Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states

A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises. The orthogonality of these processes provides a natural way to construct binary or multi-valued logic circuitry with arbitrary number N of logic values by using analog circuitry. Moreover, the logic values on a single wire can be made a (weighted) superposition of the N distinct logic values. Fuzzy logic is also naturally represented by a two-component superposition within the binary case (N=2). Error propagation and accumulation are suppressed. Other relevant advantages are reduced energy dissipation and leakage current problems, and robustness against circuit noise and background noises such as 1/f, Johnson, shot and crosstalk noise. Variability problems are also non-existent because the logic value is an AC signal. A similar logic system can be built with orthogonal sinusoidal signals (different frequency or orthogonal phase) however that has an extra 1/N type slowdown compared to the noise-based logic system with increasing number of N furthermore it is less robust against time delay effects than the noise-based counterpart.     

e − e + Production by a Nambu string

We analytically calculate the probability ofe ^– e ⁺ production with a given relative energy from a closed string arising from the Nambu action as a solution of a circularly oscillating string as, perhaps, the simplest generalization of the classic pointlike particle. A numerical analysis of the result is also given.     

Resonance effects in the nonadiabatic nonlinear quantum dimer

In the presence of 1/f ^β noise, we investigate the logical stochastic resonance (LSR) in an asymmetric bistable model driven by various cycling combinations of two logic inputs. The probability of correct logic outputs is calculated according to true table of logic relationships. Two major results are presented. Firstly, it is shown that the LSR effect can be obtained by changing noise strength. Over entire range of noise variance, white noise can be considered to be better than 1/f noise or 1/f ² noise to obtain clean logic operation. At a smaller noise level, 1/f noise can realize higher output probability than white noise or 1/f ² noise. In the sense, 1/f noise can be considered to be better than white noise or 1/f ². On the other hand, the correct probability can evolves nonmonotonically as noise exponent β increases, and a kind of SR-like effect can be obtained as a result of β. At certain intermediate noise variance, the output probability is able to attain its minimum at β = 1. It is also shown that actually some finite β sometime can be better than β = 0 at small range of noise variance. The study might provide some potential complement to LSR effect in the presence of 1/f ^β noise.     

中国极端干旱事件的年代际变化及其成因

研究了河北山西、黄河中下游、江淮和西北东部地区531年极端干旱事件的概率,采用古里雅冰芯δ¹⁸O含量和500年来太平洋年代际涛动指数进行了对比分析.Morlet小波分析发现四个地区的极端干旱事件概率和古里雅冰芯δ¹⁸O含量都存在着350年左右的准周期,且四个地区近500年来极端干旱事件概率的变化与古里雅冰芯δ¹⁸O含量的变化相反,在δ¹⁸O含量较高的时期,发生极端干旱事件的概率较低,反之亦然.对太平洋年代际涛动指数进行小波变换,发现80年尺度的准周期在逐渐衰弱而50年尺度的准周期却在逐渐增强.在80年或50年尺度的准周期处于控制地位时,四个地区处于极端干旱事件多发期,而在二者处于交替时期,即二者周期性均较弱的时期,处于极端干旱事件偏少期. 关键词： 干旱 冰芯 太平洋年代际涛动     

Nondifferentiable Dynamic: Two Examples

Some nondifferentiable quantities (for example, the metric signature) can be the independent physical degrees of freedom. It is supposed that in quantum gravity these degrees of freedom can fluctuate. Two examples of such quantum fluctuation are considered: a quantum interchange of the sign of two components of the 5D metric and a quantum fluctuation between Euclidean and Lorentzian metrics. The first case leads to a spin-like structure on the throat of a composite wormhole and to a possible inner structure of the string. The second case leads to a quantum birth of the non-singular Euclidean Universe with frozen 5^th dimension. The probability for such quantum fluctuations is connected with an algorithmical complexity of the Einstein equations.     

Noise effect on Grover algorithm

The decoherence effect on Grover algorithm has been studied numerically through a noise modelled by a depolarizing channel. Two types of error are introduced characterizing the qubit time evolution and gate application, so the noise is directly related to the quantum network construction. The numerical simulation concludes an exponential damping law for the successive probability of the maxima as time increases. We have obtained an allowed-error law for the algorithm: the error threshold for the allowed noise behaves as ε_th(N) ∼1/N^1.1 (N being the size of the data set). As the power of N is almost one, we consider the Grover algorithm as robust to a certain extent against decoherence. This law also provides an absolute threshold: if the free evolution error is greater than 0.043, Grover algorithm does not work for any number of qubits affected by the present error model. The improvement in the probability of success, in the case of two qubits has been illustrated by using a fault-tolerant encoding of the initial state by means of the [[7,1,3]] quantum code.     

