Linearity and iterator types for Gödel’s System

System Open image in new window is a linear λ-calculus with numbers and an iterator, which, although imposing linearity restrictions on terms, has all the computational power of Gödel’s System  Open image in new window . System Open image in new window owes its power to two features: the use of a closed reduction strategy (which permits the construction of an iterator on an open function, but only iterates the function after it becomes closed), and the use of a liberal typing rule for iterators based on iterative types. In this paper, we study these new types, and show how they relate to intersection types. We also give a sound and complete type reconstruction algorithm for System  Open image in new window .     

Consistency,Turing Computability and Gödel’s First Incompleteness Theorem

It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined with Gödel’s results and accepted theorems of recursion theory, does provide the basis for an apparent paradox. The difficulty arises when such an algorithm is embedded within a computer program of sufficient arithmetic power. The required computer program (an AI system) is described herein, and the paradox is derived. A solution to the paradox is proposed, which, it is argued, illuminates the truth status of axioms in formal models of programs and Turing machines.     

Computer Proofs in Gödel’s Class Theory with Equational Definitions for Composite and Cross

Some basic theorems about composition and other key constructs of set theory were proved using McCunes computer program OTTER, building on Quaifes modification of Gödels class theory. Our proofs use equational definitions in terms of Gödels flip and rotate functors. A new way to prove the composition of homomorphisms theorem is also presented.     

Automatic Georeferencing of Images Acquired by UAV’s

This paper implements and evaluates experimentally a procedure for automatically georeferencing images acquired by unmanned aerial vehicles (UAV’s) in the sense that ground control points (GCP) are not necessary. Since the camera model is necessary for georeferencing, this paper also proposes a completely automatic procedure for collecting corner pixels in the model plane image to solve the camera calibration problem, i.e., to estimate the camera and the lens distortion parameters. The performance of the complete georeferencing system is evaluated with real flight data obtained by a typical UAV.     

Non-determinism in Gödel’s System <Emphasis Type="Italic">T</Emphasis>

The calculus T^? is a successor-free version of Gödel’s T. It is well known that a number of important complexity classes, like e.g. the classes logspace, \(\textsc{p}\), \(\textsc{linspace}\), \(\textsc{etime}\) and \(\textsc{pspace}\), are captured by natural fragments of T^? and related calculi. We introduce the calculus T^∽, which is a non-deterministic variant of T^?, and compare the computational power of T^∽ and T^?. First, we provide a denotational semantics for T^∽ and prove this semantics to be adequate. Furthermore, we prove that \(\textsc{linspace}\subseteq \mathcal {G}^{\backsim }_{0} \subseteq \textsc{linspace}\) and \(\textsc{etime}\subseteq \mathcal {G}^{\backsim }_{1} \subseteq \textsc{pspace}\) where \(\mathcal {G}^{\backsim }_{0}\) and \(\mathcal {G}^{\backsim }_{1}\) are classes of problems decidable by certain fragments of T^∽. (It is proved elsewhere that the corresponding fragments of T^? equal respectively \(\textsc{linspace}\) and \(\textsc{etime}\).) Finally, we show a way to interpret T^∽ in T^?.     

On equitable colouring of Knödel graphs

The notion of equitable colouring was introduced by Meyer in 1973. In this paper we find the equitable chromatic number χ₌ for the line graph of Knödel graphs L(W_{Δ, n}), central graph of Knödel graphs C(W_{Δ, n}) and corona graph of Knödel graphs W_{Δ, m}° W_{Δ, n}. As a by-product we obtain a new class of graphs that confirm Equitable Colouring Conjecture.     

Generalizations of Hölder’s and some related inequalities

In this paper we establish some new generalizations and refinements of Hölder’s inequality and some related inequalities. We also show that many existing inequalities related to the Hölder inequality are special cases of the inequalities presented.     

Testing Hardy’s ladder proof of nonlocality by joint measurements of qubits

We propose an experimentally feasible scheme to test Hardy’s ladder proof of nonlocality with two qubits (two-level atoms) dispersively coupled to a driven cavity. First, we find that the required nonmaximally entangled two-qubit pure state can be prepared by only one-step two-qubit operation from the ground state $|00\rangle $ | 00 〉 , assisted by two single-qubit gates. Next, we perform two single-qubit operations to encode the local information into the prepared nonmaximally entangled state. Finally, the nonlocal correlations between the two qubits can be directly detected by the joint measurement of the two-qubit register in one of selected computational basis, implemented by probing the steady-state transmitted spectra of the driven cavity. Consequently, the Hardy’s ladder proof of nonlocality can be effectively tested. The feasibility of our proposal with the current experimental technology is also analyzed.     

Security flaw of Hölbl et al.’s protocol

Recently, Hölbl et al. [M. Hölbl, T. Welzer, B. Brumen, Improvement of the Peyravian–Jeffries’s user authentication protocol and password change protocol, Computer Communications 31 (2008) 1945–1951] have proposed an improvement of Peyravian–Jeffries’s user authentication protocol and password change protocol [M. Peyravian, C. Jeffries, Secure remote user access over insecure networks, Computer Communications 29 (5–6) (2006) 660–667]. Peyravian–Jeffries’s scheme suffers from an active off-line password-guessing attack [J. Munilla, A. Peinado, Off-line password-guessing attack to Peyravian–Jeffries’s remote user authentication protocol, Computer Communications 30 (1) (2006) 52–54], and Hölbl et al. state that their improved protocol overcomes this weakness. However, we show in this paper that although this proposed protocol prevents this active attack, it remains vulnerable to a passive (simpler) off-line password-guessing attack.     

