Semantically-Guided Goal-Sensitive Reasoning: Inference System and Completeness

We present a new method for clausal theorem proving, named SGGS from semantically-guided goal-sensitive reasoning. SGGS generalizes to first-order logic the conflict-driven clause learning (CDCL) procedure for propositional satisfiability. Starting from an initial interpretation, used for semantic guidance, SGGS employs a sequence of constrained clauses to represent a candidate model, instance generation to extend it, resolution and other inferences to explain and solve conflicts, amending the model. We prove that SGGS is refutationally complete and model complete in the limit, regardless of initial interpretation. SGGS is also goal sensitive, if the initial interpretation is properly chosen, and proof confluent, because it repairs the current model without undoing steps by backtracking. Thus, SGGS is a complete first-order method that is simultaneously model-based à la CDCL, semantically-guided, goal-sensitive, and proof confluent.     

A Priori knowledge based secure payload estimation

Many contemporary steganographic schemes aim to embed fixed-length secret message in the cover while minimizing the stego distortion. However, in some cases, the secret message sender requires to embed a variable-length secret payload within his expected stego security. This kind of problem is named as secure payload estimation (SPE). In this paper, we propose a practical SPE approach for individual cover. The stego security metric we adopt here is the detection error rate of steganalyzer (P _E ). Our method is based on a priori knowledge functions, which are two kinds of functions to be determined before the estimation. The first function is the relation function of detection error rate and stego distortion (P _E ? D function). The second function reflects the relationship between stego distortion and payload rate (D ? α) of the chosen cover. The P _E ? D is the general knowledge, which is calculated from image library. On the other hand, D ? α is for specific cover, which is needed to be determined on site. The estimating procedure is as follows: firstly, the sender solves the distortion D under his expected P _E via P _E ? D, and then calculates the corresponding secure payload α via D ? α of the cover. For on-site operations, the most time-consuming part is calculating D ? α function for cover image, which costs 1 time of STC coding. Besides this, the rest on-site operations are solving single-variable formulas, which can be easily tackled. Our approach is an efficient and practical solution for SPE problem.     

On s-uniform property of compressing sequences derived from primitive sequences modulo odd prime powers

Let Z/(p^e) be the integer residue ring modulo p^e with p an odd prime and e ≥ 2. We consider the suniform property of compressing sequences derived from primitive sequences over Z/(p^e). We give necessary and sufficient conditions for two compressing sequences to be s-uniform with α provided that the compressing map is of the form ?(x₀, x₁,...,x_e?1) = g(x_e?1) + η(x₀, x₁,..., x_e?2), where g(x_e?1) is a permutation polynomial over Z/(p) and η is an (e ? 1)-variable polynomial over Z/(p).     

Tackling heterogeneous concept drift with the Self-Adjusting Memory (SAM)

Instance matching is the problem of determining whether two instances describe the same real-world entity or not. Instance matching plays a key role in data integration and data cleansing, especially for building a knowledge base. For example, we can regard each article in encyclopedias as an instance, and a group of articles which refers to the same real-world object as an entity. Therefore, articles about Washington should be distinguished and grouped into different entities such as Washington, D.C (the capital of the USA), George Washington (first president of the USA), Washington (a state of the USA), Washington (a village in West Sussex, England), Washington F.C. (a football club based in Washington, Tyne and Wear, England), Washington, D.C. (a novel). In this paper, we proposed a novel instance matching approach Active Instance Matching with Pairwise Constraints, which can bring the human into the loop of instance matching. The proposed approach can generate candidate pairs in advance to reduce the computational complexity, and then iteratively select the most informative pairs according to the uncertainty, influence, connectivity and diversity of pairs. We evaluated our approach one two publicly available datasets AMINER and WIDE-NUS and then applied our approach to the two large-scale real-world datasets, Baidu Baike and Hudong Baike, to build a Chinese knowledge base. The experiments and practice illustrate the effectiveness of our approach.     

