In this article we show the rough outline of a computer algorithm to generate lower bounds on the exponential function of (in principle) arbitrary precision. We implemented this to generate all necessary analytic terms for the Boltzmann machine partition function thus leading to lower bounds of any order. It turns out that the extra variational parameters can be optimized analytically. We show ...

Domain Theory and Rough Set Theory are relatively independent but have much close relationship worthy of further investigation. In this paper, we propose the notion of (orientated) lower concept formula (for short, lcf) of relational information systems and study the order-theoretic properties of the derived lcf systems. Particularly, we show that every orientated lcf system is an algebraic lat...

Let A be a subset of {1, 2, . . . , n} such that the sum of no two distinct elements of A is a prime number. Such a subset is called a prime-sumset-free subset of {1, 2, . . . , n}. A prime-sumset-free subset is called an extremal prime-sumset-free subset of {1, 2, . . . , n} if A ∪ {a} is not a prime-sumset-free subset for any a ∈ {1, 2, . . . , n} \ A. We prove that if n ≥ 10 then there is no...

In this paper, we study lower bound techniques for branchand-bound algorithms for maximum parsimony, with a focus on gene order data. We give a simple O(n) time dynamic programming algorithm for computing the maximum circular ordering lower bound. The well-known gene order phylogeny program, GRAPPA, currently implements the brute-force exponential time algorithm and the Swap-as-yougo heuristic....

Let q ∈ (1, 2) and x ∈ [0, 1 q−1 ]. We say that a sequence (εi) ∞ i=1 ∈ {0, 1}N is an expansion of x in base q (or a q-expansion) if

BACKGROUND The aim of the present study was to investigate the effect of near-work on lower and higher-order aberrations, and its progression over a 9-month period during the school year. METHODS Data from 24 young-adult myopic eyes, and 24 non-myopic eyes were used in this investigation. The lower-order aberrations, coma, spherical aberration (SA), and total root mean square (RMS) of higher ...

We study the growth rate on the number obstructions (forbidden minors) for families of graphs that are based on parameterized graph problems. Our main result shows that if the de ning graph problem is NP-complete then the growth rate on the number of obstructions must be super-polynomial or else the polynomial-time hierarchy must collapse to P 3 . We illustrate the rapid growth rate of paramete...

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

In this paper we consider three parameter generalized exponential distribution. Exact expressions and some recurrence relations for single and product moments of lower generalized order statistics are derived. Further the results are deduced for moments of order statistics and lower records and characterization of this distribution has been considered on using the conditional moment of the lowe...

The presence of non-Gaussian ambient channel noise in wireless systems can degrade the performance of existing equalizers and signal detectors. In this paper, we investigate the problem of blind equalization in noisy communication channels by addressing the negative e6ects of heavy-tailed noise to the original constant modulus algorithm (CMA). We propose a new CM criterion employing fractional ...