Automatic Recognition of Tractability in Inference Relations

A procedure is given for recognizing sets of inference rules that generate polynomial time decidable inference relations. The procedure can automatically recognize the tractability of the inference rules underlying congruence closure. The recognition of tractability for that particular rule set constitutes mechanical verification of a theorem originally proved independently by Kozen and Shostak. The procedure is algorithmic, rather than heuristic, and the class of automatically recognizable tractable rule sets can be precisely characterized. A series of examples of rule sets whose tractability is non-trivial, yet machine recognizable, is also given. The technical framework developed here is viewed as a first step toward a general theory of tractable inference relations.

An Efficient Correspondence Based Algorithm for 2D and 3D Model Based Recognition

A polynomial time algorithm (pruned correspondence search, PCS) with good average case performance for solving a wide class of geometric maximal matching problems, including the problem of recognizing 3D objects from a single 2D image, is presented. Efficient verification algorithms, based on a linear representation of location constraints, are given for the case of affine transformations among vector spaces and for the case of rigid 2D and 3D transformations with scale. Some preliminary experiments suggest that PCS is a practical algorithm. Its similarity to existing correspondence based algorithms means that a number of existing techniques for speedup can be incorporated into PCS to improve its performance.

Resolving Ambiguity in Nonmonotonic Inheritance Hierarchies

This paper describes a theory of inheritance theories. We present an original theory of inheritance in nonmonotonic hierarchies. The structures on which this theory is based delineate a framework that subsumes most inheritance theories in the literature, providing a new foundation for inheritance. * Our path-based theory is sound and complete w.r.t. a direct model-theoretic semantics. * Both the credulous and the skeptical conclusions of this theory are polynomial-time computable. * We prove that true skeptical inheritance is not contained in the language of path-based inheritance. Because our techniques are modular w.r.t. the definition of specificity, they generalize to provide a unified framework for a broad class of inheritance theories. By describing multiple inheritance theories in the same "language" of credulous extensions, we make principled comparisons rather than the ad-hoc examination of specific examples makes up most of the comparative inheritance work.

Equivalence and Reduction of Hidden Markov Models

This report studies when and why two Hidden Markov Models (HMMs) may represent the same stochastic process. HMMs are characterized in terms of equivalence classes whose elements represent identical stochastic processes. This characterization yields polynomial time algorithms to detect equivalent HMMs. We also find fast algorithms to reduce HMMs to essentially unique and minimal canonical representations. The reduction to a canonical form leads to the definition of 'Generalized Markov Models' which are essentially HMMs without the positivity constraint on their parameters. We discuss how this generalization can yield more parsimonious representations of stochastic processes at the cost of the probabilistic interpretation of the model parameters.

Robust 2-D Model-Based Object Recognition

Techniques, suitable for parallel implementation, for robust 2D model-based object recognition in the presence of sensor error are studied. Models and scene data are represented as local geometric features and robust hypothesis of feature matchings and transformations is considered. Bounds on the error in the image feature geometry are assumed constraining possible matchings and transformations. Transformation sampling is introduced as a simple, robust, polynomial-time, and highly parallel method of searching the space of transformations to hypothesize feature matchings. Key to the approach is that error in image feature measurement is explicitly accounted for. A Connection Machine implementation and experiments on real images are presented.

Low temperature heat capacity of (S)-ibuprofen

Molar heat capacities of ( S)-ibuprofen were precisely measured with a small sample precision automated adiabatic calorimeter over the temperature range from 80 to 370 K. Experimental heat capacities were fitted into a polynomial equation of heat capacities ( C-p,C- m) with reduced temperature ( X), [ X = f(T)]. The polynomial equations for ( S)-ibuprofen were C-p,C- m(s) = - 39.483 X-4 - 66. 649 X-3 + 95. 196 X-2 + 210. 84 X + 172. 98 in solid state and C-p,C- m(L) = 7. 191X(3) + 4. 2774 X-2 + 56. 365 X + 498. 5 in liquid state. The thermodynamic functions relative to the reference temperature of 298. 15 K, H-T - H-298.15 and S-T - S-298.15, were derived for the( S)-ibuprofen. A fusion transition at T-m = (324. 15 +/- 0. 02) K was found from the C-p - T curve. The molar enthalpy and entropy of the fusion transition were determined to be (18. 05 +/- 0. 31) kJ.mol(-1) and (55. 71 +/- 0. 95) J.mol(-1).K-1, respectively. The purity of the ( S)-ibuprofen was determined to be 99. 44% on the basis of the heat capacity measurement. Finally, the heat capacities of ( S)-ibuprofen and racemic ibuprofen were compared.

Thermodynamic properties of ethanol and gasoline blended fuel

The heat capacities (C-p) of five types of gasohol (50 wt % ethanol and 50 wt % unleaded gasoline 93(#) (E50), 60 wt % ethanol and 40 wt % unleaded gasoline 93(#) (E60), 70 wt % ethanol and 30 wt % unleaded gasoline 93(#) (E70), 80 wt % ethanol and 20 wt % unleaded gasoline 93(#) (E80), and 90 wt % ethanol and 10 wt % unleaded gasoline 93(#) (E90), where the "93" denotes the octane number) were measured by adiabatic calorimetry in the temperature range of 78-320 K. A glass transition was observed at 95.61, 96.14, 96.56, 96.84, and 97.08 K for samples from the E50, E60, E70, E80, and E90 systems, respectively. A liquid-solid phase transition and a solid-liquid phase transition were observed in the respective temperature ranges of 118-153 and 155-163 K for E50, 117-150 and 151-164 K for E60, 115-154 and 154-166 K for E70, 113-152 and 152-167 K for E80, and 112-151 and 1581-167 K for E90. The polynomial equations of Cp and the excess heat capacities (C-p(E)), with respect to the thermodynamic temperature, were established through least-squares fitting. Based on the thermodynamic relationship and the equations obtained, the thermodynamic functions and the excess thermodynamic functions of the five gasohol samples were derived.

