Canonical characters on quasi-symmetric functions and bivariate Catalan numbers

Every character on a graded connected Hopf algebra decomposes uniquely as a product of an even character and an odd character (Aguiar, Bergeron, and Sottile, math.CO/0310016). We obtain explicit formulas for the even and odd parts of the universal character on the Hopf algebra of quasi-symmetric functions. They can be described in terms of Legendre's beta function evaluated at half-integers, or in terms of bivariate Catalan numbers: $$C(m,n)=\frac{(2m)!(2n)!}{m!(m+n)!n!}.$$ Properties of characters and of quasi-symmetric functions are then used to derive several interesting identities among bivariate Catalan numbers and in particular among Catalan numbers and central binomial coefficients

Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras

We develop a theory of multigraded (i.e., $N^l$-graded) combinatorial Hopf algebras modeled on the theory of graded combinatorial Hopf algebras developed by Aguiar, Bergeron, and Sottile [Compos. Math. 142 (2006), 1--30]. In particular we introduce the notion of canonical $k$-odd and $k$-even subalgebras associated with any multigraded combinatorial Hopf algebra, extending simultaneously the work of Aguiar et al. and Ehrenborg. Among our results are specific categorical results for higher level quasisymmetric functions, several basis change formulas, and a generalization of the descents-to-peaks map.Comment: 49 pages. To appear in the Journal of Algebraic Combinatoric

My Son, Listen to the Instruction of Your Father : An Analysis of How the Father’s Rhetoric in Proverbs 1-7 Continues and Climaxes in Proverbs 8-9

Liu, Hsiao-Yung (Samuel) My Son, Listen to the Instruction of Your Father: An Analysis of How the Father Rhetoric in Proverbs 1-7 Continues and Climaxes in Proverbs 8-9. Ph.D. diss., Concordia Seminary, 2007. 200 pp. This dissertation proposes the thesis that the father\u27s rhetoric in Prov 1-7 continues and climaxes in Prov 8-9, thus supporting the unity of Prov 1-9. Although diverse voices and genres make the reading of Prov 1-9 difficult, there still exists the unifying perspective of the implied speaker in the text, which is the father\u27s rhetoric, Therefore, assuming that one single author or editor completed the current text in Prov 1- 9, this investigation proposes that the Sitz im Leben of the text is family and the speaker is a father, whose rhetoric is the key to a unified reading of Proverbs 1-9. That is, the same person who says directly in the fatherly discourses, My son, listen to the instruction of your father (Prov 1:8; see also 2:1; 3:1; 3:21; 4:10, 20; 5:1; 6:1; 6:20; 7:1) is also the one using the wisdom poems of Proverbs 8-9 to communicate indirectly. In other words, this speaking father uses the figure of personified Wisdom in Prov 8-9 as the rhetorical/imagery device to continue and to climax what he has said in the previous discourses (Prov 1-7) so that the speaker obtains a stronger rhetorical/ persuasive effect upon the listener (the listening son) and makes him listen/obey. In order to find a unity in the text, scholars try to fill the gap made by the difference/ discontinuity of the father\u27s voice (Prov 1-7) and wisdom\u27s voice (Prov 8-9), providing different interpretations in the structure and reading of the text. To explain how the continuity and climax are set up, this study examines the work of both form-redactional critics and feminist critics on Proverbs 1-9. While both offer interesting insights, neither deals adequately with the challenges of the text, particularly in the area of discontinuity ( e.g., the discontinuity existing between the fatherly discourses [Prov 1-7] and the wisdom poems [Prov 8-9]). Responding to the discontinuity and dialoguing with these two methods, this study employs rhetorical criticism to demonstrate how the father\u27s rhetoric in Prov 1-7 continues and climaxes in Prov 8-9, thus creating a unity within the nine chapters. In the content of the dissertation, this study will argue the thesis step by step. Chapter 1 provides a general introduction concerning the setting, assumption, rationale, demarcation and outlines of this dissertation. Chapter 2 gives an overview of the secondary literature regarding form-redactional and feminist criticism, showing how these studies are able to explain the text and structure but are inadequate to approach Prov 1-7 and 8-9 holistically. Chapter 3 is the introduction to the methodology that this study follows. This study uses rhetorical criticism to help prove its thesis. Chapter 4 demonstrates the rhetorical strategies concerning how this study develops the rationale in this thesis. Chapter 5 investigates the structure and content arrangement of the father\u27s rhetoric in the compositional dimension, in which symmetry and repetition are the two principles used to investigate the inclusio, center, chiasmus, contrast, and climax of the text. Chapter 6 deals with the persuasive dimension, particularly with the stylistic elements, the speaker\u27s ethos, the listener\u27s pathos and imagery devices. Chapter 7 presents the conclusions of this study based on all that has gone before. The thesis that the father\u27s rhetoric in Prov 1-7 continues and climaxes in Prov 8-9 will be confirmed

