Showing papers on "Product (mathematics) published in 2002"

Feature-oriented product line engineering

Abstract: The feature-oriented reuse method analyzes and models a product line's commonalities and differences in terms of product features and uses the analysis results to develop architectures and components. The article illustrates, with a home integration system example, how FORM brings efficiency into product line development.

Extending feature diagrams with uml multiplicities

Abstract: Feature diagrams are an important product of domain analysis for product lines or system families, respectively They describe relations between requirements and distinguish between common and variable characteristics Feature diagrams, as part of the feature model, form the basis for configuring the system Current principles do not supply a complete description of the semantics of relationships and dependencies between features Thus, the development of methods and tools for elaborating configurations is not possible This paper presents some enhancements to feature diagrams In addition the paper deals with the inclusion of feature models in the development process of product lines Index terms: domain analysis, software product lines, system families, software reuse, feature modeling

Product variety optimization under modular architecture

Abstract: In this paper, product variety design is discussed under an optimization viewpoint. Product variety design means the challenge to simultaneously design multiple products for achieving higher optimality beyond ordinary design methods for a single product. When the possibilities of computational optimization for product variety design under fixed product architecture are explored, optimization is demanded to determine the contents of modules and their combinations under fixed modular architecture. This indicates that product variety optimization includes three classes of optimization problems: attribute assignment, module combination, and simultaneous design of both. Following problem classification, the domains and situations of such optimization problems are investigated. Then, two typical optimization examples are demonstrated through aircraft design for simultaneous optimal attribute assignment and through design of television receiver circuits for optimal module combination, respectively. The discussion concludes with the roles of problem classification and the direction of future works.

Coproduct and star product in field theories on Lie-algebra noncommutative space-times

Abstract: We propose a new approach to field theory on \ensuremath{\kappa}-Minkowski noncommutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical noncommutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the \ensuremath{\kappa}-Poincar\'e coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in \ensuremath{\kappa}-Minkowski the coproduct and the star product must indeed treat momenta in a nonsymmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in \ensuremath{\kappa}-Minkowski field theories it is convenient to introduce the concepts of ``planar'' and ``nonplanar'' Feynman loop diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical noncommutative space-times.

