Towards an Interaction-based Integration of MKM Services into End-User Applications

The Semantic Alliance (SAlly) Framework, first presented at MKM 2012, allows integration of Mathematical Knowledge Management services into typical applications and end-user workflows. From an architecture allowing invasion of spreadsheet programs, it grew into a middle-ware connecting spreadsheet, CAD, text and image processing environments with MKM services. The architecture presented in the original paper proved to be quite resilient as it is still used today with only minor changes. This paper explores extensibility challenges we have encountered in the process of developing new services and maintaining the plugins invading end-user applications. After an analysis of the underlying problems, I present an augmented version of the SAlly architecture that addresses these issues and opens new opportunities for document type agnostic MKM services.Comment: 14 pages, 7 figure

The MMT API: A Generic MKM System

The MMT language has been developed as a scalable representation and interchange language for formal mathematical knowledge. It permits natural representations of the syntax and semantics of virtually all declarative languages while making MMT-based MKM services easy to implement. It is foundationally unconstrained and can be instantiated with specific formal languages. The MMT API implements the MMT language along with multiple backends for persistent storage and frontends for machine and user access. Moreover, it implements a wide variety of MMT-based knowledge management services. The API and all services are generic and can be applied to any language represented in MMT. A plugin interface permits injecting syntactic and semantic idiosyncrasies of individual formal languages.Comment: Conferences on Intelligent Computer Mathematics (CICM) 2013 The final publication is available at http://link.springer.com

Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed. Views interconnect these developments and establish that the axiomatizations are equivalent in the sense of being mutually interpretable. A realm also contains an external interface that is convenient for users of the library who want to apply the concepts and facts of the theory without delving into the details of how the concepts and facts were developed. We illustrate the utility of realms through a series of examples. We also give an outline of the mechanisms that are needed to create and maintain realms.Comment: As accepted for CICM 201

A Universal Machine for Biform Theory Graphs

Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages and emphasize computation. Combining the complementary strengths of both approaches while mending their complementary weaknesses has been an important goal of the mechanized mathematics community for some time. We pick up on the idea of biform theories and interpret it in the MMTt/OMDoc framework which introduced the foundations-as-theories approach, and can thus represent both logics and programming languages as theories. This yields a formal, modular framework of biform theory graphs which mixes specifications and implementations sharing the module system and typing information. We present automated knowledge management work flows that interface to existing specification/programming tools and enable an OpenMath Machine, that operationalizes biform theories, evaluating expressions by exhaustively applying the implementations of the respective operators. We evaluate the new biform framework by adding implementations to the OpenMath standard content dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final publication is available at http://link.springer.com

Which one is better: presentation-based or content-based math search?

Mathematical content is a valuable information source and retrieving this content has become an important issue. This paper compares two searching strategies for math expressions: presentation-based and content-based approaches. Presentation-based search uses state-of-the-art math search system while content-based search uses semantic enrichment of math expressions to convert math expressions into their content forms and searching is done using these content-based expressions. By considering the meaning of math expressions, the quality of search system is improved over presentation-based systems

Fostering Intrapreneurship through the Implementation of Internal Corporate Accelerators

Today’s markets are characterized by fast and radical changes, posing an essential challenge to established companies. Startups, yet, seem to be more capable in developing radical innovations to succeed in those volatile markets. Thus, established companies started to experiment with various approaches to implement startup-like structures in their organization. Internal corporate accelerators (ICAs) are a novel form of corporate venturing, aiming to foster bottom-up innovations through intrapreneurship. However, ICAs still lack empirical investigations. This work contributes to a deeper understanding of the interface between the ICA and the core organization and the respective support activities (resource access and support services) that create an innovation-supportive work environment for the intrapreneurial team. The results of this qualitative study, comprising 12 interviews with ICA teams out of two German high-tech companies, show that the resources provided by ICAs differ from the support activities of external accelerators. Further, the study shows that some resources show both supportive as well as obstructive potential for the intrapreneurial teams within the ICA

Formalizing Mathematical Knowledge as a Biform Theory Graph: A Case Study

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory graph is a network of theories connected by meaning-preserving theory morphisms that map the formulas of one theory to the formulas of another theory. Theory graphs are in turn well suited for formalizing mathematical knowledge at the most convenient level of abstraction using the most convenient vocabulary. We are interested in the problem of whether a body of mathematical knowledge can be effectively formalized as a theory graph of biform theories. As a test case, we look at the graph of theories encoding natural number arithmetic. We used two different formalisms to do this, which we describe and compare. The first is realized in ${\rm CTT}_{\rm uqe}$, a version of Church's type theory with quotation and evaluation, and the second is realized in Agda, a dependently typed programming language.Comment: 43 pages; published without appendices in: H. Geuvers et al., eds, Intelligent Computer Mathematics (CICM 2017), Lecture Notes in Computer Science, Vol. 10383, pp. 9-24, Springer, 201

