Deterministic Extractors for Small-Space Sources

We give polynomial-time, deterministic randomness extractors for sources generated in small space, where we model space s sources on n{0,1} as sources generated by width s2 branching programs. Specifically, there is a constant η>0 such that for any ζ>n−η, our algorithm extracts m=(δ−ζ)n bits that are exponentially close to uniform (in variation distance) from space s sources with min-entropy δn, where s=Ω(ζ3n). Previously, nothing was known for δ≤1/2, even for space 0. Our results are obtained by a reduction to the class of total-entropy independent sources. This model generalizes both the well-studied models of independent sources and symbol-fixing sources. These sources consist of a set of r independent smaller sources over ℓ{0,1}, where the total min-entropy over all the smaller sources is k. We give deterministic extractors for such sources when k is as small as polylog(r), for small enough ℓ.Engineering and Applied Science

Extractors for Adversarial Sources via Extremal Hypergraphs

Randomness extraction is a fundamental problem that has been studied for over three decades. A well-studied setting assumes that one has access to multiple independent weak random sources, each with some entropy. However, this assumption is often unrealistic in practice. In real life, natural sources of randomness can produce samples with no entropy at all or with unwanted dependence. Motivated by this and applications from cryptography, we initiate a systematic study of randomness extraction for the class of adversarial sources defined as follows. A weak source $\mathbf{X}$ of the form $\mathbf{X}_1,...,\mathbf{X}_N$, where each $\mathbf{X}_i$ is on $n$ bits, is an $(N,K,n,k)$-source of locality $d$ if the following hold: (1) Somewhere good sources: at least $K$ of the $\mathbf{X}_i$\u27s are independent, and each contains min-entropy at least $k$. We call these $\mathbf{X}_i$\u27s good sources, and their locations are unknown. (2) Bounded dependence: each remaining (bad) source can depend arbitrarily on at most $d$ good sources. We focus on constructing extractors with negligible error, in the regime where most of the entropy is contained within a few sources instead of across many (i.e., $k$ is at least polynomial in $K$). In this setting, even for the case of $0$-locality, very little is known prior to our work. For $d \geq 1$, essentially no previous results are known. We present various new extractors for adversarial sources in a wide range of parameters, and some of our constructions work for locality $d = K^{\Omega(1)}$. As an application, we also give improved extractors for small-space sources. The class of adversarial sources generalizes several previously studied classes of sources, and our explicit extractor constructions exploit tools from recent advances in extractor machinery, such as two-source non-malleable extractors and low-error condensers. Thus, our constructions can be viewed as a new application of non-malleable extractors. In addition, our constructions combine the tools from extractor theory in a novel way through various sorts of explicit extremal hypergraphs. These connections leverage recent progress in combinatorics, such as improved bounds on cap sets and explicit constructions of Ramsey graphs, and may be of independent interest

Deterministic extractors

textComputer Science

Deterministic Extractors for Bit-Fixing Sources and Exposure-Resilient Cryptography

Abstract We give an efficient deterministic algorithm which ex-tracts \Omega (n2g) almost-random bits from sources where n 12 +g of the n bits are uniformly random and the rest are fixed inadvance. This improves on previous constructions which required that at least n=2 of the bits be random. Our construc-tion also gives explicit adaptive exposure-resilient functions and in turn adaptive all-or-nothing transforms. For sourceswhere instead of bits the values are chosen from [d], ford? 2, we give an algorithm which extracts a constant frac-tion of the randomness. We also give bounds on extractin

Creating seamless self-checkout areas in supermarkets using automatic customer exit control

