Series which are both max-plus and min-plus rational are unambiguous

Consider partial maps from the free monoid into the field of real numbers with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure to build an unambiguous automaton from a max-plus automaton and a min-plus one that recognize the same series

Higher order peak algebras

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection of formal power series with noncommutative coefficients.Comment: 20 pages, AMS LaTe

Modeling Commercial Processes and Customer Behaviors to Estimate

We propose a formal model for estimating the diffusion rate of a new product on a coherent market. Our approach is based on a discrete probabilistic modeling of customer behaviors and of commercial processes.Diffusion of innovation, diffusion rate, marketing, customer behavior, product diffusion

Some consequences of a Fatou property of the tropical semiring

We show in this paper that the tropical semiring (integers equiped with (max,+) operations) has the Fatou property and study the consequences of this property with respect to decidability properties

The Neoproterozoic to recent evolution of SW Gondwana - From an orogen to a passive continental margin environment induced by the "plate" and "plume mode".

The overarching goal of this thesis is the reconstruction of a coherent Late Neoproterozoic to recent time-temperature-evolution to connect individual geological stages (environments) of the Wilson Cycle, and consequently, follow the development from an active orogeny to an intraplate and later passive continental margin environment induced by the interaction of the “plate“ and “plume mode”. The research is based on the thermochronological analysis of Neoproterozoic basement rocks along the South Atlantic passive continental margins in SE Brazil and NW Namibia as well as the numerical modeling of the collected data. Moreover, the study combines multiple geological archives, e.g. geo- and thermochronological data from the published geological record and the stratigraphic records of sedimentary basins to constrain the entire timetemperature-evolution. In addition, the research aims to retrieve signals and traces of the Paraná-Etendeka vertical and horizontal plume movement during the Mesozoic SW Gondwana intraplate environment. It quantifies the possibly plume-induced rock and surface uplift (dynamic topography) preceding the Paraná-Etendeka Large Igneous Province integrating all available thermochronological data sets along the South Atlantic passive continental margins and the stratigraphic records of the major sedimentary basins surrounding the Paraná-Etendeka Large Igneous Province. By combining multiple geological archives, this thesis succeeds to reconstruct a possible and coherent Late Neoproterozoic to recent time-temperature evolution. Thereby, this research quantifies the timing, magnitude und rates of cooling and heating, or rather exhumation and subsidence during the development of the individual geological environments. The thesis therefore comprises the post-Pan African/Brasiliano orogenic cooling of rocks, the burial and subsidence involving the heating of the Neoproterozoic basement rocks during the Late Paleozoic Gondwana intraplate basin formation, and the thermal overprint caused by the Paraná-Etendeka flood basalt deposition and magmatic activity and following cooling during the post-South Atlantic rift and breakup exhumation. Furthermore, signals and traces of the Paraná-Etendeka plume movement causing large scale rock and surface uplift prior to the emplacement of the Paraná-Etendeka Large Igneous Province are retrieved. As a result, it is possible to determine spatial and temporal ranges for the plume movement-influenced area on the Earth’s surface during the Mesozoic SW Gondwana intraplate environment. Thereby, this thesis contributes to the understanding of the complex evolution of the individual yet interconnected geological environments and the dynamic interplay of the driving endo- and exogenous forces

Determining Provenance of Glacial Material in Southwestern Ohio

During the last glacial maximum, ice moved south from Canada to cover much of the northern United States. This included the northern and western portions of Ohio. As the ice migrated it picked up Canadian bedrock which it transported and then left in Ohio when the ice retreated. The goal of this project was to determine the provenance (the source of origin) of the glacial material that is located in Greene, Clark, Montgomery, Logan, and Champaign Counties in Ohio. To determine where in southern Canada the material in these counties came from, this project included literature review into the glacial history of both Ohio and southeastern Canada and review on the stratigraphy of southeastern Canada. Pebble, cobble, and boulder sized fragments were evaluated from two surface mines, one kame (glacial deposit), several glacial erratics, and multiple drilled cores from around the five counties. Multiple criteria such as size, roundness, fossils, foliations, and basic composition were used to categorize the rocks. Combining the stratigraphy of southeastern Canada found though the literature review and the sample analysis results, a map showing the source of the glacial material, direction of ice flow, and material destination has been created in Google Earth and PowerPoint. The types of rocks found in the samples appear to have originated from southern Ontario and Quebec, specifically from the Sudbury County area in southern Ontario as well as Ottawa County in Ontario and Les Collines-de-l\u27Outaouais County in Quebec. These areas have the closest exposed bedrock to Ohio that are of similar material to what was found during sample analysis. When compared with the direction of the ice flow, the results are consistent with the flow direction

Size-Change Abstraction and Max-Plus Automata

Max-plus automata (over ℕ ∪ − ∞) are finite devices that map input words to non-negative integers or − ∞. In this paper we present (a) an algorithm allowing to compute the asymptotic behaviour of max-plus automata, and (b) an application of this technique to the evaluation of the computational time complexity of programs

A preferred vision for administering elementary schools : a reflective essay

In a clearing in the woods, I see a bricked schoolhouse with kids of all ages outside laughing and playing. The sun is splashing down on the landscape like a blanket covering a canopy bed. The teachers are lingering around the playground communicating with each other about the day\u27s events and the principal grinning from ear to ear thinking about everything around him that makes up this school. This is a vision I have in my mind of the perfect school and the perfect administrative position. I also have to think about all of the people who came before me that paved the way for me to make this vision of mine a possibility. I truly respect the hard work in planning and drawing up ideas that they thought this new nation needed to become a respected country for all to see. This educational vision started many years ago with the introduction of the United States to the world; and since then, improvements have constantly sprouted to form the new way of education