Computing the Exact Number of Similarity Classes in the Longest Edge Bisection of Tetrahedra

Showing whether the longest-edge (LE) bisection of tetrahedra meshes degenerates the stability condition or not is still an open problem. Some reasons, in part, are due to the cost for achieving the computation of similarity classes of millions of tetrahedra. We prove the existence of tetrahedra where the LE bisection introduces, at most, 37 similarity classes. This family of new tetrahedra was roughly pointed out by Adler in 1983. However, as far as we know, there has been no evidence confirming its existence. We also introduce a new data structure and algorithm for computing the number of similarity tetrahedral classes based on integer arithmetic, storing only the square of edges. The algorithm lets us perform compact and efficient high-level similarity class computations with a cost that is only dependent on the number of similarity classes.

RepeatsDB in 2021: improved data and extended classification for protein tandem repeat structures

The RepeatsDB database (URL: https://repeatsdb.org/) provides annotations and classification for protein tandem repeat structures from the Protein Data Bank (PDB). Protein tandem repeats are ubiquitous in all branches of the tree of life. The accumulation of solved repeat structures provides new possibilities for classification and detection, but also increasing the need for annotation. Here we present RepeatsDB 3.0, which addresses these challenges and presents an extended classification scheme. The major conceptual change compared to the previous version is the hierarchical classification combining top levels based solely on structural similarity (Class > Topology > Fold) with two new levels (Clan > Family) requiring sequence similarity and describing repeat motifs in collaboration with Pfam. Data growth has been addressed with improved mechanisms for browsing the classification hierarchy. A new UniProt-centric view unifies the increasingly frequent annotation of structures from identical or similar sequences. This update of RepeatsDB aligns with our commitment to develop a resource that extracts, organizes and distributes specialized information on tandem repeat protein structures.

Identification information sensors of robot systems

<span lang="IN">At the present time, the complexity of identification is to find such a description, in which the image (information) of each class would have identified similar properties. The task is to make the transformed description includes the whole set of input images, united by the similarity class by the given ratio.</span><span lang="IN">Using the ordinates of an autocorrelation function is an inseparable shift in the center of gravity of an image, which leads to a change of such description.</span><span lang="IN">Nicest, the concept of an invariant description of information arises, this is an autocorrelation function, which is invariant to the description of any displacements of the image in the vertical and horizontal directions.</span><span lang="IN">The problem of finding an optimal decision rule arises, which, in a number of cases, can be constructed on the basis of a method, based on the definition of the maximum incomplete coefficient of similarity.</span><span lang="IN">Using this method, the solutions, that are almost unintelligible to the errors that arise due to the effects of interference, are found. Therefore, in increments</span><span lang="EN-US"> k</span><span lang="IN">, this rule passes into the Bayes’ rule.</span>

Rough Set Extension under Incomplete Information System with “?” Values

Classical rough set theory (RST) can't process incomplete information system (IIS) because it is based on an indiscernibility relation which is a kind of equivalent relation. In the literature a non-symmetric similarity relation based rough set model (NS-RSM) has been introduced as an extended model under IIS with ``?" values directly. Unfortunately, in this model objects in the same similarity class are not necessarily similar to each other and may belong to different target classes. In this paper, a new inequivalent relation called Maximal Limited Consistent block relation (MLC) is proposed. The proposed MLC relation improves the lower approximation accuracy by finding the maximal limited blocks of indiscernible objects in IIS with ``?" values. Maximal Limited Similarity rough set model (MLS) is introduced as an integration between our proposed relation (MLC) and NS-RSM. The resulted MLS model works efficiently under IIS with ``?" values. Finally, an illustrative example is given to validate MLS model. Furthermore, approximation accuracy comparisons have been conducted among NS-RSM and MLS. The results of this work demonstrate that the MLS model outperform NS-RSM.

Social Categories are Natural Kinds, not Objective Types (and Why it Matters Politically)

There is growing support for the view that social categories like men and women refer to “objective types.” An objective type is a similarity class for which the axis of similarity is an objective rather than nominal or fictional property. Such types are independently real and causally relevant, yet their unity does not derive from an essential property. Given this tandem of features, it is not surprising why empirically-minded researchers interested in fighting oppression and marginalization have found this ontological category so attractive: objective types have the ontological credentials to secure the reality (and thus political representation) of social categories, and yet they do not impose exclusionary essences that also naturalize and legitimize social inequalities. This essay argues that, from the perspective of these political goals of fighting oppression and marginalization, the category of objective types is in fact a Trojan horse; it looks like a gift, but it ends up creating trouble. I argue that objective type classifications often lack empirical adequacy, and as a result they lack political adequacy. I also provide, and in reference to the normative goals described above, several arguments for preferring a social ontology of natural kinds with historical essences.

Tropes

Trope theory is the view that the world is (wholly or partly) constituted by so-called tropes, which are entities most often characterized as a kind of abstract particular or particular property. Very little is uncontroversial when it comes to tropes and the theory or theories in which tropes (not always so-called) figure. What attracts many to the theory is that it, in occupying a sort of middle position in between classical nominalism (according to which all there is, is particular) and classical realism (according to which there is a separate and fundamental category of properties), appears to avoid some of the troubles befalling either of those views. More precisely, by accepting the existence of entities that are, or that at least behave like, properties, the trope theorist avoids the charge, often made against classical nominalists, of positing entities that are somehow too unstructured to be able to fulfill all of our explanatory needs. And by not accepting the existence of universals, the trope theorist avoids having to accept the existence of a kind of entity many find mysterious, counterintuitive, and “unscientific.” Apart from this very thin core assumption—that there are tropes—different trope theories need not have very much in common. Most trope theorists (but not all) believe that there is nothing but tropes. Most of these one-category trope theorists (but, again, not all) hold that distinct concrete particulars (which are understood by most, but again not all, as bundles of tropes) are the same—for example, have the same color—when (some of) the tropes that characterize them are members of the same (exact) similarity class. And most (but not all) hold that resemblance between tropes is determined by the tropes’ individual, intrinsic nature, which is taken as a primitive.