On two unimodal descent polynomials

The descent polynomials of separable permutations and derangements are both demonstrated to be unimodal. Moreover, we prove that the $\gamma$-coefficients of the first are positive with an interpretation parallel to the classical Eulerian polynomial, while the second is spiral, a property stronger than unimodality. Furthermore, we conjecture that they are both real-rooted.Comment: 16 pages, 4 figure

Boundary Algebra: A Simple Notation for Boolean Algebra and the Truth Functors

Boundary algebra [BA] is a simpler notation for Spencer-Brown’s (1969) primary algebra [pa], the Boolean algebra 2, and the truth functors. The primary arithmetic [PA] consists of the atoms ‘()’ and the blank page, concatenation, and enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction. Inserting letters denoting the presence or absence of () into a PA formula yields a BA formula. The BA axioms are "()()=()" (A1), and "(()) [=?] may be written or erased at will” (A2). Repeated application of these axioms to a PA formula yields a member of B= {(),?} called its simplification. (a) has two intended interpretations: (a) ? a? (Boolean algebra 2), and (a) ? ~a (sentential logic). BA is self-dual: () ? 1 [dually 0] so that B is the carrier for 2, ab ? a?b [a?b], and (a)b [(a(b))] ? a=b, so that ?=() [()=?] follows trivially and B is a poset. The BA basis abc= bca (Dilworth 1938), a(ab)= a(b), and a()=() (Bricken 2002) facilitates clausal reasoning and proof by calculation. BA also simplifies normal forms and Quine’s (1982) truth value analysis. () ? true [false] yields boundary logic.G. Spencer Brown; boundary algebra; boundary logic; primary algebra; primary arithmetic; Boolean algebra; calculation proof; C.S. Peirce; existential graphs.

Boundary Algebra: A Simpler Approach to Boolean Algebra and the Sentential Connectives

Boundary algebra [BA] is a algebra of type , and a simplified notation for Spencer-Brown’s (1969) primary algebra. The syntax of the primary arithmetic [PA] consists of two atoms, () and the blank page, concatenation, and enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction. Inserting letters denoting, indifferently, the presence or absence of () into a PA formula yields a BA formula. The BA axioms are A1: ()()= (), and A2: “(()) [abbreviated ‘⊥’] may be written or erased at will,” implying (⊥)=(). The repeated application of A1 and A2 simplifies any PA formula to either () or ⊥. The basis for BA is B1: abc=bca (concatenation commutes & associates); B2, ⊥a=a (BA has a lower bound, ⊥); B3, (a)a=() (BA is a complemented lattice); and B4, (ba)a=(b)a (implies that BA is a distributive lattice). BA has two intended models: (1) the Boolean algebra 2 with base set B={(),⊥}, such that () ⇔ 1 [dually 0], (a) ⇔ a′, and ab ⇔ a∪b [a∩b]; and (2) sentential logic, such that () ⇔ true [false], (a) ⇔ ~a, and ab ⇔ a∨b [a∧b]. BA is a self-dual notation, facilitates a calculational style of proof, and simplifies clausal reasoning and Quine’s truth value analysis. BA resembles C.S. Peirce’s graphical logic, the symbolic logics of Leibniz and W.E. Johnson, the 2 notation of Byrne (1946), and the Boolean term schemata of Quine (1982).Boundary algebra; boundary logic; primary algebra; primary arithmetic; Boolean algebra; calculation proof; G. Spencer-Brown; C.S. Peirce; existential graphs

Ecological Restoration and Rural Livelihoods in Central India

Ecological restoration has the potential to provide a multitude of benefits, such as conserving biodiversity and supporting natural-resources dependent livelihoods. Tropical dry forests (TDFs) occur in densely populated human-modified landscapes in the tropics and are susceptible to degradation, making them an important biome to restore when degraded. TDFs are also socio-ecological systems, where local people rely on the forest for subsistence and livelihoods and effectively manage them for desire outcomes. People’s reliance on TDFs necessitates restoration projects to take into account more than biophysical and abiotic considerations when they are designed. In this decade of restoration, while there is the much-needed impetus to restore degraded land, to achieve enduring and just outcomes at large spatial scales, restoration projects need to more intentionally address local considerations, such as traditional land tenure systems and livelihood strategies, and goals such as socio-economic development. At the same time, to guide restoration efforts and realistically forecast the consequences of these efforts in the future, there is a need for rapid and accurate assessment tools to quantify the impact of restoration on biodiversity and people at several time steps. In Chapter 1, I use India, a country with high biophysical potential for restoration, as a case study to demonstrate a people-centric approach for identifying restoration opportunities. I find that there is a large overlap between areas of high biophysical restoration potential and high poverty, indicating potential and need to pursue restoration in a manner that addresses both ecological and social goals. In Chapter 2, I study a commonly adopted livelihood strategy, seasonal migration, in forest-dependent communities in India. I find that households in more agricultural and prosperous districts experience lower rates of migration but are more sensitive to climatic variability than households in poorer districts. In Chapter 3, I examine the impact of ecological restoration of a tropical dry forest in central India (CI). I find no significant difference in the cumulative number of bird species detected, but a significant difference in bird communities across the sites. In the lower frequencies dominated by birds and insects, I find that restored sites were positively associated with acoustic space occupancy in comparison to unrestored and low Lantana density (LLD) sites. In Chapter 4, I study the combined socio-ecological outcomes of restoration in the same sites in CI. I find that in the absence of alternative, people rely on Lantana camara, an invasive shrub, for subsistence and livelihoods, in the form of firewood and farm boundaries. I do not find any significant effect of restoration or LLD on people’s perception of ease of forest use, except for the distances covered for grazing, an important indicator of restoration success in this landscape. Finally, I also find that restoration is not associated with any significant changes in soundscapes in the higher frequency ranges dominated by insects and bats. Taken together, my chapters contribute to a greater understanding of the potential for restoration to meet social and ecological goals, the vulnerability of the livelihoods of people living on forest-fringes of TDFs to climate variability and expected and unexpected socio-ecological outcomes of restoration

