Some remarks on barycentric-sum problems over cyclic groups

We derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer l such that each subset A of G with at least l elements contains a subset with k elements {g_1, ..., g_k} satisfying g_1 + ... + g_k = k g_j for some 1 <= j <= k.Comment: to appear in European Journal of Combinatoric

Remarks on the plus-minus weighted Davenport constant

For $(G,+)$ a finite abelian group the plus-minus weighted Davenport constant, denoted $\mathsf{D}_{\pm}(G)$, is the smallest $\ell$ such that each sequence $g_1 ... g_{\ell}$ over $G$ has a weighted zero-subsum with weights +1 and -1, i.e., there is a non-empty subset $I \subset \{1,..., \ell\}$ such that $\sum_{i \in I} a_i g_i =0$ for $a_i \in \{+1,-1\}$. We present new bounds for this constant, mainly lower bounds, and also obtain the exact value of this constant for various additional types of groups

Inverse results for weighted Harborth constants

For a finite abelian group $(G,+)$ the Harborth constant is defined as the smallest integer $\ell$ such that each squarefree sequence over $G$ of length $\ell$ has a subsequence of length equal to the exponent of $G$ whose terms sum to $0$. The plus-minus weighted Harborth constant is defined in the same way except that the existence of a plus-minus weighted subsum equaling $0$ is required, that is, when forming the sum one can chose a sign for each term. The inverse problem associated to these constants is the problem of determining the structure of squarefree sequences of maximal length that do not yet have such a zero-subsum. We solve the inverse problems associated to these constant for certain groups, in particular for groups that are the direct sum of a cyclic group and a group of order two. Moreover, we obtain some results for the plus-minus weighted Erd\H{o}s--Ginzburg--Ziv constant

On the Olson and the Strong Davenport constants

A subset $S$ of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of $S$ is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant. We determine the maximal cardinality of such sets for several new types of groups; in particular, $p$-groups with large rank relative to the exponent, including all groups with exponent at most five. These results are derived as consequences of more general results, establishing new lower bounds for the cardinality of zero-sumfree sets for various types of groups. The quality of these bounds is explored via the treatment, which is computer-aided, of selected explicit examples. Moreover, we investigate a closely related notion, namely the maximal cardinality of minimal zero-sum sets, i.e., the Strong Davenport constant. In particular, we determine its value for elementary $p$-groups of rank at most $2$, paralleling and building on recent results on this problem for the Olson constant

On the bipartite independence number of a balanced bipartite graph

AbstractThe bipartite independence number αBIP of a bipartite graph G is the maximum order of a balanced independent set of G. Let δ be the minimum degree of the graph. When G itself is balanced, we establish some relations between αBIP and the size or the connectivity of G. We also prove that the condition αBIP⩽δ(resp.αBIP⩽δ−1) implies that G is hamiltonian (resp. Hamilton-biconnected), thus improving a result of Fraisse

Caracterización del efecto memoria de forma asistido bajo esfuerzos constantes en cintas delgadas de TiNiCu.

Las aleaciones con memoria de forma (AMF) son materiales cuyas características son aprovechadas en el desarrollo de actuadores. No obstante, la adición de elementos aleantes a la matriz de la AMF deriva en una alteración de propiedades significativa para el efecto de memoria de forma; por ende, este trabajo tiene como principal objetivo el estudio termomecánico de cintas delgadas tomando en cuenta la medición de las variables físicas involucradas en el efecto de memoria de forma: deformación, tensión, temperatura y porcentaje de recuperación. Dicho efecto es explicado en la sección de antecedentes

Multi-wise and constrained fully weighted Davenport constants and interactions with coding theory

We consider two families of weighted zero-sum constants for finite abelian groups. For a finite abelian group $( G , + )$, a set of weights $W \subset \mathbb{Z}$, and an integral parameter $m$, the $m$-wise Davenport constant with weights $W$ is the smallest integer $n$ such that each sequence over $G$ of length $n$ has at least $m$ disjoint zero-subsums with weights $W$. And, for an integral parameter $d$, the $d$-constrained Davenport constant with weights $W$ is the smallest $n$ such that each sequence over $G$ of length $n$ has a zero-subsum with weights $W$ of size at most $d$. First, we establish a link between these two types of constants and several basic and general results on them. Then, for elementary $p$-groups, establishing a link between our constants and the parameters of linear codes as well as the cardinality of cap sets in certain projective spaces, we obtain various explicit results on the values of these constants