Catoptric tadpoles

Fermionic string perturbation theory is known to suffer from an ambiguity in the form of a total derivative in the moduli space. For a class of backgrounds (including R¹⁰, orbifolds and theories with no U(1) factors in gauge group) we show that these ambiguities for the partition function of heterotic string theory at any genus are proportional to massless physical tadpoles in the theory at lower genera and hence vanish in stable vacua. We also find that in R¹⁰ the cosmological constant at a given genus is proportional to the cosmological constant at lower genera. This enables us to give an inductive argument for the vanishing of the cosmological constant in R¹⁰ to all orders in string perturbation theory. We also address the ambiguity and finiteness of n-point functions. Our results indicate that in R¹⁰ the ambiguity can be absorbed by a renormalization of the string coupling constant and the string tension. The expected sources of divergence in the n-point function in arbitrary tachyon-free backgrounds, besides the usual infrared divergences for d ≤ 4, are shown to be proportional to tadpoles of physical massless fields. For type II strings in arbitrary backgrounds, we show by explicit calculations that the ambiguity vanishes at g = 2.     

Checking key integrity efficiently for high-speed quantum key distribution using combinatorial group testing

With the increasing key generation rate in practical quantum key distribution, checking key integrity efficiently becomes an important problem. Since the original method that utilizes one hash value for a key string has to discard all the key bits even if just one error bit exists, it may eventually limit the practical rate of key generation. In this paper, we propose a new scheme based on combinatorial group testing to identify the rare error bits so as to avoid dropping all the key bits. Experimental results show that the scheme can precisely locate the error bits if the number of error bits is within the maximum guaranteed number set by the scheme while the overhead is insignificant (for a 10⁶-bit key, additional bits: 0.1% of the key; hashing time: 16 ms; checking time: 22 ms) and it can still keep the majority of the correct bits (95%) even if the number of error bits is 10 times of the maximum. The results also indicate that the minimum key size for the CGT-based scheme to gain an advantage over the original method is about 2 × 10⁴ bits.     

On loop corrections to string theory effective actions

We make some comments concerning the structure of loop corrections to the effective action (EA) for massless fields of a string. The singular part of the α′→0 limit of the one-loop EA in the open (super)string theory is studied and is shown to be in correspondence with the ultraviolet divergent part of the one-loop effective action in the (super) Yang-Mills theory. In particular, we reproduce the known result about the absence of Λ^D−4 F_μν² one-loop infinities in D = 26 Yang-Mills theory starting from the open Bose string theory. We also discuss the path integral representation for EA (EA = generalized partition function for the σ-model) and use it to compute the open string theory EA on the disc and the annulus.     

Large N 2D Yang-Mills Theory and Topological String Theory

We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A= 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's “Ω^-1 points ”. We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach. Received: 3 March 1994 / Accepted: 2 February 1995     

Heterotic string from a higher dimensional perspective

The (abelian bosonic) heterotic string effective action, equations of motion and Bianchi identity at order α^′ in ten dimensions, are shown to be equivalent to a higher dimensional action, its derived equations of motion and Bianchi identity. The two actions are the same up to the gauge fields: the latter are absorbed in the higher dimensional fields and geometry. This construction is inspired by heterotic T-duality, which becomes natural in this higher dimensional theory.We also prove the equivalence of the heterotic string supersymmetry conditions with higher dimensional geometric conditions. Finally, some known Kähler and non-Kähler heterotic solutions are shown to be trivially related from this higher dimensional perspective, via a simple exchange of directions. This exchange can be encoded in a heterotic T-duality, and it may also lead to new solutions.     

Quantum vortex strings: A review

The quantum worldsheet dynamics of vortex strings contains information about the 4d non-Abelian gauge theory in which the string lives. Here I tell this story. The string worldsheet theory is typically some variant of the CP^N-1 sigma-model, describing the orientation of the string in a U(N) gauge group. Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories have been known since the 1970s. The vortex string provides a quantitative link between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning parameters, the CP^N-1 sigma-model can be coaxed to flow to an interacting conformal fixed point which is related to the 4d Argyres-Douglas fixed point. For theories with N=1 supersymmetry, the worldsheet theory suffers dynamical supersymmetry breaking and, more interestingly, supersymmetry restoration, in a way which captures the physics of Seiberg’s quantum deformed moduli space.     

