Multiplying matrices using n arithmetic operations

It is widely known that the lower bound for the algorithmic complexity of square matrix multiplication resorts to at least $n^2$ arithmetic operations. The justification builds upon the following reasoning: given that there are $2 n^2$ numbers in the input matrices, any algorithm necessarily must operate on each at least once. In this paper, we show that this is not necessarily the case for certain instances of the problem, for instance matrices with natural number entries. We present an algorithm performing a single multiplication and $(n - 1)$ sums, therefore using n arithmetic operations. The ingenuity of the approach relies on encoding the original $2n^2$ elements as two numbers of much greater magnitude. Thus, though processing each of the inputs at least once, it relies on a lower count of arithmetic operations. In the computational model used to analyze this problem, such encoding operation is not available, thus it is not clear this work affects the currently accepted complexity results for matrix multiplication, but the new algorithm complexity (when taking into account the encodings) is $3n^2 + 2n - 1$ operations. In addition, given the exponential increase in multiplication operands magnitude, its practical usage is constrained to certain instances of the problem. Nonetheless, this work presents a novel mathematically inspired algorithm while pointing towards an alternative research path, which opens the possibility of novel algorithms and a taxonomy of matrix multiplications and associated complexities

A novel 3D dual hollow fibre bioreactor for the production of human red blood cells

Blood shortage is one of the biggest concerns of the World Health Organization. The reason: while around 30% of the industrialized world population will require a life-saving transfusion sometime during their lives, only 6% of the total population actually donates blood that can only be stored for up to 42 days. Despite the huge efforts that have been made to awaken the population to proactively donate blood (according to the World Health Organization 2009a, apporximately 85 million units of blood are collected annually worldwide), there is still a large shortage around the world. Hence, other alternatives have been suggested to address this. Since the first attempts, in the late 1940s, to produce an alternative to blood donation in the laboratory, several breakthroughs were made, most of them focusing on the synthetic route: the search for a chemical molecule that could replace the main vital function of red blood cells (RBCs) - oxygenation of the body cells (Kimball 1994). Nevertheless, several issues, mainly regarding the stability and controlled oxygen release by these molecules, still pose serious barriers for the success of this option (Kimball 1994). Nevertheless, several issues, mainly regarding the stability and controlled oxygen release by these molecules, still pose serious barriers for the success of this option (Kimball 1994). Hence, the focus on blood substitutes is now being directed to blood itself. My PhD project in the Department of Chemical Engineering of Imperial College London aimed at mimicking nature's bioreactor to produce human blood: the Bone Marrow (BM), a three-dimensional (3D) structure comprised of a vascularized support matrix, cellular constituents, and humoral factors. The BM 3D spatial configuration generates micro-concentration gradients that modulate cellular self-renewal, differentiation and apoptosis - mimicked by a 3D scaffold that can be rendered bioactive by coating with extracellular proteins. On the other hand, the BM vascular system ensures the supply of nutrients and removal of harmful metabolites, as well as the collection of maturing cells formed in the marrow cavity - mimicked by an intricate selectively-permeable membrane system that both renews the microenvironment and harvests mature RBCs. I have combined these two bio-inspired characteristics of the marrow into the first ex vivo 3D dual hollow fibre bioreactor (DHFB) that allows addressing mass transfer challenges faced by state-of-the-art technology and the continuous production and release of RBCs. This system was shown to be biocompatible, and allowed the differentiation of cord blood stem cells into mature enucleated RBCs under a cocktail composed of 100ng.mL-1 stem cell factor and 2,000U.ml-1 erythropoietin over 31 days. Mature enucleated RBCs could be prpduced exclusively ex vivo in a 3-dimension feeder-free culture. This technology has the potential to allow cost-effective production of clinically-relevant numbers of red blood cells with selective cell harvesting in a closed hematopoietic system

Mining Malware Specifications through Static Reachability Analysis

International audienceAbstract. The number of malicious software (malware) is growing out of control. Syntactic signature based detection cannot cope with such growth and manual construction of malware signature databases needs to be replaced by computer learning based approaches. Currently, a single modern signature capturing the semantics of a malicious behavior can be used to replace an arbitrarily large number of old-fashioned syntactical signatures. However teaching computers to learn such behaviors is a challenge. Existing work relies on dynamic analysis to extract malicious behaviors, but such technique does not guarantee the coverage of all behaviors. To sidestep this limitation we show how to learn malware signatures using static reachability analysis. The idea is to model binary programs using pushdown systems (that can be used to model the stack operations occurring during the binary code execution), use reachability analysis to extract behaviors in the form of trees, and use subtrees that are common among the trees extracted from a training set of malware files as signatures. To detect malware we propose to use a tree automaton to compactly store malicious behavior trees and check if any of the subtrees extracted from the file under analysis is malicious. Experimental data shows that our approach can be used to learn signatures from a training set of malware files and use them to detect a test set of malware that is 5 times the size of the training set

