Optimal query complexity for estimating the trace of a matrix

Given an implicit $n\times n$ matrix $A$ with oracle access $x^TA x$ for any $x\in \mathbb{R}^n$, we study the query complexity of randomized algorithms for estimating the trace of the matrix. This problem has many applications in quantum physics, machine learning, and pattern matching. Two metrics are commonly used for evaluating the estimators: i) variance; ii) a high probability multiplicative-approximation guarantee. Almost all the known estimators are of the form $\frac{1}{k}\sum_{i=1}^k x_i^T A x_i$ for $x_i\in \mathbb{R}^n$ being i.i.d. for some special distribution. Our main results are summarized as follows. We give an exact characterization of the minimum variance unbiased estimator in the broad class of linear nonadaptive estimators (which subsumes all the existing known estimators). We also consider the query complexity lower bounds for any (possibly nonlinear and adaptive) estimators: (1) We show that any estimator requires $\Omega(1/\epsilon)$ queries to have a guarantee of variance at most $\epsilon$. (2) We show that any estimator requires $\Omega(\frac{1}{\epsilon^2}\log \frac{1}{\delta})$ queries to achieve a $(1\pm\epsilon)$-multiplicative approximation guarantee with probability at least $1 - \delta$. Both above lower bounds are asymptotically tight. As a corollary, we also resolve a conjecture in the seminal work of Avron and Toledo (Journal of the ACM 2011) regarding the sample complexity of the Gaussian Estimator.Comment: full version of the paper in ICALP 201

Interaction between willow species and their caterpillar grazers

The first aim of this investigation was to determine the effect of leaf removal either by grazing or hand cutting on the photosynthetic ability of the Salix species. The second aim was to investigate any change of leaf quality to feeding insect larvae which occurred as a consequence of the removal. Thirdly, the selectivity of the larvae between different Salix species and its effect on the larval development were studied. The leaf removal by grazing or hand cutting did not decrease the leaf fresh weight in Salix viminalis (submitted to two intensities of treatment) or in S. vitellina, after a period of recovery. The total leaf production in both species was similar to the control. In S. cinerea the grazing reduced the leaf weight and the total leaf production. The leaf size was reduced also. The leaves of previously grazed or hand cut Salix viminalis plants had no depressive effect on the growth of the Geometridae larvae "G". A similar result was obtained with the larvae of the sawfly Amauronematus sagmarius feeding on S. rotundifolia. The Geometridae larvae "G" selected Salix viminalis (58% of the total food consumption) rather than S. cinerea in a choice experiment. S. viminalis promoted a faster growth of the larvae "G" when transferred to it from their previous food plant S. cinerea. The growth of the sawfly larvae was faster on S. fragilis, the species selected by the female for oviposition, than on S. rotundifolia. The death rate of the larvae of Amauronematus sagmarius was higher on both S. viminalis and S. cinerea than on S. vitellina, selected by the adult female for egg laying. Finally, the young leaves of S. rotundifolia promoted a higher death rate in the first generation of Amauronematus sagmarius larvae than the old leaves. The time required for pupation was shorter on the diet of young leaves in the first and second larval generations

Differential expression of endogenous plant cell wall degrading enzyme genes in the stick insect (Phasmatodea) midgut

BACKGROUND: Stick and leaf insects (Phasmatodea) are an exclusively leaf-feeding order of insects with no record of omnivory, unlike other “herbivorous” Polyneoptera. They represent an ideal system for investigating the adaptations necessary for obligate folivory, including plant cell wall degrading enzymes (PCWDEs). However, their physiology and internal anatomy is poorly understood, with limited genomic resources available. RESULTS: We de novo assembled transcriptomes for the anterior and posterior midguts of six diverse Phasmatodea species, with RNA-Seq on one exemplar species, Peruphasma schultei. The latter’s assembly yielded >100,000 transcripts, with over 4000 transcripts uniquely or more highly expressed in specific midgut sections. Two to three dozen PCWDE encoding gene families, including cellulases and pectinases, were differentially expressed in the anterior midgut. These genes were also found in genomic DNA from phasmid brain tissue, suggesting endogenous production. Sequence alignments revealed catalytic sites on most PCWDE transcripts. While most phasmid PCWDE genes showed homology with those of other insects, the pectinases were homologous to bacterial genes. CONCLUSIONS: We identified a large and diverse PCWDE repertoire endogenous to the phasmids. If these expressed genes are translated into active enzymes, then phasmids can theoretically break plant cell walls into their monomer components independently of microbial symbionts. The differential gene expression between the two midgut sections provides the first molecular hints as to their function in living phasmids. Our work expands the resources available for industrial applications of animal-derived PCWDEs, and facilitates evolutionary analysis of lower Polyneopteran digestive enzymes, including the pectinases whose origin in Phasmatodea may have been a horizontal transfer event from bacteria. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1471-2164-15-917) contains supplementary material, which is available to authorized users

