This paper investigates the closure properties of multi-inkdot nondeterministic Turing machines with sublogarithmic space. We show that the class of sets accepted by the Turing machines is not closed under concatenation with regular set, Kleene closure, length-preserving homomorphism, and intersection.

This paper describes a logarithmic compression ADC using a subranging TDC and the transient response of a comparator. We utilized the settling time of the comparator for a logarithmic compression instead of a logarithmic amplifier. The settling time of the comparator is inversely proportional to the logarithm of an input voltage. In the proposed ADC, an input voltage is converted into a pulse whose width represents the settling time of the comparator. Subsequently, the TDC converts the pulse width into a binary code. The supply voltage of the proposed ADC can be reduced more than a conventional logarithmic ADC because an analog to digital conversion takes place in the time domain. We confirmed through a 0.18-µm CMOS circuit simulation that the proposed ADC achieves a resolution of 11 bits, a sampling rate of 20 MS/s, a dynamic range of 59 dB and a power consumption of 9.8 mW at 1.5 V operation.

In this paper, sequential prediction is studied. The typical assumptions about the probabilistic model in sequential prediction are following two cases. One is the case that a certain probabilistic model is given and the parameters are unknown. The other is the case that not a certain probabilistic model but a class of probabilistic models is given and the parameters are unknown. If there exist some parameters and some models such that the distributions that are identified by them equal the source distribution, an assumed model or a class of models can represent the source distribution. This case is called that specifiable condition is satisfied. In this study, the decision based on the Bayesian principle is made for a class of probabilistic models (not for a certain probabilistic model). The case that specifiable condition is not satisfied is studied. Then, the asymptotic behaviors of the cumulative logarithmic loss for individual sequence in the sense of almost sure convergence and the expected loss, i.e. redundancy are analyzed and the constant terms of the asymptotic equations are identified.

A 10-bit digital-to-analog converter (DAC) with a small area is proposed for data-driver integrated circuits of active-matrix liquid crystal display systems. The 10-bit DAC consists of a 7-bit resistor string, a 7-bit two-step decoder, a 2-bit logarithmic time interpolator, and a buffer amplifier. The proposed logarithmic time interpolation is achieved by controlling the charging time of a first-order low-pass filter composed of a resistor and a capacitor. The 7-bit two-step decoder that follows the 7-bit resistor string outputs an analog signal of the stepped wave with two voltage levels using the additional 1-bit digital code for the logarithmic time interpolation. The proposed 10-bit DAC is implemented using a 0.35-µm CMOS process and its supply voltage is scalable from 3.3V to 5.0V. The area of the proposed 10-bit logarithmic time interpolation DAC occupies 57% of that of the conventional 10-bit resistor-string DAC. The DNL and INL of the implemented 10-bit DAC are +0.29/-0.30 and +0.47/-0.36 LSB, respectively.

Considering the non-linear properties of the human visual system, many non-linear operators and models have been developed, particularly the logarithmic image processing (LIP) model proposed by Jourlin and Pinoli, which has been proved to be physically justified in several laws of the human visual system and has been successfully applied in image processing areas. Recently, several modifications based on this logarithmic mathematical framework have been presented, such as parameterized logarithmic image processing (PLIP), pseudo-logarithmic image processing, homomorphic logarithmic image processing. In this paper, a new single parameter logarithmic model for image processing with an adaptive parameter-based Sobel edge detection algorithm is presented. On the basis of analyzing the distributive law, the subtractive law, and the isomorphic property of the PLIP model, the five parameters in PLIP are replaced by a single parameter to ensure the completeness of the model and physical constancy with the nature of an image, and then an adaptive parameter-based Sobel edge detection algorithm is proposed. By using an image noise estimation method to evaluate the noise level of image, the adaptive parameter in the single parameter LIP model is calculated based on the noise level and grayscale value of a corresponding image area, followed by the single-parameter LIP-based Sobel operation to overcome the noise-sensitive problem of classical LIP-based Sobel edge detection methods, especially in the dark area of an image, while retaining edge sensitivity. Compared with the classical LIP and PLIP model, the given single parameter LIP achieves satisfactory results in noise suppression and edge accuracy.