The basis of product emotions

Abstract: This paper introduces a conceptual model for the process underlying emotional responses that result from the perception of consumer products. The model distinguishes different kinds of emotions on the basis of eliciting conditions. It is based on the presumption that all emotional reactions result from an appraisal process in which the individual appraises the product as favouring or harming one or several of his concerns. In this process of appraisal, the personal concern gives the stimulus emotional relevance. The model describes the various ways in which products can act as emotional stimuli and the matching concerns that can either correspond or collide with these stimuli. Products can act as stimuli in three different ways: the product as such, the product (or designer) as an agent, and the products as a promise for future usage or ownership. The corresponding concerns that are addressed are respectively: attitudes, standards, and goals. By revealing the cognitive basis of product emotions, the model can be used to explain the nature and, often, mixed character of product emotions. The paper illustrates a possible application of the model in a tool for designers. INTRODUCTION After being neglected for many years, a sudden interest in product affect has emerged. The affective side of product experience has become a ‘hot topic’, which is probably best illustrated by this conference and similar events over the past few years (e.g., Overbeeke & Hekkert, 1999). A difficulty of affective concepts such as pleasure and emotion is that they are probably as intangible as they are appealing. Although some interesting and promising studies have been reported, the research field is still short of conceptual clarity and therefore lacks consensus on what the actual subject of study should be. In fact, both the concepts of pleasure and emotion are somewhat undifferentiated, they are used as collective nouns for all kinds of affective phenomena. Design literature tends to refer to these when studying anything that is so-called intangible, non-functional, non-rational, or, for that matter, non-cognitive. Some of the reported studies involve ‘experiential needs’ (Holbrook, 1982), ‘affective responses’ (Derbaix & Pham, 1991), ‘emotional benefits’ (Desmet, Tax & Overbeeke, 2000), ‘customer delight’ (Burns, Barrett & Evans, 2000) and ‘pleasure’ (Jordan & Servaes, 1995). Naturally, it is inherent to any newly emerging research field that the emulsion has not even started to crystallise. On the other hand, an adequate definition of the subject of study would probably facilitate fruitful discussions between researchers. In our view, a model of product emotions can help to get a grip on the concept of product pleasure and emotions. This paper introduces such a structured model that distinguishes different kind of product emotions on the basis of their eliciting conditions. The model adheres to the cognitive (functional) view on emotions and finds its roots in a structure developed by Ortony, Clore and Collins (1988). A first step in developing the model is to Desmet, P.M.A., & Hekkert, P. (2002). The basis of product emotions. In: W. Green and P. Jordan (Eds.), Pleasure with Products, beyond usability (60-68). London: Taylor & Francis. clarify the relationship between the concepts of pleasure and emotion. PLEASURE AND EMOTIONS The concept of affect refers to a large variety of psychological states such as emotions, feelings, moods, sentiments, and passions. Each of these affective states varies in duration, impact and eliciting conditions. Of these states, emotions are most relevant for product experience because only they imply a one-to-one relationship between the affective state and a particular object: one is afraid of something, angry at someone, happy about something, and so on (Frijda, 1986). The other affective states, such as feelings and moods, do not involve a specific object. For example, a moody person will find it difficult to pinpoint the exact cause of his mood. In the study of affective reactions to products, the object, i.e., the product, is the starting-point. Subsequently, the model of product affect presented in this paper focuses specifically on emotions. The place of pleasure in emotions is debatable. Both the propositions that pleasure is an emotion, and that it is not, are defensible. On the one hand, pleasure is an emotion if it is merely used as an equivalent of ‘fun’ or ‘enjoyment’. In this connotation pleasure is included in many of the taxonomies of emotions found in literature (e.g., Russell & Lanius, 1984). On the other hand, this view on pleasure seems to be rather narrow for the current application. Design research literature refers to pleasure as a product benefit that exceeds just proper functioning. In other words, pleasure is an emotional benefit that supplements product functionality. In this sense, pleasure covers all pleasant emotional reactions, of which the experience of fun is just one example. Valence (a bipolar ranging from pleasant to unpleasant) is a dimension frequently discovered in scaling procedures of emotion terms. If pleasure is regarded as a dimension of emotions, it can be used to describe emotions, but it is not an emotion as such. This notion befits everyday experience: one never feels pleasant as such. One feels happy, cheerful, surprised, inspired, etc. Although each of these emotions might be pleasant, that does not make pleasantness an emotion. Therefore, in the light of this paper, pleasure is defined as any pleasant emotional response elicited by product design. It might seem difficult, if not impossible, to find general relationships between product appearance and emotional responses because emotions are essentially personal. Nevertheless, although people differ in their emotional responses to products, general rules can be identified in the underlying process of emotion eliciting. A view that distinguishes such general rules is the cognitive view on emotions. THEORY OF EMOTION The cognitive, functionalist position on emotions posits that emotions serve an adaptive purpose. In this view, emotions are considered the mechanisms that signal when events are favourable or harmful to one’s concerns. This implies that in each emotion-eliciting stimulus some concern can be identified. These concerns are more or less stable preferences for certain states of the world; they are our personal motives in life (Frijda, 1986). Examples of human concerns are concerns for respect, safety, and self-esteem. For instance, we all have the concern of being treated with the respect we believe we deserve. When a person receives a degrading comment from a colleague, he will probably find this event conflicting with this concern for respect. Consequently, this person will experience a negative emotion such as shame or anger. The preceding example illustrates that the linking of the stimulus to the concern precedes the actual emotional response. This process of ‘signalling the emotional relevancy of an event’ is most commonly conceptualised as ‘a process of Desmet, P.M.A., & Hekkert, P. (2002). The basis of product emotions. In: W. Green and P. Jordan (Eds.), Pleasure with Products, beyond usability (60-68). London: Taylor & Francis. appraisal’ (e.g., Arnold, 1960; Frijda, 1986). Appraisal theories assert that it is not events per se that determine emotional responses, but evaluations and interpretations of events. Because emotions are intentional and essentially involve concerns, they seem to require an explanation that invokes these concerns. Moreover, as this paper focuses on emotions specifically elicited by products, the explanation should also include eliciting conditions. A good starting point for a model of product emotions is the model developed by Ortony et al. (1988) because it particularly focuses on this relationship between different types of concerns and the eliciting conditions. stimulus concern appraisal product as object attitude appealingness product as agent (action of) standard praiseworthyness product as event goal desirability Figure 1: Model of product emotions MODEL OF PRODUCT EMOTIONS According to the cognitive model of Ortony et al. (1988) there are three major aspects of the world we can focus on: events, agents, or objects. We focus on events (e.g., a football match) for their consequences (e.g., loss of your favourite team), we focus on agents (e.g., a dog) for their actions (e.g., barking at you), and we focus on objects (e.g., a painting) because we are interested in certain properties of them as such (e.g., its composition). Central to Ortony et al’s view is the position that emotions are valenced reactions to one of these perspectives on the world. Based on this division they developed a structure of emotion types that are logically related to one of these three aspects. In focusing on product emotions, at first side, it may seem tempting to restrict ourselves to the third class ‘products as objects’. Our major claim is however that all three perspectives are relevant when products are simply perceived with one of our senses, i.e., without requiring physical interaction with the product. What we will present here is an adjusted version of the original model in which those elements are adopted that cover emotions that may result from product perception. This adapted model is presented in Figure 1. Figures 2, 3, and 4 each show examples of one of the three classes of product emotions. Products as objects To start with the most obvious and simple branch of the structure in Figure 1, products are objects. Like all objects, products, or aspects of products, can be viewed as such in terms of their appealingness. Products are simply liked or disliked for their appearance, for the way they look. The emotional reactions are basically unstructured and comprise attraction emotions such as love, attracted-to, disgust, and boredom. attitude appealingness product as objec