Making Doubling Metrics Geodesic

The starting point of our research is the following problem: given a doubling metric ?=(V,d), can one (efficiently) find an unweighted graph G′=(V′,E′) with V?V′ whose shortest-path metric d′ is still doubling, and which agrees with d on V×V? While it is simple to show that the answer to the above question is negative if distances must be preserved exactly. However, allowing a (1+ε) distortion between d and d′ enables us bypass this hurdle, and obtain an unweighted graph G′ with doubling dimension at most a factor O(log?ε ^?1) times the doubling dimension of G.More generally, this paper gives algorithms that construct graphs G′ whose convex (or geodesic) closure has doubling dimension close to that of ?, and the shortest-path distances in G′ closely approximate those of ? when restricted to V×V. Similar results are shown when the metric ? is an additive (tree) metric and the graph G′ is restricted to be a tree.     

Knowledge State Algorithms

We introduce the novel concept of knowledge states. The knowledge state approach can be used to construct competitive randomized online algorithms and study the trade-off between competitiveness and memory. Many well-known algorithms can be viewed as knowledge state algorithms. A knowledge state consists of a distribution of states for the algorithm, together with a work function which approximates the conditional obligations of the adversary. When a knowledge state algorithm receives a request, it then calculates one or more “subsequent” knowledge states, together with a probability of transition to each. The algorithm uses randomization to select one of those subsequents to be the new knowledge state. We apply this method to randomized k-paging. The optimal minimum competitiveness of any randomized online algorithm for the k-paging problem is the kth harmonic number, \(H_{k}=\sum^{k}_{i=1}\frac{1}{i}\). Existing algorithms which achieve that optimal competitiveness must keep bookmarks, i.e., memory of the names of pages not in the cache. An H _k -competitive randomized algorithm for that problem which uses O(k) bookmarks is presented, settling an open question by Borodin and El-Yaniv. In the special cases where k=2 and k=3, solutions are given using only one and two bookmarks, respectively.     

Some properties of binaryn-Tuples with reference to cyclic codes

This article gives a geometric interpretation of a product (already introduced in literature) betweenn-tuples, based on the use of «associate, polynomials». In the second part of the work, a number of algebraic considerations are made, which give a characterization of the ringsR _n of all binaryn-tuples.     

Some lower bounds on the algebraic immunity of functions given by their trace forms

The algebraic immunity of a Boolean function is a parameter that characterizes the possibility to bound this function from above or below by a nonconstant Boolean function of a low algebraic degree. We obtain lower bounds on the algebraic immunity for a class of functions expressed through the inversion operation in the field GF(2 ⁿ ), as well as for larger classes of functions defined by their trace forms. In particular, for n ≥ 5, the algebraic immunity of the function Tr _n (x ^?1) has a lower bound ?2√n + 4? ? 4, which is close enough to the previously obtained upper bound ?√n? + ?n/?√n?? ? 2. We obtain a polynomial algorithm which, give a trace form of a Boolean function f, computes generating sets of functions of degree ≤ d for the following pair of spaces. Each function of the first (linear) space bounds f from below, and each function of the second (affine) space bounds f from above. Moreover, at the output of the algorithm, each function of a generating set is represented both as its trace form and as a polynomial of Boolean variables.     

On the optimal choice of quality metric in image compression: a soft computing approach

Images take lot of computer space; in many practical situations, we cannot store all original images, we have to use compression. Moreover, in many such situations, compression ratio provided by even the best lossless compression is not sufficient, so we have to use lossy compression. In a lossy compression, the reconstructed image ? is, in general, different from the original image I. There exist many different lossy compression methods, and most of these methods have several tunable parameters. In different situations, different methods lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. A natural idea is to select the compression method for which the average value of some metric d(I,?) is the smallest possible. The question is then: which quality metric should we choose? In this paper, we show that under certain reasonable symmetry conditions, L ^p metrics d(I,?)=∫|I(x)??(x)| ^p dx are the best, and that the optimal value of p can be selected depending on the expected relative size r of the informative part of the image.     

Propelinear codes related to some classes of optimal codes

A code is said to be propelinear if its automorphism group contains a subgroup that acts regularly on codewords. We show propelinearity of complements of cyclic codes C _1,i , (i, 2 ^m ? 1) = 1, of length n = 2 ^m ? 1, including the primitive two-error-correcting BCH code, to the Hamming code; the Preparata code to the Hamming code; the Goethals code to the Preparata code; and the Z₄-linear Preparata code to the Z₄-linear perfect code.     

