Tropical cycles and Chow polytopes

The Chow polytope of an algebraic cycle in a torus depends only on its tropicalisation. Generalising this, we associate a Chow polytope to any abstract tropical variety in a tropicalised toric variety. Several significant polyhedra associated to tropical varieties are special cases of our Chow polytope. The Chow polytope of a tropical variety $X$ is given by a simple combinatorial construction: its normal subdivision is the Minkowski sum of $X$ and a reflected skeleton of the fan of the ambient toric variety.Comment: 22 pp, 3 figs. Added discussion of arbitrary ambient toric varieties; several improvements suggested by Eric Katz; some rearrangemen

The Function of Normative Process‐Requirements

This paper discusses whether rationality, morality or prudence impose process‐requirements upon us. It has been argued that process‐requirements fulfil two essential functions within a system of rational, moral or prudential requirements. These functions are considered to prove the existence of process‐requirements. First, process‐requirements are deemed necessary to ensure that rationality, morality or prudence can guide our deliberations and actions. Second, their existence is regarded as essential for the correctness of our ordinary explanations of why a person possesses a certain degree of morality, rationality or prudence. However, I argue that these two functions are unable to show the existence of process‐requirements. Instead, I propose a different essential function for process‐requirements: they are necessary for attributing the correct degree of rationality, morality or prudence to a subject who is not entirely rational, moral or prudent. This function, I argue, necessitates the existence of process‐requirements

Conjugacy Growth and Conjugacy Width of Certain Branch Groups

The conjugacy growth function counts the number of distinct conjugacy classes in a ball of radius $n$. We give a lower bound for the conjugacy growth of certain branch groups, among them the Grigorchuk group. This bound is a function of intermediate growth. We further proof that certain branch groups have the property that every element can be expressed as a product of uniformly boundedly many conjugates of the generators. We call this property bounded conjugacy width. We also show how bounded conjugacy width relates to other algebraic properties of groups and apply these results to study the palindromic width of some branch groups.Comment: Final version, to appear in IJA

Combinatorial Sutured TQFT as Exterior Algebra

The idea of a sutured topological quantum field theory was introduced by Honda, Kazez and Mati\'c (2008). A sutured TQFT associates a group to each sutured surface and an element of this group to each dividing set on this surface. The notion was originally introduced to talk about contact invariants in Sutured Floer Homology. We provide an elementary example of a sutured TQFT, which comes from taking exterior algebras of certain singular homology groups. We show that this sutured TQFT coincides with that of Honda et al. using $\Z_2$-coefficients. The groups in our theory, being exterior algebras, naturally come with the structure of a ring with unit. We give an application of this ring structure to understanding tight contact structures on solid tori

Freedom of science

Purpose – The purpose of this paper is to highlight the importance of "freedom of science"("academic freedom")for the advancement of society and mankind, which, however, is permanently endangered by powerful organisations, groups and individuals, who in pursuit of their one-sided interests are seeking to constrain information about the truth. As a broad term, freedom of science embraces freedom in research, learning, teachingand publication. All of these activities should be dedicated to identifying the truth and learning about the truth. Design/methodology/approach – Three theoretical approaches are of importance for framing issues related to freedom of science, which in this paper are integrated into the framework of mindset agency theory: freedom is a value; "freedom" is claimed by agents who pursue specific interests (goals), which might constrain others; and individuals are agents who are interacting with each other within a social system–cooperation, ignorance or conflict. Findings – Freedom as a value is at the core of intellectual autonomy. Intellectual autonomy is a necessarycondition for innovation and advancement of knowledge. The observable modes of interaction/coexistenceamong researchers are influenced by individual research goals and by the researchers' access to resources, which may be deliberately constrained by opponents or other researchers as competitors. Research limitations/implications – For further research, which is beyond this paper, the authors can refer to: analyses of challenges of "academic freedom" – in terms of ethics, protection of individual humanrights, political pressures and conflicts of interests; the issues of truth, i.e. the impact of fake news andcreation of "alternate facts"; and the relation between academic freedom and employment (academic tenure) inpresent-day societies. Owing to lack of space, this paper cannot deal with the danger emerging from powerful organisations or powerful individuals, who are challenging freedom of science. Social implications–If there is no freedom of science then social progress is constrained. If there is no access to right data, decisions will be wrong. Originality/value – So far, a comprehensive cybernetic model was not published, which supports systems thinking about scholars and teachers (inter)acting in research organisations

Dostoevsky, Raskolnikov, and Freedom in Crime and Punishment

An analysis of the character of Raskolnikov in Dostoevsky\u27s Crime and Punishment and his journey towards a truer understanding of freedom. This paper comments on \u27freedom\u27 as understood by St. Thomas Aquinas and Aristotle, and applies this view of freedom to the characters of Raskolnikov, Sonya, Svidrigailov and Porfiry. The paper shows how the Thomistic-Aristotelian view of freedom is prevalent in this work by Dostoevsky

Consciousness as Presence: An Exploration of the Illusion of Self

Buddhism teaches that ‘self’ as a substantial, enduring entity is an illusion. But for self to be an illusion there must be something in our experience that is misinterpreted as self. What is this? The notion of an experiential self plays an important role in phenomenological investigations of conscious experience. Does the illusion of self consist in mistaking a purely experiential self for a substantial self? I argue against this and locate the source of the illusion in time-consciousness. It is the essence of consciousness to flow, but the flow of consciousness presupposes an experiential present. The experiential present — an abiding sense of ‘now’ — is the dimension through which experiences are experienced as streaming. It is this, I argue, that is misinterpreted as an enduring self. I support my account by arguing that the synchronic and diachronic unity of consciousness can be accounted for in terms of impersonal, temporal experience, and that conceiving of consciousness as the presence-dimension rather than as the I-dimension affords a solution to the brain-bisection puzzle