Secure logarithmic audio watermarking scheme based on the human auditory system Abstract This paper proposes a high capacity audio watermarking algorithm in the logarithm domain based on the absolute threshold of hearing of the human auditory system (HAS), which makes this scheme a novel technique. When considering the fact that the human ear requires more precise samples at low amplitudes (soft sounds), the use of the logarithm helps us design a logarithmic quantization algorithm. The key idea is to divide the selected frequency band into short frames and quantize the samples based on the HAS. Using frames and the HAS improves the robustness, since embedding a secret bit into a set of samples is more reliable than embedding it into a single sample. In addition, the quantization level is adjusted according to the HAS. Apart from remarkable capacity, transparency and robustness, this scheme provides three parameters (frequency band, scale factor and frame size) which facilitate the regulation of the watermarking properties. The experimental results show that the method has a high capacity (800-7,000 bits per second), without significant perceptual distortion (ODG [1) and provides robustness against common audio signal processing such as added noise, filtering and MPEG compression (MP3). Traditional data protection methods, such as encryption, are not enough for audio copyright enforcement. Digital watermarking is a popular technique for digital data protection and digital rights management [26, 27] . According to the International Federation of Phonographic Industry (IFPI) [3] , audio watermarking should meet the following requirements: (a) imperceptibility: the watermarking scheme should not affect the perceptual quality of audioin this paper, this is achieved using a psychoacoustic model to guarantee that the watermarking process does not distort the cover audio signal-(b) capacity: refers to the number of bits that can be embedded into the audio signal within a second and (c) robustness: the embedded watermark data should not be removed or eliminated by common audio signal processing operations and attacks, such as additive and multiplicative noise, MP3 compression, and filtering. All these requirements are often conflicting with each other, which makes the design of high capacity, transparent and robust audio watermarking schemes a challenging task.. Several research results exist for watermarking in the logarithm and cepstrum domains. Lee et al. [4] introduced a digital audio watermarking such that the watermark is embedded into cepstrum coefficients of the audio signal using techniques analogous to spread spectrum communications. Li and Yu [5] suggested a robust and transparent audio data embedding method in the cepstrum domain. BCH code-based robust audio data hiding in the cepstrum domain is presented in [7] . Hsieh et al. [6] suggested an audio watermarking technique based on the time energy features. Li et al. [8] proposed an audio watermarking scheme in the cepstrum domain based on the statistical mean manipulation. The embedded watermark is robust against MP3 compression and additive noise. Hu and Chen [9] proposed cepstral watermarking that manipulates the statistic mean. To avoid sharp discontinuities in the frame boundaries caused by the watermarking process, a small transition area is deliberately placed between frames, leading to an improvement in perceived quality as well. Ko et al. [21] suggested a digital watermarking method based on the log scaling of frequency in the decoding process for robust detection. Yang et al. [10] is the first technique on applying log-polar mapping to audio watermarking. The log-polar mapping is only applied to the frequency index, not to the transform coefficients, which prevents the reconstruction distortion of inverse log-polar transform and reduces the computational cost.. Watermarking methods based on the human auditory system (HAS) have been suggested in different previous works, such as [1, 2, 11, 30] . Garcia [1] proposed an algorithm to estimate the masking threshold in the psychoacoustic model of the HAS. Tsai et al. [2] proposed an intelligent audio watermarking method based on the characteristics of the HAS and neural networks in the DCT domain. Also, in [11] , the watermark is embedded into selected DCT coefficients of the host audio signal such that the signal to noise ratio is maintained at a level which is audibly annoying to the HAS. Lie and Chang [30] proposed an algorithm that maintains an energy relation between every three sample sections to represent the embedded bit information by scaling up or down corresponding amplitudes and conserving audio waveforms that are perceivable to human ears.. When considering the embedding domain, audio watermarking techniques can be classified into time domain and frequency domain methods. In [12, 13] , which were proposed by the authors of this paper, the discrete/fast Fourier transform (DFT/FFT) domain is selected to embed watermarks for taking benefit of the translation-invariant property of the FFT coefficients to resist small distortions in the time domain. In fact, as compared to time domain schemes, transform-based methods provide better perceptual quality and robustness against common attacks at the price of increasing the computational burden.. This paper presents an audio watermarking algorithm in the logarithm domain based on the HAS. Changing the quantization level based on the HAS in the logarithm domain makes the algorithm a novel and useful idea. Based on the requirements, a frequency band, a frame size and a scaling factor are selected and each secret bit is embedded into a frame. In addition to very high capacity, imperceptible distortion and robustness against common attacks, which make this scheme outperform other works in the literature, the other main features of the proposed algorithm are as follows: (1) using logarithm coefficients enhances the robustness, (2) watermark extraction is blind without using the host signal, (3) adjusting the quantization level based on the HAS improves transparency and robustness making it possible to enhance them at a same time, which is a significant challenge of many techniques, (4) embedding a single secret bit into a frame with an adjustable frame size provides a convenient solution to obtain a trade-off between the properties of the watermarking system, and (5) an encryption technique enhances the security of the system in such a way that an attacker, even if he/she knows the watermarking method, cannot extract the raw secret bits since a key is required to decrypt them.. The remainder of this paper is organized as follows. A brief overview of the HAS is given in Sect. 2. Section 3 combines the above techniques to propose a new method for audio watermarking. Moreover, the detailed watermark embedding and extraction algorithms are explained in that section. The experimental results and comparison with other schemes are given in Sect. 4 and, finally, relevant conclusions are drawn in Sect. 5. This paper suggests an audio watermarking algorithm in the logarithm domain based on the HAS. The human ear requires more precise samples at low amplitudes (soft sounds) and taking advantage of the logarithm it is possible to design a logarithmic quantization algorithm to exploit this property. Adjusting the quantization level based on the HAS in the logarithm domain results in a very high capacity, imperceptible distortion and robustness. The most notable features of the proposed algorithm are as follows:. (1) blind watermark extraction, (2) adaptive quantization based on the HAS that improves transparency and robustness, making it possible to enhance them simultaneously, which is a main challenge of many techniques; and (3) embedding a single secret bit into all samples of a frame, with an adjustable frame size, delivers a suitable solution to obtain a convenient trade-off between the properties of the watermarking system. The experimental results show that the scheme provides high capacity (800-7,000 bps), without significant perceptual distortion (ODG is greater than -1) whilst achieving robustness against common audio signal processing, such as added noise, filtering and MPEG compression (MP3).

