The existence of superluminal particles is consistent with the kinematics of Einstein's special theory of relativity

Within an axiomatic framework of kinematics, we prove that the existence of faster than light particles is logically independent of Einstein's special theory of relativity. Consequently, it is consistent with the kinematics of special relativity that there might be faster than light particles.Comment: 19 pages, 3 figure

Impossibility of Gathering, a Certification

Recent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that self-organise and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and proofs of correctness. This paper builds upon a previously proposed formal framework to certify the correctness of impossibility results regarding distributed algorithms that are dedicated to autonomous mobile robots evolving in a continuous space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. A fundamental (but not yet formally certified) result, due to Suzuki and Yamashita, states that this simple task is impossible for two robots executing deterministic code and initially located at distinct positions. Not only do we obtain a certified proof of the original impossibility result, we also get the more general impossibility of gathering with an even number of robots, when any two robots are possibly initially at the same exact location.Comment: 10

Axioms for consensus functions on the n-cube

An elementary general result is proved that allows for simple characterizations of well-known location/consensus functions (median, mean and center) on the n-cube. In addition, alternate new characterizations are given for the median and anti-median functions on the n-cube.Comment: 12 page

Means and covariance functions for geostatistical compositional data: an axiomatic approach

This work focuses on the characterization of the central tendency of a sample of compositional data. It provides new results about theoretical properties of means and covariance functions for compositional data, with an axiomatic perspective. Original results that shed new light on the geostatistical modeling of compositional data are presented. As a first result, it is shown that the weighted arithmetic mean is the only central tendency characteristic satisfying a small set of axioms, namely continuity, reflexivity and marginal stability. Moreover, this set of axioms also implies that the weights must be identical for all parts of the composition. This result has deep consequences on the spatial multivariate covariance modeling of compositional data. In a geostatistical setting, it is shown as a second result that the proportional model of covariance functions (i.e., the product of a covariance matrix and a single correlation function) is the only model that provides identical kriging weights for all components of the compositional data. As a consequence of these two results, the proportional model of covariance function is the only covariance model compatible with reflexivity and marginal stability

No Profitable Decomposition in Quasi-Linear Allocation Problems

We study the problem of allocating a bundle of perfectly divisible private goods from an axiomatic point of view, in situations where compensations can be made through monetary transfers. The key property we impose on the allocation rule requires that no agent should be able to gain by decomposing the problem into sequences of subproblems. Combined with additional standard properties, it leads to a characterization of the rule that shares the total surplus equally. Hence a traditional welfarist rule emerges as the unique consequence of our axioms phrased in a natural economic environment.Social Choice; Axiomatic Bargaining; Welfarism; Egalitarianism

Review of Wittgenstein’s Philosophical Investigations by David Stern (2004)(review revised 2019)

Overall Stern does a fine analysis of Wittgenstein (W) and is one of the top W scholars, but in my view, they all fall short of a full appreciation, as I explain at length in this review and many others. If one does not understand W (and preferably Searle also), then I don't see how one could have more than a superficial understanding of philosophy and of higher order thought and thus of all complex behavior (psychology, sociology, anthropology, history, literature, society). In a nutshell, W demonstrated that when you have shown how a sentence is used in the context of interest, there is nothing more to say. I will start with a few notable quotes and then give what I think are the minimum considerations necessary to understand Wittgenstein, philosophy and human behavior. As Stern is aware, throughout W’s works, understanding is bedeviled by possible alternative and consequently often infelicitous translations from often unedited and handwritten German notes, with “Satz” being frequently incorrectly rendered as “proposition” (which is a testable or falsifiable statement) when referring to our non-falsifiable psychological axioms, as opposed to the correct “sentence”, which CAN be applied to our axiomatic true-only statements such as “these are my hands” or “Tyrannosaurs were large carnivorous dinosaurs that lived about 50 million years ago”. Finally, let me suggest that with the perspective I have encouraged here, W is at the center of contemporary philosophy and psychology and is not obscure, difficult or irrelevant, but scintillating, profound and crystal clear and that to miss him is to miss one of the greatest intellectual adventures possible. Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019

Should we discount future generations’ welfare? A survey on the “pure” discount rate debate.

In A Mathematical Theory of Saving (1928), Frank Ramsey not only laid the foundations of the fruitful optimal growth literature, but also launched a major moral debate: should we discount future generations’ well-being? While Ramsey regarded such “pure” discounting as “ethically indefensible”, several philosophers and economists have developed arguments justifying the “pure” discounting practice since the early 1960s. This essay consists of a survey of those arguments. After a brief examination of the – often implicit – treatment of future generations’ welfare by utilitarian thinkers before Ramsey’s view was expressed, later arguments of various kinds are analysed. It is argued that, under the assumption of perfect certainty regarding future human life, the “pure” discounting practice seems ethically untenable. However, once we account for the uncertainty regarding future generations’ existence, “pure” discounting seems more acceptable, even if strong criticisms still remain, especially regarding the adequateness of the expected utility theory in such a normative context. those limits would be faced by any other consequences-based ethical theory in front of Different Number Choices.

Random assignment with multi-unit demands

We consider the multi-unit random assignment problem in which agents express preferences over objects and objects are allocated to agents randomly based on the preferences. The most well-established preference relation to compare random allocations of objects is stochastic dominance (SD) which also leads to corresponding notions of envy-freeness, efficiency, and weak strategyproofness. We show that there exists no rule that is anonymous, neutral, efficient and weak strategyproof. For single-unit random assignment, we show that there exists no rule that is anonymous, neutral, efficient and weak group-strategyproof. We then study a generalization of the PS (probabilistic serial) rule called multi-unit-eating PS and prove that multi-unit-eating PS satisfies envy-freeness, weak strategyproofness, and unanimity.Comment: 17 page