The benefit of exploiting label dependence in multi-label classification is known to be closely dependent on the type of loss to be minimized. In this paper, we show that the subsets of labels that appear as irreducible factors in the factorization of the conditional distribution of the label set given the input features play a pivotal role for multi-label classification in the context of 0/1 l...

We introduce a $C^*$-algebra $\mathscr{A}_V$ of variety $V$ over the number field $K$ and $\mathscr{A}_G$ reductive group $G$ ring adeles $K$. Using Pimsner's Theorem we construct an embedding $\mathscr{A}_V\hookrightarrow \mathscr{A}_G$, where is $G$-coherent variety, e.g. Shimura $G$. The analog Langlands reciprocity for $C^*$-algebras. It follows from $K$-theory inclusion $\mathscr{A}_V\subs...

We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty. We are concerned with the following question: Which algebras are homomorphic images of subdirectly irreducible algebras? A necessary condition, discovered...

‎‎here we construct and count all ordinary irreducible characters of sylow $p$-subgroups of the steinberg triality groups ${}^3d_4(p^{3m})$.

For a given transitive binary relation e on a set E, the transitive closures of open (i.e., co-transitive in e) sets, called the regular closed subsets, form an ortholattice Reg(e), the extended permutohedron on e. This construction, which contains the poset Clop(e) of all clopen sets, is a common generalization of known notions such as the generalized permutohedron on a partially ordered set o...

suppose $g$ is a finite group, $a$ and $b$ are conjugacy classes of $g$ and $eta(ab)$ denotes the number of conjugacy classes contained in $ab$. the set of all $eta(ab)$ such that $a, b$ run over conjugacy classes of $g$ is denoted by $eta(g)$.the aim of this paper is to compute $eta(g)$, $g in { d_{2n}, t_{4n}, u_{6n}, v_{8n}, sd_{8n}}$ or $g$ is a decomposable group of order $2pq$, a group of...

In Domain Theory quasicontinuous domains pop up from time to time generalizing slightly the powerful notion of a continuous domain. It is the aim of this paper to show that quasicontinuous domains occur in a natural way in relation to the powerdomains of finitely generated and compact saturated subsets. Properties of quasicontinuous domains seem to be best understood from that point of view. Th...

Consider a graph with vertex set S. A word in the alphabet S has the intervening neighbours property if any two occurrences of the same letter are separated by all its graph neighbours. For a Coxeter graph, words represent group elements. Speyer recently proved that words with the intervening neighbours property are irreducible if the group is infinite and irreducible. We present a new and shor...

If there exists a nonempty, proper subset S of the set of all (n + 1)(n + 2)/2 inertias such that S ⊆ i(A) is sufficient for any n × n zero-nonzero pattern A to be inertially arbitrary, then S is called a critical set of inertias for zero-nonzero patterns of order n. If no proper subset of S is a critical set, then S is called a minimal critical set of inertias. In [3], Kim, Olesky and Driessch...

Let $S \subset \mathbb P^3$ be a very general sextic surface over complex numbers. $\mathcal{M}(H, c_2)$ the moduli space of rank $2$ stable bundles on $S$ with fixed first Chern class $H$ and second $c_2$. In this article we study configuration points certain reduced zero dimensional subschemes satisfying Cayley-Bacharach property, which leads to existence non-trivial sections memeber for smal...