On largest volume simplices and sub-determinants

We show that the problem of finding the simplex of largest volume in the convex hull of $n$ points in $\mathbb{Q}^d$ can be approximated with a factor of $O(\log d)^{d/2}$ in polynomial time. This improves upon the previously best known approximation guarantee of $d^{(d-1)/2}$ by Khachiyan. On the other hand, we show that there exists a constant $c>1$ such that this problem cannot be approximated with a factor of $c^d$, unless $P=NP$. % This improves over the $1.09$ inapproximability that was previously known. Our hardness result holds even if $n = O(d)$, in which case there exists a \bar c\,^{d}-approximation algorithm that relies on recent sampling techniques, where $\bar c$ is again a constant. We show that similar results hold for the problem of finding the largest absolute value of a subdeterminant of a $d\times n$ matrix

Recurring patterns of atrial fibrillation in surface ECG predict restoration of sinus rhythm by catheter ablation

Background Non-invasive tools to help identify patients likely to benefit from catheter ablation (CA) of atrial fibrillation (AF) would facilitate personalised treatment planning. Aim To investigate atrial waveform organisation through recurrence plot indices (RPI) and their ability to predict CA outcome. Methods One minute 12-lead ECG was recorded before CA from 62 patients with AF (32 paroxysmal AF; 45 men; age 57±10 years). Organisation of atrial waveforms from i) TQ intervals in V1 and ii) QRST suppressed continuous AF waveforms (CAFW), were quantified using RPI: percentage recurrence (PR), percentage determinism (PD), entropy of recurrence (ER). Ability to predict acute (terminating vs. non-terminating AF), 3-month and 6-month postoperative outcome (AF vs. AF free) were assessed. Results RPI either by TQ or CAFW analysis did not change significantly with acute outcome. Patients arrhythmia-free at 6-month follow-up had higher organisation in TQ intervals by PD (

On the convergence of the affine hull of the Chv\'atal-Gomory closures

Given an integral polyhedron P and a rational polyhedron Q living in the same n-dimensional space and containing the same integer points as P, we investigate how many iterations of the Chv\'atal-Gomory closure operator have to be performed on Q to obtain a polyhedron contained in the affine hull of P. We show that if P contains an integer point in its relative interior, then such a number of iterations can be bounded by a function depending only on n. On the other hand, we prove that if P is not full-dimensional and does not contain any integer point in its relative interior, then no finite bound on the number of iterations exists.Comment: 13 pages, 2 figures - the introduction has been extended and an extra chapter has been adde

Recurring patterns in stationary intervals of abdominal uterine electromyograms during gestation

Abdominal uterine electromyograms (uEMG) studies have focused on uterine contractions to describe the evolution of uterine activity and preterm birth (PTB) prediction. Stationary, non-contracting uEMG has not been studied. The aim of the study was to investigate the recurring patterns in stationary uEMG, their relationship with gestation age and PTB, and PTB predictivity. A public database of 300 (38 PTB) three-channel (S1-S3) uEMG recordings of 30 min, collected between 22 and 35 weeks' gestation, was used. Motion and labour contraction-free intervals in uEMG were identified as 5-min weak-sense stationarity intervals in 268 (34 PTB) recordings. Sample entropy (SampEn), percentage recurrence (PR), percentage determinism (PD), entropy (ER), and maximum length (L MAX) of recurrence were calculated and analysed according to the time to delivery and PTB. Random time series were generated by random shuffle (RS) of actual data. Recurrence was present in actual data (p<0.001) but not RS. In S3, PR (p<0.005), PD (p<0.01), ER (p<0.005), and L MAX (p<0.05) were higher, and SampEn lower (p<0.005) in PTB. Recurrence indices increased (all p<0.001) and SampEn decreased (p<0.01) with decreasing time to delivery, suggesting increasingly regular and recurring patterns with gestation progression. All indices predicted PTB with AUC≥0.62 (p<0.05). Recurring patterns in stationary non-contracting uEMG were associated with time to delivery but were relatively poor predictors of PTB

Comparison of laparoscopic partial nephrectomy performed with AirSeal® system vs. standard insufflator: results from a referral center

ObjectiveTo compare perioperative and oncologic surgical outcomes during laparoscopic partial nephrectomy (LPN) performed by standard carbon dioxide insufflation, with those from surgeries in which the AirSeal® intelligent insufflation system was used for renal tumors.Materials and methodsA total of 27 patients with renal tumor were identified, 14 underwent LPN with AirSeal® (group A) and 13 LPN with standard insufflator (group B), respectively. Demographic baseline characteristics were similar in the two groups.ResultsThe size of the tumor was largest in group B (29.64 vs. 32.1 mm). The mean operative time was shorter in the AirSeal® group [group A: mean 109.0 min, median 107.5 min, interquartile range (IQR) 85; group B: mean 121.0 min, median 120.0 min, IQR 50.0]. Positive margin rates were absent in the two groups. Estimated blood loss presented a difference in the perioperative period (group A: mean 1.5 g/dL, median 1.45 g/dL; group B: mean 2.15 g/dL, median 2.2 g/dL). Time to ischemia was found to be shorter in group A with a median of 18 min compared to a median of 20 min in group B. No subcutaneous emphysema, pneumothorax, and pneumomediastinum cases occurred in either group. A postoperative complication developed in one patient requiring superselective embolization.ConclusionIn selected patients, our preliminary surgical experience has shown that the LPN procedure performed with the aid of the AirSeal® intelligent insufflation system can be used to treat even medium-/high-complexity kidney lesions, with a reduction in operating times, lower rates of complications, and perioperative blood loss.Clinical trial registrationAirSealV1