IST Austria Thesis

In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion. In the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta universality conjecture for the last remaining universality type. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime. In the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure

FinBook: literary content as digital commodity

This short essay explains the significance of the FinBook intervention, and invites the reader to participate. We have associated each chapter within this book with a financial robot (FinBot), and created a market whereby book content will be traded with financial securities. As human labour increasingly consists of unstable and uncertain work practices and as algorithms replace people on the virtual trading floors of the worlds markets, we see members of society taking advantage of FinBots to invest and make extra funds. Bots of all kinds are making financial decisions for us, searching online on our behalf to help us invest, to consume products and services. Our contribution to this compilation is to turn the collection of chapters in this book into a dynamic investment portfolio, and thereby play out what might happen to the process of buying and consuming literature in the not-so-distant future. By attaching identities (through QR codes) to each chapter, we create a market in which the chapter can ‘perform’. Our FinBots will trade based on features extracted from the authors’ words in this book: the political, ethical and cultural values embedded in the work, and the extent to which the FinBots share authors’ concerns; and the performance of chapters amongst those human and non-human actors that make up the market, and readership. In short, the FinBook model turns our work and the work of our co-authors into an investment portfolio, mediated by the market and the attention of readers. By creating a digital economy specifically around the content of online texts, our chapter and the FinBook platform aims to challenge the reader to consider how their personal values align them with individual articles, and how these become contested as they perform different value judgements about the financial performance of each chapter and the book as a whole. At the same time, by introducing ‘autonomous’ trading bots, we also explore the different ‘network’ affordances that differ between paper based books that’s scarcity is developed through analogue form, and digital forms of books whose uniqueness is reached through encryption. We thereby speak to wider questions about the conditions of an aggressive market in which algorithms subject cultural and intellectual items – books – to economic parameters, and the increasing ubiquity of data bots as actors in our social, political, economic and cultural lives. We understand that our marketization of literature may be an uncomfortable juxtaposition against the conventionally-imagined way a book is created, enjoyed and shared: it is intended to be

Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

Root-knot nematodes: abundance in organic farming, differentiation among populations, microbes attached to juveniles in soil, and bacterial antagonists

