Cancellation Of Terms Research Articles

Overcoming roundoff errors in the first-order amplitude for general state-to-state transitions in hydrogen by projectile impact

A computer program to calculate the amplitude for general state-to-state transitions in hydrogen from the analytical result has the potential for significant numerical round-off errors whenever the sum of the angular momenta of the two states is greater than four and the projectile’s impact parameter is less than the ratio of its energy to velocity. This arises from high-order cancellation of terms in the MacDonald functions in that analytical result, whose polynomial portions have been found to obey a new multiplication theorem. The cost for correcting this instability is the replacement of a finite series of MacDonald functions by an infinite series via the multiplication theorem for the full MacDonald function.

Probability theory for 3-layer remote sensing in ideal gas law environment

We extend the probability model for 3-layer radiative transfer [Opt. Express 20, 10004 (2012)] to ideal gas conditions where a correlation exists between transmission and temperature of each of the 3 layers. The effect on the probability density function for the at-sensor radiances is surprisingly small, and thus the added complexity of addressing the correlation can be avoided. The small overall effect is due to (a) small perturbations by the correlation on variance population parameters and (b) cancellation of perturbation terms that appear with opposite signs in the model moment expressions.

Probing the extensive nature of entropy

We have devised a general numerical scheme applied to a system of independent, distinguishable, non-interacting particles, to demonstrate in a direct manner the extensive nature of statistical entropy. Working within the microcanonical ensemble, our methods enable one to directly monitor the approach to the thermodynamic limit (N → ∞) in a manner that has not been known before. We show that (sN − s∞) → N−α where sN is the entropy per particle for N particles and S∞ is the entropy per particle in the thermodynamic limit. We demonstrate universal behaviour by considering a number of different systems each defined by its unique single-particle spectrum. Various thermodynamic quantities as a function of N may be computed using our methods; in this paper, we focus on the entropy, the chemical potential and the temperature. Our results are applicable to systems of finite size, e.g. nano-particle systems. Furthermore, we demonstrate a new phenomenon, referred to as entropic interference, which manifests as a cancellation of terms in the thermodynamic limit and which results in the additive nature of entropy.

Making Polynomials Robust to Noise

$ \newcommand{\R}{{\mathbb R}} \newcommand{\zoon}{\{0,1\}^n} \newcommand{\tildeg}{\,\deg\hspace{-18pt}\widetilde{\rule{0mm}{6pt}\hspace{18pt}}} \newcommand{\robust}{{\operatorname{robust}}} $ A basic question in any model of computation is how to reliably compute a given function when its inputs are subject to noise. Buhrman, Newman, Röhrig, and de Wolf (2003) posed the noisy computation problem for real polynomials. We give a complete solution to this problem. For any $\delta>0$ and any polynomial $p\colon\zoon\to[-1,1],$ we construct a corresponding polynomial $p_\robust\colon\R^n\to\R$ of degree $O(\deg p+\log1/\delta)$ that is robust to noise in the inputs: $|p(x)-p_\robust(x+\epsilon)|<\delta$ for all $x\in\zoon$ and all $\epsilon\in[-1/3,1/3]^n$. This result is optimal with respect to all parameters. We construct $p_\robust$ explicitly for each $p$. Previously, it was open to give such a construction even for $p=x_1\oplus x_2\oplus \cdots\oplus x_n$ (Buhrman et al., 2003). The proof contributes a technique of independent interest, which allows one to force partial cancellation of error terms in a polynomial. An extended abstract of this article appeared in the Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing (STOC'12), pages 747--758, 2012.

