An octonion algebra originating in combinatorics

C.H. Yang discovered a polynomial version of the classical Lagrange identity expressing the product of two sums of four squares as another sum of four squares. He used it to give short proofs of some important theorems on composition of delta-codes (now known as T-sequences). We investigate the possible new versions of his polynomial Lagrange identity. Our main result shows that all such identities are equivalent to each other.Comment: 11 pages, A simpler proof of the main theorem, due to Alberto Elduque, is inserted. The paper will appear in the Proc. Amer. Math. So

Symmetric Hadamard matrices of orders 268, 412, 436 and 604

We construct many symmetric Hadamard matrices of small order by using the so called propus construction. The necessary difference families are constructed by restricting the search to the families which admit a nontrivial multiplier. Our main result is that we have constructed, for the first time, symmetric Hadamard matrices of order 268, 412, 436 and 604.Comment: 12 page

Construction of symmetric Hadamard matrices of order 4v4v for v=47,73,113v=47,73,113

We continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders $4v$ with odd $v\le41$. In this paper we cover the cases $v=43,45,47,49,51$. The odd integers $v<120$ for which no symmetric Hadamard matrices of order $4v$ are known are the following: $$47,59,65,67,73,81,89,93,101,103,107,109,113,119.$$ By using the propus construction, we found several symmetric Hadamard matrices of order $4v$ for $v=47,73,113$.Comment: 16 pages, 3 figures, 1 tabl

Baryonic Generating Functions

We show how it is possible to use the plethystic program in order to compute baryonic generating functions that count BPS operators in the chiral ring of quiver gauge theories living on the world volume of D branes probing a non compact CY manifold. Special attention is given to the conifold theory and the orbifold C^2/Z_2 times C, where exact expressions for generating functions are given in detail. This paper solves a long standing problem for the combinatorics of quiver gauge theories with baryonic moduli spaces. It opens the way to a statistical analysis of quiver theories on baryonic branches. Surprisingly, the baryonic charge turns out to be the quantized Kahler modulus of the geometry.Comment: 44 pages, 7 figures; fonts change

SQCD: A Geometric Apercu

We take new algebraic and geometric perspectives on the old subject of SQCD. We count chiral gauge invariant operators using generating functions, or Hilbert series, derived from the plethystic programme and the Molien-Weyl formula. Using the character expansion technique, we also see how the global symmetries are encoded in the generating functions. Equipped with these methods and techniques of algorithmic algebraic geometry, we obtain the character expansions for theories with arbitrary numbers of colours and flavours. Moreover, computational algebraic geometry allows us to systematically study the classical vacuum moduli space of SQCD and investigate such structures as its irreducible components, degree and syzygies. We find the vacuum manifolds of SQCD to be affine Calabi-Yau cones over weighted projective varieties.Comment: 49 pages, 1 figur

Creating university spin-offs: A science-based design perspective

Academic entrepreneurship by means of university spin-offs commercializes technological breakthroughs, which may otherwise remain unexploited. However, many universities face difficulties in creating spin-offs. This article adopts a science-based design approach to connect scholarly research with the pragmatics of effectively creating university spin-offs. This approach serves to link the practice of university spin-off creation, via design principles, to the scholarly knowledge in this area. As such, science-based design promotes the interplay between emergent and deliberate design processes. This framework is used to develop a set of design principles that are practice based as well as grounded in the existing body of research on university spin-offs. A case-study of spin-off creation at a Dutch university illustrates the interplay between initial processes characterized by emergent design and the subsequent process that was more deliberate in nature. This case study also suggests there are two fundamentally different phases in building capacity for university spin-off creation. First, an infrastructure for spin-off creation (including a collaborative network of investors, managers and advisors) is developed that then enables support activities to individual spin-off ventures. This study concludes that to build and increase capacity for creating spin-offs, universities should do the following: (1) create university-wide awareness of entrepreneurship opportunities, stimulate the development of entrepreneurial ideas, and subsequently screen entrepreneurs and ideas by programs targeted at students and academic staff; (2) support start-up teams in composing and learning the right mix of venturing skills and knowledge by providing access to advice, coaching, and training; (3) help starters in obtaining access to resources and developing their social capital by creating a collaborative network organization of investors, managers, and advisors; (4) set clear and supportive rules and procedures that regulate the university spin-off process, enhance fair treatment of involved parties, and separate spin-off processes from academic research and teaching; and (5) shape a university culture that reinforces academic entrepreneurship by creating norms and exemplars that motivate entrepreneurial behavior. These and other results of this study illustrate how science-based design can connect scholarly research to the pragmatics of actually creating spin-offs in academic institutions

On the Black-Hole/Qubit Correspondence

The entanglement classification of four qubits is related to the extremal black holes of the 4-dimensional STU model via a time-like reduction to three dimensions. This correspondence is generalised to the entanglement classification of a very special four-way entanglement of eight qubits and the black holes of the maximally supersymmetric N = 8 and exceptional magic N = 2 supergravity theories.Comment: 32 pages, very minor changes at the start of Sec. 4.1. Version to appear in The European Physical Journal - Plu

Hysteroscopic Myomectomy: the Guidelines of the International Society for Gynecologic Endoscopy (ISGE)

Objective: With this publication, the International Society for Gynecologic Endoscopy (ISGE) aims to provide the clinicians with the recommendations arising from the best evidence currently available on hysteroscopic myomectomy (HM). Study design: The ISGE Task Force for HM defined key clinical questions, which led the search of Medline/PubMed and the Cochrane Database. We selected and analyzed relevant English-language articles, published from January 2005 to June 2021, including original works, reviews and the guidelines previously published by the European Society for Gynecological Endoscopy (ESGE) and the American Association of Gynecologic Laparoscopists (AAGL), in which bibliographies were also checked in order to identify additional references, using the medical subject heading (MeSH) term "Uterine Myomectomy" (MeSH Unique ID: D063186) in combination with ''Myoma" (MeSH Unique ID: D009214) and ''Hysteroscopy" (MeSH Unique ID: D015907). We developed the recommendations through multiple cycles of literature analysis and expert discussion. Results: The ISGE Task Force did develop 10 grade 1A-C and 4 grade 2A-C recommendations. For planning HM, evaluation of the uterus with saline infusion sonohysterography (SIS) or combined assessment by transvaginal ultrasound (TVUS) and diagnostic hysteroscopy is recommended (Grade 1A). The use of STEPW (Size, Topography, Extension of the base, Penetration and lateral Wall position) classification system of submucosal leiomyoma (LM) is recommended to predict the complex surgeries, incomplete removal of the LM, long operative time, fluid overload and other major complications (grade 1B). For type 0 LMs, in addition to resectoscopy (slicing technique), morcellation is recommended, being faster and having a shorter learning curve with respect to resectoscopy (grade 1C). For type 1-2 LMs, slicing technique is currently recommended (grade 1C). A fluid deficit of 1000 mL also in case of bipolar myomectomy with saline solution, in healthy women of reproductive age, contains low risk for major complications. Lower thresholds (750 mL) for fluid deficit should be considered in the elderly and in women with cardiovascular, renal or other co-morbidities (Grade 1B). Conclusion: HM is the most effective conservative minimally invasive gynecologic intervention for submucous LM. The set of 14 ISGE recommendations can significantly contribute to the success of HM and the safety of patients for whom the choice of appropriate surgical technique, as well as the surgeon's awareness and measures to prevent complications are of the utmost importance.info:eu-repo/semantics/publishedVersio