Given any collection of data cells in a data space X, consider the problem of finding the optimal partition of the data cells into blocks which are unions of cells. The algorithms we describe can be used to find the optimal partition of a set of data cells in any dimension. These algorithms work for any objective function that is strictly convex and additive on the blocks of a partition. We des...

Definition of the partition function of U(1) gauge theory is extended to a class of fourmanifolds containing all compact spaces and the asymptotically locally flat (ALF) ones including the multi-Taub–NUT sopaces. The partition function is calculated via zetafunction regularization and heat kernel techniques with special attention to its modular properties. In the compact case, compared with the...

We study how the number c(X) of components of a graph X can be expressed through the number and properties of the components of a quotient graph X/∼ . We partially rely on classic qualifications of graph homomorphisms such as locally constrained homomorphisms and on the concept of equitable partition and orbit partition. We introduce the new definitions of pseudo-covering homomorphism and of co...

This paper is primarily an overview of data link design efforts in IBM pertinent to local area networks (LANs) using both multimode fiber (MMF) and single-mode (SMF) links, with emphasis on MMF links operating at short wavelengths. Device models (laser and receiver) and multimode fiber models are discussed, as well as noise aspects (modal and mode partition noise). In addition, new simulation a...

The combination of Further Division of Partition Space (FDPS) and Flexible Neural Tree (FNT) is proposed to improve the neural network classification performance. FDPS, which divide partition space into many partitions that will attach to different classes automatically, is a novel technique for neural network classification. FNT is a neural network’s structure which uses flexible tree model. T...

Multi-label classification is a generalization of binary classification where the task consists in predicting sets of labels. With the availability of ever larger datasets, the multi-label setting has become a natural one in many applications, and the interest in solving multi-label problems has grown significantly. As expected, deep learning approaches are now yielding state-of-the-art perform...

We demonstrate a two phase classification method, first of individual pixels, then of fixed regions of pixels for scene classification—the task of assigning posteriors that characterize an entire image. This can be realized with a probabilistic graphical model (PGM), without the characteristic segmentation and aggregation tasks characteristic of visual object recognition. Instead the spatial as...

The spectra of states containing charmed and beauty quarks, and their regularities, are reviewed.

We show that the shifted rank, or srank, of any partition λ with distinct parts equals the lowest degree of the terms appearing in the expansion of Schur’s Qλ function in terms of power sum symmetric functions. This gives an affirmative answer to a conjecture of Clifford. As pointed out by Clifford, the notion of the srank can be naturally extended to a skew partition λ/μ as the minimum number ...

This paper surveys the recent literature on the endogenous formation of economic coalitions, in particular, the partition function literature that allows for externalities across coalitions. Various economic coalitions are classified either as coalitions with positive externalities (output cartels, R&D coalitions with spillovers, public-goods (environmental) coalitions, free-trade areas) or as ...