Outer Bounds on the Sum Rate of the K-User MIMO Gaussian Interference Channel

This paper derives outer bounds on the sum rate of the K-user MIMO Gaussian interference channel (GIC). Three outer bounds are derived, under different assumptions of cooperation and providing side information to receivers. The novelty in the derivation lies in the careful selection of side information, which results in the cancellation of the negative differential entropy terms containing signal components, leading to a tractable outer bound. The overall outer bound is obtained by taking the minimum of the three outer bounds. The derived bounds are simplified for the MIMO Gaussian symmetric IC to obtain outer bounds on the generalized degrees of freedom (GDOF). The relative performance of the bounds yields insight into the performance limits of multiuser MIMO GICs and the relative merits of different schemes for interference management. These insights are confirmed by establishing the optimality of the bounds in specific cases using an inner bound on the GDOF derived by the authors in a previous work. It is also shown that many of the existing results on the GDOF of the GIC can be obtained as special cases of the bounds, e.g., by setting K=2 or the number of antennas at each user to 1.

On the Compression and Blocking Distortion of Semiconductor-Based Varactors

The effective capacitance of variable reactors (varactors) can be modulated by the magnitude of applied RF signals, resulting in troublesome detuning issues in resonators constructed with these devices. In this paper, the fundamental causes behind these issues are investigated through the use of Volterra series. It is concluded that two major distortion mechanisms, namely, compression and blocking, are responsible for this effective capacitance change under RF excitation. In light of this observation, different varactor configurations are proposed and investigated, yielding novel devices with much smaller capacitance variation, typically on the order of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\sim} {\hbox {0.1}}\mathchar"707B {\hbox{0.5}}\%$</tex></formula> compared to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\sim} {\hbox {10}}\mathchar"707B {\hbox{50}}\%$</tex></formula> for conventional semiconductor-based varactors. With this improvement, the resonance frequency shift of a 2-GHz resonator is decreased from <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\sim {\hbox {300}}}$</tex></formula> to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\sim {\hbox {5}}}~{\hbox {MHz}}$</tex></formula> for worst case conditions, a property essential to tunable high- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Q$</tex> </formula> filter applications. Among all analyzed structures, the varactor topology that facilitates cancelation of all important distortion products has been experimentally tested. These measurements demonstrate successful cancellation of both compression and blocking terms, resulting in capacitance variation below 0.5% in worst case scenarios.

Modified NLMF adaptation of Volterra filters used for nonlinear acoustic echo cancellation

When dealing with adaptive nonlinear filters used in acoustic echo cancellation, the tradeoff between convergence rate and steady-state error is an important issue. This tradeoff is favorably addressed here using a modified version of the normalized least-mean-fourth (NLMF) algorithm applied to an adaptive second-order Volterra structure. A convergence rate improvement is obtained at the same steady-state error by amending the step size of the conventional NLMF algorithm using a new step-size function that depends on the norm of an error vector of a certain length. The efficiency of the proposed method is compared with that of the conventional adapted second-order Volterra filter for nonlinear acoustic echo cancellation in terms of echo return loss enhancement (ERLE). From simulations conducted for input signals with different probability density functions, the new approach is shown to outperform the normalized least-mean-square (NLMS) second-order Volterra filter in terms of the convergence rate of the same steady-state error. The proposed technique was also tested in acoustic scenarios with impulse noise and separately with distinct local signal powers. The performance of the method was also compared to that of the traditional NLMF algorithm and of the variable NLMF (XE-NLMF) algorithm.

Guidelines for the design and implementation of the ARPCC control applied to grid-connected converters

This paper presents implementation details of the adaptive robust predictive current control (ARPCC) applied to a grid-connected converter, such as feed-forward cancellation protocol, the selection of the observer gain and adaptive parameters or the sampling options, needed to get the best performance of this control. The feed-forward term cancellation permits to achieve a very low harmonic distortion in current waveforms when the voltage sensing circuits are well calibrated. A detailed gain adjustment protocol of the voltage sensing circuits is presented in this paper. Moreover, a control design procedure based on the observer gain Lo boundaries and the adaptive parameters has been presented and experimentally tested. Finally, different sampling options in the analog-to-digital conversion process are presented, offering programming solutions to achieve the higher stability margins or a compromise between stability margins and time available for other DSP operations.

