Narrow Results

We propose that the effective dimensionality of the space we live in depends on the length scale we are probing. As the length scale increases, new dimensions open up. At short scales the space is lower dimensional; at the intermediate scales the space is three-dimensional; and at large scales, the space is effectively higher dimensional. This setup allows for some fundamental problems in cosmology, gravity, and particle physics to be attacked from a new perspective. The proposed framework, among the other things, offers a new approach to the cosmological constant problem and results in striking collider phenomenology and may explain elongated jets observed in cosmic-ray data.

Online Analytical Processing, or OLAP, is an approach to answering multidimensional analytical (MDA) queries in an interactive way. However, the traditional OLAP approaches can only deal with structured data, but not unstructured textual data like tweets. To address this problem, we propose a Latent Dirichlet Allocation (LDA)-based model, called Multilayered Semantic LDA (MS-LDA), which detects the hidden layered interests from Twitter data based on LDA. The layered dimension of interests can be further used to apply OLAP techniques to Twitter data. Furthermore, MS-LDA employs the semantic similarity among words of tweets based on word2vec, and also the social relationship among twitters, to improve its effectiveness. The extensive experiments demonstrate that MS-LDA can effectively extract the dimension hierarchy of tweeters' interests for OLAP.

A new calculus based on fractal subsets of the real line is formulated. In this calculus, an integral of order α, 0 < α ≤ 1, called F^α-integral, is defined, which is suitable to integrate functions with fractal support F of dimension α. Further, a derivative of order α, 0 < α ≤ 1, called F^α-derivative, is defined, which enables us to differentiate functions, like the Cantor staircase, "changing" only on a fractal set. The F^α-derivative is local unlike the classical fractional derivative. The F^α-calculus retains much of the simplicity of ordinary calculus. Several results including analogues of fundamental theorems of calculus are proved.

The integral staircase function, which is a generalization of the functions like the Cantor staircase function, plays a key role in this formulation. Further, it gives rise to a new definition of dimension, the γ-dimension.

Spaces of F^α-differentiable and F^α-integrable functions are analyzed. Analogues of Sobolev Spaces are constructed on F and F^α-differentiability is generalized using Sobolev-like construction.

F^α-differential equations are equations involving F^α-derivatives. They can be used to model sublinear dynamical systems and fractal time processes, since sublinear behaviors are associated with staircase-like functions which occur naturally as their solutions. As examples, we discuss a fractal-time diffusion equation, and one-dimensional motion of a particle undergoing friction in a fractal medium.

Calculus on fractals, or F^α-calculus, developed in a previous paper, is a calculus based fractals F ⊂ R, and involves F^α-integral and F^α-derivative of orders α, 0 < α ≤ 1, where α is the dimension of F. The F^α-integral is suitable for integrating functions with fractal support of dimension α, while the F^α-derivative enables us to differentiate functions like the Cantor staircase. Several results in F^α-calculus are analogous to corresponding results in ordinary calculus, such as the Leibniz rule, fundamental theorems, etc. The functions like the Cantor staircase function occur naturally as solutions of F^α-differential equations. Hence the latter can be used to model processes involving fractal space or time, which in particular include a class of dynamical systems exhibiting sublinear behaviour.

In this paper we show that, as operators, the F^α-integral and F^α-derivative are conjugate to the Riemann integral and ordinary derivative respectively. This is accomplished by constructing a map ψ which takes F^α-integrable functions to Riemann integrable functions, such that the corresponding integrals on appropriate intervals have equal values. Under suitable conditions, a restriction of ψ also takes F^α-differentiable functions to ordinarily differentiable functions such that their values at appropriate points are equal. Further, this conjugacy is generalized to one between Sobolev spaces in ordinary calculus and F^α-calculus.

This conjugacy is useful, among other things, to find solutions to F^α-differential equations: they can be mapped to ordinary differential equations, and the solutions of the latter can be transformed back to get those of the former. This is illustrated with a few examples.

In this paper we classify non-commutative quadrics and study their homological properties. In fact we find all non-commutative algebras of degree 2 up to isomorphism and we study these algebras via their homomorphic images onto the polynomial algebra k[x,y] as well as the Ext¹(k(p), k(q))-groups, where k(p) and k(q) are one-dimensional simple modules. Moreover some general results on simple finite-dimensional modules are obtained. Some of these results are applied to the special cases of non-commutative quadrics.

In today's knowledge-based business, knowledge is the only source of competitive advantage for engineering industries. Knowledge sharing plays an important role in the success of knowledge management (KM). Knowledge sharing barriers (KSBs) become obstacles for KM to achieve the goals of the industries. In this paper, three categories of KSBs have been identified such as individual, organisational and technological. The main purpose of this research is to measure the effectiveness of individual, organisational and technological KSBs which helps the managers for taking decision to enhance the successful knowledge sharing strategy in the engineering industries. In this paper, an analytical network process (ANP) framework has been developed with the help of identified determinants, dimensions and enablers to evaluate the effectiveness of alternatives such as individual, organisational and technological KSBs. As per evaluation, the organisational KSBs have the maximum effect on knowledge sharing followed by technological and individual KSBs.

