On the number of pancake stacks requiring four flips to be sorted

Using existing classification results for the 7- and 8-cycles in the pancake graph, we determine the number of permutations that require 4 pancake flips (prefix reversals) to be sorted. A similar characterization of the 8-cycles in the burnt pancake graph, due to the authors, is used to derive a formula for the number of signed permutations requiring 4 (burnt) pancake flips to be sorted. We furthermore provide an analogous characterization of the 9-cycles in the burnt pancake graph. Finally we present numerical evidence that polynomial formulae exist giving the number of signed permutations that require $k$ flips to be sorted, with $5\leq k\leq9$.Comment: We have finalized for the paper for publication in DMTCS, updated a reference to its published version, moved the abstract to its proper location, and added a thank you to the referees. The paper has 27 pages, 6 figures, and 2 table

Cycles in the burnt pancake graphs

The pancake graph $P_n$ is the Cayley graph of the symmetric group $S_n$ on $n$ elements generated by prefix reversals. $P_n$ has been shown to have properties that makes it a useful network scheme for parallel processors. For example, it is $(n-1)$-regular, vertex-transitive, and one can embed cycles in it of length $\ell$ with $6\leq\ell\leq n!$. The burnt pancake graph $BP_n$, which is the Cayley graph of the group of signed permutations $B_n$ using prefix reversals as generators, has similar properties. Indeed, $BP_n$ is $n$-regular and vertex-transitive. In this paper, we show that $BP_n$ has every cycle of length $\ell$ with $8\leq\ell\leq 2^n n!$. The proof given is a constructive one that utilizes the recursive structure of $BP_n$. We also present a complete characterization of all the $8$-cycles in $BP_n$ for $n \geq 2$, which are the smallest cycles embeddable in $BP_n$, by presenting their canonical forms as products of the prefix reversal generators.Comment: Added a reference, clarified some definitions, fixed some typos. 42 pages, 9 figures, 20 pages of appendice

Effects of Human vs. Automatic Feedback on Students' Understanding of AI Concepts and Programming Style

The use of automatic grading tools has become nearly ubiquitous in large undergraduate programming courses, and recent work has focused on improving the quality of automatically generated feedback. However, there is a relative lack of data directly comparing student outcomes when receiving computer-generated feedback and human-written feedback. This paper addresses this gap by splitting one 90-student class into two feedback groups and analyzing differences in the two cohorts' performance. The class is an intro to AI with programming HW assignments. One group of students received detailed computer-generated feedback on their programming assignments describing which parts of the algorithms' logic was missing; the other group additionally received human-written feedback describing how their programs' syntax relates to issues with their logic, and qualitative (style) recommendations for improving their code. Results on quizzes and exam questions suggest that human feedback helps students obtain a better conceptual understanding, but analyses found no difference between the groups' ability to collaborate on the final project. The course grade distribution revealed that students who received human-written feedback performed better overall; this effect was the most pronounced in the middle two quartiles of each group. These results suggest that feedback about the syntax-logic relation may be a primary mechanism by which human feedback improves student outcomes.Comment: Published in SIGCSE '20: Proceedings of the 51st ACM Technical Symposium on Computer Science Educatio

An Algorithm to Enumerate Grid Signed Permutation Classes

In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are equivalent to the permutation classes that can be enumerated by polynomials. Furthermore, we apply our results to genome rearrangements and establish that the number of signed permutations with fixed prefix reversal and reversal distance is given by polynomials that can be computed by our algorithm.Comment: Corrected typos and extended some explanations. Final version included in the Proceedings of The International Symposium on Symbolic and Algebraic Computation, ISSAC 202

A Novel Pseudo-Random Number Generator Based on Multi-Objective Optimization for Image-Cryptographic Applications

