Consider a decision problem that cannot be 1 ? approximated by circuits of a given size in the sense that any such circuit fails to give the correct answer on at least a fraction of instances. We show that for any such problem there is a speciic \hard-core" set of inputs which is at least a fraction of all inputs and on which no circuit of a slightly smaller size can get even a small advantage ...

This paper reviews some of the work in the area of statistical circuit design. While space does not permit a more then superficial survey of the entire field, specific emphasis is placed on those techniques more familiar to the authors.

Let G be the Cartesian product of a regular tree T and finite connected transitive graph H. It is shown in [4] that Free Uniform Spanning Forest (FSF) this may not connected, but dependence connectedness on H remains somewhat mysterious. We study case when positive weight w put edges H-copies G, conjecture FSF exhibits phase transition. For large enough we show while for wide family T, disconne...

In the crystal structure of the title compound, (C3H11NOP)2[PdCl4], (di-methyl-phosphor-yl)methanaminium (dpmaH(+)) cations are connected head-to-tail by strong N-H⋯O hydrogen bonds, forming inversion-related cyclic dimers. The square-planar [PdCl4](2-) counter-dianion is located about a center of inversion. The dications and the [PdCl4](2-) dianions are connected by medium-strong N-H⋯Cl hydrog...

BACKGROUND CONTEXT The X-STOP interspinous decompression device, as a treatment for neurogenic intermittent claudication (NIC) because of lumbar spinal stenosis (LSS), has been shown to be superior to nonoperative control treatment. Current Food and Drug Administration labeling limits X-STOP use to NIC patients with a maximum of 25° concomitant lumbar scoliosis. This value was arrived at arbitr...

We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by reduced-order modeling techniques dynamical systems. The cornerstone proposed maximum volume algorithm. demonstrate efficiency on networks pre-trained different datasets. show that in many practical cases it possible to replace convolutional layers with much smaller fully-connected relati...