Phenomenological consequences of sub-leading terms in see-saw formulas

Several aspects of next-to-leading (NLO) order corrections to see-saw formulas are discussed and phenomenologically relevant situations are identified. We generalize the formalism to calculate the NLO terms developed for the type I see-saw to variants like the inverse, double or linear see-saw, i.e., to cases in which more than two mass scales are present. In the standard type I case with very heavy fermion singlets the sub-leading terms are negligible. However, effects in the percent regime are possible when sub-matrices of the complete neutral fermion mass matrix obey a moderate hierarchy, e.g. weak scale and TeV scale. Examples are cancellations of large terms leading to small neutrino masses, or inverse see-saw scenarios. We furthermore identify situations in which no NLO corrections to certain observables arise, namely for mu-tau symmetry and cases with a vanishing neutrino mass. Finally, we emphasize that the unavoidable unitarity violation in see-saw scenarios with extra fermions can be calculated with the formalism in a straightforward manner.

Cancellation of 4-derivative terms in Volkov-Akulov action

Recently Kuzenko and McCarty observed the cancellation of 4-derivative terms in the $D=4 {\cal N}=1$ Volkov-Akulov supersymmetric action for the fermionic Nambu-Goldstone field. Here is presented a simple algebraic proof of the cancellation based on using the Majorana bispinors and Fiertz identities. The cancellation shows a difference between the Volkov-Akulov action and the effective superfield action recently studied by Komargodski and Seiberg and containing one 4-derivative term. We find out that the cancellation effect takes place in coupling of the Nambu-Goldstone fermion with the Dirac field. Equivalence between the KS and the VA Lagrangians is proved up to the first order in the interaction constant of the NG fermions.

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A clocked high-pass-filter-based offset cancellation technique for high-gain biomedical amplifiers

In this article, a simple offset cancellation technique based on a clocked high-pass filter with extremely low output offset is presented. The configuration uses the on-resistance of a complementary metal oxide semiconductor (CMOS) transmission gate (X-gate) and tunes the lower 3-dB cut-off frequency with a matched pair of floating capacitors. The results compare favourably with the more complex auto-zeroing and chopper stabilisation techniques of offset cancellation in terms of power dissipation, component count and bandwidth, while reporting inferior output noise performance. The design is suitable for use in biomedical amplifier systems for applications such as ENG-recording. The system is simulated in Spectre Cadence 5.1.41 using 0.6 μm CMOS technology and the total block gain is ∼83.0 dB while the phase error is <5°. The power consumption is 10.2 mW and the output offset obtained for an input monotone signal of 5 μVpp is 1.28 μV. The input-referred root mean square noise voltage between 1 and 5 kHz is 26.32 nV/√Hz.

Numerical orbital Fourier space approach to polymer band‐structure calculations

AbstractThe periodic symmetry of polymer chains can be applied via Bloch functions to polymer band structure calculations (Delhalle and Harris, Phys Rev B 1985, 31, 6755). The possibility of replacing Gaussian orbitals with numerically defined orbitals in this approach is discussed. Two modifications of the theory to overcome problems with the cancellation of divergent terms are described. Result for a LiH chain are compared with analytic Gaussian orbital results. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Experimental correlation of nitroxide recollision spin exchange with free volume and compressibility in alkane and aromatic compounds

Diffusion of perdeuterated tempone (PDT) in various nonpolar hydrocarbon solvents on both the large and microscopic scales is examined through electron paramagnetic resonance spectroscopy. Spectral line broadening and hyperfine spacing are measured in order to extract both the Heisenberg spin-exchange rate as well as the average recollision times between spin-probe pairs. Probe recollision is responsible for a linear component to the dependence of the line shift on spectral broadening which has been identified in recent years. The present study extends the work of a previous paper by Kurban et al. [J. Chem. Phys. 129, 064501 (2008)], in which it was reported that recollision rates for PDT formed a common curve across n-alkanes when plotted with respect to free volume and to isothermal compressibility. It is now found that such common curves occur within distinct chemical families, in particular, the alkane and aromatic groups. Within each chemical family, the spin probe recollision rate correlates with free volume and compressibility independently of the geometry of the particular solvent. All solvents show significantly enhanced recollisional diffusion over the Stokes-Einstein (SE) prediction at high temperatures. The spin-exchange rate forms a common curve with respect to T/eta for all alkanes except cyclohexane and another common curve in all three aromatic compounds. It is reasoned that although all spin-exchange rates are near to the SE prediction, the semblance of hydrodynamic behavior is superficial and arises incidentally from mathematical cancellation of terms in a generalized diffusion coefficient. As a collision pair coexists for a time within a solvation shell, the recollision time places a lower limit on the lifetime of the solvent cage. Although molecular dynamics simulations conducted thus far have yielded cage lifetimes lower than the measured recollision times, this is attributable to the fact that such simulations have mostly examined cage configurations too small to harbor a spin-exchange encounter, and is also likely due to restrictive mathematical definitions of cage lifetimes that are employed in such simulations.