Algorithmic derivation of isochronicity conditions

Hill, Joe M., Lloyd, Noel G., Pearson, Jane M., 'Algorithmic derivation of isochronicity conditions', Nonlinear Analysis (2007) 67, 52-69.

Optimization of physical and optical properties of biodegradable edible films based on pea starch and guar gum

The influence of process variables (pea starch, guar gum and glycerol) on the viscosity (V), solubility (SOL), moisture content (MC), transparency (TR), Hunter parameters (L, a, and b), total color difference (ΔE), yellowness index (YI), and whiteness index (WI) of the pea starch based edible films was studied using three factors with three level Box–Behnken response surface design. The individual linear effect of pea starch, guar and glycerol was significant (p < 0.05) on all the responses. However, a value was only significantly (p < 0.05) affected by pea starch and guar gum in a positive and negative linear term, respectively. The effect of interaction of starch × glycerol was also significant (p < 0.05) on TR of edible films. Interaction between independent variables starch × guar gum had a significant impact on the b and YI values. The quadratic regression coefficient of pea starch showed a significant effect (p < 0.05) on V, MC, L, b, ΔE, YI, and WI; glycerol level on ΔE and WI; and guar gum on ΔE and SOL value. The results were analyzed by Pareto analysis of variance (ANOVA) and the second order polynomial models were developed from the experimental design with reliable and satisfactory fit with the corresponding experimental data and high coefficient of determination (R2) values (>0.93). Three-dimensional response surface plots were established to investigate the relationship between process variables and the responses. The optimized conditions with the goal of maximizing TR and minimizing SOL, YI and MC were 2.5 g pea starch, 25% glycerol and 0.3 g guar gum. Results revealed that pea starch/guar gum edible films with appropriate physical and optical characteristics can be effectively produced and successfully applied in the food packaging industry.

O wielomianach cyklotomicznych

Wydział Matematyki i Informatyki

On Learning Counting Functions With Queries

We investigate the problem of learning disjunctions of counting functions, which are general cases of parity and modulo functions, with equivalence and membership queries. We prove that, for any prime number p, the class of disjunctions of integer-weighted counting functions with modulus p over the domain Znq (or Zn) for any given integer q ≥ 2 is polynomial time learnable using at most n + 1 equivalence queries, where the hypotheses issued by the learner are disjunctions of at most n counting functions with weights from Zp. The result is obtained through learning linear systems over an arbitrary field. In general a counting function may have a composite modulus. We prove that, for any given integer q ≥ 2, over the domain Zn2, the class of read-once disjunctions of Boolean-weighted counting functions with modulus q is polynomial time learnable with only one equivalence query, and the class of disjunctions of log log n Boolean-weighted counting functions with modulus q is polynomial time learnable. Finally, we present an algorithm for learning graph-based counting functions.

Bounds on the Power of Constant-Depth Quantum Circuits

We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, our results imply EQNC^0 ⊆ P, where EQNC^0 is the constant-depth analog of the class EQP. On the other hand, we adapt and extend ideas of Terhal and DiVincenzo [?] to show that, for any family

Determining Acceptance Possibility for a Quantum Computation is Hard for PH

It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation.

Optimal Scheduling of Secondary Content for Aggregation in Video-on-Demand Systems

Dynamic service aggregation techniques can exploit skewed access popularity patterns to reduce the costs of building interactive VoD systems. These schemes seek to cluster and merge users into single streams by bridging the temporal skew between them, thus improving server and network utilization. Rate adaptation and secondary content insertion are two such schemes. In this paper, we present and evaluate an optimal scheduling algorithm for inserting secondary content in this scenario. The algorithm runs in polynomial time, and is optimal with respect to the total bandwidth usage over the merging interval. We present constraints on content insertion which make the overall QoS of the delivered stream acceptable, and show how our algorithm can satisfy these constraints. We report simulation results which quantify the excellent gains due to content insertion. We discuss dynamic scenarios with user arrivals and interactions, and show that content insertion reduces the channel bandwidth requirement to almost half. We also discuss differentiated service techniques, such as N-VoD and premium no-advertisement service, and show how our algorithm can support these as well.

On the Complexity of Quantum ACC

For any q > 1, let MOD_q be a quantum gate that determines if the number of 1's in the input is divisible by q. We show that for any q,t > 1, MOD_q is equivalent to MOD_t (up to constant depth). Based on the case q=2, Moore has shown that quantum analogs of AC^(0), ACC[q], and ACC, denoted QAC^(0)_wf, QACC[2], QACC respectively, define the same class of operators, leaving q > 2 as an open question. Our result resolves this question, implying that QAC^(0)_wf = QACC[q] = QACC for all q. We also prove the first upper bounds for QACC in terms of related language classes. We define classes of languages EQACC, NQACC (both for arbitrary complex amplitudes) and BQACC (for rational number amplitudes) and show that they are all contained in TC^(0). To do this, we show that a TC^(0) circuit can keep track of the amplitudes of the state resulting from the application of a QACC operator using a constant width polynomial size tensor sum. In order to accomplish this, we also show that TC^(0) can perform iterated addition and multiplication in certain field extensions.