Testing Linearity against Non-Signaling Strategies

Non-signaling strategies are collections of distributions with certain non-local correlations. They have been studied in Physics as a strict generalization of quantum strategies to understand the power and limitations of Nature\u27s apparent non-locality. Recently, they have received attention in Theoretical Computer Science due to connections to Complexity and Cryptography. We initiate the study of Property Testing against non-signaling strategies, focusing first on the classical problem of linearity testing (Blum, Luby, and Rubinfeld; JCSS 1993). We prove that any non-signaling strategy that passes the linearity test with high probability must be close to a quasi-distribution over linear functions. Quasi-distributions generalize the notion of probability distributions over global objects (such as functions) by allowing negative probabilities, while at the same time requiring that "local views" follow standard distributions (with non-negative probabilities). Quasi-distributions arise naturally in the study of Quantum Mechanics as a tool to describe various non-local phenomena. Our analysis of the linearity test relies on Fourier analytic techniques applied to quasi-distributions. Along the way, we also establish general equivalences between non-signaling strategies and quasi-distributions, which we believe will provide a useful perspective on the study of Property Testing against non-signaling strategies beyond linearity testing

Perturbation Theory Reloaded: Analytical Calculation of Non-linearity in Baryonic Oscillations in the Real Space Matter Power Spectrum

We compare the non-linear matter power spectrum in real space calculated analytically from 3rd-order perturbation theory with N-body simulations at 1<z<6. We find that the perturbation theory prediction agrees with the simulations to better than 1% accuracy in the weakly non-linear regime where the dimensionless power spectrum, Delta^2(k)=k^3P(k)/2pi^2, which approximately gives variance of matter density field at a given k, is less than 0.4. While the baryonic acoustic oscillation features are preserved in the weakly non-linear regime at z>1, the shape of oscillations is distorted from the linear theory prediction. Nevertheless, our results suggest that one can correct the distortion caused by non-linearity almost exactly. We also find that perturbation theory, which does not contain any free parameters, provides a significantly better fit to the simulations than the conventional approaches based on empirical fitting functions to simulations. The future work would include perturbation theory calculations of non-linearity in redshift space distortion and halo biasing in the weakly non-linear regime.Comment: 6 pages, 7 figures, submitted to ApJ. (v2) Four figures have been added to show the residual between theory and N-body simulations for clarity, the dependence of non-linearity on sigma8, and convergence tests of the results. An artificial numerical smoothing of baryonic oscillations from COSMICS has been fixed in Fig.

High Linearity Millimeter Wave Power Amplifiers with Novel Linearizer Techniques

Millimeter-wave communications have experienced phenomenal growth in recent years when limited frequency spectrum is occupied by the ever-developing communication services. The power amplifier, as the key component in the transmitter/receiver module of communication systems, affects performance of the whole system directly and receives much attention. For minimized distortion and optimum system performance, the non-constant en- velope modulation schemes used in communication systems have challenging requirements on linearity. As linearity is related to communication quality directly, several linearization techniques, such as predistortion and feedforward, are applied to power amplifier design. Predistortion method has the advantages over other techniques in relatively simple struc- ture and reasonable linearity improvement. But current predistortion circuits have quite limited performance improvement and relatively large insertion loss, which indicate the need for further research. In most of millimeter-wave amplifier design, great effort has been spent on output power or gain, while linearity is often ignored. As almost all the predistortion circuits operate at the RF frequencies, the linearized millimeter-wave com- munication circuit is still relatively immature and very challenging. This project is dedicated to solve the linearity problem faced by millimeter-wave power amplifier in communication systems, which lacks of e®ective techniques in this field. Linearity improvement with the predistortion method will be the key issue in this project and some original ideas for predistortion circuit design will be applied to millimeter-wave amplifiers. In this thesis, several predistortion circuits with novel structure were proposed, which provide a new approach for linearity improvement for millimeter-wave power am- plifier. A millimeter-wave power ampli¯er for LMDS applications built on GaAs pHEMT technology was developed to a high engineering standard, which works as the test bench for linearization. Actual operation and parasitic elements at tens of gigahertz have been taken into consideration during the design. Firstly, two novel predistorter structures based on the amplifier were proposed, one is based on an amplifier with a fixed bias circuit and the other is based on an amplifier with a nonlinear signal dependant bias circuit. These novel structures can improve the linearity while improving other metrics simultaneously, which can effectively solve the problem of insertion loss faced by the conventional structures. Besides this, an original predistortion circuit design methodology derived from frequency to signal amplitude transformation was proposed. Based on this methodology, several transfer functions were proposed and related predistortion circuits were built to linearize the power amplifier. As this methodology is quite different from the traditional approach, it can improve the linearity signifficantly while other metrics are affected slightly and has a broad prospect for application

