AC 0 circuits of size n log n augmented with log n MODm gates, for every odd integer m and any sufficiently small . As a consequence, for every odd integer m, we obtain a pseudorandom generator, based on the MOD2 function, for circuits of size S containing log S MODm gates. Our results are based on recent bounds of exponential sums that were previously introduced for proving lower bounds for MA...

Decision Support Systems under Multiple Objectives (MODSS) has been classified as a specific type of system within the broad family of DSS and has been one of the most active areas of research. However, despite its theoretical development large scale real-world applications of multi-objective decision making (MODM) methods had been seriously lacking due to the technical knowledge and expertise ...

We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e AC◦MODm circuits. We show that the following holds for several types of gates G: by adding a gate of type G at the output, it is possible to obtain an equivalent probabilistic depth 2 circuit of quasipolynomial size consisting of a gate of type G at the output and a ...

Let C be a threshold logic circuit computing a Boolean function MODm : {0, 1}n → {0, 1}, where n ≥ 1 and m ≥ 2. Then C outputs “0” if the number of “1”s in an input x ∈ {0, 1}n to C is a multiple of m and, otherwise, C outputs “1.” The function MOD2 is the so-called PARITY function, and MODn+1 is the OR function. Let s be the size of the circuit C, that is, C consists of s threshold gates, and ...

This paper describes a project that extends the multiple objective decision support system (MODSS) by offering knowledge-based guidance to an intelligent multiple objective decision support system (IMODSS). This IMODSS integrates expert system (ES), multiple objective decision-making (MODM) methodologies, graphical user interface (GUI) and decision support systems (DSS) technologies. This IMODS...

A multiple-objective decision support system (MODSS) may have several multiple objective decision making (MODM) methods in its method base. As some methods are more suitable than others for some decision cases or for some decision makers, a guide system is very useful to help users systematically towards the selection of their most appropriate methods. This paper presents an intelligent guide s...

We use a Ramsey-theoretic argument to obtain the first lower bounds for approximations over Zm by nonlinear polynomials: A degree-2 polynomial over Zm (m odd) must differ from the parity function on at least a 1=2 1=2(logn) (1) fraction of all points in the Boolean n-cube. A degree-O(1) polynomial over Zm (m odd) must differ from the parity function on at least a 1=2 o(1) fraction of all points...

Control charts are widely implemented in firms to establish and maintain statistical control of a process which leads to the improved quality and productivity. Design of control charts requires that the engineer selects a sample size, a sampling frequency and the control limits for the chart. In this paper, a possible combination of design parameters is considered as a decision making unit whic...

This paper will investigate the optimum portfolio for an investor, taking into account 5 criteria. The mean variance model of portfolio optimization that was introduced by Markowitz includes two objective functions; these two criteria, risk and return do not encompass all of the information about investment; information like annual dividends, S&P star ranking and return in later years which is ...