The Shapley-Folkman Theorem and the Range of a Bounded Measure: An Elementary and Unified Treatment

We present proofs, based on the Shapley-Folkman theorem, of the convexity of the range of a strongly continuous, finitely additive measure, as well as that of an atomless, countably additive measure. We also present proofs, based on diagonalization and separation arguments respectively, of the closure of the range of a purely atomic or purely nonatomic countably additive measure. A combination of these results yields Lyapunov's celebrated theorem on the range of a countably additive measure. We also sketch, through a comprehensive bibliography, the pervasive diversity of the applications of the Shapley-Folkman theorem in mathematical economics.

Exploiting the user interaction context for automatic task detection

Detecting the task a user is performing on her computer desktop is important for providing her with contextualized and personalized support. Some recent approaches propose to perform automatic user task detection by means of classifiers using captured user context data. In this paper we improve on that by using an ontology-based user interaction context model that can be automatically populated by (i) capturing simple user interaction events on the computer desktop and (ii) applying rule-based and information extraction mechanisms. We present evaluation results from a large user study we have carried out in a knowledge-intensive business environment, showing that our ontology-based approach provides new contextual features yielding good task detection performance. We also argue that good results can be achieved by training task classifiers `online' on user context data gathered in laboratory settings. Finally, we isolate a combination of contextual features that present a significantly better discriminative power than classical ones

A Philosophy of Mutuality in Martin Buber\u27s Writings--Implications for Mainstreaming

The study suggests a relationship which exists between Martin Buber\u27s philosophy of mutuality and a humanistic educational mainstreaming. Mandated by parent-initiated legislation, mainstreaming is intended to reduce the isolation of the handicapped by including them as nearly as possible within the larger group in the regular class, and by giving them greater access to educational resources. This becomes problematic even for those handicapped children in nearest physical proximity. Among the obstacles are society\u27s frequent exclusionist response to the different reflected in the school\u27s preference for homogeneity, and the ideas of competition which dominate education. The literature indicates that mainstreaming in its present stage is largely a one-sided effort to change the handicapped through individual remedial instruction. There is less evidence suggesting a substantial coinciding effort to make the structure of the regular class conducive to their inclusion. In the introductory chapter, a need is proposed to develop such a structure, to clarify how any child, not only the handicapped, may be educated as an individual by strengthening the bonds of human contact. Once the essential human relational element is defined, special methods and techniques can be brought to serve it. Buber\u27s thought is relevant to this problem, since his concern was for the humanization of the modern institution by means of the growth of mutuality between its members. Therefore, the various aspects of mutuality as indicated in his writings are researched and applied to mainstreaming. Biographical information reveals Buber’s attentiveness to the phenomena of human difference and communication between the different. Chapter III states that there is a potentiality in all human beings which can be actualized through mutual relation. The components of mutuality, namely, uniqueness, awareness, responsibility, and others are studied. A bond of mutuality exists between two persons engaged in spontaneous communication when they have become presences, each for the other. It is only when each becomes aware of the other\u27s presence as a whole, and as a unique person of equal worth, and responds as a whole person on that basis, that mutuality can be established. Based on a Jewish w^rld affirming tradition and his philosophical anthropology, Buber attributes to all people the capacity to enter into mutuality. The second basic human relation is the partial and detached perception of the other as an object which can be categorized, used, and even changed. In the remaining chapters, Buber\u27s evolutionary view of education is presented as a conscious experiment toward equity and humaneness. The greatness of the genuine teacher is seen in an Impartial, yet personal involvement with pupils which imbues them with courage and enables a confirming relation to their world. Hence, Buber advocates strong participatory roles for the teacher and child. Kis goal of character education Is fostered in the community of achievement founded on mutuality between children in their common learning pursuit. Community provides a sense of belonging, educates to responsibility, and it is the essential bearer of knowledge. The teacher helps pupils to experience their world of people subjectively, and helps them to see the unity behind the diversity of aspects. This presupposes an objectivity which sets limits to biases, an openness to the facts and how they interrelate by which prejudice is replaced with a realistic value judgment. Individual experience is not weakened, rather it is enriched by differing experience. This epistemology links to an openness to humanity, an integrative perception of the world, and an independent world view. The conclusions emphasize quality education as generalizable to all students; education as inclusive; education as conscious and willed; education for community; and education for uniqueness defined by awareness and responsible service

A Philosophy of Mutuality in Martin Buber\u27s Writings--Implications for Mainstreaming

