Local Rademacher Complexity for Multi-Label Learning

© 1992-2012 IEEE. We analyze the local Rademacher complexity of empirical risk minimization-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the multi-label predictor, we instead minimize the tail sum of the singular values of the predictor in multi-label learning. Benefiting from the use of the local Rademacher complexity, our algorithm, therefore, has a sharper generalization error bound. Compared with methods that minimize over all singular values, concentrating on the tail singular values results in better recovery of the low-rank structure of the multi-label predictor, which plays an important role in exploiting label correlations. We propose a new conditional singular value thresholding algorithm to solve the resulting objective function. Moreover, a variance control strategy is employed to reduce the variance of variables in optimization. Empirical studies on real-world data sets validate our theoretical results and demonstrate the effectiveness of the proposed algorithm for multi-label learning

Dimensionality-dependent generalization bounds for k-dimensional coding schemes

© 2016 Massachusetts Institute of Technology. The k-dimensional coding schemes refer to a collection of methods that attempt to represent data using a set of representative k-dimensional vectors and include nonnegative matrix factorization, dictionary learning, sparse coding, k-means clustering, and vector quantization as special cases. Previous generalization bounds for the reconstruction error of the k-dimensional coding schemes are mainly dimensionality-independent. A major advantage of these bounds is that they can be used to analyze the generalization error when data are mapped into an infinite- or high-dimensional feature space. However, many applications use finite-dimensional data features. Can we obtain dimensionality-dependent generalization bounds for k-dimensional coding schemes that are tighter than dimensionality-independent bounds when data are in a finite-dimensional feature space? Yes. In this letter, we address this problem and derive a dimensionality-dependent generalization bound for k-dimensional coding schemes by bounding the covering number of the loss function class induced by the reconstruction error. The bound is of order O((mk ln(mkn)/n)λn, where m is the dimension of features, k is the number of the columns in the linear implementation of coding schemes, and n is the size of sample, λn > 0.5 when n is finite and λn = 0.5 when n is infinite. We show that our bound can be tighter than previous results because it avoids inducing the worst-case upper bound on k of the loss function. The proposed generalization bound is also applied to some specific coding schemes to demonstrate that the dimensionality-dependent bound is an indispensable complement to the dimensionality-independent generalization bounds

Two types of generalized integrable decompositions and new solitary-wave solutions for the modified Kadomtsev-Petviashvili equation with symbolic computation

The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N-coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry Lax pairs. In these two cases, the decomposed (1+1)-dimensional nonlinear systems both have a couple of different Lax representations, which means that there are two linear systems associated with the mKP equation under the same constraint between the potential and eigenfunctions. For each Lax representation of the decomposed (1+1)-dimensional nonlinear systems, the corresponding Darboux transformation is further constructed such that a series of explicit solutions of the mKP equation can be recursively generated with the assistance of symbolic computation. In illustration, four new families of solitary-wave solutions are presented and the relevant stability is analyzed.Comment: 23 page

Phylomitogenomics elucidates the evolution of symbiosis in Thoracotremata (Decapoda: Cryptochiridae, Pinnotheridae, Varunidae)

BackgroundThoracotremata belong to the large group of “true” crabs (infraorder Brachyura), and they exhibit a wide range of physiological and morphological adaptations to living in terrestrial, freshwater and marine habitats. Moreover, the clade comprises various symbiotic taxa (Aphanodactylidae, Cryptochiridae, Pinnotheridae, some Varunidae) that are specialised in living with invertebrate hosts, but the evolutionary history of these symbiotic crabs is still partially unresolved.MethodsHere we assembled and characterised the complete mitochondrial genomes (hereafter mitogenomes) of three gall crab species (Cryptochiridae): Kroppcarcinus siderastreicola, Opecarcinus hypostegus and Troglocarcinus corallicola. A phylogenetic tree of the Thoracotremata was reconstructed using 13 protein-coding genes and two ribosomal RNA genes retrieved from three new gall crab mitogenomes and a further 72 available thoracotreme mitogenomes. Furthermore, we applied a comparative analysis to characterise mitochondrial gene order arrangement, and performed a selection analysis to test for selective pressure of the protein-coding genes in symbiotic Cryptochiridae, Pinnotheridae, and Varunidae (Asthenognathus inaequipes and Tritodynamia horvathi).ResultsThe results of the phylogenetic reconstruction confirm the monophyly of Cryptochiridae, which clustered separately from the Pinnotheridae. The latter clustered at the base of the tree with robust branch values. The symbiotic varunids A. inaequipes and T. horvathi clustered together in a clade with free-living Varunidae species, highlighting that symbiosis in the Thoracotremata evolved independently on multiple occasions. Different gene orders were detected in symbionts and free-living species when compared with the ancestral brachyuran gene order. Lastly, the selective pressure analysis detected two positively selected sites in the nad6 gene of Cryptochiridae, but the evidence for positive selection in Pinnotheridae and A. inaequipes and T. horvathi was weak. Adaptive evolution of mitochondrial protein-coding genes is perhaps related to the presumably higher energetic demands of a symbiotic lifestyle.<br/

