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1008.0938
|
Emergence of Zipf's Law in the Evolution of Communication
|
nlin.AO cond-mat.stat-mech cs.IT math-ph math.IT math.MP physics.soc-ph
|
Zipf's law seems to be ubiquitous in human languages and appears to be a
universal property of complex communicating systems. Following the early
proposal made by Zipf concerning the presence of a tension between the efforts
of speaker and hearer in a communication system, we introduce evolution by
means of a variational approach to the problem based on Kullback's Minimum
Discrimination of Information Principle. Therefore, using a formalism fully
embedded in the framework of information theory, we demonstrate that Zipf's law
is the only expected outcome of an evolving, communicative system under a
rigorous definition of the communicative tension described by Zipf.
|
1008.0941
|
Timing matters: Lessons From The CA Literature On Updating
|
cs.MA nlin.AO nlin.CG
|
In the present article we emphasize the importance of modeling time in the
context of agent-based models. To this end, we present a (selective) survey of
the Cellular Automata-literature on updating and draw parallels to the issue of
agent activation in agent-based models. By means of two simple models,
Schelling's segregation model and Epstein's demographic prisoner's dilemma we
investigate the influence of choosing different regimes of agent activation.
Our experiments indicate that timing is not a critical issue for very simple
models but bears huge influence on model behavior and results as soon as the
degree of complexity increases only so slightly. After a brief review of the
way commonly used ABM simulation environments handle the issue of timing, we
draw some tentative conclusions about the importance of timing and the need for
more research towards that direction, similar to the concerted effort on
updating in cellular automata.
|
1008.0961
|
On the Shannon Cipher System With a Wiretapper Guessing Subject to
Distortion and Reliability Requirements
|
cs.IT math.IT
|
In this paper we discuss the processes in the Shannon cipher system with
discrete memoryless source and a guessing wiretapper. The wiretapper observes a
cryptogram of $N$-vector of ciphered messages in the public channel and tries
to guess successively the vector of messages within given distortion level
$\Delta$ and small probability of error less than $\exp \{-NE\}$ with positive
reliability index $E$. The security of the system is measured by the expected
number of guesses which wiretapper needs for the approximate reconstruction of
the vector of source messages. The distortion, the reliability criteria and the
possibility of upper limiting the number of guesses extend the approach studied
by Merhav and Arikan. A single-letter characterization is given for the region
of pairs $(R_L,R)$ (of the rate $R_L$ of the maximum number of guesses $L(N)$
and the rate $R$ of the average number of guesses) in dependence on key rate
$R_K$, distortion level $\Delta$ and reliability $E$.
|
1008.1043
|
Aggregate Interference Modeling in Cognitive Radio Networks with Power
and Contention Control
|
cs.IT math.IT
|
In this paper, we present an interference model for cognitive radio (CR)
networks employing power control, contention control or hybrid power/contention
control schemes. For the first case, a power control scheme is proposed to
govern the transmission power of a CR node. For the second one, a contention
control scheme at the media access control (MAC) layer, based on carrier sense
multiple access with collision avoidance (CSMA/CA), is proposed to coordinate
the operation of CR nodes with transmission requests. The probability density
functions of the interference received at a primary receiver from a CR network
are first derived numerically for these two cases. For the hybrid case, where
power and contention controls are jointly adopted by a CR node to govern its
transmission, the interference is analyzed and compared with that of the first
two schemes by simulations. Then, the interference distributions under the
first two control schemes are fitted by log-normal distributions with greatly
reduced complexity. Moreover, the effect of a hidden primary receiver on the
interference experienced at the receiver is investigated. It is demonstrated
that both power and contention controls are effective approaches to alleviate
the interference caused by CR networks. Some in-depth analysis of the impact of
key parameters on the interference of CR networks is given via numerical
studies as well.
|
1008.1047
|
Robust Adaptive Beamforming Based on Steering Vector Estimation via
Semidefinite Programming Relaxation
|
cs.IT math.IT math.OC stat.AP
|
We develop a new approach to robust adaptive beamforming in the presence of
signal steering vector errors. Since the signal steering vector is known
imprecisely, its presumed (prior) value is used to find a more accurate
estimate of the actual steering vector, which then is used for obtaining the
optimal beamforming weight vector. The objective for finding such an estimate
of the actual signal steering vector is the maximization of the beamformer
output power, while the constraints are the normalization condition and the
requirement that the estimate of the steering vector does not converge to an
interference steering vector. Our objective and constraints are free of any
design parameters of non-unique choice. The resulting optimization problem is a
non-convex quadratically constrained quadratic program, which is NP hard in
general. However, for our problem we show that an efficient solution can be
found using the semi-definite relaxation technique. Moreover, the strong
duality holds for the proposed problem and can also be used for finding the
optimal solution efficiently and at low complexity. In some special cases, the
solution can be even found in closed-form. Our simulation results demonstrate
the superiority of the proposed method over other previously developed robust
adaptive beamforming methods for several frequently encountered types of signal
steering vector errors.
|
1008.1079
|
Perfect Omniscience, Perfect Secrecy and Steiner Tree Packing
|
cs.IT math.CO math.IT
|
We consider perfect secret key generation for a ``pairwise independent
network'' model in which every pair of terminals share a random binary string,
with the strings shared by distinct terminal pairs being mutually independent.
The terminals are then allowed to communicate interactively over a public
noiseless channel of unlimited capacity. All the terminals as well as an
eavesdropper observe this communication. The objective is to generate a perfect
secret key shared by a given set of terminals at the largest rate possible, and
concealed from the eavesdropper.
First, we show how the notion of perfect omniscience plays a central role in
characterizing perfect secret key capacity. Second, a multigraph representation
of the underlying secrecy model leads us to an efficient algorithm for perfect
secret key generation based on maximal Steiner tree packing. This algorithm
attains capacity when all the terminals seek to share a key, and, in general,
attains at least half the capacity. Third, when a single ``helper'' terminal
assists the remaining ``user'' terminals in generating a perfect secret key, we
give necessary and sufficient conditions for the optimality of the algorithm;
also, a ``weak'' helper is shown to be sufficient for optimality.
|
1008.1096
|
The Naming Game in Social Networks: Community Formation and Consensus
Engineering
|
physics.soc-ph cond-mat.stat-mech cs.MA
|
We study the dynamics of the Naming Game [Baronchelli et al., (2006) J. Stat.
Mech.: Theory Exp. P06014] in empirical social networks. This stylized
agent-based model captures essential features of agreement dynamics in a
network of autonomous agents, corresponding to the development of shared
classification schemes in a network of artificial agents or opinion spreading
and social dynamics in social networks. Our study focuses on the impact that
communities in the underlying social graphs have on the outcome of the
agreement process. We find that networks with strong community structure hinder
the system from reaching global agreement; the evolution of the Naming Game in
these networks maintains clusters of coexisting opinions indefinitely. Further,
we investigate agent-based network strategies to facilitate convergence to
global consensus.
|
1008.1140
|
On Two Strong Converse Theorems for Stationary Discrete Memoryless
Channels
|
cs.IT math.IT
|
In 1973, Arimoto proved the strong converse theorem for the discrete
memoryless channels stating that when transmission rate $R$ is above channel
capacity $C$, the error probability of decoding goes to one as the block length
$n$ of code word tends to infinity. He proved the theorem by deriving the
exponent function of error probability of correct decoding that is positive if
and only if $R>C$. Subsequently, in 1979, Dueck and K\"orner determined the
optimal exponent of correct decoding. Arimoto's bound has been said to be equal
to the bound of Dueck and K\"orner. However its rigorous proof has not been
presented so far. In this paper we give a rigorous proof of the equivalence of
Arimoto's bound to that of Dueck and K\"orner.
|
1008.1145
|
Linear Beamforming for the Spatially Correlated MISO broadcast channel
|
cs.IT math.IT
|
A spatially correlated broadcast setting with M antennas at the base station
and M users (each with a single antenna) is considered. We assume that the
users have perfect channel information about their links and the base station
has only statistical information about each user's link. The base station
employs a linear beamforming strategy with one spatial eigen-mode allocated to
each user. The goal of this work is to understand the structure of the
beamforming vectors that maximize the ergodic sum-rate achieved by treating
interference as noise. In the M = 2 case, we first fix the beamforming vectors
and compute the ergodic sum-rate in closed-form as a function of the channel
statistics. We then show that the optimal beamforming vectors are the dominant
generalized eigenvectors of the covariance matrices of the two links. It is
difficult to obtain intuition on the structure of the optimal beamforming
vectors for M > 2 due to the complicated nature of the sum-rate expression.
Nevertheless, in the case of asymptotic M, we show that the optimal beamforming
vectors have to satisfy a set of fixed-point equations.
|
1008.1150
|
Modeling the growth of fingerprints improves matching for adolescents
|
cs.CV stat.AP
|
We study the effect of growth on the fingerprints of adolescents, based on
which we suggest a simple method to adjust for growth when trying to recover a
juvenile's fingerprint in a database years later. Based on longitudinal data
sets in juveniles' criminal records, we show that growth essentially leads to
an isotropic rescaling, so that we can use the strong correlation between
growth in stature and limbs to model the growth of fingerprints proportional to
stature growth as documented in growth charts. The proposed rescaling leads to
a 72% reduction of the distances between corresponding minutiae for the data
set analyzed. These findings were corroborated by several verification tests.
In an identification test on a database containing 3.25 million right index
fingers at the Federal Criminal Police Office of Germany, the identification
error rate of 20.8% was reduced to 2.1% by rescaling. The presented method is
of striking simplicity and can easily be integrated into existing automated
fingerprint identification systems.
|
1008.1188
|
Data visualization in political and social sciences
|
cs.GR cs.CE cs.CY
|
The basic objective of data visualization is to provide an efficient
graphical display for summarizing and reasoning about quantitative information.
During the last decades, political science has accumulated a large corpus of
various kinds of data such as comprehensive factbooks and atlases,
characterizing all or most of existing states by multiple and objectively
assessed numerical indicators within certain time lapse. As a consequence,
there exists a continuous trend for political science to gradually become a
more quantitative scientific field and to use quantitative information in the
analysis and reasoning. It is believed that any objective analysis in political
science must be multidimensional and combine various sources of quantitative
information; however, human capabilities for perception of large massifs of
numerical information are limited. Hence, methods and approaches for
visualization of quantitative and qualitative data (and, especially
multivariate data) is an extremely important topic. Data visualization
approaches can be classified into several groups, starting from creating
informative charts and diagrams (statistical graphics and infographics) and
ending with advanced statistical methods for visualizing multidimensional
tables containing both quantitative and qualitative information. In this
article we provide a short review of existing methods of data visualization
methods with applications in political and social science.
|
1008.1191
|
Improved Fast Similarity Search in Dictionaries
|
cs.IR cs.DS
|
We engineer an algorithm to solve the approximate dictionary matching
problem. Given a list of words $\mathcal{W}$, maximum distance $d$ fixed at
preprocessing time and a query word $q$, we would like to retrieve all words
from $\mathcal{W}$ that can be transformed into $q$ with $d$ or less edit
operations. We present data structures that support fault tolerant queries by
generating an index. On top of that, we present a generalization of the method
that eases memory consumption and preprocessing time significantly. At the same
time, running times of queries are virtually unaffected. We are able to match
in lists of hundreds of thousands of words and beyond within microseconds for
reasonable distances.
|
1008.1270
|
Proceedings Twelfth Annual Workshop on Descriptional Complexity of
Formal Systems
|
cs.FL cs.CC cs.DM cs.IT cs.LO math.IT
|
The 12th annual workshop, Descriptional Complexity of Formal Systems 2010, is
taking place in Saskatoon, Canada, on August 8-10, 2010. It is jointly
organized by the IFIP Working Group 1.2 on Descriptional Complexity and by the
Department of Computer Science at the University of Saskatchewan. This volume
contains the papers of the invited lectures and the accepted contributions.
|
1008.1284
|
Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding
|
math.NT cs.CR cs.IT math.IT
|
We develop a framework for solving polynomial equations with size constraints
on solutions. We obtain our results by showing how to apply a technique of
Coppersmith for finding small solutions of polynomial equations modulo integers
to analogous problems over polynomial rings, number fields, and function
fields. This gives us a unified view of several problems arising naturally in
cryptography, coding theory, and the study of lattices. We give (1) a
polynomial-time algorithm for finding small solutions of polynomial equations
modulo ideals over algebraic number fields, (2) a faster variant of the
Guruswami-Sudan algorithm for list decoding of Reed-Solomon codes, and (3) an
algorithm for list decoding of algebraic-geometric codes that handles both
single-point and multi-point codes. Coppersmith's algorithm uses lattice basis
reduction to find a short vector in a carefully constructed lattice; powerful
analogies from algebraic number theory allow us to identify the appropriate
analogue of a lattice in each application and provide efficient algorithms to
find a suitably short vector, thus allowing us to give completely parallel
proofs of the above theorems.
|
1008.1309
|
Towards arrow-theoretic semantics of ontologies: conceptories
|
cs.LO cs.AI math.CT
|
In context of efforts of composing category-theoretic and logical methods in
the area of knowledge representation we propose the notion of conceptory. We
consider intersection/union and other constructions in conceptories as
expressive alternative to category-theoretic (co)limits and show they have
features similar to (pro-, in-)jections. Then we briefly discuss approaches to
development of formal systems built on the base of conceptories and describe
possible application of such system to the specific ontology.
|
1008.1328
|
Semantic Oriented Agent based Approach towards Engineering Data
Management, Web Information Retrieval and User System Communication Problems
|
cs.AI
|
The four intensive problems to the software rose by the software industry
.i.e., User System Communication / Human Machine Interface, Meta Data
extraction, Information processing & management and Data representation are
discussed in this research paper. To contribute in the field we have proposed
and described an intelligent semantic oriented agent based search engine
including the concepts of intelligent graphical user interface, natural
language based information processing, data management and data reconstruction
for the final user end information representation.
|
1008.1333
|
An Agent based Approach towards Metadata Extraction, Modelling and
Information Retrieval over the Web
|
cs.AI
|
Web development is a challenging research area for its creativity and
complexity. The existing raised key challenge in web technology technologic
development is the presentation of data in machine read and process able format
to take advantage in knowledge based information extraction and maintenance.
Currently it is not possible to search and extract optimized results using full
text queries because there is no such mechanism exists which can fully extract
the semantic from full text queries and then look for particular knowledge
based information.
|
1008.1335
|
Designing a Dynamic Components and Agent based Approach for Semantic
Information Retrieval
|
cs.IR
|
In this paper based on agent and semantic web technologies we propose an
approach .i.e., Semantic Oriented Agent Based Search (SOAS), to cope with
currently existing challenges of Meta data extraction, modeling and information
retrieval over the web. SOAS is designed by keeping four major requirements
.i.e., Automatic user request handling, Dynamic unstructured full text reading,
Analysing and modeling, Semantic query generation and optimized result
classifier. The architecture of SOAS is consisting of an agent called Personal
Agent (PA) and five dynamic components .i.e., Request Processing Unit (RPU),
Agent Locator (AL), Agent Communicator (AC), List Builder (LB) and Result
Generator (RG). Furthermore, in this paper we briefly discuss Semantic Web and
some already existing in time proposed and implemented semantic based
approaches.
|
1008.1337
|
PDM based I-SOAS Data Warehouse Design
|
cs.DB
|
This research paper briefly describes the industrial contributions of Product
Data Management in any organization's technical and managerial data management.
Then focusing on some current major PDM based problems i.e. Static and
Unintelligent Search, Platform Independent System and Successful PDM System
Implementation, briefly presents a semantic based solution i.e. I-SOAS. Majorly
this research paper is about to present and discuss the contributions of I-SOAS
in any organization's technical and system data management.
|
1008.1339
|
Removal of Communication Gap
|
cs.DB
|
This research is about an online forum designed and developed to improve the
communication process between alumni, new, old and upcoming students. In this
research paper we present targeted problems, designed architecture, used
technologies in development and final end product in detail.
|
1008.1343
|
Spectrum of Sizes for Perfect Deletion-Correcting Codes
|
cs.IT cs.DM math.CO math.IT
|
One peculiarity with deletion-correcting codes is that perfect
$t$-deletion-correcting codes of the same length over the same alphabet can
have different numbers of codewords, because the balls of radius $t$ with
respect to the Levenshte\u{\i}n distance may be of different sizes. There is
interest, therefore, in determining all possible sizes of a perfect
$t$-deletion-correcting code, given the length $n$ and the alphabet size~$q$.
In this paper, we determine completely the spectrum of possible sizes for
perfect $q$-ary 1-deletion-correcting codes of length three for all $q$, and
perfect $q$-ary 2-deletion-correcting codes of length four for almost all $q$,
leaving only a small finite number of cases in doubt.
|
1008.1357
|
Social Networks and Spin Glasses
|
cs.SI cs.CY
|
The networks formed from the links between telephones observed in a month's
call detail records (CDRs) in the UK are analyzed, looking for the
characteristics thought to identify a communications network or a social
network. Some novel methods are employed. We find similarities to both types of
network. We conclude that, just as analogies to spin glasses have proved
fruitful for optimization of large scale practical problems, there will be
opportunities to exploit a statistical mechanics of the formation and dynamics
of social networks in today's electronically connected world.
|
1008.1366
|
Efficient Dealiased Convolutions without Padding
|
cs.CE physics.comp-ph
|
Algorithms are developed for calculating dealiased linear convolution sums
without the expense of conventional zero-padding or phase-shift techniques. For
one-dimensional in-place convolutions, the memory requirements are identical
with the zero-padding technique, with the important distinction that the
additional work memory need not be contiguous with the input data. This
decoupling of data and work arrays dramatically reduces the memory and
computation time required to evaluate higher-dimensional in-place convolutions.
The technique also allows one to dealias the higher-order convolutions that
arise from Fourier transforming cubic and higher powers. Implicitly dealiased
convolutions can be built on top of state-of-the-art fast Fourier transform
libraries: vectorized multidimensional implementations for the complex and
centered Hermitian (pseudospectral) cases have been implemented in the
open-source software FFTW++.
|
1008.1387
|
Codes over Matrix Rings for Space-Time Coded Modulations
|
cs.IT math.IT
|
It is known that, for transmission over quasi-static MIMO fading channels
with n transmit antennas, diversity can be obtained by using an inner fully
diverse space-time block code while coding gain, derived from the determinant
criterion, comes from an appropriate outer code. When the inner code has a
cyclic algebra structure over a number field, as for perfect space-time codes,
an outer code can be designed via coset coding. More precisely, we take the
quotient of the algebra by a two-sided ideal which leads to a finite alphabet
for the outer code, with a cyclic algebra structure over a finite field or a
finite ring. We show that the determinant criterion induces various metrics on
the outer code, such as the Hamming and Bachoc distances. When n=2,
partitioning the 2x2 Golden code by using an ideal above the prime 2 leads to
consider codes over either M2(F_2) or M2(F_2[i]), both being non-commutative
alphabets. Matrix rings of higher dimension, suitable for 3x3 and 4x4 perfect
codes, give rise to more complex examples.
|
1008.1393
|
Towards Nonstationary, Nonparametric Independent Process Analysis with
Unknown Source Component Dimensions
|
stat.ME cs.IT math.DS math.IT math.ST stat.TH
|
The goal of this paper is to extend independent subspace analysis (ISA) to
the case of (i) nonparametric, not strictly stationary source dynamics and (ii)
unknown source component dimensions. We make use of functional autoregressive
(fAR) processes to model the temporal evolution of the hidden sources. An
extension of the ISA separation principle--which states that the ISA problem
can be solved by traditional independent component analysis (ICA) and
clustering of the ICA elements--is derived for the solution of the defined fAR
independent process analysis task (fAR-IPA): applying fAR identification we
reduce the problem to ISA. A local averaging approach, the Nadaraya-Watson
kernel regression technique is adapted to obtain strongly consistent fAR
estimation. We extend the Amari-index to different dimensional components and
illustrate the efficiency of the fAR-IPA approach by numerical examples.
|
1008.1394
|
Towards Design and Implementation of a Language Technology based
Information Processor for PDM Systems
|
cs.IR cs.CL cs.SE
|
Product Data Management (PDM) aims to provide 'Systems' contributing in
industries by electronically maintaining organizational data, improving data
repository system, facilitating with easy access to CAD and providing
additional information engineering and management modules to access, store,
integrate, secure, recover and manage information. Targeting one of the
unresolved issues i.e., provision of natural language based processor for the
implementation of an intelligent record search mechanism, an approach is
proposed and discussed in detail in this manuscript. Designing an intelligent
application capable of reading and analyzing user's structured and unstructured
natural language based text requests and then extracting desired concrete and
optimized results from knowledge base is still a challenging task for the
designers because it is still very difficult to completely extract Meta data
out of raw data. Residing within the limited scope of current research and
development; we present an approach capable of reading user's natural language
based input text, understanding the semantic and extracting results from
repositories. To evaluate the effectiveness of implemented prototyped version
of proposed approach, it is compared with some existing PDM Systems, in the end
the discussion is concluded with an abstract presentation of resultant
comparison amongst implemented prototype and some existing PDM Systems.
|
1008.1398
|
Semi-Supervised Kernel PCA
|
cs.LG
|
We present three generalisations of Kernel Principal Components Analysis
(KPCA) which incorporate knowledge of the class labels of a subset of the data
points. The first, MV-KPCA, penalises within class variances similar to Fisher
discriminant analysis. The second, LSKPCA is a hybrid of least squares
regression and kernel PCA. The final LR-KPCA is an iteratively reweighted
version of the previous which achieves a sigmoid loss function on the labeled
points. We provide a theoretical risk bound as well as illustrative experiments
on real and toy data sets.
|
1008.1427
|
Optimal Feedback Systems with Analogue Adaptive Transmitters
|
cs.IT math.IT
|
The paper presents original approach to concurrent optimization of the
transmitting and receiving parts of adaptive communication systems (CS) with
feedback channels. The results of research show a possibility and the way of
designing the systems transmitting the signals with a bit rate equal to the
capacity of the forward channel under given bit-error rate (BER). The results
of work can be used for design of different classes of high-efficient low
energy/size/cost CS, as well as allow further development and extension.