The study suggests a relationship which exists between Martin Buber\u27s philosophy of mutuality and a humanistic educational mainstreaming. Mandated by parent-initiated legislation, mainstreaming is intended to reduce the isolation of the handicapped by including them as nearly as possible within the larger group in the regular class, and by giving them greater access to educational resources. This becomes problematic even for those handicapped children in nearest physical proximity. Among the obstacles are society\u27s frequent exclusionist response to the different reflected in the school\u27s preference for homogeneity, and the ideas of competition which dominate education. The literature indicates that mainstreaming in its present stage is largely a one-sided effort to change the handicapped through individual remedial instruction. There is less evidence suggesting a substantial coinciding effort to make the structure of the regular class conducive to their inclusion. In the introductory chapter, a need is proposed to develop such a structure, to clarify how any child, not only the handicapped, may be educated as an individual by strengthening the bonds of human contact. Once the essential human relational element is defined, special methods and techniques can be brought to serve it. Buber\u27s thought is relevant to this problem, since his concern was for the humanization of the modern institution by means of the growth of mutuality between its members. Therefore, the various aspects of mutuality as indicated in his writings are researched and applied to mainstreaming. Biographical information reveals Buber’s attentiveness to the phenomena of human difference and communication between the different. Chapter III states that there is a potentiality in all human beings which can be actualized through mutual relation. The components of mutuality, namely, uniqueness, awareness, responsibility, and others are studied. A bond of mutuality exists between two persons engaged in spontaneous communication when they have become presences, each for the other. It is only when each becomes aware of the other\u27s presence as a whole, and as a unique person of equal worth, and responds as a whole person on that basis, that mutuality can be established. Based on a Jewish w^rld affirming tradition and his philosophical anthropology, Buber attributes to all people the capacity to enter into mutuality. The second basic human relation is the partial and detached perception of the other as an object which can be categorized, used, and even changed. In the remaining chapters, Buber\u27s evolutionary view of education is presented as a conscious experiment toward equity and humaneness. The greatness of the genuine teacher is seen in an Impartial, yet personal involvement with pupils which imbues them with courage and enables a confirming relation to their world. Hence, Buber advocates strong participatory roles for the teacher and child. Kis goal of character education Is fostered in the community of achievement founded on mutuality between children in their common learning pursuit. Community provides a sense of belonging, educates to responsibility, and it is the essential bearer of knowledge. The teacher helps pupils to experience their world of people subjectively, and helps them to see the unity behind the diversity of aspects. This presupposes an objectivity which sets limits to biases, an openness to the facts and how they interrelate by which prejudice is replaced with a realistic value judgment. Individual experience is not weakened, rather it is enriched by differing experience. This epistemology links to an openness to humanity, an integrative perception of the world, and an independent world view. The conclusions emphasize quality education as generalizable to all students; education as inclusive; education as conscious and willed; education for community; and education for uniqueness defined by awareness and responsible service

Chemoenzymatic Synthesis of Cryptophycin Anticancer Agents by an Ester Bond-Forming Non-ribosomal Peptide Synthetase Module

Cryptophycins (Crp) are a group of cyanobacterial depsipeptides with activity against drug-resistant tumors. Although they have been shown to be promising, further efforts are required to return these highly potent compounds to the clinic through a new generation of analogues with improved medicinal properties. Herein, we report a chemosynthetic route relying on themultifunctional enzyme CrpD-M2 that incorporates a 2-hydroxy acid moiety (unit D) into Crp analogues. CrpD-M2 is a unique nonribosomal peptide synthetase (NRPS) module comprised of condensation-adenylation-ketoreduction-thiolation (C-A-KR-T) domains. We interrogated A-domain 2-keto and 2-hydroxy acid activation and loading, and KR domain activity in the presence of NADPH and NADH. The resulting 2-hydroxy acid was elongated with three synthetic Crp chain elongation intermediate analogues through ester bond formation catalyzed by CrpD-M2 C domain. Finally, the enzyme-bound seco-Crp products were macrolactonized by the Crp thioesterase. Analysis of these sequential steps was enabled through LC-FTICR-MS of enzyme-bound intermediates and products. This novel chemoenzymatic synthesis of Crp involves four sequential catalytic steps leading to the incorporation of a 2-hydroxy acid moiety in the final chain elongation intermediate. The presented work constitutes the first example where a NRPS-embedded KR domain is employed for assembly of a fully elaborated natural product, and serves as a proof-of-principle for chemoenzymatic synthesis of new Crp analogues

On Large Games with a Bio-Social Typology

We present a comprehensive theory of large non-anonymous games in which agents have a name and a determinate social-type and/or biological trait to resolve the dissonance of a (matching-pennies type) game with an exact pure-strategy Nash equilibrium with finite agents, but without one when modeled on the Lebesgue unit interval. We (i) establish saturated player spaces as both necessary and sufficient for an existence result for Nash equilibrium in pure strategies, (ii) clarify the relationship between pure, mixed and behavioral strategies via the exact law of large numbers in a framework of Fubini extension, (iii) illustrate corresponding asymptotic results.

Membrane protein assembly patterns reflect selection for non-proliferative structures

AbstractMembrane proteins that regulate solute movement are often built from multiple copies of an identical polypeptide chain. These complexes represent striking examples of self-assembling systems that recruit monomers only until a prescribed level for function is reached. Here we report that three modes of assembly – distinguished by sequence and stoichiometry – describe all helical membrane protein complexes currently solved to high resolution. Using the 13 presently available non-redundant homo-oligomeric structures, we show that two of these types segregate with protein function: one produces energy-dependent transporters, while the other builds channels for passive diffusion. Given such limited routes to functional complexes, membrane proteins that self-assemble exist on the edge of aggregation, susceptible to mutations that may underlie human diseases