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

Normalization of Arabic Dialects into Modern Standard Arabic using BERT and GPT-2

We present an encoder-decored based model for normalization of Arabic dialects using both BERT and GPT-2 based models. Arabic is a language of many dialects that not only differ from the Modern Standard Arabic (MSA) in terms of pronunciation but also in terms of morphology, grammar and lexical choice. This diversity can be troublesome even to a native Arabic speaker let alone a computer. Several NLP tools work well for MSA and in some of the main dialects but fail to cover Arabic language as a whole. Based on our manual evaluation, our model normalizes sentences entirely correctly 46\% of the time and almost correctly 26\% of the time

Weighted norm inequalities for integral transforms with splitting kernels

We obtain necessary and sufficient conditions on weights for a wide class ofintegral transforms to be bounded between weighted $L^p-L^q$ spaces, with$1\leq p\leq q\leq \infty$. The kernels $K(x,y)$ of such transforms are onlyassumed to satisfy upper bounds given by products of two functions, one in eachvariable. The obtained results are applicable to a number of transforms, some of whichare included here as particular examples. Some of the new results derived hereare the characterization of weights for the boundedness of the$\mathscr{H}_\alpha$ (or Struve) transform in the case $\alpha>\frac{1}{2}$, orthe characterization of power weights for which the Laplace transform isbounded in the limiting cases $p=1$ or $q=\infty$

Interpolation and moduli spaces of vector bundles on very general blowups of the projective plane

In this paper, we study certain moduli spaces of vector bundles on the blowupof the projective plane in at least 10 very general points. Moduli spaces ofsheaves on general type surfaces may be nonreduced, reducible and evendisconnected. In contrast, moduli spaces of sheaves on minimal rationalsurfaces and certain del Pezzo surfaces are irreducible and smooth along thelocus of stable bundles. We find examples of moduli spaces of vector bundles onmore general blowups of the projective plane that are disconnected and havecomponents of different dimensions. In fact, assuming the SHGH Conjecture, wecan find moduli spaces with arbitrarily many components of arbitrarily largedimension