764 research outputs found
Speeding up Cylindrical Algebraic Decomposition by Gr\"obner Bases
Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought
of as two, rather different, methods of looking at systems of equations and, in
the case of Cylindrical Algebraic Decomposition, inequalities. However, even
for a mixed system of equalities and inequalities, it is possible to apply
Gr\"obner bases to the (conjoined) equalities before invoking CAD. We see that
this is, quite often but not always, a beneficial preconditioning of the CAD
problem.
It is also possible to precondition the (conjoined) inequalities with respect
to the equalities, and this can also be useful in many cases.Comment: To appear in Proc. CICM 2012, LNCS 736
Reliability of Harvested Rainfall as an Auxiliary Source of Non-potable Water
AbstractRainwater harvesting is an ancient practice that involves collecting, storing, and using precipitationto meeton-site water needs. This paper develops and demonstrates guidelines for sizing the capacity of storage tanks to provide areliable continuous supply of harvested rainwater for residential households. Operation of the rainwater harvesting system is simulated with a stochastic mass balance performed on an Excel spreadsheet. The daily volume of rainwater in an unbounded tank is tracked to determine the maximum accumulated deficit on a monthly basis. Results are summarized in dimensionless charts showing the minimum size of a rainwater storage tankneeded to meet water demands at specified levels of reliability
Constructing Mutually Unbiased Bases in Dimension Six
The density matrix of a qudit may be reconstructed with optimal efficiency if
the expectation values of a specific set of observables are known. In dimension
six, the required observables only exist if it is possible to identify six
mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard
matrix, we construct all others mutually unbiased to it, using algebraic
computations performed by a computer program. We repeat this calculation many
times, sampling all known complex Hadamard matrices, and we never find more
than two that are mutually unbiased. This result adds considerable support to
the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical
approximations and corrected the number of triples existing for non-affine
families (cf Table 3
Hipster: Integrating Theory Exploration in a Proof Assistant
This paper describes Hipster, a system integrating theory exploration with
the proof assistant Isabelle/HOL. Theory exploration is a technique for
automatically discovering new interesting lemmas in a given theory development.
Hipster can be used in two main modes. The first is exploratory mode, used for
automatically generating basic lemmas about a given set of datatypes and
functions in a new theory development. The second is proof mode, used in a
particular proof attempt, trying to discover the missing lemmas which would
allow the current goal to be proved. Hipster's proof mode complements and
boosts existing proof automation techniques that rely on automatically
selecting existing lemmas, by inventing new lemmas that need induction to be
proved. We show example uses of both modes
On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation
The Conte-Musette method has been modified for the search of only elliptic
solutions to systems of differential equations. A key idea of this a priory
restriction is to simplify calculations by means of the use of a few Laurent
series solutions instead of one and the use of the residue theorem. The
application of our approach to the quintic complex one-dimensional
Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave
form. We also find restrictions on coefficients, which are necessary conditions
for the existence of elliptic solutions for the CGLE5. Using the investigation
of the CGLE5 as an example, we demonstrate that to find elliptic solutions the
analysis of a system of differential equations is more preferable than the
analysis of the equivalent single differential equation.Comment: LaTeX, 21 page
A CDCL-style calculus for solving non-linear constraints
In this paper we propose a novel approach for checking satisfiability of
non-linear constraints over the reals, called ksmt. The procedure is based on
conflict resolution in CDCL style calculus, using a composition of symbolical
and numerical methods. To deal with the non-linear components in case of
conflicts we use numerically constructed restricted linearisations. This
approach covers a large number of computable non-linear real functions such as
polynomials, rational or trigonometrical functions and beyond. A prototypical
implementation has been evaluated on several non-linear SMT-LIB examples and
the results have been compared with state-of-the-art SMT solvers.Comment: 17 pages, 3 figures; accepted at FroCoS 2019; software available at
<http://informatik.uni-trier.de/~brausse/ksmt/
Complotype affects the extent of down-regulation by Factor I of the C3b feedback cycle in vitro.
Sera from a large panel of normal subjects were typed for three common polymorphisms, one in C3 (R102G) and two in Factor H (V62I and Y402H), that influence predisposition to age-related macular degeneration and to some forms of kidney disease. Three groups of sera were tested; those that were homozygous for the three risk alleles; those that were heterozygous for all three; and those homozygous for the low-risk alleles. These groups vary in their response to the addition of exogenous Factor I when the alternative complement pathway is activated by zymosan. Both the reduction in the maximum amount of iC3b formed and the rate at which the iC3b is converted to C3dg are affected. For both reactions the at-risk complotype requires higher doses of Factor I to produce similar down-regulation. Because iC3b reacting with the complement receptor CR3 is a major mechanism by which complement activation gives rise to inflammation, the breakdown of iC3b to C3dg can be seen to have major significance for reducing complement-induced inflammation. These findings demonstrate for the first time that sera from subjects with different complement alleles behave as predicted in an in-vitro assay of the down-regulation of the alternative complement pathway by increasing the concentration of Factor I. These results support the hypothesis that exogenous Factor I may be a valuable therapeutic aid for down-regulating hyperactivity of the C3b feedback cycle, thereby providing a treatment for age-related macular degeneration and other inflammatory diseases of later life.This is the author's accepted manuscript and will be under embargo until the 13th of August 2015. This final version is available from Wiley in Clinical & Experimental Immunology at http://onlinelibrary.wiley.com/doi/10.1111/cei.12437/abstract
Exotic solutions in string theory
Solutions of classical string theory, correspondent to the world sheets,
mapped in Minkowsky space with a fold, are considered. Typical processes for
them are creation of strings from vacuum, their recombination and annihilation.
These solutions violate positiveness of square of mass and Regge condition. In
quantum string theory these solutions correspond to physical states |DDF>+|sp>
with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199
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