Large Scale Clustering with Variational EM for Gaussian Mixture Models

How can we efficiently find large numbers of clusters in large data sets with high-dimensional data points? Our aim is to explore the current efficiency and large-scale limits in fitting a parametric model for clustering to data distributions. To do so, we combine recent lines of research which have previously focused on separate specific methods for complexity reduction. We first show theoretically how the clustering objective of variational EM (which reduces complexity for many clusters) can be combined with coreset objectives (which reduce complexity for many data points). Secondly, we realize a concrete highly efficient iterative procedure which combines and translates the theoretical complexity gains of truncated variational EM and coresets into a practical algorithm. For very large scales, the high efficiency of parameter updates then requires (A) highly efficient coreset construction and (B) highly efficient initialization procedures (seeding) in order to avoid computational bottlenecks. Fortunately very efficient coreset construction has become available in the form of light-weight coresets, and very efficient initialization has become available in the form of AFK-MC$^2$ seeding. The resulting algorithm features balanced computational costs across all constituting components. In applications to standard large-scale benchmarks for clustering, we investigate the algorithm's efficiency/quality trade-off. Compared to the best recent approaches, we observe speedups of up to one order of magnitude, and up to two orders of magnitude compared to the $k$-means++ baseline. To demonstrate that the observed efficiency enables previously considered unfeasible applications, we cluster the entire and unscaled 80 Mio. Tiny Images dataset into up to 32,000 clusters. To the knowledge of the authors, this represents the largest scale fit of a parametric data model for clustering reported so far

Molecular Taxonomy of the Lichen Genus Heterodermia

Heterodermia is lichen consisting of a fungus and algae. Morphology and chemistry cannot provide definitive evidence for the identity of Heterodermia because various species have very similar morphologies that cannot always be distinguished. Other species only differ by the presence or absence of secondary chemicals detected. by specific chemical tests, which makes distinguishing between two species difficult. The objective of this project is to use Restriction Fragment Length Polymorphisms (RFLPs) to determine how closely related each Heterodermia species is to one another. RFLPs will also be used to determine how closely related a species is to its equal in another geographical location. ITS-I and ITS-2, the regions surrounding the 5.Ss ribosomal DNA sequence, is the location of interest because they arc noncoding regions and will accumulate mutations even among closely related taxa. Lichen material was homogenized in protcinase k enzyme and digested with TRI reagent (Sigma). Regions ITS-I and ITS-2 were isolated and purified using PCR with primers ITS-5 and ITS-4, which arc located in the 3\u27 end of the ssU rDNAon the+ strand and in the 5\u27 end of the lsU rDNA on the- strand, respectively. After the PCR step, the eight species of Heterodennia and one control, Anaptychia palmatula, were divided into two groups based on the sizes of the PCR products, which were e 600 hp andw 800 hp. Both groups were digested with EcoR I, qo I, and Hinfi. All species displayed different restriction patterns except for H. leucomela and H. barberifera. These two species will be further studied by DNA sequencing to see how close of a relationship they have. Five species were compared with their equals from other geographical locations. Three species displayed similar restriction patterns between the two geographical locations. One species, H. casarettiana displayed different restriction patterns. Another species, H speciosa, produced a PCR fragment of a size that did not match the other strain examined. Restriction digest analysis confirmed this finding. Based on these experiments, discovery of a new species or subspecies is possible. Future experiments will include DNA sequencing

Axial patterning of the chondrichthyan pharyngeal endoskeleton and the origin of the jaw

Classical comparative anatomical hypotheses propose that the upper and lower jaw evolved through modification of dorsal and ventral gill arch skeletal elements, respectively. These hypotheses were based largely on the skeletal anatomy of chondrichthyans (sharks, skates and holocephalans), but remain largely untested from a developmental perspective. Here, I test 1) whether jaws and gill arches ancestrally shared common developmental patterning mechanisms, and 2) whether the mandibular arch might carry anatomical vestiges of an ancestral gill-arch-like condition. To do this, I have used embryos of a cartilaginous fish, the little skate (Leucoraja erinacea), which has retained an ancestral organisation of the jaw and gill arch endoskeleton, and which possesses a reduced gill-like structure (a “pseudobranch”) on the back of the mandibular arch. Using candidate and RNAseq/differential gene expression analysis and mRNA in situ hybridisation, I find broad conservation of dorsoventral patterning mechanisms within pharyngeal arches – embryonic structures which contain the progenitors of the jaw and gill arch skeleton – as well as unique transcriptional features that may underpin distinct jaw and gill arch morphologies. The latter include unique gene expression features of jaw and gill arch muscle progenitors, and of developing gill lamellae. Finally, it has been historically speculated that the chondrichthyan pseudobranch derives from the hyoid (i.e. 2nd pharyngeal) arch. I demonstrate here, by cell lineage tracing, that the pseudobranch is, in fact, mandibular arch derived, that it shares gene expression features with developing gills, and that its supporting spiracular cartilage develops under the influence of a shh-expressing signalling centre, in a manner that parallels that shh-dependent development of branchial rays (i.e. cartilaginous appendages that support the respiratory lamellae of the gill arches). Taken together, this dissertation presents evidence for serial homology of the jaw and gill arch skeleton, and of an ancestral gill-arch nature of the mandibular arch of vertebrates

Fe2-homogenization of micromorphic elasto-plastic materials

In this work, a homogenization strategy for a micromorphic–type inelastic material is presented. In the spirit of FE2, a representative volume element is attached to each macroscopic quadrature point. Due to the inherent length scale of the micromorphic continuum, size effects for inelastic behavior are obtained on RVE–level. A focus is placed on the computation of the homogenized algorithmic tangent. It is determined via sensitivity analyses with respect to the boundary conditions imposed on the RVE. Following this procedure, costly single–scale computations with dense meshes can be replaced by a robust homogenization approach with optimal convergence rates

The thermal Hall effect of spin excitations in a Kagome magnet

At low temperatures, the thermal conductivity of spin excitations in a magnetic insulator can exceed that of phonons. However, because they are charge neutral, the spin waves are not expected to display a thermal Hall effect in a magnetic field. Recently, this semiclassical notion has been upended in quantum magnets in which the spin texture has a finite chirality. In the Kagome lattice, the chiral term generates a Berry curvature. This results in a thermal Hall conductivity $\kappa_{xy}$ that is topological in origin. Here we report observation of a large $\kappa_{xy}$ in the Kagome magnet Cu(1-3, bdc) which orders magnetically at 1.8 K. The observed $\kappa_{xy}$ undergoes a remarkable sign-reversal with changes in temperature or magnetic field, associated with sign alternation of the Chern flux between magnon bands. We show that thermal Hall experiments probe incisively the effect of Berry curvature on heat transport.Comment: 6 pages, 3 figure

Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterize the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of three-dimensional numerical examples serve to elucidate the theory