This paper presents an efficient approach for logarithmic and anti-logarithmic converters which can be used in the arithmetic unit of hybrid number system processors and logarithm/exponent function generators in DSP applications. By employing the novel quasi-symmetrical difference method with only the simple shift-add logic and the look-up table, the proposed approach can reduce the hardware area and improve the conversion speed significantly while achieve similar accuracy compared with the previous methods. The implementation results in both FPGA and 0.18-µm CMOS technology are also presented and discussed.

In this letter, we propose an extension to the classical logarithmic total variation (LTV) model for face recognition under variant illumination conditions. LTV treats all facial areas with the same regularization parameters, which inevitably results in the loss of useful facial details and is harmful for recognition tasks. To address this problem, we propose to assign the regularization parameters which balance the large-scale (illumination) and small-scale (reflectance) components in a spatially adaptive scheme. Face recognition experiments on both Extended Yale B and the large-scale FERET databases demonstrate the effectiveness of the proposed method.

This paper investigates the closure properties of 1-inkdot nondeterministic Turing machines and 1-inkdot alternating Turing machines with only universal states which have sublogarithmic space. We show for example that the classes of sets accepted by these Turing machines are not closed under length-preserving homomorphism, concatenation with regular set, Kleene closure, and complementation.

Most learning-based super-resolution methods neglect the illumination problem. In this paper we propose a novel method to combine blind single-frame super-resolution and shadow removal into a single operation. Firstly, from the pattern recognition viewpoint, blur identification is considered as a classification problem. We describe three methods which are respectively based on Vector Quantization (VQ), Hidden Markov Model (HMM) and Support Vector Machines (SVM) to identify the blur parameter of the acquisition system from the compressed/uncompressed low-resolution image. Secondly, after blur identification, a super-resolution image is reconstructed by a learning-based method. In this method, Logarithmic-wavelet transform is defined for illumination-free feature extraction. Then an initial estimation is obtained based on the assumption that small patches in low-resolution space and patches in high-resolution space share a similar local manifold structure. The unknown high-resolution image is reconstructed by projecting the intermediate result into general reconstruction constraints. The proposed method simultaneously achieves blind single-frame super-resolution and image enhancement especially shadow removal. Experimental results demonstrate the effectiveness and robustness of our method.

This paper investigates the accepting powers of two-way alternating Turing machines (2ATM's) with only existential (universal) states which have inkdots and sublogarithmic space. It is shown that for sublogarithmic space-bounded computations, (i) multi-inkdot 2ATM's with only existential states and the ones with only universal states are incomparable, (ii) k-inkdot 2ATM's are better than k-inkdot 2ATM's with only existential (universal) states, k ≥ 0, and (iii) the class of sets accepted by multi-inkdot 2ATM's with only existential (universal) states is not closed under complementation.

This paper investigates some fundamental properties of one-way alternating pushdown automata with sublinear space. We first show that one-way nondeterministic pushdown automata are incomparale with one-way alternating pushdown automata with only universal states, for spaces between log log n and log n, and also for spaces between log n and n/log n. We then show that there exists an infinite space hierarchy among one-way alternating pushdown automata with only universal states which have sublinear space.

This paper investigates closure properties of one-pebble Turing machines with sublogarithmic space. It shows that for any function log log n L(n) = o(log n), neither of the classes of languages accepted by L(n) space-bounded deterministic and self-verifying nondeterministic one-pebble Turing machines is closed under concatenation, Kleene closure, and length-preserving homomorphism.

This paper introduces a 1-inkdot two-way alternating pushdown automaton which is a two-way alternating pushdown automaton (2apda) with the additional power of marking at most 1 tape-cell on the input (with an inkdot) once. We first investigate a relationship between the accepting powers of sublogarithmically space-bounded 2apda's with and without 1 inkdot, and show, for example, that sublogarithmically space-bounded 2apda's with 1 inkdot are more powerful than those which have no inkdots. We next investigate an alternation hierarchy for sublogarithmically space-bounded 1-inkdot 2apda's, and show that the alternation hierarchy on the first level for 1-inkdot 2apda's holds, and we also show that 1-inkdot two-way nondeterministic pushdown automata using sublogarithmic space are incomparable with 1-inkdot two-way alternating pushdown automata with only universal states using the same space.

The technique of replica placement has been extensively employed to improve client perceived performance and disperse server workload. In this paper, we study some well-known algorithms of replica placement on the network and observe the logarithmic relationship between replica number and total access cost. Numerous simulations are done and it is found that some replica algorithms obey the logarithmic relationship with high correlation coefficients. A logrithmic function is proposed about replica number and total access cost. The logarithmic relationship is applied to the minimum facility problem and a function is deduced to get the optimal replica number.