A characterization of product BMO by commutators

Abstract: In this paper we establish a commutator estimate which allows one to concretely identify the product BMO space, BMO(R2+ x R2+), of A. Chang and R. Fefferman, as an operator space on L2(R2). The one-parameter analogue of this result is a well-known theorem of Nehari [8]. The novelty of this paper is that we discuss a situation governed by a twoparameter family of dilations, and so the spaces H 1 and BMO have a more complicated structure. Here R2+ denotes the upper half-plane and BMO(R2+ • R2+) is defined to be the dual of the real-variable Hardy space H 1 on the product domain R2+ x R2+. There are several equivalent ways to define this latter space, and the reader is referred to [5] for the various characterizations. We will be more interested in the biholomorphic analogue of H 1, which can be defined in terms of the boundary values of biholomorphic functions on R 2 • R2+ and will be denoted throughout by Hi(R2+ • cf. [10]. In one variable, the space L2(R) decomposes as the direct sum H 2 ( R ) | where H2(R) is defined as the boundary values of functions in H2(R2+) and H2(R) denotes the space of complex conjugate of functions in H2(R). The space L2(R2), therefore, decomposes as the direct sum of the four spaces H 2 ( R ) | H2(R)@H2(R) , H 2 ( R ) | and H 2 ( R ) | where the tensor products are the Hilbert space tensor products. Let P~-,• denote the orthogonal projection of L2(R 2) onto the holomorphic/anti-holomorphic subspaces, in the first and second variables, respectively, and let Hj denote the one-dimensional Hilbert transform in the j t h variable, j -1 , 2. In terms of the projections P+,• HI=P+,++P+,--P-,+-P-,and H2=P+,++P-,+-P+,--P_,_.

