between two parties, the new paradox appears already in a one-way signaling, even without creating the time loop. As shown in the…

We consider a dichotomy for analytic families of trees stating that either there is a colouring of the nodes for which all but finitely many levels of every tree are nonhomogeneous, or else the family contains an uncountable antichain. This…

Two types of approximation to the paradoxical Russell Set are presented, one approximating it from below, one from above. It is shown that any lower approximation gives rise to a better approximation containing it, and that any upper…

This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…

We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics…

In arXiv:1107.4675 Ralph uses our post-selection model of closed timelike curves (P-CTC) to construct an "unproven-theorem" paradox, and claims that this voids our argument that P-CTCs are able to resolve such types of paradoxes. Here we…

It was recently realised that quantum theory allows for so-called causally nonseparable processes, which are incompatible with any definite causal order. This was first suggested on a rather abstract level by the formalism of process…

Identifying causal relations from purely observational data typically requires additional assumptions on relations and/or noise. Most current methods restrict their analysis to datasets that are assumed to have pure linear or nonlinear…

Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes…

We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about…

Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine…

Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…

Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…

It is often argued that superluminal velocities and nontrivial spacetime topologies, allowed by the theory of relativity, may lead to causal paradoxes. By emphasizing that the notion of causality assumes the existence of a time arrow (TA)…

Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system…

Machine learning algorithms have achieved superhuman performance in specific complex domains. However, learning online from few examples and compositional learning for efficient generalization across domains remain elusive. In humans, such…