O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Coulomb, Landau and Maximally Abelian Gauge Fixing in Lattice QCD with Multi-GPUs A lattice gauge theory framework for simulations on graphic processing units (GPUs) using NVIDIA's CUDA is presented. The code comprises template classes that take care of an optimal data pattern to ensure coalesced reading from device memory to achieve maximum performance. In this work we concentrate on applications for lattice gauge fixing in 3+1 dimensional SU(3) lattice gauge field theories. We employ the overrelaxation, stochastic relaxation and simulated annealing algorithms which are perfectly suited to be accelerated by highly parallel architectures like GPUs. The applications support the Coulomb, Landau and maximally Abelian gauges. Moreover, we explore the evolution of the numerical accuracy of the SU(3) valued degrees of freedom over the runtime of the algorithms in single (SP) and double precision (DP). Therefrom we draw conclusions on the reliability of SP and DP simulations and suggest a mixed precision scheme that performs the critical parts of the algorithm in full DP while retaining 80-90% of the SP performance. Finally, multi-GPUs are adopted to overcome the memory constraint of single GPUs. A communicator class which hides the MPI data exchange at the boundaries of the lattice domains, via the low bandwidth PCI-Bus, effectively behind calculations in the inner part of the domain is presented. Linear scaling using 16 NVIDIA Tesla C2070 devices and a maximum performance of 3.5 Teraflops on lattices of size down to 64 3 × 256 is demonstrated. Quantum Chromodynamics (QCD) is nowadays, 40 years after its birth, widely accepted as the correct theory of the strong nuclear force which binds the protons and neutrons in the cores of atoms. The guiding principle in the construction of QCD was the local gauge symmetry which has led before to the very successful theory of quantum electrodynamics (QED) that describes the interactions of electrons and light. Local gauge symmetry is the freedom to perform a transformation of the vector fields of the theory, independently at each point of space-time, without changing the physics the theory describes.. Lattice QCD which lives on a discretized space-time background opposed to the continuous world of the original theory, offers a formulation of the gauge theory that is well suited to be simulated on a computer and hence can be used to test the theory against experiment. Furthermore, lattice simulations can help to gain insights in the highly nontrivial, nonperturbative regime of the interactions between quarks and gluons which are the degrees of freedom of QCD.. The gauge symmetry, given below in its discrete version, states that physical observables will remain unchanged if a local transformation of the form g(x)U µ (x)g(x +μ) † (1) is being carried out. Here, the gauge fields or link variables U µ (x) as well as the gauge transformations g(x) are elements of the underlying gauge group which is SU(3) in the case of QCD. The index µ = 0, . . . , 3 refers to the direction in four dimensional space-time and with x +μ we denote the neighbor lattice site of x in the µ-direction. The link variables of lattice QCD are connected to the algebra valued continuum gauge fields A µ (x) via. Whereas physical observables that can be measured in experiments must be independent of the gauge, fixing the gauge, i.e., choosing a particular gauge transformation g(x) for all x, is essential when, e.g., studying gauge dependent quantities like the fundamental two point functions of the theory.. As a typical example of a gauge condition that may be enforced at all space-time points x, we consider the manifestly covariant Landau gauge. here stated in the language of continuum field theories. As we will discuss in the next Section, the continuum gauge condition Eq. (3) translates to a large scale optimization problem in lattice QCD with O(V N 2 c ) degrees of freedom where V = N 3 s ×N t is the 3+1 dimensional lattice volume. Consequently, the process of fixing the gauge on the lattice demands a major part of the whole simulation's computer time and the possible acceleration by highly parallel hardware architectures like graphic processing units (GPUs) will be of great practical use.. A more conceptual issue of gauge fixing is that the set of gauge transformations g(x) that fulfill a desired gauge condition is far from being unique. The set of gauge equivalent configurations of a given gauge field is called the gauge orbit. The gauge fixing condition can be depicted as a hypersurface living in the space of all gauge fields. Each of the multiple intersections of the gauge orbit with the gauge fixing hypersurface is called a Gribov copy.. Gribov copies play a crucial role in restoring the BRST symmetry on the lattice: fixing a gauge via the Faddeev-Popov procedure on the lattice for a compact group boils down to inserting the sum over signs of the corresponding Faddeev-Popov determinants evaluated at all the Gribov copies. Neuberger [1] showed that the sum for any covariant gauge turns out to be zero for any standard model gauge group, SU(N), and for compact U(1), making the expectation value of a gauge-fixed observable 0/0. The zero comes up because each Gribov copy comes in pairs with opposite sign of the Faddeev-Popov determinant. This in turn makes it impossible to construct a BRST symmetry on the lattice. This is called the Neuberger 0/0 problem. Following a topological interpretation of the Neuberger 0/0 problem, in Refs. [2, 3] a modified lattice Landau gauge was proposed which evaded the problem. There, because the Faddeev-Popov is shown to be strictly positive (semi-)definite, the cancellation is avoided. However, it is yet to be shown that the number of Gribov copies in the modified lattice Landau gauge is independent of the background gauge field. Interestingly, recently, a deep relation between lattice gauge fixing and lattice supersymmetry has been proposed in Ref. [4, 5] : the partition functions of a class of supersymmetric Yang-Mills theories can be viewed as a gauge fixing partition functionà la Faddeev-Popov and the "Gribov copies" are then nothing but the classical configurations of the theory.. A possible way out of the problem of the existence of Gribov copies is to restrict the gauge fixing hypersurface to a region which the gauge orbit intersects only once. An example thereof is the so-called Fundamental Modular Region [6] which contains only that intersection of the gauge orbit which corresponds to the global optimum of the gauge condition. Unfortunately, no algorithm is known which finds the global optimum of the gauge condition within finite simulation time. Simulated annealing, however, has been shown to highly favor optima closer to the global optimum [7, 8] and moreover it can be shown that, in the limit of infinite time, simulated annealing actually converges to the global maximum.. Recently, the problem of counting Gribov copies has gained a renewed interest. In Refs. [9] , an explicit formula of the number of Gribov copies for any number of lattice sites is analytically derived for lattice Landau gauge for the one-dimensional compact U(1) case. In Refs. [10, 11] , a novel method based on Algebraic Geometry [12, 13, 14] , which can count all the Gribov copies, was proposed. Although the method has only been able to work for small lattices, it is the only known method which guarantees to find all Gribov copies and hence it can work as a benchmark for other methods. One such alternative method is plain brute force, i.e., running a standard optimization algorithm over and over again from different starting points on the gauge orbit and collecting the results consecutively. Clearly, a high performance lattice gauge fixing code is essential for this task and since here one primarily focuses on small lattices, GPUs are favorable given the fact that CPU parallelization techniques are very limited for lattices of small extent.. In this work we present a set of applications for lattice gauge fixing based on the family of relaxation algorithms and simulated annealing. The applications are based on the CUDA accelerated Lattice-Graz-Tübingen code 1 that is written in CUDA C/C++ and makes heavy use of template classes in order to facilitate the extension to a broad variety of applications. Besides the standard relaxation algorithm [15] , we support overrelaxation [16] and stochastic relaxation [17] to overcome the problem of critical slowing down. Moreover, the simulated annealing algorithm [7] with a heatbath kernel and microcanonical updates which increases the probability to reach the Funda-mental Modular Region has been implemented and tested. The code can be used to fix gauge configurations to the covariant Landau gauge ∂ µ A µ = 0, µ = 0, . . . , 3, the Coulomb gauge ∂ i A i = 0, i = 1, 2, 3 and the maximally Abelian gauge.. Previous utilizations of GPUs in the field of lattice QCD mainly focused on solvers of linear systems [18, 21] A first attempt of porting lattice gauge fixing with the overrelaxation algorithm to the GPU has been reported in [26, 27] . An alternative approach based