Finding Subcube Heavy Hitters in Analytics Data Streams

Data streams typically have items of large number of dimensions. We study the fundamental heavy-hitters problem in this setting. Formally, the data stream consists of $d$-dimensional items $x_1,\ldots,x_m \in [n]^d$. A $k$-dimensional subcube $T$ is a subset of distinct coordinates $\{ T_1,\cdots,T_k \} \subseteq [d]$. A subcube heavy hitter query ${\rm Query}(T,v)$, $v \in [n]^k$, outputs YES if $f_T(v) \geq \gamma$ and NO if $f_T(v) < \gamma/4$, where $f_T$ is the ratio of number of stream items whose coordinates $T$ have joint values $v$. The all subcube heavy hitters query ${\rm AllQuery}(T)$ outputs all joint values $v$ that return YES to ${\rm Query}(T,v)$. The one dimensional version of this problem where $d=1$ was heavily studied in data stream theory, databases, networking and signal processing. The subcube heavy hitters problem is applicable in all these cases. We present a simple reservoir sampling based one-pass streaming algorithm to solve the subcube heavy hitters problem in $\tilde{O}(kd/\gamma)$ space. This is optimal up to poly-logarithmic factors given the established lower bound. In the worst case, this is $\Theta(d^2/\gamma)$ which is prohibitive for large $d$, and our goal is to circumvent this quadratic bottleneck. Our main contribution is a model-based approach to the subcube heavy hitters problem. In particular, we assume that the dimensions are related to each other via the Naive Bayes model, with or without a latent dimension. Under this assumption, we present a new two-pass, $\tilde{O}(d/\gamma)$-space algorithm for our problem, and a fast algorithm for answering ${\rm AllQuery}(T)$ in $O(k/\gamma^2)$ time. Our work develops the direction of model-based data stream analysis, with much that remains to be explored.Comment: To appear in WWW 201

The Bacillus subtilis signaling protein SpoIVB defines a new family of serine peptidases

The protein SpoIVB plays a key role in signaling in the sigma (K) checkpoint of Bacillus subtilis. This regulatory mechanism coordinates late gene expression during development in this organism and we have recently shown SpoIVB to be a serine peptidase. SpoIVB signals by transiting a membrane, undergoing self-cleavage, and then by an unknown mechanism activating a zinc metalloprotease, SpoIVFB, which cleaves pro-sigma (K) to its active form, sigma (K), in the outer mother cell chamber of the developing cell. In this work we have characterized the serine peptidase domain of SpoIVB. Alignment of SpoIVB with homologues from other spore formers has allowed site-specific mutagenesis of all potential active site residues within the peptidase domain. We have defined the putative catalytic domain of the SpoIVB serine peptidase as a 160-amino-acid residue segment at the carboxyl terminus of the protein. His236 and Ser378 are the most important residues for proteolysis, with Asp363 being the most probable third member of the catalytic triad. In addition, we have shown that mutations at residues Asn290 and His394 lead to delayed signaling in the sigma (K) checkpoint. The active site residues suggest that SpoIVB and its homologues from other spore formers are members of a new family of serine peptidases of the trypsin superfamily

Drosophila RecQ4 Is Directly Involved in Both DNA Replication and the Response to UV Damage in S2 Cells.

The RecQ4 protein shows homology to both the S.cerevisiae DNA replication protein Sld2 and the DNA repair related RecQ helicases. Experimental data also suggest replication and repair functions for RecQ4, but the precise details of its involvement remain to be clarified.Here we show that depletion of DmRecQ4 by dsRNA interference in S2 cells causes defects consistent with a replication function for the protein. The cells show reduced proliferation associated with an S phase block, reduced BrdU incorporation, and an increase in cells with a subG1 DNA content. At the molecular level we observe reduced chromatin association of DNA polymerase-alpha and PCNA. We also observe increased chromatin association of phosphorylated H2AvD--consistent with the presence of DNA damage and increased apoptosis.Analysis of DmRecQ4 repair function suggests a direct role in NER, as the protein shows rapid but transient nuclear localisation after UV treatment. Re-localisation is not observed after etoposide or H₂O₂ treatment, indicating that the involvement of DmRecQ4 in repair is likely to be pathway specific.Deletion analysis of DmRecQ4 suggests that the SLD2 domain was essential, but not sufficient, for replication function. In addition a DmRecQ4 N-terminal deletion could efficiently re-localise on UV treatment, suggesting that the determinants for this response are contained in the C terminus of the protein. Finally several deletions show differential rescue of dsRNA generated replication and proliferation phenotypes. These will be useful for a molecular analysis of the specific role of DmRecQ4 in different cellular pathways