Shadow Prices in Territory Division

We consider a geographic optimization problem in which we are given a region R, a probability density function f(?) defined on R, and a collection of n utility density functions u _i (?) defined on R. Our objective is to divide R into n sub-regions R _i so as to “balance” the overall utilities on the regions, which are given by the integrals \(\iint _{R_{i}}f(x)u_{i}(x)\, dA\). Using a simple complementary slackness argument, we show that (depending on what we mean precisely by “balancing” the utility functions) the boundary curves between optimal sub-regions are level curves of either the difference function u _i (x) ? u _j (x) or the ratio u _i (x)/u _j (x). This allows us to solve the problem of optimally partitioning the region efficiently by reducing it to a low-dimensional convex optimization problem. This result generalizes, and gives very short and constructive proofs of, several existing results in the literature on equitable partitioning for particular forms of f(?) and u _i (?). We next give two economic applications of our results in which we show how to compute a market-clearing price vector in an aggregate demand system or a variation of the classical Fisher exchange market. Finally, we consider a dynamic problem in which the density function f(?) varies over time (simulating population migration or transport of a resource, for example) and derive a set of partial differential equations that describe the evolution of the optimal sub-regions over time. Numerical simulations for both static and dynamic problems confirm that such partitioning problems become tractable when using our methods.     

On Cosets of Weight 4 of Binary BCH Codes with Minimum Distance 8 and Exponential Sums

We study coset weight distributions of binary primitive (narrow-sense) BCH codes of length n = 2 ^m (m odd) with minimum distance 8. In the previous paper [1], we described coset weight distributions of such codes for cosets of weight j = 1, 2, 3, 5, 6. Here we obtain exact expressions for the number of codewords of weight 4 in terms of exponential sums of three types, in particular, cubic sums and Kloosterman sums. This allows us to find the coset distribution of binary primitive (narrow-sense) BCH codes with minimum distance 8 and also to obtain some new results on Kloosterman sums over finite fields of characteristic 2.     

Patent Protection in a Model of Economic Growth in Multiple Regions

We study the effects of patent protection on economic growth in the ith region when this ith region is part of an aggregate economy of i?=?1,…,N regions. The regulatory authority in the ith region attempts to curtail the monopoly power of patent holding input producers by requiring them to charge a price that is parametrically related to the unconstrained monopoly price. Our analysis generates three results. First, we show the manner in which the equilibrium growth rate of the ith region is related to the above mentioned parameter. Second, we demonstrate the impact that changes in the stringency of patent protection have on the ith region’s equilibrium growth rate. Finally, we explain why eliminating the monopoly distortion does not maximize social welfare in the ith region.     

Two-armed bandit problem for parallel data processing systems

We consider application of the two-armed bandit problem to processing a large number N of data where two alternative processing methods can be used. We propose a strategy which at the first stages, whose number is at most r ? 1, compares the methods, and at the final stage applies only the best one obtained from the comparison. We find asymptotically optimal parameters of the strategy and observe that the minimax risk is of the order of N ^α , where α = 2 ^r?1/(2 ^r ? 1). Under parallel processing, the total operation time is determined by the number r of stages but not by the number N of data.     

Negation-Limited Complexity of Parity and Inverters

In negation-limited complexity, one considers circuits with a limited number of NOT gates, being motivated by the gap in our understanding of monotone versus general circuit complexity, and hoping to better understand the power of NOT gates. We give improved lower bounds for the size (the number of AND/OR/NOT) of negation-limited circuits computing Parity and for the size of negation-limited inverters. An inverter is a circuit with inputs x ₁,…,x _n and outputs ¬ x ₁,…,¬ x _n . We show that: (a) for n=2 ^r ?1, circuits computing Parity with r?1 NOT gates have size at least 6n?log?₂(n+1)?O(1), and (b) for n=2 ^r ?1, inverters with r NOT gates have size at least 8n?log?₂(n+1)?O(1). We derive our bounds above by considering the minimum size of a circuit with at most r NOT gates that computes Parity for sorted inputs x ₁≥???≥x _n . For an arbitrary r, we completely determine the minimum size. It is 2n?r?2 for odd n and 2n?r?1 for even n for ?log?₂(n+1)??1≤r≤n/2, and it is ?3n/2??1 for r≥n/2. We also determine the minimum size of an inverter for sorted inputs with at most r NOT gates. It is 4n?3r for ?log?₂(n+1)?≤r≤n. In particular, the negation-limited inverter for sorted inputs due to Fischer, which is a core component in all the known constructions of negation-limited inverters, is shown to have the minimum possible size. Our fairly simple lower bound proofs use gate elimination arguments in a somewhat novel way.     