on the steepest descent method has been presented in [28] . For a more general discussion of lattice gauge fixing and its problems we refer the reader to [29] .. The remainder of this work is organized as follows: in Sec. 2 the optimization problem is stated and the algorithms of choice are presented. In Sec. 3 we summarize some hardware properties of the NVIDIA GPUs that we use for our investigation and moreover briefly discuss NVIDIA's programming environment CUDA. Next, in Sec. 4, we give details of our implementation and the cuLGT framework and moreover discuss numerical accuracy issues. To overcome the memory constraint of single GPUs we extend our implementation to support multi-GPUs; all details thereto are presented in Sec. 5. Finally, in Sec. 6 we show various performance results for single and multiple GPUs and furthermore present some convergence results of the algorithms. In Sec. 7 we summarize and conclude. We presented a CUDA implementation for gauge fixing in lattice gauge field theories based on the relaxation algorithms. The code is based on the cuLGT package 9 and supports the Landau, Coulomb and maximally Abelian gauge fixing conditions.. The implementation and the various optimization strategies have been discussed in detail. We showed that simulated annealing and overrelaxation can heavily be accelerated by employing GPUs. We listed convergence results in different floating point precisions and concluded that a mixed precision ansatz that performs only the critical parts of the simulation in double 9 Both is available for downloaded under www.cuLGT.com.. precision is a good compromise in terms of precision (∼ 10 −5 relative to DP) and performance (80% − 90% of SP).. A maximum sustained performance of 370 GFlops on a single GTX 580 has been reached and moreover linear scaling on 16 Tesla cards with 3.5 Teraflops, given that the number of time-slices per device does not fall below 16 .. Lastly, we demonstrated how the combination of simulated annealing and the various relaxation flavors can be tuned in such a way that either fast convergence to the gauge of choice is reached or alternatively that a gauge functional value as high as possible is obtained.. We are currently preparing tests on the Kepler architecture, updates on Kepler performance will be available on our homepage shortly. and update types. Let us consider for example an overrelaxation update for Landau gauge. The latter consists of calculating g(x) according to Eq. (19) plus a first order approximation of the exponentiation g(x) → g ω (x). In the cuLGT code, the sum of Eq. (19) is done on the Quaternion objects. Extracting the four reals of Quaternion representation of a SU(2) subgroup element of SU (3) Subsequently, the overrelaxation update g(x) → g ω (x) is calculated. Counting each operation in Fig. A.11 as one floating point operation (rsqrt corresponds to two operations), the effective number of flop for the overrelaxation update is 22 per lattice site and SU(2) subgroup, thus 66 for SU (3) .. Summing up, the overrelaxation algorithm in SU(3) for Landau gauge requires. • 192 flop to gather the neighboring links U µ (x), U µ (x −μ),. • 66 flop for the overrelaxation update,. • 2016 flop to apply the new g(x) to U µ (x), U µ (x −μ) and thus in total 2274 flop/site. Note that we do not take the extra Flops for the reconstruction of the third row of the SU(3) matrices into account.. For the heatbath kernel of the simulated annealing algorithm the number of flops cannot be calculated correctly because of the non-deterministic loops with random-number-dependent termination conditions. We counted the flops as if every loop is only run once and each RNG call is counted as one flop. Both choices are very conservative. Therefore, a comparison of simulated annealing implementations should be based on pure time measurements. In this Section, we firstly examine the performance of the code on various devices including multiple GPUs. There, we pick the Landau gauge overrelaxation kernel as a representative for all kernels and gauges. Secondly, we outline a few sample results obtained by the application of our lattice gauge fixing code.

O O O B I B I O B I O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I B I O O O O O O O O O O O O O O O O B I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B I O


Contaminant source characterization in water distribution systems using binary signals This paper presents a simulation-optimization-based method for identification of contamination source characteristics in a water distribution system using filtered data from threshold-based binary water quality signals. The effects of quality and quantity of the data on the accuracy of the source identification methodology are investigated. This study also addresses the issue of non-uniqueness in contaminant source identification under various data availability conditions. To establish the robustness and applicability of the methodology, numerous scenarios are investigated for a wide range of contamination incidents associated with two different networks. Results indicate that, even though use of lower resolution sensors lead to more non-unique solutions, the true source location is always included among these solutions. Water distribution systems (WDSs) are vital for supplying safe drinking water to the public, and they are vulnerable to contamination that can be introduced into the system either deliberately or accidentally. The fate and transport of a contaminant and the extent of the contaminant spread through the network depend on the characteristics of the network topology and the resulting hydraulic conditions of the network.. Networks of sensors can be used as an early warning system (EWS) to detect sudden deterioration in water quality.. They are meant to supplement conventional water quality monitoring by providing timely information on unusual threats to a water supply system. The goal of an EWS is to reliably identify a contamination event in the distribution systems in time to allow an effective targeted response that reduces or avoids entirely the adverse effects of contamination on the system. The contaminant source characterization (i.e. identifying the contaminant source location and injection pattern) problem has been approached as an inverse problem by many researchers (e.g. Waanders Because the amount of information is reduced in a Boolean signal versus a continuous signal, the solutions to the contaminant characterization problem will have a high degree of non-uniqueness and be sensitive to many related sensor parameters and uncertainties. In comparison to earlier work, this paper presents a new methodology that identifies a set of non-unique solutions in a single execution of the optimization algorithm to reconstruct the contamination characteristics based on binary signals. This study also conducts an extensive sensitivity investigation to evaluate the robustness of the approach when considering the sensitivity of the binary signal to the detection threshold level that acutely affects the quality of the information. Sensitivity of a sensor may impact its utility as well as cost (USEPA , Section 3.1.7). Thus, in addition to lowering of information quantity due to inherent data filtering in a binary signal, the sensitivity of the sensor affects the quality of the information used to estimate the source characteristics. Accuracy and precision of an inverse solution are also affected by the amount of observations available in the network, which depends on the number and the placement of the sensors in the network. The applicability of the proposed new method considering these factors and sensitivities is investigated for an array of contamination events in two different illustrative WDS networks. This paper presents an evolutionary algorithm-based methodology for characterizing a pollutant source during a contamination event in a WDS that is being monitored using a set of sensors that report binary signals indicating the presence/absence of contamination. The source characteristics were reconstructed using these binary signals.. The accuracy of contaminant source characterization depends primarily on the amount and quality of the data available. The effects of sensor sensitivity on the accuracy and degree of non-uniqueness were studied. It was observed For each scenario reported in this section (i.e. Scenarios 1-11), 50 random trials were carried out to assess the robustness of the solution approach. For each trial, prediction error was calculated using Equation (1) for all scenarios except for Scenario 1 where Equation (8) The solution to the optimization model represented by Equations (1)- (7) would ideally identify the true contaminant source location and the injection pattern. Because of data limitations, however, the solution to Equations (1)- (7) is likely to yield non-unique source characteristics to fit the observations equally well. Specifically, there may be data quality limitations resulting from, for example, measurement errors and filtering effects, as well as quantity limitations resulting from, for example, discrete measurements and limited number of