Cross-Composition: A New Technique for Kernelization Lower Bounds

We introduce a new technique for proving kernelization lower bounds, called cross-composition. A classical problem L cross-composes into a parameterized problem Q if an instance of Q with polynomially bounded parameter value can express the logical OR of a sequence of instances of L. Building on work by Bodlaender et al. (ICALP 2008) and using a result by Fortnow and Santhanam (STOC 2008) we show that if an NP-complete problem cross-composes into a parameterized problem Q then Q does not admit a polynomial kernel unless the polynomial hierarchy collapses. Our technique generalizes and strengthens the recent techniques of using OR-composition algorithms and of transferring the lower bounds via polynomial parameter transformations. We show its applicability by proving kernelization lower bounds for a number of important graphs problems with structural (non-standard) parameterizations, e.g., Chromatic Number, Clique, and Weighted Feedback Vertex Set do not admit polynomial kernels with respect to the vertex cover number of the input graphs unless the polynomial hierarchy collapses, contrasting the fact that these problems are trivially fixed-parameter tractable for this parameter. We have similar lower bounds for Feedback Vertex Set.Comment: Updated information based on final version submitted to STACS 201

Kernelization Lower Bounds By Cross-Composition

We introduce the cross-composition framework for proving kernelization lower bounds. A classical problem L AND/OR-cross-composes into a parameterized problem Q if it is possible to efficiently construct an instance of Q with polynomially bounded parameter value that expresses the logical AND or OR of a sequence of instances of L. Building on work by Bodlaender et al. (ICALP 2008) and using a result by Fortnow and Santhanam (STOC 2008) with a refinement by Dell and van Melkebeek (STOC 2010), we show that if an NP-hard problem OR-cross-composes into a parameterized problem Q then Q does not admit a polynomial kernel unless NP \subseteq coNP/poly and the polynomial hierarchy collapses. Similarly, an AND-cross-composition for Q rules out polynomial kernels for Q under Bodlaender et al.'s AND-distillation conjecture. Our technique generalizes and strengthens the recent techniques of using composition algorithms and of transferring the lower bounds via polynomial parameter transformations. We show its applicability by proving kernelization lower bounds for a number of important graphs problems with structural (non-standard) parameterizations, e.g., Clique, Chromatic Number, Weighted Feedback Vertex Set, and Weighted Odd Cycle Transversal do not admit polynomial kernels with respect to the vertex cover number of the input graphs unless the polynomial hierarchy collapses, contrasting the fact that these problems are trivially fixed-parameter tractable for this parameter. After learning of our results, several teams of authors have successfully applied the cross-composition framework to different parameterized problems. For completeness, our presentation of the framework includes several extensions based on this follow-up work. For example, we show how a relaxed version of OR-cross-compositions may be used to give lower bounds on the degree of the polynomial in the kernel size.Comment: A preliminary version appeared in the proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) under the title "Cross-Composition: A New Technique for Kernelization Lower Bounds". Several results have been strengthened compared to the preliminary version (http://arxiv.org/abs/1011.4224). 29 pages, 2 figure

Progress on single barrier varactors for submillimeter wave power generation

Theoretical work on Single Barrier Varactor (SBV) diodes, indicate that the efficiency for a multiplier has a maximum for a considerably smaller capacitance variation than previously thought. The theoretical calculations are performed, both with a simple theoretical model and a complete computer simulation using the method of harmonic balance. Modeling of the SBV is carried out in two steps. First, the semiconductor transport equations are solved simultaneously using a finite difference scheme in one dimension. Secondly, the calculated I-V, and C-V characteristics are input to a multiplier simulator which calculates the optimum impedances, and output powers at the frequencies of interest. Multiple barrier varactors can also be modeled in this way. Several examples on how to design the semiconductor layers to obtain certain characteristics are given. The calculated conversion efficiencies of the modeled structures, in a multiplier circuit, are also presented. Computer simulations for a case study of a 750 GHz multiplier show that InAs diodes perform favorably compared to GaAs diodes. InAs and InGaAs SBV diodes have been fabricated and their current vs. voltage characteristics are presented. In the InAs diode, was the large bandgap semiconductor AlSb used as barrier. The InGaAs diode was grown lattice matched to an InP substrate with InAlAs as a barrier material. The current density is greatly reduced for these two material combinations, compared to that of GaAs/AlGaAs SBV diodes. GaAs based diodes can be biased to higher voltages than InAs diodes

