Axiomatic Point Research Articles

Journalistic cultures in the context of the conflict of civilizations

The subject of the research is journalism as a social institution. Modern media industries are becoming maximally polarized and involved in the process of promoting and defending certain values, as a result of which we see an unprecedented information confrontation that is one way or another transforming the world community. Media researchers are beginning to recognize the untenability of the idea of a universal culture in the field of journalism. Based on these premises, the object of the study was journalistic culture, which includes the choice of methods for collecting information and creating a media product. The work used axiomatic (the specificity of the method is that at the beginning of the process a set of basic provisions is specified that do not require proof and are taken as explicit, in fact, they are an axiom), analysis and synthesis, combining the conclusions obtained during the previous research method into a single whole. The novelty of the study is seen in the fact that for the first time, when studying the functions of journalism, a conclusion is drawn about the need to move away from globalization ideas from an axiomatic point of view. It can be observed that in recent years, social networks, instant messengers and channels, which are capable of completely reformatting the mentality of society and even the way people think, can have an increasing influence. Based on the results of the study, the following conclusions can be drawn: trends and communication flows are now created mainly in social networks and the services that support them, and communication is then effective when it actively unfolds in the online media space. Numerous social networks of different types, while entertaining, involve their audience in the communication process and offer the opportunity for cultural and political socialization.

The Approximation of Fourth Order Nonlinear Variational Inequalities

In this paper we deal with existence and the approximation of the solution of the elliptic variational inequality from an abstract axiomatic point of view. We give an error estimate for the dierence of the two solutions in an appropriate norm. Also, we present some computational results.

Phragmén’s voting methods and justified representation

In the late 19th century, Swedish mathematician Edvard Phragmén proposed a load-balancing approach for selecting committees based on approval ballots. We consider three committee voting rules resulting from this approach: two optimization variants—one minimizing the maximum load and one minimizing the variance of loads—and a sequential variant. We study Phragmén ’s methods from an axiomatic point of view, focusing on properties capturing proportional representation. We show that the sequential variant satisfies proportional justified representation, which is a rare property for committee monotonic methods. Moreover, we show that the optimization variants satisfy perfect representation. We also analyze the computational complexity of Phragmén ’s methods and provide mixed-integer programming based algorithms for computing them.

Lost in Taxation

Cost–Benefit Analysis (CBA) was developed to assess the net socioeconomic benefits of a wide variety of projects in many fields. In this context, it is relevant to investigate how this method is actually used for project evaluation, and whether its merits and limitations are properly understood by a wider community of economists. In this study, we showcase a debate that took place in Italy in 2019 about an important high-speed rail project, following the publication of a CBA that received much criticism. To learn from this episode, we find it useful to set up a meta-model of CBA that allows the formalisation of a large number of CBA calculations (including potentially ill-founded calculations) and to verify their validity. With this meta model, we review the criticisms formulated during the 2019 CBA debate focusing on two salient topics; whether CBA should include taxation and whether the Rule-of-Half measure of users’ surplus is valid. Our analysis suggests: (1) That the proposed meta-equation can help in structuring the scientific debate regarding CBA and the relevant economic discussion about a given project; (2) with few exceptions, the criticisms formulated regarding the 2019 CBA on these topics were incorrect, mostly incoherent, also from an axiomatic point of view. This indicates that ill-founded methods are at risk of becoming well-accepted in the larger community of economists, with the risk of lowering the general quality of policy recommendations they can formulate. This underlines the need for economists to revise the misguided views of CBA.

Scientific value of the quantum tests of equivalence principle in light of Hilbert’s sixth problem

In his sixth problem, Hilbert called for an axiomatic approach to theoretical physics with an aim to achieve precision and rigour in scientific reasoning, where logic and language (semantics) of physics play pivotal roles. It is from such a point of view, that we investigate the scientific value of the modern experiments to perform quantum tests of equivalence principle. Determination of Planck constant involves the use of acceleration due to gravity of the Earth (g) that results in the force on a test mass. The equivalence between the inertial mass and gravitational mass of a test object is assumed in the process of logically defining g from the relevant hypotheses of physics. Consequently, if Planck constant is used as input in any experiment (or in the associated theory that finds such an experiment) that is designed to test the equivalence between inertial and gravitational mass, then it is equivalent to establish a scientific truth by implicitly assuming it, i.e. a tautology. There are several notable examples which plague the frontiers of current scientific research which claim to make quantum test of equivalence principle. We question the scientific value of such experiments from Hilbert’s axiomatic point of view. This work adds to the recently reported semantic obstacle in any axiomatic attempt to put ‘quantum’ and ‘gravity’ together, albeit with an experimental tint.