observations. Therefore, the solution approach should be able to conduct a global search and be able to identify simultaneously the set of potential source characteristics that provide an equally good fit to the given observations. The niched co-evolution strategies (NCES) search procedure (Zechman & Ranjithan , ) was used to solve the above model. Also, given the possibility of error in modeling of the physical distribution network, it is also important to identify nearoptimal solutions that might fit the real observations. The NCES procedure also provides this capability. In this work, the original NCES (implemented in Java) was reimplemented (in C) to provide improved computational performance as well as enhanced capability to use parallel computing resources for the WDS simulations (Kumar ).. NCES conducts a global search using evolution strategies (ES), a generalized heuristic optimization approach. An ES works in a continuous space and has the capability to selfadapt its major algorithmic parameters such as selection and mutation. ES starts with a randomly initialized population of μ individuals. A probabilistic mutation operator is applied to produce ν new solutions each generation. The next set of individuals is selected from either a combined set of parent and offspring solutions (denoted as (μ þ ν) selection). or from the set of offspring alone (denoted as (μ,ν) selection).. The standard ES is extended in NCES to generate a set of alternative solutions that performs equally well in terms of fit- While one subpopulation focuses its search on finding the optimal solution based on the prediction error (E in Equation (1)), the other subpopulations search for alternatives based on the current best prediction error value as well as the degree of difference among the alternative solutions. In the results presented in this paper, every solution that is within one mis-hit from the best prediction error value is considered as a viable alternative solution.. NCES was applied and tested on two water distribution networks to study: (1) the effect of the sensitivity of binary signals (quality of data) on the accuracy and non-uniqueness of the solutions to such source identification problems;. (2) the effect of the quantity of available data (i.e. number of installed sensors) on the solutions to source identification problems and (3) the robustness of the method when applied to a set of different contamination scenarios and networks.

O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Estimation of transitional probabilities of discrete event systems from cross-sectional survey and its application in tobacco control Abstract-In order to find better strategies to control tobacco use, it is often critical to know the transitional probabilities among various stages of tobacco use. Traditionally, such probabilities are estimated by performing longitudinal surveys, which are often time-consuming and expensive. In this paper, we propose a method to estimate transitional probabilities from cross-sectional survey data, which is more cost-effective to obtain and hence abundant. The method is based on a discrete event system framework. We introduce state probabilities and transitional (event) probabilities to the conventional discrete event system models. We derive various equations that can be used to estimate the transitional probabilities. We test the method using crosssectional data of the National Survey on Drug Use and Health. The estimated transitional probabilities can be used in predicting the future smoking behavior for decision-making, planning and evaluation of various tobacco control programs. Reducing tobacco use remains a significant public health challenge in the new millennium despite decades of effort in tobacco control. Exposure to tobacco is associated with 440,000 deaths each year in the United States and costs the nation $50 -$75 billion in medical expense alone. The Healthy People 2010 aims at reducing current smokers to 16% among adolescents and 12% among adults by the year 2010. However data from the Behavioral Risk Factor Surveillance System indicate that the adult smoking rate has fluctuated at around 22% since 1990. Data from the Youth Risk Behavior Surveillance System indicate that adolescent smoking prevalence rate increased from 27.5% in 1991 to 36.4% in 1997 before it started to decline in 1999. There is a large gap between the current levels of tobacco use and the tobacco control objective, underscoring the need for immediate actions to advance our tobacco control strategy.. Smoking behavior can best be modeled as a discrete event system, where discrete states describe the different stages of tobacco use and events describe the transitions from one state (stage) to another. In order to find the best strategies in tobacco control programs and to understand the smoking behavior progression, it is often critical to know the transitional (or event) probabilities among various stages of tobacco use. Traditionally, such probabilities are estimated by performing longitudinal surveys; that is, by surveying the same group of people over a long period of time.. Longitudinal surveys are often time-consuming, expensive, and hence less performed. On the other hand, crosssectional survey, where samples of a population are surveyed at the same time is much easy to perform. Hence much more cross-sectional surveys have been conducted and more data are available. The question is therefore: can we estimate the transitional probabilities from cross-sectional survey data? Intuitively, one may think that the answer shall be negative. But, in fact, as we will show that there is information contained in cross-sectional surveys that allows us to derive the transitional probabilities.. To this end, we will extend the conventional framework of discrete event systems by introducing state probabilities and transitional probabilities. To completely model the smoking behavior, we use the following five states:. • NS -nerve-smoker, who has never smoked by the time of the survey.. • EX -experimenter, who smokes but not on a regular basis after initiation.. • SS -self stopper, an ex-experimenter who stopped smoking for at least 12 months.. • RS -regular smoker, who smokes on a daily or regular basis (including habitual and addicted smokers).. • QU -quitter, an ex-regular smoker who stopped smoking for at least 12 months. We will establish various equations that relate the probabilities of the above states with the transitional probabilities based on data available in cross-sectional surveys. In particular, we will use 2000 National Survey on Drug Use and Health (NSDUH).. The transitional probabilities can be used to predict the effectiveness of various tobacco control strategies. By considering the effects of various tobacco control programs on the transitional probabilities, we can predict the impact of these programs to the tobacco use in the future. This paper is organized as follows. In Section II, we will discuss advantages and disadvantages of cross-sectional surveys and longitudinal surveys. We will also discuss tobacco use and tobacco control. This section will provide the background and demonstrate the significance of the problem to be solved. In Section III, we will introduce the mathematical model of smoking behavior, derive equations for estimating transitional probabilities, and apply the results to derive the probabilities from cross-sectional surveys. In Section IV, we will use the transitional probabilities to predict future smoking behavior. Such predications will help us to evaluate various tobacco control programs. In Section V, we calculate various sensitivity functions from the model we established. We emphasize that although this paper mainly focus on tobacco behavior and tobacco control, the methods established in this study can be extended to describe other substance use behaviors. Indeed, the methods of deriving transitional probabilities from cross-sectional survey data have a wide range of applications. We derived a smoking behavior model based on the PDES. We then estimated the transitional probabilities from the survey data of 2000 NSDUH using the model. There are several important applications of this model. Using the estimated transitional probabilities, we can predict the smoking behavior with respect to the changes in transitional probabilities for certain age groups. Knowing the effects of tobacco control programs to the transitional probabilities, we can then evaluate various tobacco control problems and hence provide insides to the policy makers in their decision ThA03.1 making. We also derived sensitivity functions of various transitional probabilities to the state probabilities. These functions can serve as analytical tools for comparing the effects of these transitional probabilities to the final outcome of tobacco control. Overall, the paper shows that transitional probabilities can be estimated from crosssectional survey data and hence to describe the dynamics of behavior progression systems. In addition to smoking behavior and tobacco control, this novel approach can be applied to analyze other health risk behaviors with crosssectional survey data.