Coherent state induced star product on R λ 3 and the fuzzy sphere

Abstract: Using the Hopf fibration and starting from a four-dimensional noncommutative Moyal plane ${R}_{\ensuremath{\theta}}^{2}\ifmmode\times\else\texttimes\fi{}{R}_{\ensuremath{\theta}}^{2}$ we obtain a star product for the noncommutative (fuzzy) ${R}_{\ensuremath{\lambda}}^{3}$ defined by $[{x}^{i}{,x}^{j}]=i\ensuremath{\lambda}{\ensuremath{\epsilon}}_{\mathrm{ijk}}{x}^{k}.$ Furthermore, we show that there is a projection function which allows us to reduce the functions on ${R}_{\ensuremath{\lambda}}^{3}$ to that of the fuzzy sphere, and hence we introduce a new star product on the fuzzy sphere. We will then briefly discuss how using our method one can extract information about the field theory on the fuzzy sphere and ${R}_{\ensuremath{\lambda}}^{3}$ from the corresponding field theories on ${R}_{\ensuremath{\theta}}^{2}\ifmmode\times\else\texttimes\fi{}{R}_{\ensuremath{\theta}}^{2}$ space.

Image recognition inventory management system

Abstract: A method and system that includes a microprocessor device with memory adapted to receive input corresponding to a report at an instant of time of an amount of product in a product display in a business, and further adapted to store the data in the memory. The method and system also include a central computer for receiving and processing the data from the microprocessor device so that the computer is configured to create a planogram which optimizes the display of the product by maximizing the amount of desired product and minimizes the amount of undesired product to be displayed. The central computer further contacts product suppliers so that the quantity of supplied product always meets the requirements of the planogram.

Castelnuovo-Mumford regularity of products of ideals

Abstract: We discuss the behavior of the Castelnuovo-Mumford regularity under certain operations on ideals and modules, like products or powers. In particular, we show that reg(IM) can be larger than reg(M)+reg(I) even when I is an ideal of linear forms and M is a module with a linear resolution. On the other hand, we show that any product of ideals of linear forms has a linear resolution. We also discuss the case of polymatroidal ideals and show that any product of determinantal ideals of a generic Hankel matrix has a linear resolution.

System for homogeneously mixing plural incoming product streams of different composition

Abstract: A continuous mixer (32) is disclosed which can be used for mixing of incoming product streams (22, 24) of different characteristics respectively to yield a final product stream (26) of predetermined, consistent characteristics. The mixer (32) includes an elongates housing (42) having a pair of product input ports (50, 52) and an output (64), with a pair of elongated, axially rotatable, mixing screws (44, 46) located within the housing (42). The screws (44, 46) include a series of outwardly projecting mixing elements (114) preferably of pyramidal design and arrayed in a helical pattern along the length of the screws (44, 46). The mixer (32) may be used in a processing system (20, 200) having individual product lines (28, 30, 204, 206) coupled to the mixer (32), and is especially useful for processing of incoming meat streams (22, 24) of different fat/lean ratios, to give a final comminuted output stream (26) of an intermediate and essentially constant fat/lean ratio. Preferably, the product lines (204, 206) are each equipped with a combine preblender and pumping device (202).

An Elementary Counterexample to the Finiteness Conjecture

Abstract: We prove that there exist (infinitely many) values of the real parameters a and b for which the matrices ( \begin{array}{ll} 1 & 1 \\ 0 & 1 \end{array} \right) \qquad \mbox{ and } \qquad b \left( \begin{array}{ll} 1 & 0 \\ 1 & 1 \end{array} \right) $$ have the following property: all infinite periodic products of the two matrices converge to zero, but there exists a nonperiodic product that doesn't. Our proof is self-contained and fairly elementary; it uses only elementary facts from the theory of formal languages and from linear algebra. It is not constructive in that we do not exhibit any explicit values of a and b with the stated property; the problem of finding explicit matrices with this property remains open.

