Virtue, habit and neuroscience

Neuroscience has much to offer to our understanding of human action, including its ethical dimensions. However, while neuroscience has been applied to questions of personal identity, emotion and moral decision-making, its implications for the classical notion of virtue have hardly been considered. This likely has much to do with the way in which the classical notion of virtue, together with closely related concepts of nature and habit, has been forgotten or distorted within the context of modern thought. As a consequence, the standard neuroscientific concept of habit as automatic and routine behavior is fundamentally opposed to teleological activity and thus cannot be reconciled with the classical concept of habit that is essential to virtue. The recovery of the classical notion of virtue in contemporary philosophy invites us to rethink the neuroscientific concept of habit in light of a different view of human behavior for which plasticity is not just indeterminacy but rather openness to freedom and growth.

The geometric index and attractors of homeomorphisms of

In this paper we focus on compacta $K \subseteq \mathbb {R}^3$ which possess a neighbourhood basis that consists of nested solid tori $T_i$ . We call these sets toroidal. Making use of the classical notion of the geometric index of a curve inside a torus, we introduce the self-geometric index of a toroidal set K, which roughly captures how each torus $T_{i+1}$ winds inside the previous $T_i$ as $i \rightarrow +\infty $ . We then use this index to obtain some results about the realizability of toroidal sets as attractors for homeomorphisms of $\mathbb {R}^3$ .

Path combinatorics and light leaves for quiver Hecke algebras

We recast the classical notion of “standard tableaux" in an alcove-geometric setting and extend these classical ideas to all “reduced paths" in our geometry. This broader path-perspective is essential for implementing the higher categorical ideas of Elias–Williamson in the setting of quiver Hecke algebras. Our first main result is the construction of light leaves bases of quiver Hecke algebras. These bases are richer and encode more structural information than their classical counterparts, even in the case of the symmetric groups. Our second main result provides path-theoretic generators for the “Bott–Samelson truncation" of the quiver Hecke algebra.

Hybrid manuscripts

Manuscripts are usually seen as collections of material artefacts that are the by-products of authoring. Manuscripts are central in studies on authors and are used to disambiguate and reconstruct significant literary works. Digital scholarly editions are, for instance, hypertext systems that enable the collaborative, distributed study of digitised material manuscripts. However, digital and web authoring challenge the classical notion of manuscript as they generate traces that are different in form and nature (e.g. logs) while enabling a variety of collaborative practices. We address the epistemic differences between material and digital artefacts, highlighting what aspects of authoring they reflect and providing a digital-aware reframing of the manuscript.

Some inequalities for exponentially convex functions on time scales

In this paper, we introduce the notion of exponentially convex functions on time scales and then we establish Hermite-Hadamard type inequalities for this class of functions. As special case, we derive this double inequality in the context of classical notion of exponentially convex functions and convex functions. Moreover, we prove some new integral inequalities for n-times continuously differentiable functions with exponentially convex first Δ-derivative.

Analytical Sociology and Symbolic Interactionism: Bridging the Intra-disciplinary Divide

The aim of the present article is to contribute to the development of the Desire-Belief-Opportunity-model from a symbolic interactionist perspective. The main argument is that this model needs to incorporate the classical notion of definition of the situation to be able to account for the formative impact of interaction on the formation of actor’s beliefs, as well as the complex interdependency between two of its key components, namely the beliefs and the action opportunities of the actor. It is argued that the theoretical advancement of the DBO-model in this particular direction is not only feasible but also brings it considerably closer to the analytical refinement and the empirical validation it currently lacks.

Asymptotic expansion in measure and strong ergodicity

In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalizes expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain structure theorems for asymptotically expanding actions, showing that they admit exhaustions by domains of expansion. As an application, we recover a recent result of Marrakchi, characterizing strong ergodicity in terms of local spectral gaps. We also show that homogeneous strongly ergodic actions are always expanding in measure and establish a connection between asymptotic expansion in measure and asymptotic expanders by means of approximating spaces.

Optimal Identifying Codes in Oriented Paths and Circuits

Identifying codes in graphs are related to the classical notion of dominating sets [1]. Since there first introduction in 1998 [2], they have been widely studied and extended to several application, such as: detection of faulty processor in multiprocessor systems, locating danger or threats in sensor networks. Let G=(V,E) an unoriented connected graph. The minimum identifying code in graphs is the smallest subset of vertices C, such that every vertex in V have a unique set of neighbors in C. In our work, we focus on finding minimum cardinality of an identifying code in oriented paths and circuits

Systemic optimal risk transfer equilibrium

We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the Bühlmann’s classical notion of an Equilibrium Risk Exchange. We provide sufficient general assumptions that guarantee existence, uniqueness, and Pareto optimality of such a SORTE. In both the Bühlmann and the SORTE definition, each agent is behaving rationally by maximizing his/her expected utility given a budget constraint. The two approaches differ by the budget constraints. In Bühlmann’s definition the vector that assigns the budget constraint is given a priori. On the contrary, in the SORTE approach, the vector that assigns the budget constraint is endogenously determined by solving a systemic utility maximization. SORTE gives priority to the systemic aspects of the problem, in order to optimize the overall systemic performance, rather than to individual rationality.

Radiative Transfer and Generalized Wind

Dissimilar flows can be compared by exploiting the fact that all flux densities divided by their conjugate volume densities form velocity fields, which have been described as generalized winds. These winds are an extension of the classical notion of wind in fluids which puts these distinct processes on a common footing, leading to thermodynamical implications. This paper extends this notion from fluids to radiative transfer in the context of a classical two-stream atmosphere, leading to such velocities for radiative energy and entropy. These are shown in this paper to exhibit properties for radiation previously only thought of in terms of fluids, such as the matching of velocity fields where entropy production stops.