The axiomatic and the operational approaches to resource theories of magic do not coincide

Stabilizer operations (SO) occupy a prominent role in fault-tolerant quantum computing. They are defined operationally by the use of Clifford gates, Pauli measurements, and classical control. These operations can be efficiently simulated on a classical computer, a result which is known as the Gottesman–Knill theorem. However, an additional supply of magic states is enough to promote them to a universal, fault-tolerant model for quantum computing. To quantify the needed resources in terms of magic states, a resource theory of magic has been developed. SO are considered free within this theory; however, they are not the most general class of free operations. From an axiomatic point of view, these are the completely stabilizer-preserving (CSP) channels, defined as those that preserve the convex hull of stabilizer states. It has been an open problem to decide whether these two definitions lead to the same class of operations. In this work, we answer this question in the negative, by constructing an explicit counter-example. This indicates that recently proposed stabilizer-based simulation techniques of CSP maps are strictly more powerful than Gottesman–Knill-like methods. The result is analogous to a well-known fact in entanglement theory, namely, that there is a gap between the operationally defined class of local operations and classical communication and the axiomatically defined class of separable channels.

Advancing rural as ‘something more than a human estate’: Exploring UK sheep-shaping

Periodically, the topic of defining rural is addressed within rural social science scholarship but done so in overwhelmingly human terms. This paper engages with this observation, arguing the simple but axiomatic point that the rural is not solely a human taxonomic creation but expresses a space that integrally and intimately involves the more-than-human. Consequently, the latter should be strongly, firmly and richly represented up-front within the defining rural debate. Adopting an established if, to date, still anthropocentricised three-fold model of rural space, the paper argues that each dimension – localities, representations, lives – feature the more-than-human in both passive and active ways. Overall, bringing more-than-human perspectives much further to the fore consolidates the idea of rural as inherently co-produced, a ‘baroque assemblage’ containing many more-than-human living things. Accounts of animals within such a rural must recognise their emplacing from a diversity of foci, interests and consequences. The paper begins to introduce details of this diverse co-production with respect to one ubiquitous rural animal, the sheep. It illustrates the ‘ensheeping’ of rural localities, representations and lives, with the practical significance of this brought together and drawn out through two rival accounts of sheep within the Lake District National Park. Finally, the seemingly modest call for rural studies to embrace animals more fully is argued to be enhanced today by ongoing and potentially imminent experiences impacting strongly on rural places.

Of fear and fantasy, fact and fiction: Interrogating canonical Indian literary historiography towards comprehending partition of Bengal in post-Independence Indian (English) fictional space

A victim of the partition of Eastern India/undivided Bengal, a refugee is one who has ironically left behind the real but has carried on forever indelibly imprinted in memory that which is lost and remembered in superlatives, thus moving and simultaneously resisting to move. Remaining mentally anchored forever on ‘Bengal’s shore’ and having been denied the moment of adequate articulation of the loss in factual terms partly due to immediate trauma and partly due to the inherent politics of the language of standard literary expression vis-à-vis spoken language (Bangla vs Bangal respectively) with its hierarchic positionings, as well as the politics of state policy that attributed partition of Western India primordial signification, the Bengali Hindu refugee migrating from erstwhile East Pakistan (and now Bangladesh) to India, has never ‘really’ spoken and this is the hypothesis of this argument. Thus, what is heard, being far removed from the historical moment of rupture that was partition and with the loss of that fateful generation is bound to be ‘fiction’ and not ‘fact’. This paper proposes that since the refugee voice was denied adequate articulation of the ‘facts’ and the ‘fears’ resultant from partition in this part of Eastern India, that historical moment of perception and documentation has been irretrievably lost. Hence any attempt at documenting the same now shall obviously result in fictionalization of and fantasizing the loss as is evident in original and translational post-Independence Indian English Fiction -the moment of loss being the moment of fictional genesis. This paper also puts forward the necessity of identifying two specific periods beyond ‘independence’ whose axiomatic point would be the partition of Eastern India/ undivided Bengal viz. pre-partition and post-partition Indian Literature. The same shall apply to Indian English Literature both in original and translation.