Dense matter with eXTP

In this White Paper we present the potential of the Enhanced X-ray Timing and Polarimetry (eXTP) mission for determining the nature of dense matter; neutron star cores host an extreme density regime which cannot be replicated in a terrestrial laboratory. The tightest statistical constraints on the dense matter equation of state will come from pulse profile modelling of accretion-powered pulsars, burst oscillation sources, and rotation-powered pulsars. Additional constraints will derive from spin measurements, burst spectra, and properties of the accretion flows in the vicinity of the neutron star. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Science, the eXTP mission is expected to be launched in the mid 2020s.Comment: Accepted for publication on Sci. China Phys. Mech. Astron. (2019

Localisation of gamma-ray bursts from the combined SpIRIT+HERMES-TP/SP nano-satellite constellation

Multi-messenger observations of the transient sky to detect cosmic explosions and counterparts of gravitational wave mergers critically rely on orbiting wide-FoV telescopes to cover the wide range of wavelengths where atmospheric absorption and emission limit the use of ground facilities. Thanks to continuing technological improvements, miniaturised space instruments operating as distributed-aperture constellations are offering new capabilities for the study of high energy transients to complement ageing existing satellites. In this paper we characterise the performance of the upcoming joint SpIRIT + HERMES-TP/SP nano-satellite constellation for the localisation of high-energy transients through triangulation of signal arrival times. SpIRIT is an Australian technology and science demonstrator satellite designed to operate in a low-Earth Sun-synchronous Polar orbit that will augment the science operations for the equatorial HERMES-TP/SP. In this work we simulate the improvement to the localisation capabilities of the HERMES-TP/SP when SpIRIT is included in an orbital plane nearly perpendicular (inclination = 97.6$^\circ$) to the HERMES orbits. For the fraction of GRBs detected by three of the HERMES satellites plus SpIRIT, the combined constellation is capable of localising 60% of long GRBs to within ~ 30 deg$^2$ on the sky, and 60% of short GRBs within ~ 1850 deg$^2$. Based purely on statistical GRB localisation capabilities (i.e., excluding systematic uncertainties and sky coverage), these figures for long GRBs are comparable to those reported by the Fermi GBM. Further improvements by a factor of 2 (or 4) can be achieved by launching an additional 4 (or 6) SpIRIT-like satellites into a Polar orbit, which would both increase the fraction of sky covered by multiple satellite elements, and enable $\geq$ 60% of long GRBs to be localised within a radius of ~ 1.5$^\circ$ on the sky.Comment: 17 pages, 10 figures, 1 table. Accepted for publication in PAS

IXPE instrument integration, testing and verification

The Imaging X-ray Polarimetry Explorer (IXPE) is a scientific observatory with the purpose of expand observation space adding polarization property to the X-ray source's currently measured characteristics. The mission selected in the context of NASA Small Explorer (SMEX) is a collaboration between NASA and ASI that will provide to observatory the instrumentation of focal plane. IXPE instrument is composed by three photoelectric polarimeters based on the Gas Pixel Detector (GPD) design, integrated by INFN inside the detector unit (DU) that comprises of the electrical interfaces required to control and communicate with the GPD. The three DUs are interfaced with spacecraft through a detector service unit (DSU) that collect scientific and ancillary data and provides a basically data handling and interfaces to manage the three DUs. AIV has been planned to combine calibration of DUs and Instrument integration and verification activities. Due the tight schedule and the scientific and functional requirements to be verified, in IAPS/INAF have been assembled two equipment's that work in parallel. The flight model of each DU after the environmental tests campaign was calibrated on-ground using the Instrument Calibration Equipment (ICE) and subsequently integrated in the instrument in the AIV-T process on a AIV and Calibration Equipment (ACE), both the facilities managed by Electrical Ground Support Equipment (EGSE) that emulate the spacecraft interfaces of power supply, functional and thermal control and scientific data collection. AIV activities test functionalities and nominal/off-nominal orbits activities of IXPE instrument each time a calibrated DU is connected to DSU flight model completing step by step the full instrument. Here we describe the details of instrumentation and procedures adopted to make possible the full integration and test activities compatibly with calibration of IXPE Instrument

Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array

Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we describe a search for an isotropic stochastic gravitational-wave background (GWB) using observations of 30 millisecond pulsars from the third data release of the Parkes Pulsar Timing Array (PPTA), which spans 18 years. Using current Bayesian inference techniques we recover and characterize a common-spectrum noise process. Represented as a strain spectrum $h_c = A(f/1 {\rm yr}^{-1})^{\alpha}$, we measure $A=3.1^{+1.3}_{-0.9} \times 10^{-15}$ and $\alpha=-0.45 \pm 0.20$ respectively (median and 68% credible interval). For a spectral index of $\alpha=-2/3$, corresponding to an isotropic background of GWs radiated by inspiraling supermassive black hole binaries, we recover an amplitude of $A=2.04^{+0.25}_{-0.22} \times 10^{-15}$. However, we demonstrate that the apparent signal strength is time-dependent, as the first half of our data set can be used to place an upper limit on $A$ that is in tension with the inferred common-spectrum amplitude using the complete data set. We search for spatial correlations in the observations by hierarchically analyzing individual pulsar pairs, which also allows for significance validation through randomizing pulsar positions on the sky. For a process with $\alpha=-2/3$, we measure spatial correlations consistent with a GWB, with an estimated false-alarm probability of $p \lesssim 0.02$ (approx. $2\sigma$). The long timing baselines of the PPTA and the access to southern pulsars will continue to play an important role in the International Pulsar Timing Array.Comment: 19 pages, 10 figures, Accepted for publication in ApJ

US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report

This white paper summarizes the workshop "U.S. Cosmic Visions: New Ideas in Dark Matter" held at University of Maryland on March 23-25, 2017.Comment: 102 pages + reference