AND-compression of NP-complete Problems: Streamlined Proof and Minor Observations

Recently, images on the Web and personal computers are prevalent around the human’s life. To retrieve effectively those images, there are many AIA (Automatic Image Annotation) algorithms. However, it still suffers from low-level accuracy since it couldn’t overcome the semantic-gap be tween low-level features (‘color’,‘texture’ and ‘shape’) and high-level semantic meanings (e.g., ‘sky’,‘beach’). Namely, AIA techniques annotates images with many noisy key words. Refinement process has been appeared in these days and it tries to remove noisy keywords by using Knowledge-base and boosting candidate keywords. Because of limitless of candidate keywords and the incorrectness of web-image textual descriptions, this is the time we need to have deterministic polynomial time algorithm. We show that finding optimal solution for removing noisy keywords in the graph is NP-Complete problem and propose new methodology for KBIAR (Knowledge Based Image Annotation Refinement) using the randomized approximation graph algorithm as the general deterministic polynomial time algorithm.

Chapter 1 - Behaviour, analysis and design of steel frames

Introduction: Transtibial amputees tend to isolate themselves because they lack confidence in performing daily tasks; rehabilitation processes such as the use of prostheses are carried out for their social reintegration, where postural stability must be ensured, and activities allowed in diverse contexts. Objective: Verify the contribution of each leg and direction (anterior/posterior and medial/lateral) of the center of pressure (CoP) in the static postural stability of unilateral transtibial amputees due to landmines using information theory. Methodology: A quantitative experimental design was applied to examine the displacement and velocity of the CoP using infometric measurements in nine transtibial amputees, and the non-parametric U Mann-Whitney test was applied to recognize statistically notable differences (p <0.05) between each leg. Results: There are statistically notable differences between the legs in the variables of displacement and velocity. Each leg contributes differently to the control of the static bipedal posture, and their behavior in the directions of movement of the CoP differs from each other, but they work together to generate compensation strategies that allow maintaining stability. Conclusions: The use of information theory made it possible to evaluate stability objectively, without specifying the kind of relationship between this and the input variables, which favored the recognition of the CoP shift as its best discriminant in comparison with velocity. Transtibial amputees control static bipedal posture with the non-amputated leg to compensate for the loss of lower leg afferents and efferents due to the amputation. The results demonstrate the suitability of using information theory in the evaluation of lateralized postural control in pathological conditions.

This paper traces the application of information theory to philosophical problems of mind and meaning from the earliest days of the creation of the mathematical theory of communication. The use of information theory to understand purposive behavior, learning, pattern recognition, and more marked the beginning of the naturalization of mind and meaning. From the inception of information theory, Wiener, Turing, and others began trying to show how to make a mind from informational and computational materials. Over the last 50 years, many philosophers saw different aspects of the naturalization of the mind, though few saw at once all of the pieces of the puzzle that we now know. Starting with Norbert Wiener himself, philosophers and information theorists used concepts from information theory to understand cognition. This paper provides a window on the historical sequence of contributions made to the overall project of naturalizing the mind by philosophers from Shannon, Wiener, and MacKay, to Dennett, Sayre, Dretske, Fodor, and Perry, among others. At some time between 1928 and 1948, American engineers and mathematicians began to talk about `Theory of Information' and `Information Theory,' understanding by these terms approximately and vaguely a theory for which Hartley's `amount of information' is a basic concept. I have been unable to find out when and by whom these names were first used. Hartley himself does not use them nor does he employ the term `Theory of Transmission of Information,' from which the two other shorter terms presumably were derived. It seems that Norbert Wiener and Claude Shannon were using them in the Mid-Forties. (Yehoshua Bar-Hillel, 1955)

: The bibliography contains 756 citations of work that have been done relevant to psychology in information theory. Information theory is distinguished from the broader disciplines of communication theory and cybernetics by the use of a particular measure of amount of information.

Econometric use of information theory in dynamic models is briefly reviewed for both modelling and estimation purposes. As an example, two types of stochastic process models, one linear and the other logistic, are developed for application in economic growth models. These models are suitable for understanding the structure of the growth-inducing and growth-retarding effects of exports in the phenomenal economic growth in the newly industrializing countries of Asia over the last two decades.

