641 research outputs found

    Strategic planning for a SME

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    The purpose of this research is to find competitive advantages for an organisation and prepare a long-term strategic planning for the SME. In a New Zealand context, small business enterprises play vital roles in business and the economic sector. However, most small business do not have specific competitive advantage and long-term strategies to compete in the market. Both qualitative and quantitative approaches have been used as mixed method research. Interviews and surveys have been done. Using those methods, researchers are intended to use the most effective implementation methodology to find out the best solution to the problem and cause of a SME. Location and customer satisfaction have been identified as the prime factors for the firm to run the business successfully. The business has been operating smoothly without using any further strategies to compete in the market. Recommendations involve pricing, advertising and stock management

    Strategic planning for a SME

    Get PDF
    The purpose of this research is to find competitive advantages for an organisation and prepare a long-term strategic planning for the SME. In a New Zealand context, small business enterprises play vital roles in business and the economic sector. However, most small business do not have specific competitive advantage and long-term strategies to compete in the market. Both qualitative and quantitative approaches have been used as mixed method research. Interviews and surveys have been done. Using those methods, researchers are intended to use the most effective implementation methodology to find out the best solution to the problem and cause of a SME. Location and customer satisfaction have been identified as the prime factors for the firm to run the business successfully. The business has been operating smoothly without using any further strategies to compete in the market. Recommendations involve pricing, advertising and stock management

    Ideal-Theoretic Explanation of Capacity-Achieving Decoding

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    In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is specified by some ideals in a polynomial ring, messages are polynomials and their encoding is the residue modulo the ideals. We present an alternate way of viewing this class of codes in terms of linear operators, and show that this alternate view makes their algorithmic list-decodability amenable to analysis. Our framework leads to a new class of codes that we call affine Folded Reed-Solomon codes (which are themselves a special case of the broader class we explore). These codes are common generalizations of the well-studied Folded Reed-Solomon codes and Univariate Multiplicity codes, while also capturing the less-studied Additive Folded Reed-Solomon codes as well as a large family of codes that were not previously known/studied. More significantly our framework also captures the algorithmic list-decodability of the constituent codes. Specifically, we present a unified view of the decoding algorithm for ideal-theoretic codes and show that the decodability reduces to the analysis of the distance of some related codes. We show that good bounds on this distance lead to capacity-achieving performance of the underlying code, providing a unifying explanation of known capacity-achieving results. In the specific case of affine Folded Reed-Solomon codes, our framework shows that they are list-decodable up to capacity (for appropriate setting of the parameters), thereby unifying the previous results for Folded Reed-Solomon, Multiplicity and Additive Folded Reed-Solomon codes

    On the Probabilistic Degree of OR over the Reals

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    We study the probabilistic degree over R of the OR function on n variables. For epsilon in (0,1/3), the epsilon-error probabilistic degree of any Boolean function f:{0,1}^n -> {0,1} over R is the smallest non-negative integer d such that the following holds: there exists a distribution of polynomials Pol in R[x_1,...,x_n] entirely supported on polynomials of degree at most d such that for all z in {0,1}^n, we have Pr_{P ~ Pol}[P(z) = f(z)] >= 1- epsilon. It is known from the works of Tarui (Theoret. Comput. Sci. 1993) and Beigel, Reingold, and Spielman (Proc. 6th CCC 1991), that the epsilon-error probabilistic degree of the OR function is at most O(log n * log(1/epsilon)). Our first observation is that this can be improved to O{log (n atop <= log(1/epsilon))}, which is better for small values of epsilon. In all known constructions of probabilistic polynomials for the OR function (including the above improvement), the polynomials P in the support of the distribution Pol have the following special structure: P(x_1,...,x_n) = 1 - prod_{i in [t]} (1- L_i(x_1,...,x_n)), where each L_i(x_1,..., x_n) is a linear form in the variables x_1,...,x_n, i.e., the polynomial 1-P(bar{x}) is a product of affine forms. We show that the epsilon-error probabilistic degree of OR when restricted to polynomials of the above form is Omega(log (n over <= log(1/epsilon))/log^2 (log (n over <= log(1/epsilon))})), thus matching the above upper bound (up to polylogarithmic factors)

    On the Probabilistic Degree of OR over the Reals

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    We study the probabilistic degree over reals of the OR function on nn variables. For an error parameter ϵ\epsilon in (0,1/3), the ϵ\epsilon-error probabilistic degree of any Boolean function ff over reals is the smallest non-negative integer dd such that the following holds: there exists a distribution DD of polynomials entirely supported on polynomials of degree at most dd such that for all z{0,1}nz \in \{0,1\}^n, we have PrPD[P(z)=f(z)]1ϵPr_{P \sim D} [P(z) = f(z) ] \geq 1- \epsilon. It is known from the works of Tarui ({Theoret. Comput. Sci.} 1993) and Beigel, Reingold, and Spielman ({ Proc. 6th CCC} 1991), that the ϵ\epsilon-error probabilistic degree of the OR function is at most O(logn.log1/ϵ)O(\log n.\log 1/\epsilon). Our first observation is that this can be improved to Olog(nlog1/ϵ)O{\log {{n}\choose{\leq \log 1/\epsilon}}}, which is better for small values of ϵ\epsilon. In all known constructions of probabilistic polynomials for the OR function (including the above improvement), the polynomials PP in the support of the distribution DD have the following special structure:P=1(1L1).(1L2)...(1Lt)P = 1 - (1-L_1).(1-L_2)...(1-L_t), where each Li(x1,...,xn)L_i(x_1,..., x_n) is a linear form in the variables x1,...,xnx_1,...,x_n, i.e., the polynomial 1P(x1,...,xn)1-P(x_1,...,x_n) is a product of affine forms. We show that the ϵ\epsilon-error probabilistic degree of OR when restricted to polynomials of the above form is Ω(loga/log2a)\Omega ( \log a/\log^2 a ) where a=log(nlog1/ϵ)a = \log {{n}\choose{\leq \log 1/\epsilon}}. Thus matching the above upper bound (up to poly-logarithmic factors)
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