Ramsey's Theorem for Pairs and kk Colors as a Sub-Classical Principle of Arithmetic

The purpose is to study the strength of Ramsey's Theorem for pairs restricted to recursive assignments of $k$-many colors, with respect to Intuitionistic Heyting Arithmetic. We prove that for every natural number $k \geq 2$, Ramsey's Theorem for pairs and recursive assignments of $k$ colors is equivalent to the Limited Lesser Principle of Omniscience for $\Sigma^0_3$ formulas over Heyting Arithmetic. Alternatively, the same theorem over intuitionistic arithmetic is equivalent to: for every recursively enumerable infinite $k$-ary tree there is some $i < k$ and some branch with infinitely many children of index $i$.Comment: 17 page

逆数学と可算代数系

Tohoku University山崎武課

Probabilistic methods for distributed information dissemination

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 457-484).The ever-increasing growth of modern networks comes with a paradigm shift in network operation. Networks can no longer be abstracted as deterministic, centrally controlled systems with static topologies but need to be understood as highly distributed, dynamic systems with inherent unreliabilities. This makes many communication, coordination and computation tasks challenging and in many scenarios communication becomes a crucial bottleneck. In this thesis, we develop new algorithms and techniques to address these challenges. In particular we concentrate on broadcast and information dissemination tasks and introduce novel ideas on how randomization can lead to powerful, simple and practical communication primitives suitable for these modern networks. In this endeavor we combine and further develop tools from different disciplines trying to simultaneously addresses the distributed, information theoretic and algorithmic aspects of network communication. The two main probabilistic techniques developed to disseminate information in a network are gossip and random linear network coding. Gossip is an alternative to classical flooding approaches: Instead of nodes repeatedly forwarding information to all their neighbors, gossiping nodes forward information only to a small number of (random) neighbors. We show that, when done right, gossip disperses information almost as quickly as flooding, albeit with a drastically reduced communication overhead. Random linear network coding (RLNC) applies when a large amount of information or many messages are to be disseminated. Instead of routing messages through intermediate nodes, that is, following a classical store-and-forward approach, RLNC mixes messages together by forwarding random linear combinations of messages. The simplicity and topology-obliviousness of this approach makes RLNC particularly interesting for the distributed settings considered in this thesis. Unfortunately the performance of RLNC was not well understood even for the simplest such settings. We introduce a simple yet powerful analysis technique that allows us to prove optimal performance guarantees for all settings considered in the literature and many more that were not analyzable so far. Specifically, we give many new results for RLNC gossip algorithms, RLNC algorithms for dynamic networks, and RLNC with correlated data. We also provide a novel highly efficient distributed implementation of RLNC that achieves these performance guarantees while buffering only a minimal amount of information at intermediate nodes. We then apply our techniques to improve communication primitives in multi-hop radio networks. While radio networks inherently support broadcast communications, e.g., from one node to all surrounding nodes, interference of simultaneous transmissions makes multihop broadcast communication an interesting challenge. We show that, again, randomization holds the key for obtaining simple, efficient and distributed information dissemination protocols. In particular, using random back-off strategies to coordinate access to the shared medium leads to optimal gossip-like communications and applying RLNC achieves the first throughput-optimal multi-message communication primitives. Lastly we apply our probabilistic approach for analyzing simple, distributed propagation protocols in a broader context by studying algorithms for the Lovász Local Lemma. These algorithms find solutions to certain local constraint satisfaction problems by randomly fixing and propagating violations locally. Our two main results show that, firstly, there are also efficient deterministic propagation strategies achieving the same and, secondly, using the random fixing strategy has the advantage of producing not just an arbitrary solution but an approximately uniformly random one. Both results lead to simple, constructions for a many locally consistent structures of interest that were not known to be efficiently constructable before.by Bernhard Haeupler.Ph.D

Critical Thinking Skills Profile of High School Students In Learning Science-Physics

This study aims to describe Critical Thinking Skills high school students in the city of Makassar. To achieve this goal, the researchers conducted an analysis of student test results of 200 people scattered in six schools in the city of Makassar. The results of the quantitative descriptive analysis of the data found that the average value of students doing the interpretation, analysis, and inference in a row by 1.53, 1.15, and 1.52. This value is still very low when compared with the maximum value that may be obtained by students, that is equal to 10.00. This shows that the critical thinking skills of high school students are still very low. One fact Competency Standards science subjects-Physics is demonstrating the ability to think logically, critically, and creatively with the guidance of teachers and demonstrate the ability to solve simple problems in daily life. In fact, according to Michael Scriven stated that the main task of education is to train students and or students to think critically because of the demands of work in the global economy, the survival of a democratic and personal decisions and decisions in an increasingly complex society needs people who can think well and make judgments good. Therefore, the need for teachers in the learning device scenario such as: driving question or problem, authentic Investigation: Science Processes

