OpenRaiser/Intern-Atlas huggingface dataset:
On the information-theoretic structure of distributed measurements
Venue: arXiv cs.IT 2012
Year: 2012

The internal structure of a measuring device, which depends on what its components are and how they are organized, determines how it categorizes its inputs. This paper presents a geometric approach to studying the internal structure of measurements performed by distributed systems such as probabilistic cellular automata. It constructs the quale, a family of sections of a suitably defined presheaf, whose elements correspond to the measurements performed by all subsystems of a distributed system. Using the quale we quantify (i) the information generated by a measurement; (ii) the extent to which a measurement is context-dependent; and (iii) whether a measurement is decomposable into independent submeasurements, which turns out to be equivalent to context-dependence. Finally, we show that only indecomposable measurements are more informative than the sum of their submeasurements.
Experiment-driven Characterization of Full-Duplex Wireless Systems
Venue: arXiv cs.IT 2012
Year: 2012

We present an experiment-based characterization of passive suppression and active self-interference cancellation mechanisms in full-duplex wireless communication systems. In particular, we consider passive suppression due to antenna separation at the same node, and active cancellation in analog and/or digital domain. First, we show that the average amount of cancellation increases for active cancellation techniques as the received self-interference power increases. Our characterization of the average cancellation as a function of the self-interference power allows us to show that for a constant signal-to-interference ratio at the receiver antenna (before any active cancellation is applied), the rate of a full-duplex link increases as the self-interference power increases. Second, we show that applying digital cancellation after analog cancellation can sometimes increase the self-interference, and thus digital cancellation is more effective when applied selectively based on measured suppression values. Third, we complete our study of the impact of self-interference cancellation mechanisms by characterizing the probability distribution of the self-interference channel before and after cancellation.
Nearest Neighbour Decoding with Pilot-Assisted Channel Estimation for Fading Multiple-Access Channels
Venue: arXiv cs.IT 2012
Year: 2012

We study a noncoherent multiple-input multiple-output (MIMO) fading multiple-access channel (MAC), where the transmitters and the receiver are aware of the statistics of the fading, but not of its realisation. We analyse the rate region that is achievable with nearest neighbour decoding and pilot-assisted channel estimation and determine the corresponding pre-log region, which is defined as the limiting ratio of the rate region to the logarithm of the SNR as the SNR tends to infinity.
Matrix powers algorithms for trust evaluation in PKI architectures
Venue: arXiv cs.CR 2012
Year: 2012

This paper deals with the evaluation of trust in public-key infrastructures. Different trust models have been proposed to interconnect the various PKI components in order to propagate the trust between them. In this paper we provide a new polynomial algorithm using linear algebra to assess trust relationships in a network using different trust evaluation schemes. The advantages are twofold: first the use of matrix computations instead of graph algorithms provides an optimized computational solution; second, our algorithm can be used for generic graphs, even in the presence of cycles. Our algorithm is designed to evaluate the trust using all existing (finite) trust paths between entities as a preliminary to any exchanges between PKIs. This can give a precise evaluation of trust, and accelerate for instance cross-certificate validation.
On the Feasibility of Maintenance Algorithms in Dynamic Graphs
Venue: arXiv cs.CC 2012
Year: 2012

Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly disconnected) graph over time naturally leads to the important complexity question: is it better to calculate a new solution from scratch or to adapt the known solution on the prior graph to quickly provide a solution of guaranteed quality for the changed graph? In this paper, we demonstrate that the former is the best approach in some cases, but that there are cases where the latter is feasible. We prove that, under certain conditions, hard problems cannot even be approximated in any reasonable complexity bound --- i.e., even with a large amount of time, having a solution to a very similar graph does not help in computing a solution to the current graph. To achieve this, we formalize the idea as a maintenance algorithm. Using r-Regular Subgraph as the primary example we show that W[1]-hardness for the parameterized approximation problem implies the non-existence of a maintenance algorithm for the given approximation ratio. Conversely we show that Vertex Cover, which is fixed-parameter tractable, has a 2-approximate maintenance algorithm. The implications of NP-hardness and NPO-hardness are also explored.
Fractal Structure of Equipotential Curves on a Continuum Percolation Model
Venue: arXiv cs.NA 2012
Year: 2012

We numerically investigate the electric potential distribution over a two-dimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal conductivity. Using the finite difference method, we solve the generalized Laplace equation and show that in the potential distribution, there appear the {\it{quasi-equipotential clusters}} which approximately and locally have the same values like steps and stairs. Since the quasi-equipotential clusters has the fractal structure, we compute the fractal dimension of equipotential curves and its dependence on the volume fraction over $[0,1]$. The fractal dimension in [1.00, 1.257] has a peak at the percolation threshold $p_c$.
Upper bounds for centerlines
Venue: arXiv cs.CG 2012
Year: 2012

