Under Martin’s axiom, collapsing of the continuum by Sacks forcing S is characterized by the additivity of Marczewski’s ideal (see [4]). We show that the same characterization holds true if d = c proving that under this hypothesis there are no small uncountable maximal antichains in S. We also construct a partition of 2 into c perfect sets which is a maximal antichain in S and show that s-sets ...

High-speed observations (for example, Lauterborn and Bolle 1975, Tomita and Shima 1990, Frost and Sturtevant 1986) clearly show that though a collapsing cavitation bubble approaches its minimum size as a coherent single volume, it usually reappears in the first rebounding frame as a cloud of much smaller bubbles or as a highly distorted single volume (see, for example, figure 2). This paper exp...

We present an algorithm for learning a quadratic Gaussian metric (Mahalanobis distance) for use in classification tasks. Our method relies on the simple geometric intuition that a good metric is one under which points in the same class are simultaneously near each other and far from points in the other classes. We construct a convex optimization problem whose solution generates such a metric by...

This paper presents a framework for analyzing distribution of sequentially equivalent nodes in a hierarchical design. This information can be used for selectively collapsing hierarchical modules into 'super-modules' resulting in improved optimization and better placement decisions. Our framework is capable of comparing any two modules in the design hierarchy in terms of logic sharing. Our curre...

Though Berman and others have provided powerful techniques to collapse nondeterministic degrees at and above nondeterministic linear space, and Immerman and Szelepcsenyi have provided techniques that collapse even sublinear nondeterministic space classes, it has remained an open problem whether any collapses could be proven for sublinear nondeterministic space degrees. This paper provides the f...

The collapsing variant of focal segmental glomerulosclerosis (FSGS) is a renal injury that may be idiopathic or associated with various factors; it is characterized by glomerular collapse, which leads to steroid-resistant nephrotic syndrome (NS) and progressive chronic renal failure. FSGS has not been well studied in children, in which most of the cases are idiopathic. We report six cases of th...