On singular moduli that are S-units

Recently Yu. Bilu, P. Habegger and L. K\"uhne proved that no singular modulus can be a unit in the ring of algebraic integers. In this paper we study for which sets S of prime numbers there is no singular modulus that is an S-units. Here we prove that when the set S contains only primes congruent to 1 modulo 3 then no singular modulus can be an S-unit. We then give some remarks on the general case and we study the norm factorizations of a special family of singular moduli.Comment: Version changed according to the referee's comments. The final version appears in Manuscripta Mathematica, https://doi.org/10.1007/s00229-020-01230-

Regional Transit Service, Inc. and Amalgamated Transit Union, Local No. 282

In the Matter of Fact-Finding Between AMALGAMATED TRANSIT UNION, LOCAL NO. 282 And REGIONAL TRANSIT SERVICE, INC. PERB Case No. M2008-063. Before: Dennis J. Campagna, Esq. – Fact Finder

Greece Central School District and Greece Teachers Association

In the Matter of Fact-Finding Between Greece Central School District and Greece Teachers Association. PERB Case No. M2007-072. Before: Dennis J. Campagna, Esq. – Fact Finder

Finding Associations and Computing Similarity via Biased Pair Sampling

This version is ***superseded*** by a full version that can be found at http://www.itu.dk/people/pagh/papers/mining-jour.pdf, which contains stronger theoretical results and fixes a mistake in the reporting of experiments. Abstract: Sampling-based methods have previously been proposed for the problem of finding interesting associations in data, even for low-support items. While these methods do not guarantee precise results, they can be vastly more efficient than approaches that rely on exact counting. However, for many similarity measures no such methods have been known. In this paper we show how a wide variety of measures can be supported by a simple biased sampling method. The method also extends to find high-confidence association rules. We demonstrate theoretically that our method is superior to exact methods when the threshold for "interesting similarity/confidence" is above the average pairwise similarity/confidence, and the average support is not too low. Our method is particularly good when transactions contain many items. We confirm in experiments on standard association mining benchmarks that this gives a significant speedup on real data sets (sometimes much larger than the theoretical guarantees). Reductions in computation time of over an order of magnitude, and significant savings in space, are observed.Comment: This is an extended version of a paper that appeared at the IEEE International Conference on Data Mining, 2009. The conference version is (c) 2009 IEE

Wappingers Central School District and Wappingers Federation of Transit, Custodial and Maintenance Workers Wappingers Central School District and Wappingers Federation of Transit, Custodial and Maintenance Workers

In the Matter of Fact-Finding Between: WAPPINGERS CENTRAL SCHOOL DISTRICT, -And- WAPPINGERS FEDERATION OF WORKERS. PERB CASE NO. M2006-193. Before: Dennis J. Campagna, Esq

Red Hook Central School District and Red Hook Faculty Association

In the matter of the fact-finding between the Red Hook Central School District, employer, and the Red Hook Faculty Association, union. PERB case no. M2009-079. Before: Dennis J. Campagna, Esq., fact finder

Orchestrating the spatial planning process: from Business Process Management to 2nd generation Planning Support Systems

Metaplanning can be considered as a necessary step for improving collaboration, transparency and accountability in sustainable and democratic spatial decision-making process. This paper reports current findings on the operational implementation of the metaplanning concept developed by the authors relying on Business Process Management methods and techniques. Two solutions are presented which implement spatial planning process workflows thanks to the development of original spatial data and processing services connectors to a Business Process Management suite. These results can be considered as a first step towards the development of 2nd generation Planning Support Systems

What is the effect of long-term coaching engagements on the business coach’s process and approach?

The aim of this project was to examine whether changes occur to the process and approach of business coaches’ practices during long-term business coaching engagements. This was accomplished by reviewing literature, then gathering new data to provide a richer, deeper understanding of business coaches’ experiences and analyzing their reflections regarding their long-term business coaching activities. Within the coaching industry, techniques, competencies, values and ethics are routinely addressed in coach training programs, however, the occurrence and dynamics of long-term engagements has been mostly overlooked by the coaching community, as evidenced by the scarcity of literature and research on this topic to date. A mixed-method approach was used for data collection, which included a survey and semi-structured interviews. Thematic analysis revealed evidence that the coach’s initial process or model often changes when working with a ‘longevity client,’ though the foundational premise of being fully present and asking targeted questions does not. The evolving and deepening relationship between coach and client was identified as a key component driving changes to the coach’s work. The data revealed that often the business coach’s role expands beyond the traditional definition of coaching to include more input and direction. A confirmed finding from this research is that long-term business coaching engagements are an embedded component of the coaching spectrum. As such, this research provides the basis for further exploration regarding the benefits, expectations, and outcomes of long-term coaching. This project surfaced issues that are ripe of further research, both for long-term engagements and for coaching at large; knowing when and how to terminate client engagements, client friendships, dependency within the dyad, the evolution and breadth of coaching services and financial considerations within the coaching agreement. This research lays an expanded and documented foundation for the coaching industry to more fully explore the interactive dynamics of long-term business coaching engagements and their impact on both the coach and client