We explore the use of information theory as a tool to express and quantify notions of information content and information transfer for representing and analyzing data, using examples from database design, data integration and data anonymization. We also examine the computational challenges associated with information-theoretic primitives, indicating how they might be computed efficiently.

This paper describes the use of information theory to model the interactions between various design agents in a design/manufacturing organization. In typical multidisciplinary design environments, the design attribute space is constrained by the requirements and compatibility conditions introduced by interacting disciplines. A key factor toward efficient design lies in the recognition of this constrained design space, and in communicating this to the designers during the initial stages of the design process. As a result, engineering information systems that support the multidisciplinary design activities must incorporate these constraints, and provide designers with a uniform mechanism that will assist design attribute awareness, provide decision discriminators and model design attribute dependencies. The concept of entropy as defined in information theory will be used to quantify both the information content of a design as well as the design attribute space. Specifically, we shall investigate how this model may be used for a class of parametric design problems.

The use of information theory to design waveforms for the measurement of extended radar targets exhibiting resonance phenomena is investigated. The target impulse response is introduced to model target scattering behavior. Two radar waveform design problems with constraints on waveform energy and duration are then solved. In the first, a deterministic target impulse response is used to design waveform/receiver-filter pairs for the optimal detection of extended targets in additive noise. In the second, a random target impulse response is used to design waveforms that maximize the mutual information between a target ensemble and the received signal in additive Gaussian noise. The two solutions are contrasted to show the difference between the characteristics of waveforms for extended target detection and information extraction. The optimal target detection solution places as much energy as possible in the largest target scattering mode under the imposed constraints on waveform duration and energy. The optimal information extraction solution distributes the energy among the target scattering modes in order to maximize the mutual information between the target ensemble and the received radar waveform. >

The use of information theory in evaluating the contribution of radiological and laboratory investigations to diagnosis and management

In this note we show that Ky Fan's minimax theorem and its several generalizations such as Konig's minimax theorem [6], M. Neumann's minimax theorem [8] and Fuchssteiner-Konig's minimax theorem [3] are equivalent. We also give a direct proof for Fuchssteiner-Konig's minimax theorem on the basis of Eidelheit's well-known seperation theorem.

The convex sets strict separation is very useful to obtain mathematical optimization results. The minimax theorem, a key result in Game Theory is an example. It will be outlined in this work.

Using shape grammars and extremal optimization in 3D IC layout design

We consider the problem of fair allocation of indivisible items among $n$ agents with additive valuations, when agents have equal entitlements to the goods, and there are no transfers. Best-of-Both-Worlds (BoBW) fairness mechanisms aim to give all agents both an ex-ante guarantee (such as getting the proportional share in expectation) and an ex-post guarantee. Prior BoBW results have focused on ex-post guarantees that are based on the to one paradigm, such as envy-free up to one item (EF1). In this work we attempt to give every agent a high value ex-post, and specifically, a constant fraction of his maximin share (MMS). The up to one item paradigm fails to give such a guarantee, and it is not difficult to present examples in which previous BoBW mechanisms give agents only a $\frac{1}{n}$ fraction of their MMS. Our main result is a deterministic polynomial time algorithm that computes a distribution over allocations that is ex-ante proportional, and ex-post, every allocation gives every agent at least his proportional share up to one item, and more importantly, at least half of his MMS. Moreover, this last ex-post guarantee holds even with respect to a more demanding notion of a share, introduced in this paper, that we refer to as the truncated proportional share (TPS). Our guarantees are nearly best possible, in the sense that one cannot guarantee agents more than their proportional share ex-ante, and one cannot guarantee agents more than a $\frac{n}{2n-1}$ fraction of their TPS ex-post.

In this work we relate the deterministic complexity of factoring polynomials (over finite fields) to certain combinatorial objects we call m-schemes. We extend the known conditional deterministic subexponential time polynomial factoring algorithm for finite fields to get an underlying m-scheme. We demonstrate how the properties of m-schemes relate to improvements in the deterministic complexity of factoring polynomials over finite fields assuming the generalized Riemann Hypothesis (GRH). In particular, we give the first deterministic polynomial time algorithm (assuming GRH) to find a nontrivial factor of a polynomial of prime degree n where (n-1) is a smooth number.