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The behavior of the vector Adler function at spacelike momenta is studied in the framework of a covariant chiral quark model with instanton-like quark-quark interaction. This function describes the transition between the high energy asymptotically free region of almost massless current quarks to the low energy hadronized regime with massive constituent quarks. The model reproduces the Adler function and V-A correlator extracted from the ALEPH and OPAL data on hadronic τ lepton decays, transformed into the Euclidean domain via dispersion relations. The leading order contribution from hadronic part of the photon vacuum polarization to the anomalous magnetic moment of the muon, , is estimated.

We derive a series expansion by Hermite polynomials for the price of an arithmetic Asian option. This requires the computation of moments and correlators of the underlying asset price which for a polynomial jump–diffusion process are given analytically; hence, no numerical simulation is required to evaluate the series. This allows to derive analytical expressions for the option Greeks. The weight function defining the Hermite polynomials is a Gaussian density with scale $b$. We find that the rate of convergence of the series depends on $b$, for which we prove a lower bound to guarantee convergence. Numerical examples show that the series expansion is accurate but unstable for initial values of the underlying process far from zero, mainly due to rounding errors.

The Amsterdam–ASTRON Radio Transients Facility and Analysis Center (AARTFAAC) all-sky monitor is a sensitive, real-time transient detector based on the Low Frequency Array (LOFAR). It generates images of the low frequency radio sky with spatial resolution of tens of arcmin, MHz bandwidths, and a time cadence of a few seconds, while simultaneously but independently observing with LOFAR. The image timeseries is then monitored for short and bright radio transients. On detection of a transient, a low latency trigger will be generated for LOFAR, which can interrupt its schedule to carry out follow-up observations of the trigger location at high sensitivity and resolutions. In this paper, we describe our heterogeneous, hierarchical design to manage the 259Gbps raw data rate and large scale computing to produce real-time images with minimum latency. We discuss the implementation of the instrumentation, its performance and scalability.

Radio telescopes that employ arrays of many antennas are in operation, and ever larger ones are being designed and proposed. Signals from the antennas are combined by cross-correlation. While the cost of most components of the telescope is proportional to the number of antennas N, the cost and power consumption of cross-correlation are proportional to $N^2$ and dominate at sufficiently large N. Here, we report the design of an integrated circuit (IC) that performs digital cross-correlations for arbitrarily many antennas in a power-efficient way. It uses an intrinsically low-power architecture in which the movement of data between devices is minimized. In a large system, each IC performs correlations for all pairs of antennas but for a portion of the telescope’s bandwidth (the so-called “FX” structure). In our design, the correlations are performed in an array of 4096 complex multiply-accumulate (CMAC) units. This is sufficient to perform all correlations in parallel for 64 signals (N=32 antennas with two opposite-polarization signals per antenna). When N is larger, the input data are buffered in an on-chip memory and the CMACs are reused as many times as needed to compute all correlations. The design has been synthesized and simulated so as to obtain accurate estimates of the ICs size and power consumption. It is intended for fabrication in a 32nm silicon-on-insulator process, where it will require less than 12mm² of silicon area and achieve an energy efficiency of 1.76–3.3pJ per CMAC operation, depending on the number of antennas. Operation has been analyzed in detail up to $N=4096$. The system-level energy efficiency, including board-level I/O, power supplies, and controls, is expected to be 5–7pJ per CMAC operation. Existing correlators for the JVLA ($N=32$) and ALMA ($N=64$) telescopes achieve about 5000pJ and 1000pJ, respectively using application-specific ICs (ASICs) in older technologies. To our knowledge, the largest-N existing correlator is LEDA at $N=256$; it uses GPUs built in 28nm technology and achieves about 1000pJ. Correlators being designed for the SKA telescopes ($N=128$ and $N=512$) using FPGAs in 16nm technology are predicted to achieve about 100pJ.