A Novel SALL4/OCT4 Transcriptional Feedback Network for Pluripotency of Embryonic Stem Cells

Background: SALL4 is a member of the SALL gene family that encodes a group of putative developmental transcription factors. Murine Sall4 plays a critical role in maintaining embryonic stem cell (ES cell) pluripotency and self-renewal. We have shown that Sall4 activates Oct4 and is a master regulator in murine ES cells. Other SALL gene members, especially Sall1 and Sall3 are expressed in both murine and human ES cells, and deletions of these two genes in mice lead to perinatal death due to developmental defects. To date, little is known about the molecular mechanisms controlling the regulation of expressions of SALL4 or other SALL gene family members. Methodology/Principal Findings: This report describes a novel SALL4/OCT4 regulator feedback loop in ES cells in balancing the proper expression dosage of SALL4 and OCT4 for the maintenance of ESC stem cell properties. While we have observed that a positive feedback relationship is present between SALL4 and OCT4, the strong self-repression of SALL4 seems to be the “break” for this loop. In addition, we have shown that SALL4 can repress the promoters of other SALL family members, such as SALL1 and SALL3, which competes with the activation of these two genes by OCT4. Conclusions/Significance: Our findings, when taken together, indicate that SALL4 is a master regulator that controls its own expression and the expression of OCT4. SALL4 and OCT4 work antagonistically to balance the expressions of other SALL gene family members. This novel SALL4/OCT4 transcription regulation feedback loop should provide more insight into the mechanism of governing the “stemness” of ES cells

SALL4 Expression in Gonocytes and Spermatogonial Clones of Postnatal Mouse Testes

The spermatogenic lineage is established after birth when gonocytes migrate to the basement membrane of seminiferous tubules and give rise to spermatogonial stem cells (SSC). In adults, SSCs reside within the population of undifferentiated spermatogonia (Aundiff) that expands clonally from single cells (Asingle) to form pairs (Apaired) and chains of 4, 8 and 16 Aaligned spermatogonia. Although stem cell activity is thought to reside in the population of Asingle spermatogonia, new research suggests that clone size alone does not define the stem cell pool. The mechanisms that regulate self-renewal and differentiation fate decisions are poorly understood due to limited availability of experimental tools that distinguish the products of those fate decisions. The pluripotency factor SALL4 (sal-like protein 4) is implicated in stem cell maintenance and patterning in many organs during embryonic development, but expression becomes restricted to the gonads after birth. We analyzed the expression of SALL4 in the mouse testis during the first weeks after birth and in adult seminiferous tubules. In newborn mice, the isoform SALL4B is expressed in quiescent gonocytes at postnatal day 0 (PND0) and SALL4A is upregulated at PND7 when gonocytes have colonized the basement membrane and given rise to spermatogonia. During steady-state spermatogenesis in adult testes, SALL4 expression overlapped substantially with PLZF and LIN28 in Asingle, Apaired and Aaligned spermatogonia and therefore appears to be a marker of undifferentiated spermatogonia in mice. In contrast, co-expression of SALL4 with GFRα1 and cKIT identified distinct subpopulations of Aundiff in all clone sizes that might provide clues about SSC regulation. Collectively, these results indicate that 1) SALL4 isoforms are differentially expressed at the initiation of spermatogenesis, 2) SALL4 is expressed in undifferentiated spermatogonia in adult testes and 3) SALL4 co-staining with GFRα1 and cKIT reveals distinct subpopulations of Aundiff spermatogonia that merit further investigation. © 2013 Gassei, Orwig

The effect of a worldwide tax system on tax management of foreign subsidiaries

Under a worldwide tax system, firms pay taxes on their domestic income and repatriated foreign income, whereas under a territorial tax system repatriated foreign income is exempt from taxation. We examine whether worldwide tax systems reduce the incentives of multinational corporations to engage in tax management in their foreign subsidiaries. Using two quasi-natural experiments, we show that multinationals lower the effective tax rates in their foreign subsidiaries after countries switch from a worldwide to a territorial tax system. Thus, multinationals subject to a worldwide tax system face competitive disadvantages compared to competitors from countries with a territorial tax system