O O O O O B I I O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O


Facial expression transfer method based on frequency analysis Abstract. We propose a novel expression transfer method based on an analysis of the frequency of multi-expression facial images. We locate the facial features automatically and describe the shape deformations between a neutral expression and non-neutral expressions. The subtle expression changes are important visual clues to distinguish different expressions. These changes are more salient in the frequency domain than in the image domain. We extract the subtle local expression deformations for the source subject, coded in the wavelet decomposition. This information about expressions is transferred to a target subject. The resulting synthesized image preserves both the facial appearance of the target subject and the expression details of the source subject.This method is extended to dynamic expression transfer to allow a more precise interpretation of facial expressions.Experiments on Japanese Female Facial Expression (JAFFE), the extended Cohn-Kanade (CK+) and PIE facial expression databases show the superiority of our method over the state-of-the-art method. Emotions are often conveyed through body gestures or facial expressions rather than verbal communication [1] [2] . Thus, automatic facial expression analysis is an interesting research topic.. There have been many recent achievements in related research sub-areas such as facial landmark localization [3] [4] [5] [6] [7] [8] , tracking and recognition [9] [10] . Realistic facial expression synthesis is useful for affective computing, human computer interaction [11] [12] , realistic computer animation [13] and facial surgery planning [14] [15], etc. There are more than 20 groups of facial muscles innervated by facial nerves [16] , which control actions of the face (eg. opening or closing of eyes or mouth) and variations in local appearance (eg. facial wrinkles and furrows).. Psychologists Ekman and Friesen developed a facial action coding system (FACS) based on the movements of facial muscles and their effects on the expression [17] . They divided the face into 44 action units (AU) and analyzed the motion characteristics and their effects on associated expressions. Many expression synthesis approaches had concentrated on capturing expressions through AUs. Platt and Badler proposed a model of the muscles to simulate FACS to synthesize facial expression [18] . Waters extended this model to a hierarchical one [19] , in which facial muscles were divided into linear muscles and sphincter muscles to control the skin stretch and shrinkage, respectively. Based on Water's method, Koch et al. used a finite element method to simulate the physical structure of the human face [20] . These models emphasized the simulation of muscle movements. They are relatively simple compared with the one developed by Lee et al. [21] . Lee's model has a three-level structure of skin, bone and muscle, based on physiology. Thus, it can synthesize much more realistic expressions. But the complicated structure and heavy calculation load prevented its application in practice. FACS was used to define a non-continuous and non-uniform scale for scoring the strength of facial activities. It was hard to identify subtle facial activities. Thus, the valuable information contained in subtle expression changes can be lost [22] . The subtle local appearance variations are usually the main components of micro-expressions, which are important clues to distinguish different expressions. For example, without the micro-expressions, 'fear' and 'surprise' are hard to distinguish. In addition, micro-expressions reflect the emotion and inner working of people. As a result, photo-realistic facial expression synthesis is an active research area.. Darwin revealed the consistency of expressions among different races and genders [23] . This is because the shape deformations are similar for the same expression. However, the local appearance deformations, viz., the expression details, are quite person-specific. Therefore, a person-specific expression transfer, which clones the expression of a source subject to a target subject, has a wide range of applications. However, the subtle appearance deformations are difficult to synthesize. In this study, we locate the facial landmarks automatically in order to describe the shape deformation, and extract and transfer the subtle local expressions using frequency analysis. Since dynamic variations are important in interpreting facial expression [24] [25] [26] , we extend our work to dynamic expression transfer. The effectiveness of the proposed algorithm is verified on Japanese Female Facial Expression (JAFFE), the extended Cohn-Kanade (CK+) [27] and PIE databases.. The remainder of this paper is structured as follows. Section 2 provides an overview of the related work. Section 3 presents the facial landmark localization and face alignment methods. Section 4 proposes the static expression transfer method based on frequency analysis. We extend the expression transfer method to dynamic expression synthesis in Section 5. Section 6 details the evaluation of the proposed method as well as the experimental setup. Finally, Section 7 concludes the paper. A static facial expression transfer method based on frequency domain analysis is proposed. We locate the facial landmarks automatically and use them to describe the shape deformation between neutral expressions and the non-neutral expressions. We adopt a wavelet transform to divide images into four frequency bands and transfer the fine details of the expression. Our method is insensitive to illumination variation. Since the dynamic variations are important in interpreting facial expression precisely, we extend our work to dynamic expression transfer. The experiments on the CK+, JAFFE and PIE databases show that our method can synthesize images, while preserving both the facial landmarks of the target subject and the expression details of the source subject. Experiments show that this dynamic expression transfer is superior to the state-of-the-art methods. The proposed method can be widely applied in practice because it only needs a small training set. Our synthesis method involves local facial landmark detection and expression transfer. Below, we give a concise overview of relevant prior work on these two topics.. The Active Shape Model (ASM) [28] used a parametric deformable model to fit the shape of human face. It learned the variation modes of a shape from a set of training examples.. Transformation and shape parameters were estimated iteratively to fit the mean shape of the observed object. The Active Appearance Model (AAM) [29] [30] integrated facial texture with the ASM to fit the facial shape better. Matthews and Baker [31] proposed a computationally efficient AAM algorithm with rapid convergence to improve the fitting. The shapes of multi-view faces can be fitted through a gradient-descent search [32] . A vectorial regression function was learned from the training image with an Explicit Shape Regression (ESR) model to locate the facial landmarks.. A two-level boosted regression, shape-indexed features and a correlation-based feature selection method were combined with an ESR model to locate the facial landmarks more accurately [5] . In [6] , local binary features were learned using a regression tree to preserve the most discriminative information contained in the local texture around each facial landmark. The local binary features improved the efficiency of facial landmark detection.. Zhu and Ramanan [7] used a multi-tree model to handle different expressions. Each expression was modeled by a deformable model of the joint distribution of parts, consisting of local patches around facial landmarks. The Histogram of Oriented Gradient (HoG) features were used to describe the local patches. Each branch of the multi-tree model corresponds to one expression, but different trees share a pool of parts. The deformable model was trained by a latent support vector machine (LSVM). Since the human face is non-rigid and large nonlinear deformations occur in extreme expressions, [4] used a Haar-like feature based Adaboost face detector [33] to initialize the face location, then adopted a Supervised Descent Method (SDM) to refine the locations of facial landmarks. [8] presented a state-of-the-art method for facial landmark detection with super-real time performance, which used an ensemble of regression trees to estimate the