One of the classic combinatorial problems, presented in nearly every introductory text, is enumerating the number of distinct paths on an m x n rectangular lattice from bottom left to top right. (For an example, see Exercise 42 on page 240 of [1].) For this paper, we

Abstract: It is known that the projective tensor product X ˆ⊗πY and the injective tensor product X ˇ⊗εY of Banach lattices X and Y may not be Banach lattices, while the Fremlin projective tensor product X ˆ ⊗ |π|Y and the Wittstock injective tensor product X ˇ ⊗ |ε|Y of Banach lattices X and Y are always Banach lattices. In this talk, we will discuss under what circumstances X ˆ⊗πY and X ˇ⊗εY are Banach lattices, and under what circumstances some geometric properties can be inherited from two Banach spaces X and Y to their tensor products X ˆ⊗πY and X ˇ⊗εY, and from two Banach lattices X and Y to their tensor products X ˆ ⊗ |π|Y and X ˇ ⊗ |ε|Y. Extension of maps on operator spaces and completely rank nonincreasing linear maps

The number of nongonadal nuclei in the free-living soil nematode Caenorhabditis elegans increases from about 550 in the newly hatched larva to about 810 in the mature hermaphrodite and to about 970 in the mature male. The pattern of cell divisions which leads to this increase is essentially

from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature. In some cases the finite horizon optimal control problem solved on-line is exactly

such techniques, however, requires a thermal model that is practical for architectural studies. This paper describes HotSpot, an accurate yet fast model based on an equivalent circuit of thermal resistances and capacitances that correspond to microarchitecture blocks and essential aspects of the thermal package

matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic

Abstract For a large collection of random variables, pairwise conditional independence and mutual conditional independence are shown to be essentially equivalent -i.e., equivalent to up to null sets. Unlike in the finite setting, a large collection of random variables remains essentially

In-network data aggregation is essential for wireless sensor networks where resources (e.g., bandwidth, energy) are limited. In a previously proposed data dissemination scheme, data is opportunistically aggregated at the intermediate nodes on a low-latency tree which may not necessarily be energy

substantial computational or other inefficiencies. Here it is shown that each Markov-equivalence class is uniquely determined by a single chain graph, the essential graph, that is itself simultaneously Markov equivalent to all ADGs in the equivalence class. Essential graphs are characterized, a polynomial

Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure form. The equivalence has mostly been stated informally, but an approximation in the sense of Le Cam