Statistical properties of strings

We investigate numerically the configurational statistics of strings. The algorithm models an ensemble of global U(1) cosmic strings, or equivalently vortices in superfluid ⁴He. We use a new method which avoids the specification of boundary conditions on the lattice. We therefore do not have the artificial distinction between short and long string loops or a “second phase” in the string network statistics associated with strings winding around a toroidal lattice. Our lattice is also tetrahedral, which avoids ambiguities associated with the cubic lattices of previous work. We find that the percentage of infinite string is somewhat lower than on cubic lattices, 63% instead of 80%. We also investigate the Hagedorn transition, at which infinite string percolate, controlling the string density by rendering one of the equilibrium states more probable. We measure the percolation threshold, the critical exponent associated with the divergence of a suitably defined susceptibility of the string loops, and that associated with the divergence of the correlation length.     

Superstring compactification on homogeneous coset spaces with torsion

Compactifications of the heterotic string on M⁴×K are investigated, where M⁴ is four- Minkowski spacetime and K is a six-dimensional compact coset manifold with torsion. The β-functions of the underlying two-dimensional nonlinear σ-model, as well as the central charge of the Virasoro algebra, are argued to vanish for K=SU(3)/U(1)×U(1) and G₂/SU(3) with a particular choice of torsion and radius of the manifold. These two coset spaces may provide therefore a perturbative solution of the classical string field equations.     

String cosmology in LRS Bianchi type-II dusty Universe with time-decaying vacuum energy density Λ

A model of a cloud formed by massive strings is used as a source of LRS Bianchi type-II with time-decaying vacuum energy density Λ. To construct string cosmological models, we have used the energy–momentum tensor for such strings as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings: (i) massive string and (ii) Nambu string. The expansion θ in the model is assumed to be proportional to the shear σ. This condition leads to A = βB ^m , where A and B are the metric coefficients, m is a constant and β is an integrating constant. Our models are in accelerating phase which is consistent with the recent observations of supernovae type-Ia. The physical and geometrical behaviour of these models are also discussed.     

Superstring on pp-wave orbifold from large-N quiver gauge theory

We extend the proposal of Berenstein, Maldacena and Nastase to the Type IIB superstring propagating on a pp-wave over the R ⁴/Z _k orbifold. We show that first-quantized free string theory is described correctly by the large-N, fixed gauge coupling limit of [U(N)] ^k quiver gauge theory. We propose a precise map between gauge theory operators and string states for both untwisted and twisted sectors. We also compute leading-order perturbative correction to the anomalous dimensions of these operators. The result is in agreement with the value deduced from the string energy spectrum, thus substantiating our proposed operator-state map. Received: 14 March 2002 / Published online: 5 July 2002     

Measures of Information and Error Laws

The logarithm of joint error densities for themost common means are shown to be proportional to thedifference of two weighted means which discriminatebetween a complete, nonuniform probability distribution and the uniform distribution. The difference inthe weighted means is related to a new Shannon-typeinequality for the discrimination between twoprobability distributions. Measures of the distancebetween the two distributions are determined, and a newstatistic, comparable to ², is derivedfrom a first-order approximatiom of the directeddivergence. Comparison is made between the error lawsand the method of maximum likelihood.     

Adjoint Wilson lines and the effective gluon mass

The effective mass of the gluon is defined in terms of the energy stored in the string between adjoint sources. For SU(2) lattice gauge theory, I present Monte Carlo evidence that this mass scales correctly in the weak coupling regime and hence is non-zero and finite in the continuum limit. Various systematic errors (chief among them are temperature effects) still make it difficult to give a precise numerical value for this mass at zero temperature, but a range of 500 to 800 MeV seems reasonable (using a value for the string tension of (420 MeV)²). Some attempt is made to relate this quantity to a true “constituent gluon mass.”     

Comparison of three-jet events with QCD shower models

Distributions of particles in three-jet events from e⁺e^? → hadrons are compared with different fragmentation schemes, i.e. the Lund string model, independent parton fragmentation and QCD shower models. Effects specific to the string scheme, which have been seen in the data, are also reproduced by QCD shower models if soft gluon interference effects are included.