An Exact Algorithm for the Generalized List TT-Coloring Problem

The generalized list $T$-coloring is a common generalization of many graph coloring models, including classical coloring, $L(p,q)$-labeling, channel assignment and $T$-coloring. Every vertex from the input graph has a list of permitted labels. Moreover, every edge has a set of forbidden differences. We ask for such a labeling of vertices of the input graph with natural numbers, in which every vertex gets a label from its list of permitted labels and the difference of labels of the endpoints of each edge does not belong to the set of forbidden differences of this edge. In this paper we present an exact algorithm solving this problem, running in time $\mathcal{O}^*((\tau+2)^n)$, where $\tau$ is the maximum forbidden difference over all edges of the input graph and $n$ is the number of its vertices. Moreover, we show how to improve this bound if the input graph has some special structure, e.g. a bounded maximum degree, no big induced stars or a perfect matching

Assigning channels via the meet-in-the-middle approach

We study the complexity of the Channel Assignment problem. By applying the meet-in-the-middle approach we get an algorithm for the $\ell$-bounded Channel Assignment (when the edge weights are bounded by $\ell$) running in time $O^*((2\sqrt{\ell+1})^n)$. This is the first algorithm which breaks the $(O(\ell))^n$ barrier. We extend this algorithm to the counting variant, at the cost of slightly higher polynomial factor. A major open problem asks whether Channel Assignment admits a $O(c^n)$-time algorithm, for a constant $c$ independent of $\ell$. We consider a similar question for Generalized T-Coloring, a CSP problem that generalizes \CA. We show that Generalized T-Coloring does not admit a $2^{2^{o\left(\sqrt{n}\right)}} {\rm poly}(r)$-time algorithm, where $r$ is the size of the instance.Comment: SWAT 2014: 282-29

Tight lower bound for the channel assignment problem

We study the complexity of the Channel Assignment problem. A major open problem asks whether Channel Assignment admits an $O(c^n)$-time algorithm, for a constant $c$ independent of the weights on the edges. We answer this question in the negative i.e. we show that there is no $2^{o(n\log n)}$-time algorithm solving Channel Assignment unless the Exponential Time Hypothesis fails. Note that the currently best known algorithm works in time $O^*(n!) = 2^{O(n\log n)}$ so our lower bound is tight

Chemically triggered formation of two-dimensional epitaxial quantum dot superlattices

Two dimensional superlattices of epitaxially connected quantum dots enable size-quantization effects to be combined with high charge carrier mobilities, an essential prerequisite for highly performing QD devices based on charge transport. Here, we demonstrate that surface active additives known to restore nanocrystal stoichiometry can trigger the formation of epitaxial superlattices of PbSe and PbS quantum dots. More specifically, we show that both chalcogen-adding (sodium sulfide) and lead oleate displacing (amines) additives induce small area epitaxial superlattices of PbSe quantum dots. In the latter case, the amine basicity is a sensitive handle to tune the superlattice symmetry, with strong and weak bases yielding pseudohexagonal or quasi-square lattices, respectively. Through density functional theory calculations and in situ titrations monitored by nuclear magnetic resonance spectroscopy, we link this observation to the concomitantly different coordination enthalpy and ligand displacement potency of the amine. Next to that, an initial similar to 10% reduction of the initial ligand density prior to monolayer formation and addition of a mild, lead oleate displacing chemical trigger such as aniline proved key to induce square superlattices with long-range, square micrometer order; an effect that is the more pronounced the larger the quantum dots. Because the approach applies to PbS quantum dots as well, we conclude that it offers a reproducible and rational method for the formation of highly ordered epitaxial quantum dot superlattices

Imaging CF\u3csub\u3e3\u3c/sub\u3eI conical intersection and photodissociation dynamics with ultrafast electron diffraction

Conical intersections play a critical role in excited-state dynamics of polyatomic molecules because they govern the reaction pathways of many nonadiabatic processes. However, ultrafast probes have lacked sufficient spatial resolution to image wave-packet trajectories through these intersections directly. Here, we present the simultaneous experimental characterization of one-photon and two-photon excitation channels in isolated CF3I molecules using ultrafast gas-phase electron diffraction. In the two-photon channel, we have mapped out the real-space trajectories of a coherent nuclear wave packet, which bifurcates onto two potential energy surfaces when passing through a conical intersection. In the one-photon channel, we have resolved excitation of both the umbrella and the breathing vibrational modes in the CF3 fragment in multiple nuclear dimensions. These findings benchmark and validate ab initio nonadiabatic dynamics calculations. Includes supplementary materials. Movie S1 attached below

TiO2@BSA nano-composites investigated through orthogonal multi-techniques characterization platform.

Abstract Biocompatible coating based on bovine serum albumin (BSA) was applied on two different TiO2 nanoparticles (aeroxide P25 and food grade E171) to investigate properties and stability of resulting TiO2@BSA composites, under the final perspective to create a "Safe-by-Design" coating, able to uniform, level off and mitigate surface chemistry related phenomena, as naturally occurring when nano-phases come in touch with proteins enriched biological fluids. The first step towards validating the proposed approach is a detailed characterization of surface chemistry with the quantification of amount and stability of BSA coating deposited on nanoparticles' surfaces. At this purpose, we implemented an orthogonal multi-techniques characterization platform, providing important information on colloidal behavior, particle size distribution and BSA-coating structure of investigated TiO2 systems. Specifically, the proposed orthogonal approach enabled the quantitative determination of bound and free (not adsorbed) BSA, a key aspect for the design of intentionally BSA coated nano-structures, in nanomedicine and, overall, for the control of nano-surface reactivity. In fact, the BSA-coating strategy developed and the orthogonal characterisation performed can be extended to different designed nanomaterials in order to further investigate the protein-corona formation and promote the implementation of BSA engineered coating as a strategy to harmonize the surface reactivity and minimize the biological impact

Recursion Relations in pp-adic Mellin Space

In this work, we formulate a set of rules for writing down $p$-adic Mellin amplitudes at tree-level. The rules lead to closed-form expressions for Mellin amplitudes for arbitrary scalar bulk diagrams. The prescription is recursive in nature, with two different physical interpretations: one as a recursion on the number of internal lines in the diagram, and the other as reminiscent of on-shell BCFW recursion for flat-space amplitudes, especially when viewed in auxiliary momentum space. The prescriptions are proven in full generality, and their close connection with Feynman rules for real Mellin amplitudes is explained. We also show that the integrands in the Mellin-Barnes representation of both real and $p$-adic Mellin amplitudes, the so-called pre-amplitudes, can be constructed according to virtually identical rules, and that these pre-amplitudes themselves may be re-expressed as products of particular Mellin amplitudes with complexified conformal dimensions.Comment: 45 pages + appendices, several figure