IMPROVING PROJECT MANAGEMENT FOR SUSTAINABLE DEVELOPMENT

Institutional and Behavioral Economics,

Alloying effects on the optical properties of Ge1−x_{1-x}Six_x nanocrystals from TDDFT and comparison with effective-medium theory

We present the optical spectra of Ge$_{1-x}$Si$_x$ alloy nanocrystals calculated with time-dependent density-functional theory in the adiabatic local-density ap proximation (TDLDA). The spectra change smoothly as a function of the compositio n $x$. On the Ge side of the composition range, the lowest excitations at the ab sorption edge are almost pure Kohn-Sham independent-particle HOMO-LUMO transitio ns, while for higher Si contents strong mixing of transitions is found. Within T DLDA the first peak is slightly higher in energy than in earlier independent-par ticle calculations. However, the absorption onset and in particular its composit ion dependence is similar to independent-particle results. Moreover, classical depolarization effects are responsible for a very strong suppression of the abs orption intensity. We show that they can be taken into account in a simpler way using Maxwell-Garnett classical effective-medium theory. Emission spectra are in vestigated by calculating the absorption of excited nanocrystals at their relaxe d geometry. The structural contribution to the Stokes shift is about 0.5 eV. Th e decomposition of the emission spectra in terms of independent-particle transit ions is similar to what is found for absorption. For the emission, very weak tra nsitions are found in Ge-rich clusters well below the strong absorption onset.Comment: submitted to Phys. Rev.

Subnormalized states and trace-nonincreasing maps

We investigate the set of completely positive, trace-nonincreasing linear maps acting on the set M_N of mixed quantum states of size N. Extremal point of this set of maps are characterized and its volume with respect to the Hilbert-Schmidt (Euclidean) measure is computed explicitly for an arbitrary N. The spectra of partially reduced rescaled dynamical matrices associated with trace-nonincreasing completely positive maps belong to the N-cube inscribed in the set of subnormalized states of size N. As a by-product we derive the measure in M_N induced by partial trace of mixed quantum states distributed uniformly with respect to HS-measure in $M_{N^2}$.Comment: LaTeX, 21 pages, 4 Encapsuled PostScript figures, 1 tabl

Measurement efficiency and n-shot read out of spin qubits

We consider electron spin qubits in quantum dots and define a measurement efficiency e to characterize reliable measurements via n-shot read outs. We propose various implementations based on a double dot and quantum point contact (QPC) and show that the associated efficiencies e vary between 50% and 100%, allowing single-shot read out in the latter case. We model the read out microscopically and derive its time dynamics in terms of a generalized master equation, calculate the QPC current and show that it allows spin read out under realistic conditions.Comment: 5 pages, 1 figur

The detached dust shells around the carbon AGB stars R Scl and V644 Sco

Detached shells are believed to be created during a thermal pulse, and constrain the time scales and physical properties of one of the main drivers of late stellar evolution. We aim at determining the morphology of the detached dust shells around the carbon AGB stars R Scl and V644 Sco, and compare this to observations of the detached gas shells. We observe the polarised, dust-scattered stellar light around these stars using the PolCor instrument mounted on the ESO 3.6m telescope. Observations were done with a coronographic mask to block out the direct stellar light. The polarised images clearly show the detached shells. Using a dust radiative transfer code to model the dust-scattered polarised light, we constrain the radii and widths of the shells to 19.5 arcsec and 9.4 arcsec for the detached dust shells around R Scl and V644 Sco, respectively. Both shells have an overall spherical symmetry and widths of approx. 2 arcsec. For R Scl we can compare the observed dust emission directly with high spatial-resolution maps of CO(3-2) emission from the shell observed with ALMA. We find that the dust and gas coincide almost exactly, indicating a common evolution. The data presented here for R Scl are the most detailed observations of the entire dusty detached shell to date. For V644 Sco these are the first direct measurements of the detached shell. Also here we find that the dust most likely coincides with the gas shell. The observations are consistent with a scenario where the detached shells are created during a thermal pulse. The determined radii and widths will constrain hydrodynamical models describing the pre-pulse mass loss, the thermal pulse, and post-pulse evolution of the star