Product Space Research Articles

Decomposing dynamical subprocesses for compositional generalization

A striking feature of human cognition is an exceptional ability to rapidly adapt to novel situations. It is proposed this relies on abstracting and generalizing past experiences. While previous research has explored how humans detect and generalize single sequential processes, we have a limited understanding of how humans adapt to more naturalistic scenarios, for example, complex, multisubprocess environments. Here, we propose a candidate computational mechanism that posits compositional generalization of knowledge about subprocess dynamics. In two samples (N = 238 and N = 137), we combined a novel sequence learning task and computational modeling to ask whether humans extract and generalize subprocesses compositionally to solve new problems. In prior learning, participants experienced sequences of compound images formed from two graphs' product spaces (group 1: G1 and G2, group 2: G3 and G4). In transfer learning, both groups encountered compound images from the product of G1 and G3, composed entirely of new images. We show that subprocess knowledge transferred between task phases, such that in a new task environment each group had enhanced accuracy in predicting subprocess dynamics they had experienced during prior learning. Computational models utilizing predictive representations, based solely on the temporal contiguity of experienced task states, without an ability to transfer knowledge, failed to explain these data. Instead, behavior was consistent with a predictive representation model that maps task states between prior and transfer learning. These results help advance a mechanistic understanding of how humans discover and abstract subprocesses composing their experiences and compositionally reuse prior knowledge as a scaffolding for new experiences.

Agricultural economic complexity and regional inequalities: a new approach using census data from Brazil

ABSTRACT The paper presents an original application of economic complexity to the agricultural sector aiming to determine its suitability to measure and depict regional structural inequalities across Brazilian regions. Using census data, we calculate agricultural complexity indexes for products (PCI-Agro) and regions (ECI-Agro) and the agricultural product space. We show that higher PCI-Agro is associated with higher levels of productivity, education, income and human development. Also, we found that ECI-Agro is associated with higher productivity in agriculture. The econometric evidence points to an inverted ‘U’-shape curve relationship between ECI-Agro and agricultural productivity, which has significant policy implications.

The structure and dynamics of the auto parts industry: Product space and complexity perspectives

Economic structures are strong determinants of diversification, growth, innovation, inequality, and many other socio-economic outcomes; however, structural change's effect on specific industries remains unexplored. This study investigates Japan's automotive components industry, analyzing its productive structure (the auto parts product space) and structural change process. We develop exploratory and econometric analyses that unify the measures of product relatedness and complexity. The firm-level data analysis shows that specific structural properties in international and domestic economies also exist in the automobile industry. This fractal structure implies that common principles and regularities underlie the formation of productive structures, notwithstanding the economies’ size, maturity, and industrial scope differences. The exploratory and econometric analyses indicate that the events of a product's appearance are not random but are significantly contingent on the network topology of the product space. Furthermore, network topology significantly impacts the development of complex products with sophisticated capabilities.

Accelerating green growth: The effect of technological innovation on production capabilities spillovers in developing economies

This research addresses how technological innovation affects the spillovers of production capabilities into the green sectors in countries with developing economies. It examines the evolution of green production capabilities for 226 countries between 2003 and 2015 and identifies the key sectors driving the spillovers of production capabilities. It delves into the patterns observed in the evolution of these capabilities, considering the diverse economic classifications. Finally, it hones in on 72 developing countries that face unique challenges in their pursuit of green economic growth, exploring the effect of technological innovations on the spillovers of production capabilities into their green sectors. Using the ‘Green Sector Space’, an extension of the Product Space methodology, statistical analysis, and Partial Least Square Structural Equation Modeling, the findings of this analysis highlight significant disparities in green production capabilities in developing economies compared to other economic classifications. Additionally, the significant and dominant role non-green sectors have in driving the spillovers of production capabilities into the green sectors, demonstrating a significantly higher dominance observed in developing countries. Finally, the results underscore technological innovations’ significant and positive effect on the spillovers of production capabilities from non-green to green sectors in developing countries, which exhibits a path-dependent evolution pattern. Conversely, it does not have a significant effect on the spillovers between the green sectors. The findings address a gap in the literature by revealing the positive and significant effect of technological innovations on path-dependent green product development. This analysis recommends interventions in developing economies that heavily rely on non-green sectors to leverage technological innovations and diversify their green production capabilities for accelerated green growth.

