On the Decidability of Semilinearity for Semialgebraic Sets and Its Implications for Spatial Databases

AbstractSeveral authors have suggested using first-order logic over the real numbers to describe spatial database applications. Geometric objects are then described by polynomial inequalities with integer coefficients involving the coordinates of the objects. Such geometric objects are called semialgebraic sets. Similarly, queries are expressed by polynomial inequalities. The query language thus obtained is usually referred to as FO+poly. From a practical point of view, it has been argued that a linear restriction of this so-called polynomial model is more desirable. In the so-called linear model, geometric objects are described by linear inequalities and are called semilinear sets. The language of the queries expressible by linear inequalities is usually referred to as FO+linear. As part of a general study of the feasibility of the linear model, we show in this paper that semilinearity is decidable for semialgebraic sets. In doing so, we point out important subtleties related to the type of the coefficients in the linear inequalities used to describe semilinear sets. An important concept in the development of the paper is regular stratification. We point out the geometric significance, as well as its significance in the context of FO+linear and FO+poly computations. The decidability of semilinearity of semialgebraic sets has an important consequence. It has been shown that it is undecidable whether a query expressible in FO+poly is linear, i.e., maps spatial databases of the linear model into spatial databases of the linear model. It follows now that, despite this negative result, there exists a syntactically definable language precisely expressing the linear queries expressible in FO+poly

Calculation of Effective Coulomb Interaction for Pr3+Pr^{3+}, U4+U^{4+}, and UPt3UPt_3

In this paper, the Slater integrals for a screened Coulomb interaction of the the Yukawa form are calculated and by fitting the Thomas-Fermi wavevector, good agreement is obtained with experiment for the multiplet spectra of $Pr^{3+}$ and $U^{4+}$ ions. Moreover, a predicted multiplet spectrum for the heavy fermion superconductor $UPt_3$ is shown with a calculated Coulomb U of 1.6 eV. These effective Coulomb interactions, which are quite simple to calculate, should be useful inputs to further many-body calculations in correlated electron metals.Comment: 8 pages, revtex, 3 uuencoded postscript figure

Perturbation-based stochastic multi-scale computational homogenization method for woven textile composites

In this paper, a stochastic homogenization method that couples the state-of-the-art computational multi-scale homogenization method with the stochastic finite element method, is proposed to predict the statistics of the effective elastic properties of textile composite materials. Uncertainties associated with the elastic properties of the constituents are considered. Accurately modeling the fabric reinforcement plays an important role in the prediction of the effective elastic properties of textile composites due to their complex structure. The p-version finite element method is adopted to refine the analysis. Performance of the proposed method is assessed by comparing the mean values and coefficients of variation for components of the effective elastic tensor obtained from the present method against corresponding results calculated by using Monte Carlo simulation method for a plain-weave textile composite. Results show that the proposed method has sufficient accuracy to capture the variability in effective elastic properties of the composite induced by the variation of the material properties of the constituents

Strategic directions in constraint programming

An abstract is not available

Virtual testing of advanced composites, cellular materials and biomaterials: A review

This paper documents the emergence of virtual testing frameworks for prediction of the constitutive responses of engineering materials. A detailed study is presented, of the philosophy underpinning virtual testing schemes: highlighting the structure, challenges and opportunities posed by a virtual testing strategy compared with traditional laboratory experiments. The virtual testing process has been discussed from atomistic to macrostructural length scales of analyses. Several implementations of virtual testing frameworks for diverse categories of materials are also presented, with particular emphasis on composites, cellular materials and biomaterials (collectively described as heterogeneous systems, in this context). The robustness of virtual frameworks for prediction of the constitutive behaviour of these materials is discussed. The paper also considers the current thinking on developing virtual laboratories in relation to availability of computational resources as well as the development of multi-scale material model algorithms. In conclusion, the paper highlights the challenges facing developments of future virtual testing frameworks. This review represents a comprehensive documentation of the state of knowledge on virtual testing from microscale to macroscale length scales for heterogeneous materials across constitutive responses from elastic to damage regimes

Triple Engineering

status: publishe

An Expressive Language for Linear Spatial Database Queries (Extended Abstract)