|
1008.1438
|
Harmonic Analysis and Qualitative Uncertainty Principle
|
cs.IT math-ph math.CA math.IT math.MP
|
This paper investigates the mathematical nature of qualitative uncertainty
principle (QUP), which plays an important role in mathematics, physics and
engineering fields. Consider a 3-tuple (K, H1, H2) that K: H1 -> H2 is an
integral operator. Suppose a signal f in H1, {\Omega}1 and {\Omega}2 are
domains on which f, Kf define respectively. Does this signal f vanish if
|{\Sigma}(f)|<|{\Omega}1|and|{\Sigma}(Kf)|<|{\Omega}2|? The excesses and
deficiencies of integral kernel K({\omega}, t) are found to be greatly related
to this general formulation of QUP. The complete point theory of integral
kernel is so established to deal with the QUP. This theory addresses the
density and linear independence of integral kernels. Some algebraic and
geometric properties of complete points are presented. It is shown that the
satisfaction of QUP depends on the existence of some complete points. By
recognizing complete points of their corresponding integral kernels, the QUP
with Fourier transform, Wigner-Ville distribution, Gabor transform and wavelet
are studied. It is shown the QUP only holds for good behaved integral
operators. An investigation of full violation of QUP shows that L2 space is
large for high resolution harmonic analysis. And the invertible linear integral
transforms whose kernels are complete in L2 probably lead to the satisfaction
of QUP. It indicates the performance limitation of linear integral transforms
in harmonic analysis. Two possible ways bypassing uncertainty principle,
nonlinear method and sparse representation, are thus suggested. The notion of
operator family is developed and is applied to understand remarkable
performances of recent sparse representation.
|
1008.1455
|
The Diversity-Multiplexing Tradeoff of the Dynamic Decode-and-Forward
Protocol on a MIMO Half-Duplex Relay Channel
|
cs.IT math.IT
|
The diversity-multiplexing tradeoff of the dynamic decode-and-forward
protocol is characterized for the half-duplex three-terminal (m,k,n)-relay
channel where the source, relay and the destination terminals have m, k and n
antennas, respectively. It is obtained as a solution to a simple, two-variable,
convex optimization problem and this problem is solved in closed form for
special classes of relay channels, namely, the (1,k,1) relay channel, the
(n,1,n) relay channel and the (2,k,2) relay channel. Moreover, the tradeoff
curves for a certain class of relay channels, such as the (m,k,n>k) channels,
are identical to those for the decode-and-forward protocol for the full duplex
channel while for other classes of channels they are marginally lower at high
multiplexing gains. Our results also show that for some classes of relay
channels and at low multiplexing gains the diversity orders of the dynamic
decode-and-forward protocol protocol are greater than those of the static
compress-and-forward protocol which in turn is known to be tradeoff optimal
over all {\em static} half duplex protocols. In general, the dynamic
decode-and-forward protocol has a performance that is comparable to that of the
static compress-and-forward protocol which, unlike the dynamic
decode-and-forward protocol, requires global channel state information at the
relay node. Its performance is also close to that of the decode-and-forward
protocol over the full-duplex relay channel thereby indicating that the
half-duplex constraint can be compensated for by the dynamic operation of the
relay wherein the relay switches from the receive to the transmit mode based on
the source-relay channel quality.
|
1008.1484
|
A note on communicating between information systems based on including
degrees
|
cs.AI
|
In order to study the communication between information systems, Gong and
Xiao [Z. Gong and Z. Xiao, Communicating between information systems based on
including degrees, International Journal of General Systems 39 (2010) 189--206]
proposed the concept of general relation mappings based on including degrees.
Some properties and the extension for fuzzy information systems of the general
relation mappings have been investigated there. In this paper, we point out by
counterexamples that several assertions (Lemma 3.1, Lemma 3.2, Theorem 4.1, and
Theorem 4.3) in the aforementioned work are not true in general.
|
1008.1516
|
The Hitchhiker's Guide to Affiliation Networks: A Game-Theoretic
Approach
|
cs.GT cs.SI
|
We propose a new class of game-theoretic models for network formation in
which strategies are not directly related to edge choices, but instead
correspond more generally to the exertion of social effort. The observed social
network is thus a byproduct of an expressive strategic interaction, which can
more naturally explain the emergence of complex social structures. Within this
framework, we present a natural network formation game in which agent utilities
are locally defined and that, despite its simplicity, produces a rich class of
equilibria that exhibit structural properties commonly observed in social
networks - such as triadic closure - that have proved elusive in most existing
models.
Specifically, we consider a game in which players organize networking events
at a cost that grows with the number of attendees. An event's cost is assumed
by the organizer but the benefit accrues equally to all attendees: a link is
formed between any two players who see each other at more than a certain number
r of events per time period. The graph of connections so obtained is the social
network of the model.
We analyze the Nash equilibria of this game when each player derives a
benefit a>0 from all her neighbors in the network and when the costs are
linear, i.e., when the cost of an event with L invitees is b+cL, with b>0 and
c>0. For a/cr > 1 and b sufficiently small, all Nash equilibria have the
complete graph as their social network; for a/cr < 1 the Nash equilibria
correspond to a rich class of social networks, all of which have substantial
clustering in the sense that the clustering coefficient is bounded below by the
inverse of the average degree. Additionally, for any degree sequence with
finite mean, and not too many vertices of degree one or two, we can construct a
Nash equilibrium producing a social network with the given degree sequence.
|
1008.1566
|
Separate Training for Conditional Random Fields Using Co-occurrence Rate
Factorization
|
cs.LG cs.AI
|
The standard training method of Conditional Random Fields (CRFs) is very slow
for large-scale applications. As an alternative, piecewise training divides the
full graph into pieces, trains them independently, and combines the learned
weights at test time. In this paper, we present \emph{separate} training for
undirected models based on the novel Co-occurrence Rate Factorization (CR-F).
Separate training is a local training method. In contrast to MEMMs, separate
training is unaffected by the label bias problem. Experiments show that
separate training (i) is unaffected by the label bias problem; (ii) reduces the
training time from weeks to seconds; and (iii) obtains competitive results to
the standard and piecewise training on linear-chain CRFs.
|
1008.1610
|
New Constant-Weight Codes from Propagation Rules
|
cs.IT cs.DM math.IT
|
This paper proposes some simple propagation rules which give rise to new
binary constant-weight codes.
|
1008.1611
|
Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition
Codes
|
cs.IT cs.DM math.CO math.IT
|
An optimal constant-composition or constant-weight code of weight $w$ has
linear size if and only if its distance $d$ is at least $2w-1$. When $d\geq
2w$, the determination of the exact size of such a constant-composition or
constant-weight code is trivial, but the case of $d=2w-1$ has been solved
previously only for binary and ternary constant-composition and constant-weight
codes, and for some sporadic instances.
This paper provides a construction for quasicyclic optimal
constant-composition and constant-weight codes of weight $w$ and distance
$2w-1$ based on a new generalization of difference triangle sets. As a result,
the sizes of optimal constant-composition codes and optimal constant-weight
codes of weight $w$ and distance $2w-1$ are determined for all such codes of
sufficiently large lengths. This solves an open problem of Etzion.
The sizes of optimal constant-composition codes of weight $w$ and distance
$2w-1$ are also determined for all $w\leq 6$, except in two cases.
|
1008.1615
|
Optimal Partitioned Cyclic Difference Packings for Frequency Hopping and
Code Synchronization
|
cs.IT cs.DM math.CO math.IT
|
Optimal partitioned cyclic difference packings (PCDPs) are shown to give rise
to optimal frequency-hopping sequences and optimal comma-free codes. New
constructions for PCDPs, based on almost difference sets and cyclic difference
matrices, are given. These produce new infinite families of optimal PCDPs (and
hence optimal frequency-hopping sequences and optimal comma-free codes). The
existence problem for optimal PCDPs in ${\mathbb Z}_{3m}$, with $m$ base blocks
of size three, is also solved for all $m\not\equiv 8,16\pmod{24}$.
|
1008.1617
|
Query-Efficient Locally Decodable Codes of Subexponential Length
|
cs.CC cs.DM cs.IT math.IT math.NT math.RA
|
We develop the algebraic theory behind the constructions of Yekhanin (2008)
and Efremenko (2009), in an attempt to understand the ``algebraic niceness''
phenomenon in $\mathbb{Z}_m$. We show that every integer $m = pq = 2^t -1$,
where $p$, $q$ and $t$ are prime, possesses the same good algebraic property as
$m=511$ that allows savings in query complexity. We identify 50 numbers of this
form by computer search, which together with 511, are then applied to gain
improvements on query complexity via Itoh and Suzuki's composition method. More
precisely, we construct a $3^{\lceil r/2\rceil}$-query LDC for every positive
integer $r<104$ and a $\left\lfloor (3/4)^{51}\cdot 2^{r}\right\rfloor$-query
LDC for every integer $r\geq 104$, both of length $N_{r}$, improving the $2^r$
queries used by Efremenko (2009) and $3\cdot 2^{r-2}$ queries used by Itoh and
Suzuki (2010).
We also obtain new efficient private information retrieval (PIR) schemes from
the new query-efficient LDCs.
|
1008.1643
|
A Learning Algorithm based on High School Teaching Wisdom
|
cs.AI cs.LG
|
A learning algorithm based on primary school teaching and learning is
presented. The methodology is to continuously evaluate a student and to give
them training on the examples for which they repeatedly fail, until, they can
correctly answer all types of questions. This incremental learning procedure
produces better learning curves by demanding the student to optimally dedicate
their learning time on the failed examples. When used in machine learning, the
algorithm is found to train a machine on a data with maximum variance in the
feature space so that the generalization ability of the network improves. The
algorithm has interesting applications in data mining, model evaluations and
rare objects discovery.
|
1008.1653
|
The Magic Number Problem for Subregular Language Families
|
cs.FL cs.IT math.IT
|
We investigate the magic number problem, that is, the question whether there
exists a minimal n-state nondeterministic finite automaton (NFA) whose
equivalent minimal deterministic finite automaton (DFA) has alpha states, for
all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n).
A number alpha not satisfying this condition is called a magic number (for n).
It was shown in [11] that no magic numbers exist for general regular languages,
while in [5] trivial and non-trivial magic numbers for unary regular languages
were identified. We obtain similar results for automata accepting subregular
languages like, for example, combinational languages, star-free, prefix-,
suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free
languages, showing that there are only trivial magic numbers, when they exist.
For finite languages we obtain some partial results showing that certain
numbers are non-magic.
|
1008.1659
|
The Maximal Subword Complexity of Quasiperiodic Infinite Words
|
cs.FL cs.DM cs.IT math.IT
|
We provide an exact estimate on the maximal subword complexity for
quasiperiodic infinite words. To this end we give a representation of the set
of finite and of infinite words having a certain quasiperiod q via a finite
language derived from q. It is shown that this language is a suffix code having
a bounded delay of decipherability. Our estimate of the subword complexity now
follows from this result, previously known results on the subword complexity
and elementary results on formal power series.
|
1008.1673
|
Space and the Synchronic A-Ram
|
cs.CL cs.PL
|
Space is a circuit oriented, spatial programming language designed to exploit
the massive parallelism available in a novel formal model of computation called
the Synchronic A-Ram, and physically related FPGA and reconfigurable
architectures. Space expresses variable grained MIMD parallelism, is modular,
strictly typed, and deterministic. Barring operations associated with memory
allocation and compilation, modules cannot access global variables, and are
referentially transparent. At a high level of abstraction, modules exhibit a
small, sequential state transition system, aiding verification. Space deals
with communication, scheduling, and resource contention issues in parallel
computing, by resolving them explicitly in an incremental manner, module by
module, whilst ascending the ladder of abstraction. Whilst the Synchronic A-Ram
model was inspired by linguistic considerations, it is also put forward as a
formal model for reconfigurable digital circuits. A programming environment has
been developed, that incorporates a simulator and compiler that transform Space
programs into Synchronic A-Ram machine code, consisting of only three bit-level
instructions, and a marking instruction. Space and the Synchronic A-Ram point
to novel routes out of the parallel computing crisis.
|
1008.1674
|
Balanced distribution-energy inequalities and related entropy bounds
|
math.FA cs.IT math.IT math.SP
|
Let $A$ be a self-adjoint operator acting over a space $X$ endowed with a
partition. We give lower bounds on the energy of a mixed state $\rho$ from its
distribution in the partition and the spectral density of $A$. These bounds
improve with the refinement of the partition, and generalize inequalities by
Li-Yau and Lieb--Thirring for the Laplacian in $\R^n$. They imply an
uncertainty principle, giving a lower bound on the sum of the spatial entropy
of $\rho$, as seen from $X$, and some spectral entropy, with respect to its
energy distribution. On $\R^n$, this yields lower bounds on the sum of the
entropy of the densities of $\rho$ and its Fourier transform. A general
log-Sobolev inequality is also shown. It holds on mixed states, without
Markovian or positivity assumption on $A$.
|
1008.1695
|
Biometric Authentication using Nonparametric Methods
|
cs.CV
|
The physiological and behavioral trait is employed to develop biometric
authentication systems. The proposed work deals with the authentication of iris
and signature based on minimum variance criteria. The iris patterns are
preprocessed based on area of the connected components. The segmented image
used for authentication consists of the region with large variations in the
gray level values. The image region is split into quadtree components. The
components with minimum variance are determined from the training samples. Hu
moments are applied on the components. The summation of moment values
corresponding to minimum variance components are provided as input vector to
k-means and fuzzy k-means classifiers. The best performance was obtained for
MMU database consisting of 45 subjects. The number of subjects with zero False
Rejection Rate [FRR] was 44 and number of subjects with zero False Acceptance
Rate [FAR] was 45. This paper addresses the computational load reduction in
off-line signature verification based on minimal features using k-means, fuzzy
k-means, k-nn, fuzzy k-nn and novel average-max approaches. FRR of 8.13% and
FAR of 10% was achieved using k-nn classifier. The signature is a biometric,
where variations in a genuine case, is a natural expectation. In the genuine
signature, certain parts of signature vary from one instance to another. The
system aims to provide simple, fast and robust system using less number of
features when compared to state of art works.
|
1008.1710
|
Introduction to the 26th International Conference on Logic Programming
Special Issue
|
cs.AI cs.LO
|
This is the preface to the 26th International Conference on Logic Programming
Special Issue
|
1008.1715
|
The universality of iterated hashing over variable-length strings
|
cs.DB cs.DS
|
Iterated hash functions process strings recursively, one character at a time.
At each iteration, they compute a new hash value from the preceding hash value
and the next character. We prove that iterated hashing can be pairwise
independent, but never 3-wise independent. We show that it can be almost
universal over strings much longer than the number of hash values; we bound the
maximal string length given the collision probability.
|
1008.1723
|
Role of Ontology in Semantic Web Development
|
cs.AI
|
World Wide Web (WWW) is the most popular global information sharing and
communication system consisting of three standards .i.e., Uniform Resource
Identifier (URL), Hypertext Transfer Protocol (HTTP) and Hypertext Mark-up
Language (HTML). Information is provided in text, image, audio and video
formats over the web by using HTML which is considered to be unconventional in
defining and formalizing the meaning of the context...
|
1008.1744
|
High-resolution scalar quantization with R\'enyi entropy constraint
|
cs.IT math.IT
|
We consider optimal scalar quantization with $r$th power distortion and
constrained R\'enyi entropy of order $\alpha$. For sources with an absolutely
continuous distribution the high rate asymptotics of the quantizer distortion
has long been known for $\alpha=0$ (fixed-rate quantization) and $\al pha=1$
(entropy-constrained quantization). For a large class of absolutely continuous
source distributions we determine the sharp asymptotics of the optimal
quantization distortion for $\alpha\in [-\infty,0)\cup (0,1)$. The
achievability proof is based on finding (asymptotically) optimal quantizers via
the companding approach, and is thus constructive.
|
1008.1766
|
Soft-Decoding-Based Strategies for Relay and Interference Channels:
Analysis and Achievable Rates Using LDPC Codes
|
cs.IT math.IT
|
We provide a rigorous mathematical analysis of two communication strategies:
soft decode-and-forward (soft-DF) for relay channels, and soft partial
interference-cancelation (soft-IC) for interference channels. Both strategies
involve soft estimation, which assists the decoding process. We consider LDPC
codes, not because of their practical benefits, but because of their analytic
tractability, which enables an asymptotic analysis similar to random coding
methods of information theory. Unlike some works on the closely-related
demodulate-and-forward, we assume non-memoryless, code-structure-aware
estimation. With soft-DF, we develop {\it simultaneous density evolution} to
bound the decoding error probability at the destination. This result applies to
erasure relay channels. In one variant of soft-DF, the relay applies Wyner-Ziv
coding to enhance its communication with the destination, borrowing from
compress-and-forward. To analyze soft-IC, we adapt existing techniques for
iterative multiuser detection, and focus on binary-input additive white
Gaussian noise (BIAWGN) interference channels. We prove that optimal
point-to-point codes are unsuitable for soft-IC, as well as for all strategies
that apply partial decoding to improve upon single-user detection (SUD) and
multiuser detection (MUD), including Han-Kobayashi (HK).
|
1008.1770
|
A complex network approach to robustness and vulnerability of spatially
organized water distribution networks
|
physics.soc-ph cs.CE cs.SI math.CO
|
In this work, water distribution systems are regarded as large sparse planar
graphs with complex network characteristics and the relationship between
important topological features of the network (i.e. structural robustness and
loop redundancy) and system resilience, viewed as the antonym to structural
vulnerability, are assessed. Deterministic techniques from complex networks and
spectral graph theory are utilized to quantify well-connectedness and estimate
loop redundancy in the studied benchmark networks. By using graph connectivity
and expansion properties, system robustness against node/link failures and
isolation of the demand nodes from the source(s) are assessed and network
tolerance against random failures and targeted attacks on their bridges and cut
sets are analyzed. Among other measurements, two metrics of meshed-ness and
algebraic connectivity are proposed as candidates for quantification of
redundancy and robustness, respectively, in optimization design models. A brief
discussion on the scope and limitations of the provided measurements in the
analysis of operational reliability of water distribution systems is presented.
|
1008.1846
|
An algorithmic information-theoretic approach to the behaviour of
financial markets
|
q-fin.TR cs.CE cs.IT math.IT
|
Using frequency distributions of daily closing price time series of several
financial market indexes, we investigate whether the bias away from an
equiprobable sequence distribution found in the data, predicted by algorithmic
information theory, may account for some of the deviation of financial markets
from log-normal, and if so for how much of said deviation and over what
sequence lengths. We do so by comparing the distributions of binary sequences
from actual time series of financial markets and series built up from purely
algorithmic means. Our discussion is a starting point for a further
investigation of the market as a rule-based system with an 'algorithmic'
component, despite its apparent randomness, and the use of the theory of
algorithmic probability with new tools that can be applied to the study of the
market price phenomenon. The main discussion is cast in terms of assumptions
common to areas of economics in agreement with an algorithmic view of the
market.
|
1008.1970
|
The Shannon Cipher System with a Guessing Wiretapper: General Sources
|
cs.IT math.IT
|
The Shannon cipher system is studied in the context of general sources using
a notion of computational secrecy introduced by Merhav & Arikan. Bounds are
derived on limiting exponents of guessing moments for general sources. The
bounds are shown to be tight for iid, Markov, and unifilar sources, thus
recovering some known results. A close relationship between error exponents and
correct decoding exponents for fixed rate source compression on the one hand
and exponents for guessing moments on the other hand is established.
|
1008.1977
|
Guessing Revisited: A Large Deviations Approach
|
cs.IT math.IT
|
The problem of guessing a random string is revisited. A close relation
between guessing and compression is first established. Then it is shown that if
the sequence of distributions of the information spectrum satisfies the large
deviation property with a certain rate function, then the limiting guessing
exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the
rate function. Other sufficient conditions related to certain continuity
properties of the information spectrum are briefly discussed. This approach
highlights the importance of the information spectrum in determining the
limiting guessing exponent. All known prior results are then re-derived as
example applications of our unifying approach.
|
1008.1986
|
For the sake of simplicity: Unsupervised extraction of lexical
simplifications from Wikipedia
|
cs.CL
|
We report on work in progress on extracting lexical simplifications (e.g.,
"collaborate" -> "work together"), focusing on utilizing edit histories in
Simple English Wikipedia for this task. We consider two main approaches: (1)
deriving simplification probabilities via an edit model that accounts for a
mixture of different operations, and (2) using metadata to focus on edits that
are more likely to be simplification operations. We find our methods to
outperform a reasonable baseline and yield many high-quality lexical
simplifications not included in an independently-created manually prepared
list.
|
1008.2005
|
Approximation Analysis of Influence Spread in Social Networks
|
cs.DM cs.CC cs.SI
|
In the context of influence propagation in a social graph, we can identify
three orthogonal dimensions - the number of seed nodes activated at the
beginning (known as budget), the expected number of activated nodes at the end
of the propagation (known as expected spread or coverage), and the time taken
for the propagation. We can constrain one or two of these and try to optimize
the third. In their seminal paper, Kempe et al. constrained the budget, left
time unconstrained, and maximized the coverage: this problem is known as
Influence Maximization.
In this paper, we study alternative optimization problems which are naturally
motivated by resource and time constraints on viral marketing campaigns. In the
first problem, termed Minimum Target Set Selection (or MINTSS for short), a
coverage threshold n is given and the task is to find the minimum size seed set
such that by activating it, at least n nodes are eventually activated in the
expected sense. In the second problem, termed MINTIME, a coverage threshold n
and a budget threshold k are given, and the task is to find a seed set of size
at most k such that by activating it, at least n nodes are activated, in the
minimum possible time. Both these problems are NP-hard, which motivates our
interest in their approximation.
For MINTSS, we develop a simple greedy algorithm and show that it provides a
bicriteria approximation. We also establish a generic hardness result
suggesting that improving it is likely to be hard. For MINTIME, we show that
even bicriteria and tricriteria approximations are hard under several
conditions. However, if we allow the budget to be boosted by a logarithmic
factor and allow the coverage to fall short, then the problem can be solved
exactly in PTIME.
Finally, we show the value of the approximation algorithms, by comparing them
against various heuristics.
|
1008.2008
|
Rate-Constrained Simulation and Source Coding IID Sources
|
cs.IT math.IT
|
Necessary conditions for asymptotically optimal sliding-block or stationary
codes for source coding and rate-constrained simulation of memoryless sources
are presented and used to motivate a design technique for trellis-encoded
source coding and rate-constrained simulation. The code structure has intuitive
similarities to classic random coding arguments as well as to ``fake process''
methods and alphabet-constrained methods. Experimental evidence shows that the
approach provides comparable or superior performance in comparison with
previously published methods on common examples, sometimes by significant
margins.
|
1008.2028
|
Discovering shared and individual latent structure in multiple time
series
|
stat.ML cs.AI stat.ME
|
This paper proposes a nonparametric Bayesian method for exploratory data
analysis and feature construction in continuous time series. Our method focuses
on understanding shared features in a set of time series that exhibit
significant individual variability. Our method builds on the framework of
latent Diricihlet allocation (LDA) and its extension to hierarchical Dirichlet
processes, which allows us to characterize each series as switching between
latent ``topics'', where each topic is characterized as a distribution over
``words'' that specify the series dynamics. However, unlike standard
applications of LDA, we discover the words as we learn the model. We apply this
model to the task of tracking the physiological signals of premature infants;
our model obtains clinically significant insights as well as useful features
for supervised learning tasks.
|
1008.2066
|
Information transfer with small-amplitude signals
|
q-bio.NC cs.IT math.IT
|
We study the optimality conditions of information transfer in systems with
memory in the low signal-to-noise ratio regime of vanishing input amplitude. We
find that the optimal mutual information is represented by a maximum-variance
of the signal time course, with correlation structure determined by the Fisher
information matrix. We provide illustration of the method on a simple
biologically-inspired model of electro-sensory neuron. Our general results
apply also to the study of information transfer in single neurons subject to
weak stimulation, with implications to the problem of coding efficiency in
biological systems.
|
1008.2069
|
Information capacity in the weak-signal approximation
|
cs.IT math.IT q-bio.NC
|
We derive an approximate expression for mutual information in a broad class
of discrete-time stationary channels with continuous input, under the
constraint of vanishing input amplitude or power. The approximation describes
the input by its covariance matrix, while the channel properties are described
by the Fisher information matrix. This separation of input and channel
properties allows us to analyze the optimality conditions in a convenient way.
We show that input correlations in memoryless channels do not affect channel
capacity since their effect decreases fast with vanishing input amplitude or
power. On the other hand, for channels with memory, properly matching the input
covariances to the dependence structure of the noise may lead to almost
noiseless information transfer, even for intermediate values of the noise
correlations. Since many model systems described in mathematical neuroscience
and biophysics operate in the high noise regime and weak-signal conditions, we
believe, that the described results are of potential interest also to
researchers in these areas.
|
1008.2081
|
Random Information Spread in Networks
|
math.CO cs.DM cs.SI math.PR
|
Let G=(V,E) be an undirected loopless graph with possible parallel edges and
s and t be two vertices of G. Assume that vertex s is labelled at the initial
time step and that every labelled vertex copies its labelling to neighbouring
vertices along edges with one labelled endpoint independently with probability
p in one time step. In this paper, we establish the equivalence between the
expected s-t first arrival time of the above spread process and the notion of
the stochastic shortest s-t path. Moreover, we give a short discussion of
analytical results on special graphs including the complete graph and s-t
series-parallel graphs. Finally, we propose some lower bounds for the expected
s-t first arrival time.
|
1008.2093
|
Notes on Lattice-Reduction-Aided MMSE Equalization
|
cs.IT math.IT
|
Over the last years, novel low-complexity approaches to the equalization of
MIMO channels have gained much attention. Thereby, methods based on lattice
basis reduction are of special interest, as they achieve the optimum diversity
order. In this paper, a tutorial overview on LRA equalization optimized
according to the MMSE criterion is given. It is proven that applying the
zero-forcing BLAST algorithm to a suitably augmented channel matrix (the
inverse of the square root of the correlation matrix of the data symbols times
the noise variance forms its lower part) results in the optimum solution. This
fact is already widely used but lacks a formal proof. It turns out that it is
more important to take the correlations of the data correctly into account than
what type of lattice reduction actually is used.
|
1008.2121
|
Constraint Propagation for First-Order Logic and Inductive Definitions
|
cs.LO cs.AI
|
Constraint propagation is one of the basic forms of inference in many
logic-based reasoning systems. In this paper, we investigate constraint
propagation for first-order logic (FO), a suitable language to express a wide
variety of constraints. We present an algorithm with polynomial-time data
complexity for constraint propagation in the context of an FO theory and a
finite structure. We show that constraint propagation in this manner can be
represented by a datalog program and that the algorithm can be executed
symbolically, i.e., independently of a structure. Next, we extend the algorithm
to FO(ID), the extension of FO with inductive definitions. Finally, we discuss
several applications.
|
1008.2122
|
Secret Key and Private Key Constructions for Simple Multiterminal Source
Models
|
cs.IT cs.CR math.IT
|
We propose an approach for constructing secret and private keys based on the
long-known Slepian-Wolf code, due to Wyner, for correlated sources connected by
a virtual additive noise channel. Our work is motivated by results of Csisz\'ar
and Narayan which highlight innate connections between secrecy generation by
multiple terminals that observe correlated source signals and Slepian-Wolf
near-lossless data compression. Explicit procedures for such constructions and
their substantiation are provided. The performance of low density parity check
channel codes in devising a new class of secret keys is examined.
|
1008.2147
|
Quantum Tagging: Authenticating Location via Quantum Information and
Relativistic Signalling Constraints
|
quant-ph cs.CR cs.IT math.IT
|
We define the task of {\it quantum tagging}, that is, authenticating the
classical location of a classical tagging device by sending and receiving
quantum signals from suitably located distant sites, in an environment
controlled by an adversary whose quantum information processing and
transmitting power is unbounded. We define simple security models for this task
and briefly discuss alternatives.
We illustrate the pitfalls of naive quantum cryptographic reasoning in this
context by describing several protocols which at first sight appear
unconditionally secure but which, as we show, can in fact be broken by
teleportation-based attacks. We also describe some protocols which cannot be
broken by these specific attacks, but do not prove they are unconditionally
secure.
We review the history of quantum tagging protocols, which we first discussed
in 2002 and described in a 2006 patent (for an insecure protocol). The
possibility has recently been reconsidered by other authors. All the more
recently discussed protocols of which we are aware were either previously
considered by us in 2002-3 or are variants of schemes then considered, and all
are provably insecure.
|
1008.2159
|
Submodular Functions: Learnability, Structure, and Optimization
|
cs.DS cs.DM cs.LG
|
Submodular functions are discrete functions that model laws of diminishing
returns and enjoy numerous algorithmic applications. They have been used in
many areas, including combinatorial optimization, machine learning, and
economics. In this work we study submodular functions from a learning theoretic
angle. We provide algorithms for learning submodular functions, as well as
lower bounds on their learnability. In doing so, we uncover several novel
structural results revealing ways in which submodular functions can be both
surprisingly structured and surprisingly unstructured. We provide several
concrete implications of our work in other domains including algorithmic game
theory and combinatorial optimization.