Experimental investigation of the performance of different modulation techniques under controlled FSO turbulence channel

This paper experimentally investigates and compares the performance of the free space optics system employing three different modulation schemes, on-off keying (OOK) with nonreturn- to-zero (NRZ) and return-to-zero (RZ) and the binary phase shift keying (BPSK) operating under the turbulent atmosphere. The received average signal is measured and used to characterize the strength of the turbulence. The experiment is performed with a temperature gradient of 4 degrees at a wind velocity of 4 m/s. The temperature gradient within the controlled channel results in turbulence of a log irradiance variance of 0.002, which is classified as a very weak turbulence. The received signal eye diagram and power histograms are presented and analyzed for performance evaluation of the selected modulation schemes in the weak turbulence model

Experimental study of bit error rate of free space optics communications in laboratory controlled turbulence

This paper reports experimental results for the performance of an free space optical (FSO) communication link employing different modulation schemes under the influence of the atmospheric scintillation. A dedicated experimental atmospheric simulation chamber has been developed where weak and medium turbulence can be generated and its effect on the FSO link is investigated. The experimental data obtained is compared to the theoretical prediction. The paper also shows that the effect on the data transmission performance depends on the position of turbulence source positioned within the chamber

Critical Crossover Between Yosida-Kondo Dominant Regime and Magnetic Frustration Dominant Regime in the System of a Magnetic Trimer on a Metal Surface

Quantum Monte Carlo simulations were carried out for the system of a magnetic trimer on a metal surface. The magnetic trimer is arranged in two geometric configurations, viz., isosceles and equilateral triangles. The calculated spectral density and magnetic susceptibility show the existence of two phases: Yosida-Kondo dominant phase and magnetic frustration dominant phase. Furthermore, a critical transition between these two phases can be induced by changing the configuration of the magnetic trimers from isosceles to equilateral triangle.Comment: 8 pages, 4 figures; accepted for publication in J. Phys. Soc. Jp

Differential gene expression of bone anabolic factors and trabecular bone architectural changes in the proximal femoral shaft of primary hip osteoarthritis patients

Previous studies have shown a generalised increase in bone mass in patients with osteoarthritis (OA). Using molecular histomorphometry, this study examined the in vivo expression of mRNA encoding bone anabolic factors and collagen type I genes (COL1A1, COL1A2) in human OA and non-OA bone. Bone samples were obtained from the intertrochanteric (IT) region of the proximal femur, a skeletal site distal to the active site of disease, from individuals with hip OA at joint replacement surgery and from autopsy controls. Semi-quantitative reverse transcription-polymerase chain reaction analysis revealed elevated mRNA expression levels of alkaline phosphatase (p < 0.002), osteocalcin (OCN) (p < 0.0001), osteopontin (p < 0.05), COL1A1 (p < 0.0001), and COL1A2 (p < 0.002) in OA bone compared to control, suggesting possible increases in osteoblastic biosynthetic activity and/or bone turnover at the IT region in OA. Interestingly, the ratio of COL1A1/COL1A2 mRNA was almost twofold greater in OA bone compared to control (p < 0.001), suggesting the potential presence of collagen type I homotrimer at the distal site. Insulin-like growth factor (IGF)-I, IGF-II, and transforming growth factor-β1 mRNA levels were similar between OA and control bone. Bone histomorphometric analysis indicated that OA IT bone had increased surface density of bone (p < 0.0003), increased trabecular number (Tb.N) (p < 0.0003), and decreased trabecular separation (Tb.Sp) (p < 0.0001) compared to control bone. When the molecular and histomorphometric data were plotted, positive associations were observed in the controls for OCN/glyceraldehyde-3-phosphate dehydrogenase (GAPDH) versus bone tissue volume (r = 0.82, p < 0.0007) and OCN/GAPDH versus Tb.N (r = 0.56, p < 0.05) and a negative association was observed for OCN/GAPDH versus Tb.Sp (r = -0.64, p < 0.02). These relationships were not evident in trabecular bone from patients with OA, suggesting that bone regulatory processes leading to particular trabecular structures may be altered in this disease. The finding of differential gene expression, as well as architectural changes and differences in molecular histomorphometric associations between OA and controls, at a skeletal site distal to the active site of joint degeneration supports the concept of generalised involvement of bone in the pathogenesis of OA