Matching image sets via adaptive multi convex hull

Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image set. Existing multi-model approaches extract local models by clustering each image set individually only once, with fixed clusters used for matching with various image sets. This may not be optimal for discrimination, as undesirable environmental conditions (eg. illumination and pose variations) may result in the two closest clusters representing different characteristics of an object (eg. frontal face being compared to non-frontal face). To address the above problem, we propose a novel approach to enhance nearest points based methods by integrating affine/convex hull classification with an adapted multi-model approach. We first extract multiple local convex hulls from a query image set via maximum margin clustering to diminish the artificial variations and constrain the noise in local convex hulls. We then propose adaptive reference clustering (ARC) to constrain the clustering of each gallery image set by forcing the clusters to have resemblance to the clusters in the query image set. By applying ARC, noisy clusters in the query set can be discarded. Experiments on Honda, MoBo and ETH-80 datasets show that the proposed method outperforms single model approaches and other recent techniques, such as Sparse Approximated Nearest Points, Mutual Subspace Method and Manifold Discriminant Analysis.

Dictionary learning and sparse coding on Grassmann manifolds : an extrinsic solution

Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping, which enables us to devise a closed-form solution for updating a Grassmann dictionary, atom by atom. Furthermore, to handle non-linearity in data, we propose a kernelised version of the dictionary learning algorithm. Experiments on several classification tasks (face recognition, action recognition, dynamic texture classification) show that the proposed approach achieves considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelised Affine Hull Method and graph-embedding Grassmann discriminant analysis.

Improved image set classification via joint sparse approximated nearest subspaces

Existing multi-model approaches for image set classification extract local models by clustering each image set individually only once, with fixed clusters used for matching with other image sets. However, this may result in the two closest clusters to represent different characteristics of an object, due to different undesirable environmental conditions (such as variations in illumination and pose). To address this problem, we propose to constrain the clustering of each query image set by forcing the clusters to have resemblance to the clusters in the gallery image sets. We first define a Frobenius norm distance between subspaces over Grassmann manifolds based on reconstruction error. We then extract local linear subspaces from a gallery image set via sparse representation. For each local linear subspace, we adaptively construct the corresponding closest subspace from the samples of a probe image set by joint sparse representation. We show that by minimising the sparse representation reconstruction error, we approach the nearest point on a Grassmann manifold. Experiments on Honda, ETH-80 and Cambridge-Gesture datasets show that the proposed method consistently outperforms several other recent techniques, such as Affine Hull based Image Set Distance (AHISD), Sparse Approximated Nearest Points (SANP) and Manifold Discriminant Analysis (MDA).

The eight variable homogeneous degree three bent functions

We determine the affine equivalence classes of the eight variable degree three homogeneous bent functions using a new algorithm. Our algorithm applies to general bent functions and can systematically determine the automorphism groups. We provide a partial verification of the enumeration of eight variable degree three homogeneous bent functions obtained by Meng et al. We determine the affine equivalence classes of these functions.

A computational model for BMP movement in sea urchin embryos

Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction–diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly.

The antigen 43 structure reveals a molecular velcro-like mechanism of autotransporter-mediated bacterial clumping

Aggregation and biofilm formation are critical mechanisms for bacterial resistance to host immune factors and antibiotics. Autotransporter (AT) proteins, which represent the largest group of outer-membrane and secreted proteins in Gram-negative bacteria, contribute significantly to these phenotypes. Despite their abundance and role in bacterial pathogenesis, most AT proteins have not been structurally characterized, and there is a paucity of detailed information with regard to their mode of action. Here we report the structure–function relationships of Antigen 43 (Ag43a), a prototypic self-associating AT protein from uropathogenic Escherichia coli. The functional domain of Ag43a displays a twisted L-shaped β-helical structure firmly stabilized by a 3D hydrogen-bonded scaffold. Notably, the distinctive Ag43a L shape facilitates self-association and cell aggregation. Combining all our data, we define a molecular “Velcro-like” mechanism of AT-mediated bacterial clumping, which can be tailored to fit different bacterial lifestyles such as the formation of biofilms.

kmth price sealed-bid auctions with general independent values and equilibrium linear mark-ups

A generalised bidding model is developed to calculate a bidder’s expected profit and auctioners expected revenue/payment for both a General Independent Value and Independent Private Value (IPV) kmth price sealed-bid auction (where the mth bidder wins at the kth bid payment) using a linear (affine) mark-up function. The Common Value (CV) assumption, and highbid and lowbid symmetric and asymmetric First Price Auctions and Second Price Auctions are included as special cases. The optimal n bidder symmetric analytical results are then provided for the uniform IPV and CV models in equilibrium. Final comments concern implications, the assumptions involved and prospects for further research.

