Minimum Weight Resolving Sets of Grid Graphs

For a simple graph $G=(V,E)$ and for a pair of vertices $u,v \in V$, we say that a vertex $w \in V$ resolves $u$ and $v$ if the shortest path from $w$ to $u$ is of a different length than the shortest path from $w$ to $v$. A set of vertices ${R \subseteq V}$ is a resolving set if for every pair of vertices $u$ and $v$ in $G$, there exists a vertex $w \in R$ that resolves $u$ and $v$. The minimum weight resolving set problem is to find a resolving set $M$ for a weighted graph $G$ such that$\sum_{v \in M} w(v)$ is minimum, where $w(v)$ is the weight of vertex $v$. In this paper, we explore the possible solutions of this problem for grid graphs $P_n \square P_m$ where $3\leq n \leq m$. We give a complete characterisation of solutions whose cardinalities are 2 or 3, and show that the maximum cardinality of a solution is $2n-2$. We also provide a characterisation of a class of minimals whose cardinalities range from $4$ to $2n-2$.Comment: 21 pages, 10 figure

Computational methods for the discovery and analysis of genes and other functional DNA sequences

The need for automating genome analysis is a result of the tremendous amount of genomic data. As of today, a high-throughput DNA sequencing machine can run millions of sequencing reactions in parallel, and it is becoming faster and cheaper to sequence the entire genome of an organism. Public databases containing genomic data are growing exponentially, and hence the rise in demand for intuitive automated methods of DNA analysis and subsequent gene identification. However, the complexity of gene organization makes automation a challenging task, and smart algorithm design and parallelization are necessary to perform accurate analyses in reasonable amounts of time. This work describes two such automated methods for the identification of novel genes within given DNA sequences. The first method utilizes negative selection patterns as an evolutionary rationale for the identification of additional members of a gene family. As input it requires a known protein coding gene in that family. The second method is a massively parallel data mining algorithm that searches a whole genome for inverted repeats (palindromic sequences) and identifies potential precursors of non-coding RNA genes. Both methods were validated successfully on the fully sequenced and well studied plant species, Arabidopsis thaliana --Abstract, page iv

L'Asie de l'Est remplit-elle les conditions d'une zone monétaire optimale? L'analyse des chocs macroéconomiques

Ce papier analyse la possibilité d'une union monétaire en Asie de l'Est en nous basant sur les critères traditionnels de la théorie des zones monétaires optimales. Nous examinons essentiellement le degré de corrélation des chocs, considérés comme exogènes, pour les pays concernés afin de voir s'ils sont symétriques ou asymétriques. Nous prenons l'Union européenne comme point de comparaison. De toute évidence, l'analyse des taux de croissance faît apparaître des dispersions et celle des taux d'inflation nous montre que des efforts indispensables restent à fournir en matière de coopération monétaire. En développant un modèle VAR structurel, basé sur la méthodologie inspirée des travaux de Blanchard et Quah [1989], nous montrons que les chocs macroéconomiques sont assez hétérogènes dans cette région appuyant l'hypothèse de dispersion relativement élevée des taux de croissance

The Impact of External Shocks in East Asia: Lessons from a Structural VAR Model with Block Exogeneity

In this paper, we examine the relative importance of external shocks in domestic fluctuations of East Asian countries and check if these shocks lead to asymmetric or symmetric reactions between the considered economies. To this end, we estimate, over the period 1990.1-2010.4, a structural VAR model with block exogeneity (SVARX model) relying on a comprehensive set of external shocks. We firstly document a rising impact of these external shocks on domestic variables since the mid 1990s. Finally, real oil price and U.S. GDP shocks have a significant impact on domestic activity and lead to more symmetric responses, compared to U.S. monetary shock and MSCI Index financial shocks.external shocks, East Asia, SVARX model.

A quantitative study of gene identification techniques based on evolutionary rationales

Current gene identification (GI) techniques typically rely on matching biological or chemical properties of specific genes, specific species, specific ecotypes, etc...In this thesis, a new automated GI technique is proposed, and compared against another computer-based technique proposed earlier. Both methods utilize EST data available from NCBI databases to discover previously unknown genes. The newly proposed method identifies one gene family at a time and is based on a distinctive negative selection pattern (NSP) of differences, which is seen between the coding regions of gene family members. The other technique, called ESTminer, attempts genome-wide gene family identification for any organism, by detecting single nucleotide polymorphisms between potential family members. In this thesis, a complete automated analysis of both techniques is presented --Abstract, page iii

L'Asie de l'Est remplit-elle les conditions d'une zone monétaire optimale? L'analyse des chocs macroéconomiques

Ce papier analyse la possibilité d'une union monétaire en Asie de l'Est en nous basant sur les critères traditionnels de la théorie des zones monétaires optimales. Nous examinons essentiellement le degré de corrélation des chocs, considérés comme exogènes, pour les pays concernés afin de voir s'ils sont symétriques ou asymétriques. Nous prenons l'Union européenne comme point de comparaison. De toute évidence, l'analyse des taux de croissance faît apparaître des dispersions et celle des taux d'inflation nous montre que des efforts indispensables restent à fournir en matière de coopération monétaire. En développant un modèle VAR structurel, basé sur la méthodologie inspirée des travaux de Blanchard et Quah [1989], nous montrons que les chocs macroéconomiques sont assez hétérogènes dans cette région appuyant l'hypothèse de dispersion relativement élevée des taux de croissance.Zones monétaires optimales, (A)symétrie des chocs, Asie

Minimum rank and zero forcing number for butterfly networks

The minimum rank of a simple graph $G$ is the smallest possible rank over all symmetric real matrices $A$ whose nonzero off-diagonal entries correspond to the edges of $G$. Using the zero forcing number, we prove that the minimum rank of the butterfly network is $\frac19\left[(3r+1)2^{r+1}-2(-1)^r\right]$ and that this is equal to the rank of its adjacency matrix