An exponential separation between MA and AM proofs of proximity

Interactive proofs of proximity allow a sublinear-time verifier to check that a given input is close to the language, using a small amount of communication with a powerful (but untrusted) prover. In this work we consider two natural minimally interactive variants of such proofs systems, in which the prover only sends a single message, referred to as the proof. The first variant, known as MA-proofs of Proximity (MAP), is fully non-interactive, meaning that the proof is a function of the input only. The second variant, known as AM-proofs of Proximity (AMP), allows the proof to additionally depend on the verifier's (entire) random string. The complexity of both MAPs and AMPs is the total number of bits that the verifier observes - namely, the sum of the proof length and query complexity. Our main result is an exponential separation between the power of MAPs and AMPs. Specifically, we exhibit an explicit and natural property Pi that admits an AMP with complexity O(log n), whereas any MAP for Pi has complexity Omega~(n^{1/4}), where n denotes the length of the input in bits. Our MAP lower bound also yields an alternate proof, which is more general and arguably much simpler, for a recent result of Fischer et al. (ITCS, 2014). Lastly, we also consider the notion of oblivious proofs of proximity, in which the verifier's queries are oblivious to the proof. In this setting we show that AMPs can only be quadratically stronger than MAPs. As an application of this result, we show an exponential separation between the power of public and private coin for oblivious interactive proofs of proximity

On the Complexity of Value Iteration

Value iteration is a fundamental algorithm for solving Markov Decision Processes (MDPs). It computes the maximal n-step payoff by iterating n times a recurrence equation which is naturally associated to the MDP. At the same time, value iteration provides a policy for the MDP that is optimal on a given finite horizon n. In this paper, we settle the computational complexity of value iteration. We show that, given a horizon n in binary and an MDP, computing an optimal policy is EXPTIME-complete, thus resolving an open problem that goes back to the seminal 1987 paper on the complexity of MDPs by Papadimitriou and Tsitsiklis. To obtain this main result, we develop several stepping stones that yield results of an independent interest. For instance, we show that it is EXPTIME-complete to compute the n-fold iteration (with n in binary) of a function given by a straight-line program over the integers with max and + as operators. We also provide new complexity results for the bounded halting problem in linear-update counter machines

Neural information extraction from natural language text

Natural language processing (NLP) deals with building computational techniques that allow computers to automatically analyze and meaningfully represent human language. With an exponential growth of data in this digital era, the advent of NLP-based systems has enabled us to easily access relevant information via a wide range of applications, such as web search engines, voice assistants, etc. To achieve it, a long-standing research for decades has been focusing on techniques at the intersection of NLP and machine learning. In recent years, deep learning techniques have exploited the expressive power of Artificial Neural Networks (ANNs) and achieved state-of-the-art performance in a wide range of NLP tasks. Being one of the vital properties, Deep Neural Networks (DNNs) can automatically extract complex features from the input data and thus, provide an alternative to the manual process of handcrafted feature engineering. Besides ANNs, Probabilistic Graphical Models (PGMs), a coupling of graph theory and probabilistic methods have the ability to describe causal structure between random variables of the system and capture a principled notion of uncertainty. Given the characteristics of DNNs and PGMs, they are advantageously combined to build powerful neural models in order to understand the underlying complexity of data. Traditional machine learning based NLP systems employed shallow computational methods (e.g., SVM or logistic regression) and relied on handcrafting features which is time-consuming, complex and often incomplete. However, deep learning and neural network based methods have recently shown superior results on various NLP tasks, such as machine translation, text classification, namedentity recognition, relation extraction, textual similarity, etc. These neural models can automatically extract an effective feature representation from training data. This dissertation focuses on two NLP tasks: relation extraction and topic modeling. The former aims at identifying semantic relationships between entities or nominals within a sentence or document. Successfully extracting the semantic relationships greatly contributes in building structured knowledge bases, useful in downstream NLP application areas of web search, question-answering, recommendation engines, etc. On other hand, the task of topic modeling aims at understanding the thematic structures underlying in a collection of documents. Topic modeling is a popular text-mining tool to automatically analyze a large collection of documents and understand topical semantics without actually reading them. In doing so, it generates word clusters (i.e., topics) and document representations useful in document understanding and information retrieval, respectively. Essentially, the tasks of relation extraction and topic modeling are built upon the quality of representations learned from text. In this dissertation, we have developed task-specific neural models for learning representations, coupled with relation extraction and topic modeling tasks in the realms of supervised and unsupervised machine learning paradigms, respectively. More specifically, we make the following contributions in developing neural models for NLP tasks: 1. Neural Relation Extraction: Firstly, we have proposed a novel recurrent neural network based architecture for table-filling in order to jointly perform entity and relation extraction within sentences. Then, we have further extended our scope of extracting relationships between entities across sentence boundaries, and presented a novel dependency-based neural network architecture. The two contributions lie in the supervised paradigm of machine learning. Moreover, we have contributed in building a robust relation extractor constrained by the lack of labeled data, where we have proposed a novel weakly-supervised bootstrapping technique. Given the contributions, we have further explored interpretability of the recurrent neural networks to explain their predictions for the relation extraction task. 2. Neural Topic Modeling: Besides the supervised neural architectures, we have also developed unsupervised neural models to learn meaningful document representations within topic modeling frameworks. Firstly, we have proposed a novel dynamic topic model that captures topics over time. Next, we have contributed in building static topic models without considering temporal dependencies, where we have presented neural topic modeling architectures that also exploit external knowledge, i.e., word embeddings to address data sparsity. Moreover, we have developed neural topic models that incorporate knowledge transfers using both the word embeddings and latent topics from many sources. Finally, we have shown improving neural topic modeling by introducing language structures (e.g., word ordering, local syntactic and semantic information, etc.) that deals with bag-of-words issues in traditional topic models. The class of proposed neural NLP models in this section are based on techniques at the intersection of PGMs, deep learning and ANNs. Here, the task of neural relation extraction employs neural networks to learn representations typically at the sentence level, without access to the broader document context. However, topic models have access to statistical information across documents. Therefore, we advantageously combine the two complementary learning paradigms in a neural composite model, consisting of a neural topic and a neural language model that enables us to jointly learn thematic structures in a document collection via the topic model, and word relations within a sentence via the language model. Overall, our research contributions in this dissertation extend NLP-based systems for relation extraction and topic modeling tasks with state-of-the-art performances

