Hopf monoids from class functions on unitriangular matrices

We build, from the collection of all groups of unitriangular matrices, Hopf monoids in Joyal's category of species. Such structure is carried by the collection of class function spaces on those groups, and also by the collection of superclass function spaces, in the sense of Diaconis and Isaacs. Superclasses of unitriangular matrices admit a simple description from which we deduce a combinatorial model for the Hopf monoid of superclass functions, in terms of the Hadamard product of the Hopf monoids of linear orders and of set partitions. This implies a recent result relating the Hopf algebra of superclass functions on unitriangular matrices to symmetric functions in noncommuting variables. We determine the algebraic structure of the Hopf monoid: it is a free monoid in species, with the canonical Hopf structure. As an application, we derive certain estimates on the number of conjugacy classes of unitriangular matrices.Comment: Final Version, 32 pages, accepted in "Algebra and Number Theory

Towards detecting and solving aspect conflicts and interferences using unit tests

Aspect Oriented Programming (AOP) is a programming paradigm that aims at solving the problem of crosscutting concerns being normally scattered throughout several units of an application.Although an important step forward in the search for modularity, by breaking the notion of encapsulation introduced by Object Oriented Programming (OOP), AOP has proven to be prone to numerous problems caused by conflicts and interferences between aspects.This paper presents work that explores the proven unit testing techniques as a mean to help developers describe the behavior of their aspects and to advise them about possible conflicts and interferences

Iterative character constructions for algebra groups

We construct a family of orthogonal characters of an algebra group which decompose the supercharacters defined by Diaconis and Isaacs. Like supercharacters, these characters are given by nonnegative integer linear combinations of Kirillov functions and are induced from linear supercharacters of certain algebra subgroups. We derive a formula for these characters and give a condition for their irreducibility; generalizing a theorem of Otto, we also show that each such character has the same number of Kirillov functions and irreducible characters as constituents. In proving these results, we observe as an application how a recent computation by Evseev implies that every irreducible character of the unitriangular group \UT_n(q) of unipotent $n\times n$ upper triangular matrices over a finite field with $q$ elements is a Kirillov function if and only if $n\leq 12$. As a further application, we discuss some more general conditions showing that Kirillov functions are characters, and describe some results related to counting the irreducible constituents of supercharacters.Comment: 22 page

Odometria visual monocular em robôs para a agricultura com camara(s) com lentes "olho de peixe"

One of the main challenges in robotics is to develop accurate localization methods that achieve acceptable runtime performances.One of the most common approaches is to use Global Navigation Satellite System such as GPS to localize robots.However, satellite signals are not full-time available in some kind of environments.The purpose of this dissertation is to develop a localization system for a ground robot.This robot is inserted in a project called RoMoVi and is intended to perform tasks like crop monitoring and harvesting in steep slope vineyards.This vineyards are localized in the Douro region which are characterized by the presence of high hills.Thus, the context of RoMoVi is not prosperous for the use of GPS-based localization systems.Therefore, the main goal of this work is to create a reliable localization system based on vision techniques and low cost sensors.To do so, a Visual Odometry system will be used.The concept of Visual Odometry is equivalent to wheel odometry but it has the advantage of not suffering from wheel slip which is present in these kind of environments due to the harsh terrain conditions.Here, motion is tracked computing the homogeneous transformation between camera frames, incrementally.However, this approach also presents some open issues.Most of the state of art methods, specially those who present a monocular camera system, don't perform good motion estimations in pure rotations.In some of them, motion even degenerates in these situations.Also, computing the motion scale is a difficult task that is widely investigated in this field.This work is intended to solve these issues.To do so, fisheye lens cameras will be used in order to achieve wide vision field of views

Incremental modular testing for AOP

By designing systems as sets of modules that can be composed into larger applications, developers unleasha multitude of advantages. The promise of AOP (Aspect-Oriented Programming) is to enable developers toorganize crosscutting concerns into separate units of modularity making it easier to accomplish this vision.However, AOP does not allow unit tests to be untangled, which impairs the development of properly testedindependent modules. This paper presents a technique that enables developers to encapsulate crosscuttingconcerns using AOP and still be able to develop reusable unit tests. Our approach uses incremental testingand invasive aspects to modify and adapt tests. The approach was evaluated in a medium scale project withpromising results. Without using the proposed technique, due to the presence of invasive aspects, some unittests would have to be discarded or modified to accommodate the changes made by them. This would havea profound impact on the overall modularity and, in particular, on the reusability of those modules. We willshow that this technique enables proper unit tests that can be reused even when coupled with aspect-orientedcode

Combinatorial Hopf algebra of superclass functions of type DD

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr\'e and Neto. Also, we make further comments with respect to types B and C. Type A was explores by M. Aguiar et. al (2010), thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.Comment: Last section modified. Recent development added and correction with respect to previous version state

Empirical Evaluation of a Live Environment for Extract Method Refactoring

Complex software can be hard to read, adapt, and maintain. Refactoring it can create cleaner and self-explanatory code. Refactoring tools try to guide developers towards better code, with more quality. However, most of them take too long to provide feedback, support, and guidance on how developers should improve their software. To reduce this problem, we explored the concept of Live Refactoring, focusing on visually suggesting and applying refactorings, in real-time. With this in mind, we developed a Live Refactoring Environment that visually identifies, recommends, and applies Extract Method refactorings. To validate it, we conducted an empirical experiment. Early results showed that our approach improved several code quality metrics. Besides, we also concluded that our results were significantly different and better than the ones from refactoring the code manually without further help

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