High Linearity Millimeter Wave Power Amplifiers with Novel Linearizer Techniques

Millimeter-wave communications have experienced phenomenal growth in recent years when limited frequency spectrum is occupied by the ever-developing communication services. The power amplifier, as the key component in the transmitter/receiver module of communication systems, affects performance of the whole system directly and receives much attention. For minimized distortion and optimum system performance, the non-constant en- velope modulation schemes used in communication systems have challenging requirements on linearity. As linearity is related to communication quality directly, several linearization techniques, such as predistortion and feedforward, are applied to power amplifier design. Predistortion method has the advantages over other techniques in relatively simple struc- ture and reasonable linearity improvement. But current predistortion circuits have quite limited performance improvement and relatively large insertion loss, which indicate the need for further research. In most of millimeter-wave amplifier design, great effort has been spent on output power or gain, while linearity is often ignored. As almost all the predistortion circuits operate at the RF frequencies, the linearized millimeter-wave com- munication circuit is still relatively immature and very challenging. This project is dedicated to solve the linearity problem faced by millimeter-wave power amplifier in communication systems, which lacks of e®ective techniques in this field. Linearity improvement with the predistortion method will be the key issue in this project and some original ideas for predistortion circuit design will be applied to millimeter-wave amplifiers. In this thesis, several predistortion circuits with novel structure were proposed, which provide a new approach for linearity improvement for millimeter-wave power am- plifier. A millimeter-wave power ampli¯er for LMDS applications built on GaAs pHEMT technology was developed to a high engineering standard, which works as the test bench for linearization. Actual operation and parasitic elements at tens of gigahertz have been taken into consideration during the design. Firstly, two novel predistorter structures based on the amplifier were proposed, one is based on an amplifier with a fixed bias circuit and the other is based on an amplifier with a nonlinear signal dependant bias circuit. These novel structures can improve the linearity while improving other metrics simultaneously, which can effectively solve the problem of insertion loss faced by the conventional structures. Besides this, an original predistortion circuit design methodology derived from frequency to signal amplitude transformation was proposed. Based on this methodology, several transfer functions were proposed and related predistortion circuits were built to linearize the power amplifier. As this methodology is quite different from the traditional approach, it can improve the linearity signifficantly while other metrics are affected slightly and has a broad prospect for application

Transient Orthogonality Catastrophe in a Time Dependent Nonequilibrium Environment

We study the response of a highly-excited time dependent quantum many-body state to a sudden local perturbation, a sort of orthogonality catastrophe problem in a transient non-equilibrium environment. To this extent we consider, as key quantity, the overlap between time dependent wave-functions, that we write in terms of a novel two-time correlator generalizing the standard Loschmidt Echo. We discuss its physical meaning, general properties, and its connection with experimentally measurable quantities probed through non-equilibrium Ramsey interferometry schemes. Then we present explicit calculations for a one dimensional interacting Fermi system brought out of equilibrium by a sudden change of the interaction, and perturbed by the switching on of a local static potential. We show that different scattering processes give rise to remarkably different behaviors at long times, quite opposite from the equilibrium situation. In particular, while the forward scattering contribution retains its power law structure even in the presence of a large non-equilibrium perturbation, with an exponent that is strongly affected by the transient nature of the bath, the backscattering term is a source of non-linearity which generates an exponential decay in time of the Loschmidt Echo, reminiscent of an effective thermal behavior.Comment: v3: minor changes, published versio

Borne sur le degré des polynômes presque parfaitement non-linéaires

19 pagesThe vectorial Boolean functions are employed in cryptography to build block coding algorithms. An important criterion on these functions is their resistance to the differential cryptanalysis. Nyberg defined the notion of almost perfect non-linearity (APN) to study resistance to the differential attacks. Up to now, the study of functions APN was especially devoted to power functions. Recently, Budaghyan and al. showed that certain quadratic polynomials were APN. Here, we will give a criterion so that a function is not almost perfectly non-linear. H. Janwa showed, by using Weil's bound, that certain cyclic codes could not correct two errors. A. Canteaut showed by using the same method that the functions powers were not APN for a too large value of the exponent. We use Lang and Weil's bound and a result of P. Deligne on the Weil's conjectures (or more exactly improvements given by Ghorpade and Lachaud) about surfaces on finite fields to generalize this result to all the polynomials. We show therefore that a polynomial cannot be APN if its degree is too large

Locally Biased Galaxy Formation and Large Scale Structure

We examine the influence of the morphology-density(MD) relation and a wide range of simple models for biased galaxy formation on statistical measures of large scale structure. We contrast the behavior of local biasing models, in which the efficiency of galaxy formation is determined by density, geometry, or velocity dispersion of the local mass distribution, with that of non-local biasing models, in which galaxy formation is modulated coherently over scales larger than the galaxy correlation length. If morphological segregation of galaxies is governed by a local MD relation, then the correlation function of E/S0 galaxies should be steeper and stronger than that of spiral galaxies on small scales, as observed, while on large scales the correlation functions of E/S0 and spiral galaxies should have the same shape but different amplitudes. Similarly, all of our local bias models produce scale-independent amplification of the correlation function and power spectrum in the linear and mildly non-linear regimes; only a non-local biasing mechanism can alter the shape of the power spectrum on large scales. Moments of the biased galaxy distribution retain the hierarchical pattern of the mass moments, but biasing alters the values and scale-dependence of the hierarchical amplitudes S3 and S4. Pair-weighted moments of the galaxy velocity distribution are sensitive to the details of the biasing prescription. The non-linearity of the relation between galaxy density and mass density depends on the biasing prescription and the smoothing scale, and the scatter in this relation is a useful diagnostic of the physical parameters that determine the bias. Although the sensitivity of galaxy clustering statistics to the details of biasing is an obstacle to testing cosmological models, it is an asset for testing galaxy formation theories.Comment: 47 pages including 17 Figures, submitted to Ap