Deconstruction of green product innovation drivers for regional export-oriented industrial enterprises in China: the product space perspective

Achieving green economic growth requires enterprises to develop and promote green products that balance environmental protection, intensive resource utilization, and sustainable development. However, under the externality assumption, the green market is often faced with the challenge of insufficient supply. Based on 2004–2018 panel data covering regional industrial enterprises in 30 provinces in China, this study empirically tests the composite driving mechanism of the effect of an increase in the regional green production capacity, organizational factors, and environmental policies on the green product innovation (GPI) of regional export-oriented industrial enterprises (REIEs). This study finds that the increase in regional green production capacity directly drives an improvement in REIEs’ GPI level, that the regional green technology level and degree of human capital accumulation are indirect driving channels between capacity increases and product innovation, and that environmental regulations and green credit have a positive moderating effect on the influence of increasing green production capacity on GPI. Further threshold regression analysis reveals that increasing green production capacity, foreign direct investment, digitization, and trade openness have an inverted U-shaped promoting effect on GPI and that the proportion of local government expenditure shows a diminishing marginal utility effect on GPI.

A duality and free boundary approach to adverse selection

Adverse selection is a version of the principal-agent problem that includes monopolist nonlinear pricing, where a monopolist with known costs seeks a profit-maximizing price menu facing a population of potential consumers whose preferences are known only in the aggregate. For multidimensional spaces of agents and products, Rochet and Choné (Econometrica, 1998) reformulated this problem as a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a quasilinear sensitivity to prices. We characterize solutions to this problem by identifying a dual minimization problem. This duality allows us to reduce the solution of the square example of Rochet–Choné to a novel free boundary problem, giving the first analytical description of an overlooked market segment.

Tensor product space for studying the interaction of bipartite states of light with nanostructures

Tensor product space for studying the interaction of bipartite states of light with nanostructures

Conditions for tractability of the weighted $$L_p$$-discrepancy and integration in non-homogeneous tensor product spaces

AbstractWe study tractability properties of the weighted $$L_p$$ L p -discrepancy, where the weights model the influence of different coordinates. A discrepancy is said to be tractable if the minimal number N of points, such that the discrepancy is less than the initial discrepancy times an error threshold $$\varepsilon $$ ε , does not grow exponentially fast with the dimension and $$\varepsilon ^{-1}$$ ε - 1 . In this case there are various notions of tractabilities used in order to classify the exact rate. In the present paper we prove matching sufficient conditions (upper bounds) and neccessary conditions (lower bounds) for polynomial and weak tractability for all $$p \in (1, \infty )$$ p ∈ ( 1 , ∞ ) and we prove a necessary condition for strong polynomial tractability. The proofs of the lower bounds are based on a powerful general result for the information complexity of integration with positive quadrature rules for tensor product spaces. As a second application of this general result we consider the integration of polynomials of degree at most 2.

On k-WUR and its generalizations

We introduce two notions called k-weakly uniform rotundity (k-WUR) and k-weakly locally uniform rotundity (k-WLUR) in real Banach spaces. These are natural generalizations of the well-known concepts k-UR and WUR. By introducing two best approximation notions namely k-weakly strong Chebyshevity and k-weakly uniform strong Chebyshevity, we generalize some of the existing results to k-WUR and k-WLUR spaces. In particular, we present characterizations of k-WUR spaces in terms of k-weakly uniformly strong Chebyshevness. Also, the inheritance of the notions k-WUR and k-WLUR by quotient spaces are discussed. Further, we provide a necessary and sufficient condition for an infinite l p -product space to be k-WUR (respectively, k-WLUR). As a consequence, we observe that the notions WUR and k-WUR coincide for an infinite l p -product of a Banach space.

