On the String Consensus Problem and the Manhattan Sequence Consensus Problem

In the Manhattan Sequence Consensus problem (MSC problem) we are given $k$ integer sequences, each of length $l$, and we are to find an integer sequence $x$ of length $l$ (called a consensus sequence), such that the maximum Manhattan distance of $x$ from each of the input sequences is minimized. For binary sequences Manhattan distance coincides with Hamming distance, hence in this case the string consensus problem (also called string center problem or closest string problem) is a special case of MSC. Our main result is a practically efficient $O(l)$-time algorithm solving MSC for $k\le 5$ sequences. Practicality of our algorithms has been verified experimentally. It improves upon the quadratic algorithm by Amir et al.\ (SPIRE 2012) for string consensus problem for $k=5$ binary strings. Similarly as in Amir's algorithm we use a column-based framework. We replace the implied general integer linear programming by its easy special cases, due to combinatorial properties of the MSC for $k\le 5$. We also show that for a general parameter $k$ any instance can be reduced in linear time to a kernel of size $k!$, so the problem is fixed-parameter tractable. Nevertheless, for $k\ge 4$ this is still too large for any naive solution to be feasible in practice.Comment: accepted to SPIRE 201

Hybrid quantum computing with ancillas

In the quest to build a practical quantum computer, it is important to use efficient schemes for enacting the elementary quantum operations from which quantum computer programs are constructed. The opposing requirements of well-protected quantum data and fast quantum operations must be balanced to maintain the integrity of the quantum information throughout the computation. One important approach to quantum operations is to use an extra quantum system - an ancilla - to interact with the quantum data register. Ancillas can mediate interactions between separated quantum registers, and by using fresh ancillas for each quantum operation, data integrity can be preserved for longer. This review provides an overview of the basic concepts of the gate model quantum computer architecture, including the different possible forms of information encodings - from base two up to continuous variables - and a more detailed description of how the main types of ancilla-mediated quantum operations provide efficient quantum gates.Comment: Review paper. An introduction to quantum computation with qudits and continuous variables, and a review of ancilla-based gate method

Numerical semigroups with large embedding dimension satisfy Wilf's conjecture

We give an affirmative answer to Wilf's conjecture for numerical semigroups satisfying 2 \nu \geq m, where \nu and m are respectively the embedding dimension and the multiplicity of a semigroup. The conjecture is also proved when m \leq 8 and when the semigroup is generated by a generalized arithmetic sequence.Comment: 13 page

Regina Lectures on Fat Points

These notes are a record of lectures given in the Workshop on Connections Between Algebra and Geometry at the University of Regina, May 29--June 1, 2012. The lectures were meant as an introduction to current research problems related to fat points for an audience that was not expected to have much background in commutative algebra or algebraic geometry (although sections 8 and 9 of these notes demand somewhat more background than earlier sections).Comment: 32 pages, 3 figure

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

A deep cut ellipsoid algorithm for convex programming

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported

Hypoxic Pulmonary Vasoconstriction in Humans:Tale or Myth

Hypoxic Pulmonary vasoconstriction (HPV) describes the physiological adaptive process of lungs to preserves systemic oxygenation. It has clinical implications in the development of pulmonary hypertension which impacts on outcomes of patients undergoing cardiothoracic surgery. This review examines both acute and chronic hypoxic vasoconstriction focusing on the distinct clinical implications and highlights the role of calcium and mitochondria in acute versus the role of reactive oxygen species and Rho GTPases in chronic HPV. Furthermore it identifies gaps of knowledge and need for further research in humans to clearly define this phenomenon and the underlying mechanism