Vyndaqel (Tafamidis) market entry in Portugal

The main objective of this pedagogical case study is to analyse the market entry dynamics of pharmaceutical innovative drugs in Portugal, and the role and impact of the different stakeholders in this process. The case focuses on the market entry of Vyndaqel (Tafamidis) Pfizer’s orphan innovative product to treat TTR-FAP, “paramiloidose”, a highly incapacitating rare disease that has more than 2.000 diagnosed patients in Portugal, one of the highest prevalence worldwide and an incidence of 100 new patients every year. In terms of methodology it were used two main sources of information. Regarding secondary data sources it was made an exhaustive search using the main specialty search engines regarding the Tafamidis case, market access, orphan drugs and market entry context in Portugal and Europe. In terms of primary data it were conducted 7 direct interviews with the main case stakeholders. The pedagogical case study focuses on 5 main questions that provide the base of the discussion for the classes. First it is analysed the rationale behind the introduction of Tafamidis in Portugal, and its relevance for Pfizer, namely due to the previous investment made with the acquisition of FoldRX by $400M, the company that developed the product in the first place. It is also analysed the point of view of the NHS, and the reasoning behind drug reimbursement that considered not only the technical (efficacy and safety) and financial benefits of the drug, but also the social impact, due to the major role played by patient associations’ actions and coverage provided by the media that impacted the reimbursement decision. Finally it is analysed the vertical financing methodology that was selected by the Ministry of Health for drug acquisition by 2 public hospitals, that served as reference centres for the treatment of this diseas

Towards a framework for multi-directional model transformations

The Query/View/Transformation Relations (QVT-R) standard for bidirectional model transformation is notorious for its underspecified semantics. When restricted to transformations between pairs of models, most of the ambiguities and omissions have been addressed in recent work. Nevertheless, the application of the QVT-R language is not restricted to that scenario, and similar issues remain unexplored for the multidirectional case (maintaining consistency between more than two models), that has been overlooked so far. In this paper we first discuss ambiguities and omissions in the QVT-R standard concerning the mutidirectional transformation scenario, and then propose a simple extension and formalization of the checking and enforcement semantics that clarifies some of them. We also discuss how such proposal could be implemented in our Echo bidirectional model transformation tool. Ours is just a small step towards making QVT-R a viable language for bidirectional transformation in realistic applications, and a considerable amount of basic research is still needed to fully accomplish that goal.(undefined

Matrices as arrows! A biproduct approach to typed linear algebra

Motivated by the need to formalize generation of fast running code for linear algebra applications, we show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category with biproducts. This shifts the traditional view of matrices as indexed structures to a type-level perspective analogous to that of the pointfree algebra of programming. The derivation of fusion, cancellation and abide laws from the biproduct equations makes it easy to calculate algorithms implementing matrix multiplication, the kernel operation of matrix algebra, ranging from its divide-and-conquer version to the conventional, iterative one. From errant attempts to learn how particular products and coproducts emerge from biproducts, we not only rediscovered block-wise matrix com- binators but also found a way of addressing other operations calculation- ally such as e.g. Gaussian elimination. A strategy for addressing vector- ization along the same lines is also given.FCT, Mondrian Project funded by contract PTDC/EIA-CCO/108302/2008

Mapeamento semi-automático da formação barreiras na região norte do estado do Rio de Janeiro, a partir de dados SRTM

A Formação Barreiras é uma unidade estratigráfica que ocupa uma expressiva faixa do litoral brasileiro, desde o estado do Amapá até o Rio de Janeiro. A área de estudo localiza-se na região norte do estado do Rio de Janeiro, entre a divisa com o Espírito Santo (rio Itabapoana) e a cidade de Campos dos Goytacazes, área de ocorrência mais expressiva da Formação Barreiras no estado do Rio de Janeiro, apresentando as características típicas de tabuleiros e falésias, com amplos vales fluviais, contrastando com o relevo colinoso e dissecado do embasamento e com a área plana, de cordões arenosos da planície quaternária. O principal objetivo deste estudo é o mapeamento semi-automático da Formação Barreiras através da análise de variáveis geomorfométricas, como declividade e curvatura, dentre outras, extraídas a partir de modelo digital de terreno proveniente da SRTM/NASA. Buscou-se promover uma comparação com os mapas existentes para a área de estudo, bem como a metodologia empregada em cada trabalho e os dados utilizados por seus autores, além de aprofundar a discussão sobre a utilização de variáveis geomorfométricas na identificação e mapeamento de feições que tenham uma assinatura geomorfológica bem definida, em específico a Formação Barreiras. A metodologia envolveu diversas etapas, como as sucessivas suavizações aplicadas no MDT utilizado, com o objetivo de eliminar imperfeições que pudessem interferir na classificação das variáveis, e posteriormente a extração, classificação e combinação das variáveis, chegando então ao mapa final. O modelo resultante de cada uma das variáveis foi analisado primeiramente de forma separada, analisando-se o modo como cada variável contribuiria para o resultado final, verificando também as características, a importância e as limitações de cada variável. O mapa final não apresentou grandes diferenças, em termos de contornos gerais, em relação aos mapas já existentes para a Formação Barreiras na área de estudo. No entanto, é de fácil percepção vantagens relacionadas à economia de tempo e a um maior detalhamento proporcionado pelo método semi-automático, frente ao método visual