Cooperation in Games and Epistemic Readings of Independence-Friendly Sentences

In the literature on logics of imperfect information it is often stated, incorrectly, that the Game-Theoretical Semantics of Independence-Friendly (IF) quantifiers captures the idea that the players of semantical games are forced to make some moves without knowledge of the moves of other players. We survey here the alternative semantics for IF logic that have been suggested in order to enforce this “epistemic reading” of sentences. We introduce some new proposals, and a more general logical language which distinguishes between “independence from actions” and “independence from strategies”. New semantics for IF logic can be obtained by choosing embeddings of the set of IF sentences into this larger language. We compare all the semantics proposed and their purported game-theoretical justifications, and disprove a few claims that have been made in the literature.     

Guaranteeing Response Times for Aperiodic Tasks in Global Multiprocessor Scheduling

We provide a constant time schedulability test for an on-line multiprocessor server handling aperiodic tasks. Dhall's effect is avoided by dividing the tasks in two priority classes based on task utilization: heavy and light. We prove that if the load on the multiprocessor server stays below U _threshold = 3 ? √7 ≈ 35.425%, the server can accept an incoming aperiodic task and guarantee that the deadlines of all accepted tasks will be met. The same number 35.425% is also a threshold for a task to be characterized as heavy.The bound U _threshold = 3 ? √7≈ 35.425% is easy-to-use, but not sharp if we know the number of processors in the multiprocessor system. Assuming the server to be equipped with m processors, we calculate a formula for the sharp bound U _threshold (m), which converges to U _threshold from above as m → ∞.The results are based on a utilization function u(x) = 2(1 ? x)/(2 + √2+2x). By using this function, the performance of the multiprocessor server can in some cases be improved beyond U _threshold(m) by paying the extra overhead of monitoring the individual utilization of the current tasks.     

Sufficient Conditions for Monotonicity of the Undetected Error Probability for Large Channel Error Probabilities

The performance of a linear error-detecting code in a symmetric memoryless channel is characterized by its probability of undetected error, which is a function of the channel symbol error probability, involving basic parameters of a code and its weight distribution. However, the code weight distribution is known for relatively few codes since its computation is an NP-hard problem. It should therefore be useful to have criteria for properness and goodness in error detection that do not involve the code weight distribution. In this work we give two such criteria. We show that a binary linear code C of length n and its dual code C^⊥ of minimum code distance d^⊥ are proper for error detection whenever d^⊥ ≥ ?n/2? + 1, and that C is proper in the interval [(n + 1 ? 2d^⊥)/(n ? d^⊥); 1/2] whenever ?n/3? + 1 ≤ d^⊥ ≤ ?n/2?. We also provide examples, mostly of Griesmer codes and their duals, that satisfy the above conditions.     

Advanced methods for the estimation of an unknown projection from a map

This article presents three new methods (M5, M6, M7) for the estimation of an unknown map projection and its parameters. Such an analysis is beneficial and interesting for historic, old, or current maps without information about the map projection; it could improve their georeference. The location similarity approach takes into account the residuals on the corresponding features; the minimum is found using the non-linear least squares. For the shape similarity approach, the minimized objective function ? takes into account the spatial distribution of the features, together with the shapes of the meridians, parallels and other 0D-2D elements. Due to the non-convexity and discontinuity, its global minimum is determined using the global optimization, represented by the differential evolution. The constant values of projection φ _k , λ _k , φ ₁, λ ₀, and map constants R,ΔX,ΔY, α (in relation to which the methods are invariant) are estimated. All methods are compared and the results are presented for the synthetic data as well as for 8 early maps from the Map Collection of the Charles University and the David Rumsay Map Collection. The proposed algorithms have been implemented in the new version of the detectproj software.     

On transitive partitions of an <Emphasis Type="Italic">n</Emphasis>-cube into codes

We present methods to construct transitive partitions of the set E ⁿ of all binary vectors of length n into codes. In particular, we show that for all n = 2 ^k ? 1, k ≥ 3, there exist transitive partitions of E ⁿ into perfect transitive codes of length n.