541 research outputs found
Minimal half-spaces and external representation of tropical polyhedra
We give a characterization of the minimal tropical half-spaces containing a
given tropical polyhedron, from which we derive a counter example showing that
the number of such minimal half-spaces can be infinite, contradicting some
statements which appeared in the tropical literature, and disproving a
conjecture of F. Block and J. Yu. We also establish an analogue of the
Minkowski-Weyl theorem, showing that a tropical polyhedron can be equivalently
represented internally (in terms of extreme points and rays) or externally (in
terms of half-spaces containing it). A canonical external representation of a
polyhedron turns out to be provided by the extreme elements of its tropical
polar. We characterize these extreme elements, showing in particular that they
are determined by support vectors.Comment: 19 pages, 4 figures, example added with a new figure, figures
improved, references update
Radiocarbon positive-ion mass spectrometry
Proof-of-principle of a new mass spectrometric technique for radiocarbon measurement is demonstrated. Interfering nitrogen and hydrocarbon molecules are largely eliminated in a charge-exchange cell operating on non-metallic gas. The positive-to-negative ion conversion is the reverse of that conventionally used in accelerator mass spectrometry (AMS) and is compatible with plasma ion sources that may be significantly more efficient and capable of greater output than are AMS sputter ion sources. The Nanogan electron cyclotron resonance (ECR) ion source employed exhibited no sample memory and the >50 kyrs age range of AMS was reproduced. A bespoke prototype new instrument is now required to optimise the plasma and cell physics and to realise hypothetical performance gains over AMS
Computing the vertices of tropical polyhedra using directed hypergraphs
We establish a characterization of the vertices of a tropical polyhedron
defined as the intersection of finitely many half-spaces. We show that a point
is a vertex if, and only if, a directed hypergraph, constructed from the
subdifferentials of the active constraints at this point, admits a unique
strongly connected component that is maximal with respect to the reachability
relation (all the other strongly connected components have access to it). This
property can be checked in almost linear-time. This allows us to develop a
tropical analogue of the classical double description method, which computes a
minimal internal representation (in terms of vertices) of a polyhedron defined
externally (by half-spaces or hyperplanes). We provide theoretical worst case
complexity bounds and report extensive experimental tests performed using the
library TPLib, showing that this method outperforms the other existing
approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section
5 (using directed hypergraphs), detailed appendix; v3: major revision of the
article (adding tropical hyperplanes, alternative method by arrangements,
etc); v4: minor revisio
Tropical analogues of a Dempe-Franke bilevel optimization problem
We consider the tropical analogues of a particular bilevel optimization
problem studied by Dempe and Franke and suggest some methods of solving these
new tropical bilevel optimization problems. In particular, it is found that the
algorithm developed by Dempe and Franke can be formulated and its validity can
be proved in a more general setting, which includes the tropical bilevel
optimization problems in question. We also show how the feasible set can be
decomposed into a finite number of tropical polyhedra, to which the tropical
linear programming solvers can be applied.Comment: 11 pages, 1 figur
Reachability problems for products of matrices in semirings
We consider the following matrix reachability problem: given square
matrices with entries in a semiring, is there a product of these matrices which
attains a prescribed matrix? We define similarly the vector (resp. scalar)
reachability problem, by requiring that the matrix product, acting by right
multiplication on a prescribed row vector, gives another prescribed row vector
(resp. when multiplied at left and right by prescribed row and column vectors,
gives a prescribed scalar). We show that over any semiring, scalar reachability
reduces to vector reachability which is equivalent to matrix reachability, and
that for any of these problems, the specialization to any is
equivalent to the specialization to . As an application of this result and
of a theorem of Krob, we show that when , the vector and matrix
reachability problems are undecidable over the max-plus semiring
. We also show that the matrix, vector, and scalar
reachability problems are decidable over semirings whose elements are
``positive'', like the tropical semiring .Comment: 21 page
Cyclic projectors and separation theorems in idempotent convex geometry
Semimodules over idempotent semirings like the max-plus or tropical semiring
have much in common with convex cones. This analogy is particularly apparent in
the case of subsemimodules of the n-fold cartesian product of the max-plus
semiring it is known that one can separate a vector from a closed subsemimodule
that does not contain it. We establish here a more general separation theorem,
which applies to any finite collection of closed semimodules with a trivial
intersection. In order to prove this theorem, we investigate the spectral
properties of certain nonlinear operators called here idempotent cyclic
projectors. These are idempotent analogues of the cyclic nearest-point
projections known in convex analysis. The spectrum of idempotent cyclic
projectors is characterized in terms of a suitable extension of Hilbert's
projective metric. We deduce as a corollary of our main results the idempotent
analogue of Helly's theorem.Comment: 20 pages, 1 figur
Direct Power Control Scheme Based on Disturbance Rejection Principle for Three-Phase PWM AC/DC Converter under Different Input Voltage Conditions
Conventional direct power control (DPC) technique is a simple and efficient control strategy for three-phase PWM rectifier. However, its performance is deteriorated when the converter is supplied by unbalanced or distorted grid voltages. This paper describes the design and implementation of a new configuration of DPC based on disturbance rejection principle to achieve near-sinusoidal input current waveforms of the converter under different input voltage conditions. In the proposed DPC scheme, instantaneous active and reactive powers provided by harmonic component of input currents are directly controlled using a predefined switching table. In order to achieve full rejection of the effect of any disturbance on the quality of input currents, the reference of both controlled powers are directly given from the outside of the controller and are equal to zero. Moreover, prior knowledge of disturbance's nature, calculation of positive and negative sequences of unbalanced input voltages and content harmonic extraction are not required for the proposed DPC. Compared to the conventional DPC, the proposed one uses a PLL block to extract the fundamental of input currents and defining the position of the grid voltage vector in α-β plane without any passive filters. Finally, the simulation results have verified the validity of the proposed DPC and have proven an excellent performance under different input voltage conditions. Full disturbance rejection and good robustness towards supply voltage disturbances are the main advantages of the proposed DPC compared to the conventional one
Stability and convergence in discrete convex monotone dynamical systems
We study the stable behaviour of discrete dynamical systems where the map is
convex and monotone with respect to the standard positive cone. The notion of
tangential stability for fixed points and periodic points is introduced, which
is weaker than Lyapunov stability. Among others we show that the set of
tangentially stable fixed points is isomorphic to a convex inf-semilattice, and
a criterion is given for the existence of a unique tangentially stable fixed
point. We also show that periods of tangentially stable periodic points are
orders of permutations on letters, where is the dimension of the
underlying space, and a sufficient condition for global convergence to periodic
orbits is presented.Comment: 36 pages, 1 fugur
Droplet actuation induced by coalescence: experimental evidences and phenomenological modeling
This paper considers the interaction between two droplets placed on a
substrate in immediate vicinity. We show here that when the two droplets are of
different fluids and especially when one of the droplet is highly volatile, a
wealth of fascinating phenomena can be observed. In particular, the interaction
may result in the actuation of the droplet system, i.e. its displacement over a
finite length. In order to control this displacement, we consider droplets
confined on a hydrophilic stripe created by plasma-treating a PDMS substrate.
This controlled actuation opens up unexplored opportunities in the field of
microfluidics. In order to explain the observed actuation phenomenon, we
propose a simple phenomenological model based on Newton's second law and a
simple balance between the driving force arising from surface energy gradients
and the viscous resistive force. This simple model is able to reproduce
qualitatively and quantitatively the observed droplet dynamics
- …