Finding branch-decompositions of matroids, hypergraphs, and more

Given $n$ subspaces of a finite-dimensional vector space over a fixed finite field $\mathcal F$, we wish to find a "branch-decomposition" of these subspaces of width at most $k$, that is a subcubic tree $T$ with $n$ leaves mapped bijectively to the subspaces such that for every edge $e$ of $T$, the sum of subspaces associated with leaves in one component of $T-e$ and the sum of subspaces associated with leaves in the other component have the intersection of dimension at most $k$. This problem includes the problems of computing branch-width of $\mathcal F$-represented matroids, rank-width of graphs, branch-width of hypergraphs, and carving-width of graphs. We present a fixed-parameter algorithm to construct such a branch-decomposition of width at most $k$, if it exists, for input subspaces of a finite-dimensional vector space over $\mathcal F$. Our algorithm is analogous to the algorithm of Bodlaender and Kloks (1996) on tree-width of graphs. To extend their framework to branch-decompositions of vector spaces, we developed highly generic tools for branch-decompositions on vector spaces. The only known previous fixed-parameter algorithm for branch-width of $\mathcal F$-represented matroids was due to Hlin\v{e}n\'y and Oum (2008) that runs in time $O(n^3)$ where $n$ is the number of elements of the input $\mathcal F$-represented matroid. But their method is highly indirect. Their algorithm uses the non-trivial fact by Geelen et al. (2003) that the number of forbidden minors is finite and uses the algorithm of Hlin\v{e}n\'y (2005) on checking monadic second-order formulas on $\mathcal F$-represented matroids of small branch-width. Our result does not depend on such a fact and is completely self-contained, and yet matches their asymptotic running time for each fixed $k$.Comment: 73 pages, 10 figure

Double resonance of Raman transitions in a degenerate Fermi gas

We measure momentum-resolved Raman spectra of a spin-polarized degenerate Fermi gas of $^{173}$Yb atoms for a wide range of magnetic fields, where the atoms are irradiated by a pair of counterpropagating Raman laser beams as in the conventional spin-orbit coupling scheme. Double resonance of first- and second-order Raman transitions occurs at a certain magnetic field and the spectrum exhibits a doublet splitting for high laser intensities. The measured spectral splitting is quantitatively accounted for by the Autler-Townes effect. We show that our measurement results are consistent with the spinful band structure of a Fermi gas in the spatially oscillating effective magnetic field generated by the Raman laser fields.Comment: 7 pages, 6 figure

Efficient and effective human action recognition in video through motion boundary description with a compact set of trajectories

Human action recognition (HAR) is at the core of human-computer interaction and video scene understanding. However, achieving effective HAR in an unconstrained environment is still a challenging task. To that end, trajectory-based video representations are currently widely used. Despite the promising levels of effectiveness achieved by these approaches, problems regarding computational complexity and the presence of redundant trajectories still need to be addressed in a satisfactory way. In this paper, we propose a method for trajectory rejection, reducing the number of redundant trajectories without degrading the effectiveness of HAR. Furthermore, to realize efficient optical flow estimation prior to trajectory extraction, we integrate a method for dynamic frame skipping. Experiments with four publicly available human action datasets show that the proposed approach outperforms state-of-the-art HAR approaches in terms of effectiveness, while simultaneously mitigating the computational complexity

Bis[(2,2-dimethyl­propano­yloxy)meth­yl] {[2-(6-amino-9H-purin-9-yl)eth­oxy]meth­yl}phospho­nate–succinic acid (2/1)

The title compound, C20H32N5O8P·0.5C4H6O4, is composed of two 9-{2-[bis­(pivaloyloxymeth­oxy)phosphinylmeth­oxy]eth­yl}adenine, commonly known as adefovir dipivoxil (AD), mol­ecules linked to the carb­oxy­lic acid groups of succinic acid (SA). The asymmetric unit contains one mol­ecule of AD and half a mol­ecule of SA, which sits on an inversion center. Both adenine units in the two AD mol­ecules make AD–SA N—H⋯O and SA–AD O—H⋯N hydrogen bonds to SA. In addition, the inter­molecular AD–AD N—H⋯O—P hydrogen bond serves to stabilize the cocrystal. There is also a π–π stacking inter­action [inter­planar spacing 3.34 (19) Å] between adjacent inversion-related adenine groups

KIOM-79 Prevents Lens Epithelial Cell Apoptosis and Lens Opacification in Zucker Diabetic Fatty Rats

Damage of lens epithelial cells (LECs) has been implicated in cataract formation. The aim of this study was to investigate the protective effect of KIOM-79, a combination of four plant extracts, on LECs. We examined the levels of advanced glycation end products (AGEs), nuclear factor-kappaB (NF-κB) activation and inducible nitric oxide synthase (iNOS) expression in LECs during cataract development using the Zucker diabetic fatty (ZDF) rat, an animal model of type 2 diabetes. KIOM-79 was orally administered by gavage to ZDF rats once a day for 13 weeks. Apoptosis was detected by TUNEL assay, and NF-κB activation and iNOS expression were studied by southwestern histochemistry and immunohistochemistry, respectively. In diabetic cataractous lenses, TUNEL-positive LECs were markedly increased 20-fold, and AGEs were highly accumulated (2.7-fold) in LECs. In addition, both NF-κB activation, and iNOS expression were significantly enhanced 3- to 5-fold, respectively, compared to levels found in normal ZL rats. However, the administration of KIOM-79 delayed the development of diabetic cataracts and prevented LEC apoptosis (70%) through the inhibition of AGEs, NF-κB-activation and iNOS expression. These observations suggest that KIOM-79 is useful in inhibiting diabetic cataractogenesis and acts through an antiapoptotic mechanism to protect LECs from injury

Why community-based tourism and rural tourism in developing and developed nations are treated differently? A review

Rural community tourism initiatives in developed nations share most positive and negative characteristics with community-based tourism (CBT) initiatives in developing nations. They also share many barriers and conditions for tourism development. What makes them different is the context in which they operate. This paper identifies the main conditions that explain these differences through a review of findings from 103 location-specific case studies and other available literature that provides empirical evidence. The paper also explores the usage of the concepts of CBT and rural tourism. The findings are discussed under seven categories: Definitions, socioeconomic and cultural factors, policy and governance, land ownership, community cohesiveness, assimilation of external stakeholders, and type of visitors. It is argued that it is the developing-/developed-nation context, and not objectively established criteria, which largely dictates authors’ narratives with corresponding takes on tourism development and subsequent recommendations. The paper engages in a discussion about case-study research, its weaknesses and tendencies, providing some recommendations on how to increase the contribution of case studies to knowledge, and calls for more research on externally assisted non-Indigenous communitytourism initiatives in developed nations