Local Testing for Membership in Lattices

Motivated by the structural analogies between point lattices and linear error-correcting codes, and by the mature theory on locally testable codes, we initiate a systematic study of local testing for membership in lattices. Testing membership in lattices is also motivated in practice, by applications to integer programming, error detection in lattice-based communication, and cryptography. Apart from establishing the conceptual foundations of lattice testing, our results include the following: 1. We demonstrate upper and lower bounds on the query complexity of local testing for the well-known family of code formula lattices. Furthermore, we instantiate our results with code formula lattices constructed from Reed-Muller codes, and obtain nearly-tight bounds. 2. We show that in order to achieve low query complexity, it is sufficient to design one-sided non-adaptive canonical tests. This result is akin to, and based on an analogous result for error-correcting codes due to Ben-Sasson et al. (SIAM J. Computing 35(1) pp1-21)

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

Effect of damage by 2-MeV He ions on the normal and superconducting properties of magnesium diboride

We have studied the effect of damage induced by 2-MeV alpha particles on the critical temperature, Tc, and resistivity of MgB2 thin films. This technique allows defects to be controllably introduced into MgB2 in small successive steps. Tc decreases linearly as the intragrain resistivity at 40 K increases, while the intergrain connectivity is not changed. Tc is ultimately reduced to less than 7 K and we see no evidence for a saturation of Tc at about 20 K, contrary to the predictions of the Tc of MgB2 in the dirty limit of interband scattering.Comment: 14 pages and 3 figures; Submitted to Applied Physics Letter

High-field superconductivity in alloyed MgB2 thin films

We investigated the effect of alloying on the upper critical field $H_{c2}$ in 12 $MgB_2$ films, in which disorder was introduced by growth, carbon doping or He-ion irradiation, finding a significant $H_{c2}$ enhancement in C-alloyed films, and an anomalous upward curvature of $H_{c2}(T)$. Record high values of $H_{c2}^{\perp}(4.2) \simeq 35T$ and $H_{c2}\|(4.2) \simeq 51T$ were observed perpendicular and parallel to the ab plane, respectively. The temperature dependence of $H_{c2}(T)$ is described well by a theory of dirty two-gap superconductivity. Extrapolation of the experimental data to T=0 suggests that $H_{c2}\|(0)$ approaches the paramagnetic limit of $\sim 70T$

The microRNA regulated SBP-box genes SPL9 and SPL15 control shoot maturation in Arabidopsis

Throughout development the Arabidopsis shoot apical meristem successively undergoes several major phase transitions such as the juvenile-to-adult and floral transitions until, finally, it will produce flowers instead of leaves and shoots. Members of the Arabidopsis SBP-box gene family of transcription factors have been implicated in promoting the floral transition in dependence of miR156 and, accordingly, transgenics constitutively over-expressing this microRNA are delayed in flowering. To elaborate their roles in Arabidopsis shoot development, we analysed two of the 11 miR156 regulated Arabidopsis SBP-box genes, i.e. the likely paralogous genes SPL9 and SPL15. Single and double mutant phenotype analysis showed these genes to act redundantly in controlling the juvenile-to-adult phase transition. In addition, their loss-of-function results in a shortened plastochron during vegetative growth, altered inflorescence architecture and enhanced branching. In these aspects, the double mutant partly phenocopies constitutive MIR156b over-expressing transgenic plants and thus a major contribution to the phenotype of these transgenics as a result of the repression of SPL9 and SPL15 is strongly suggested

Analysis of conserved microRNAs in floral tissues of sexual and apomictic Boechera species