On fuzzy inner products constructed by fuzzy numbers in linear spaces

In this paper a new definition for fuzzy inner product spaces is presented. Just as the set of real numbers can be embedded in a set of fuzzy numbers, a crisp inner product space can be considered as a special case of fuzzy inner product spaces. An example is given to demonstrate that, the new definition is a nontrivial generalization for the crisp inner product spaces. Under certain restrictions, a fuzzy inner product space can become a fuzzy normed space. Based on some elementary properties for the families of semi-inner products of endpoints, the linearly topological structure of new spaces is discussed. Moreover, the orthogonality between two vectors is considered and a fuzzy version of Pythagorean theorem is given.

Intractability results for integration in tensor product spaces

We prove lower bounds on the worst-case error of numerical integration in tensor product spaces. The information complexity is the minimal number N of function evaluations that is necessary such that the N-th minimal error is less than a factor ε times the initial error, i.e., the error for N=0, where ε belongs to (0,1). We are interested to which extent the information complexity depends on the number d of variables of the integrands. If the information complexity grows exponentially fast in d, then the integration problem is said to suffer from the curse of dimensionality.Under the assumption of the existence of a worst-case function for the uni-variate problem, we present two methods for providing lower bounds on the information complexity. The first method is based on a suitable decomposition of the worst-case function and can be seen as a generalization of the method of decomposable reproducing kernels. The second method, although only applicable for positive quadrature rules, does not require a suitable decomposition of the worst-case function. Rather, it is based on a spline approximation of the worst-case function and can be used for analytic functions. Several applications of both methods are presented.

On ((Τ ) ̃^*-N)^η-Fuzzy Soft Quasi Normal Operators

The concept of fuzzy soft sets is considered more versatile and widely applicable than traditional soft set theory, as the latter struggles to handle the fuzziness of problem parameters effectively. In this study, we introduce and describe the fuzzy soft quasinormal operator in a more concise manner. This operator is defined on a fuzzy soft Hilbert space, based on the notion of a fuzzy soft vector space, which has been adapted to an FS-inner product space in this work. We present various characterizations and results related to the fuzzy soft quasinormal operator, demonstrating that it serves as an appropriate example of FS-Hilbert spaces, alongside other related examples. Furthermore, we explore the relationships between these categories. Finally, we provide some fundamental guidelines on this topic.

Some Applications of Cauchy-Schwarz Inequality on Lightlike Warped Product Submanifolds

The well-known Cauchy-Schwarz inequality is a fundamental tool of analysis in Hilbert spaces. It is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is the most important and widely used inequalities in mathematics. We explore that inequality in case of lightlike warped product hypersurface of lorentzian space form to reach to the existence of minimal screen conformal lightlike hypersurface.

The phase space distance between collider events

How can one fully harness the power of physics encoded in relativistic N-body phase space? Topologically, phase space is isomorphic to the product space of a simplex and a hypersphere and can be equipped with explicit coordinates and a Riemannian metric. This natural structure that scaffolds the space on which all collider physics events live opens up new directions for machine learning applications and implementation. Here we present a detailed construction of the phase space manifold and its differential line element, identifying particle ordering prescriptions that ensure that the metric satisfies necessary properties. We apply the phase space metric to several binary classification tasks, including discrimination of high-multiplicity resonance decays or boosted hadronic decays of electroweak bosons from QCD processes, and demonstrate powerful performance on simulated data. Our work demonstrates the many benefits of promoting phase space from merely a background on which calculations take place to being geometrically entwined with a theory’s dynamics.

Research On the Application of Augmented Reality Technology in Cultural and Creative Products: Taking the Imperial Palace Calendar as An Example

In the context of Internet +, many emerging technologies are widely used in the field of cultural and creative products. Because of its interactive experience, fun and entertainment, function extension and other technical characteristics, augmented reality technology has become a bridge linking virtual and real world, and has brought a new idea for the innovation and development of cultural and creative products. Its advantage lies in the realization of real-time interaction, three-way registration, virtual reality interaction and other functional characteristics, so that cultural and creative products have the advantages of multi-dimensional information, user selective transmission, virtual reality interaction, improve product experience, break time and space restrictions, and expand product functionality. It has met the diversified and personalized consumption needs of consumers, and has become an important way for the innovation and development of cultural and creative products, subverting the development mode of traditional cultural and creative products. This paper analyzes the advantages of augmented reality technology in the application of cultural and creative products by taking the cultural and creative products of Beijing Palace Museum - the Palace Museum calendar as an example. This paper discusses how to use augmented reality technology to enhance the experience of cultural and creative products, including thematic, interactive and cultural aspects. Through in-depth exploration of cultural connotation and creative expression, we can create unique and attractive cultural and creative products, meet the needs of modern consumers, and promote the protection and inheritance of traditional Chinese culture.

