We consider pairs of maps from a discrete group Γ to the unitary group. The deficiencies of these maps from being homomorphisms may be great, but if they are close to each other then we call such pairs balanced. We show that balanced pairs determine elements in the K group of the classifying space of the group. We also show that a Fredholm representation of Γ determines balanced pairs.

There exists a balanced ternary design with block size 3 and index 2 on 2v P2 + 4 and 2v P2 + 1 elements with a hole of size v, for all positive integers v and P2, such that v ~ 2P2 + 1. As an application of this result, we determine the numbers of common triples in two simple balanced ternary designs with block size 3 and index 2, for P2 = 3 and 4.

State-of-the-art classification algorithms suffer when the data is skewed towards one class. This led to the development of a number of techniques to cope with unbalanced data. However, as confirmed by our experimental comparison, no technique appears to work consistently better in all conditions. We propose to use a racing method to select adaptively the most appropriate strategy for a given u...

We study balancedness properties of words given by the Arnoux-Rauzy and Brun multi-dimensional continued fraction algorithms. We show that almost all Brun words on 3 letters and Arnoux-Rauzy words over arbitrary alphabets are finitely balanced; in particular, boundedness of the strong partial quotients implies balancedness. On the other hand, we provide examples of unbalanced Brun words on 3 le...

The purpose of this paper is to evaluate the efficiency of the East German economy at the firm level using an unbalanced panel over the transition period 1994 to 1998. We adopt a translog stochastic frontier model to estimate technical efficiency in eastern and western Germany. The results indicate that firms in eastern Germany are significantly less efficient than firms in western Germany. The...

Recall that some of the unknown parameters in our brand sales model are specified as categoryand brand-specific while others are not (see Equation 6 in the paper). To estimate this model we have data available for 2,831 brands over a period of 21 quarters starting in quarter 4/2000 until quarter 4/2005. Since the brand sales model includes lagged sales the first quarter is inherently lost. In a...

A conjecture of Batyrev and Manin relates arithmetic properties of varieties with ample anticanonical class to geometric invariants. We analyze the geometry underlying these invariants using the Minimal Model Program and then apply our results to primitive Fano threefolds.

A balanced ternary design of order v with block size three, index 2 and P2 = 1 is a collection of multi-subsets of size 3 (of type { x, y, z} or {x, x, y }) called blocks, in which each unordered pair of distinct elements occurs twice possibly in one block and in which each element is repeated in just one block. So there are precisely v blocks of type {x, x, y}. Necessarily v == 0 (mod 3). We d...

Since there is no model available for mixed differential-mode and common-mode transmission, this report gives a measurement setup to determine the channel transfert function of the differential-mode and common-mode channels, as well as the leaked channel from the differential-mode to the common-mode and conversely at the transmitting end and the receiving end. This measurement setup consists of...

Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids.