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1201.6313
|
On X-Channels with Feedback and Delayed CSI
|
cs.IT math.IT
|
The sum degrees of freedom (DoF) of the two-user MIMO X-channel is
characterized in the presence of output feedback and delayed channel state
information (CSI). The number of antennas at each transmitters is assumed to be
M and the number of antennas at each of the receivers is assumed to be N. It is
shown that the sum DoF of the two-user MIMO X-channel is the same as the sum
DoF of a two-user MIMO broadcast channel with 2M transmit antennas, and N
antennas at each receiver. Hence, for this symmetric antenna configuration,
there is no performance loss in the sum degrees of freedom due to the
distributed nature of the transmitters. This result highlights the usefulness
of feedback and delayed CSI for the MIMO X-channel.
The K-user X-channel with single antenna at each transmitter and each
receiver is also studied. In this network, each transmitter has a message
intended for each receiver. For this network, it is shown that the sum DoF with
partial output feedback alone is at least 2K/(K+1). This lower bound is
strictly better than the best lower bound known for the case of delayed CSI
assumption for all values of K.
|
1201.6322
|
The Cooperative Cleaners Problem in Stochastic Dynamic Environments
|
cs.MA
|
In this paper we study the strengths and limitations of collaborative teams
of simple agents. In particular, we discuss the efficient use of "ant robots"
for covering a connected region on the $Z^{2}$ grid, whose area is unknown in
advance and which expands stochastically. Specifically, we discuss the problem
where an initial connected region of $S_0$ boundary tiles expand outward with
probability $p$ at every time step. On this grid region a group of $k$ limited
and simple agents operate, in order to clean the unmapped and dynamically
expanding region. A preliminary version of this problem was discussed in
[1],[2] involving a deterministic expansion of a region in the grid.In this
work we extend the model and examine cases where the spread of the region is
done stochastically, where each tile has some probability $p$ to expand, at
every time step. For this extended model we obtain an analytic probabilistic
lower bounds for the minimal number of agents and minimal time required to
enable a collaborative coverage of the expanding region, regardless of the
algorithm used and the robots' hardware and software specifications. In
addition, we present an impossibility result, for a variety of regions that
would be impossible to completely clean, regardless of the algorithm used.
Finally, we validate the analytic bounds using extensive empirical computer
simulation results.
|
1201.6339
|
Epidemics on Interconnected Networks
|
physics.soc-ph cond-mat.dis-nn cs.SI
|
Populations are seldom completely isolated from their environment.
Individuals in a particular geographic or social region may be considered a
distinct network due to strong local ties, but will also interact with
individuals in other networks. We study the susceptible-infected-recovered
(SIR) process on interconnected network systems, and find two distinct regimes.
In strongly-coupled network systems, epidemics occur simultaneously across the
entire system at a critical infection strength $\beta_c$, below which the
disease does not spread. In contrast, in weakly-coupled network systems, a
mixed phase exists below $\beta_c$ of the coupled network system, where an
epidemic occurs in one network but does not spread to the coupled network. We
derive an expression for the network and disease parameters that allow this
mixed phase and verify it numerically. Public health implications of
communities comprising these two classes of network systems are also mentioned.
|
1201.6358
|
Deterministic Polynomial-Time Algorithms for Designing Short DNA Words
|
cs.DS cs.CE cs.IT math.IT
|
Designing short DNA words is a problem of constructing a set (i.e., code) of
n DNA strings (i.e., words) with the minimum length such that the Hamming
distance between each pair of words is at least k and the n words satisfy a set
of additional constraints. This problem has applications in, e.g., DNA
self-assembly and DNA arrays. Previous works include those that extended
results from coding theory to obtain bounds on code and word sizes for
biologically motivated constraints and those that applied heuristic local
searches, genetic algorithms, and randomized algorithms. In particular, Kao,
Sanghi, and Schweller (2009) developed polynomial-time randomized algorithms to
construct n DNA words of length within a multiplicative constant of the
smallest possible word length (e.g., 9 max{log n, k}) that satisfy various sets
of constraints with high probability. In this paper, we give deterministic
polynomial-time algorithms to construct DNA words based on derandomization
techniques. Our algorithms can construct n DNA words of shorter length (e.g.,
2.1 log n + 6.28 k) and satisfy the same sets of constraints as the words
constructed by the algorithms of Kao et al. Furthermore, we extend these new
algorithms to construct words that satisfy a larger set of constraints for
which the algorithms of Kao et al. do not work.
|
1201.6371
|
Standard decomposition of expansive ergodically supported dynamics
|
math.DS cs.IT math.GR math.IT
|
In this work we introduce the notion of weak quasigroups, that are quasigroup
operations defined almost everywhere on some set. Then we prove that the
topological entropy and the ergodic period of an invertible expansive
ergodically supported dynamical system $(X,T)$ with the shadowing property
establishes a sufficient criterion for the existence of quasigroup operations
defined almost everywhere outside of universally null sets and for which $T$ is
an automorphism. Furthermore, we find a decomposition of the dynamics of $T$ in
terms of $T$-invariant weak topological subquasigroups.
|
1201.6397
|
List Decoding of Matrix-Product Codes from nested codes: an application
to Quasi-Cyclic codes
|
cs.IT math.IT
|
A list decoding algorithm for matrix-product codes is provided when $C_1,...,
C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We
estimate the probability of getting more than one codeword as output when the
constituent codes are Reed-Solomon codes. We extend this list decoding
algorithm for matrix-product codes with polynomial units, which are
quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for
matrix-product codes with polynomial units.
|
1201.6398
|
Conditional and unconditional information inequalities: an algebraic
example
|
cs.IT math.IT math.PR
|
We provide a simple example showing that some conditional information
inequalities (even in a weak form) cannot be derived from unconditional
inequalities.
|
1201.6402
|
A Note on Disk Drag Dynamics
|
cs.PF cs.DB physics.class-ph
|
The electrical power consumed by typical magnetic hard disk drives (HDD) not
only increases linearly with the number of spindles but, more significantly, it
increases as very fast power-laws of speed (RPM) and diameter. Since the
theoretical basis for this relationship is neither well-known nor readily
accessible in the literature, we show how these exponents arise from
aerodynamic disk drag and discuss their import for green storage capacity
planning.
|
1201.6425
|
No input symbol should occur more frequently than 1-1/e
|
cs.IT math.IT
|
Consider any discrete memoryless channel (DMC) with arbitrarily but finite
input and output alphabets X, Y respectively. Then, for any capacity achieving
input distribution all symbols occur less frequently than 1-1/e$. That is, \[
\max\limits_{x \in \mathcal{X}} P^*(x) < 1-\frac{1}{e} \] \noindent where
$P^*(x)$ is a capacity achieving input distribution. Also, we provide
sufficient conditions for which a discrete distribution can be a capacity
achieving input distribution for some DMC channel. Lastly, we show that there
is no similar restriction on the capacity achieving output distribution.
|
1201.6453
|
A Greedy Algorithm of Data-Dependent User Selection for Fast Fading
Gaussian Vector Broadcast Channels
|
cs.IT math.IT
|
User selection (US) with Zero-forcing beamforming is considered in fast
fading Gaussian vector broadcast channels with perfect channel state
information (CSI) at the transmitter. A novel criterion for US is proposed,
which depends on both CSI and the data symbols, while conventional criteria
only depend on CSI. Since the optimization of US based on the proposed
criterion is infeasible, a greedy algorithm of data-dependent US is proposed to
perform the optimization approximately. An overhead issue arises in fast fading
channels: On every update of US, the transmitter might inform each user whether
he/she has been selected, using a certain fraction of resources. This overhead
results in a significant rate loss for fast fading channels. In order to
circumvent this overhead issue, iterative detection and decoding schemes are
proposed on the basis of belief propagation. The proposed iterative schemes
require no information about whether each user has been selected. The proposed
US scheme is compared to a data-independent US scheme. The complexity of the
two schemes is comparable to each other for fast fading channels. Numerical
simulations show that the proposed scheme can outperform the data-independent
scheme for fast fading channels in terms of energy efficiency, bit error rate,
and achievable sum rate.
|
1201.6459
|
A Matroidal Framework for Network-Error Correcting Codes
|
cs.IT math.IT
|
We abstract the essential aspects of network-error detecting and correcting
codes to arrive at the definitions of matroidal error detecting networks and
matroidal error correcting networks. An acyclic network (with arbitrary sink
demands) is then shown to possess a scalar linear error detecting (correcting)
network code if and only if it is a matroidal error detecting (correcting)
network associated with a representable matroid. Therefore, constructing such
network-error correcting and detecting codes implies the construction of
certain representable matroids that satisfy some special conditions, and vice
versa. We then present algorithms which enable the construction of matroidal
error detecting and correcting networks with a specified capability of
network-error correction. Using these construction algorithms, a large class of
hitherto unknown scalar linearly solvable networks with multisource multicast
and multiple-unicast network-error correcting codes is made available for
theoretical use and practical implementation, with parameters such as number of
information symbols, number of sinks, number of coding nodes, error correcting
capability, etc. being arbitrary but for computing power (for the execution of
the algorithms). The complexity of the construction of these networks is shown
to be comparable to the complexity of existing algorithms that design multicast
scalar linear network-error correcting codes. Finally we also show that linear
network coding is not sufficient for the general network-error detection
problem with arbitrary demands. In particular, for the same number of
network-errors, we show a network for which there is a nonlinear network-error
detecting code satisfying the demands at the sinks, while there are no linear
network-error detecting codes that do the same.
|
1201.6462
|
Active Learning of Custering with Side Information Using $\eps$-Smooth
Relative Regret Approximations
|
cs.LG
|
Clustering is considered a non-supervised learning setting, in which the goal
is to partition a collection of data points into disjoint clusters. Often a
bound $k$ on the number of clusters is given or assumed by the practitioner.
Many versions of this problem have been defined, most notably $k$-means and
$k$-median.
An underlying problem with the unsupervised nature of clustering it that of
determining a similarity function. One approach for alleviating this difficulty
is known as clustering with side information, alternatively, semi-supervised
clustering. Here, the practitioner incorporates side information in the form of
"must be clustered" or "must be separated" labels for data point pairs. Each
such piece of information comes at a "query cost" (often involving human
response solicitation). The collection of labels is then incorporated in the
usual clustering algorithm as either strict or as soft constraints, possibly
adding a pairwise constraint penalty function to the chosen clustering
objective.
Our work is mostly related to clustering with side information. We ask how to
choose the pairs of data points. Our analysis gives rise to a method provably
better than simply choosing them uniformly at random. Roughly speaking, we show
that the distribution must be biased so as more weight is placed on pairs
incident to elements in smaller clusters in some optimal solution. Of course we
do not know the optimal solution, hence we don't know the bias. Using the
recently introduced method of $\eps$-smooth relative regret approximations of
Ailon, Begleiter and Ezra, we can show an iterative process that improves both
the clustering and the bias in tandem. The process provably converges to the
optimal solution faster (in terms of query cost) than an algorithm selecting
pairs uniformly.
|
1201.6465
|
An Information-Spectrum Approach to the Capacity Region of General
Interference Channel
|
cs.IT math.IT
|
This paper is concerned with general interference channels characterized by a
sequence of transition (conditional) probabilities. We present a general
formula for the capacity region of the interference channel with two pairs of
users. The formula shows that the capacity region is the union of a family of
rectangles, where each rectangle is determined by a pair of spectral inf-mutual
information rates. Although the presented formula is usually difficult to
compute, it provides us useful insights into the interference channels. For
example, the formula suggests us that the simplest inner bounds (obtained by
treating the interference as noise) could be improved by taking into account
the structure of the interference processes. This is verified numerically by
computing the mutual information rates for Gaussian interference channels with
embedded convolutional codes.
|
1201.6468
|
Broadcast Channels with Confidential Messages by Randomness Constrained
Stochastic Encoder
|
cs.IT math.IT
|
In coding schemes for the wire-tap channel or the broadcast channels with
confidential messages, it is well known that the sender needs to use a
stochastic encoding to avoid the information about the transmitted confidential
message to be leaked to an eavesdropper. In this paper, it is investigated that
the trade-off between the rate of the random number to realize the stochastic
encoding and the rates of the common, private, and confidential messages. For
the direct theorem, the superposition coding scheme for the wire-tap channel
recently proposed by Chia and El Gamal is employed, and its strong security is
proved. The matching converse theorem is also established. Our result clarifies
that a combination of the ordinary stochastic encoding and the channel
prefixing by the channel simulation is suboptimal.
|
1201.6499
|
Power Control in Multiuser Mulicarrier Wireless Data Networks
|
cs.IT math.IT
|
A game-theoretic model is presented to study the management of transmission
power in a wireless data network. We propose a power game for a multiuser
multicarrier setting where all the users are assumed to transmit at equal rate.