Unveiling complementarities between mangrove restoration and global sustainable development goals

Indonesia, renowned as the most mangrove-rich nation, has committed to extensive mangrove restoration policies, but the effects of these policies have yet to be systematically evaluated. Our study conducts a comprehensive network analysis to investigate the synergies between mangrove restoration policy and global Sustainable Development Goals (SDGs) achievements by exploring their interactions. This investigation follows the ‘product space’ method in economics and creates the ‘Mangrove-SDG space’ to assess each metric pair's co-occurrence and comparative advantages with validated stability. Our analysis unveils a tripartite structure, encompassing socio-economic and environmental clusters, each significantly contributing to global sustainability and a distinctive mangrove cluster tied to land attributes. At the Goal level, mangrove loss showcases robust synergies with SDGs 12 (Responsible Consumption and Production) and 13 (Climate Change), and mangrove metrics such as tropical storm frequency and mangrove change, indicating strong interdependences between mangrove forests and SDGs. The result indicates that improved performance of climate change and responsible consumption can greatly enhance mangrove forests' performance in alleviating mangrove loss and reducing tropical storms. Moreover, our analysis underscores the central roles played by ‘bridge’ Goals. Indicator-level space details how they warrant prioritization because of their cascade synergistic enhancements across widely interconnected indicators, triggering systematic positive improvements. Turning to Indonesia, we advocate a strategic shift from solely expanding mangrove extent to focusing on four critical policy priorities: effective nitrogen management, enhancing Ramsar site efficiency, optimizing logistic performance, and addressing urban population conditions. These priorities are pivotal to seeking complementarities between Indonesia's international sustainability commitment and fostering mangrove restoration success.

How do smartphone users access the internet? An exploratory analysis of mobile web browser use

In this article, we use a top tasks survey ( n = 466) and unmoderated interviews ( n = 101) to explore how smartphone users access the internet: through browsers or standalone applications. We found a surprising number of users surveyed rely on mobile browsers to conduct internet-based tasks ordinarily associated with standalone apps, such as reading emails (34%), watching videos (24%), and listening to music (16%). Interviews revealed several practical and socioeconomic explanations for “browser-centric” smartphone use, including memory conservation on inexpensive mobile handsets and privacy management. We discuss the implications for information systems and technology adoption theories and for applied researchers who work in mobile product spaces.

On A-orthogonally diagonalizable operators on semi-inner product spaces

On A-orthogonally diagonalizable operators on semi-inner product spaces

On minimal surfaces in ℍ2 × ℝ space

Abstract A surface is minimal if the mean curvature ℋ mean {\mathcal{H}_{\rm mean}} vanishes everywhere. In this paper, we study some surfaces in the product space ℍ 2 × ℝ {\mathbb{H}^{2}\times\mathbb{R}} . In particular, we completely classify minimal surfaces.

Related technological density and regional industrial upgrading from perspective of product space theory: evidence from China

ABSTRACT When the product space theory is applied to study regional technology and industry evolution, both the theory exploitation and practical application are not comprehensive and detailed enough. This article traces the connotation of ‘density’ in the product space theory, explains the micro-foundation of regional industrial upgrading from a firm’s perspective, and abstracts industrial upgrading into four processes at two stages. Empirical research shows that an increase in related technological density (i.e. the average proximity of related technologies in a certain region) is beneficial for all processes of industrial upgrading. Marketization has a positive moderating effect on the static stage but a certain ‘counterproductive’ effect on the dynamic stage. Regional heterogeneity analysis shows that, on the whole, the industrial upgrading effect of the related technological density increase is relatively stronger on static processes but relatively weaker on dynamic processes in eastern China, and such results may be attributed to differences in regional resource dependence.