Asymptotically distribution-free goodness-of-fit testing for tail copulas

Let $(X_1,Y_1),\ldots,(X_n,Y_n)$ be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima $\bigvee_{i=1}^nX_i$ and $\bigvee_{i=1}^nY_i$ is then characterized by the marginal extreme value indices and the tail copula $R$. We propose a procedure for constructing asymptotically distribution-free goodness-of-fit tests for the tail copula $R$. The procedure is based on a transformation of a suitable empirical process derived from a semi-parametric estimator of $R$. The transformed empirical process converges weakly to a standard Wiener process, paving the way for a multitude of asymptotically distribution-free goodness-of-fit tests. We also extend our results to the $m$-variate ($m>2$) case. In a simulation study we show that the limit theorems provide good approximations for finite samples and that tests based on the transformed empirical process have high power.Comment: Published at http://dx.doi.org/10.1214/14-AOS1304 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

LHC Charge Asymmetry as Constraint on Models for the Tevatron Top Anomaly

The forward-backward asymmetry $A_{FB}^{t\bar t}$ in top quark production at the Tevatron has been observed to be anomalously large by both CDF and D0. It has been suggested that a model with a $W'$ coupling to $td$ and $ub$ might explain this anomaly, and other anomalies in $B$ mesons. Single-top-quark production in this model is large, and arguably in conflict with Tevatron measurements. However the model might still be viable if $A_{FB}^{t\bar t}$ is somewhat smaller than its current measured central value. We show that even with smaller couplings, the model can be discovered (or strongly excluded) at the LHC using the 2010 data sets. We find that a suitable charge-asymmetry measurement is a powerful tool that can be used to constrain this and other sources of anomalous single-top production, and perhaps other new high-energy charge-asymmetric processes.Comment: 25 pages, 4 figures, note adde

Quantum computation with un-tunable couplings

Most quantum computer realizations require the ability to apply local fields and tune the couplings between qubits, in order to realize single bit and two bit gates which are necessary for universal quantum computation. We present a scheme to remove the necessity of switching the couplings between qubits for two bit gates, which are more costly in many cases. Our strategy is to compute in and out of carefully designed interaction free subspaces analogous to decoherence free subspaces, which allows us to effectively turn off and turn on the interactions between the encoded qubits. We give two examples to show how universal quantum computation is realized in our scheme with local manipulations to physical qubits only, for both diagonal and off diagonal interactions.Comment: 5 pages, 2 figure

Building Morphological Chains for Agglutinative Languages

In this paper, we build morphological chains for agglutinative languages by using a log-linear model for the morphological segmentation task. The model is based on the unsupervised morphological segmentation system called MorphoChains. We extend MorphoChains log linear model by expanding the candidate space recursively to cover more split points for agglutinative languages such as Turkish, whereas in the original model candidates are generated by considering only binary segmentation of each word. The results show that we improve the state-of-art Turkish scores by 12% having a F-measure of 72% and we improve the English scores by 3% having a F-measure of 74%. Eventually, the system outperforms both MorphoChains and other well-known unsupervised morphological segmentation systems. The results indicate that candidate generation plays an important role in such an unsupervised log-linear model that is learned using contrastive estimation with negative samples.Comment: 10 pages, accepted and presented at the CICLing 2017 (18th International Conference on Intelligent Text Processing and Computational Linguistics

Storage by trapping and spatial staggering of multiple interacting solitons in Λ\Lambda-type media

In this paper we investigate the properties of self induced transparency (SIT) solitons, propagating in a $\Lambda$-type medium. It was found that the interaction between SIT solitons can lead to trapping with their phase preserved in the ground state coherence of the medium. These phases can be altered in a systematic way by the application of appropriate light fields, such as additional SIT solitons. Furthermore, multiple independent SIT solitons can be made to propagate as bi-solitons through their mutual interaction with a separate light field. Finally, we demonstrate that control of the SIT soliton phase can be used to implement an optical exclusive-or gate.Comment: 7 pages, 7 figure

A model for the force stretching double-stranded chain molecules

We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $\beta-$sheets in protein, by including the constant force stretching at one end of molecules as in a typical single-molecule experiment. The conformations of double-stranded regions of the chain are calculated based on polymer graph-theoretic approach [S-J. Chen and K. A. Dill, J. Chem. Phys. {\bf109}, 4602(1998)], while the unpaired single-stranded regions are treated as self-avoiding walks. Sequence dependence and excluded volume interaction are taken into account explicitly. Two classes of conformations, hairpin and RNA secondary structure are explored. For the hairpin conformations, all possible end-to-end distances corresponding to the different types of double-stranded regions are enumerated exactly. For the RNA secondary structure conformations, a new recursive formula incorporating the secondary structure and end-to-end distribution has been derived. Using the model, we investigate the extension-force curves, contact and population distributions and re-entering phenomena, respectively. we find that the force stretching homogeneous chains of hairpin and secondary structure conformations are very different: the unfolding of hairpins is two-state, while unfolding the latter is one-state. In addition, re-entering transitions only present in hairpin conformations, but are not observed in secondary structure conformations.Comment: 19 pages, 28 figure