Scale adaptive tracking using mean shift and efficient feature matching

The mean shift tracker has achieved great success in visual object tracking due to its efficiency being nonparametric. However, it is still difficult for the tracker to handle scale changes of the object. In this paper, we associate a scale adaptive approach with the mean shift tracker. Firstly, the target in the current frame is located by the mean shift tracker. Then, a feature point matching procedure is employed to get the matched pairs of the feature point between target regions in the current frame and the previous frame. We employ FAST-9 corner detector and HOG descriptor for the feature matching. Finally, with the acquired matched pairs of the feature point, the affine transformation between target regions in the two frames is solved to obtain the current scale of the target. Experimental results show that the proposed tracker gives satisfying results when the scale of the target changes, with a good performance of efficiency.

An algorithm for constructing Hjelmslev planes

Projective Hjelmslev planes and affine Hjelmslev planes are generalisations of projective planes and affine planes. We present an algorithm for constructing projective Hjelmslev planes and affine Hjelmslev planes that uses projective planes, affine planes and orthogonal arrays. We show that all 2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelmslev planes can be constructed in this way. As a corollary it is shown that all $2$-uniform affine Hjelmslev planes are sub-geometries of $2$-uniform projective Hjelmslev planes.

On the efficacy of Fourier series approximations for pricing European options

This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the halfrange cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together,these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

3-Phenylisoquinolin-1(2H)-one

The title compound, C15H11NO, consists of a planar isoquinolinone group to which a phenyl ring is attached in a twisted fashion [dihedral angle = 39.44 (4)degrees]. The crystal packing is dominated by intermolecular N-H center dot center dot center dot O and C-H center dot center dot center dot O hydrogen bonds which define centrosymmetric dimeric entitities.

Equivariant Birch-Swinnerton-Dyer Conjecture for the Base Change of Elliptic Curves: An Example

Let E be an elliptic curve defined over Q and let K/Q be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for h(1)(E x(Q) K)(1) viewed as amotive over Q with coefficients in Q[G] relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper I prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S-3-extension of Q.

1-(2,4-Dichlorophenyl)-3-[4-(dimethylamino)-phenyl]prop-2-enone

In the title compound, C17H15Cl2NO, the dimethylaminophenyl group is close to coplanar with the central propenone group [dihedral angle =13.1 (1)degrees between the mean planes], while the dichlorophenyl group is twisted from the plane [dihedral angle = 64.0 (1)degrees].In the crystal, C-H center dot center dot center dot O and weak C-H center dot center dot center dot pi interactions are formed between molecules.

Measuring the traction profile on sportsfields: Equipment development and testing

Traction is recognised as an important component of the overall playability and safety of a sportsfield. It relates to the "grip", or footing, provided through an athlete's shoe when in contact with the surface, and is normally measured by the torque generated when a weighted studded disc apparatus is dropped onto the turf and twisted manually. This paper describes the development of an automated traction tester, which mechanises the dropping and twisting of the weighted studded disc. By standardising these operational stages, more repeatable and reliable results can be expected than from the original hand-operated design where positioning of the disc and speed of rotation are controlled manually and so can vary from one measurement to the next. As well as measuring the maximum torque reached during rotation of the studded disc, the automated traction tester generates a profile of torque showing changes over time and calculates the angle through which the studded disc moved before reaching maximum torque. These aspects are now covered by a utility patent (PAT/AU/2004270767). Use of the automated traction tester is illustrated by comparative data for a range of warm-season turfgrasses, by comparisons of traction under different surface conditions generated by wear on Cynodon dactylon cultivars, and by the effects of environment, management and playing patterns on traction across a multi-use sports stadium.

Bibulocystis gloriosa sp nov (Pucciniales) on Caesalpinia scortechinii in Queensland, with comments on Spumula caesalpiniae

A rust causing leaf spotting and distortion of twigs and branches of Caesalpinia scortechinii in Queensland is described as the new species Bibulocystis gloriosa. Uredinia and telia occur on spotted pinnules, and pycnia, aecial uredinia and telia on galled and twisted leaf rachides, twigs and branches. B. gloriosa is similar to Bibulocystis viennotii on Albizia granulosa in New Caledonia in having a macrocyclic life cycle with all spore states, and teliospores with two fertile cells and two cysts. It differs in having aecial urediniospores and urediniospores with uniformly thickened walls and several scattered germ pores, rather than the apically thickened walls and equatorial germ pores of B. viennotii. Teliospores in the two species are similar in size, but those of B. gloriosa have proportionally larger fertile cells and smaller cysts than in B. viennotii. To date, B. gloriosa is known from only two localities in south-eastern Queensland. Comparison with the type specimen of Spumula caesalpiniae on Caesalpinia nuga from Indonesia has shown that the two rusts are generically distinct.