positions of facial landmark accurately from a sparse subset of pixel intensities. The ensemble of regression trees was learned based on gradient boosting. The appropriate priors exploiting the structure of image data is helpful to efficient feature selection.. To transfer expression, the facial texture of the target subject was warped to the shape of the source subject, given the correspondence of the key facial landmarks [34] . The warped expression captures the shape motions of different expressions but ignores the micro-expressions. Liu et al. [35] represented the grey level of each point on the face image with the Lambertian model. Then, they calculated the ratio between the neutral and the non-neutral expression at each point to obtain an expression ratio image. They used this expression ratio image to transfer the non-neutral expression to other neutral faces. In [36] , [37] and [38] , multi-expression faces were arranged as a tensor data. In [36] , a High Order Singular Value Decomposition (HOSVD) [39] was applied to the AAM [40] coefficients of the training faces to obtain a generative model. In this model, AAM coefficients of training images were factorized into identity and expression subspaces. The test face image was represented by the AAM coefficients, which were reconstructed by estimating its identity and expression coefficients in the generative model. The solved identity coefficients were combined with the remaining expression coefficients in the expression subspace of the generative model to synthesize multi-expression face images. In [37] , a generative model of shape and texture is built in order to obtain the identity and expression coefficients, separately. The expression transfer was realized by swapping the expression coefficients of the source and target subjects. [38] proposed a tensor-based AAM, in which texture is aligned with the normalized shape of the AAM. The expression coefficients of the test face were synthesized by linearly combining the expression coefficients of training faces in the latent expression subspace. A texture variation ratio between the neutral and non-neutral expressions was used to transform the expression of the test face. However, the expression variations are often strongly nonlinear, thus the expression coefficient estimation for the test image may not be accurate. The expression variation ratio is not adaptive to the nonlinear variation of extreme expressions. [41] incorporated the expression manifold with the Tensor-AAM model to synthesize dynamic expressions of the training face. The Bilinear Kernel Reduced Rank Regression (BKRRR) method for static general expression synthesis was proposed in [15] . It synthesizes general expressions on the face of a target subject. Zhang and Wei [2] used TensorFace combined with an expression manifold to synthesize the dynamic expressions of a training face, then extracted and transferred the dynamic expression details of the training face to the target face. For extensive reviews on facial expression synthesis, we refer the reader to [42] and [43] .. Since the facial landmarks around eyes, nose, mouth and eyebrows etc. are required to describe the shape correspondence between different expressions, we use state-of-the-art method proposed in [8] to detect the facial landmarks (See Fig.1 ) in this study. We use AAM to separate and align the shapes and texture of multi-expression faces. Since the expression details are more easily observed using frequencies, we adopt the wavelet transform to divide images into four frequency bands and then transfer the details of expressions. We extend this work to dynamic expression transfer, to obtain highly realistic and natural looking facial animations. In summary, our main contributions include: 1) a proposal (See Fig.1 ) for a static expression transfer method based on frequency analysis; 2) the extension of the static expression transfer to dynamic expression transfer; 3) a unified automatic dynamic expression transfer framework including facial landmark localization, expression alignment, dynamic shape synthesis, expression warping, expression detail extraction and transferring.

O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I O O B I O O O O O B I O O O O O O O O O O O O O O O O O


Recovering Over-/Underexposed Regions in Photographs Abstract. When taking pictures using a commodity camera in a scene with strong or harsh lighting, such as a sunny day outdoors, we often see a loss of highlight details (over-exposure) in some bright regions and a loss of shadow details (under-exposure) in some dark regions. In this paper, we developed a wavelet tight frame based approach to reconstruct a well-exposed image with better visibility on details from the one with over/underexposed regions. There are two modules in the proposed approach: one in lightness channel that in-paints the clipped lightness and adjustes image contrast; and the other in chromatic channels that in-paints the saturated colour regions. The experiments showed that our method can effectively repair over/under-exposed regions and it performed better than other existing methods on tested real photographs.Key words. image in-painting, contrast enhancement, wavelet, tight frame, sparse approximation AMS subject classifications. 68U10, 65J22,65T601. Introduction. In digital photography, exposure controls how much light can reach the image sensor and the lightness of a photograph is determined by the amount of light shown. There is a physical limitation on the lightness contrast that a camera can capture, term as dynamic range. An outdoor scene with strong or harsh lighting often has a much wider dynamic range than the bearing capacity of a regular image sensor, which then will lead to a loss of highlight/shadow details in the resulting photograph. For example, the dynamic range of a regular digital camera is about 10 3 : 1 while the dynamic range of an outdoor scene in a sunny day ranges from 10 5 to 10 9 : 1. When recording such a high dynamic range (HDR) scene using a commodity camera with low dynamic range (LDR), some bright parts of the scene would be recorded as "white" which is described as over-exposure; and some dark areas with interesting details would be indistinguishable from"black" in the image which is described as under-exposure. In other words, the lightness values of those over-exposed pixels are clipped at the maximum value (= 1) such that these pixels only show white colour, as the values of three colour channels (red, green, blue) at these pixels are also the maximum value. Similarly, the lightness values of under-exposed pixels are too small, close to the minimum value (= 0), such that the image details can hardly be visually perceived. See Figure 1 .1 for an illustration of two photographs with over-exposed and under-exposed regions.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


An efficient and inexpensive method for activity recognition within a smart home based on load signatures of appliances With the increasing demand in terms of non-intrusive appliance load monitoring (NIALM), more and more smart meters and smart analyzers were released on the market to extract well-defined load signatures and/or for performing autonomously the various monitoring operations as needed. Nevertheless, this hardware proves to be very expensive and not necessarily accessible to all. Moreover, most applications resulting of the use of these smart devices simply refer to energy saving and costs reducing of energy consumption. Thus, this paper proposes a new algorithmic method for an application field that is still very lightly exploited, i.e. the activity recognition of reduced-autonomy residents living in a smart habitat through load signatures. This one is based on steady-state operations and signatures and its extraction process of load signatures of appliances is carried out in a three-dimensional space through a single power analyzer which is non-intrusive (NIALM). This approach has been tested and verified rigorously through daily scenarios reproduced in the smart home prototype in a laboratory.. Hence, we can affirm that, with an exceptionally minimal investment and the exploitation of especially limited data, our method can recognize the use of appliances with high precision and low-cost allowing us to compete with other approaches which are much more expensive and require supplementary equipment. In the last few years, the research done on appliance load monitoring has been more specifically observed in the