In the ORTHOGONAL VECTORS (OV) problem, we wish to determine if there is an orthogonal pair of vectors among n Boolean vectors in d dimensions. TheOV Conjecture (OVC) posits that OV requires n time to solve, for all d = ω(logn). Assuming the OVC, optimal time lower bounds have been proved for many prominent problems in P, such as Edit Distance, Frechet Distance, Longest Common Subsequence, and ...

The inner ear and cochleovestibular ganglion (CVG) derive from a specialized region of head ectoderm termed the otic placode. During embryogenesis, the otic placode invaginates into the head to form the otic vesicle (OV), the primordium of the inner ear and CVG. Non-autonomous cell signaling from the hindbrain to the OV is required for inner ear morphogenesis and neurogenesis. In this study, we...

Dual canonical bases of the quantum general linear supergroup are constructed which are invariant under the multiplication of the quantum Berezinian. By setting the quantum Berezinian to identity, we obtain dual canonical bases of the quantum special linear supergroup Oq(SLm|n). We apply the canonical bases to study invariant subalgebras of the quantum supergroups under left and right translati...

Caspian kutum fish (Rutilus frisii) wild broodstocks were caught by gillnet during their upstream migration and subjected to short-time confinement stress and their physiological responses have been examined. Thirty fish (average weight of 1217.6 g) were divided into three experimental groups CO (control), OV (ovaprim) and CO+OV (cortisol+ovaprim) and placed into rearing tanks (10 fish tank-1; ...

Let Bn := {b0, b1, . . . , bn} (n = 0, 1, . . . , N ; N ∈ N) be the sets of linearly independent functions. We give a simple method of construction the dual functions Dn := { d (n) 0 , d (n) 1 , . . . , d (n) n } (0 ≤ n ≤ N) satisfying the following conditions: spanDn = spanBn and 〈 bi, d (n) j 〉 = δij (0 ≤ i, j ≤ n ≤ N), where δii = 1, δij = 0 for i 6= j, and 〈·, ·〉 is a given inner product. T...

The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type A. The construction of a basis for the coordinate algebra of the n × n quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a bas...

We review multilevel hierarchies under the special aspect of their potential for abstraction and grouping. Motivated by claims to ’bridge the representational gap between image and model features’ and by the growing importance of topological properties we discuss several extensions to dual graph pyramids: structural simplification should preserve important topological properties and content abs...

To integer programming problems, computational algebraic approaches using Gröbner bases or standard pairs via the discreteness of toric ideals have been studied in recent years. Although these approaches have not given improved time complexity bound compared with existing methods for solving integer programming problems, these give algebraic analysis of their structures. In this paper, we focus...