Introduction of a product family penalty function using physical programming

Abstract: In an effort to increase customization for today's highly competitive global markets, many companies are looking to product families to increase product variety and shorten product lead-times while reducing costs. The key to a successful product family is the product platform around which the product family is derived. Building on our previous work in product family design, we introduce a product family penalty function (PFPF) in this paper to aid in the selection of common parameters and scaling variables for scaled-based families of products derived from product platforms. The implementation of the PFPF utilizes the powerful physical programming paradigm to formulate the problem in terms of physically meaningful parameters. To demonstrate the proposed approach, a family of electric motors is developed and compared against previous results. We find that the PFPF enables us to properly balance commonality and performance within the product family through the judicious selection of scaling variables and the common parameters that constitute the product platform. Nomenclature Product Family: a group of related products that share common features, components, and subsystems; and satisfy a variety of market niches. A product family comprises a set of variables, features or components that remain constant from product to product (product platform), and others that vary from product to product. The modification of features from product to product within a given family can be effected through scaling (Scale-Based Product Family), or through the addition, substitution and exclusion of modules (Module-Based Product Family).

Feature Interaction and Dependencies: Modeling Features for Reengineering a Legacy Product Line

Abstract: Reengineering a legacy product line has been addressed very little by current product line research activities. This paper introduces a method to investigate feature dependencies and interactions, which restricts the variants that can be derived from the legacy product line assets. Reorganizing the product line assets with respect to new requirements requires more knowledge than what is easily provided by the classical feature-modeling approaches. Hence, adding all the feature dependencies and interactions into the feature tree results in unreadable and unmanageable feature models that fail to achieve their original goals.We therefore propose two complementary views to represent the feature model. One view shows the hierarchical refinement of features similar to common feature-modeling approaches in a feature tree. The second view describes what kind of dependencies and interactions there are between various features.We show two examples of feature dependencies and interactions in the context of an engine-control software product line, and we demonstrate how our approach helps to define correct product configurations from product line variants.

System and method of changing attributes of an image-based product

Abstract: A system and method for changing attributes of an image-based product in which an attribute of a first image is automatically identified and a new value for a product attribute of the image-based product is automatically selected based on the image attribute. Also, a user interface can be provided that allows a user to actuate a user interface control in order to select a new value for a product attribute of an image-based product. Such techniques can be used to offer image-based products for sale over a computer network such as the Internet so that the user can change attributes of the image-based products before ordering.

Characterization, formulation, and stability of Neupogen (Filgrastim), a recombinant human granulocyte-colony stimulating factor.

Abstract: G-CSF is an extremely well-known and well-characterized molecule. Both the natural glycosylated form and the E. coli-produced nonglycosylated form are biologically active. A thorough understanding of the primary, secondary, and tertiary structures has enabled a rational approach to purification, folding, and formulation. Although the product can be considered mature, and testing and development of the second-generation formulation are complete, chemical and physical analysis of the product continue. It is this continued effort to understand the chemistry and stability of the product that ensure a safe and efficacious molecule.

La production de l’espace

Abstract: An excerpt from the book by Henri Lefebvre introduces the basic principle of his theory and what is followed by explanations and implications. The main point -- space (social) is the product (social) -- is considered in the problematic vein. The author wonders about what hides this truth of (social) space, which consists in that it is the product (social). His response is -- a double illusion, each side of which suggests another, reinforce each, it is justified: first, the illusion of transparency, and second -- of density ("realistic" illusion). What follows is a detailed analysis of these illusions.

On the complexity of matrix product

Abstract: We prove a lower bound of Ω(m2 log m) for the size of any arithmetic circuit for the product of two matrices, over the real or complex numbers, as long as the circuit doesn't use products with field elements of absolute value larger than 1 (where mxm is the size of each matrix). That is, our lower bound is super-linear in the number of inputs and is applied for circuits that use addition gates, product gates and products with field elements of absolute value up to 1. More generally, for any c = c(m) ρ 1, we obtain a lower bound of Ω(m2 log2c m) for the size of any arithmetic circuit for the product of two matrices (over the real or complex numbers), as long as the circuit doesn't use products with field elements of absolute value larger than c. We also prove size-depth tradeoffs for such circuits.