interest of customers of the utilities. In fact, as each appliance has a load signature specific to its operation, which varies with the time and its mode of function, it helps to determine the energy consumption, the frequency, the time and the exact moment of use of an appliance. The impacts of these scientific studies about the appliance load monitoring are that the latter is used to determine the average power consumption of each household device to then establish the energy balance of a residence for safety [2, 4, 11, 14] , economical [2, 4, 5, 13] and ecological purposes [1, 2, 5, 17] . Briefly, they consisted in associating a device with the proper load signature extracted from smart meters and analyzers. Consequently, the real challenge, with respect to the appliance load monitoring, is the identification of the load signatures according to the operation mode of the appliances, because these must be accurate and distinct as much as possible so that overlap and, subsequently, misidentifications are avoided.. Initially, the methods used to accomplish this task were intrusive, but now, most researchers in this area proceed by means of non-intrusive methods [2] - [25] . Several of them suggested monitoring methods for extracting the characteristics of devices so as to obtain load signatures in two-dimensional spaces [4, [11] [12] [13] , in three-dimensional spaces [7, 16, 21] or with more than three features [3, 14] . Moreover, there exist three types of approaches to describe the load signatures: the technique with steady-state operations [4, 12] , the process with transient operations 1 [7] or a mixture of both [3, 14, 18, 24, 25] . The systems that are reserved for these previous methods are provided with analyzers with diverse sampling rates, which introduce a gap between the accuracy of each approach. Most of them involve major costs and sometimes require additional sensors or equipment to get greater precision for feature extraction of appliances, which generally introduces a certain degree of intrusiveness [4, 7, 11] and important inconveniences [12] - [13] that the suggested method takes care of avoiding while delivering a particularly high precision.. Currently, some methods, to recognize the activities of a person in a smart home, exist. These methods rely on RFID technology, sensors, etc. [20, 26] . The main issues with these approaches are the intrusiveness for the resident and the important quantity of hardware for maintenance it requires. Consequently, in this paper, to provide a solution to these problems, a cheap NIALM system for identifying load signatures of appliances with the aim to ensure the recognition of activities is proposed. Our conceptual contribution consists in developing a NIALM system for activity recognition of patients with Alzheimer's disease living in a smart home. This is achieved through the extraction of the load signatures represented by three features of the appliances and based on power analysis at the steadystate. Secondly, our practical contribution is a complete implementation of this system within a real smart home environment provided with a power analyzer which is centralized in a single point, either the main electric panel, and the monitored household appliances used daily. Finally, we rigorously tested our load appliance monitoring system with some real scenarios of activities with some household devices among the 16 monitored appliances in order to demonstrate its efficiency in this specific use context. Our procedure then enables analysis of the power consumption of appliances to make the recognition of --- 1 Sometimes the transient operations appeals to turn-on transient energy (PQUT) activities within a smart home for Elders and cognitively-impaired people. Indeed, our method was developed in order to recognize the lifestyle of the smart home's resident and to detect unusual situations or simply ongoing activities. Therefore, the focus will aim on the temporal and spatial aspects of detected events to address the recognition of activities. Regrettably, this scope is still disregarded, since, for the time being, very few researchers are dedicated to this issue [22] - [23] . Nevertheless, this remains of paramount importance given the aging population and the need for autonomy that is felt among cognitively-impaired people in our society. Thus, considering our method, which involves low investments and demonstrates accuracy comparable to the quality approaches, it appears to be a very interesting technological advance with an incredible potential to be developed.. The sections of this document are structured as follow. The second section defines terminology and concepts. The third explains the features used for our method. Then, the fourth part presents both phases of our new contribution based on steady-state signatures in a two-dimensional space. Subsequently, the fifth section describes the implementation of our system and the experimental methodology used in this case. In Section 6, the analysis and comparison of the test results are discussed. Subsequently, Section 7 presents the limitations of our approach. Next, Section 8 elaborates and provides details on the related works concerning the various methods used to describe and monitor load signatures of appliances. Finally in the last section, the potential development opportunities in the near future through our contribution are presented. In this paper, we presented an economical and efficient method for activity recognition within a smart home. As discussed, we proposed a contribution in the field of activity recognition through an inexpensive NIALM system which is based on load signatures represented in a threedimensional space and power analysis at the steadystate. At the light of the assessment of related works, this suggested method considerably reduces the expenses related to material, installation and maintenance in reason of its centralization. Actually, this system was implemented with a single analyzer and proved to be a way to proceed which is accessible and simple. Consequently, we could potentially apply it to an ordinary existing house with a resident suffering from the Alzheimer's disease. Next, an implementation of our new method within a smart home was presented. Then, we demonstrated, by rigorous experiments (e.g.: real scenarios [26] ) on our inexpensive NIALM system that this approach is really efficient, accurate and simple to apply in comparison with other methods (see Table 7 ). These results are due to the centralization and to the nonintrusive nature of our system, what it allows an easy integration in an existing house. Finally, it is essential to mention that there are very few papers published about this kind of method of proceeding to activity recognition within smart home.. Although our results are promising, we consider that there are some limitations to which we will have to remedy. For example, a suitable solution has to be found to resolve the restriction to plug the appliances, because for the moment being, the residents have to respect a particular schema of connections. We will also attempt to enlarge our database gradually to increase the capacity of recognizing different household appliances. Moreover, we would like to investigate if certain machine learning techniques could be applied in order to help selecting the most discriminative features from the raw load signatures extracted to see whether or not it improves the performance of activity recognition. Eventually, our algorithm will slightly be modified so that it records each event as it occurs, and not only when the use is completed. Moreover, we ought to eventually verify this method on a real patient in a smart home, with new scenarios, to be ensured that the monitoring report operates well and that important details are not overlooked pertaining to the activity recognition. Consequently, we will be able to draw a portrait of daily living of each resident of a smart home. Beforehand, some intrusive processes [3, 4, 13] were used to extract the load signature for the appliances. Instead of having a single analyzer installed in the main electrical panel, this method included a sensor for each monitored device. It complicated the implementation of the system to perform the feature analysis and required more energy to operate. In summary, despite the advantage of accuracy it involved, this method necessitated obviously larger investment compared to nonintrusive methods. Consequently, the NIALM approaches have emerged.

