Related papers: Conditional and unconditional information inequali…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
We establish an equivalence between two forms of the composition condition for the Abel differential equation with trigonometric coefficients.
We introduce a weak division-like property for noncommutative rings: a nontrivial ring is fadelian if for all nonzero $a,x$ there exist $b,c$ such that $x=ab+ca$. We prove properties of fadelian rings, and construct examples of such rings…
Income inequality and redistribution policies are modeled with a minimal, endogenous model of a simple foraging economy. Significant income inequalities emerge from the model for populations of equally capable individuals presented with…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, which…
This paper concerns the assessment of the effects of actions from a combination of nonexperimental data and causal assumptions encoded in the form of a directed acyclic graph in which some variables are presumed to be unobserved. We provide…
In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…
We give a visually appealing counterexample to the proposition that unbiased estimators are better than biased estimators.
We consider decision-making under incomplete information about an unknown state of nature. We show that a decision problem yields a higher value of information than another, uniformly across information structures, if and only if it is…
Nonlinear PDE's having {\bf given} conditional symmetries are constructed. They are obtained starting from the invariants of the "conditional symmetry" generator and imposing the extra condition given by the characteristic of the symmetry.…
We reformulate the information causality in a more general framework by adopting the results of signal propagation and computation in a noisy circuit. In our framework, the information causality leads to a broad class of Tsirelson…
We study the separation of positive and negative data examples in terms of description logic (DL) concepts and formulas of decidable FO fragments, in the presence of an ontology. In contrast to previous work, we add a signature that…
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
This work introduces a framework for quantifying the information content of logical propositions through the use of implication hypergraphs. We posit that a proposition's informativeness is primarily determined by its relationships with…
Several recent works in communication systems have proposed to leverage the power of neural networks in the design of encoders and decoders. In this approach, these blocks can be tailored to maximize the transmission rate based on…
In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.
A simple sufficient condition for certain cyclic algebras of odd degree d to be split is presented. It employs certain binary forms of degree d and the values they represent. A similar sufficient condition for certain Albert algebras not to…
In this paper, we introduce a large class of (so-called) conditional indicators, on a complete probability space with respect to a sub $\sigma$-algebra. A conditional indicator is a positive mapping, which is not necessary linear, but may…
In many expert and everyday reasoning contexts it is very useful to reason on the basis of defeasible assumptions. For instance, if the information at hand is incomplete we often use plausible assumptions, or if the information is…