Self-Contacts, Self-Concentration, and the Composition Dependence of the Glass Transition Temperature in Polymer Mixtures

Self-concentration, a consequence of chain connectivity, is an important factor in determining the properties of polymer mixtures. It is proposed that self-concentration has two components. First, there is a “covalent connectivity effect”, which manifests itself in the probability that a site adjacent to a chosen segment on a chain is occupied by a like or unlike segment; second, there is a “conformational connectivity effect” that is a consequence of a chain bending back on itself through both local and long-range factors that depend on the flexibility of the chain. This latter component is modeled using a contact point approach developed in previous work. If the covalent connectivity effect is treated using a lattice model, there is a cancelation of terms and noncovalent contacts do not contribute to self-concentration in calculating the average properties of polymer blends. Nevertheless, when covalent contacts are included together with conformational self-contacts in order to calculate the composition...

A revised electronic Hessian for approximate time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) at the generalized gradient level of approximation (GGA) has shown systematic errors in the calculated excitation energies. This is especially the case for energies representing electron transitions between two separated regions of space or between orbitals of different spatial extents. It will be shown that these limitations can be attributed to the electronic ground state Hessian G(GGA). Specifically, we shall demonstrate that the Hessian G(GGA) can be used to describe changes in energy due to small perturbations of the electron density (Deltarho), but it should not be applied to one-electron excitations involving the density rearrangement (Deltarho) of a full electron charge. This is in contrast to Hartree-Fock theory where G(HF) has a trust region that is accurate for both small perturbations and one-electron excitations. The large trust radius of G(HF) can be traced back to the complete cancellation of Coulomb and exchange terms in Hartree-Fock (HF) theory representing self-interaction (complete self-interaction cancellation, CSIC). On the other hand, it is shown that the small trust radius for G(GGA) can be attributed to the fact that CSIC is assumed for GGA in the derivation of G(GGA) although GGA (and many other approximate DFT schemes) exhibits incomplete self-interaction cancellation (ISIC). It is further shown that one can derive a new matrix G(R-DFT) with the same trust region as G(HF) by taking terms due to ISIC properly into account. Further, with TD-DFT based on G(R-DFT), energies for state-to-state transitions represented by a one-electron excitation (psi(i)-->psi(a)) are approximately calculated as DeltaE(ai). Here DeltaE(ai) is the energy difference between the ground state Kohn-Sham Slater determinant and the energy of a Kohn-Sham Slater determinant where psi(i) has been replaced by psi(a). We make use of the new Hessian in two numerical applications involving charge-transfer excitations. It is concluded that higher than second order response theory (involving ISIC terms) must be used in approximate TD-DFT, in order to describe charge-transfer excitations.

Downlink co-channel interference cancellation in multihop relay networks

In this paper, we study the use of iterative multi-user detectors for co-channel interference suppression in wireless cellular systems. We investigate the benefits of using iterative interference cancellation in the mobile receiver in the downlink scenario of traditional single-hop wireless cellular networks as well as two-hop relay networks. To illustrate these benefits, as an example we consider a receiver with a single receive antenna that is capable of detecting and cancelling a single in-band interferer that uses the same coding and modulation scheme as the desired signal. Simulation results show significant improvements with iterative interference cancellation in terms of the average system throughput and outage probability. Because the interference canceller is so effective, more aggressive frequency reuse schemes can be now considered, such as using smaller cluster sizes, using 3-sectored cells where all sectors share the same frequency band, and using non-orthogonal channels for relaying.