M-fivebranes wrapped on supersymmetric cycles. II

Abstract: We construct $D=11$ supergravity solutions dual to the twisted field theories arising when M-theory fivebranes wrap supersymmetric cycles. The cases considered are M-fivebranes wrapped on (i) a complex Lagrangian four-cycle in a $D=8$ hyper-K\"ahler manifold corresponding to a $D=2$ field theory with (2,1) supersymmetry, (ii) a product of two holomorphic two-cycles in a product of two Calabi-Yau twofolds corresponding to a $D=2$ field theory with (2,2) supersymmetry, and (iii) a product of a holomorphic two-cycle and a special Lagrangian three-cycle in a product of a Calabi-Yau twofold and a Calabi-Yau threefold corresponding to a quantum mechanics with two supercharges. In each case we construct BPS equations and find IR superconformal fixed points corresponding to new examples of AdS/CFT duality arising from the twisted field theories.

Product order method and system

Abstract: Method with which a mobile user in a mobile network (4) can order products (1), with the following steps:recording an image corresponding to the product (1) to be ordered, linking the image data with a personal identification of the mobile user, transmitting the linked order message (31) to a server (5) in said mobile radio network (4), comparing said image data with images stored in a product database (50), each of said image in said database (50) being linked with an identification of the product provider (8), sending a message (52) containing an identification of the ordered product (1) and of the ordering mobile user to said product provider (8).

The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results

Abstract: We study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such models have been studied in physics as simple exemplars of systems exhibiting slow relaxation. In our “East” model the natural conjecture is that the relaxation time τ(p), that is 1/(spectral gap), satisfies log τ(p)∼\(\tfrac{{\log ^2 (1/p)}}{{\log 2}}\) as p↓0. We prove this up to a factor of 2. The upper bound uses the Poincare comparison argument applied to a “wave” (long-range) comparison process, which we analyze by probabilistic techniques. Such comparison arguments go back to Holley (1984, 1985). The lower bound, which atypically is not easy, involves construction and analysis of a certain “coalescing random jumps” process.

Canonical Symbolic Analysis of Large Analog Circuits with Determinant Decision Diagrams

Abstract: Symbolic analysis has many applications in the design of analog circuits. Existing approaches rely on two forms of symbolic-expression representation: expanded sum-of-product form and arbitrarily nested form. Expanded form suffers the problem that the number of product terms grows exponentially with the size of a circuit. Nested form is neither canonical nor amenable to symbolic manipulation. In this paper, we present a new approach to exact and canonical symbolic analysis by exploiting the sparsity and sharing of product terms. It consists of representing the symbolic determinant of a circuit matrix by a graph??-??called a determinant decision diagram (DDD)??-??and performing symbolic analysis by graph manipulations. We show that DDD construction, as well as many symbolic analysis algorithms, takes time almost linear in the number of DDD vertices. We describe an efficient DDD-vertex-ordering heuristic and prove that it is optimum for ladder-structured circuits. For practical analog circuits, the numbers of DDD vertices are several orders of magnitude less than the numbers of product terms. The algorithms have been implemented and compared respectively to symbolic analyzers ISAAC and Maple-V in generating the expanded sum-of-product expressions, and SCAPP in generating the nested sequences of expressions.

System and method of managing inventory

Abstract: An inventory management system and method which wirelessly interrogate product labels to determine inventory. The system includes an electronic price label system including electronic displays which display price information and interrogators which wirelessly obtain identification information from product labels, and a computer which receives first identification information from first product labels affixed to first instances of a product adjacent one of the electronic displays and one of the interrogators, determines a first amount of the product from the first identification information, receives second identification information from second product labels affixed to second instances of the product which have been sold, determines a second amount of the product from the second identification information, receives third identification information from third product labels affixed to third instances of the product adjacent the electronic price label, and determines a third amount of the product from the third identification information representing a current inventory amount.

