For an Artinian (n− 1)-Auslander algebra Λ with global dimension n(≥ 2), we show that if Λ admits a trivial maximal (n − 1)-orthogonal subcategory of modΛ, then Λ is a Nakayama algebra. Further, for a finite-dimensional algebra Λ over an algebraically closed field K, we show that Λ is a basic and connected (n−1)-Auslander algebra Λ with global dimension n(≥ 2) admitting a trivial maximal (n− 1)...

This paper focuses on the statistical based Probabilistic Neural Network (PNN) for pattern classification problems with Expectation – Maximization (EM) chosen as the training algorithm. This brings about the problem of random initialization, which means, the user has to predefine the number of clusters through trial and error. Global k-means is used to solve this and to provide a deterministic ...

Earth’s climate has alternated between greenhouse (warm) and icehouse (cool) modes throughout the Phanerozoic (Figure 1A). At present, Earth is in the midst of an icehouse climate. Nevertheless, the rise of industrialization in the last two centuries has led to a dramatic increase in atmospheric CO 2 from the burning of fossil fuels, which, in turn, has led to signifi cant global warming (e.g.,...

We consider two-layered perceptions consisting of N binary input units, K binary hidden units and one binary output unit, in the limit N >> K > or = 1. We prove that the weights of a regular irreducible network are uniquely determined by its input-output map up to some obvious global symmetries. A network is regular if its K weight vectors from the input layer to the K hidden units are linearly...

Distributed constraint optimization (DCOP) is a promising approach to coordination, scheduling and task allocation in multi agent networks. In large-scale or low-bandwidth networks, finding the global optimum is often impractical. K-optimality is a promising new approach: for the first time it provides us a set of locally optimal algorithms with quality guarantees as a fraction of global optimu...

A finite-dimensional global attractor A can be embedded, using some linear map L, into a Euclidean space R k of sufficiently high dimension. The Holder exponent ̈ y1 Ž . of L depends upon k and upon t A , the ‘‘thickness exponent’’ of A. We show that global attractors which are uniformly bounded in the Sobolev spaces H s for Ž . all s ) 0 have t A s 0. It follows, using a result of B. R. Hunt an...

The global rise of multidrug-resistant gram-negative bacteria represents an increasing threat to patient safety. From the first observation of a carbapenem-resistant gram-negative bacteria a global spread of extended-spectrum beta-lactamases and carbapenemases producing Klebsiella pneumoniae has been observed. Treatment options for multidrug-resistant K. pneumoniae are actually limited to combi...

Kernel k-means is an extension of the standard k -means clustering algorithm that identifies nonlinearly separable clusters. In order to overcome the cluster initialization problem associated with this method, we propose the global kernel k-means algorithm, a deterministic and incremental approach to kernel-based clustering. Our method adds one cluster at each stage, through a global search pro...

In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-1 update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence guarantees are established for third order tensors of rank k in d dimensions, wh...

The optimal gapped local alignment score of two random sequences follows a Gumbel distribution. The Gumbel distribution has two parameters, the scale parameter lambda and the pre-factor k. Presently, the basic local alignment search tool (BLAST) programs (BLASTP (BLAST for proteins), PSI-BLAST, etc.) use all time-consuming computer simulations to determine the Gumbel parameters. Because the sim...