Conservation of Coral-Associated Fauna

Coral reefs are some of the most biodiverse ecosystems harboring thousands of species, many of them symbionts that play important roles in the survival of their hosts. These associated taxa, mostly invertebrates, remain largely unstudied and the conservation status of the majority of these species is not assessed. With coral reefs under severe global and local threats, effective conservation measures based on a whole ecosystem approach are needed. The IUCN Red List is the most up to date inventory of species’ conservation status, yet does not include symbiont fauna of important host organisms. Here we suggest including associated taxa in future endangerment assessments, especially those living in obligate symbiosis

Diversification and distribution of gall crabs (Brachyura: Cryptochiridae: <i>Opecarcinus</i>) associated with Agariciidae corals

Coral reefs are home to the greatest diversity of marine life, and many species on reefs live in symbiotic associations. Studying the historical biogeography of symbiotic species is key to unravelling (potential) coevolutionary processes and explaining species richness patterns. Coral-dwelling gall crabs (Cryptochiridae) live in obligate symbiosis with a scleractinian host, and are ideally suited to study the evolutionary history between heterogeneous taxa involved in a symbiotic relationship. The genus Opecarcinus Kropp and Manning, 1987, like its host coral family Agariciidae, occurs in both Indo-Pacific and Caribbean seas, and is the only cryptochirid genus with a circumtropical distribution. Here, we use mitochondrial and nuclear DNA gene fragments of Opecarcinus specimens sampled from 21 Indo-Pacific localities and one Atlantic (Caribbean) locality. We applied several species delimitation tests to characterise species diversity, inferred a Bayesian molecular-clock time-calibrated phylogeny to estimate divergence times and performed an ancestral area reconstruction. Time to the most recent common ancestor (tMRCA) of Opecarcinus is estimated at 15−6 Mya (middle Miocene—late Miocene). The genus harbours ~ 15 undescribed species as well as several potential species complexes. There are indications of strict host-specificity patterns in certain Opecarcinus species in the Indo-Pacific and Atlantic, however, a robust phylogeny reconstruction of Agariciidae corals—needed to test this further—is currently lacking. The Indo-West Pacific was inferred to be the most probable ancestral area, from where the Opecarcinus lineage colonised the Western Atlantic and subsequently speciated into O. hypostegus. Opecarcinus likely invaded from the Indo-West Pacific across the East Pacific Barrier to the Atlantic, before the full closure of the Isthmus of Panama. The subsequent speciation of O. hypostegus, is possibly associated with newly available niches in the Caribbean, in combination with genetic isolation following the closure of the Panama Isthmus

Signature of high temperature superconductivity in electron doped Sr2IrO4

Sr2IrO4 was predicted to be a high temperature superconductor upon electron doping since it highly resembles the cuprates in crystal structure, electronic structure and magnetic coupling constants. Here we report a scanning tunneling microscopy/spectroscopy (STM/STS) study of Sr2IrO4 with surface electron doping by depositing potassium (K) atoms. At the 0.5-0.7 monolayer (ML) K coverage, we observed a sharp, V-shaped gap with about 95% loss of density of state (DOS) at EFand visible coherence peaks. The gap magnitude is 25-30 meV for 0.5-0.6 ML K coverage and it closes around 50 K. These behaviors exhibit clear signature of superconductivity. Furthermore, we found that with increased electron doping, the system gradually evolves from an insulating state to a normal metallic state, via a pseudogap-like state and possible superconducting state. Our data suggest possible high temperature superconductivity in electron doped Sr2IrO4, and its remarkable analogy to the cuprates.Comment: 11 pages, 5 figure

Shape complexity and fractality of fracture surfaces of swelled isotactic polypropylene with supercritical carbon dioxide

We have investigated the fractal characteristics and shape complexity of the fracture surfaces of swelled isotactic polypropylene Y1600 in supercritical carbon dioxide fluid through the consideration of the statistics of the islands in binary SEM images. The distributions of area $A$, perimeter $L$, and shape complexity $C$ follow power laws $p(A)\sim A^{-(\mu_A+1)}$, $p(L)\sim L^{-(\mu_L+1)}$, and $p(C)\sim C^{-(\nu+1)}$, with the scaling ranges spanning over two decades. The perimeter and shape complexity scale respectively as $L\sim A^{D/2}$ and $C\sim A^q$ in two scaling regions delimited by $A\approx 10^3$. The fractal dimension and shape complexity increase when the temperature decreases. In addition, the relationships among different power-law scaling exponents $\mu_A$, $\mu_B$, $\nu$, $D$, and $q$ have been derived analytically, assuming that $A$, $L$, and $C$ follow power-law distributions.Comment: RevTex, 6 pages including 7 eps figure