Lattice-based locality sensitive hashing is optimal

Locality sensitive hashing (LSH) was introduced by Indyk and Motwani (STOC ‘98) to give the first sublinear time algorithm for the c-approximate nearest neighbor (ANN) problem using only polynomial space. At a high level, an LSH family hashes “nearby” points to the same bucket and “far away” points to different buckets. The quality of measure of an LSH family is its LSH exponent, which helps determine both query time and space usage. In a seminal work, Andoni and Indyk (FOCS ‘06) constructed an LSH family based on random ball partitionings of space that achieves an LSH exponent of 1/c2 for the ℓ2 norm, which was later shown to be optimal by Motwani, Naor and Panigrahy (SIDMA ‘07) and O’Donnell, Wu and Zhou (TOCT ‘14). Although optimal in the LSH exponent, the ball partitioning approach is computationally expensive. So, in the same work, Andoni and Indyk proposed a simpler and more practical hashing scheme based on Euclidean lattices and provided computational results using the 24-dimensional Leech lattice. However, no theoretical analysis of the scheme was given, thus leaving open the question of finding the exponent of lattice based LSH. In this work, we resolve this question by showing the existence of lattices achieving the optimal LSH exponent of 1/c2 using techniques from the geometry of numbers. At a more conceptual level, our results show that optimal LSH space partitions can have periodic structure. Understanding the extent to which additional structure can be imposed on these partitions, e.g. to yield low space and query complexity, remains an important open problem

Lattice-based locality sensitive hashing is optimal

Locality sensitive hashing (LSH) was introduced by Indyk and Motwani (STOC ‘98) to give the first sublinear time algorithm for the c-approximate nearest neighbor (ANN) problem using only polynomial space. At a high level, an LSH family hashes “nearby” points to the same bucket and “far away” points to different buckets. The quality of measure of an LSH family is its LSH exponent, which helps determine both query time and space usage. In a seminal work, Andoni and Indyk (FOCS ‘06) constructed an LSH family based on random ball partitionings of space that achieves an LSH exponent of 1/c2 for the l2 norm, which was later shown to be optimal by Motwani, Naor and Panigrahy (SIDMA ‘07) and O’Donnell, Wu and Zhou (TOCT ‘14). Although optimal in the LSH exponent, the ball partitioning approach is computationally expensive. So, in the same work, Andoni and Indyk proposed a simpler and more practical hashing scheme based on Euclidean lattices and provided computational results using the 24-dimensional Leech lattice. However, no theoretical analysis of the scheme was given, thus leaving open the question of finding the exponent of lattice based LSH. In this work, we resolve this question by showing the existence of lattices achieving the optimal LSH exponent of 1/c2 using techniques from the geometry of numbers. At a more conceptual level, our results show that optimal LSH space partitions can have periodic structure. Understanding the extent to which additional structure can be imposed on these partitions, e.g. to yield low space and query complexity, remains an important open problem

Small Molecules Target the Interaction between Tissue Transglutaminase and Fibronectin

Tissue transglutaminase (TG2) is a multi-functional protein, with enzymatic, GTP-ase and scaffold properties. TG2 interacts with fibronectin (FN) through its N-terminus domain, stabilizing integrin complexes, which regulate cell adhesion to the matrix. Through this mechanism, TG2 participates in key steps involved in metastasis in ovarian and other cancers. High throughput screening identified several small molecule inhibitors (SMIs) for the TG2/FN complex. Rational medicinal chemistry optimization of the hit compound (TG53) led to second generation analogues (MT1–6). ELISA demonstrated that these analogues blocked TG2/FN interaction and bio-layer interferometry (BLI) showed that the SMIs bound to TG2. The compounds also potently inhibited cancer cell adhesion to FN and decreased outside-in signaling mediated through the focal adhesion kinase (FAK). Blockade of TG2/FN interaction by the small molecules caused membrane ruffling, delaying the formation of stable focal contacts and mature adhesions points and disrupted organization of the actin cytoskeleton. In an in vivo model measuring intraperitoneal (ip) dissemination, MT4 and MT6 inhibited the adhesion of ovarian cancer (OC) cells to the peritoneum. Pre-treatment with MT4 also sensitized OC cells to paclitaxel. The data support continued optimization of the new class of SMIs that block the TG2/FN complex at the interface between cancer cells and the tumor niche

Small Molecules Target the Interaction between Tissue Transglutaminase and Fibronectin

Tissue transglutaminase (TG2) is a multi-functional protein, with enzymatic, GTP-ase and scaffold properties. TG2 interacts with fibronectin (FN) through its N-terminus domain, stabilizing integrin complexes, which regulate cell adhesion to the matrix. Through this mechanism, TG2 participates in key steps involved in metastasis in ovarian and other cancers. High throughput screening identified several small molecule inhibitors (SMIs) for the TG2/FN complex. Rational medicinal chemistry optimization of the hit compound (TG53) led to second generation analogues (MT1–6). ELISA demonstrated that these analogues blocked TG2/FN interaction and bio-layer interferometry (BLI) showed that the SMIs bound to TG2. The compounds also potently inhibited cancer cell adhesion to FN and decreased outside-in signaling mediated through the focal adhesion kinase (FAK). Blockade of TG2/FN interaction by the small molecules caused membrane ruffling, delaying the formation of stable focal contacts and mature adhesions points and disrupted organization of the actin cytoskeleton. In an in vivo model measuring intraperitoneal (ip) dissemination, MT4 and MT6 inhibited the adhesion of ovarian cancer (OC) cells to the peritoneum. Pre-treatment with MT4 also sensitized OC cells to paclitaxel. The data support continued optimization of the new class of SMIs that block the TG2/FN complex at the interface between cancer cells and the tumor niche

Non-Destructive and Micro-Invasive Techniques for Characterizing the Ancient Roman Mosaic Fragments

The color characteristics, vibration spectra, phase and mineral composition, internal structural organization of several fragments of the ancient Roman mosaics from the Roman Mosaic Museum, Constanta, Romania were studied by non-destructive (Chromatic analysis, Neutron Diffraction, Neutron Tomography) and micro-invasive techniques (Optical Microscopy, X-ray Diffraction, Field Emission Scanning Electron Microscopy–Energy Dispersive X-ray Spectroscopy, Raman Spectroscopy, Wavelength Dispersion X-ray Fluorescence). These investigations were performed in order to characterize the original Roman mosaic fragments. The major and minor phase components of the studied mosaic fragments were determined, the crystal structure of the main phases was analyzed, and their three-dimension spatial arrangement was reconstructed. The similar composition of the major phases of all mosaic fragments can indicate a generic recipe for making mosaic elements, but minor phases were presumably added for coloring of mosaic pieces. Some degradation areas inside the volume of the mosaic fragments were found by means of neutron diffraction and neutron tomography methods. These degradation areas are probably related to the formation of iron hydroxides during chemical interactions of mosaic fragments with the sea and urban polluted atmosphere