At equilibrium, each user is shown to transmit over a single carrier, as in
[Mehskati et al., 2006]. We derive the necessary conditions on the path gains
when the Nash equilibrium point exists. We further prove the existence of the
Nash equilibrium point using the concept of locally gross direction preserving
map. A greedy algorithm is proposed and its correctness is established, where
each user acts selfishly to achieve the Nash equilibrium point.
|
1201.6511
|
Ontologies for the Integration of Air Quality Models and 3D City Models
|
cs.AI
|
The holistic approach to sustainable urban planning implies using different
models in an integrated way that is capable of simulating the urban system. As
the interconnection of such models is not a trivial task, one of the key
elements that may be applied is the description of the urban geometric
properties in an "interoperable" way. Focusing on air quality as one of the
most pronounced urban problems, the geometric aspects of a city may be
described by objects such as those defined in CityGML, so that an appropriate
air quality model can be applied for estimating the quality of the urban air on
the basis of atmospheric flow and chemistry equations.
In this paper we first present theoretical background and motivations for the
interconnection of 3D city models and other models related to sustainable
development and urban planning. Then we present a practical experiment based on
the interconnection of CityGML with an air quality model. Our approach is based
on the creation of an ontology of air quality models and on the extension of an
ontology of urban planning process (OUPP) that acts as an ontology mediator.
|
1201.6527
|
Control Communication Complexity of Distributed Actions
|
cs.SY
|
Recent papers have treated {\em control communication complexity} in the
context of information-based, multiple agent control systems including
nonlinear systems of the type that have been studied in connection with quantum
information processing. The present paper continues this line of investigation
into a class of two-agent distributed control systems in which the agents
cooperate in order to realize common goals that are determined via independent
actions undertaken individually by the agents. A basic assumption is that the
actions taken are unknown in advance to the other agent. These goals can be
conveniently summarized in the form of a {\em target matrix}, whose entries are
computed by the control system responding to the choices of inputs made by the
two agents. We show how to realize such target matrices for a broad class of
systems that possess an input-output mapping that is bilinear. One can classify
control-communication strategies, known as {\em control protocols}, according
to the amount of information sharing occurring between the two agents.
Protocols that assume no information sharing on the inputs that each agent
selects and protocols that allow sufficient information sharing for identifying
the common goals are the two extreme cases. Control protocols will also be
evaluated and compared in terms of cost functionals given by integrated
quadratic functions of the control inputs. The minimal control cost of the two
classes of control protocols are analyzed and compared. The difference in the
control costs between the two classes reflects an inherent trade-off between
communication complexity and control cost.
|
1201.6530
|
Random Feature Maps for Dot Product Kernels
|
cs.LG cs.CG math.FA stat.ML
|
Approximating non-linear kernels using feature maps has gained a lot of
interest in recent years due to applications in reducing training and testing
times of SVM classifiers and other kernel based learning algorithms. We extend
this line of work and present low distortion embeddings for dot product kernels
into linear Euclidean spaces. We base our results on a classical result in
harmonic analysis characterizing all dot product kernels and use it to define
randomized feature maps into explicit low dimensional Euclidean spaces in which
the native dot product provides an approximation to the dot product kernel with
high confidence.
|
1201.6533
|
Cyclic codes over $M_2(\F_2)$
|
cs.IT math.IT math.RA
|
The ring in the title is the first non commutative ring to have been used as
alphabet for block codes. The original motivation was the construction of some
quaternionic modular lattices from codes. The new application is the
construction of space time codes obtained by concatenation from the Golden
code. In this article, we derive structure theorems for cyclic codes over that
ring, and use them to characterize the lengths where self dual cyclic codes
exist. These codes in turn give rise to formally self dual quaternary codes.
|
1201.6548
|
Orthogonal Multiple Access with Correlated Sources: Feasible Region and
Pragmatic Schemes
|
cs.IT math.IT
|
In this paper, we consider orthogonal multiple access coding schemes, where
correlated sources are encoded in a distributed fashion and transmitted,
through additive white Gaussian noise (AWGN) channels, to an access point (AP).
At the AP, component decoders, associated with the source encoders, iteratively
exchange soft information by taking into account the source correlation. The
first goal of this paper is to investigate the ultimate achievable performance
limits in terms of a multi-dimensional feasible region in the space of channel
parameters, deriving insights on the impact of the number of sources. The
second goal is the design of pragmatic schemes, where the sources use
"off-the-shelf" channel codes. In order to analyze the performance of given
coding schemes, we propose an extrinsic information transfer (EXIT)-based
approach, which allows to determine the corresponding multi-dimensional
feasible regions. On the basis of the proposed analytical framework, the
performance of pragmatic coded schemes, based on serially concatenated
convolutional codes (SCCCs), is discussed.
|
1201.6563
|
Relation Strength-Aware Clustering of Heterogeneous Information Networks
with Incomplete Attributes
|
cs.DB
|
With the rapid development of online social media, online shopping sites and
cyber-physical systems, heterogeneous information networks have become
increasingly popular and content-rich over time. In many cases, such networks
contain multiple types of objects and links, as well as different kinds of
attributes. The clustering of these objects can provide useful insights in many
applications. However, the clustering of such networks can be challenging since
(a) the attribute values of objects are often incomplete, which implies that an
object may carry only partial attributes or even no attributes to correctly
label itself; and (b) the links of different types may carry different kinds of
semantic meanings, and it is a difficult task to determine the nature of their
relative importance in helping the clustering for a given purpose. In this
paper, we address these challenges by proposing a model-based clustering
algorithm. We design a probabilistic model which clusters the objects of
different types into a common hidden space, by using a user-specified set of
attributes, as well as the links from different relations. The strengths of
different types of links are automatically learned, and are determined by the
given purpose of clustering. An iterative algorithm is designed for solving the
clustering problem, in which the strengths of different types of links and the
quality of clustering results mutually enhance each other. Our experimental
results on real and synthetic data sets demonstrate the effectiveness and
efficiency of the algorithm.
|
1201.6564
|
Shortest Path and Distance Queries on Road Networks: An Experimental
Evaluation
|
cs.DB
|
Computing the shortest path between two given locations in a road network is
an important problem that finds applications in various map services and
commercial navigation products. The state-of-the-art solutions for the problem
can be divided into two categories: spatial-coherence-based methods and
vertex-importance-based approaches. The two categories of techniques, however,
have not been compared systematically under the same experimental framework, as
they were developed from two independent lines of research that do not refer to
each other. This renders it difficult for a practitioner to decide which
technique should be adopted for a specific application. Furthermore, the
experimental evaluation of the existing techniques, as presented in previous
work, falls short in several aspects. Some methods were tested only on small
road networks with up to one hundred thousand vertices; some approaches were
evaluated using distance queries (instead of shortest path queries), namely,
queries that ask only for the length of the shortest path; a state-of-the-art
technique was examined based on a faulty implementation that led to incorrect
query results. To address the above issues, this paper presents a comprehensive
comparison of the most advanced spatial-coherence-based and
vertex-importance-based approaches. Using a variety of real road networks with
up to twenty million vertices, we evaluated each technique in terms of its
preprocessing time, space consumption, and query efficiency (for both shortest
path and distance queries). Our experimental results reveal the characteristics
of different techniques, based on which we provide guidelines on selecting
appropriate methods for various scenarios.
|
1201.6565
|
The Filter-Placement Problem and its Application to Minimizing
Information Multiplicity
|
cs.DB
|
In many information networks, data items -- such as updates in social
networks, news flowing through interconnected RSS feeds and blogs, measurements
in sensor networks, route updates in ad-hoc networks -- propagate in an
uncoordinated manner: nodes often relay information they receive to neighbors,
independent of whether or not these neighbors received the same information
from other sources. This uncoordinated data dissemination may result in
significant, yet unnecessary communication and processing overheads, ultimately
reducing the utility of information networks. To alleviate the negative impacts
of this information multiplicity phenomenon, we propose that a subset of nodes
(selected at key positions in the network) carry out additional information
filtering functionality. Thus, nodes are responsible for the removal (or
significant reduction) of the redundant data items relayed through them. We
refer to such nodes as filters. We formally define the Filter Placement problem
as a combinatorial optimization problem, and study its computational complexity
for different types of graphs. We also present polynomial-time approximation
algorithms and scalable heuristics for the problem. Our experimental results,
which we obtained through extensive simulations on synthetic and real-world
information flow networks, suggest that in many settings a relatively small
number of filters are fairly effective in removing a large fraction of
redundant information.
|
1201.6566
|
Fast and Exact Top-k Search for Random Walk with Restart
|
cs.DB
|
Graphs are fundamental data structures and have been employed for centuries
to model real-world systems and phenomena. Random walk with restart (RWR)
provides a good proximity score between two nodes in a graph, and it has been
successfully used in many applications such as automatic image captioning,
recommender systems, and link prediction. The goal of this work is to find
nodes that have top-k highest proximities for a given node. Previous approaches
to this problem find nodes efficiently at the expense of exactness. The main
motivation of this paper is to answer, in the affirmative, the question, `Is it
possible to improve the search time without sacrificing the exactness?'. Our
solution, {it K-dash}, is based on two ideas: (1) It computes the proximity of
a selected node efficiently by sparse matrices, and (2) It skips unnecessary
proximity computations when searching for the top-k nodes. Theoretical analyses
show that K-dash guarantees result exactness. We perform comprehensive
experiments to verify the efficiency of K-dash. The results show that K-dash
can find top-k nodes significantly faster than the previous approaches while it
guarantees exactness.
|
1201.6567
|
Densest Subgraph in Streaming and MapReduce
|
cs.DB
|
The problem of finding locally dense components of a graph is an important
primitive in data analysis, with wide-ranging applications from community
mining to spam detection and the discovery of biological network modules. In
this paper we present new algorithms for finding the densest subgraph in the
streaming model. For any epsilon>0, our algorithms make O((log n)/log
(1+epsilon)) passes over the input and find a subgraph whose density is
guaranteed to be within a factor 2(1+epsilon) of the optimum. Our algorithms
are also easily parallelizable and we illustrate this by realizing them in the
MapReduce model. In addition we perform extensive experimental evaluation on
massive real-world graphs showing the performance and scalability of our
algorithms in practice.
|
1201.6568
|
Mining Attribute-structure Correlated Patterns in Large Attributed
Graphs
|
cs.DB
|
In this work, we study the correlation between attribute sets and the
occurrence of dense subgraphs in large attributed graphs, a task we call
structural correlation pattern mining. A structural correlation pattern is a
dense subgraph induced by a particular attribute set. Existing methods are not
able to extract relevant knowledge regarding how vertex attributes interact
with dense subgraphs. Structural correlation pattern mining combines aspects of
frequent itemset and quasi-clique mining problems. We propose statistical
significance measures that compare the structural correlation of attribute sets
against their expected values using null models. Moreover, we evaluate the
interestingness of structural correlation patterns in terms of size and
density. An efficient algorithm that combines search and pruning strategies in
the identification of the most relevant structural correlation patterns is
presented. We apply our method for the analysis of three real-world attributed
graphs: a collaboration, a music, and a citation network, verifying that it
provides valuable knowledge in a feasible time.
|
1201.6569
|
Aggregation in Probabilistic Databases via Knowledge Compilation
|
cs.DB
|
This paper presents a query evaluation technique for positive relational
algebra queries with aggregates on a representation system for probabilistic
data based on the algebraic structures of semiring and semimodule. The core of
our evaluation technique is a procedure that compiles semimodule and semiring
expressions into so-called decomposition trees, for which the computation of
the probability distribution can be done in time linear in the product of the
sizes of the probability distributions represented by its nodes. We give
syntactic characterisations of tractable queries with aggregates by exploiting
the connection between query tractability and polynomial-time decomposition
trees. A prototype of the technique is incorporated in the probabilistic
database engine SPROUT. We report on performance experiments with custom
datasets and TPC-H data.
|
1201.6583
|
Empowerment for Continuous Agent-Environment Systems
|
cs.AI cs.LG
|
This paper develops generalizations of empowerment to continuous states.
Empowerment is a recently introduced information-theoretic quantity motivated
by hypotheses about the efficiency of the sensorimotor loop in biological
organisms, but also from considerations stemming from curiosity-driven
learning. Empowemerment measures, for agent-environment systems with stochastic
transitions, how much influence an agent has on its environment, but only that
influence that can be sensed by the agent sensors. It is an
information-theoretic generalization of joint controllability (influence on
environment) and observability (measurement by sensors) of the environment by
the agent, both controllability and observability being usually defined in
control theory as the dimensionality of the control/observation spaces. Earlier
work has shown that empowerment has various interesting and relevant
properties, e.g., it allows us to identify salient states using only the
dynamics, and it can act as intrinsic reward without requiring an external
reward. However, in this previous work empowerment was limited to the case of
small-scale and discrete domains and furthermore state transition probabilities
were assumed to be known. The goal of this paper is to extend empowerment to
the significantly more important and relevant case of continuous vector-valued
state spaces and initially unknown state transition probabilities. The
continuous state space is addressed by Monte-Carlo approximation; the unknown
transitions are addressed by model learning and prediction for which we apply
Gaussian processes regression with iterated forecasting. In a number of
well-known continuous control tasks we examine the dynamics induced by
empowerment and include an application to exploration and online model
learning.
|
1201.6604
|
Gaussian Processes for Sample Efficient Reinforcement Learning with
RMAX-like Exploration
|
cs.AI cs.LG
|
We present an implementation of model-based online reinforcement learning
(RL) for continuous domains with deterministic transitions that is specifically
designed to achieve low sample complexity. To achieve low sample complexity,
since the environment is unknown, an agent must intelligently balance
exploration and exploitation, and must be able to rapidly generalize from
observations. While in the past a number of related sample efficient RL
algorithms have been proposed, to allow theoretical analysis, mainly
model-learners with weak generalization capabilities were considered. Here, we
separate function approximation in the model learner (which does require
samples) from the interpolation in the planner (which does not require
samples). For model-learning we apply Gaussian processes regression (GP) which
is able to automatically adjust itself to the complexity of the problem (via
Bayesian hyperparameter selection) and, in practice, often able to learn a
highly accurate model from very little data. In addition, a GP provides a
natural way to determine the uncertainty of its predictions, which allows us to
implement the "optimism in the face of uncertainty" principle used to
efficiently control exploration. Our method is evaluated on four common
benchmark domains.
|
1201.6615
|
Feature Selection for Value Function Approximation Using Bayesian Model
Selection
|
cs.AI cs.LG
|
Feature selection in reinforcement learning (RL), i.e. choosing basis
functions such that useful approximations of the unkown value function can be
obtained, is one of the main challenges in scaling RL to real-world
applications. Here we consider the Gaussian process based framework GPTD for
approximate policy evaluation, and propose feature selection through marginal
likelihood optimization of the associated hyperparameters. Our approach has two
appealing benefits: (1) given just sample transitions, we can solve the policy
evaluation problem fully automatically (without looking at the learning task,
and, in theory, independent of the dimensionality of the state space), and (2)
model selection allows us to consider more sophisticated kernels, which in turn
enable us to identify relevant subspaces and eliminate irrelevant state
variables such that we can achieve substantial computational savings and
improved prediction performance.
|
1201.6626
|
Learning RoboCup-Keepaway with Kernels
|
cs.AI cs.LG cs.MA
|
We apply kernel-based methods to solve the difficult reinforcement learning
problem of 3vs2 keepaway in RoboCup simulated soccer. Key challenges in
keepaway are the high-dimensionality of the state space (rendering conventional
discretization-based function approximation like tilecoding infeasible), the
stochasticity due to noise and multiple learning agents needing to cooperate
(meaning that the exact dynamics of the environment are unknown) and real-time
learning (meaning that an efficient online implementation is required). We
employ the general framework of approximate policy iteration with
least-squares-based policy evaluation. As underlying function approximator we
consider the family of regularization networks with subset of regressors
approximation. The core of our proposed solution is an efficient recursive
implementation with automatic supervised selection of relevant basis functions.
Simulation results indicate that the behavior learned through our approach
clearly outperforms the best results obtained earlier with tilecoding by Stone
et al. (2005).
|
1201.6655
|
Learning Performance of Prediction Markets with Kelly Bettors
|
cs.AI q-fin.GN
|
In evaluating prediction markets (and other crowd-prediction mechanisms),
investigators have repeatedly observed a so-called "wisdom of crowds" effect,
which roughly says that the average of participants performs much better than
the average participant. The market price---an average or at least aggregate of
traders' beliefs---offers a better estimate than most any individual trader's
opinion. In this paper, we ask a stronger question: how does the market price
compare to the best trader's belief, not just the average trader. We measure
the market's worst-case log regret, a notion common in machine learning theory.
To arrive at a meaningful answer, we need to assume something about how traders
behave. We suppose that every trader optimizes according to the Kelly criteria,
a strategy that provably maximizes the compound growth of wealth over an
(infinite) sequence of market interactions. We show several consequences.
First, the market prediction is a wealth-weighted average of the individual
participants' beliefs. Second, the market learns at the optimal rate, the
market price reacts exactly as if updating according to Bayes' Law, and the
market prediction has low worst-case log regret to the best individual
participant. We simulate a sequence of markets where an underlying true
probability exists, showing that the market converges to the true objective
frequency as if updating a Beta distribution, as the theory predicts. If agents
adopt a fractional Kelly criteria, a common practical variant, we show that
agents behave like full-Kelly agents with beliefs weighted between their own
and the market's, and that the market price converges to a time-discounted
frequency. Our analysis provides a new justification for fractional Kelly
betting, a strategy widely used in practice for ad-hoc reasons. Finally, we
propose a method for an agent to learn her own optimal Kelly fraction.
|
1201.6681
|
An Alternative Proof of an Extremal Entropy Inequality
|
cs.IT math.IT
|
This paper first focuses on deriving an alternative approach for proving an
extremal entropy inequality (EEI), originally presented in [11]. The proposed
approach does not rely on the channel enhancement technique, and has the
advantage that it yields an explicit description of the optimal solution as
opposed to the implicit approach of [11]. Compared with the proofs in [11], the
proposed alternative proof is also simpler, more direct, more
information-theoretic, and has the additional advantage that it offers a new
perspective for establishing novel as well as known challenging results such
the capacity of the vector Gaussian broadcast channel, the lower bound of the
achievable rate for distributed source coding with a single quadratic
distortion constraint, and the secrecy capacity of the Gaussian wire-tap
channel. The second part of this paper is devoted to some novel applications of
the proposed mathematical results. The proposed mathematical techniques are
further exploited to obtain a more simplified proof of the EEI without using
the entropy power inequality (EPI), to build the optimal solution for a special
class of broadcasting channels with private messages and to obtain a mutual
information-based performance bound for the mean square-error of a linear
Bayesian estimator of a Gaussian source embedded in an additive noise channel.
|
1201.6685
|
A Factor Graph Approach to Clock Offset Estimation in Wireless Sensor
Networks
|
cs.IT math.IT
|
The problem of clock offset estimation in a two way timing message exchange
regime is considered when the likelihood function of the observation time
stamps is Gaussian, exponential or log-normally distributed. A parametrized
solution to the maximum likelihood (ML) estimation of clock offset, based on
convex optimization, is presented, which differs from the earlier approaches
where the likelihood function is maximized graphically. In order to capture the
imperfections in node oscillators, which may render a time-varying nature to
the clock offset, a novel Bayesian approach to the clock offset estimation is
proposed by using a factor graph representation of the posterior density.
Message passing using the max-product algorithm yields a closed form expression
for the Bayesian inference problem. Several lower bounds on the variance of an
estimator are derived for arbitrary exponential family distributed likelihood
functions which, while serving as stepping stones to benchmark the performance
of the proposed clock offset estimators, can be useful in their own right in
classical as well Bayesian parameter estimation theory. To corroborate the
theoretical findings, extensive simulation results are discussed for classical
as well as Bayesian estimators in various scenarios. It is observed that the
performance of the proposed estimators is fairly close to the fundamental
limits established by the lower bounds.
|
1202.0015
|
On the equivalence between Stein and de Bruijn identities
|
cs.IT math.IT
|
This paper focuses on proving the equivalence between Stein's identity and de
Bruijn's identity. Given some conditions, we prove that Stein's identity is
equivalent to de Bruijn's identity. In addition, some extensions of de Bruijn's
identity are presented. For arbitrary but fixed input and noise distributions,
there exist relations between the first derivative of the differential entropy
and the posterior mean. Moreover, the second derivative of the differential
entropy is related to the Fisher information for arbitrary input and noise
distributions. Several applications are presented to support the usefulness of
the developed results in this paper.
|
1202.0018
|
A General Approach for Securely Querying and Updating XML Data
|
cs.CR cs.DB
|
Over the past years several works have proposed access control models for XML
data where only read-access rights over non-recursive DTDs are considered. A
few amount of works have studied the access rights for updates. In this paper,
we present a general model for specifying access control on XML data in the
presence of update operations of W3C XQuery Update Facility. Our approach for
enforcing such updates specifications is based on the notion of query rewriting
where each update operation defined over arbitrary DTD (recursive or not) is
rewritten to a safe one in order to be evaluated only over XML data which can
be updated by the user. We investigate in the second part of this report the
secure of XML updating in the presence of read-access rights specified by a
security views. For an XML document, a security view represents for each class
of users all and only the parts of the document these users are able to see. We
show that an update operation defined over a security view can cause disclosure
of sensitive data hidden by this view if it is not thoroughly rewritten with
respect to both read and update access rights. Finally, we propose a security
view based approach for securely updating XML in order to preserve the
confidentiality and integrity of XML data.
|
1202.0022
|
Time-varying Clock Offset Estimation in Two-way Timing Message Exchange
in Wireless Sensor Networks Using Factor Graphs
|
cs.IT math.IT
|
The problem of clock offset estimation in a two-way timing exchange regime is
considered when the likelihood function of the observation time stamps is
exponentially distributed. In order to capture the imperfections in node
oscillators, which render a time-varying nature to the clock offset, a novel
Bayesian approach to the clock offset estimation is proposed using a factor
graph representation of the posterior density. Message passing using the
max-product algorithm yields a closed form expression for the Bayesian
inference problem.
|
1202.0024
|
Predicting epidemic outbreak from individual features of the spreaders
|
physics.soc-ph cs.SI q-bio.PE
|
Knowing which individuals can be more efficient in spreading a pathogen
throughout a determinate environment is a fundamental question in disease
control. Indeed, over the last years the spread of epidemic diseases and its
relationship with the topology of the involved system have been a recurrent
topic in complex network theory, taking into account both network models and
real-world data. In this paper we explore possible correlations between the
heterogeneous spread of an epidemic disease governed by the
susceptible-infected-recovered (SIR) model, and several attributes of the
originating vertices, considering Erd\"os-R\'enyi (ER), Barab\'asi-Albert (BA)
and random geometric graphs (RGG), as well as a real case of study, the US Air
Transportation Network that comprises the US 500 busiest airports along with
inter-connections. Initially, the heterogeneity of the spreading is achieved
considering the RGG networks, in which we analytically derive an expression for
the distribution of the spreading rates among the established contacts, by
assuming that such rates decay exponentially with the distance that separates
the individuals. Such distribution is also considered for the ER and BA models,
where we observe topological effects on the correlations. In the case of the
airport network, the spreading rates are empirically defined, assumed to be
directly proportional to the seat availability. Among both the theoretical and
the real networks considered, we observe a high correlation between the total
epidemic prevalence and the degree, as well as the strength and the
accessibility of the epidemic sources. For attributes such as the betweenness
centrality and the $k$-shell index, however, the correlation depends on the
topology considered.
|
1202.0031
|
Social Dynamics of Digg
|
cs.CY cs.SI physics.soc-ph
|
Online social media provide multiple ways to find interesting content. One
important method is highlighting content recommended by user's friends. We
examine this process on one such site, the news aggregator Digg. With a
stochastic model of user behavior, we distinguish the effects of the content
visibility and interestingness to users. We find a wide range of interest and
distinguish stories primarily of interest to a users' friends from those of
interest to the entire user community. We show how this model predicts a
story's eventual popularity from users' early reactions to it, and estimate the
prediction reliability. This modeling framework can help evaluate alternative
design choices for displaying content on the site.
|
1202.0055
|
Moving Target Parameters Estimation in Non-Coherent MIMO Radar Systems
|
cs.IT math.IT stat.AP
|
The problem of estimating the parameters of a moving target in multiple-input
multiple-output (MIMO) radar is considered and a new approach for estimating
the moving target parameters by making use of the phase information associated
with each transmit-receive path is introduced. It is required for this
technique that different receive antennas have the same time reference, but no
synchronization of initial phases of the receive antennas is needed and,
therefore, the estimation process is non-coherent. We model the target motion
within a certain processing interval as a polynomial of general order. The
first three coefficients of such a polynomial correspond to the initial
location, velocity, and acceleration of the target, respectively. A new maximum
likelihood (ML) technique for estimating the target motion coefficients is
developed. It is shown that the considered ML problem can be interpreted as the
classic "overdetermined" nonlinear least-squares problem. The proposed ML
estimator requires multi-dimensional search over the unknown polynomial
coefficients. The Cram\'er-Rao Bound (CRB) for the proposed parameter
estimation problem is derived. The performance of the proposed estimator is
validated by simulation results and is shown to achieve the CRB.
|
1202.0077
|
Datasets as Interacting Particle Systems: a Framework for Clustering
|
cond-mat.stat-mech cs.SI physics.soc-ph
|
In this paper we propose a framework inspired by interacting particle physics
and devised to perform clustering on multidimensional datasets. To this end,
any given dataset is modeled as an interacting particle system, under the
assumption that each element of the dataset corresponds to a different particle
and that particle interactions are rendered through gaussian potentials.
Moreover, the way particle interactions are evaluated depends on a parameter
that controls the shape of the underlying gaussian model. In principle,
different clusters of proximal particles can be identified, according to the
value adopted for the parameter. This degree of freedom in gaussian potentials
has been introduced with the goal of allowing multiresolution analysis. In
particular, upon the adoption of a standard community detection algorithm,
multiresolution analysis is put into practice by repeatedly running the
algorithm on a set of adjacency matrices, each dependent on a specific value of
the parameter that controls the shape of gaussian potentials. As a result,
different partitioning schemas are obtained on the given dataset, so that the
information thereof can be better highlighted, with the goal of identifying the
most appropriate number of clusters. Solutions achieved in synthetic datasets
allowed to identify a repetitive pattern, which appear to be useful in the task
of identifying optimal solutions while analysing other synthetic and real
datasets.
|
1202.0085
|
Affine cartesian codes
|
math.AC cs.IT math.AG math.CO math.IT
|
We compute the basic parameters (dimension, length, minimum distance) of
affine evaluation codes defined on a cartesian product of finite sets. Given a
sequence of positive integers, we construct an evaluation code, over a
degenerate torus, with prescribed parameters. As an application of our results,
we recover the formulas for the minimum distance of various families of
evaluation codes.
|
1202.0097
|
The capacity region of the two-receiver vector Gaussian broadcast
channel with private and common messages
|
cs.IT math.IT
|
We develop a new method for showing the optimality of the Gaussian
distribution in multiterminal information theory problems. As an application of
this method we show that Marton's inner bound achieves the capacity of the
vector Gaussian broadcast channels with common message.
|
1202.0116
|
Inference and Plausible Reasoning in a Natural Language Understanding
System Based on Object-Oriented Semantics
|
cs.CL
|
Algorithms of inference in a computer system oriented to input and semantic
processing of text information are presented. Such inference is necessary for
logical questions when the direct comparison of objects from a question and
database can not give a result. The following classes of problems are
considered: a check of hypotheses for persons and non-typical actions, the
determination of persons and circumstances for non-typical actions, planning
actions, the determination of event cause and state of persons. To form an
answer both deduction and plausible reasoning are used. As a knowledge domain
under consideration is social behavior of persons, plausible reasoning is based
on laws of social psychology. Proposed algorithms of inference and plausible
reasoning can be realized in computer systems closely connected with text
processing (criminology, operation of business, medicine, document systems).
|
1202.0119
|
Opportunistic Scheduling in Heterogeneous Networks: Distributed
Algorithms and System Capacity
|
cs.IT cs.NI math.IT
|
In this work, we design and analyze novel distributed scheduling algorithms
for multi-user MIMO systems. In particular, we consider algorithms which do not
require sending channel state information to a central processing unit, nor do
they require communication between the users themselves, yet, we prove their
performance closely approximates that of a centrally-controlled system, which
is able to schedule the strongest user in each time-slot.
Our analysis is based on a novel application of the Point-Process
approximation. This novel technique allows us to examine non-homogeneous cases,
such as non-identically distributed users, or handling various QoS
considerations, and give exact expressions for the capacity of the system under
these schemes, solving analytically problems which to date had been open.
Possible application include, but are not limited to, modern 4G networks such
as 3GPP LTE, or random access protocols.
|
1202.0135
|
On the Design of Large Scale Wireless Systems (with detailed proofs)
|
cs.IT math.IT
|
In this paper, we consider the downlink of large OFDMA-based networks and
study their performance bounds as a function of the number of - transmitters
$B$, users $K$, and resource-blocks $N$. Here, a resource block is a collection
of subcarriers such that all such collections, that are disjoint have
associated independently fading channels. In particular, we analyze the
expected achievable sum-rate as a function of above variables and derive novel
upper and lower bounds for a general spatial geometry of transmitters, a
truncated path-loss model, and a variety of fading models. We establish the
associated scaling laws for dense and extended networks, and propose design
guidelines for the regulators to guarantee various QoS constraints and, at the
same time, maximize revenue for the service providers. Thereafter, we develop a
distributed resource allocation scheme that achieves the same sum-rate scaling
as that of the proposed upper bound for a wide range of $K, B, N$. Based on it,
we compare low-powered peer-to-peer networks to high-powered single-transmitter
networks and give an additional design principle. Finally, we also show how our
results can be extended to the scenario where each of the $B$ transmitters have
$M (>1)$ co-located antennas.
|
1202.0136
|
Variable Length Lossless Coding for Variational Distance Class: An
Optimal Merging Algorithm
|
cs.IT math.IT
|
In this paper we consider lossless source coding for a class of sources
specified by the total variational distance ball centred at a fixed nominal
probability distribution. The objective is to find a minimax average length
source code, where the minimizers are the codeword lengths -- real numbers for
arithmetic or Shannon codes -- while the maximizers are the source
distributions from the total variational distance ball. Firstly, we examine the
maximization of the average codeword length by converting it into an equivalent
optimization problem, and we give the optimal codeword lenghts via a
waterfilling solution. Secondly, we show that the equivalent optimization
problem can be solved via an optimal partition of the source alphabet, and
re-normalization and merging of the fixed nominal probabilities. For the
computation of the optimal codeword lengths we also develop a fast algorithm
with a computational complexity of order ${\cal O}(n)$.
|
1202.0139
|
Factorization of Rational Curves in the Study Quadric and Revolute
Linkages
|
math.RA cs.RO math.AG
|
Given a generic rational curve $C$ in the group of Euclidean displacements we
construct a linkage such that the constrained motion of one of the links is
exactly $C$. Our construction is based on the factorization of polynomials over
dual quaternions. Low degree examples include the Bennett mechanisms and
contain new types of overconstrained 6R-chains as sub-mechanisms.
|
1202.0163
|
Spatial MAC in MIMO Communications and its Application to Underlay
Cognitive Radio
|
cs.IT math.IT
|
We propose a learning technique for MIMO secondary users (SU) to spatially
coexist with Primary Users (PU). By learning the null space of the interference
channel to the PU, the SU can utilize idle degrees of freedom that otherwise
would be unused by the PU. This learning process does not require any handshake
or explicit information exchange between the PU and the SU. The only
requirement is that the PU broadcasts a periodic beacon that is a function of
its noise plus interference power, through a low rate control channel. The
learning process is based on energy measurements, independent of the
transmission schemes of both the PU and SU, i.e. independent of their
modulation, coding etc.. The proposed learning technique also provides a novel
spatial division multiple access mechanism for equal-priority MIMO users
sharing a common channel that highly increases the spectrum utilization
compared to time based or frequency multiple access.
|
1202.0168
|
On the Capacity of Large-MIMO Block-Fading Channels
|
cs.IT math.IT
|
We characterize the capacity of Rayleigh block-fading multiple-input
multiple-output (MIMO) channels in the noncoherent setting where transmitter
and receiver have no a priori knowledge of the realizations of the fading
channel. We prove that unitary space-time modulation (USTM) is not
capacity-achieving in the high signal-to-noise ratio (SNR) regime when the
total number of antennas exceeds the coherence time of the fading channel
(expressed in multiples of the symbol duration), a situation that is relevant
for MIMO systems with large antenna arrays (large-MIMO systems). This result
settles a conjecture by Zheng & Tse (2002) in the affirmative. The
capacity-achieving input signal, which we refer to as Beta-variate space-time
modulation (BSTM), turns out to be the product of a unitary isotropically
distributed random matrix, and a diagonal matrix whose nonzero entries are
distributed as the square-root of the eigenvalues of a Beta-distributed random
matrix of appropriate size. Numerical results illustrate that using BSTM
instead of USTM in large-MIMO systems yields a rate gain as large as 13% for
SNR values of practical interest.
|
1202.0186
|
A Feasibility Test for Linear Interference Alignment in MIMO Channels
with Constant Coefficients
|
cs.IT math.IT
|
In this paper, we consider the feasibility of linear interference alignment
(IA) for multiple-input multiple-output (MIMO) channels with constant
coefficients for any number of users, antennas and streams per user; and
propose a polynomial-time test for this problem. Combining algebraic geometry
techniques with differential topology ones, we first prove a result that
generalizes those previously published on this topic. Specifically, we consider
the input set (complex projective space of MIMO interference channels), the
output set (precoder and decoder Grassmannians) and the solution set (channels,
decoders and precoders satisfying the IA polynomial equations), not only as
algebraic sets but also as smooth compact manifolds. Using this mathematical
framework, we prove that the linear alignment problem is feasible when the
algebraic dimension of the solution variety is larger than or equal to the
dimension of the input space and the linear mapping between the tangent spaces
of both smooth manifolds given by the first projection is generically
surjective. If that mapping is not surjective, then the solution variety
projects into the input space in a singular way and the projection is a
zero-measure set. This result naturally yields a simple feasibility test, which
amounts to checking the rank of a matrix. We also provide an exact arithmetic
version of the test, which proves that testing the feasibility of IA for
generic MIMO channels belongs to the bounded-error probabilistic polynomial
(BPP) complexity class.
|
1202.0191
|
Hierarchy measure for complex networks
|
physics.soc-ph cond-mat.dis-nn cond-mat.stat-mech cs.SI
|
Nature, technology and society are full of complexity arising from the
intricate web of the interactions among the units of the related systems (e.g.,
proteins, computers, people). Consequently, one of the most successful recent
approaches to capturing the fundamental features of the structure and dynamics
of complex systems has been the investigation of the networks associated with
the above units (nodes) together with their relations (edges). Most complex
systems have an inherently hierarchical organization and, correspondingly, the
networks behind them also exhibit hierarchical features. Indeed, several papers
have been devoted to describing this essential aspect of networks, however,
without resulting in a widely accepted, converging concept concerning the
quantitative characterization of the level of their hierarchy. Here we develop
an approach and propose a quantity (measure) which is simple enough to be
widely applicable, reveals a number of universal features of the organization
of real-world networks and, as we demonstrate, is capable of capturing the
essential features of the structure and the degree of hierarchy in a complex
network. The measure we introduce is based on a generalization of the m-reach
centrality, which we first extend to directed/partially directed graphs. Then,
we define the global reaching centrality (GRC), which is the difference between
the maximum and the average value of the generalized reach centralities over
the network. We investigate the behavior of the GRC considering both a
synthetic model with an adjustable level of hierarchy and real networks.
Results for real networks show that our hierarchy measure is related to the
controllability of the given system. We also propose a visualization procedure
for large complex networks that can be used to obtain an overall qualitative
picture about the nature of their hierarchical structure.
|
1202.0204
|
On the Capacity of Interference Channel with Causal and Non-causal
Generalized Feedback at the Cognitive Transmitter
|
cs.IT math.IT
|
In this paper, taking into account the effect of link delays, we investigate
the capacity region of the Cognitive Interference Channel (C-IFC), where
cognition can be obtained from either causal or non-causal generalized
feedback. For this purpose, we introduce the Causal Cognitive Interference
Channel With Delay (CC-IFC-WD) in which the cognitive user's transmission can
depend on $L$ future received symbols as well as the past ones. We show that
the CC-IFC-WD model is equivalent to a classical Causal C-IFC (CC-IFC) with
link delays. Moreover, CC-IFC-WD extends both genie-aided and causal cognitive
radio channels and bridges the gap between them. First, we derive an outer
bound on the capacity region for the arbitrary value of $L$ and specialize this
general outer bound to the strong interference case. Then, under strong
interference conditions, we tighten the outer bound. To derive the achievable
rate regions, we concentrate on three special cases: 1) Classical CC-IFC (L=0),
2) CC-IFC without delay (L=1), and 3) CC-IFC with unlimited look-ahead in which
the cognitive user non-causally knows its entire received sequence. In each
case, we obtain a new inner bound on the capacity region. Moreover, we show
that the coding strategy which we use to derive an achievable rate region for
the classical CC-IFC achieves the capacity for the classes of degraded and
semi-deterministic classical CC-IFC under strong interference conditions.
Furthermore, we extend our achievable rate regions to the Gaussian case.
Providing some numerical examples for Gaussian CC-IFC-WD, we compare the
performances of the different strategies and investigate the rate gain of the
cognitive link for different delay values.
|
1202.0206
|
Non-adaptive Group Testing: Explicit bounds and novel algorithms
|
cs.IT math.IT
|
We consider some computationally efficient and provably correct algorithms
with near-optimal sample-complexity for the problem of noisy non-adaptive group
testing. Group testing involves grouping arbitrary subsets of items into pools.
Each pool is then tested to identify the defective items, which are usually
assumed to be "sparse". We consider non-adaptive randomly pooling measurements,
where pools are selected randomly and independently of the test outcomes. We
also consider a model where noisy measurements allow for both some false
negative and some false positive test outcomes (and also allow for asymmetric
noise, and activation noise). We consider three classes of algorithms for the
group testing problem (we call them specifically the "Coupon Collector
Algorithm", the "Column Matching Algorithms", and the "LP Decoding Algorithms"
-- the last two classes of algorithms (versions of some of which had been
considered before in the literature) were inspired by corresponding algorithms
in the Compressive Sensing literature. The second and third of these algorithms
have several flavours, dealing separately with the noiseless and noisy
measurement scenarios. Our contribution is novel analysis to derive explicit
sample-complexity bounds -- with all constants expressly computed -- for these
algorithms as a function of the desired error probability; the noise
parameters; the number of items; and the size of the defective set (or an upper
bound on it). We also compare the bounds to information-theoretic lower bounds
for sample complexity based on Fano's inequality and show that the upper and
lower bounds are equal up to an explicitly computable universal constant factor
(independent of problem parameters).
|
1202.0216
|
The watershed concept and its use in segmentation : a brief history
|
cs.CV
|
The watershed is one of the most used tools in image segmentation. We present
how its concept is born and developed over time. Its implementation as an
algorithm or a hardwired device evolved together with the technology which
allowed it. We present also how it is used in practice, first together with
markers, and later introduced in a multiscale framework, in order to produce
not a unique partition but a complete hierarchy.
|
1202.0224
|
Mesoscopic structure and social aspects of human mobility
|
physics.soc-ph cond-mat.stat-mech cs.SI physics.data-an
|
The individual movements of large numbers of people are important in many
contexts, from urban planning to disease spreading. Datasets that capture human
mobility are now available and many interesting features have been discovered,
including the ultra-slow spatial growth of individual mobility. However, the
detailed substructures and spatiotemporal flows of mobility - the sets and
sequences of visited locations - have not been well studied. We show that
individual mobility is dominated by small groups of frequently visited,
dynamically close locations, forming primary "habitats" capturing typical daily
activity, along with subsidiary habitats representing additional travel. These
habitats do not correspond to typical contexts such as home or work. The
temporal evolution of mobility within habitats, which constitutes most motion,
is universal across habitats and exhibits scaling patterns both distinct from
all previous observations and unpredicted by current models. The delay to enter
subsidiary habitats is a primary factor in the spatiotemporal growth of human
travel. Interestingly, habitats correlate with non-mobility dynamics such as
communication activity, implying that habitats may influence processes such as
information spreading and revealing new connections between human mobility and
social networks.
|
1202.0241
|
Linear Programming Upper Bounds on Permutation Code Sizes From Coherent
Configurations Related to the Kendall Tau Distance Metric
|
cs.IT math.IT
|
Recent interest on permutation rank modulation shows the Kendall tau metric
as an important distance metric. This note documents our first efforts to
obtain upper bounds on optimal code sizes (for said metric) ala Delsarte's
approach. For the Hamming metric, Delsarte's seminal work on powerful linear
programming (LP) bounds have been extended to permutation codes, via
association scheme theory. For the Kendall tau metric, the same extension needs
the more general theory of coherent configurations, whereby the optimal code
size problem can be formulated as an extremely huge semidefinite programming
(SDP) problem. Inspired by recent algebraic techniques for solving SDP's, we
consider the dual problem, and propose an LP to search over a subset of dual
feasible solutions. We obtain modest improvement over a recent Singleton bound
due to Barg and Mazumdar. We regard this work as a starting point, towards
fully exploiting the power of Delsarte's method, which are known to give some
of the best bounds in the context of binary codes.
|
1202.0242
|
Weak Forms of Monotonicity and Coordination-Freeness
|
cs.DB cs.DC
|
Our earlier work titled: "Win-move is Coordination-Free (Sometimes)" has
shown that the classes of queries that can be distributedly computed in a
coordination-free manner form a strict hierarchy depending on the assumptions
of the model for distributed computations. In this paper, we further
characterize these classes by revealing a tight relationship between them and
novel weakened forms of monotonicity.
|
1202.0253
|
High-speed Flight in an Ergodic Forest
|
cs.RO cs.SY
|
Inspired by birds flying through cluttered environments such as dense
forests, this paper studies the theoretical foundations of a novel motion
planning problem: high-speed navigation through a randomly-generated obstacle
field when only the statistics of the obstacle generating process are known a
priori. Resembling a planar forest environment, the obstacle generating process
is assumed to determine the locations and sizes of disk-shaped obstacles. When
this process is ergodic, and under mild technical conditions on the dynamics of
the bird, it is shown that the existence of an infinite collision-free
trajectory through the forest exhibits a phase transition. On one hand, if the
bird flies faster than a certain critical speed, then, with probability one,
there is no infinite collision-free trajectory, i.e., the bird will eventually
collide with some tree, almost surely, regardless of the planning algorithm
governing the bird's motion. On the other hand, if the bird flies slower than
this critical speed, then there exists at least one infinite collision-free
trajectory, almost surely. Lower and upper bounds on the critical speed are
derived for the special case of a homogeneous Poisson forest considering a
simple model for the bird's dynamics. For the same case, an equivalent
percolation model is provided. Using this model, the phase diagram is
approximated in Monte-Carlo simulations. This paper also establishes novel
connections between robot motion planning and statistical physics through
ergodic theory and percolation theory, which may be of independent interest.
|
1202.0255
|
Reasoning about Unreliable Actions
|
math.LO cs.AI math.CT
|
We analyse the philosopher Davidson's semantics of actions, using a strongly
typed logic with contexts given by sets of partial equations between the
outcomes of actions. This provides a perspicuous and elegant treatment of
reasoning about action, analogous to Reiter's work on artificial intelligence.
We define a sequent calculus for this logic, prove cut elimination, and give a
semantics based on fibrations over partial cartesian categories: we give a
structure theory for such fibrations. The existence of lax comma objects is
necessary for the proof of cut elimination, and we give conditions on the
domain fibration of a partial cartesian category for such comma objects to
exist.
|
1202.0296
|
Error Performance of Multidimensional Lattice Constellations-Part I: A
Parallelotope Geometry Based Approach for the AWGN Channel
|
cs.IT math.IT
|
Multidimensional lattice constellations which present signal space diversity
(SSD) have been extensively studied for single-antenna transmission over fading
channels, with focus on their optimal design for achieving high diversity gain.
In this two-part series of papers we present a novel combinatorial geometrical
approach based on parallelotope geometry, for the performance evaluation of
multidimensional finite lattice constellations with arbitrary structure,
dimension and rank. In Part I, we present an analytical expression for the
exact symbol error probability (SEP) of multidimensional signal sets, and two
novel closed-form bounds, named Multiple Sphere Lower Bound (MLSB) and Multiple
Sphere Upper Bound (MSUB). Part II extends the analysis to the transmission
over fading channels, where multidimensional signal sets are commonly used to
combat fading degradation. Numerical and simulation results show that the
proposed geometrical approach leads to accurate and tight expressions, which
can be efficiently used for the performance evaluation and the design of
multidimensional lattice constellations, both in Additive White Gaussian Noise
(AWGN) and fading channels.
|
1202.0298
|
Error Performance of Multidimensional Lattice Constellations-Part II:
Evaluation over Fading Channels
|
cs.IT math.IT
|
This is the second part of a two-part series of papers, where the error
performance of multidimensional lattice constellations with signal space
diversity (SSD) is investigated. In Part I, following a novel combinatorial
geometrical approach which is based on parallelotope geometry, we have
presented an exact analytical expression and two closed-form bounds for the
symbol error probability (SEP) in Additive White Gaussian Noise (AWGN). In the
present Part II, we extend the analysis and present a novel analytical
expression for the Frame Error Probability (FEP) of multidimensional lattice
constellations over Nakagami-m fading channels. As the FEP of infinite lattice
constellations is lower bounded by the Sphere Lower Bound (SLB), we propose the
Sphere Upper Bound (SUB) for block fading channels. Furthermore, two novel
bounds for the FEP of multidimensional lattice constellations over block fading
channels, named Multiple Sphere Lower Bound (MSLB) and Multiple Sphere Upper
Bound (MSUB), are presented. The expressions for the SLB and SUB are given in
closed form, while the corresponding ones for MSLB and MSUB are given in closed
form for unitary block length. Numerical and simulation results illustrate the
tightness of the proposed bounds and demonstrate that they can be efficiently
used to set the performance limits on the FEP of lattice constellations of
arbitrary structure, dimension and rank.
|
1202.0302
|
Kernels on Sample Sets via Nonparametric Divergence Estimates
|
cs.LG stat.ML
|
Most machine learning algorithms, such as classification or regression, treat
the individual data point as the object of interest. Here we consider extending
machine learning algorithms to operate on groups of data points. We suggest
treating a group of data points as an i.i.d. sample set from an underlying
feature distribution for that group. Our approach employs kernel machines with
a kernel on i.i.d. sample sets of vectors. We define certain kernel functions
on pairs of distributions, and then use a nonparametric estimator to
consistently estimate those functions based on sample sets. The projection of
the estimated Gram matrix to the cone of symmetric positive semi-definite
matrices enables us to use kernel machines for classification, regression,
anomaly detection, and low-dimensional embedding in the space of distributions.
We present several numerical experiments both on real and simulated datasets to
demonstrate the advantages of our new approach.
|
1202.0305
|
The Jacobi MIMO Channel
|
cs.IT math.IT
|
This paper presents a new fading model for MIMO channels, the Jacobi fading
model. It asserts that $H$, the transfer matrix which couples the $m_t$ inputs
into $m_r$ outputs, is a sub-matrix of an $m\times m$ random (Haar-distributed)
unitary matrix. The (squared) singular values of $H$ follow the law of the
classical Jacobi ensemble of random matrices; hence the name of the channel.
One motivation to define such a channel comes from multimode/multicore optical
fiber communication. It turns out that this model can be qualitatively
different than the Rayleigh model, leading to interesting practical and
theoretical results. This work first evaluates the ergodic capacity of the
channel. Then, it considers the non-ergodic case, where it analyzes the outage
probability and the diversity-multiplexing tradeoff. In the case where
$k=m_t+m_r-m > 0$ it is shown that at least $k$ degrees of freedom are
guaranteed not to fade for any channel realization, enabling a zero outage
probability or infinite diversity order at the corresponding rates. A simple
scheme utilizing (a possibly outdated) channel state feedback is provided,
attaining the no-outage guarantee. Finally, noting that as $m$ increases, the
Jacobi model approaches the Rayleigh model, the paper discusses the
applicability of the model in other communication scenaria.
|
1202.0307
|
Protocol Coding through Reordering of User Resources, Part I: Capacity
Results
|
cs.IT math.IT
|
The vast existing wireless infrastructure features a variety of systems and
standards. It is of significant practical value to introduce new features and
devices without changing the physical layer/hardware infrastructure, but
upgrade it only in software. A way to achieve it is to apply protocol coding:
encode information in the actions taken by a certain (existing) communication
protocol. In this work we investigate strategies for protocol coding via
combinatorial ordering of the labelled user resources (packets, channels) in an
existing, primary system. Such a protocol coding introduces a new secondary
communication channel in the existing system, which has been considered in the
prior work exclusively in a steganographic context. Instead, we focus on the
use of secondary channel for reliable communication with newly introduced
secondary devices, that are low-complexity versions of the primary devices,
capable only to decode the robustly encoded header information in the primary
signals. We introduce a suitable communication model, capable to capture the
constraints that the primary system operation puts on protocol coding. We have
derived the capacity of the secondary channel under arbitrary error models. The
insights from the information-theoretic analysis are used in Part II of this
work to design practical error-correcting mechanisms for secondary channels
with protocol coding.
|
1202.0309
|
Protocol Coding through Reordering of User Resources, Part II: Practical
Coding Strategies
|
cs.IT math.IT
|
We use the term protocol coding to denote the communication strategies in
which information is encoded through the actions taken by a certain
communication protocol. In this work we investigate strategies for protocol
coding via combinatorial ordering of the labelled user resources (packets,
channels) in an existing, primary system. This introduces a new, secondary
communication channel in the existing system, which has been considered in the
prior work exclusively in a steganographic context. Instead, we focus on the
use of secondary channel for reliable communication with newly introduced
secondary devices, that are low-complexity versions of the primary devices,
capable only to decode the robustly encoded header information in the primary
signals. In Part I of the work we have characterized the capacity of the
secondary channel through information-theoretic analysis. In this paper we
consider practical strategies for protocol coding inspired by the
information-theoretic analysis. It turns out that the insights from Part I are
instrumental for devising superior design of error-control codes. This is
demonstrated by comparing the error performance to the "na"{\i}ve" strategy
which is presumably available without carrying out the analysis in Part I.
These results are clearly outlining both the conceptual novelty behind the
discussed concept of secondary channel as well as its practical applicability.
|
1202.0322
|
Large deviation analysis for quantum security via smoothing of Renyi
entropy of order 2
|
quant-ph cs.CR cs.IT math.IT
|
It is known that the security evaluation can be done by smoothing of
R\'{e}nyi entropy of order 2 in the classical and quantum settings when we
apply universal$_2$ hash functions. Using the smoothing of Renyi entropy of
order 2, we derive security bounds for $L_1$ distinguishability and modified
mutual information criterion under the classical and quantum setting, and have
derived these exponential decreasing rates. These results are extended to the
case when we apply $\varepsilon$-almost dual universal$_2$ hash functions.
Further, we apply this analysis to the secret key generation with error
correction.
|
1202.0325
|
Quantum wiretap channel with non-uniform random number and its exponent
and equivocation rate of leaked information
|
quant-ph cs.CR cs.IT math.IT
|
A usual code for quantum wiretap channel requires an auxiliary random
variable subject to the perfect uniform distribution. However, it is difficult
to prepare such an auxiliary random variable. We propose a code that requires
only an auxiliary random variable subject to a non-uniform distribution instead
of the perfect uniform distribution. Further, we evaluate the exponential
decreasing rate of leaked information and derive its equivocation rate. For
practical constructions, we also discuss the security when our code consists of
a linear error correcting code.
|
1202.0327
|
Artificial Inflation: The True Story of Trends in Sina Weibo
|
cs.CY cs.SI physics.soc-ph
|
There has been a tremendous rise in the growth of online social networks all
over the world in recent years. This has facilitated users to generate a large
amount of real-time content at an incessant rate, all competing with each other
to attract enough attention and become trends. While Western online social
networks such as Twitter have been well studied, characteristics of the popular
Chinese microblogging network Sina Weibo have not been. In this paper, we
analyze in detail the temporal aspect of trends and trend-setters in Sina
Weibo, constrasting it with earlier observations on Twitter. First, we look at
the formation, persistence and decay of trends and examine the key topics that
trend in Sina Weibo. One of our key findings is that retweets are much more
common in Sina Weibo and contribute a lot to creating trends. When we look
closer, we observe that a large percentage of trends in Sina Weibo are due to
the continuous retweets of a small amount of fraudulent accounts. These fake
accounts are set up to artificially inflate certain posts causing them to shoot
up into Sina Weibo's trending list, which are in turn displayed as the most
popular topics to users.
|
1202.0331
|
Topological Features of Online Social Networks
|
cs.SI cs.CY physics.soc-ph
|
The importance of modeling and analyzing Social Networks is a consequence of
the success of Online Social Networks during last years. Several models of
networks have been proposed, reflecting the different characteristics of Social
Networks. Some of them fit better to model specific phenomena, such as the
growth and the evolution of the Social Networks; others are more appropriate to
capture the topological characteristics of the networks. Because these networks
show unique and different properties and features, in this work we describe and
exploit several models in order to capture the structure of popular Online
Social Networks, such as Arxiv, Facebook, Wikipedia and YouTube. Our
experimentation aims at verifying the structural characteristics of these
networks, in order to understand what model better depicts their structure, and
to analyze the inner community structure, to illustrate how members of these
Online Social Networks interact and group together into smaller communities.
|
1202.0332
|
The Pulse of News in Social Media: Forecasting Popularity
|
cs.CY cs.NI cs.SI physics.soc-ph
|
News articles are extremely time sensitive by nature. There is also intense
competition among news items to propagate as widely as possible. Hence, the
task of predicting the popularity of news items on the social web is both
interesting and challenging. Prior research has dealt with predicting eventual
online popularity based on early popularity. It is most desirable, however, to
predict the popularity of items prior to their release, fostering the
possibility of appropriate decision making to modify an article and the manner
of its publication. In this paper, we construct a multi-dimensional feature
space derived from properties of an article and evaluate the efficacy of these
features to serve as predictors of online popularity. We examine both
regression and classification algorithms and demonstrate that despite
randomness in human behavior, it is possible to predict ranges of popularity on
twitter with an overall 84% accuracy. Our study also serves to illustrate the
differences between traditionally prominent sources and those immensely popular
on the social web.
|
1202.0338
|
Algebraic List-decoding of Subspace Codes
|
cs.IT math.IT
|
Subspace codes were introduced in order to correct errors and erasures for
randomized network coding, in the case where network topology is unknown (the
noncoherent case). Subspace codes are indeed collections of subspaces of a
certain vector space over a finite field. The Koetter-Kschischang construction
of subspace codes are similar to Reed-Solomon codes in that codewords are
obtained by evaluating certain (linearized) polynomials. In this paper, we
consider the problem of list-decoding the Koetter-Kschischang subspace codes.
In a sense, we are able to achieve for these codes what Sudan was able to
achieve for Reed-Solomon codes. In order to do so, we have to modify and
generalize the original Koetter-Kschischang construction in many important
respects. The end result is this: for any integer $L$, our list-$L$ decoder
guarantees successful recovery of the message subspace provided that the
normalized dimension of the error is at most $ L - \frac{L(L+1)}{2}R $ where
$R$ is the normalized packet rate. Just as in the case of Sudan's list-decoding
algorithm, this exceeds the previously best known error-correction radius
$1-R$, demonstrated by Koetter and Kschischang, for low rates $R$.
|
1202.0343
|
How Fast Can Dense Codes Achieve the Min-Cut Capacity of Line Networks?
|
cs.IT math.IT
|
In this paper, we study the coding delay and the average coding delay of
random linear network codes (dense codes) over line networks with deterministic
regular and Poisson transmission schedules. We consider both lossless networks
and networks with Bernoulli losses. The upper bounds derived in this paper,
which are in some cases more general, and in some other cases tighter, than the
existing bounds, provide a more clear picture of the speed of convergence of
dense codes to the min-cut capacity of line networks.
|
1202.0349
|
On the admissible families of components of Hamming codes
|
cs.IT math.IT
|
In this paper, we describe the properties of the $i$-components of Hamming
codes. We suggest constructions of the admissible families of components of
Hamming codes. It is shown that every $q$-ary code of length $m$ and minimum
distance 5 (for $q = 3$ the minimum distance is 3) can be embedded in a $q$-ary
1-perfect code of length $n = (q^{m}-1)/(q-1)$. It is also shown that every
binary code of length $m + k$ and minimum distance $3k + 3$ can be embedded in
a binary 1-perfect code of length $n = 2^{m}-1$.
|
1202.0351
|
The weighted tunable clustering in local-world networks with incremental
behaviors
|
physics.soc-ph cs.SI
|
Since some realistic networks are influenced not only by increment behavior
but also by tunable clustering mechanism with new nodes to be added to
networks, it is interesting to characterize the model for those actual
networks. In this paper, a weighted local-world model, which incorporates
increment behavior and tunable clustering mechanism, is proposed and its
properties are investigated, such as degree distribution and clustering
coefficient. Numerical simulations are fit to the model characters and also
display good right skewed scale-free properties. Furthermore, the correlation
of vertices in our model is studied which shows the assortative property.
Epidemic spreading process by weighted transmission rate on the model shows
that the tunable clustering behavior has a great impact on the epidemic
dynamic. Keywords: Weighted network, increment behavior, tun- able cluster,
epidemic spreading.
|
1202.0357
|
Channel Identification and its Impact on Quantum LDPC Code Performance
|
cs.IT math.IT quant-ph
|
In this work we probe the impact of channel estimation on the performance of
quantum LDPC codes. Our channel estimation is based on an optimal estimate of
the relevant decoherence parameter via its quantum Fisher information. Using
state-of-the art quantum LDPC codes designed for the quantum depolarization
channel, and utilizing various quantum probes with different entanglement
properties, we show how the performance of such codes can deteriorate by an
order of magnitude when optimal channel identification is fed into a belief
propagation decoding algorithm. Our work highlights the importance in quantum
communications of a viable channel identification campaign prior to decoding,
and highlights the trade-off between entanglement consumption and quantum LDPC
code performance.
|
1202.0366
|
Blind Null-Space Learning for MIMO Underlay Cognitive Radio Networks
|
cs.IT math.IT
|
This paper proposes a blind technique for MIMO cognitive radio Secondary
Users (SU) to transmit in the same band simultaneously with a Primary User (PU)
under a maximum interference constraint. In the proposed technique, the SU is
able to meet the interference constraint of the PU without explicitly
estimating the interference channel matrix to the PU and without burdening the
PU with any interaction with the SU.
The only condition required of the PU is that for a short time interval it
uses a power control scheme such that its transmitted power is a monotonic
function of the interference inflicted by the SU. During this time interval,
the SU iteratively modifies the spatial orientation of its transmitted signal
and measures the effect of this modification on the PU's total transmit power.
The entire process is based on energy measurements which is very desirable from
an implementation point of view.
|
1202.0372
|
Analog Network Coding in General SNR Regime
|
cs.IT math.IT
|
The problem of maximum rate achievable with analog network coding for a
unicast communication over a layered wireless relay network with directed links
is considered. A relay node performing analog network coding scales and
forwards the signals received at its input. Recently this problem has been
considered under two assumptions: (A) each relay node scales its received
signal to the upper bound of its transmit power constraint, (B) the relay nodes
in specific subsets of the network operate in the high-SNR regime. We establish
that assumption (A), in general, leads to suboptimal end-to-end rate. We also
characterize the performance of analog network coding in class of symmetric
layered networks without assumption (B).
The key contribution of this work is a lemma that states that a globally
optimal set of scaling factors for the nodes in a layered relay network that
maximizes the end-to-end rate can be computed layer-by-layer. Specifically, a
rate-optimal set of scaling factors for the nodes in a layer is the one that
maximizes the sum-rate of the nodes in the next layer. This critical insight
allows us to characterize analog network coding performance in network
scenarios beyond those that can be analyzed using the existing approaches. We
illustrate this by computing the maximum rate achievable with analog network
coding in one particular layered network, in various communication scenarios.
|
1202.0404
|
Occupational mobility network of the Romanian higher education graduates
|
physics.soc-ph cs.SI
|
Although there is a rich literature on the rate of occupational mobility,
there are important gaps in understanding patterns of movement among
occupations. We employ a network based approach to explore occupational
mobility of the Romanian university graduates in the first years after
graduation (2003 - 2008). We use survey data on their career mobility to build
an empirical occupational mobility network (OMN) that covers all their job
movements in the considered period. We construct the network as directed and
weighted. The nodes are represented by the occupations (post coded at 3 digits
according to ISCO-88) and the links are weighted with the number of persons
switching from one occupation to another. This representation of data permits
us to use the novel statistical techniques developed in the framework of
weighted directed networks in order to extract a set of stylized facts that
highlight patterns of occupational mobility: centrality, network motifs.
|
1202.0417
|
Universal communication part II: channels with memory
|
cs.IT math.IT
|
Consider communication over a channel whose probabilistic model is completely
unknown vector-wise and is not assumed to be stationary. Communication over
such channels is challenging because knowing the past does not indicate
anything about the future. The existence of reliable feedback and common
randomness is assumed. In a previous paper it was shown that the Shannon
capacity cannot be attained, in general, if the channel is not known. An
alternative notion of "capacity" was defined, as the maximum rate of reliable
communication by any block-coding system used over consecutive blocks. This
rate was shown to be achievable for the modulo-additive channel with an
individual, unknown noise sequence, and not achievable for some channels with
memory. In this paper this "capacity" is shown to be achievable for general
channel models possibly including memory, as long as this memory fades with
time. In other words, there exists a system with feedback and common randomness
that, without knowledge of the channel, asymptotically performs as well as any
block code, which may be designed knowing the channel. For non-fading memory
channels a weaker type of "capacity" is shown to be achievable.
|
1202.0425
|
Comparing network covers using mutual information
|
math-ph cs.IT math.IT math.MP physics.data-an
|
In network science, researchers often use mutual information to understand
the difference between network partitions produced by community detection
methods. Here we extend the use of mutual information to covers, that is, the
cases where a node can belong to more than one module. In our proposed
solution, the underlying stochastic process used to compare partitions is
extended to deal with covers, and the random variables of the new process are
simply fed into the usual definition of mutual information. With partitions,
our extended process behaves exactly as the conventional approach for
partitions, and thus, the mutual information values obtained are the same. We
also describe how to perform sampling and do error estimation for our extended
process, as both are necessary steps for a practical application of this
measure. The stochastic process that we define here is not only applicable to
networks, but can also be used to compare more general set-to-set binary
relations.
|
1202.0436
|
On the Fixation Probability of Superstars
|
cs.CE cs.SI q-bio.PE
|
The Moran process models the spread of genetic mutations through a
population. A mutant with relative fitness $r$ is introduced into a population
and the system evolves, either reaching fixation (in which every individual is
a mutant) or extinction (in which none is). In a widely cited paper (Nature,
2005), Lieberman, Hauert and Nowak generalize the model to populations on the
vertices of graphs. They describe a class of graphs (called "superstars"), with
a parameter $k$. Superstars are designed to have an increasing fixation
probability as $k$ increases. They state that the probability of fixation tends
to $1-r^{-k}$ as graphs get larger but we show that this claim is untrue as
stated. Specifically, for $k=5$, we show that the true fixation probability (in
the limit, as graphs get larger) is at most $1-1/j(r)$ where
$j(r)=\Theta(r^4)$, contrary to the claimed result. We do believe that the
qualitative claim of Lieberman et al.\ --- that the fixation probability of
superstars tends to 1 as $k$ increases --- is correct, and that it can probably
be proved along the lines of their sketch. We were able to run larger computer
simulations than the ones presented in their paper. However, simulations on
graphs of around 40,000 vertices do not support their claim. Perhaps these
graphs are too small to exhibit the limiting behaviour.
|
1202.0440
|
The implications of embodiment for behavior and cognition: animal and
robotic case studies
|
cs.AI
|
In this paper, we will argue that if we want to understand the function of
the brain (or the control in the case of robots), we must understand how the
brain is embedded into the physical system, and how the organism interacts with
the real world. While embodiment has often been used in its trivial meaning,
i.e. 'intelligence requires a body', the concept has deeper and more important
implications, concerned with the relation between physical and information
(neural, control) processes. A number of case studies are presented to
illustrate the concept. These involve animals and robots and are concentrated
around locomotion, grasping, and visual perception. A theoretical scheme that
can be used to embed the diverse case studies will be presented. Finally, we
will establish a link between the low-level sensory-motor processes and
cognition. We will present an embodied view on categorization, and propose the
concepts of 'body schema' and 'forward models' as a natural extension of the
embodied approach toward first representations.
|
1202.0445
|
Iterative Mode-Dropping for the Sum Capacity of MIMO-MAC with
Per-Antenna Power Constraint
|
cs.IT math.IT
|
We propose an iterative mode-dropping algorithm that optimizes input signals
to achieve the sum capacity of the MIMO-MAC with per-antenna power constraint.
The algorithm successively optimizes each user's input covariance matrix by
applying mode-dropping to the equivalent single-user MIMO rate maximization
problem. Both analysis and simulation show fast convergence. We then use the
algorithm to briefly highlight the difference in MIMO-MAC capacities under sum
and per-antenna power constraints.
|
1202.0452
|
Game Theoretic Methods for the Smart Grid
|
cs.IT cs.GT cs.NI math.IT
|
The future smart grid is envisioned as a large-scale cyber-physical system
encompassing advanced power, communications, control, and computing
technologies. In order to accommodate these technologies, it will have to build
on solid mathematical tools that can ensure an efficient and robust operation
of such heterogeneous and large-scale cyber-physical systems. In this context,
this paper is an overview on the potential of applying game theory for
addressing relevant and timely open problems in three emerging areas that
pertain to the smart grid: micro-grid systems, demand-side management, and
communications. In each area, the state-of-the-art contributions are gathered
and a systematic treatment, using game theory, of some of the most relevant
problems for future power systems is provided. Future opportunities for
adopting game theoretic methodologies in the transition from legacy systems
toward smart and intelligent grids are also discussed. In a nutshell, this
article provides a comprehensive account of the application of game theory in
smart grid systems tailored to the interdisciplinary characteristics of these
systems that integrate components from power systems, networking,
communications, and control.
|
1202.0453
|
Bounding the number of points on a curve using a generalization of
Weierstrass semigroups
|
math.AG cs.IT math.IT
|
In this article we use techniques from coding theory to derive upper bounds
for the number of rational places of the function field of an algebraic curve
defined over a finite field. The used techniques yield upper bounds if the
(generalized) Weierstrass semigroup [P. Beelen, N. Tuta\c{s}: A generalization
of the Weierstrass semigroup, J. Pure Appl. Algebra, 207(2), 2006] for an
$n$-tuple of places is known, even if the exact defining equation of the curve
is not known. As shown in examples, this sometimes enables one to get an upper
bound for the number of rational places for families of function fields. Our
results extend results in [O. Geil, R. Matsumoto: Bounding the number of
$\mathbb{F}_q$-rational places in algebraic function fields using Weierstrass
semigroups. Pure Appl. Algebra, 213(6), 2009].
|
1202.0455
|
Bounds and Invariant Sets for a Class of Switching Systems with
Delayed-state-dependent Perturbations
|
cs.SY math.OC
|
We present a novel method to compute componentwise transient bounds, ultimate
bounds, and invariant regions for a class of switching continuous-time linear
systems with perturbation bounds that may depend nonlinearly on a delayed
state. The main advantage of the method is its componentwise nature, i.e. the
fact that it allows each component of the perturbation vector to have an
independent bound and that the bounds and sets obtained are also given
componentwise. This componentwise method does not employ a norm for bounding
either the perturbation or state vectors, avoids the need for scaling the
different state vector components in order to obtain useful results, and may
also reduce conservativeness in some cases. We give conditions for the derived
bounds to be of local or semi-global nature. In addition, we deal with the case
of perturbation bounds whose dependence on a delayed state is of affine form as
a particular case of nonlinear dependence for which the bounds derived are
shown to be globally valid. A sufficient condition for practical stability is
also provided. The present paper builds upon and extends to switching systems
with delayed-state-dependent perturbations previous results by the authors. In
this sense, the contribution is three-fold: the derivation of the
aforementioned extension; the elucidation of the precise relationship between
the class of switching linear systems to which the proposed method can be
applied and those that admit a common quadratic Lyapunov function (a question
that was left open in our previous work); and the derivation of a technique to
compute a common quadratic Lyapunov function for switching linear systems with
perturbations bounded componentwise by affine functions of the absolute value
of the state vector components.
|
1202.0457
|
Exact Scalar Minimum Storage Coordinated Regenerating Codes
|
cs.IT cs.DC math.IT
|
We study the exact and optimal repair of multiple failures in codes for
distributed storage. More particularly, we examine the use of interference
alignment to build exact scalar minimum storage coordinated regenerating codes
(MSCR). We show that it is possible to build codes for the case of k = 2 and d
> k by aligning interferences independently but that this technique cannot be
applied as soon as k > 2 and d > k. Our results also apply to adaptive
regenerating codes.
