Vision tasks with constrained camera motion have been discussed for a long time since Active Vision appeared. As an example, Camera under planar motion can often simplify the works, like camera self-calibration, scene reconstruction and robot self-location. In this paper, we provide detail information on the algebraic characteristic and geometric interpretation of planar motion. It does help to...

The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decision diagram (ADD) or variants thereof provides canonical forms to represent and manipulate Boolean functions and pseudo-Boolean functions efficiently. ADD and OBDD-based symbolic a...

We introduce new moduli of smoothness for functions f ∈ Lp[−1, 1]∩Cr−1(−1, 1), 1 ≤ p ≤ ∞, r ≥ 1, that have an (r − 1)st locally absolutely continuous derivative in (−1, 1), and such that φrf (r) is in Lp[−1, 1], where φ(x) = (1 − x2)1/2. These moduli are equivalent to certain weighted DT moduli, but our definition is more transparent and simpler. In addition, instead of applying these weighted ...

We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algebraic numbers. One motivation is to explain the method’s good performance in practice. We improve the previously known bound by a factor of dτ , where d is the polynomial degree and τ bounds the coefficient bitsize, thu...

In a previous work (“Abstract Data Type Systems”, TCS 173(2), 1997), the last two authors presented a combined language made of a (strongly normalizing) algebraic rewrite system and a typed λ-calculus enriched by pattern-matching definitions following a certain format, called the “General Schema”, which generalizes the usual recursor definitions for natural numbers and similar “basic inductive ...

Given polynomials f1, . . . , fk, g1, . . . , gs inQ[X1, . . . , Xn], we consider the semi-algebraic set S defined by: f1 = . . . = fk = 0 g1 ≥ 0, . . . , gs ≥ 0 and focus on the problem of computing at least one point in each connected component of S. We first study how to solve this problem by considering S as the union of solutions sets of polynomial systems of equations and strict inequalit...

Gian-Carlo Rota was one of the most original and colorful mathematicians of the twentieth century. His work on the foundations of combinatorics focused on revealing the algebraic structures that lie behind diverse combinatorial areas and created a new area of algebraic combinatorics. His graduate courses influenced generations of students. Written by two of his former students, this book is bas...

In this paper we consider the structural analysis problem for differential-algebraic systems with conditional equations. This problem consists, given a conditional differential-algebraic system, in verifying if the system is structurally nonsingular for every state, and if not in finding a state in which the system is structurally singular. We give a formulation for this problem as an integer l...

We study variants of classical stable matching problems in which there is an additional requirement for a stable matching, namely that there should not be two participants who would prefer to exchange partners. The problem is motivated by the experience of real-world medical matching schemes that use stable matchings, where cases have arisen in which two participants discovered that each of the...

In the literature, the matchings between spacetimes have been most of the times implicitly assumed to preserve some of the symmetries of the problem involved. But no definition for this kind of matching was given until recently. Loosely speaking, the matching hypersurface is restricted to be tangent to the orbits of a desired local group of symmetries admitted at both sides of the matching and ...