Prenatal Diagnosis of Gómez-López-Hernández Syndrome.

Gómez-López-Hernández syndrome (GLHS), also known as cerebello-trigeminal-dermal dysplasia, is an extremely rare neurocutaneous disease, classically described by the triad of rhombencephalosynapsis (RES), bilateral focal alopecia, and trigeminal anesthesia. The clinical and radiographic spectrum of GLHS is now known to be broader, including craniofacial and supratentorial anomalies, as well as neurodevelopmental issues. Here, we present a case of antenatally diagnosed GLHS with RES, hydrocephaly, and craniofacial anomalies identified on ultrasound (low-set ears with posterior rotation, hypertelorism, midface hypoplasia, micrognathia, and anteverted nares) which were confirmed by autopsy after termination of pregnancy at 23 weeks of gestation. As no known genetic causes have been identified and the classical triad is not applicable to prenatal imaging, prenatal diagnosis of GLHS is based on neuroimaging and the identification of supporting features. In presence of an RES associated with craniofacial abnormalities in prenatal (brachycephaly, turricephaly, low-set ears, midface retrusion, micrognathia), GLHS should be considered as "possible" according to postnatal criteria

A Formal Study of the Privacy Concerns in Biometric-Based Remote Authentication Schemes

With their increasing popularity in cryptosystems, biometrics have attracted more and more attention from the information security community. However, how to handle the relevant privacy concerns remains to be troublesome. In this paper, we propose a novel security model to formalize the privacy concerns in biometric-based remote authentication schemes. Our security model covers a number of practical privacy concerns such as identity privacy and transaction anonymity, which have not been formally considered in the literature. In addition, we propose a general biometric-based remote authentication scheme and prove its security in our security model

Variability of polycyclic aromatic hydrocarbons and their oxidative derivatives in wintertime Beijing, China

Ambient particulate matter (PM) can contain a mix of different toxic species derived from a wide variety of sources. This study quantifies the diurnal variation and nocturnal abundance of 16 polycyclic aromatic hydrocarbons (PAHs), 10 oxygenated PAHs (OPAHs) and 9 nitrated PAHs (NPAHs) in ambient PM in central Beijing during winter. Target compounds were identified and quantified using gas chromatography-time-of-flight mass spectrometry (GC-Q-ToF-MS). The total concentration of PAHs varied between 18 and 297 ngm-3 over 3 h daytime filter samples and from 23 to 165 ngm-3 in 15 h night-time samples. The total concentrations of PAHs over 24 h varied between 37 and 180 ngm-3 (mean: 97±43 ngm-3). The total daytime concentrations during high particulate loading conditions for PAHs, OPAHs and NPAHs were 224, 54 and 2.3 ngm-3, respectively. The most abundant PAHs were fluoranthene (33 ngm-3), chrysene (27 ngm-3), pyrene (27 ngm-3), benzo[a]pyrene (27 ngm-3), benzo[b]fluoranthene (25 ngm-3), benzo[a]anthracene (20 ngm-3) and phenanthrene (18 ngm-3). The most abundant OPAHs were 9,10-anthraquinone (18 ngm-3), 1,8-naphthalic anhydride (14 ngm-3) and 9-fluorenone (12 ngm-3), and the three most abundant NPAHs were 9-nitroanthracene (0.84 ngm-3), 3-nitrofluoranthene (0.78 ngm-3) and 3-nitrodibenzofuran (0.45 ngm-3). Σ PAHs and Σ OPAHs showed a strong positive correlation with the gas-phase abundance of NO, CO, SO2 and HONO, indicating that PAHs and OPAHs can be associated with both local and regional emissions. Diagnostic ratios suggested emissions from traffic road and coal combustion were the predominant sources of PAHs in Beijing and also revealed the main source of NPAHs to be secondary photochemical formation rather than primary emissions. PM2.5 and NPAHs showed a strong correlation with gas-phase HONO. 9- Nitroanthracene appeared to undergo a photodegradation during the daytime and showed a strong positive correlation with ambient HONO (R D 0:90, P <0:001). The lifetime excess lung cancer risk for those species that have available toxicological data (16 PAHs, 1 OPAH and 6 NPAHs) was calculated to be in the range 10-5 to 10-3 (risk per million people ranges from 26 to 2053 cases per year)