Marketing and Sustainability

Abstract: 'Marketing and sustainability' is based on an original booklet written by Martin Charter in 1990. The text has been updated and re-written to take account of the changing and emerging debate of marketing’s role in relation to sustainable development. This booklet has been produced as a supporting publication for the Sustainable Marketing Knowledge Network (Smart: Know-Net) a web-based information and communication platform for marketers interested in sustainability, available at www.cfsd.org.uk/smart-know-net

Method and system for ultrasonic sealing of food product packaging

Abstract: A method and system for ultrasonic sealing of food product packaging is provided. The ultrasonic sealing system preferably includes a food product packaging-positioning system that delivers food product packaging and food product into direct on-item-packaging forming box (116). The direct on-item-packaging forming box (116) then receives the food product packaging (113) and forms it directly around the supplied food product (121) forming a partially packaged food product. The partially packaged food product is then ultrasonically edge sealed around the food product by an ultrasonic food product packaging fin-sealing unit (130) forming a partially sealed food product packaging. The partially sealed food product packaging then enters a food product packaging end-sealing unit (140) which ultrasonically seals and crimps the ends of the food product packaging resulting in a fully packaged and ultrasonically sealed food product (124).

Bayesian product recommendation engine

Abstract: The invention provides a method of generating a recommendation for a product type. A plurality of product attributes associated with the product type is provided. A sampled set of consumer values is received. At least one user preference corresponding to the product attributes is received. A plurality of consumer values based on the at least one user preference and the sample set of consumer values is calculated, and at least one product recommendation is determined based on the calculated consumer values.

Product‐centered processing: Manufacture of chemical‐based consumer products

Abstract: A systematic framework for product-centered processing is useful particularly in developing chemical-based consumer product manufacturing processes. The objective is to provide directions and guidelines toward the development of a process for manufacturing a product with the desired performance in reduced time and effort. The product performance, represented by several quality factors, is related to product ingredients and structural attributes, as well as the process flowsheet and operating conditions. The procedure consists of five steps. First, the product functionality, form, and packaging are defined. Second, relevant quality factors are identified. Third, necessary ingredients are selected and product microstructure is determined. Fourth, the manufacturing process is designed in light of the desired product properties. Limitations on achievable product quality are also identified. Finally, the product and process are evaluated with the help of experimental data. The framework is illustrated using industrial examples, including the production of dry toner, laundry detergent, shampoo, and cosmetic lotion.

Local L-Functions for Split Spinor Groups

Abstract: We study the local L-functions for Levi subgroups in split spinor groups defined via the Langlands-Shahidi method and prove a conjecture on their holomorphy in a half plane. These results have been used in the work of Kim and Shahidi on the functorial product for GL2 GL3.

Multiscale analysis and validation of the MODIS LAI product

Abstract: The development of appropriate ground-based validation techniques is critical to assessing uncertainties associated with satellite data-based products. In this paper, the second of a two-part series, we present a method for validation of the Moderate Resolution Imaging Spectroradiometer Leaf Area Index (MODIS LAI) product with emphasis on the sampling strategy for field data collection. Using a hierarchical scene model, we divided 30-m resolution LAI and NDVI images from Maun (Botswana), Harvard Forest (USA) and Ruokulahti Forest (Finland) into individual scale images of classes, region and pixel. Isolating the effects associated with different landscape scales through decomposition of semivariograms not only shows the relative contribution of different characteristic scales to the overall variation, but also displays the spatial structure of the different scales within a scene. We find that (1) patterns of variance at the class, region and pixel scale at these sites are different with respect to the dominance in order of the three levels of landscape organization within a scene; (2) the spatial structure of LAI shows similarity across the three sites, that is, ranges of semivariograms from scale of pixel, region and class are less than 1000 m. Knowledge gained from these analyses aids in formulation of sampling strategies for validation of biophysical products derived from moderate resolution sensors such as MODIS. For a homogeneous (within class) site, where the scales of class and region account for most of the spatial variation, a sampling strategy should focus more on using accurate land cover maps and selection of regions. However, for a heterogeneous (within class) site, accurate point measurements and GPS readings are needed.

Computing special values of motivic L-functions

Abstract: We present an algorithm to compute values L(s) and derivatives of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Gamma-factor is a product of any number of Gamma-functions Gamma((s+l(j))/2) with complex l(j), not necessarily distinct. The algorithm relies on the known (or conjectural) functional equation for L(s).