Matrices of inversions for permutations: Recognition and Applications

This work provides a criterion for a binary strictly upper triangle matrices to be a matrix of inversions for a permutation. It admits an invariant matrices for permutations to being well recognizable. Then it provides a complete algorithmic classi…cation of elements in the symmetric group Sn. Also it gives an algorithm for generating and writing a permutation in a unique canonical form, as a word of transpositions

Solving the recognition problem of Lorenz braids via matrices of inversions for permutations

In this work, we present some needed results about matrices of inversions for permutations. Then we apply it for solving the recognition problem of Lorenz braids. Each Lorenz braid is uniquely determined by a unique simple binary matrix. Then, we got a quick algorithm for counting the trip number (minimal braid index) hence, crossing number and minimal braid representative of the Lorenz knots

Some Properties of Certain Multivalent Analytic Functions Involving the Cătas Operator

We introduce a certain subclass of multivalent analytic functions by making use of the principle of subordination between these functions and Cătas operator. Such results as subordination and superordination properties, convolution properties, inclusion relationships, distortion theorems, inequality properties, and sufficient conditions for multivalent starlikeness are provide. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained

Factoring Products of Braids via Garside Normal Form

Braid groups are infinite non-abelian groups naturally arising from geometric braids. For two decades they have been proposed for cryptographic use. In braid group cryptography public braids often contain secret braids as factors and it is hoped that rewriting the product of braid words hides individual factors. We provide experimental evidence that this is in general not the case and argue that under certain conditions parts of the Garside normal form of factors can be found in the Garside normal form of their product. This observation can be exploited to decompose products of braids of the form ABC when only B is known. Our decomposition algorithm yields a universal forgery attack on WalnutDSA™, which is one of the 20 proposed signature schemes that are being considered by NIST for standardization of quantum-resistant public-key cryptography. Our attack on WalnutDSA™ can universally forge signatures within seconds for both the 128-bit and 256-bit security level, given one random message-signature pair. The attack worked on 99.8% and 100% of signatures for the 128-bit and 256-bit security levels in our experiments. Furthermore, we show that the decomposition algorithm can be used to solve instances of the conjugacy search problem and decomposition search problem in braid groups. These problems are at the heart of other cryptographic schemes based on braid groups.SCOPUS: cp.kinfo:eu-repo/semantics/published22nd IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2019; Beijing; China; 14 April 2019 through 17 April 2019ISBN: 978-303017258-9Volume Editors: Sako K.Lin D.Publisher: Springer Verla

Some properties of certain multivalent analytic functions involving the Catas operator,

We introduce a certain subclass of multivalent analytic functions by making use of the principle of subordination between these functions and Cȃtas operator. Such results as subordination and superordination properties, convolution properties, inclusion relationships, distortion theorems, inequality properties, and sufficient conditions for multivalent starlikeness are provide. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained

Self-assembly and dynamics of magnetic holes

Nonmagnetic particles in magnetized ferrofluids have been denoted magnetic holes and are in many ways ideal model systems to test various forms of particle self assembly and dynamics. Some case studies to be reviewed here include:Chaining of magnetic holesBraid theory and Zipf relation used in dynamics of magnetic microparticlesInteractions of magnetic holes in ferrofluid layersThe objectives of these works have been to find simple characterizations of complex behavior of particles with dipolar interactions

Blood Substitution: An Experimental Study

Priming fluids for cardiopulmonary bypass have been extremely varied, with resultant hemodilution. Furthermore, major surgeries utilizing cardiopulmonary bypass require multiple postoperative transfusions of blood and blood products. The appeal of having a readily available blood substitute for major cardiovascular and neurosurgical operations could prove to be a life saver, while also eliminating the risk of diseases transmitted by transfusion. Blood substitutes could also lessen the reported complications resulting from blood damage due to prolonged circulation of the blood by the extracorporeal pump. A technique was examined in 15 dogs using hypothermia for maximum metabolic suppression, incorporating an aqueous blood substitute (Cryomedical Sciences, Inc., Rockville, MD). The anesthetized animals were cannulated for extracorporeal pump oxygenation. As temperature was lowered the dogs were exsanguinated and volume replaced with blood substitute to lower the hematocrit to <1 %. After 3 hours of cardiac arrest and continuous perfusion at a core temperature < 10°C, rewarming began. When temperature reached ≥ 10°C, the blood substitute was drained and the animals were autotransfused. The heart was started at l5°C and spontaneous respiration resumed at 29°C. Using the first generation blood substitute the survival rate was maximal (100%) at 2.5 hrs under 10°C and 3 hours of cardiac arrest. Research is underway on a new blood substitute, which is to serve as a universal hypothermic preservation solution (in situ organ preservation). When perfected, combining total blood substitution and cooling to ultraprofound (< 10°C) levels may prove beneficial in sustaining cerebral ischemia for prolonged time periods, without incurring major metabolic debt. This may provide significant benefits for neurovascular surgery by prolonging the safe limits of cardiac arrest for several hours, rendering currently inoperable tumors and aneurysms more approachable, as well as a multitude of cardiovascular applications. In addition, this technique could find application in other interventional techniques, including systemic trauma resuscitation and transplantation cases

A Linear Algebraic Attack on the AAFG1 Braid Group Cryptosystem

Our purpose is to describe a promising linear algebraic attack on the AAFG1 braid group cryptosystem proposed in [2] employing parameters suggested by the authors. Our method employs the well known Burau matrix representation of the braid group and techniques from computational linear algebra and provide evidence which shows that at least a certain class of keys are weak. We argue that if AAFG1 is to be viable the parameters must be fashioned to defend against this attack.