We propose a high-sensitivity and wide-dynamic-range position sensor using logarithmic-response and correlation circuit. The 3-D measurement system using the proposed position sensor has advantages to applications, for example a walking robot and a recognition system on vehicles, which require both of availability in various backgrounds and safe light projection for human eyes. The position sensor with a 64 64 pixel array has been developed and successfully tested. We describe the sensitivity of position detection as SBR (Signal-to-Background Ratio). The minimum SBR of the sensor is -13.9 dB lower than standard sensors. High sensitivity under -10 dB SBR is realized in a dynamic range of 41.7 dB in terms of background illumination. Experimental results of position detection and 3-D measurement in a strong background illumination are also presented.

This paper investigates a hierarchical property based on the number of inkdots in the accepting powers of sublogarithmic space-bounded multi-inkdot two-way alternating Turing machines with only universal states. For each k1 and any function L(n), let strong-2UTMk(L(n)) (weak-2UTMk(L(n))) be the class of sets accepted by strongly (weakly) L(n) space-bounded k-inkdot two-way alternating Turing machines with only universal states. We show that for each k1, strong-2UTMk+1(log log n) - weak-2UTMk(o(log n)) Ø.

We sketch two algorithms that solve the undirected st-connectivity problem in a small amount of space. One is due to Nisan, Szemeredy and Wigderson, and takes space O(log3/2n), where n denotes the number of nodes in a give undirected graph. This is the first algorithm that overcame the Savitch barrier on the space complexity of the problem. The other is due to Tarui and this author, and takes space O(sw(G)2 log2 n), where sw(G) denotes the separation-width of a given graph G. Their result implies that the st-connectivity problem can be solved in logarithmic space for any class of graphs with separation-width bounded above by a predetermined constant. This class is one of few nontrivial classes for which the st-connectivity problem can be solved in logarithmic space.

A 2-GHz monolithic Si-bipolar logarithmic/ limiting amplifier is described. It features a waveform-dependent current phase shifter that compensates for the intrinsic dependence of unit-amplifier phase shifts on input signal amplitudes and layout techniques that minimize crosstalk in Si substrate. The amplifier dissipates 250 mW at a 3-V supply, which is less than 1/4 of that of previously reported ICs. The dynamic range of a received signal strength indicator (RSSI) is 60 dB and the limited-output phase deviation is less than 7 deg. at 2 GHz. Therefore, this amplifier is quite suitable for single-conversion transceivers for broadband wireless access systems.

This paper investigates the accepting powers of multi-inkdot two-way alternating pushdown automata (Turing machines) with sublogarithmic space and constant leaf-size. For each k1, and each m0, let weak-ASPACEm [L(n),k] denote the class of languages accepted by simultaneously weakly L(n) space-bounded and k leaf-bounded m-inkdot two-way alternating Turing machines, and let strong-2APDAm[L(n),k] denote the class of languages accepted by simultaneously strongly L(n) space-bounded and k leaf-bounded m-inkdot two-way alternating pushdown automata. We show that(1) strong-2APDAm [log log n,k+1]weak-ASPACEm[o(log n),k]φfor each k1 and each m1, and(2) strong-2APDA(m+1) [log log n,k]weak-ASPACEm[o(log n),k]φfor each k1 and each m0.

This paper investigates some fundamental properties of alternating one-way (or two-way) pushdown automata (pda's) with sublogarithmic space. We first show that strongly (weakly) sublogarithmic space-bounded two-way alternating pda's are more powerful than one-way alternating pda's with the same space-bound. Then, we show that weakly sublogarithmic space-bounded two-way (one-way) alternating pda's are more powerful than two-way (one-way) nondeterministic pda's and alternating pda's with only universal states using the same space, and we also show that weakly sublogarithmic space-bounded one-way nondeterministic Turing machines are incomparable with one-way alternating Turing machines with only universal states using the same space. Furthermore, we investigate several fundamental closure properties, and show that the class of languages accepted by weakly sublogarithmic space-bounded one-way alternating pda's and the class of languages accepted by sublogarithmic space-bounded two-way deterministic pda's (nondeterministic pda's, alternating pda's with only universal states) are not closed under concatenation, Kleene closure, and length preserving homomorphism. Finally, we briefly investigate a relationship between 'strongly' and 'weakly'.