Viability of FPGAs in wireless sensor networks

Dentro del contexto del proyecto de tesis planteado, se aborda el problema del control y las comunicaciones en las luminarias de los sistemas inteligentes de alumbrado público. En los trabajos reportados en la literatura sobre el tema planteado, se encuentra el problema particular de la implementación de protocolos digitales de comunicaciones en las luminarias, y especialmente en la implementación del protocolo Digital Addressable Lighting Interface (DALI) en redes de sensores inalámbricos. Desafortunadamente los microcontroladores que habitualmente se emplean en los nodos de sensores inalámbricos, no integran periféricos para este tipo de protocolos, por lo que suelen implementarse por software. Un punto de oportunidad es implementar este tipo de protocolos en hardware mediante una FPGA y de esta forma demostrar su viabilidad en nodos de sensores inalámbricos. En esta tesis se presenta una solución para implementar por hardware el protocolo DALI para controlar sistemas de iluminación inteligente. La novedad de este trabajo es la descripción portable del protocolo DALI implementado en forma de un bridge de comunicaciones en una FPGA de bajo coste, bajo consumo de energía y poca cantidad de recursos lógicos, para ser embebida en un nodo sensor inalámbrico. El protocolo se ha descrito en lenguaje VHDL siguiendo los estándares 1076-93 y 1076.3-97. Las contribuciones de este trabajo demuestran la viabilidad de la utilización de FPGAs en redes de sensores inalámbricos, que en este caso se utilizan para implementar el bridge DALI y resolver el problema de la interfaz de comunicación.Within the context of the proposed thesis project, the problem of control and communications for luminaires in intelligent public lighting systems is addressed. In the works reported in the literature on the subject, we can find the particular problem of the implementation of digital communication protocols for luminaires, and specifically the implementation of the Digital Addressable Lighting Interface (DALI) protocol in wireless sensor networks. Unfortunately, the microcontrollers that are commonly used in wireless sensor nodes do not integrate peripherals for this type of protocol, so they are usually implemented by software. A point of opportunity is to implement this type of protocols in hardware through an FPGA and thus demonstrate its viability in wireless sensor nodes. In this thesis, a solution is presented to implement the DALI protocol by hardware to control intelligent lighting systems. The novelty of this work is the portable description of the DALI protocol implemented in the form of a communications bridge in a low-cost FPGA, with low power consumption and few logical resources, which will be embedded in a wireless sensor node. The protocol has been described in VHDL language following the 1076-93 and 1076.3-97 standards. The contributions of this work demonstrate the feasibility of using FPGAs in wireless sensor networks, which in this case are used to implement the DALI bridge and solve the communication interface problem

Ontological approach to derive product configurations from a Software Product Line Reference Architecture

Software Product Lines (SPL) based on reuse, claim to improve evolution, time to market and decrease software development costs. Concrete software products or systems, members of the SPL family, are derived by instantiating a generic Reference Architecture (RA), holding common and variant components. The construction of RA is a complex and costly task, as well as its usage for product derivation, due to the huge number of variants, essentially caused by non functional requirements variability. In consequence, the selection of an RA instance or Feasible Solution (FS), meeting RA constraints and customer requirements, is not straightforward. In this work RA is built by a bottom-up process from existing products; RA and its instances are represented by a non-directed connected graph. The HIS-RA Ontology also represents RA and captures Healthcare Integrated Information Systems (HIS) domain knowledge. Moreover, FS must be connected (the induced graph by FS in RA has no isolated components), consistent (it verifies consistency rules among FS components), and working (it meets domain functional (FR) and non functional (NFR) requirements). The main goal of this paper is to define a semiautomatic process (FFSP), to derive consistency rules using the HIS-RA Ontology built-in reasoning capabilities, to construct consistent, connected and working FS. Software quality is considered by FFSP  in the traceability between FR and NFR, and it is specified by ISO/IEC 25010, to guarantee RA evolution and the overall concrete product configuration quality. FFSP is validated on a HIS domain a case study