We characterise Mod classes in terms of #P functions, where the membership is determined by co-primality or gcd testing of the function value (Theorem 3.1), instead of residue (mod k) testing. Imposing a restriction on the range of the functions gives a characterisation of the intersection of Mod classes (Theorem 3.2). These intersection classes, which we denote by Mod ∩k P , are interesting be...

Let [x] be the integral part of x. Let p > 5 be a prime. In the paper we mainly determine P[p/4] x=1 1 xk (mod p2), p−1 [p/4] (mod p3), Pp−1 k=1 2 k (mod p3) and Pp−1 k=1 2 k2 (mod p2) in terms of Euler and Bernoulli numbers. For example, we have

In this paper we present a system for the reconstruction of 3 D mod els of architectural scenes from single or multiple uncalibrated images. T he partial 3 D mod el of a build ing is recovered from a single image using geometric constraints such as parallelism and orthogonality, which are likely to be found in most architectural scenes. T he approximate corner positions of a build ing are selec...

We present a data structure | the Mod{2{OBDD's that considerably extend OBDD's (ordered binary decision diagrams) as well as ESOP's (EXOR{sum{of{ products). Many Boolean function of practical interest like hidden weighted bit function, indirect storage access function, important symmetric functions have exponential size optimal OBDD's and/or ESOP's (even multilevel EXOR{expressions) but (low de...

Modular gates are known to be immune for the random restriction techniques of Ajtai Ajt83], Furst, Saxe, Sipser FSS84], Yao Yao85] and H astad H as86]. We demonstrate here a random clustering technique which overcomes this diiculty and is capable to prove generalizations of several known modular circuit lower bounds of Barrington, Straubing, Th erien BST90], Krause and Pudll ak KP94], and other...

Consider a (MODq;MODp) circuit, where the inputs of the bottom MODp gates are degree-d polynomials with integer coefficients of the input variables (p, q are different primes). Using our main tool — the Degree Decreasing Lemma — we show that this circuit can be converted to a (MODq;MODp) circuit with linear polynomials on the input-level with the price of increasing the size of the circuit. Thi...

For the computer-aided diagnosis of tumor diseases knowledge about the position, size and type of the lymph nodes is needed to compute the tumor classification (TNM). For the computer-aided planning of subsequent surgeries like the Neck Dissection spatial information about the lymph nodes is also important. Thus, an efficient and exact segmentation method for lymph nodes in CT data is necessary...

Serious video games have been proposed as a means to engage students with the Science, Technology, Engineering, Mathematics (STEM) curriculum, but there is limited research on the required game elements and teaching practices. In particular, there is limited evidence on the effects of the storytelling element and of student involvement in making games on the learning performance and on the atti...

We discuss protein post-translational modification (PTM) from an information processing perspective. PTM at multiple sites on a protein creates a combinatorial explosion in the number of potential 'mod-forms', or global patterns of modification. Distinct mod-forms can elicit distinct downstream responses, so that the overall response depends partly on the effectiveness of a particular mod-form ...

Adding modular predicates yields a generalization of first-order logic FO over words. The expressive power of FO[<,MOD] with order comparison x < y and predicates for x ≡ i mod n has been investigated by Barrington, Compton, Straubing and Thérien. The study of FO[<,MOD]fragments was initiated by Chaubard, Pin and Straubing. More recently, Dartois and Paperman showed that definability in the two...