Exact Solution of the Discrete (1+1)-dimensional RSOS Model with Field and Surface Interactions

We present the solution of a linear Restricted Solid--on--Solid (RSOS) model in a field. Aside from the origins of this model in the context of describing the phase boundary in a magnet, interest also comes from more recent work on the steady state of non-equilibrium models of molecular motors. While similar to a previously solved (non-restricted) SOS model in its physical behaviour, mathematically the solution is more complex. Involving basic hypergeometric functions ${}_3\phi_2$, it introduces a new form of solution to the lexicon of directed lattice path generating functions.Comment: 10 pages, 2 figure

Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page

Encouraging female entrepreneurship in Jordan: environmental factors, obstacles and challenges

The number of female entrepreneurs and their contribution to the economy is steadily rising. Yet research suggests that female entrepreneurs face more challenges and barriers than their male counterparts. This is expected to be even more prevalent in Islamic contexts, which are characterised by conservative and patriarchal societies. In this research, 254 female business students from a private and a public university responded to a questionnaire that gauges their perceptions about potential barriers to entrepreneurship in Jordan and whether the business education they are receiving helps to prepare them for future entrepreneurial activity. Our results help to form a basis on which a deeper understanding of the phenomena can be achieved through more in depth future research. Among the main environmental factors that worry potential female entrepreneurs are the weakness of Jordanian economy, lack of finance, fear of risk, gender inequality and inability to maintain a work and private life balance. Our results also show that students are really not aware of the opportunities available to them and are unable to make a proper assessment. We call on both universities and the Jordanian government to put more emphasis on practical entrepreneurial education and encouraging women to play a much more active role within the workforce

NERONE: Neural Robust Scheduling Evaluator"

ICAMES2003, ENSO, Bogazici University, Istanbu

Planet populations inferred from debris discs: insights from 178 debris systems in the ISPY, LEECH and LIStEN planet-hunting surveys

We know little about the outermost exoplanets in planetary systems, because our detection methods are insensitive to moderate-mass planets on wide orbits. However, debris discs can probe the outer-planet population, because dynamical modelling of observed discs can reveal properties of perturbing planets. We use four sculpting and stirring arguments to infer planet properties in 178 debris-disc systems from the ISPY, LEECH and LIStEN planet-hunting surveys. Similar analyses are often conducted for individual discs, but we consider a large sample in a consistent manner. We aim to predict the population of wide-separation planets, gain insight into the formation and evolution histories of planetary systems, and determine the feasibility of detecting these planets in the near future. We show that a `typical' cold debris disc likely requires a Neptune- to Saturn-mass planet at 10-100 au, with some needing Jupiter-mass perturbers. Our predicted planets are currently undetectable, but modest detection-limit improvements (e.g. from JWST) should reveal many such perturbers. We find that planets thought to be perturbing debris discs at late times are similar to those inferred to be forming in protoplanetary discs, so these could be the same population if newly formed planets do not migrate as far as currently thought. Alternatively, young planets could rapidly sculpt debris before migrating inwards, meaning that the responsible planets are more massive (and located further inwards) than debris-disc studies assume. We combine self-stirring and size-distribution modelling to show that many debris discs cannot be self-stirred without having unreasonably high masses; planet- or companion-stirring may therefore be the dominant mechanism in many (perhaps all) debris discs. Finally, we provide catalogues of planet predictions, and identify promising targets for future planet searches.Comment: 41 pages, 16 figures, accepted for publication in A&

Hole-free Partially Directed Animals

We consider the class of hole-free partially directed animals. This is the class of all polyominoes P such that every cell of P can be reached from any cell in the first column of P with a path (inside P) which makes only North, South and East steps, and such that there is not a finite region of empty unitary squares which is surrounded by cells belonging to P. We provide a generation algorithm that allows us to enumerate in constant amortized time using O(n) space