O O O O O O B I O O B I O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Self-sustaining non-repetitive activity in a large scale neuronal-level model of the hippocampal circuit The mammalian hippocampus is involved in spatial representation and memory storage and retrieval, and much research is ongoing to elucidate the cellular and system-level mechanisms underlying these cognitive functions. Modeling may be useful to link network-level activity patterns to the relevant features of hippocampal anatomy and electrophysiology. Investigating the effects of circuit connectivity requires simulations of a number of neurons close to real scale. To this end, we construct a model of the hippocampus with 16 distinct neuronal classes (including both local and projection cells) and 200,000 individual neurons. The number of neurons in each class and their interconnectivity are drawn from rat anatomy. Here we analyze the emergent network activity and how it is affected by reducing either the size or the connectivity diversity of the model. When the model is run with a simple variation of the McCulloch-Pitts formalism, self-sustaining non-repetitive activity patterns consistently emerge. Specific firing threshold values are narrowly constrained for each cell class upon multiple runs with different stochastic wiring and initial conditions, yet these values do not directly affect network stability. Analysis of the model at different network sizes demonstrates that a scale reduction of one order of magnitude drastically alters network dynamics, including the variability of the output range, the distribution of firing frequencies, and the duration of self-sustained activity. Moreover, comparing the model to a control condition with an equivalent number of (excitatory/inhibitory balanced) synapses, but removing all class-specific information (i.e. collapsing the network to homogeneous random connectivity) has surprisingly similar effects to downsizing the total number of neurons. The reduced-scale model is also compared directly with integrate-and-fire simulations, which capture considerably more physiological detail at the single-cell level, but still fail to reproduce the full behavioral complexity of the large-scale model. Thus network size, cell class diversity, and connectivity details may all be critical to generate self-sustained non-repetitive activity patterns. The mammalian hippocampus is involved in spatial representation and memory storage and retrieval, and much research is ongoing to elucidate the cellular and systemlevel mechanisms underlying these cognitive tasks. Modeling may be useful to link network-level activity patterns to the relevant features of hippocampal anatomy and electrophysiology. Investigating the effects of circuit connectivity requires simulations of a number of neurons close to real scale. Here, we construct a model of the hippocampus with 16 distinct neuronal classes [1, 2] (including both local and projection cells) and 200,000 individual McCulloch-Pitts neurons [3] . The number of neurons in each class and their interconnectivity are drawn from rat anatomy [1] .

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Alternating Turing machines for inductive languages ABSTRACT. We show that alternating Turing machines, with a novel and natural definition of acceptance, accept precisely the inductive (Π 1 1 ) languages. Total alternating machines, that either accept or reject each input, accept precisely the hyper-elementary (∆ 1 1 ) languages. Moreover, bounding the permissible number of alternations yields a characterization of the levels of the arithmetical hierarchy. Notably, these results use simple finite computing devices, with finitary and discrete operational semantics, and neither the results nor their proofs make any use of transfinite ordinals.Our characterizations elucidate the analogy between the polynomial-time hierarchy and the arithmetical hierarchy, as well as between their respective limits, namely polynomial-space and Π 1 1 . Inductive definitions via first-order positive operators constitute a broad computation paradigm. A fundamental result of computation theory, formulated in various guises over the last century, identifies the languages obtained by such definitions with those explicitly definable by Π 1 1 formulas, that is where second order quantification, over functions or relations, is restricted to positive occurrences of ∀. This central link was first discovered by Suslin in 1916 for sets of real numbers [16] . Kleene independently rediscovered the correspondence for sets of natural numbers (and so for languages) [6, 5] . Spector formulated the basic notions more explicitly [15] , and Moschovakis, Barwise, and Gandy established the characterization for near-arbitrary countable first-order structures in 1971. This characterization of Π 1 1 in terms of inductive definability endows it with many of the structural properties of the computably enumerable (RE) sets, and suggests an analogy between computability based on finite processes, captured by Σ 0 1 , and a generalized form of computability based on infinite processes.. Our aim here is to capture the full power of inductive definability by a novel and natural definition of acceptance for alternating Turing machines. This is unrelated to notions of "infinite-time computations" that have been investigated repeatedly over the decades.. Alternation in computational and definitional processes is an idea that has appeared and reappeared in various guises over the last 50 odd years. Kleene's definition of the arithmetical hierarchy 1 1 ). Moreover, when up to k alternations are allowed, we obtain the k'th levels of the arithmetical hierarchy. Also, if a language L is accepted by a machine which is total, in the sense that every input is either accepted or rejected, then L is hyper-arithmetical (∆ 1 1 ). Note that our machines are no different from traditional alternating Turing machines: the difference lies only in the definition of acceptance. In particular, no infinitary rules, such as game quantifiers or random assignments, are used. We thus obtain here a direct correspondence between Π 1 1 and polynomial space, and between the arithmetical hierarchy and the polynomial-time hierarchy. The two sides of this correspondence are characterized by the same alternating Turing machines, but with a global (potentially infinitary) definition of acceptance for the former, and a local one for the latter.. The author is grateful to Yiannis Moschovakis for important comments on an early draft of this paper. The combined use of existential and universal nondeterminism has been of interest primarily in Computational Complexity theory, but has not been considered thus far as a tool in the foundations of computing. This is because the semantics of acceptance has been defined "locally", that is in terms of the relation between computational configurations and their immediate descendants. That semantics implies that acceptance (and rejection) are witnessed by finite computation trees, and thus cannot lead us beyond the semi-decidable (RE) languages. Viewed from another angle, the closure properties involved are Π 0 1 , and so the accepted languages are defined by strict-Π 1 1 formulas (see §3.1 above).. We showed here that a very natural alternative semantics for universal nondeterminism changes the picture radically, as the languages accepted are precisely the Π 1 1 ones. This further illustrates the foundational analogy between alternation in feasible time with local semantics, which yields PSpace as a limit of the PTime Hierarchy (starting with PTime and NP), and alternation for arbitrary computations with global semantics, which yields Π Generalized models of computation that go beyond computability have been studied extensively, of course. The novelty of the approach here is that it refers to the very same hardware as traditional Turing machines (albeit with both modes of nondeterminism), but redefines the notion of acceptance, in a way that remains consistent with the underlying, intuitive, intent.. The ability to refer to both computational complexity and higher recursion theory using the same machine models has the potential of suggesting analogies between results, and thereby transfer of results. We believe that this will provide insights and additional machine-based proofs for Higher Recursion Theory.. The approach developed here seems to also break with past works in this area in that it dispenses with transfinite recurrence and induction over Kleene's constructive ordinals, and does not use any transfinite stage-comparison technique. Instead, the proofs use inductive definitions directly.. Directly dealing with inductive definitions, without calibrating them by ordinals provides, in fact, a closer analogy with finite computing. Computation traces of machines and of programs are construed intuitively as finite objects, without direct reference to the natural numbers, either as clocking computation steps or as codes for computational objects. Wit the frequent use of "structural induction" and "structural recurrence." It is, therefore, natural to expect that higher-order computation traces can be studied directly, without a detour through transfinite clocking by constructive ordinals. The proof of Theorem 4.2 achieves precisely that.

B I I O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O