CONTROLLING CHAOS VIA STATE FEEDBACK CANCELLATION IN A NOISY CHAOTIC SYSTEM

Combining a modified Independent Component Analysis (ICA) and a feedback cancellation of nonlinear terms, the approach of engineering control can efficiently govern a noisy chaotic system. The methodology is easy to comprehend and to implement, but previous knowledge of the system dynamics is needed.

Nitroxide spin exchange due to re-encounter collisions in a series of n-alkanes

Bimolecular collisions between perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-l-oxyl molecules in three alkanes have been studied by measuring the electron paramagnetic resonance (EPR) spectral changes induced by spin exchange. We define an "encounter" to be a first-time collision followed by a series of re-encounters prior to the diffusing pair's escaping each other's presence. The present work stems from a recent proposal [B. L. Bales et al., J. Phys. Chem. A 107, 9086 (2003)] that an unexpected linear dependence of the spin-exchange-induced EPR line shifts on spin-exchange frequency can be explained by re-encounters of the same probe pair during one encounter. By employing nonlinear least-squares fitting, full use of the information available from the spectral changes allows us to study encounters and re-encounters separately. The encounter rate constants appear to be dominated by hydrodynamic forces, forming a common curve for hexane, decane, and hexadecane when plotted against T/eta, where eta is the shear viscosity. Unexpectedly, encounters are not dependent on the ratio mu = a/a(s), where a and a(s) are the van der Waals radii of the nitroxide probe and the solvent, respectively. It is argued that the near coincidence of the resulting encounter rate constant with the hydrodynamic prediction is likely due to a near cancellation of terms in the general diffusion coefficient. Thus, the semblance of hydrodynamic behavior is coincidental rather than intrinsic. In contrast, the mean times between re-encounters do depend on the relative sizes of probe and solvent. For hexane at lower temperatures, the Stokes-Einstein equation apparently describes re-encounters well; however, at higher temperatures and for decane and hexadecane, departures from the hydrodynamic prediction become larger as mu becomes smaller. This is in qualitative agreement with the theory of microscopic diffusion of Hynes et al. [J. Chem. Phys. 70, 1456 (1979)]. These departures are well correlated with the free volume available in the solvent; thus, the mean times between re-encounters form a common curve when plotted versus the free volume. Because free volume is manifested macroscopically by the isothermal compressibility, it is expected and observed that the re-encounter rate also forms a common curve across all three solvents when plotted with respect to compressibility. The existence of a common curve for alkanes raises the prospect of using EPR to determine the compressibility of substances such as fossil fuels and biological membranes.

Multiaccess Channels with State Known to Some Encoders and Independent Messages

We consider a state-dependent multiaccess channel (MAC) with state noncausally known to some encoders. For simplicity of exposition, we focus on a two-encoder model in which one of the encoders has noncausal access to the channel state. The results can in principle be extended to any number of encoders with a subset of them being informed. We derive an inner bound for the capacity region in the general discrete memoryless case and specialize to a binary noiseless case. In binary noiseless case, we compare the inner bounds with trivial outer bounds obtained by providing the channel state to the decoder. In the case of maximum entropy channel state, we obtain the capacity region for binary noiseless MAC with one informed encoder. For a Gaussian state-dependent MAC with one encoder being informed of the channel state, we present an inner bound by applying a slightly generalized dirty paper coding (GDPC) at the informed encoder and a trivial outer bound by providing channel state to the decoder also. In particular, if the channel input is negatively correlated with the channel state in the random coding distribution, then GDPC can be interpreted as partial state cancellation followed by standard dirty paper coding. The uninformed encoders benefit from the state cancellation in terms of achievable rates, however, it seems that GDPC cannot completely eliminate the effect of the channel state on the achievable rate region, in contrast to the case of all encoders being informed. In the case of infinite state variance, we provide an inner bound and also provide a nontrivial outer bound for this case which is better than the trivial outer bound.