Bi-intuitionistic logic (BINT) is a conservative extension of intuitionistic logic to include the duals of each logical connective. One leading question with respect to BINT is, what does BINT look like across the three arcs – logic, typed λ-calculi, and category theory – of the Curry-HowardLambek correspondence? Categorically, BINT can be seen as a mixing of two worlds: the first being intuiti...

To improve the class separability of Fisher linear discriminant analysis (FDA) for large category problems, we investigate the weighted Fisher criterion (WFC) by integrating weighting functions for dimensionality reduction. The objective of WFC is to maximize the sum of weighted distances of all class pairs. By setting larger weights for the most confusable classes, WFC can improve the class se...

• For square contingency tables with ordered categories, this paper proposes some distance subsymmetry models. The one model indicates that the cumulative probability that an observation will fall in row category i or below and column category i + k (k ≥ 2) or above, is equal to the probability that it falls in column category i or below and row category i+k or above. This paper also gives the ...

We introduce an explicit diagrammatic syntax for PROs and PROPs, which are used in the theory of operads. By means of diagram rewriting, we obtain presentations of PROs by generators and relations, and in some cases, we even get convergent rewrite systems. This diagrammatic syntax is useful for practical computations, but also for theoretical results. Moreover, rewriting is strongly related to ...

The theory of  continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory.  The $K$-frames were  introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of  $K$-frames, there are many differences between...

We propose a definition of the Chow group of a rigid tensor triangulated category. The basic idea is to allow “generalized” cycles, with nonintegral coefficients. The precise choice of relations is open to some fine-tuning. Hypothesis 1. Let K be an essentially small tensor triangulated category. Let us assume that its triangular spectrum in the sense of [1], Spc(K) = { P ⊂ K ∣∣P is prime}, is ...

A predictive pricing method based on k-means++ clustering and multiple linear regression is proposed to solve the unreasonable initial of used cars evaluate model's low accuracy. To begin, all vehicles are divided into three categories transaction period data sample. The K-Means++ algorithm then cluster best-selling cars, a equation fitted for each category as prediction evaluation. Finally, re...

We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Köthe sequence spaces. In this setting, the “of course” connective of linear logic has a quite simple structure of commutative Hopf algebra. The co-Kleisli category of this linear category is a cartesian closed category of entire mappings. ...

For a Hopf algebra H over a commutative ring k, the category MH of right Hopf modules is equivalent to the category Mk of k-modules, that is, the comparison functor −⊗k H : Mk → MH is an equivalence (Fundamental theorem of Hopf modules). This was proved by Larson and Sweedler via the notion of coinvariants McoH for any M ∈ MH . The coinvariants functor (−) coH : MH → Mk is right adjoint to the ...

Introduction The development of the formal theory of monads, begun in [23] and continued in [15], shows that much of the theory of monads [1] can be generalized from the setting of the 2-category Cat of small categories, functors and natural transformations to that of a general 2-category. The generalization, which involves defining the 2-category Mnd(K) of monads, monad maps and monad 2-cells ...