In zwei umfassenden Untersuchungen im Herbst 2009 und 2011 wurde die Verbreitung und die Abundanz pflanzenparasitärer Nematoden an den verschiedenen Feldfrüchten in einer Bio-Farm in Ägypten erfasst. Insgesamt wurden elf Genera gefunden, von denen Wurzelgallen-Nematoden (Meloidogyne spp.) in beiden Untersuchungen am häufigsten und mit der höchsten Anzahl in den Proben gefunden wurde. Weitere oft gefundene Genera waren Tylenchorhynchus, Rotylenchulus, Helicotylenchus und Pratylenchus. Davon ausgehend beschäftigten sich die weiteren Arbeiten mit Meloidogyne, und zwar mit der Differenzierung von Populationen, der Anheftung von Mikroorganismen an die Juvenile (J2) im Boden, und der biologischen Kontrolle durch Bakterienstämme, die als Antagonisten von pilzlichen Pathogenen bekannt sind. Die untersuchten Populationen und/oder Rassen von Meloidogyne incognita zeigten phänotypische Unterschiede in ihren Vermehrungsmustern an einem Set von Wirtspflanzen. Damit einhergehend konnten auch genetische Unterschiede anhand einer neu entwickelten Methode zur Amplifikation des Pathogenitätsgens msp1 und der elektrophoretischen Auftrennung der PCR-Produkte von Genvarianten im Denaturierungsgradienten (DGGE) nachgewiesen werden. Für drei Ackerböden aus verschiedenen Regionen in Deutschland wurde unterschiedliche Suppressivität ihrer mikrobiellen Gemeinschaften gegen Meloidogyne hapla im Gewächshaus gezeigt. Mit Kultivierungs-unabhängigen Methoden wurde untersucht, welche Mikroorganismen an die J2 in den Böden anheften, um die zu identifizieren, die mit J2 im suppressivsten der drei Böden spezifisch interagierten (Kleinwanzleben). Die Mikroorganismen, die an den J2 nach Inkubation im Boden haften blieben, unterschieden sich zwischen den drei Böden. In PCR-DGGE Fingerprints von ITS-Fragmenten bzw. 16S rRNA Genen wurden viele Pilze und Bakterien detektiert, die an den J2 aber nicht im umgebenden Boden abundant waren. Während sich einige davon in allen drei Böden an den J2 anreicherten, waren andere spezifisch für einen Bodentyp. Mittels Pyrosequenzierung von 16S rRNA Gen-Amplikons konnten die mit J2 im suppressivsten Boden assoziierten abundantesten Bakterienarten beschrieben werden. Viele davon waren verwandt mit infektiösen Arten wie Shigella spp., während Malikia spinosa und Rothia amarae am häufigsten detektiert wurden. Krankheitskomplexe aus Nematode und Pilz können erhebliche synergistische Ertragsverluste verursachen. Bakterienstämme, die als Antagonisten von phytopathogenen Pilzen bekannt sind, wurden auf ihr Potential zur biologischen Kontrolle von M. incognita untersucht. Sameninokulation führte bei den meisten Stämmen zu einer signifikanten Reduktion der Vermehrung des Nematoden an Tomatenwurzeln. Für die drei besten Isolate, Bacillus subtilis Sb4-23, Mc2-Re2 und Mc5- Re2, wurden die zugrundeliegenden Mechanismen untersucht. Die Stämme konnten den Nematoden sowohl direkt durch Metabolite beeinträchtigen, die im Kulturüberstand zu finden sind, als auch indirekt über Induktion systemischer Resistenz der Pflanze. Im experimentellen Vergleich der direkten und Pflanzenvermittelten Effekte zeigte sich, dass letzteres der dominierende Kontrollmechanismus dieser Antagonisten ist. Zusammen genommen könnten diese Befunde als Basis für eine verbesserte Strategie zum integrierten Management von Wurzelgallen-Nematoden im biologischen Landbau dienen.Two surveys were conducted to determine the frequency and abundance of plantparasitic nematodes associated with different crops at an organic farm in Egypt, during autumn 2009 and 2011. Eleven genera of plant-parasitic nematodes were detected. Root-knot nematodes (Meloidogyne spp.) showed the highest abundance and frequency of all plant-parasitic nematodes during the two surveys. Commonly detected genera were Tylenchorhynchus, Rotylenchulus, Helicotylenchus and Pratylenchus. Further studies on Meloidogyne were carried out with regard to discrimination among populations, attachment of microbes to juveniles (J2) in soil, and biocontrol through bacterial strains which were known as antagonists of fungal pathogens. Meloidogyne incognita populations and/or races that showed differential pattern of reproduction on a set of host plants, could be differentiated based on a newly developed PCR-DGGE system to electrophorecically separate variants of the pathogenicity gene msp1. Three arable soils from different regions of Germany were shown to vary in the suppressiveness of their indigenous microbial communities against Meloidogyne hapla. Attachment of microbes to J2 in these three soils was investigated by cultivation-independent methods to identify those which specifically interacted with J2 in the most suppressive soil (Kleinwanzleben). The three soils differed in the microbes attached to J2. PCR-DGGE fingerprints of amplified ITS fragments or 16S rRNA genes showed many fungi and bacteria that were abundant on J2 but not in the surrounding soil, some of which seemed to be present in all three soils while most were soil type specific. Many bacteria associated with J2 from the most suppressive soil were closely related to infectious species like Shigella spp., while most abundant were Malikia spinosa and Rothia amarae as determined by 16S rRNA gene amplicon pyrosequencing. Nematode-fungus disease complexes can cause dramatic synergistic yield losses. Bacterial strains known as antagonists of phytopathogenic fungi were evaluated with respect to their biocontrol potential towards M. incognita. Seed inoculation with most of the strains significantly reduced propagation of nematode on tomato roots. The best strains Bacillus subtilis Sb4-23, Mc2-Re2, and Mc5- Re2 were further studied for their mode-of-action. The strains were able to affect the nematodes directly by metabolites present in culture supernatants and indirectly by induced systemic resistance of the plant. Experimental comparison of direct and plantmediated effects suggested that the latter was the major control mechanism of these antagonists. Overall, these findings may improve the basis for integrated management strategies of root-knot nematodes in organic farming