<p>Abstract</p> <p>Background</p> <p>Apomixis or asexual seed formation represents a potentially important agronomic trait whose introduction into crop plants could be an effective way to fix and perpetuate a desirable genotype through successive seed generations. However, the gene regulatory pathways underlying apomixis remain unknown. In particular, the potential function of microRNAs, which are known to play crucial roles in many aspects of plant growth and development, remains to be determined with regards to the switch from sexual to apomictic reproduction.</p> <p>Results</p> <p>Using bioinformatics and microarray validation procedures, 51 miRNA families conserved among angiosperms were identified in <it>Boechera</it>. Microarray assay confirmed 15 of the miRNA families that were identified by bioinformatics techniques. 30 cDNA sequences representing 26 miRNAs could fold back into stable pre-miRNAs. 19 of these pre-miRNAs had miRNAs with <it>Boechera</it>-specific nucleotide substitutions (NSs). Analysis of the Gibbs free energy (ΔG) of these pre-miRNA stem-loops with NSs showed that the <it>Boechera</it>-specific miRNA NSs significantly (p ≤ 0.05) enhance the stability of stem-loops. Furthermore, six transcription factors, the Squamosa promoter binding protein like SPL6, SPL11 and SPL15, Myb domain protein 120 (MYB120), RELATED TO AP2.7 DNA binding (RAP2.7, TOE1 RAP2.7) and TCP family transcription factor 10 (TCP10) were found to be expressed in sexual or apomictic ovules. However, only SPL11 showed differential expression with significant (p ≤ 0.05) up-regulation at the megaspore mother cell (MMC) stage of ovule development in apomictic genotypes.</p> <p>Conclusions</p> <p>This study constitutes the first extensive insight into the conservation and expression of microRNAs in <it>Boechera </it>sexual and apomictic species. The miR156/157 target squamosa promoter binding protein-like 11 (SPL11) was found differentially expressed with significant (p ≤ 0.05) up-regulation at the MMC stage of ovule development in apomictic genotypes. The results also demonstrate that nucleotide changes in mature miRNAs significantly (p ≤ 0.05) enhance the thermodynamic stability of pre-miRNA stem-loops.</p

Identification and characterization of 27 conserved microRNAs in citrus

MicroRNAs (miRNAs) are a class of non-protein-coding small RNAs. Considering the conservation of many miRNA genes in different plant genomes, the identification of miRNAs from non-model organisms is both practicable and instrumental in addressing miRNA-guided gene regulation. Citrus is an important staple fruit tree, and publicly available expressed sequence tag (EST) database for citrus are increasing. However, until now, little has been known about miRNA in citrus. In this study, 27 known miRNAs from Arabidopsis were searched against citrus EST databases for miRNA precursors, of which 13 searched precursor sequences could form fold-back structures similar with those of Arabidopsis. The ubiquitous expression of those 13 citrus microRNAs and other 13 potential citrus miRNAs could be detected in citrus leaf, young shoot, flower, fruit and root by northern blotting, and some of them showed differential expression in different tissues. Based on the fact that miRNAs exhibit perfect or nearly perfect complementarity with their target sequences, a total of 41 potential targets were identified for 15 citrus miRNAs. The majority of the targets are transcription factors that play important roles in citrus development, including leaf, shoot, and root development. Additionally, some other target genes appear to play roles in diverse physiological processes. Four target genes have been experimentally verified by detection of the miRNA-mediated mRNA cleavage in Poncirus trifoliate. Overall, this study in the identification and characterization of miRNAs in citrus can initiate further study on citrus miRNA regulation mechanisms, and it can help us to know more about the important roles of miRNAs in citrus

Silencing of the Violaxanthin De-Epoxidase Gene in the Diatom Phaeodactylum tricornutum Reduces Diatoxanthin Synthesis and Non-Photochemical Quenching

Diatoms are a major group of primary producers ubiquitous in all aquatic ecosystems. To protect themselves from photooxidative damage in a fluctuating light climate potentially punctuated with regular excess light exposures, diatoms have developed several photoprotective mechanisms. The xanthophyll cycle (XC) dependent non-photochemical chlorophyll fluorescence quenching (NPQ) is one of the most important photoprotective processes that rapidly regulate photosynthesis in diatoms. NPQ depends on the conversion of diadinoxanthin (DD) into diatoxanthin (DT) by the violaxanthin de-epoxidase (VDE), also called DD de-epoxidase (DDE). To study the role of DDE in controlling NPQ, we generated transformants of P. tricornutum in which the gene (Vde/Dde) encoding for DDE was silenced. RNA interference was induced by genetic transformation of the cells with plasmids containing either short (198 bp) or long (523 bp) antisense (AS) fragments or, alternatively, with a plasmid mediating the expression of a self-complementary hairpin-like construct (inverted repeat, IR). The silencing approaches generated diatom transformants with a phenotype clearly distinguishable from wildtype (WT) cells, i.e. a lower degree as well as slower kinetics of both DD de-epoxidation and NPQ induction. Real-time PCR based quantification of Dde transcripts revealed differences in transcript levels between AS transformants and WT cells but also between AS and IR transformants, suggesting the possible presence of two different gene silencing mediating mechanisms. This was confirmed by the differential effect of the light intensity on the respective silencing efficiency of both types of transformants. The characterization of the transformants strengthened some of the specific features of the XC and NPQ and confirmed the most recent mechanistic model of the DT/NPQ relationship in diatoms