A Concessions-Based Procedure for Meta-Bargaining Problems

In 1950, Nash’s seminal paper introduced the axiomatic approach to the analysis of bargaining situations. Since then, many bargaining solutions have been proposed and axiomatically analyzed. The fact that agents, when face with a bargaining problem, can come up with different solution concepts (that is, different notions of fairness and equity) was first introduced by van Damme (J Econ Theory 38:78–100, 1986) with the meta-bargaining model. In this paper we present and axiomatically analyze a procedure for solving meta-bargaining problems, which we call Unanimous–Concession. As an example, we show that the Nash solution is the result of the meta-bargaining process we define, when agents have dual egalitarian criteria. Finally, we compare, from an axiomatic point of view, our proposal with other meta-bargaining procedures.

From paradigm to paradox – contemporary mainstream theoretical reflections for fieldwork in lowland South America


 
 
 This essay intends to address perspectives and reflections on nature and culture in the contemporary anthropological literature . Dialogically engaging with Ingold, Wag- ner, Viveiros de Castro, Descola and Strathern, I aim to demonstrate the implications of understanding culture as an axiomatic point of differentiation of human nature, or as re-elaboration of materiality through human action . This reflection calls us to rethink the Western scientific epistemology, along with its presupposed ontological order . Such questioning unfolds in the elaboration of the ethnographic text, which in turn is the result of a dialectical process that speaks not only of one culture, but of two, and especially of our gaze on the Other . In the ethnographic text, an anthropologist and a native are the potential locus of reproduction of their culture . Through this approach we extend the implications of epistemological concerns to fieldwork practices and to the art of under- standing other knowledge systems .
 
 

An axiomatic approach to finite means

In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications.

On the linearity property for allocation problems and bankruptcy problems

This work provides an analysis of linear rules for bankruptcy problems and allocation problems from an axiomatic point of view and we extend the study of the additivity property presented in Bergantiños and Méndez-Naya [1] and Bergantiños and Vidal-Puga [2]. We offer a decomposition for the space of allocation problems into direct sum of subspaces that are relevant to the study of linear rules and obtain characterizations of certain classes of rules. Furthermore, for bankruptcy problems we propose an alternative version of the additivity property.

On cardinalities of finite interval-valued hesitant fuzzy sets

Certain extensions of the classical fuzzy sets have been studied in depth since they have a remarkable importance in many practical situations. We focus on finite interval-valued hesitant fuzzy sets, as they generalize the most usual sets (fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets), so the results obtained can be immediately adapted to these types of sets. In addition, their membership functions are much more manageable than type-2 fuzzy sets.In this work, the cardinality of finite interval-valued hesitant fuzzy sets is studied from an axiomatic point of view, together with several properties that this definition satisfies, which enable to relate it to the classical definitions of cardinality given by other authors for fuzzy sets.

Phragmén’s Voting Methods and Justified Representation

In the late 19th century, Lars Edvard Phragmén proposed a load-balancing approach for selecting committees based on approval ballots. We consider three committee voting rules resulting from this approach: two optimization variants one minimizing the maximal load and one minimizing the variance of loads —and a sequential variant. We study Phragmén's methods from an axiomatic point of view, focussing on justified representation and related properties that have recently been introduced by Aziz et al. (2015a) and Sánchez-Fernández et al. (2017). We show that the sequential variant satisfies proportional justified representation, making it the first known polynomial-time computable method with this property. Moreover, we show that the optimization variants satisfy perfect representation. We also analyze the com- putational complexity of Phragmén's methods and provide mixed-integer programming based algorithms for computing them.