|
1202.0460
|
A Cooperative Bayesian Nonparametric Framework for Primary User Activity
Monitoring in Cognitive Radio Network
|
cs.IT cs.GT math.IT
|
This paper introduces a novel approach that enables a number of cognitive
radio devices that are observing the availability pattern of a number of
primary users(PUs), to cooperate and use \emph{Bayesian nonparametric}
techniques to estimate the distributions of the PUs' activity pattern, assumed
to be completely unknown. In the proposed model, each cognitive node may have
its own individual view on each PU's distribution, and, hence, seeks to find
partners having a correlated perception. To address this problem, a coalitional
game is formulated between the cognitive devices and an algorithm for
cooperative coalition formation is proposed. It is shown that the proposed
coalition formation algorithm allows the cognitive nodes that are experiencing
a similar behavior from some PUs to self-organize into disjoint, independent
coalitions. Inside each coalition, the cooperative cognitive nodes use a
combination of Bayesian nonparametric models such as the Dirichlet process and
statistical goodness of fit techniques in order to improve the accuracy of the
estimated PUs' activity distributions. Simulation results show that the
proposed algorithm significantly improves the estimates of the PUs'
distributions and yields a performance advantage, in terms of reduction of the
average achieved Kullback-Leibler distance between the real and the estimated
distributions, reaching up to 36.5% relative the non-cooperative estimates. The
results also show that the proposed algorithm enables the cognitive nodes to
adapt their cooperative decisions when the actual PUs' distributions change due
to, for example, PU mobility.
|
1202.0463
|
Network Formation Games Among Relay Stations in Next Generation Wireless
Networks
|
cs.IT math.IT
|
The introduction of relay station (RS) nodes is a key feature in next
generation wireless networks such as 3GPP's long term evolution advanced
(LTE-Advanced), or the forthcoming IEEE 802.16j WiMAX standard. This paper
presents, using game theory, a novel approach for the formation of the tree
architecture that connects the RSs and their serving base station in the
\emph{uplink} of the next generation wireless multi-hop systems. Unlike
existing literature which mainly focused on performance analysis, we propose a
distributed algorithm for studying the \emph{structure} and \emph{dynamics} of
the network. We formulate a network formation game among the RSs whereby each
RS aims to maximize a cross-layer utility function that takes into account the
benefit from cooperative transmission, in terms of reduced bit error rate, and
the costs in terms of the delay due to multi-hop transmission. For forming the
tree structure, a distributed myopic algorithm is devised. Using the proposed
algorithm, each RS can individually select the path that connects it to the BS
through other RSs while optimizing its utility. We show the convergence of the
algorithm into a Nash tree network, and we study how the RSs can adapt the
network's topology to environmental changes such as mobility or the deployment
of new mobile stations. Simulation results show that the proposed algorithm
presents significant gains in terms of average utility per mobile station which
is at least 17.1% better relatively to the case with no RSs and reaches up to
40.3% improvement compared to a nearest neighbor algorithm (for a network with
10 RSs). The results also show that the average number of hops does not exceed
3 even for a network with up to 25 RSs.
|
1202.0467
|
Coalitional Games in Partition Form for Joint Spectrum Sensing and
Access in Cognitive Radio Networks
|
cs.IT math.IT
|
Unlicensed secondary users (SUs) in cognitive radio networks are subject to
an inherent tradeoff between spectrum sensing and spectrum access. Although
each SU has an incentive to sense the primary user (PU) channels for locating
spectrum holes, this exploration of the spectrum can come at the expense of a
shorter transmission time, and, hence, a possibly smaller capacity for data
transmission. This paper investigates the impact of this tradeoff on the
cooperative strategies of a network of SUs that seek to cooperate in order to
improve their view of the spectrum (sensing), reduce the possibility of
interference among each other, and improve their transmission capacity
(access). The problem is modeled as a coalitional game in partition form and an
algorithm for coalition formation is proposed. Using the proposed algorithm,
the SUs can make individual distributed decisions to join or leave a coalition
while maximizing their utilities which capture the average time spent for
sensing as well as the capacity achieved while accessing the spectrum. It is
shown that, by using the proposed algorithm, the SUs can self-organize into a
network partition composed of disjoint coalitions, with the members of each
coalition cooperating to jointly optimize their sensing and access performance.
Simulation results show the performance improvement that the proposed algorithm
yields with respect to the non-cooperative case. The results also show how the
algorithm allows the SUs to self-adapt to changes in the environment such as
the change in the traffic of the PUs, or slow mobility.
|
1202.0474
|
Relational Semantics for Databases and Predicate Calculus
|
cs.DB cs.LO
|
The relational data model requires a theory of relations in which tuples are
not only many-sorted, but can also have indexes that are not necessarily
numerical. In this paper we develop such a theory and define operations on
relations that are adequate for database use. The operations are similar to
those of Codd's relational algebra, but differ in being based on a
mathematically adequate theory of relations. The semantics of predicate
calculus, being oriented toward the concept of satisfiability, is not suitable
for relational databases. We develop an alternative semantics that assigns
relations as meaning to formulas with free variables. This semantics makes the
classical predicate calculus suitable as a query language for relational
databases.
|
1202.0480
|
Detecting Communities in Networks by Merging Cliques
|
physics.soc-ph cs.SI
|
Many algorithms have been proposed for detecting disjoint communities
(relatively densely connected subgraphs) in networks. One popular technique is
to optimize modularity, a measure of the quality of a partition in terms of the
number of intracommunity and intercommunity edges. Greedy approximate
algorithms for maximizing modularity can be very fast and effective. We propose
a new algorithm that starts by detecting disjoint cliques and then merges these
to optimize modularity. We show that this performs better than other similar
algorithms in terms of both modularity and execution speed.
|
1202.0492
|
Resolving Implementation Ambiguity and Improving SURF
|
cs.CV
|
Speeded Up Robust Features (SURF) has emerged as one of the more popular
feature descriptors and detectors in recent years. Performance and algorithmic
details vary widely between implementations due to SURF's complexity and
ambiguities found in its description. To resolve these ambiguities, a set of
general techniques for feature stability is defined based on the smoothness
rule. Additional improvements to SURF are proposed for speed and stability. To
illustrate the importance of these implementation details, a performance study
of popular SURF implementations is done. By utilizing all the suggested
improvements, it is possible to create a SURF implementation that is several
times faster and more stable.
|
1202.0501
|
Global modeling of transcriptional responses in interaction networks
|
q-bio.MN cs.CE q-bio.QM stat.AP stat.ML
|
Motivation: Cell-biological processes are regulated through a complex network
of interactions between genes and their products. The processes, their
activating conditions, and the associated transcriptional responses are often
unknown. Organism-wide modeling of network activation can reveal unique and
shared mechanisms between physiological conditions, and potentially as yet
unknown processes. We introduce a novel approach for organism-wide discovery
and analysis of transcriptional responses in interaction networks. The method
searches for local, connected regions in a network that exhibit coordinated
transcriptional response in a subset of conditions. Known interactions between
genes are used to limit the search space and to guide the analysis. Validation
on a human pathway network reveals physiologically coherent responses,
functional relatedness between physiological conditions, and coordinated,
context-specific regulation of the genes. Availability: Implementation is
freely available in R and Matlab at http://netpro.r-forge.r-project.org
|
1202.0515
|
High-Dimensional Feature Selection by Feature-Wise Kernelized Lasso
|
stat.ML cs.AI stat.ME
|
The goal of supervised feature selection is to find a subset of input
features that are responsible for predicting output values. The least absolute
shrinkage and selection operator (Lasso) allows computationally efficient
feature selection based on linear dependency between input features and output
values. In this paper, we consider a feature-wise kernelized Lasso for
capturing non-linear input-output dependency. We first show that, with
particular choices of kernel functions, non-redundant features with strong
statistical dependence on output values can be found in terms of kernel-based
independence measures. We then show that the globally optimal solution can be
efficiently computed; this makes the approach scalable to high-dimensional
problems. The effectiveness of the proposed method is demonstrated through
feature selection experiments with thousands of features.
|
1202.0518
|
Explicit capacity-achieving receivers for optical communication and
quantum reading
|
quant-ph cs.IT math.IT
|
An important practical open question has been to design explicit, structured
optical receivers that achieve the Holevo limit in the contexts of optical
communication and "quantum reading." The Holevo limit is an achievable rate
that is higher than the Shannon limit of any known optical receiver. We
demonstrate how a sequential decoding approach can achieve the Holevo limit for
both of these settings. A crucial part of our scheme for both settings is a
non-destructive "vacuum-or-not" measurement that projects an n-symbol modulated
codeword onto the n-fold vacuum state or its orthogonal complement, such that
the post-measurement state is either the n-fold vacuum or has the vacuum
removed from the support of the n symbols' joint quantum state. The sequential
decoder for optical communication requires the additional ability to perform
multimode optical phase-space displacements---realizable using a beamsplitter
and a laser, while the sequential decoder for quantum reading also requires the
ability to perform phase-shifting (realizable using a phase plate) and online
squeezing (a phase-sensitive amplifier).
|
1202.0521
|
On ML-Certificate Linear Constraints for Rank Modulation with Linear
Programming Decoding and its Application to Compact Graphs
|
math.CO cs.IT math.IT
|
Linear constraints for a matrix polytope with no fractional vertex are
investigated as intersecting research among permutation codes, rank
modulations, and linear programming methods. By focusing the discussion to the
block structure of matrices, new classes of such polytopes are obtained from
known small polytopes. This concept, called "consolidation", is applied to find
a new compact graph which is known as an approach for the graph isomorphism
problem. Encoding and decoding algorithms for our new permutation codes are
obtained from existing algorithms for small polytopes. The minimum distances
associated with Kendall-tau distance and the minimum Euclidean distance of a
code obtained by changing the basis of a permutation code may be larger than
the original one.
|
1202.0533
|
Polar coding to achieve the Holevo capacity of a pure-loss optical
channel
|
cs.IT math.IT quant-ph
|
In the low-energy high-energy-efficiency regime of classical optical
communications---relevant to deep-space optical channels---there is a big gap
between reliable communication rates achievable via conventional optical
receivers and the ultimate (Holevo) capacity. Achieving the Holevo capacity
requires not only optimal codes but also receivers that make collective
measurements on long (modulated) codeword waveforms, and it is impossible to
implement these collective measurements via symbol-by-symbol detection along
with classical postprocessing. Here, we apply our recent results on the
classical-quantum polar code---the first near-explicit, linear,
symmetric-Holevo-rate achieving code---to the lossy optical channel, and we
show that it almost closes the entire gap to the Holevo capacity in the low
photon number regime. In contrast, Arikan's original polar codes, applied to
the DMC induced by the physical optical channel paired with any conceivable
structured optical receiver (including optical homodyne, heterodyne, or
direct-detection) fails to achieve the ultimate Holevo limit to channel
capacity. However, our polar code construction (which uses the quantum fidelity
as a channel parameter rather than the classical Bhattacharyya quantity to
choose the "good channels" in the polar-code construction), paired with a
quantum successive-cancellation receiver---which involves a sequence of
collective non-destructive binary projective measurements on the joint quantum
state of the received codeword waveform---can attain the Holevo limit, and can
hence in principle achieve higher rates than Arikan's polar code and decoder
directly applied to the optical channel. However, even a theoretical recipe for
construction of an optical realization of the quantum successive-cancellation
receiver remains an open question.
|
1202.0534
|
Observability, Controllability and Local Reducibility of Linear Codes on
Graphs
|
cs.IT cs.SY math.IT
|
This paper is concerned with the local reducibility properties of linear
realizations of codes on finite graphs.
Trimness and properness are dual properties of constraint codes. A linear
realization is locally reducible if any constraint code is not both trim and
proper. On a finite cycle-free graph, a linear realization is minimal if and
only if every constraint code is both trim and proper.
A linear realization is called observable if it is one-to-one, and
controllable if all constraints are independent. Observability and
controllability are dual properties. An unobservable or uncontrollable
realization is locally reducible. A parity-check realization is uncontrollable
if and only if it has redundant parity checks. A tail-biting trellis
realization is uncontrollable if and only if its trajectories partition into
disconnected subrealizations. General graphical realizations do not share this
property.
|
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