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

A Useful Form of the Abel Bound and Its Application to Estimator Threshold Prediction

International audienceThis correspondence investigates the Abel bound in order to predict the estimators mean square error (mse) threshold effect. A tractable and computationally efficient form of this bound is derived. This form combines the Chapman–Robbins and the Cramér–Rao bounds. This bound is applied to a data-aided carrier frequency estimation problem for which a closed-form expression is provided. An indicator of the signal-to-noise ratio threshold is proposed. A comparison with recent results on the Barankin bound (Chapman–Robbins version) shows the superiority of the Abel-bound version to predict the mse threshold without increasing the computational complexity

APE1/Ref-1 knockdown in pancreatic ductal adenocarcinoma – characterizing gene expression changes and identifying novel pathways using single-cell RNA sequencing

Apurinic/apyrimidinic endonuclease 1/redox factor-1 (APE1/Ref-1 or APE1) is a multifunctional protein that regulates numerous transcription factors associated with cancer-related pathways. Because APE1 is essential for cell viability, generation of APE1-knockout cell lines and determining a comprehensive list of genes regulated by APE1 has not been possible. To circumvent this challenge, we utilized single-cell RNA sequencing to identify differentially expressed genes (DEGs) in relation to APE1 protein levels within the cell. Using a straightforward yet novel statistical design, we identified 2837 genes whose expression is significantly changed following APE1 knockdown. Using this gene expression profile, we identified multiple new pathways not previously linked to APE1, including the EIF2 signaling and mechanistic target of Rapamycin pathways and a number of mitochondrial-related pathways. We demonstrate that APE1 has an effect on modifying gene expression up to a threshold of APE1 expression, demonstrating that it is not necessary to completely knockout APE1 in cells to accurately study APE1 function. We validated the findings using a selection of the DEGs along with siRNA knockdown and qRT-PCR. Testing additional patient-derived pancreatic cancer cells reveals particular genes (ITGA1, TNFAIP2, COMMD7, RAB3D) that respond to APE1 knockdown similarly across all the cell lines. Furthermore, we verified that the redox function of APE1 was responsible for driving gene expression of mitochondrial genes such as PRDX5 and genes that are important for proliferation such as SIPA1 and RAB3D by treating with APE1 redox-specific inhibitor, APX3330. Our study identifies several novel genes and pathways affected by APE1, as well as tumor subtype specificity. These findings will allow for hypothesis-driven approaches to generate combination therapies using, for example, APE1 inhibitor APX3330 with other approved FDA drugs in an innovative manner for pancreatic and other cancer treatments

The effect of Duffing-type non-linearities and Coulomb damping on the response of an energy harvester to random excitations

Linear energy harvesters can only produce useful amounts of power when excited close to their natural frequency. Due to the uncertain nature of ambient vibrations, it has been hypothesised that such devices will perform poorly in real-world applications. To improve performance, it has been suggested that the introduction of non-linearities into such devices may extend the bandwidth over which they perform effectively. In this study, a magnetic levitation device with non-linearities similar to the Duffing oscillator is considered. The governing equations of the device are formed in which the effects of friction are considered. Analytical solutions are used to explore the effect that friction can have on the system when it is under harmonic excitations. Following this, a numerical model is formed. A differential evolution algorithm is used alongside experimental data to identify the relevant parameters of the device. The model is then validated using experimental data. Monte Carlo simulations are then used to analyse the effect of coulomb damping and Duffing-type non-linearities when the device is subjected to broadband white noise and coloured noise excitations. </jats:p

Aspirin plus calcium supplementation to prevent superimposed preeclampsia: a randomized trial

Preeclampsia is an important cause of maternal and perinatal morbidity and mortality. Previous studies have tested calcium supplementation and aspirin separately to reduce the incidence of preeclampsia but not the effects of combined supplementation. The objective of this study was to investigate the effectiveness of aspirin combined with calcium supplementation to prevent preeclampsia in women with chronic hypertension. A double-blind, placebo-controlled randomized clinical trial was carried out at the antenatal clinic of a large university hospital in São Paulo, SP, Brazil. A total of 49 women with chronic hypertension and abnormal uterine artery Doppler at 20-27 weeks gestation were randomly assigned to receive placebo (N = 26) or 100 mg aspirin plus 2 g calcium (N = 23) daily until delivery. The main outcome of this pilot study was development of superimposed preeclampsia. Secondary outcomes were fetal growth restriction and preterm birth. The rate of superimposed preeclampsia was 28.6% lower among women receiving aspirin plus calcium than in the placebo group (52.2 vs 73.1%, respectively, P=0.112). The rate of fetal growth restriction was reduced by 80.8% in the supplemented group (25 vs 4.8% in the placebo vs supplemented groups, respectively; P=0.073). The rate of preterm birth was 33.3% in both groups. The combined supplementation of aspirin and calcium starting at 20-27 weeks of gestation produced a nonsignificant decrease in the incidence of superimposed preeclampsia and fetal growth restriction in hypertensive women with abnormal uterine artery Doppler.Universidade Federal de São Paulo (UNIFESP) Departamento de ObstetríciaUniversidade Federal de São Paulo (UNIFESP) Departamento de MedicinaUniversidade Federal de São Paulo (UNIFESP) Departamento de Estatística AplicadaUNIFESP, Depto. de ObstetríciaUNIFESP, Depto. de MedicinaUNIFESP, Depto. de Estatística AplicadaSciEL

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

Impaired perceptual learning in a mouse model of Fragile X syndrome is mediated by parvalbumin neuron dysfunction and is reversible.

To uncover the circuit-level alterations that underlie atypical sensory processing associated with autism, we adopted a symptom-to-circuit approach in the Fmr1-knockout (Fmr1-/-) mouse model of Fragile X syndrome. Using a go/no-go task and in vivo two-photon calcium imaging, we find that impaired visual discrimination in Fmr1-/- mice correlates with marked deficits in orientation tuning of principal neurons and with a decrease in the activity of parvalbumin interneurons in primary visual cortex. Restoring visually evoked activity in parvalbumin cells in Fmr1-/- mice with a chemogenetic strategy using designer receptors exclusively activated by designer drugs was sufficient to rescue their behavioral performance. Strikingly, human subjects with Fragile X syndrome exhibit impairments in visual discrimination similar to those in Fmr1-/- mice. These results suggest that manipulating inhibition may help sensory processing in Fragile X syndrome

First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data

Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signalto- noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analysis methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of 11 pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched; in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far

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%)