Phenomenology and intersubjectivity in political economy: an anti-perfectionist perspective

Anti-perfectionism is a philosophical perspective combining the view of man as an imperfect and non-self-sufficient being with a scientific epistemology based on imperfect knowledge. From an epistemological perspective, it has roots in Socrates and, more recently, in the post-empiricism of Giambattista Vico, up to phenomenology. From an anthropological perspective, it is a philosophical tradition based on an awareness of the constitutive dependency of individual performance and fulfilment of man on his interaction with others. It is conceived in opposition to the individualism and perfect rationality of most social theories. The paper analyses both the philosophical and the epistemological premises of anti-perfectionism as well as its consequences in terms of economic methodology. It will specifically develop the momentary intersection of phenomenology and Austrian economics. The theory of knowledge and of sense-making of phenomenology will be discussed with particular attention to intersubjectivity, which expresses anti-perfectionism well. The interpretations of human knowledge and action of Scheler and Schütz are analysed and connected to some contemporary streams of Austrian economics

Expressiveness of SHACL Features and Extensions for Full Equality and Disjointness Tests

SHACL is a W3C-proposed schema language for expressing structural constraintson RDF graphs. Recent work on formalizing this language has revealed a strikingrelationship to description logics. SHACL expressions can use three fundamentalfeatures that are not so common in description logics. These features areequality tests; disjointness tests; and closure constraints. Moreover, SHACL ispeculiar in allowing only a restricted form of expressions (so-called targets)on the left-hand side of inclusion constraints. The goal of this paper is to obtain a clear picture of the impact andexpressiveness of these features and restrictions. We show that each of thefour features is primitive: using the feature, one can express boolean queriesthat are not expressible without using the feature. We also show that therestriction that SHACL imposes on allowed targets is inessential, as long asclosure constraints are not used. In addition, we show that enriching SHACL with "full" versions of equalitytests, or disjointness tests, results in a strictly more powerful language

A logical limit law for 231231-avoiding permutations

We prove that the class of 231-avoiding permutations satisfies a logicallimit law, i.e. that for any first-order sentence $\Psi$, in the language oftwo total orders, the probability $p_{n,\Psi}$ that a uniform random231-avoiding permutation of size $n$ satisfies $\Psi$ admits a limit as $n$ islarge. Moreover, we establish two further results about the behavior and valueof $p_{n,\Psi}$: (i) it is either bounded away from $0$, or decaysexponentially fast; (ii) the set of possible limits is dense in $[0,1]$. Ourtools come mainly from analytic combinatorics and singularity analysis.Comment: 15 pages; version 3 is the final version, ready for publication in DMTC

Efficient Algorithms for Finite Z\mathbb{Z}-Algebras

For a finite $\mathbb{Z}$-algebra $R$, i.e., for a $\mathbb{Z}$-algebra whichis a finitely generated $\mathbb{Z}$-module, we assume that $R$ is explicitlygiven by a system of $\mathbb{Z}$-module generators $G$, its relation module${\rm Syz}(G)$, and the structure constants of the multiplication in $R$. Inthis setting we develop and analyze efficient algorithms for computingessential information about $R$. First we provide polynomial time algorithmsfor solving linear systems of equations over $R$ and for basic ideal-theoreticoperations in $R$. Then we develop ZPP (zero-error probabilitic polynomialtime) algorithms to compute the nilradical and the maximal ideals of0-dimensional affine algebras $K[x_1,\dots,x_n]/I$ with $K=\mathbb{Q}$ or$K=\mathbb{F}_p$. The task of finding the associated primes of a finite$\mathbb{Z}$-algebra $R$ is reduced to these cases and solved in ZPPIF (ZPPplus one integer factorization). With the same complexity, we calculate theconnected components of the set of minimal associated primes {\rmminPrimes}(R) and then the primitive idempotents of $R$. Finally, we provethat knowing an explicit representation of $R$ is polynomial time equivalent toknowing a strong Gr\"obner basis of an ideal $I$ such that $R =\mathbb{Z}[x_1,\dots,x_n]/I$.Comment: Published in journal of Groups, Complexity, Cryptolog

Holonomic equations and efficient random generation of binary trees

Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. Rémy showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary trees. I extend this paradigm to Motzkin trees and Schröder trees and show that despite slight differences my algorithm that generates random Schröder trees has linear expected complexity and my algorithm that generates Motzkin trees is in O(n) expected complexity, only if we can implement a specific oracle with a O(1) complexity. For Motzkin trees, I propose a solution which works well for realistic values (up to size ten millions) and yields an efficient algorithm

An exercise in experimental mathematics: calculation of the algebraic entropy of a map

We illustrate the use of the notion of derived recurrences introduced earlierto evaluate the algebraic entropy of self-maps of projective spaces. We inparticular give an example, where a complete proof is still awaited, but wheredifferent approaches are in such perfect agreement that we can trust we get toan exact result. This is an instructive example of experimental mathematics.Comment: Version formatted for Open Communication in Nonlinear Physics (OCNMP) Special issue in Memory of Professor Decio Lev

Diagonal F-splitting and Symbolic Powers of Ideals

Let $J$ be any ideal in a strongly $F$-regular, diagonally $F$-split ring $R$essentially of finite type over an $F$-finite field. We show that $J^{s+t}\subseteq \tau(J^{s - \epsilon}) \tau(J^{t-\epsilon})$ for all $s, t, \epsilon> 0$ for which the formula makes sense. We use this to show a number of novelcontainments between symbolic and ordinary powers of prime ideals in thissetting, which includes all determinantal rings and a large class of toricrings in positive characteristic. In particular, we show that $P^{(2hn)}\subseteq P^n$ for all prime ideals $P$ of height $h$ in such rings.Comment: Copy edited and formatted in the EpiGA journal's styleshee

Partial-dual genus polynomial as a weight system

We prove that the partial-dual genus polynomial considered as a function onchord diagrams satisfies the four-term relation. Thus it is a weight systemfrom the theory of Vassiliev knot invariants.Comment: Final version for publication in Communications in Mathematic

One Belt One Road : une nouvelle architecture des flux mondiaux sous influence chinoise

China’s One Belt One Road (OBOR) strategy was launched in September 2013 by Xi Jinping. It is a global transports infrastructure strategy that covers both land (road and rail) and sea roads by connecting ports from Asia to Europe through Africa. With a budget of more than 1,400 billion dollars, it is one of the most important strategies on a global scale. The purpose of this article is firstly to characterize this strategy, from its foundations to the actual enactment modalities. It is then to propose an interpretation based on a Braudelian reading in terms of world economy and hegemonic posture leading to the emergence of new asian global value chains.La stratégie chinoise One Belt One Road (OBOR) a été lancée en septembre 2013 par Xi Jinping. Il s’agit d’une stratégie globale de développement d’infrastructures, notamment de transport, et de coopérations. Elle concerne aussi bien les voies terrestres (routes et fer) que les voies maritimes par la connexion de ports depuis l’Asie jusqu’à l’Europe en passant par l’Afrique. Dotée d’un budget de plus de 1 400 milliards de dollars, elle est l’une des plus importantes stratégies initiées à l’échelle mondiale. L’objet de cet article, écrit en 2018, est d’abord de caractériser cette stratégie, depuis ses fondements jusqu’aux modalités de sa mise en acte. Il s’agit ensuite d’en proposer une interprétation fondée sur une lecture braudélienne en termes d’économie-monde et de posture hégémonique conduisant à l’émergence de nouvelles global value chains asiatiques