Pseudo-random number generators (PRNGs) play an important role to ensure the security and confidentiality of image cryptographic algorithms. Their primary function is to generate a sequence of numbers that possesses unpredictability and randomness, which is crucial for the algorithms to work effectively and provide the desired level of security. However, traditional PRNGs frequently encounter limitations like insufficient randomness, predictability, and vulnerability to cryptanalysis attacks. To overcome these limitations, we propose a novel method namely an elliptic curve genetic algorithm (ECGA) for the construction of an image-dependent pseudo-random number generator (IDPRNG) that merges elliptic curves (ECs) and a multi-objective genetic algorithm (MOGA). The ECGA consists of two primary stages. First, we generate an EC-based initial sequence of random numbers using pixels of a plain-image and parameters of an EC, that depart from traditional methods of population initialization. In our proposed approach, the image itself serves as the seed for the initial population in the genetic algorithm optimization, taking into account the image-dependent nature of cryptographic applications. This allows the PRNG to adapt its behavior to the unique characteristics of the input image, leading to enhanced security and improved resistance against differential attacks. Furthermore, the use of a good initial population reduces the number of generations required by a genetic algorithm, which results in decreased computational cost. In the second stage, we use well-known operations of a genetic algorithm to optimize the generated sequence by maximizing a multi-objective fitness function that is based on both the information entropy and the period of the PRNG. By combining elliptic curves and genetic algorithms, we enhance the randomness and security of the ECGA.Comment: Keywords: Pseudo-random number generator, Elliptic curve, Genetic algorithm, Multi-objective optimizatio

Response of epilithic diatom communities to environmental gradients in subtropical temperate Brazilian rivers

This work aims to analyse the response of epilithic diatom communities to enviranmental gradients in subtropical temperate southern Brazilian rivers to contribute to the development of a widely applicable methodology for water-quality monitoring. Samples for physical, chemical and biological determination were collected monthly, fram December 2001 to November 2002 and fram March 2003 to February 2004, at 9 stations along the rivers Pardo and Pardinho in the hydrographical basin of Rio Pardo, State of Rio Grande do Sul (RS), Brazil. Physical and chemical variables (water temperature, pH, dissolved oxygen, biochemical oxygen demand, chemical oxygen demand, nitrates, nitrites, phosphates and total dissolved solids) and biological variables (epilithic diatom communities) were used as parameters for water-quality assessment. The data matrix was examined by means of a multivariate ordination using Detrended Correspondence Analysis (DCA). In total, 270 taxa were identified to specific or infra-specific levels. The results showed that of all the physical and chemical variables used, the main gradient along the DCA first axis was eutraphication, which was indicated by its significant correlation with phosphates (p < 0.00l). Hence, the species' scores on the DCA axis were used as an operational criterion for indicating their tolerance to eutrophication. From this analysis, the 10 taxa that were the most tolerant to eutrophication were: Cyclotella meneghiniana, Fallacia monoculata, Nitzschia acicularis, N. clausii, N. nana, N. palea, Nitzschia sp., Pinnularia sp., Sellaphora pupula sensu lato and Ulnaria acuso The present study showed that epilithic diatom assemblages reflect anthropogenic changes in hydrographic basins in subtropical temperate streams, especially pollution by organic enrichment and eutraphication. Key words: Diatoms, eutrophication, biomonitoring, southern Brazilian rivers.Este trabajo pretende analizar la respuesta de la comunidad de diatomeas epilíticas a gradientes ambientales en ríos brasileños templados subtropicales, con el objetivo de contribuir al desarrollo de una metodología ampliamente aplicable para la monitorización de la calidad del agua. Diversas muestras para determinaciones físicas, químicas y biológicas fueron recogidas mensualmente, de diciembre de 2001 a noviembre de 2002, y de marzo de 2003 afebrero de 2004, en nueve esta­ciones de muestre o distribuidas a lo largo de los ríos Pardo y Pardinho, localizados en la Cuenca Hidrográfica del Río Pardo, Estado del Río Grande del Sur; Brasil. Variables físicas y químicas (temperatura del agua, pH, oxígeno disuelto, demanda bioquímica de oxígeno, demanda química de oxígeno, nitratos, nitritos, fosfato y sólidos totales disueltos) y biológicas (co­munidad de diatomeas epilíticas) fueron usadas como parámetros para evaluar la calidad del agua. El conjunto de datos fue analizado por medio de una ordenación multivariante usando el Análisis de Correspondencias sin Tendencias (DCA). En total, 270 taxones fueron identificados a nivel especifico o infra-especifico. Los resultados indicaron que, entre todas las variables físicas y químicas usadas, el principal gradiente establecido a lo largo del primer eje DCA fue la eutrojización, señalada por su correlación significativa con la concentración de fosfatos (p < 0.001). De esta forma, los valores alcanzados por las especies en el primer eje DCA fueron usados como un criterio operativo para indicar su tolerancia a la eutrojización. Los 10 taxones más tolerantes a la eutrojizaciónfueron: Cyc10tella meneghiniana, Fallacia monoculata, Nitzschia acicularis, N. c1ausii, N. nana, N. palea, Nitzschia sp., Pinnularia sp., Sellaphora pupula sensu lato y Ulnaria acuso El presente estudio muestra que la comunidad de diatomeas epilíticas refleja cambios antropogénicos en ríos templados subtropicales de cuencas hidrográjicas, especialmente la contaminación por enriquecimiento orgánico y eutrofización

