Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 24 Aug 2019 11:30:26 GMT2019-08-24T11:30:26Z5081Convex hull calculations: a Matlab implementation and correctness proofs for the lrs-algorithmhttp://hdl.handle.net/10316/11428Title: Convex hull calculations: a Matlab implementation and correctness proofs for the lrs-algorithm
Authors: Kovacec, Alexander; Ribeiro, Bernardete
Abstract: This paper provides full Matlab -code and informal correctness proofs
for the lexicographic reverse search algorithm for convex hull calculations. The
implementation was tested on a 1993 486-PC for various small and some larger,
partially highly degenerate combinatorial polytopes, one of which (a certain 13-
dimensional 24 vertex polyhedron) occurs naturally in the study of a well known
problem posed by Professor Graciano de Oliveira: see end of section 1.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/114282003-01-01T00:00:00ZThe Hankel Pencil Conjecturehttp://hdl.handle.net/10316/11297Title: The Hankel Pencil Conjecture
Authors: Kovačec, Alexander; Gouveia, Maria Celeste
Abstract: The Toeplitz pencil conjecture stated in [SS1] and [SS2] is equivalent
to a conjecture for n £ n Hankel pencils of the form Hn(x) = (ci+j¡n+1); where
c0 = x is an indeterminate, cl = 0 for l < 0; and cl 2 C¤ = Cn f0g; for l ¸ 1: In this
paper it is shown to be implied by another conjecture, we call root conjecture. This
latter claims for a certain pair (mnn;mn¡1;n) of submaximal minors of certain special
Hn(x) that, viewed as elements of C[x]; there holds that roots(mnn) µ roots(mn¡1;n)
implies roots(mn¡1;n) = f1g: We give explicit formulae in the ci for these minors
and show the root conjecture for minors mnn;mn¡1;n of degree · 6: This implies
the Hankel Pencil conjecture for matrices up to size 8 £ 8: Main tools involved are
a partial parametrization of the set of solutions of systems of polynomial equations
that are both homogeneous and index sum homogeneous, and use of the Sylvester
identity for matrices.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/112972007-01-01T00:00:00ZPositive semidefinite diagonal minus tail forms are sums of squareshttp://hdl.handle.net/10316/11199Title: Positive semidefinite diagonal minus tail forms are sums of squares
Authors: Fidalgo, Carla; Kovačec, Alexander
Abstract: By a diagonal minus tail form (of even degree) we understand a real
homogeneous polynomial F(x1, ..., xn) = F(x) = D(x) − T(x), where the diagonal
part D(x) is a sum of terms of the form bix2d
i with all bi ≥ 0 and the tail T(x) a sum
of terms ai1i2...inxi1
1 ...xin
n with ai1i2...in > 0 and at least two i ≥ 1. We show that
an arbitrary change of the signs of the tail terms of a positive semidefinite diagonal
minus tail form will result in a sum of squares of polynomials.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/111992008-01-01T00:00:00ZDiagonal minus tail forms and Lasserre's sufficient conditions for sums of squareshttp://hdl.handle.net/10316/11179Title: Diagonal minus tail forms and Lasserre's sufficient conditions for sums of squares
Authors: Fidalgo, Carla; Kovačec, Alexander
Abstract: Using our recent results on diagonal minus tail forms, we give an
easily tested sufficient condition for a polynomial f(x) =
P
i2I fixi in IR[x] =
IR[x1, . . . , xn], to be a sum of squares of polynomials (sos). We show that the class
of polynomials passing this test is wider than the class passing Lasserre’s recent
conditions. Another sufficient condition for f to be sos, like Lasserre’s piecewise
linear in the fi, is also given.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/111792009-01-01T00:00:00ZOptimizing the proﬁt from a complex cascade of hydroelectric stations with recirculating waterhttp://hdl.handle.net/10316/14423Title: Optimizing the proﬁt from a complex cascade of hydroelectric stations with recirculating water
Authors: Korobeinikov, Andrei; Kovacec, Alexander; McGuinness, Mark; Pascoal, Marta; Pereira, Ana; Vilela, Sónia
Abstract: In modern reversible hydroelectric power stations it is possible to
reverse the turbine and pump water up from a downstream reservoir
to an upstream one. This allows the use of the same volume of water
repeatedly and was speciﬁcally developed for hydro-electric stations
operating with insuﬃcient water supply. Pumping water upstream
is usually done at times of low demand for electricity, to build up
reserves in order to be able to produce energy during peak hours, thus
balancing the load and making a proﬁt on the price diﬀerence.
