0^# and elementary end extensions of V_k

In this paper we prove that if k is a cardinal in L[0^#], then there is an inner model M such that M |= (V_k,E) has no elementary end extension. In particular if 0^# exists then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than aleph_1 of uncountable cofinality in L[0^#] is Mahlo in every strict inner model of L[0^#].Comment: To appear in Proc. of the AM

An experimental uncertainty implied by failure of the physical Church-Turing thesis

In this paper we prove that given a black box assumed to generate bits of a given non-recursive real $\Omega$ there is no computable decision procedure generating sequences of decisions such that if the output is indeed $\Omega$ the process eventually accepts the hypothesis while if the output is different than $\Omega$ than the procedure will eventually reject the hypothesis from a certain point on. Our decision concept does not require full certainty regarding the correctness of the decision at any point, thus better represents the validation process of physical theories. The theorem has strong implications on the falsifiability of physical theories entailing the failure of the physical Church Turing thesis. Finally we show that our decision process enables to decide whether the mean of an i.i.d. sequence of reals belongs to a specific $\Delta_2$ set of integers. This significantly strengthens the effective version of the Cover-Koplowitz theorem, beyond computable sequences of reals

Closed form solution of the maximum entropy equations with application to fast radio astronomical image formation

In this paper we analyze the maximum entropy image deconvolution. We show that given the Lagrange multiplier a closed form can be obtained for the image parameters. Using this solution we are able to provide better understanding of some of the known behavior of the maximum entropy algorithm. The solution also yields a very efficient implementation of the maximum entropy deconvolution technique used in the AIPS package. It requires the computation of a single dirty image and inversion of an elementary function per pixel.Comment: 5 page

Inherent Biases in Reference based Evaluation for Grammatical Error Correction and Text Simplification

The prevalent use of too few references for evaluating text-to-text generation is known to bias estimates of their quality ({\it low coverage bias} or LCB). This paper shows that overcoming LCB in Grammatical Error Correction (GEC) evaluation cannot be attained by re-scaling or by increasing the number of references in any feasible range, contrary to previous suggestions. This is due to the long-tailed distribution of valid corrections for a sentence. Concretely, we show that LCB incentivizes GEC systems to avoid correcting even when they can generate a valid correction. Consequently, existing systems obtain comparable or superior performance compared to humans, by making few but targeted changes to the input. Similar effects on Text Simplification further support our claims.Comment: Accepted to ACL 2018 (figures currently omitted due to technical arxiv issue

Adaptive selective sidelobe canceller beamformer with applications in radio astronomy

We propose a new algorithm, for parameter estimation that is applicable to imaging using moving and synthetic aperture arrays. The new method results in higher resolution and more accurate estimation than commonly used methods when strong interfering sources are present inside and outside the field of view (terrestrial interference, confusing sources).Comment: 10 pages. To appear in Proceedings of the IEEE 26-th Convention of Electrical and Electronics Engineers in Israel(IEEEI 2010

Eliminating Interference in LOS Massive Multi-User MIMO with a Few Transceivers

Wireless cellular communication networks are bandwidth and interference limited. An important means to overcome these resource limitations is the use of multiple antennas. Base stations equipped with a very large (massive) number of antennas have been the focus of recent research. A bottleneck in such systems is the limited number of transmit/receive chains. In this work, a line-of-sight (LOS) channel model is considered. It is shown that for a given number of interferers, it suffices that the number of transmit/receive chains exceeds the number of desired users by one, assuming a sufficiently large antenna array. From a theoretical point of view, this is the first result proving the near-optimal performance of antenna selection, even when the total number of signals (desired and interfering) is larger than the number of receive chains. Specifically, a single additional chain suffices to reduce the interference to any desired level. We prove that using the proposed selection, a simple linear receiver/transmitter for the uplink/downlink provides near-optimal rates. In particular, in the downlink direction, there is no need for complicated dirty paper coding; each user can use an optimal code for a single user interference-free channel. In the uplink direction, there is almost no gain in implementing joint decoding. The proposed approach is also a significant improvement both from system and computational perspectives. Simulation results demonstrating the performance of the proposed method are provided

Phase Noise Compensation for OFDM Systems

We describe a low complexity method for time domain compensation of phase noise in OFDM systems. We extend existing methods in several respects. First we suggest using the Karhunen-Lo\'{e}ve representation of the phase noise process to estimate the phase noise. We then derive an improved datadirected choice of basis elements for LS phase noise estimation and present its total least square counterpart problem. The proposed method helps overcome one of the major weaknesses of OFDM systems. We also generalize the time domain phase noise compensation to the multiuser MIMO context. Finally we present simulation results using both simulated and measured phased noise. We quantify the tracking performance in the presence of residual carrier offset.Comment: This paper was accepted for publication in IEEE Transactions on Signal Processin

Game of Thrones: Fully Distributed Learning for Multi-Player Bandits

We consider an N-player multi-armed bandit game where each player chooses one out of M arms for T turns. Each player has different expected rewards for the arms, and the instantaneous rewards are independent and identically distributed or Markovian. When two or more players choose the same arm, they all receive zero reward. Performance is measured using the expected sum of regrets, compared to optimal assignment of arms to players that maximizes the sum of expected rewards. We assume that each player only knows her actions and the reward she received each turn. Players cannot observe the actions of other players, and no communication between players is possible. We present a distributed algorithm and prove that it achieves an expected sum of regrets of near-O\left(\log T\right). This is the first algorithm to achieve a near order optimal regret in this fully distributed scenario. All other works have assumed that either all players have the same vector of expected rewards or that communication between players is possible.Comment: Accepted to Mathematics of Operations Research (submitted in September 2018). A preliminary version was accepted to NeurIPS 2018. This extended paper improves the regret bound to near-log(T), generalizes to unbounded and Markovian rewards and has a much better convergence rat

Automatic Metric Validation for Grammatical Error Correction

Metric validation in Grammatical Error Correction (GEC) is currently done by observing the correlation between human and metric-induced rankings. However, such correlation studies are costly, methodologically troublesome, and suffer from low inter-rater agreement. We propose MAEGE, an automatic methodology for GEC metric validation, that overcomes many of the difficulties with existing practices. Experiments with \maege\ shed a new light on metric quality, showing for example that the standard $M^2$ metric fares poorly on corpus-level ranking. Moreover, we use MAEGE to perform a detailed analysis of metric behavior, showing that correcting some types of errors is consistently penalized by existing metrics.Comment: Accepted to ACL201

The impact of random actions on opinion dynamics

Opinion dynamics have fascinated researchers for centuries. The ability of societies to learn as well as the emergence of irrational {\it herding} are equally evident. The simplest example is that of agents that have to determine a binary action, under peer pressure coming from the decisions observed. By modifying several popular models for opinion dynamics so that agents internalize actions rather than smooth estimates of what other people think, we are able to prove that almost surely the actions final outcome remains random, even though actions can be consensual or polarized depending on the model. This is a theoretical confirmation that the mechanism that leads to the emergence of irrational herding behavior lies in the loss of nuanced information regarding the privately held beliefs behind the individuals decisions.Comment: 23 pages; 7 figure