Neighborhood complexes and generating functions for affine semigroups

Given a_1,a_2,...,a_n in Z^d, we examine the set, G, of all non-negative integer combinations of these a_i. In particular, we examine the generating function f(z)=\sum_{b\in G} z^b. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z^n. In the generic case, this follows from algebraic results of D. Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice

Adhesion attenuation and enhancement in aqueous solutions

When two surfaces confine water layers between them at the nanoscale, the behaviour of these confined water molecules can deviate significantly from the behaviour of bulk water, and it could reflect on the adhesion of such surfaces. This study assesses the role of confined water layers on the adhesion of hydrophilic surfaces and how sensitive this adhesion is to the presence of contaminants. Our methodology used atomic force microscopy adhesion measurements, whereby an alumina-sputtered sphere-tipped cantilever was interacted versus a flat alumina single crystal. Testing was performed under immersed conditions using (i) water, (ii) water/dimethylformamide mixtures, (iii) water/ethanol mixtures, and (iv) water/formamide mixtures. These solutions were intended to assess the influence of dielectric constant, molecule size, and the number of hydrogen bonding opportunities available to molecules upon confinement between surfaces. It was found that dilute concentrations of ethanol and formamide decreased the adhesion. In contrast, the adhesion increased in the presence of dilute concentrations of dimethylformamide. The adhesion was attenuated by in excess of two orders of magnitude for high concentrations of the organic solutes

Neighborhood Complexes and Generating Functions for Affine Semigroups

Given a_{1}; a_{2},...a_{n} in Z^{d}, we examine the set, G, of all nonnegative integer combinations of these ai. In particular, we examine the generating function f(z) = Sum_{b in G}z^{b}. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z^{n}. In the generic case, this follows from algebraic results of D. Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice.Integer programming, Complex of maximal lattice free bodies, Generating functions

Relations and Predicates

Interest in the age-old problems of universals and individuation has received a new impetus from the current revival of ontology in the analytic tradition, the development of theories of individual properties (and the related application of mereological calculi to the analysis of predication), and the particular problems posed by relational predication and the nature of particulars. The essays explore aspects of the history of the issues and attempt to deal with the issues and with challenges to the distinctions that give rise to them. They continue the debates stemming from the revival of metaphysics rooted in Freges realism, the Austrian tradition of Brentano-Husserl-Meinong, and the early 20th century revolt against idealism embodied in writings of Moore and Russell and culminating in Wittgensteins Tractatus

Neighborhood Complexes and Generating Functions

Given a 1 , a 2 ,…, a n in Z d , we examine the set, G , of all nonnegative integer combinations of these a i . In particular, we examine the generating function f ( z ) = Sum {b in G} z b . We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z n . In the generic case, this follows from algebraic results of D . Bayer and B. Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice

The Amnesiac Lookback Option: Selectively Monitored Lookback Options and Cryptocurrencies

This study proposes a strategy to make the lookback option cheaper and more practical, and suggests the use of its properties to reduce risk exposure in cryptocurrency markets through blockchain enforced smart contracts and correct for informational inefficiencies surrounding prices and volatility. This paper generalizes partial, discretely-monitored lookback options that dilute premiums by selecting a subset of specified periods to determine payoff, which we call amnesiac lookback options. Prior literature on discretely-monitored lookback options considers the number of periods and assumes equidistant lookback periods in pricing partial lookback options. This study by contrast considers random sampling of lookback periods and compares resulting payoff of the call, put and spread options under floating and fixed strikes. Amnesiac lookbacks are priced with Monte Carlo simulations of Gaussian random walks under equidistant and random periods. Results are compared to analytic and binomial pricing models for the same derivatives. Simulations show diminishing marginal increases to the fair price as the number of selected periods is increased. The returns correspond to a Hill curve whose parameters are set by interest rate and volatility. We demonstrate over-pricing under equidistant monitoring assumptions with error increasing as the lookback periods decrease. An example of a direct implication for event trading is when shock is forecasted but its timing uncertain, equidistant sampling produces a lower error on the true maximum than random choice. We conclude that the instrument provides an ideal space for investors to balance their risk, and as a prime candidate to hedge extreme volatility. We discuss the application of the amnesiac lookback option and path-dependent options to cryptocurrencies and blockchain commodities in the context of smart contracts

Information requirements and data description in historical social research: a proposal

Description and documentation is one of the major prerequisites for disseminating and exchanging machine-readable historical sources and data. This proposal for description and documentation items is an attempt for standardizing information requirements in historical research; it does not give recommendations for all possible description and documentation needs, but instead attempts to set essential parameters for describing and documenting machine-readable historical sources and data. In the appendix to this proposal, an example using the 1851 Census of England and Wales is given to provide a detailed illustration of the proposal

Potomac River Pound-Net Survey Summer 1996: 1996 annual report

This survey had the following goals: (1) collect length and weight data on fishes captured in pound nets in the Potomac River; (2) collect length data of fish captured and released or discarded at-sea; and (3) establish length weight relations in summary statistics to provide baseline data

Terracotta Figurines in the Walker Art Building

Bulletin / Bowdoin College ; no. 335https://digitalcommons.bowdoin.edu/art-museum-exhibition-catalogs/1051/thumbnail.jp