An Axiomatic Approach to Routing

Information delivery in a network of agents is a key issue for large, complex systems that need to do so in a predictable, efficient manner. The delivery of information in such multi-agent systems is typically implemented through routing protocols that determine how information flows through the network. Different routing protocols exist each with its own benefits, but it is generally unclear which properties can be successfully combined within a given algorithm. We approach this problem from the axiomatic point of view, i.e., we try to establish what are the properties we would seek to see in such a system, and examine the different properties which uniquely define common routing algorithms used today. We examine several desirable properties, such as robustness, which ensures adding nodes and edges does not change the routing in a radical, unpredictable ways; and properties that depend on the operating environment, such as an "economic model", where nodes choose their paths based on the cost they are charged to pass information to the next node. We proceed to fully characterize minimal spanning tree, shortest path, and weakest link routing algorithms, showing a tight set of axioms for each.

Frame functions in finite-dimensional quantum mechanics and its Hamiltonian formulation on complex projective spaces

This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of so-called frame functions, introduced by Gleason to prove his celebrated theorem. In particular, the problem of associating quantum states with positive Liouville densities is tackled from an axiomatic point of view, proving a theorem classifying all possible correspondences. A similar result is established for classical-like observables (i.e. real scalar functions on the projective space) representing quantum ones. These correspondences turn out to be encoded in a one-parameter class and, in both cases, the classical-like objects representing quantum ones result to be frame functions. The requirements of [Formula: see text] covariance and (convex) linearity play a central role in the proof of those theorems. A new characterization of classical-like observables describing quantum observables is presented, together with a geometric description of the [Formula: see text]-algebra structure of the set of quantum observables in terms of classical-like ones.

Ranking authors using fractional counting of citations: An axiomatic approach

This paper analyzes from an axiomatic point of view a recent proposal for counting citations: the value of a citation given by a paper is inversely proportional to the total number of papers it cites. This way of fractionally counting citations was suggested as a possible way to normalize citation counts between fields of research having different citation cultures. It belongs to the “citing-side” approach to normalization. We focus on the properties characterizing this way of counting citations when it comes to ranking authors. Our analysis is conducted within a formal framework that is more complex but also more realistic than the one usually adopted in most axiomatic analyses of this kind.

Factorization homology of topological manifolds

Factorization homology theories of topological manifolds, after Beilinson, Drinfeld and Lurie, are homology-type theories for topological $n$-manifolds whose coefficient systems are $n$-disk algebras or $n$-disk stacks. In this work we prove a precise formulation of this idea, giving an axiomatic characterization of factorization homology with coefficients in $n$-disk algebras in terms of a generalization of the Eilenberg--Steenrod axioms for singular homology. Each such theory gives rise to a kind of topological quantum field theory, for which observables can be defined on general $n$-manifolds and not only closed $n$-manifolds. For $n$-disk algebra coefficients, these field theories are characterized by the condition that global observables are determined by local observables in a strong sense. Our axiomatic point of view has a number of applications. In particular, we give a concise proof of the nonabelian Poincar\'e duality of Salvatore, Segal, and Lurie. We present some essential classes of calculations of factorization homology, such as for free $n$-disk algebras and enveloping algebras of Lie algebras, several of which have a conceptual meaning in terms of Koszul duality.

Generalized bipolar product and sum

Aggregation functions on \([0,1]\) with annihilator 0 can be seen as a generalized product on \([0,1]\). We study the generalized product on the bipolar scale \([-1,1]\), stressing the axiomatic point of view ( compare also Greco et al. in IPMU 2014, CCIS 444, Springer International Publishing, New York, 2014). Based on newly introduced bipolar properties, such as the bipolar monotonicity, bipolar unit element, bipolar idempotent element, several kinds of generalized bipolar product are introduced and studied. A special stress is put on bipolar semicopulas, bipolar quasi-copulas and bipolar copulas. Inspired by the truncated sum on \([-1,1]\) we introduce also the class of generalized bipolar sums, which differ from uninorms due to the non-associativity.

Characterization of linear symmetric solutions for allocation problems

This paper provides an analysis of solutions for allocation problems from an axiomatic point of view, proposing a decomposition for the space of such problems into direct sum of irreducible subspaces that are relevant to the study of linear symmetric solutions. In particular, we obtain characterizations of certain classes of linear symmetric solutions involving the properties of efficiency and compatibility.