In 2008, Bukh, Matousek, and Nivasch conjectured that for every n-point set S in R^d and every k, 0 <= k <= d-1, there exists a k-flat f in R^d (a "centerflat") that lies at "depth" (k+1) n / (k+d+1) - O(1) in S, in the sense that every halfspace that contains f contains at least that many points of S. This claim is true and tight for k=0 (this is Rado's centerpoint theorem), as well as for k = d-1 (trivial). Bukh et al. showed the existence of a (d-2)-flat at depth (d-1) n / (2d-1) - O(1) (the case k = d-2). In this paper we concentrate on the case k=1 (the case of "centerlines"), in which the conjectured value for the leading constant is 2/(d+2). We prove that 2/(d+2) is an *upper bound* for the leading constant. Specifically, we show that for every fixed d and every n there exists an n-point set in R^d for which no line in R^d lies at depth larger than 2n/(d+2) + o(n). This point set is the "stretched grid"---a set which has been previously used by Bukh et al. for other related purposes. Hence, in particular, the conjecture is now settled for R^3.
Optimizing Index Deployment Order for Evolving OLAP (Extended Version)
Venue: arXiv cs.DB 2012
Year: 2012

Query workloads and database schemas in OLAP applications are becoming increasingly complex. Moreover, the queries and the schemas have to continually \textit{evolve} to address business requirements. During such repetitive transitions, the \textit{order} of index deployment has to be considered while designing the physical schemas such as indexes and MVs. An effective index deployment ordering can produce (1) a prompt query runtime improvement and (2) a reduced total deployment time. Both of these are essential qualities of design tools for quickly evolving databases, but optimizing the problem is challenging because of complex index interactions and a factorial number of possible solutions. We formulate the problem in a mathematical model and study several techniques for solving the index ordering problem. We demonstrate that Constraint Programming (CP) is a more flexible and efficient platform to solve the problem than other methods such as mixed integer programming and A* search. In addition to exact search techniques, we also studied local search algorithms to find near optimal solution very quickly. Our empirical analysis on the TPC-H dataset shows that our pruning techniques can reduce the size of the search space by tens of orders of magnitude. Using the TPC-DS dataset, we verify that our local search algorithm is a highly scalable and stable method for quickly finding a near-optimal solution.
Extended Initiality for Typed Abstract Syntax
Venue: arXiv cs.LO 2012
Year: 2012

Initial Semantics aims at interpreting the syntax associated to a signature as the initial object of some category of 'models', yielding induction and recursion principles for abstract syntax. Zsidó proves an initiality result for simply-typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of models of S in monads. However, the iteration principle her theorem provides only accounts for translations between two languages over a fixed set of object types. We generalize Zsidó's notion of model such that object types may vary, yielding a larger category, while preserving initiality of the syntax therein. Thus we obtain an extended initiality theorem for typed abstract syntax, in which translations between terms over different types can be specified via the associated category-theoretic iteration operator as an initial morphism. Our definitions ensure that translations specified via initiality are type-safe, i.e. compatible with the typing in the source and target language in the obvious sense. Our main example is given via the propositions-as-types paradigm: we specify propositions and inference rules of classical and intuitionistic propositional logics through their respective typed signatures. Afterwards we use the category--theoretic iteration operator to specify a double negation translation from the former to the latter. A second example is given by the signature of PCF. For this particular case, we formalize the theorem in the proof assistant Coq. Afterwards we specify, via the category-theoretic iteration operator, translations from PCF to the untyped lambda calculus.
Minimax-Optimal Bounds for Detectors Based on Estimated Prior Probabilities
Venue: arXiv cs.IT 2012
Year: 2012

In many signal detection and classification problems, we have knowledge of the distribution under each hypothesis, but not the prior probabilities. This paper is aimed at providing theory to quantify the performance of detection via estimating prior probabilities from either labeled or unlabeled training data. The error or {\em risk} is considered as a function of the prior probabilities. We show that the risk function is locally Lipschitz in the vicinity of the true prior probabilities, and the error of detectors based on estimated prior probabilities depends on the behavior of the risk function in this locality. In general, we show that the error of detectors based on the Maximum Likelihood Estimate (MLE) of the prior probabilities converges to the Bayes error at a rate of $n^{-1/2}$, where $n$ is the number of training data. If the behavior of the risk function is more favorable, then detectors based on the MLE have errors converging to the corresponding Bayes errors at optimal rates of the form $n^{-(1+α)/2}$, where $α>0$ is a parameter governing the behavior of the risk function with a typical value $α= 1$. The limit $α\rightarrow \infty$ corresponds to a situation where the risk function is flat near the true probabilities, and thus insensitive to small errors in the MLE; in this case the error of the detector based on the MLE converges to the Bayes error exponentially fast with $n$. We show the bounds are achievable no matter given labeled or unlabeled training data and are minimax-optimal in labeled case.
Turing degrees of multidimensional SFTs
Venue: arXiv cs.CC 2012
Year: 2012