The software industry depends intensively on its actor’s knowledge to develop its products. This knowledge is crucial to leverage innovation and market sustainability within the software industry companies. Knowledge Management (KM) processes are accomplished in the small- and medium-sized software industry companies daily, however, sometimes not formally. This paper proposes a questionnaire aimed to diagnose KM in small- and medium-sized enterprises (SME) of the software industry, namely, KMD Quest-SW. The KMD Quest-SW was designed to fill up the gap of KM diagnosis in SME in the software industry. The KMD Quest-SW has 46 statements distributed in six dimensions: so-called creation process, registration process, knowledge sharing, knowledge use, innovation process, and knowledge in the software industry. From the software industry perspective, our proposal appears as a promising tool to diagnose and map the knowledge flow in SMEs. From a scientific perspective, the questionnaire breaks new grounds for KM theoretically and practitioners to be adapted for other SME companies interested in KM.

Over the last five years, Industry 4.0 (I4.0) has gained a lot of attention from industry leaders, policymakers, and government officials worldwide. In an era where new concepts and techniques are introduced continuously, there is a lack of systematic literature review (SLR) on identifying main dimensions, levels, methods to assess the maturity and readiness level toward I4.0. To address this gap, we have chosen our primary objective to provide a critical review of existing literature on dimensions, methods, levels, and current trends to evaluate the I4.0 maturity and readiness models. A Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) methodology was adopted to make sure that there is no replication and to maintain complete transparency in the review process. A total of 53 papers were deemed relevant for thematic analysis. From the literature, we have found and proposed 10 main dimensions — Strategy and Organization, Manufacturing and Operations, Supply Chain, Business Model, IT, People, Customers, Product, Services, and Culture, to assess the I4.0 maturity and readiness levels of an organization. Further, a conceptual framework was proposed for the same. This study contributes theoretically to the development of I4.0 maturity and readiness models. So far, this is the first review paper on dimensions of I4.0 maturity and readiness models and is expected to give future researchers and practitioners a holistic guideline to design and develop I4.0 maturity and readiness models.

Background: The terminal phalanx of the fingers carries the attachment of the Flexor Digitorum Profundus (FDP) on the volar surface and the extensor on the dorsal surface. Avulsion of these tendons has traditionally been repaired with pull-through sutures. Recently, bone anchor sutures have been found to be of comparable biomechanical strength but with the added advantage of technical ease and fewer complications. However, the dimensions of the bone, at the site of insertion of the anchors, have never been studied.

Methods: Following some cases of penetration of the dorsal cortex by the anchors, we measured the antero-posterior dimensions of the terminal phalanx in 251 digits from plain radiographs and compared these with the dimensions of the commonly used bone anchors. We also compared male and female digits.

Results: The anchors were oversized in 76% of index, 78% of ring and 100% of little fingers in the female population and in 49%, 44% and 97% of index, ring and little fingers respectively in the male population.

Conclusions: This analysis of bone dimensions can be a useful guide to surgeons in choosing the appropriate implant for flexor tendon avulsions.

Type systems can be used for tracking dimensional consistency of numerical computations: we present an extension from dimensions of scalar quantities to dimensions of vectors and matrices, making use of dependent types from programming language theory. We show that our types are unique, and most general. We further show that we can give straightforward dimensioned types to many common matrix operations such as addition, multiplication, determinants, traces, and fundamental row operations.

Since my early days, Science promised a universal method to explain everything, but university science with its inner contradictions left me bored. Ortega showed that science can fossilise and become superstition. The African tropical rainforest around 1963 and audacious new thinking together with young French scientists paved the way to my later analysis of living system hierarchies. The rainforest is a great debunker of arrogant scientists. Its plants and animals are countless, its inner subdivisions are not sharp, timing of events there is imprecise. In highly complex ecosystems no situation is recurrent. Hierarchical systems analysis, chaos theory and fuzzy logic, all of the 1960-ies, show the same way. Time is no factor, but an invisible dimension, a measuring stick, and visible space is 3D. Knowledge from foreign lands and from the past often sees reality as “more or less” defined, “elastic” (“jam karet”, rubber time, in Indonesian). Our neat science predicts correctly how stars move, but not epidemics or jobless periods, or tree growth. The dilemma of structure (3D) versus becoming (4D) always was central to human thought. It is met by two axioms defining an elastic universe with fractal dimensions. First, structure is a very slow process and process is a very short-lived structure. Second, due to a short life-span, humans can only perceive infinity if broken down, folded, refolded etc., a fractal image. These axioms and some rules derived yield a logically coherent image of the universe, inclusive of but broader than science as taught in schools today.