We focus on binary classification problems; that is, we consider the problem of predicting a binary label y based on its corresponding input vector x. As in the standard machine learning formulation, we assume that the data points (x, y) are drawn from an unknown underlying distribution DXY over X × Y ; X is called the instance space and Y is the label space. We assume that Y = {±1} and X = Rd;...

For a connected graph G = (V,E), a subset U ⊆ V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. A natural condition is to impose that for any u ∈ U the subgraph induced by (V \U)∪{u} is connected. In that case U is called a minimal disconnected cut. We show that the problem of testing whether a graph has a minimal disconnected cut i...

In this note we develop some of the properties of separators of points in a multiprojective space. In particular, we prove multigraded analogs of results of Geramita, Maroscia, and Roberts relating the Hilbert function of X and X \ {P} via the degree of a separator, and Abrescia, Bazzotti, and Marino relating the degree of a separator to shifts in the minimal multigraded free resolution of the ...

Development of hydrocyclonic separation is introduced first. The characteristics of the dynamic hydrocyclone are described. The laboratory study and oilfield tests of dynamic hydrocyclones were carried out. Some photos indicating flow phenomena inside the hydrocyclone were taken and analyzed for understanding the effect of some varieties on hydrocyclonic separation. Relations of flowrate, and o...

This paper describes the results of a proof of concept effort for development of a Nautilus Centripetal Capillary Condenser (NCCC or NC) used for microgravity compatible water recovery from moist air with integral passive phase separation. Removal of liquid condensate from the air stream exiting a condenser is readily performed here on Earth. In order to perform this function in space however, ...

For undirected graphs G (V, E) and G0 (V0 , E0), say that G is a region intersection graph over G0 if there is a family of connected subsets {Ru ⊆ V0 : u ∈ V} of G0 such that {u , v} ∈ E ⇐⇒ Ru ∩ Rv , ∅. We show if G0 excludes the complete graph Kh as a minor for some h > 1, then every region intersection graph G over G0 with m edges has a balanced separator with at most ch √ m nodes, where ch i...

Pulsating technology joins ultra-efficient screens for the utmost in cuttings treatment, fluid recovery