In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). To be more precise, we prove that given any \pizu subset $P$ of $\{0,1\}^\NN$ there is a SFT $X$ such that $P\times\ZZ^2$ is recursively homeomorphic to $X\setminus U$ where $U$ is a computable set of points. As a consequence, if $P$ contains a recursive member, $P$ and $X$ have the exact same set of Turing degrees. On the other hand, we prove that if $X$ contains only non-recursive members, some of its members always have different but comparable degrees. This gives a fairly complete study of Turing degrees of SFTs.
Sparsity without the Complexity: Loss Localisation using Tree Measurements
Venue: arXiv cs.NI 2012
Year: 2012

We study network loss tomography based on observing average loss rates over a set of paths forming a tree -- a severely underdetermined linear problem for the unknown link loss probabilities. We examine in detail the role of sparsity as a regularising principle, pointing out that the problem is technically distinct from others in the compressed sensing literature. While sparsity has been applied in the context of tomography, key questions regarding uniqueness and recovery remain unanswered. Our work exploits the tree structure of path measurements to derive sufficient conditions for sparse solutions to be unique and the condition that $\ell_1$ minimization recovers the true underlying solution. We present a fast single-pass linear algorithm for $\ell_1$ minimization and prove that a minimum $\ell_1$ solution is both unique and sparsest for tree topologies. By considering the placement of lossy links within trees, we show that sparse solutions remain unique more often than is commonly supposed. We prove similar results for a noisy version of the problem.
Cutaneous Force Feedback as a Sensory Subtraction Technique in Haptics
Venue: arXiv cs.RO 2012
Year: 2012

A novel sensory substitution technique is presented. Kinesthetic and cutaneous force feedback are substituted by cutaneous feedback (CF) only, provided by two wearable devices able to apply forces to the index finger and the thumb, while holding a handle during a teleoperation task. The force pattern, fed back to the user while using the cutaneous devices, is similar, in terms of intensity and area of application, to the cutaneous force pattern applied to the finger pad while interacting with a haptic device providing both cutaneous and kinesthetic force feedback. The pattern generated using the cutaneous devices can be thought as a subtraction between the complete haptic feedback (HF) and the kinesthetic part of it. For this reason, we refer to this approach as sensory subtraction instead of sensory substitution. A needle insertion scenario is considered to validate the approach. The haptic device is connected to a virtual environment simulating a needle insertion task. Experiments show that the perception of inserting a needle using the cutaneous-only force feedback is nearly indistinguishable from the one felt by the user while using both cutaneous and kinesthetic feedback. As most of the sensory substitution approaches, the proposed sensory subtraction technique also has the advantage of not suffering from stability issues of teleoperation systems due, for instance, to communication delays. Moreover, experiments show that the sensory subtraction technique outperforms sensory substitution with more conventional visual feedback (VF).
Wireless MIMO Switching with Zero-forcing Relaying and Network-coded Relaying
Venue: arXiv cs.IT 2012
Year: 2012

A wireless relay with multiple antennas is called a multiple-input-multiple-output (MIMO) switch if it maps its input links to its output links using "precode-and-forward." Namely, the MIMO switch precodes the received signal vector in the uplink using some matrix for transmission in the downlink. This paper studies the scenario of $K$ stations and a MIMO switch, which has full channel state information. The precoder at the MIMO switch is either a zero-forcing matrix or a network-coded matrix. With the zero-forcing precoder, each destination station receives only its desired signal with enhanced noise but no interference. With the network-coded precoder, each station receives not only its desired signal and noise, but possibly also self-interference, which can be perfectly canceled. Precoder design for optimizing the received signal-to-noise ratios at the destinations is investigated. For zero-forcing relaying, the problem is solved in closed form in the two-user case, whereas in the case of more users, efficient algorithms are proposed and shown to be close to what can be achieved by extensive random search. For network-coded relaying, we present efficient iterative algorithms that can boost the throughput further.
Ensemble Risk Modeling Method for Robust Learning on Scarce Data
Venue: arXiv cs.LG 2012
Year: 2012

