Mathematics

In recent years, multilayer feedforward neural networks (NN) have been shown to be very effective tools in many different applications. A natural and essential step in continuing the diffusion of these tools in day by day use is their hardware implementation which is by far the most cost effective solution for large scale use. When the hardware implementation is contemplated, the issue of the size of the NN becomes crucial because the size is directly proportional with the cost of the implementation. In this light, any theoretical results which establish bounds on the size of a NN for a given problem is extremely important. In the same context, a particularly interesting case is that of the neural networks using limited integer weights. These networks are particularly suitable for hardware implementation because they need less space for storing the weights and the fixed point, limited precision arithmetic has much cheaper implementations in comparison with its floating point counterpart. This paper presents an entropy based analysis which completes, unifies and correlates results partially presented in [Beiu, 1996, 1997a] and [Draghici, 1997]. Tight bounds for real and integer weight neural networks are calculated.

In recent years, multilayer feedforward neural networks (NN) have been shown to be very effective tools in many different applications. A natural and essential step in continuing the diffusion of these tools in day by day use is their hardware implementation which is by far the most cost effective solution for large scale use. When the hardware implementation is contemplated, the issue of the size of the NN becomes crucial because the size is directly proportional with the cost of the implementation. In this light, any theoretical results which establish bounds on the size of a NN for a given problem is extremely important. In the same context, a particularly interesting case is that of the neural networks using limited integer weights. These networks are particularly suitable for hardware implementation because they need less space for storing the weights and the fixed point, limited precision arithmetic has much cheaper implementations in comparison with its floating point counterpart. This paper presents an entropy based analysis which completes, unifies and correlates results partially presented in [Beiu, 1996, 1997a] and [Draghici, 1997]. Tight bounds for real and integer weight neural networks are calculated.

Dangerous abbreviations are also known as "error-prone abbreviations". They are referred to as "dangerous" or "error-prone" because they can lead to misinterpretation of orders and other communications, resulting in patient harm or death. Selected medication errors arising from the use of dangerous abbreviations are highlighted in this article, along with examples of such abbreviations and strategies to eliminate their use. This column is intended to enhance the awareness of practitioners who treat and care for critical care patients of the problems associated with using ambiguous abbreviations and to provide suggestions for associated safe practices.

3D LEVEL−I 1 The locus of the point, which moves such that its distance from (1, −2, 2) is unity, is (A) x 2 + y 2 + z 2 − 2x + 4y − 4z + 8 = 0 (B) x 2 + y 2 + z 2 − 2x − 4y − 4z + 8 = 0 (C) x 2 + y 2 + z 2 + 2x + 4y − 4z + 8 = 0 (D) x 2 + y 2 + z 2 − 2x + 4y + 4z + 8 = 0 *2 The angle between the lines whose direction ratios are 1, 1, 2; 3 − 1, − 3 − 1, 4 is (A) cos −1  *3. The plane passing through the point (a, b, c) and parallel to the plane x + y + z = 0 is (A) x + y + z = a + b + c (B) x + y + z + (a + b + c) = 0 (C) x + y + z + abc = 0 (D) ax + by + cz = 0 4.