Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

Beyond Search: A Technology Probe Investigation

Purpose — We assert that researchers developing new web interaction tools should consider an array of user motives beyond query-based information retrieval. This chapter reports on two probes used to investigate user activities that go beyond search as traditionally conceived. Design/methodology — This chapter reviews research on user experiences with search engines and general web use. It then describes the design and case study of cards and pebbles, two search engine-based probes developed to help elicit new concepts for web-based experiences. Findings — Participants reflect on their experiences with the probes and offer ideas regarding how to incrementally shift the traditional search paradigm and conceive of the web in new ways. Implications/value — This investigation serves as a starting point by offering criteria that should be considered when designing new ‘beyond search’ tools

Numerical Linked-Cluster Approach to Quantum Lattice Models

We present a novel algorithm that allows one to obtain temperature dependent properties of quantum lattice models in the thermodynamic limit from exact diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach provides a systematic framework to assess finite-size effects and is valid for any quantum lattice model. Unlike high temperature expansions (HTE), which have a finite radius of convergence in inverse temperature, these calculations are accurate at all temperatures provided the range of correlations is finite. We illustrate the power of our approach studying spin models on {\it kagom\'e}, triangular, and square lattices.Comment: 4 pages, 5 figures, published versio

Poly(ADP-Ribose) glycohydrolase (PARG) vs. poly(ADP-Ribose) polymerase (PARP) – function in genome maintenance and relevance of inhibitors for anti-cancer therapy

Poly(ADP-ribose) polymerases (PARPs) are a family of enzymes that catalyze the addition of poly(ADP-ribose) (PAR) subunits onto themselves and other acceptor proteins. PARPs are known to function in a large range of cellular processes including DNA repair, DNA replication, transcription and modulation of chromatin structure. Inhibition of PARP holds great potential for therapy, especially in cancer. Several PARP1/2/3 inhibitors (PARPi) have had success in treating ovarian, breast and prostate tumors harboring defects in the homologous recombination (HR) DNA repair pathway, especially BRCA1/2 mutated tumors. However, treatment is limited to specific sub-groups of patients and resistance can occur, limiting the use of PARPi. Poly(ADP-ribose) glycohydrolase (PARG) reverses the action of PARP enzymes, hydrolysing the ribose-ribose bonds present in poly(ADP-ribose). Like PARPs, PARG is involved in DNA replication and repair and PARG depleted/inhibited cells show increased sensitivity to DNA damaging agents. They also display an accumulation of perturbed replication intermediates which can lead to synthetic lethality in certain contexts. In addition, PARG is thought to play an important role in preventing the accumulation of cytoplasmic PAR and therefore parthanatos, a caspase-independent PAR-mediated type of cell death. In contrast to PARP, the therapeutic potential of PARG has been largely ignored. However, several recent papers have demonstrated the exciting possibilities that inhibitors of this enzyme may have for cancer treatment, both as single agents and in combination with cytotoxic drugs and radiotherapy. This article discusses what is known about the functions of PARP and PARG and the potential future implications of pharmacological inhibition in anti-cancer therapy

A natural Finsler--Laplace operator

We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections nor local coordinates. We show using 1-parameter families of Katok--Ziller metrics that this Finsler--Laplace operator admits explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio

Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result

On the geometry of closed G2-structure

We give an answer to a question posed recently by R.Bryant, namely we show that a compact 7-dimensional manifold equipped with a G2-structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G2. This could be considered to be a G2 analogue of the Goldberg conjecture in almost Kahler geometry. The result was generalized by R.L.Bryant to closed G2-structures with too tightly pinched Ricci tensor. We extend it in another direction proving that a compact G2-manifold with closed fundamental form and divergence-free Weyl tensor is a G2-manifold with parallel fundamental form. We introduce a second symmetric Ricci-type tensor and show that Einstein conditions applied to the two Ricci tensors on a closed G2-structure again imply that the induced metric has holonomy group contained in G2.Comment: 14 pages, the Einstein condition in the assumptions of the Main theorem is generalized to the assumption that the Weyl tensor is divergence-free, clarity improved, typos correcte