In medical risk modeling, typical data are "scarce": they have relatively small number of training instances (N), censoring, and high dimensionality (M). We show that the problem may be effectively simplified by reducing it to bipartite ranking, and introduce new bipartite ranking algorithm, Smooth Rank, for robust learning on scarce data. The algorithm is based on ensemble learning with unsupervised aggregation of predictors. The advantage of our approach is confirmed in comparison with two "gold standard" risk modeling methods on 10 real life survival analysis datasets, where the new approach has the best results on all but two datasets with the largest ratio N/M. For systematic study of the effects of data scarcity on modeling by all three methods, we conducted two types of computational experiments: on real life data with randomly drawn training sets of different sizes, and on artificial data with increasing number of features. Both experiments demonstrated that Smooth Rank has critical advantage over the popular methods on the scarce data; it does not suffer from overfitting where other methods do.
Generalized Distributive Law for ML Decoding of Space-Time Block Codes
Venue: arXiv cs.IT 2012
Year: 2012

The problem of designing good Space-Time Block Codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well known technique of decoding STBCs as Conditional ML (CML) decoding. In this paper we introduce a new framework to construct ML decoders for STBCs based on the Generalized Distributive Law (GDL) and the Factor-graph based Sum-Product Algorithm. We say that an STBC is fast GDL decodable if the order of GDL decoding complexity of the code is strictly less than M^l, where l is the number of independent symbols in the STBC, and M is the constellation size. We give sufficient conditions for an STBC to admit fast GDL decoding, and show that both multigroup and conditionally multigroup decodable codes are fast GDL decodable. For any STBC, whether fast GDL decodable or not, we show that the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from Cyclic Division Algebras which is not multigroup or conditionally multigroup decodable, the GDL decoder provides about 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only half as complex as the CML decoder.
A Design Methodology for Folded, Pipelined Architectures in VLSI Applications using Projective Space Lattices
Venue: arXiv cs.AR 2012
Year: 2012

Semi-parallel, or folded, VLSI architectures are used whenever hardware resources need to be saved at design time. Most recent applications that are based on Projective Geometry (PG) based balanced bipartite graph also fall in this category. In this paper, we provide a high-level, top-down design methodology to design optimal semi-parallel architectures for applications, whose Data Flow Graph (DFG) is based on PG bipartite graph. Such applications have been found e.g. in error-control coding and matrix computations. Unlike many other folding schemes, the topology of connections between physical elements does not change in this methodology. Another advantage is the ease of implementation. To lessen the throughput loss due to folding, we also incorporate a multi-tier pipelining strategy in the design methodology. The design methodology has been verified by implementing a synthesis tool in C++, which has been verified as well. The tool is publicly available. Further, a complete decoder was manually protototyped before the synthesis tool design, to verify all the algorithms evolved in this paper, towards various steps of refinement. Another specific high-performance design of an LDPC decoder based on this methodology was worked out in past, and has been patented as well.
Trading Order for Degree in Creative Telescoping
Venue: arXiv cs.SC 2012
Year: 2012

We analyze the differential equations produced by the method of creative telescoping applied to a hyperexponential term in two variables. We show that equations of low order have high degree, and that higher order equations have lower degree. More precisely, we derive degree bounding formulas which allow to estimate the degree of the output equations from creative telescoping as a function of the order. As an application, we show how the knowledge of these formulas can be used to improve, at least in principle, the performance of creative telescoping implementations, and we deduce bounds on the asymptotic complexity of creative telescoping for hyperexponential terms.
A unified formulation of Gaussian vs. sparse stochastic processes - Part I: Continuous-domain theory
Venue: arXiv cs.IT 2012
Year: 2012

We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized white noise process, which may be Gaussian or not (e.g., Laplace, impulsive Poisson or alpha stable). This allows for a conceptual decoupling between the correlation properties of the process, which are imposed by the whitening operator L, and its sparsity pattern which is determined by the type of noise excitation. The latter is fully specified by a Levy measure. We show that the range of admissible innovation behavior varies between the purely Gaussian and super-sparse extremes. We prove that the corresponding generalized stochastic processes are well-defined mathematically provided that the (adjoint) inverse of the whitening operator satisfies some Lp bound for p>=1. We present a novel operator-based method that yields an explicit characterization of all Levy-driven processes that are solutions of constant-coefficient stochastic differential equations. When the underlying system is stable, we recover the family of stationary CARMA processes, including the Gaussian ones. The approach remains valid when the system is unstable and leads to the identification of potentially useful generalizations of the Levy processes, which are sparse and non-stationary. Finally, we show how we can apply finite difference operators to obtain a stationary characterization of these processes that is maximally decoupled and stable, irrespective of the location of the poles in the complex plane.