In this paper, we consider a branched model for hydroelectric
power stations interacting in a complex cascade arrangement. The
goal of this study is to provide guidance in decision-making aimed
at maximizing the proﬁt. A detailed analysis is made of a simpler
reservoir conﬁguration, which indicates that even though the problem
is nonlinear, a bang-bang type of control is optimal, where the power
stations are operated at maximum rates of ﬂow. Some simple relation-
ships between price and timing of decisions are calculated directly. A
numerical algorithm is also developed.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/144232010-01-01T00:00:00ZThe Marcus-de Oliveira conjecture, bilinear forms, and coneshttp://hdl.handle.net/10316/4662Title: The Marcus-de Oliveira conjecture, bilinear forms, and cones
Authors: Kovačec, Alexander
Abstract: The well-known determinantal cinjecture of de Oliveira and Marcus (OMC) confines the determinant det (X + Y) of the sum of normaln × n matricesX,Y to a certain region in the complex plane. Even the subconjecture obtained by specializing it ton = 4,X Hermitian andY normal is still open. We view the subconjecture as a special case of an assertion concerning a certain family of bilinear forms ofR16 ×C16 and give a method that may prove useful for establishing it for many of such matrix pairs, independent of their spectrum; in particular we apply it successfully in the case of a prominent unitary similarity of Drury's threatening OMC. Unfortunately we find the assertion, extended naturally to pairs of complex arguments to be false and the ideas outlined inapplicable for the general OMC(n=4) case. We also report on some computer experiments, formulate OMC(n=4) as a statement about cones, and find it would be implied by establishing the emptiness of certain semialgebraic sets defined by systems of quadratic and linear relations.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10316/46621999-01-01T00:00:00ZShaping graph pattern mining for financial riskhttp://hdl.handle.net/10316/44244Title: Shaping graph pattern mining for financial risk
Authors: Ribeiro, Bernardete; Chen, Ning; Kovacec, Alexander
Abstract: In recent years graph pattern mining took a prominent role in knowledge discovery in many scientific fields. From Web advertising to biology and finance, graph data is ubiquitous making pattern-based graph tools increasingly important. When it comes to financial settings, data is very complex and although many successful approaches have been proposed often they neglect the intertwined economic risk factors, which seriously affects the goodness of predictions. In this paper, we posit that financial risk analysis can be leveraged if structure can be taken into account by discovering financial motifs. We look at this problem from a graph-based perspective in two ways, by considering the structure in the inputs, the graphs themselves, and by taking into account the graph embedded structure of the data. In the first, we use gBoost combined with a substructure mining algorithm. In the second, we take a subspace learning graph embedded approach. In our experiments two datasets are used: a qualitative bankruptcy data benchmark and a real-world French database of corporate companies. Furthermore, we propose a graph construction algorithm to extract graph structure from feature vector data. Finally, we empirically show that in both graph-based approaches the financial motifs are crucial for the classification, thereby enhancing the prediction results.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/442442017-01-01T00:00:00ZOn the corners of certain determinantal rangeshttp://hdl.handle.net/10316/4598Title: On the corners of certain determinantal ranges
Authors: Kovačec, Alexander; Bebiano, Natália; Providência, João da
Abstract: Let A be a complex n×n matrix and let SO(n) be the group of real orthogonal matrices of determinant one. Define [Delta](A)={det(AoQ):Q[set membership, variant]SO(n)}, where o denotes the Hadamard product of matrices. For a permutation [sigma] on {1,...,n}, define It is shown that if the equation z[sigma]=det(AoQ) has in SO(n) only the obvious solutions (Q=([epsilon]i[delta][sigma]i,j), [epsilon]i=±1 such that [epsilon]1...[epsilon]n=sgn[sigma]), then the local shape of [Delta](A) in a vicinity of z[sigma] resembles a truncated cone whose opening angle equals , where [sigma]1, [sigma]2 differ from [sigma] by transpositions. This lends further credibility to the well known de Oliveira Marcus Conjecture (OMC) concerning the determinant of the sum of normal n×n matrices. We deduce the mentioned fact from a general result concerning multivariate power series and also use some elementary algebraic topology.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/45982007-01-01T00:00:00Z