Sensor-activity relevance in human activity recognition with wearable motion sensors and mutual information criterion

Selecting a suitable sensor configuration is an important aspect of recognizing human activities with wearable motion sensors. This problem encompasses selecting the number and type of the sensors, configuring them on the human body, and identifying the most informative sensor axes. In earlier work, researchers have used customized sensor configurations and compared their activity recognition rates with those of others. However, the results of these comparisons are dependent on the feature sets and the classifiers employed. In this study, we propose a novel approach that utilizes the time-domain distributions of the raw sensor measurements. We determine the most informative sensor types (among accelerometers, gyroscopes, and magnetometers), sensor locations (among torso, arms, and legs), and measurement axes (among three perpendicular coordinate axes at each sensor) based on the mutual information criterion. © 2013 Springer International Publishing

Evidence for Two Modes of Synergistic Induction of Apoptosis by Mapatumumab and Oxaliplatin in Combination with Hyperthermia in Human Colon Cancer Cells

Colorectal cancer is the third leading cause of cancer-related mortality in the world-- the main cause of death from colorectal cancer is hepatic metastases, which can be treated with isolated hepatic perfusion (IHP). Searching for the most clinically relevant approaches for treating colorectal metastatic disease by isolated hepatic perfusion (IHP), we developed the application of oxaliplatin concomitantly with hyperthermia and humanized death receptor 4 (DR4) antibody mapatumumab (Mapa), and investigated the molecular mechanisms of this multimodality treatment in human colon cancer cell lines CX-1 and HCT116 as well as human colon cancer stem cells Tu-12, Tu-21 and Tu-22. We showed here, in this study, that the synergistic effect of the multimodality treatment-induced apoptosis was caspase dependent and activated death signaling via both the extrinsic apoptotic pathway and the intrinsic pathway. Death signaling was activated by c-Jun N-terminal kinase (JNK) signaling which led to Bcl-xL phosphorylation at serine 62, decreasing the anti-apoptotic activity of Bcl-xL, which contributed to the intrinsic pathway. The downregulation of cellular FLICE inhibitory protein long isoform (c-FLIPL) in the extrinsic pathway was accomplished through ubiquitination at lysine residue (K) 195 and protein synthesis inhibition. Overexpression of c-FLIPL mutant (K195R) and Bcl-xL mutant (S62A) completely abrogated the synergistic effect. The successful outcome of this study supports the application of multimodality strategy to patients with colorectal hepatic metastases who fail to respond to standard chemoradiotherapy that predominantly targets the mitochondrial apoptotic pathway. © 2013 Song et al

Swirl Flow Bioreactor coupled with Cu-alginate beads: A system for the eradication of Coliform and Escherichia coli from biological effluents.

It is estimated that approximately 1.1 billion people globally drink unsafe water. We previously reported both a novel copper-alginate bead, which quickly reduces pathogen loading in waste streams and the incorporation of these beads into a novel swirl flow bioreactor (SFB), of low capital and running costs and of simple construction from commercially available plumbing pipes and fittings. The purpose of the present study was to trial this system for pathogen reduction in waste streams from an operating Dewats system in Hinjewadi, Pune, India and in both simulated and real waste streams in Seattle, Washington, USA. The trials in India, showed a complete inactivation of coliforms in the discharged effluent (Mean Log removal Value (MLRV) = 3.51), accompanied by a total inactivation of E. coli with a MLRV of 1.95. The secondary clarifier effluent also showed a 4.38 MLRV in viable coliforms during treatment. However, the system was slightly less effective in reducing E. coli viability, with a MLRV of 1.80. The trials in Seattle also demonstrated the efficacy of the system in the reduction of viable bacteria, with a LRV of 5.67 observed of viable Raoultella terrigena cells (100%)