We exhibit a coordinate-based language, called PFOL, which is sound for the linear queries computable in first-order logic over the reals and extends the latter's restriction to linear arithmetic. To evaluate its expressive power, we first consider PFOL-fin, the PFOL queries that compute finite outputs upon finite inputs. In order to study this fragment of PFOL, we also define a syntactical language, called SPFOL, which is safe with respect to queries from finite inputs to nite outputs. We show that SPFOL has the same expressive power as SafeEuQl [15], whence all ruler-and-compass constructions in the plane on finite sets of points can be expressed in SPFOL. This result gives a geometrical justification of SPFOL, and highlights the richness of PFOL-fin. Then, we define finite representations for arbitrary semilinear sets and show that there are PFOL programs for both the encoding and the decoding. This result is used (i) to identify a broad, natural class of linear queries expressible in PFOL, highlighting the richness of general PFOL, and (ii) to establish a general theorem about lifting query languages on finite databases to query languages on arbitrary linear databases. This theorem is applied to a recent result of Benedikt and Libkin [5] from finite to arbitrary semilinear sets, yielding the existence of a natural, syntactically definable fragment of FO + poly sound and complete for all FO + poly-expressible linear queries

Pricing in the fresh produce industry: How to set the right price for the right customer

The main objective of this project is to develop a pricing strategy and provide Fair-Fruit with a 4-level pricelist. As the main objective of Fair-Fruit is to attract new customers and to increase the product offering to current customers, a value-based pricing strategy will help the company to develop and maintain long-term customer relationships. Fair-Fruit deals with 4 types of customers (brokers, wholesalers, distributors, and retailers). Therefore, a value-based price strategy will allow the company to provide the best benefits to price ratio to each type of customer. The technique of conjoint analysis was used to measure the price sensitivity of each type of customer, as well as sensitivity to other product attributes. More specifically, a choice-based conjoint analysis was conducted that required respondents to make choices between fully described products. The survey was designed in such a way that the product descriptions would vary systematically in the levels of certain attributes that define the product as well as the price. The product selected for the conjoint analysis is French beans, as it is interesting for Fair-Fruit to make this product more attractive. To establish the different levels and attributes, a supply chain analysis was conducted, including a margin analysis of the fresh produce industry and a value flow chart of the different players within the supply chain. In addition, a customer value analysis was done by conducting interviews with Fair-Fruit’s current customers to ascertain what each type of customer of the company values about Fair-Fruit’s products and service. The following attributes were included in the conjoint analysis: price, order size, credit period and promotions. For each attribute, three different levels were established, except for price, for which 5 levels were set. The sample for the conjoint analysis consisted of companies within the fresh produce industry, based in the United States. Based on the supply chain analysis, conjoint analysis and customer value analysis, several conclusions could be drawn, and recommendations could be given to Fair-Fruit. These conclusions were broken down by customer type within the fresh produce supply chain. In addition, some general recommendations could also be provided to the company. It should be noted, however, that due to a low number of responses to the conjoint analysis, conclusions could only be drawn from this analysis for distributors, and not for the other types of customers. Concerning the brokers, it was found that they have lowest margin of the fresh produce industry. At the same time, they bare the most risks and purchase the highest volumes. Therefore, it would make sense for Fair-Fruit to offer them slightly lower prices. Regarding the wholesalers, a change within the industry can be observed. More and more wholesalers are establishing their own distribution network. As a result, the difference between a wholesaler and a distributor is becoming increasingly blurred.The conjoint analysis resulted in several findings concerning the distributors. First, price did not appear to be the most important factor for distributors as the analysis shows that credit period, order size, and price are considered about equally important. Moreover, the additional question added in the survey that gauged which claims customers thought were most important showed that quality comes first. After that, trust and reliability, and good communication are what matters most. This is consistent with what emerged from interviews with Fair-Fruit's customers. Finally, the supply chain analysis showed that retailers have the highest margin in the industry. This is an opportunity for the company to increase their prices up to 10% if they would decide to sell directly to retailers. Fair-Fruit would then have a similar gross margin as wholesalers and distributors. However, the company should not try to match their prices as they would then lose their competitive advantage. Additionally, Fair-Fruit should keep in mind that the sale process to retailers is more time-intensive and standardized. A general recommendation that applies to Fair-Fruit's 4 types of customers is to look at what part of the market a customer continues to sell the products to. Is this customer trading with the low end or the high end of the market? Subsequently, Fair-Fruit can adjust its prices accordingly. Based on the customer value analysis, it was revealed what Fair-Fruit's current customers value most: quality, communication, transparency, trust, and reliability. This is an opportunity A final recommendation for the company is to make use of the described methodology and the conjointly software employed during this project. By continuing the current conjoint analysis, the number of respondents would grow. This would lead to more results for the conjoint analysis and help to aim towards statistically significant results.Fair Frui