Comparative Study on the Effects of Noise in ML-Based Anxiety Detection

Wearable health devices are ushering in a new age of continuous and noninvasive remote monitoring. One application of this technology is in anxiety detection. Many advancements in anxiety detection have happened in controlled lab settings, but noise prevents these advancements from generalizing to real-world conditions. We seek to progress the field by studying how noise impacts model performance and developing models that are robust to noisy, real-world conditions and, hence, attuned to the commotion of everyday life. In this study we look to investigate why and how previous methods have failed. Using the wearable stress and affect detection (WESAD) dataset, we compare the effect of various intensities of noise on machine learning models classifying levels of physiological arousal in the three-class classification problem: baseline vs. stress vs. amusement. Before introducing noise, our baseline model performance reaches 98.7%, compared to Schmidt 2018's 80.3%. We discuss potential sources of this discrepancy in results through a careful evaluation of feature extraction and model architecture choices. Finally, after the introduction of noise, we provide a thorough analysis of the effect of noise on each model architecture

OPTIMAL INBOUND/OUTBOUND PRICING MODEL FOR REMANUFACTURING IN A CLOSED-LOOP SUPPLY CHAIN

The paper presents a model for optimizing inbound and outbound pricing for closed-loop supply chains that remanufacture reusable products. Remanufacturers create reusable products from returned used products and sell the products “as new” to manufacturers or consumers. By implementing a return subsidy, remanufacturers can encourage the consumer to return used products. Demand for the as-new components often depends on the selling price and inventory. The available inventory increases as the subsidy increases and as the price decreases. Our model can determine the optimal subsidy and selling price for used and remanufactured products, respectively. Our model uses the Karush–Kuhn–Tucker conditions to solve its nonlinear problem. Sensitivity analysis reveals how different parameters affect profit under model-optimized conditions

Tankyrase 1 and Tankyrase 2 Are Essential but Redundant for Mouse Embryonic Development

Tankyrases are proteins with poly(ADP-ribose) polymerase activity. Human tankyrases post-translationally modify multiple proteins involved in processes including maintenance of telomere length, sister telomere association, and trafficking of glut4-containing vesicles. To date, however, little is known about in vivo functions for tankyrases. We recently reported that body size was significantly reduced in mice deficient for tankyrase 2, but that these mice otherwise appeared developmentally normal. In the present study, we report generation of tankyrase 1-deficient and tankyrase 1 and 2 double-deficient mice, and use of these mutant strains to systematically assess candidate functions of tankyrase 1 and tankyrase 2 in vivo. No defects were observed in development, telomere length maintenance, or cell cycle regulation in tankyrase 1 or tankyrase 2 knockout mice. In contrast to viability and normal development of mice singly deficient in either tankyrase, deficiency in both tankyrase 1 and tankyrase 2 results in embryonic lethality by day 10, indicating that there is substantial redundancy between tankyrase 1 and tankyrase 2, but that tankyrase function is essential for embryonic development