Response of epilithic diatom communities to environmental gradients in subtropical temperate Brazilian rivers

P. 323-340This work aims to analyse the response of epilithic diatom communities to environmental gradients in subtropical temperate southern Brazilian rivers to contribute to the development of a widely applicable methodology for water-quality monitoring. Samples for physical, chemical and biological determination were collected monthly, from December 2001 to November 2002 and from March 2003 to February 2004, at 9 stations along the rivers Pardo and Pardinho in the hydrographical basin of Rio Pardo, State of Rio Grande do Sul (RS), Brazil. Physical and chemical variables (water temperature, pH, dissolved oxygen, biochemical oxygen demand, chemical oxygen demand, nitrates, nitrites, phosphates and total dissolved solids) and biological variables (epilithic diatom communities) were used as parameters for water-quality assessment. The data matrix was examined by means of a multivariate ordination using Detrended Correspondence Analysis (DCA). In total, 270 taxa were identied to specic or infra-specic levels. The results showed that of all the physical and chemical variables used, the main gradient along the DCA rst axis was eutrophication, which was indicated by its signicant correlation with phosphates ( p < 0.001). Hence, the species’ scores on the DCA axis were used as an operational criterion for indicating their tolerance to eutrophication. From this analysis, the 10 taxa that were the most tolerant to eutrophication were: Cyclotella meneghiniana, Fallacia monoculata, Nitzschia acicularis, N. clausii, N. nana, N. palea, Nitzschia sp., Pinnularia sp., Sellaphora pupula sensu lato and Ulnaria acus. The present study showed that epilithic diatom assemblages reect anthropogenic changes in hydrographic basins in subtropical temperate streams, especially pollution by organic enrichment and eutrophicationS

Funcionamiento de los lagos someros mediterráneos.

P. 2-12Aún existe un importante desconocimiento sobre el funcionamiento de las lagunas o lagos someros mediterráneos. Ante la carencia de estudios propios de estos ambientes, la abundancia de estudios en el norte de Europa ha supuesto una generalización de procesos y características potencialmente aplicables a nuestros lagos. Sin embargo, la comparación de los distintos estudios en ambas zonas demuestra que las lagunas mediterráneas presentan peculiaridades únicas y un funcionamiento significativamente diferente. Tamaños más pequeños, mayor aislamiento, fuertes oscilaciones de la lámina de agua, mayor productividad y ausencia de ciertos grupos tróficos, entre otras, son características distintivas de nuestros sistemas. Estas características tienen importantes implicaciones en la dinámica de sus poblaciones y en la estructura y funcionamiento de las comunidadesS