Historical and Conceptual Foundations of Information Physics

The main objective of this dissertation is to philosophically assess how the use of informational concepts in the field of classical thermostatistical physics has historically evolved from the late 1940s to the present day. I will first analyze in depth the main notions that form the conceptual basis on which 'informational physics' historically unfolded, encompassing (i) different entropy, probability and information notions, (ii) their multiple interpretative variations, and (iii) the formal, numerical and semantic-interpretative relationships among them. In the following, I will assess the history of informational thermophysics during the second half of the twentieth century. Firstly, I analyse the intellectual factors that gave rise to this current in the late forties (i.e., popularization of Shannon's theory, interest in a naturalized epistemology of science, etc.), then study its consolidation in the Brillouinian and Jaynesian programs, and finally claim how Carnap (1977) and his disciples tried to criticize this tendency within the scientific community. Then, I evaluate how informational physics became a predominant intellectual current in the scientific community in the nineties, made possible by the convergence of Jaynesianism and Brillouinism in proposals such as that of Tribus and McIrvine (1971) or Bekenstein (1973) and the application of algorithmic information theory into the thermophysical domain. As a sign of its radicality at this historical stage, I explore the main proposals to include information as part of our physical reality, such as Wheeler’s (1990), Stonier’s (1990) or Landauer’s (1991), detailing the main philosophical arguments (e.g., Timpson, 2013; Lombardi et al. 2016a) against those inflationary attitudes towards information. Following this historical assessment, I systematically analyze whether the descriptive exploitation of informational concepts has historically contributed to providing us with knowledge of thermophysical reality via (i) explaining thermal processes such as equilibrium approximation, (ii) advantageously predicting thermal phenomena, or (iii) enabling understanding of thermal property such as thermodynamic entropy. I argue that these epistemic shortcomings would make it impossible to draw ontological conclusions in a justified way about the physical nature of information. In conclusion, I will argue that the historical exploitation of informational concepts has not contributed significantly to the epistemic progress of thermophysics. This would lead to characterize informational proposals as 'degenerate science' (à la Lakatos 1978a) regarding classical thermostatistical physics or as theoretically underdeveloped regarding the study of the cognitive dynamics of scientists in this physical domain

Homeostatic epistemology : reliability, coherence and coordination in a Bayesian virtue epistemology

How do agents with limited cognitive capacities flourish in informationally impoverished or unexpected circumstances? Aristotle argued that human flourishing emerged from knowing about the world and our place within it. If he is right, then the virtuous processes that produce knowledge, best explain flourishing. Influenced by Aristotle, virtue epistemology defends an analysis of knowledge where beliefs are evaluated for their truth and the intellectual virtue or competences relied on in their creation. However, human flourishing may emerge from how degrees of ignorance are managed in an uncertain world. Perhaps decision-making in the shadow of knowledge best explains human wellbeing—a Bayesian approach? In this dissertation I argue that a hybrid of virtue and Bayesian epistemologies explains human flourishing—what I term homeostatic epistemology. \ud \ud Homeostatic epistemology supposes that an agent has a rational credence p when p is the product of reliable processes aligned with the norms of probability theory; whereas an agent knows that p when a rational credence p is the product of reliable processes such that: 1) p meets some relevant threshold for belief (such that the agent acts as though p were true and indeed p is true), 2) p coheres with a satisficing set of relevant beliefs and, 3) the relevant set of beliefs is coordinated appropriately to meet the integrated aims of the agent. \ud \ud Homeostatic epistemology recognizes that justificatory relationships between beliefs are constantly changing to combat uncertainties and to take advantage of predictable circumstances. Contrary to holism, justification is built up and broken down across limited sets like the anabolic and catabolic processes that maintain homeostasis in the cells, organs and systems of the body. It is the coordination of choristic sets of reliably produced beliefs that create the greatest flourishing given the limitations inherent in the situated agent. \u

Ohio State University Bulletin

Classes available for students to enroll in during the 1974-1975 academic year for The Ohio State University

The 25th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting

Papers in the following categories are presented: recent developments in rubidium, cesium, and hydrogen-based frequency standards, and in cryogenic and trapped-ion technology; international and transnational applications of precise time and time interval (PTTI) technology with emphasis on satellite laser tracking networks, GLONASS timing, intercomparison of national time scales and international telecommunication; applications of PTTI technology to the telecommunications, power distribution, platform positioning, and geophysical survey industries; application of PTTI technology to evolving military communications and navigation systems; and dissemination of precise time and frequency by means of GPS, GLONASS, MILSTAR, LORAN, and synchronous communications satellites

Exchange rate misalignments in ASEAN-5 countries

The purpose of this paper is to estimate the exchange rate misalignments for Indonesia, Malaysia, Philippines, Singapore and Thailand before the currency crisis. By employing the sticky-price monetary exchange rate model in the environment of vector error-correction, the results indicate that the Indonesia rupiah, Malaysian ringgit, Philippines peso and Singapore dollar were overvalued before the currency crisis while Thai baht was undervalued on the eve of the crisis. However, they suffered modest misalignment. Therefore, little evidence of exchange misalignment is found to exist in 1997:2. In particular, Indonesia rupiah, Malaysia ringgit, Philippines peso and Singapore dollar were only overvalued about 1 to 4 percent against US dollar while the Thai baht was only 2 percent undervalued against US dollar