Best Graph Type to Compare Discrete Groups: Bar, Dot, and Tally

Different graph types might differ in group comparison due to differences in underlying graph schemas. Thus, this study examined whether graph schemas are based on perceptual features (i.e., each graph has a specific schema) or common invariant structures (i.e., graphs share several common schemas), and which graphic type (bar vs. dot vs. tally) is the best to compare discrete groups. Three experiments were conducted using the mixing-costs paradigm. Participants received graphs with quantities for three groups in randomized positions and were given the task of comparing two groups. The results suggested that graph schemas are based on a common invariant structure. Tally charts mixed either with bar graphs or with dot graphs showed mixing costs. Yet, bar and dot graphs showed no mixing costs when paired together. Tally charts were the more efficient format for group comparison compared to bar graphs. Moreover, processing time increased when the position difference of compared groups was increased.

Transcendental Conditions, Schematism, and Naturalizing Kant’s “I think”

Considering how Kant’s synthetic unity of apperception could be “naturalized,” this paper seeks to liberate the Kantian theory of experience from any foundationalist renderings that blur the lines between the empirical and transcendental, without compromising Kant’s attempt to investigate how the invariant structures of experience condition and supply rules for our knowledge of the world. This paper begins with an overview of the Transcendental Deduction’s apperceptive “I think.” We then consider Sellars’ Myth of Jones and Sellars’ notion of noumenal reality as a “limit concept” not in metaphysical but alongside pragmatist lines, where the “in-itself” is schematized as a regulatory ideal that normatively orients science as a self-correcting enterprise. Providing a successor-account to Sellars’ naturalization of Kant’s ‘I think,’ we seek to develop hard-transcendental and soft-transcendental pragmatic conditions to describe protocols for revision and integration, proffering an anti-dogmatic metaphysical stance that, true to Kant, expands our understanding of perception and linguistic licensing to include the kind of sensory and conceptual capacities associated with sapient experience.

Universal bounds on the size of a black hole

For static black holes in Einstein gravity, if matter fields satisfy a few general conditions, we conjecture that three characteristic parameters about the spatial size of black holes, namely the outermost photon sphere area $$A_{\mathrm {ph,out}}$$ A ph , out , the corresponding shadow area $$A_{\mathrm {sh,out}}$$ A sh , out and the horizon area $$A_{{\mathcal {H}}}$$ A H satisfy a series of universal inequalities $$9A_{{\mathcal {H}}}/4\le A_{\mathrm {ph,out}}\le A_{\mathrm {sh,out}}/3\le 36\pi M^2$$ 9 A H / 4 ≤ A ph , out ≤ A sh , out / 3 ≤ 36 π M 2 , where M is the ADM mass. We present a complete proof in the spherically symmetric case and some pieces of evidence to support it in general static cases. We also discuss the properties of the photon spheres in general static spacetimes and show that, similar to horizon, photon spheres are also conformal invariant structures of the spacetimes.

Structuralism and contemporary mass art

The subject of this research is the impact of structuralism as a scientific direction upon mass art. Stable invariant structures discovered by the structuralists in multiple artworks can be observed in mass art. Structuring, which initially was a method of research, turned into one of the practical recommendations on reating new works in mass art. The goal consists in the analysis of susceptibility factors of mass culture to the ideas of structuralism and results of using methodology of structuralism in mass artistic production. The initial methodological focus of this work lied in the concept of juxtaposition of craft and art, which goes back to I. Kant and is applied in modern aesthetics. The author leans on the methods of structuring and comparative structural analysis, as well as the elements of functional analysis. The main conclusion of consists in the statement that susceptibility of mass culture to the ideas of structuralism is substantiated by its economic goals, need to possess reliable and scientifically proven tools that would ensure commercial success of the artworks. However, the patterned application of structuring methods in mass art is capable of creating only craft products, rather than actual art.

Using Lagrangian Descriptors to Uncover Invariant Structures in Chesnavich’s Isokinetic Model with Application to Roaming

Complementary to existing applications of Lagrangian descriptors as an exploratory method, we use Lagrangian descriptors to find invariant manifolds in a system where some invariant structures have already been identified. In this case, we use the parametrization of a periodic orbit to construct a Lagrangian descriptor that will be locally minimized on its invariant manifolds. The procedure is applicable (but not limited) to systems with highly unstable periodic orbits, such as the isokinetic Chesnavich CH[Formula: see text] model subject to a Hamiltonian isokinetic theromostat. Aside from its low computational requirements, the method enables us to study the invariant structures responsible for roaming in the isokinetic Chesnavich CH[Formula: see text] model.