This thesis is result of an assignment set up by Pan Oston. Pan Oston is a company who makes steel product like checkouts and kiosks for the retail market. A sizable part of Pan Oston’s revenue are checkouts and self-checkouts (SCOs). It is expected that in the future of retail these products are less relevant. This is why Pan Oston has requested the design of an improved gate that will be used in self-checkout areas and in future checkoutless stores. It is also requested to design a system that replaces the currently often used barcode scanner that automatically lets people pass the gate or block them.A gate is designed that improves upon existing gates in terms of communication, seamlessness and ease-of-use. The goal of this gate is to make it easy and pleasant for customers to leave the SCO area while supporting the SCO host by giving him/her more control. By using animated green, orange and red lights that are intuitively integrated in the gate, communication between customer and gate is optimized. Sounds are played in case of a warning or an alarm. This gives customers extra hints on what is going on but most importantly alerts the host and other store personnel of the gate’s current situation so that they are always aware even if they are not looking. The gate can be customized if needed, which is one of Pan Oston specialties. In summary the gate improves upon its competing gates in communication, looks, focus on the host and theft-prevention.For the auto-passthrough system Bluetooth Low Energy (BLE) is used. By attaching BLE signal emitter to the baskets and carts and by placing BLE signal receivers at the SCOs and gate we can keep track of who has paid and who has not and let them leave or block them accordingly. BLE is used because the system will be applied in existing and future supermarkets that use SCO areas. These are supermarkets people are often dependent on so we cannot use biometric technology like face recognition, even though these technologies are incredibly powerful. Because not all customers will like being a part of these technologies, they cannot be applied in these stores. The flip side is that it is now mandatory to use a basket or cart and no more than 1 basket or cart is allowed per group that shops together.Integrated Product Desig

Deterministic Extractors For Small-Space Sources

We give polynomial-time, deterministic randomness extractors for sources generated in small space, where we model space s sources on {0, 1} n as sources generated by width 2 s branching programs. Specifically, there is a constant η> 0 such that for any ζ> n −η, our algorithm extracts m = (δ−ζ)n bits that are exponentially close to uniform (in variation distance) from space s sources with min-entropy δn, where s = Ω(ζ 3 n). Previously, nothing was known for δ ≤ 1/2, even for space 0. Our results are obtained by a reduction to the class of total-entropy independent sources. This model generalizes both the well-studied models of independent sources and symbol-fixing sources. These sources consist of a set of r independent smaller sources over {0, 1} ℓ, where the total min-entropy over all the smaller sources is k. We give deterministic extractors for such sources when k is as small a

Query Optimization in Oracle 12c Database In-Memory

Traditional on disk row major tables have been the dominant storage mechanism in relational databases for decades. Over the last decade, however, with explosive growth in data volume and demand for faster analytics, has come the recognition that a different data representation is needed. There is widespread agreement that in-memory column-oriented databases are best suited to meet the realities of this new world. Oracle 12c Database In-memory, the industry’s first dual-format database, allows existing row major on-disk tables to have complementary in-memory columnar representations. The new storage format brings new data processing techniques and query execution algorithms and thus new challenges for the query optimizer. Execution plans that are optimal for one format may be sub-optimal for the other. In this paper, we describe the changes made in the query optimizer to generate execution plans optimized for the specific format – row major or columnar – that will be scanned during query execution. With enhancements in several areas – statistics, cost model, query transformation, access pat h and join optimization, parallelism, and cluster - awareness – the query optimizer plays a significant role in unlocking the full promise and performance of Oracle Database In-Memory

Automatic classification of strike techniques using limb trajectory data

The classification of trajectory data is required in a wide variety of movement tracking experiments. Automatic classification using machine learning techniques has the potential to greatly increase efficiency and reliability of these studies. Here, we apply supervised classification algorithms on a dataset obtained through a kickboxing experiment to classify the limb and technique that was used for each strike as well as the expertise of the person performing the strike. Beginner and expert kickboxers were asked to strike a boxing bag from several distances, producing a dataset of approximately 4000 strike trajectories. These trajectories were classified using the K-nearest neighbours (KNN) and multi-class linear support vector classification (SVC). We show that both of these algorithms are capable of correctly classifying the limb used for the strike with ∼99% prediction accuracy. Both algorithms could classify the techniques used with ∼86% accuracy. The accuracy of technique classification was improved even further by applying hierarchical classification, classifying techniques separately for each limb. Only 10% of the dataset was required as training set to approach the observed prediction accuracy. Finally, KNN was capable of classifying the strikes by skill level with 73.3% accuracy. These findings demonstrate the potential of using supervised classification on complex limb trajectory datasets