On the Conservation of Fractional Nonlinear Schrödinger Equation’s Invariants by the Local Discontinuous Galerkin Method

Using the primal formulation of the Local Discontinuous Galerkin (LDG) method, discrete analogues of the energy and the Hamiltonian of a general class of fractional nonlinear Schrödinger equation are shown to be conserved for two stabilized version of the method. Accuracy of these invariants is numerically studied with respect to the stabilization parameter and two different projection operators applied to the initial conditions. The fully discrete problem is analyzed for two implicit time step schemes: the midpoint and the modified Crank–Nicolson; and the explicit circularly exact Leapfrog scheme. Stability conditions for the Leapfrog scheme and a stabilized version of the LDG method applied to the fractional linear Schrödinger equation are derived using a von Neumann stability analysis. A series of numerical experiments with different nonlinear potentials are presented.     

Chaitin Ω numbers,Solovay machines,and Gödel incompleteness

Computably enumerable (c.e.) reals can be coded by Chaitin machines through their halting probabilities. Tuning Solovay's construction of a Chaitin universal machine for which ZFC (if arithmetically sound) cannot determine any single bit of the binary expansion of its halting probability, we show that every c.e.~random real is the halting probability of a universal Chaitin machine for which ZFC cannot determine more than its initial block of 1 bits—as soon as you get a 0, it is all over. Finally, a constructive version of Chaitin information-theoretic incompleteness theorem is proven.     

Substitution of G.728 vocoder’s codebook search module with SOM array trained by PSO-optimized supervised algorithm

Low delay-code excited linear prediction (LD-CELP) is an attractive algorithm in implementing vocoders in voice over Internet protocol networks. This algorithm has been proposed for the coding of speech at 16 kbps with toll quality. However, operation at transmission rates lower than 16 kbps is desirable, so that traffic can be accommodated during system overload conditions. In this paper, an array of self-organizing maps (SOMs) is employed instead of traditional codebook search module, recommended in ITU-T G.728, to determine the optimum index value of shape codebook. It is noted that a modified supervised training algorithm is used for SOMs in which some of the training parameters are optimized using particle swarm optimization (PSO) algorithm. Based on the occurrence frequency characteristics of codevectors, six bits for shape codebook and two bits for gain codebook are used in this work to produce a vocoder with lower bit rate as compared with traditional ITU-T G.728 vocoder. The performance comparison of the proposed SOM array trained by PSO-optimized supervised algorithm as the codebook search module in the structure of LD-CELP with a conventional implementation of LD-CELP coder shows that execution time of the algorithm is reduced up to 44 %. However, the degradation of voice quality in terms of mean opinion score, perceived evaluation of speech quality and segmental signal-to-noise ratio (SNR_seg) is acceptable.     

Modeling agent’s preferences by its designer’s social value orientation

Human social preferences have been shown to play an important role in many areas of decision-making. There is evidence from the social science literature that human preferences in interpersonal interactions depend partly on a measurable personality trait called, Social Value Orientation (SVO). Automated agents are often written by humans to serve as their delegates when interacting with other agents. Thus, one might expect an agent’s behaviour to be influenced by the SVO of its human designer. With that in mind, we present the following: first, we explore, discuss and provide a solution to the question of how SVO tests that were designed for humans can be used to evaluate agents’ social preferences. Second, we show that in our example domain there is a medium–high positive correlation between the social preferences of agents and their human designers. Third, we exemplify how the SVO information of the designer can be used to improve the performance of some other agents playing against those agents, and lastly, we develop and exemplify the behavioural signature SVO model which allows us to better predict performances when interactions are repeated and behaviour is adapted.     

Unsupervised classification of a forest’s image by texture model features

In the capacity of texture features, the parameters of the SAR model for unlabeled classification image of forest landscape are used. We compare the results for two systems of features: the SAR model and the popular Haralik statistics. The histogram clustering algorithm arrange the hierarchy of distributions better by cluster isolation.     

On Modification of Newton’s Law by a Homogeneous Distribution of Wormholes in Space

We examine a modification of Newton’s gravity by a distribution of cosmological wormholes. We show that at very large distances cosmological wormholes generate corrections which may be interpreted as if gravitons acquired effective masses. We show how the mass spectrum relates to the mean parameters of wormholes. In the leading approximation, the first effective mass is imaginary, which indicates the presence of an additional gravitational instability in the early Universe.     

Determining Young’s modulus of MEH-PPV film by fitting the unloading curve

Microsystem Technologies - The loading–unloading curves of poly(methoxy-5-(2′-ethylhexyloxy)-1,4-phyen-ylenevinylene) (MEH-PPV) films were measured using four different tests of...     

Accurate evaluation of Green’s functions in a layered medium by SDP-FLAM

Based on local Taylor expansions on the complex plane, a method for fast locating all modes (FLAM) of spectral-domain Green’s Functions in a planar layered medium is developed in this paper. SDP-FLAM, a combination of FLAM with the steepest descent path algorithm (SDP), is employed to accurately evaluate the spatial-domain Green’s functions in a layered medium. According to the theory of complex analysis, the relationship among the poles, branch points and Riemann sheets is also analyzed rigorously. To inverse the Green’s functions from spectral to spatial domain, SDP-FLAM method and discrete complex image method (DCIM) are applied to the non-near field region and the near filed region, respectively. The significant advantage of SDP-FLAM lies in its capability of calculating Green’s functions in a layered medium of moderate thickness with loss or without loss. Some numerical examples are presented to validate SDP-FLAM method. Supported by the National Natural Science Foundation of China (Grant No. 60621002), and the State Key Development Program for Basic Research of China (Grant No. 2009CB320200)