Security and Privacy Issues in Wireless Mesh Networks: A Survey

This book chapter identifies various security threats in wireless mesh network (WMN). Keeping in mind the critical requirement of security and user privacy in WMNs, this chapter provides a comprehensive overview of various possible attacks on different layers of the communication protocol stack for WMNs and their corresponding defense mechanisms. First, it identifies the security vulnerabilities in the physical, link, network, transport, application layers. Furthermore, various possible attacks on the key management protocols, user authentication and access control protocols, and user privacy preservation protocols are presented. After enumerating various possible attacks, the chapter provides a detailed discussion on various existing security mechanisms and protocols to defend against and wherever possible prevent the possible attacks. Comparative analyses are also presented on the security schemes with regards to the cryptographic schemes used, key management strategies deployed, use of any trusted third party, computation and communication overhead involved etc. The chapter then presents a brief discussion on various trust management approaches for WMNs since trust and reputation-based schemes are increasingly becoming popular for enforcing security in wireless networks. A number of open problems in security and privacy issues for WMNs are subsequently discussed before the chapter is finally concluded.Comment: 62 pages, 12 figures, 6 tables. This chapter is an extension of the author's previous submission in arXiv submission: arXiv:1102.1226. There are some text overlaps with the previous submissio

Analysis of gamma-band activity from human EEG using empirical mode decomposition

The purpose of this paper is to determine whether gamma-band activity detection is improved when a filter, based on empirical mode decomposition (EMD), is added to the pre-processing block of single-channel electroencephalography (EEG) signals. EMD decomposes the original signal into a finite number of intrinsic mode functions (IMFs). EEGs from 25 control subjects were registered in basal and motor activity (hand movements) using only one EEG channel. Over the basic signal, IMF signals are computed. Gamma-band activity is computed using power spectrum density in the 30–60 Hz range. Event-related synchronization (ERS) was defined as the ratio of motor and basal activity. To evaluate the performance of the new EMD based method, ERS was computed from the basic and IMF signals. The ERS obtained using IMFs improves, from 31.00% to 73.86%, on the original ERS for the right hand, and from 22.17% to 47.69% for the left hand. As EEG processing is improved, the clinical applications of gamma-band activity will expand.Universidad de AlcaláInstituto de Salud Carlos II

Air Force Institute of Technology Research Report 2011

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems and Engineering Management, Operational Sciences, Mathematics, Statistics and Engineering Physics