At a technical level, this research combines ideas from many areas, including
learning theory (distributional learning and PAC-style analyses), combinatorics
and optimization (matroids and submodular functions), and pseudorandomness
(lossless expander graphs).
|
1008.2160
|
An early warning method for crush
|
cs.MA
|
Fatal crush conditions occur in crowds with tragic frequency. Event
organisers and architects are often criticised for failing to consider the
causes and implications of crush, but the reality is that the prediction and
mitigation of such conditions offers a significant technical challenge. Full
treatment of physical force within crowd simulations is precise but
computationally expensive; the more common method of human interpretation of
results is computationally "cheap" but subjective and time-consuming. In this
paper we propose an alternative method for the analysis of crowd behaviour,
which uses information theory to measure crowd disorder. We show how this
technique may be easily incorporated into an existing simulation framework, and
validate it against an historical event. Our results show that this method
offers an effective and efficient route towards automatic detection of crush.
|
1008.2186
|
RDFViewS: A Storage Tuning Wizard for RDF Applications
|
cs.DB cs.AI
|
In recent years, the significant growth of RDF data used in numerous
applications has made its efficient and scalable manipulation an important
issue. In this paper, we present RDFViewS, a system capable of choosing the
most suitable views to materialize, in order to minimize the query response
time for a specific SPARQL query workload, while taking into account the view
maintenance cost and storage space constraints. Our system employs practical
algorithms and heuristics to navigate through the search space of potential
view configurations, and exploits the possibly available semantic information -
expressed via an RDF Schema - to ensure the completeness of the query
evaluation.
|
1008.2247
|
Symmetry and Uncountability of Computation
|
cs.CC cs.IT math.IT
|
This paper talk about the complexity of computation by Turing Machine. I take
attention to the relation of symmetry and order structure of the data, and I
think about the limitation of computation time. First, I make general problem
named "testing problem". And I get some condition of the P complete and NP
complete by using testing problem. Second, I make two problem "orderly problem"
and "chaotic problem". Orderly problem have some order structure. And DTM can
limit some possible symbol effectly by using symmetry of each symbol. But
chaotic problem must treat some symbol as a set of symbol, so DTM cannot limit
some possible symbol. Orderly problem is P complete, and chaotic problem is NP
complete. Finally, I clear the computation time of orderly problem and chaotic
problem. And P != NP.
|
1008.2266
|
Achievable Rates and Upper bounds for the Interference Relay Channel
|
cs.IT math.IT
|
The two user Gaussian interference channel with a full-duplex relay is
studied. By using genie aided approaches, two new upper bounds on the
achievable sum-rate in this setup are derived. These upper bounds are shown to
be tighter than previously known bounds under some conditions. Moreover, a
transmit strategy for this setup is proposed. This strategy utilizes the
following elements: Block Markov encoding combined with a Han-Kobayashi scheme
at the sources, decode and forward at the relay, and Willems' backward decoding
at the receivers. This scheme is shown to achieve within a finite gap our upper
bounds in certain cases.
|
1008.2277
|
Faithfulness in Chain Graphs: The Gaussian Case
|
stat.ML cs.AI math.ST stat.TH
|
This paper deals with chain graphs under the classic
Lauritzen-Wermuth-Frydenberg interpretation. We prove that the regular Gaussian
distributions that factorize with respect to a chain graph $G$ with $d$
parameters have positive Lebesgue measure with respect to $\mathbb{R}^d$,
whereas those that factorize with respect to $G$ but are not faithful to it
have zero Lebesgue measure with respect to $\mathbb{R}^d$. This means that, in
the measure-theoretic sense described, almost all the regular Gaussian
distributions that factorize with respect to $G$ are faithful to it.
|
1008.2297
|
An MGF-based Unified Framework to Determine the Joint Statistics of
Partial Sums of Ordered Random Variables
|
cs.IT math.IT
|
Order statistics find applications in various areas of communications and
signal processing. In this paper, we introduce an unified analytical framework
to determine the joint statistics of partial sums of ordered random variables
(RVs). With the proposed approach, we can systematically derive the joint
statistics of any partial sums of ordered statistics, in terms of the moment
generating function (MGF) and the probability density function (PDF). Our
MGF-based approach applies not only when all the K ordered RVs are involved but
also when only the Ks (Ks < K) best RVs are considered. In addition, we present
the closed-form expressions for the exponential RV special case. These results
apply to the performance analysis of various wireless communication systems
over fading channels.
|
1008.2300
|
Probabilistic Frequent Pattern Growth for Itemset Mining in Uncertain
Databases (Technical Report)
|
cs.DB
|
Frequent itemset mining in uncertain transaction databases semantically and
computationally differs from traditional techniques applied on standard
(certain) transaction databases. Uncertain transaction databases consist of
sets of existentially uncertain items. The uncertainty of items in transactions
makes traditional techniques inapplicable. In this paper, we tackle the problem
of finding probabilistic frequent itemsets based on possible world semantics.
In this context, an itemset X is called frequent if the probability that X
occurs in at least minSup transactions is above a given threshold. We make the
following contributions: We propose the first probabilistic FP-Growth algorithm
(ProFP-Growth) and associated probabilistic FP-Tree (ProFP-Tree), which we use
to mine all probabilistic frequent itemsets in uncertain transaction databases
without candidate generation. In addition, we propose an efficient technique to
compute the support probability distribution of an itemset in linear time using
the concept of generating functions. An extensive experimental section
evaluates the our proposed techniques and shows that our ProFP-Growth approach
is significantly faster than the current state-of-the-art algorithm.
|
1008.2313
|
Lagrangian method for solving Lane-Emden type equation arising in
astrophysics on semi-infinite domains
|
math-ph astro-ph.IM cs.CE math.MP math.NA
|
In this paper we propose a Lagrangian method for solving Lane-Emden equation
which is a nonlinear ordinary differential equation on semi-infinite interval.
This approach is based on a Modified generalized Laguerre functions Lagrangian
method. The method reduces the solution of this problem to the solution of a
system of algebraic equations. We also present the comparison of this work with
some well-known results and show that the present solution is acceptable.
|
1008.2322
|
An approximate solution of the MHD Falkner-Skan flow by Hermite
functions pseudospectral method
|
math-ph cs.CE math.MP math.NA physics.comp-ph physics.flu-dyn
|
Based on a new approximation method, namely pseudospectral method, a solution
for the three order nonlinear ordinary differential laminar boundary layer
Falkner-Skan equation has been obtained on the semi-infinite domain. The
proposed approach is equipped by the orthogonal Hermite functions that have
perfect properties to achieve this goal. This method solves the problem on the
semi-infinite domain without truncating it to a finite domain and transforming
domain of the problem to a finite domain. In addition, this method reduces
solution of the problem to solution of a system of algebraic equations. We also
present the comparison of this work with numerical results and show that the
present method is applicable.
|
1008.2337
|
Numerical approximations for population growth model by Rational
Chebyshev and Hermite Functions collocation approach: A comparison
|
math-ph cs.CE math.MP math.NA
|
This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF)
collocation approach to solve the Volterra's model for population growth of a
species within a closed system. This model is a nonlinear integro-differential
equation where the integral term represents the effect of toxin. This approach
is based on orthogonal functions which will be defined. The collocation method
reduces the solution of this problem to the solution of a system of algebraic
equations. We also compare these methods with some other numerical results and
show that the present approach is applicable for solving nonlinear
integro-differential equations.
|
1008.2348
|
Comparison between two common collocation approaches based on radial
basis functions for the case of heat transfer equations arising in porous
medium
|
math-ph cs.CE math.MP math.NA physics.comp-ph
|
In this paper two common collocation approaches based on radial basis
functions have been considered; one be computed through the integration process
(IRBF) and one be computed through the differentiation process (DRBF). We
investigated the two approaches on natural convection heat transfer equations
embedded in porous medium which are of great importance in the design of
canisters for nuclear wastes disposal. Numerical results show that the IRBF be
performed much better than the common DRBF, and show good accuracy and high
rate of convergence of IRBF process.
|
1008.2368
|
Construction of Rational Surfaces Yielding Good Codes
|
math.AG cs.IT math.IT math.NT
|
In the present article, we consider Algebraic Geometry codes on some rational
surfaces. The estimate of the minimum distance is translated into a point
counting problem on plane curves. This problem is solved by applying the upper
bound "\`a la Weil" of Aubry and Perret together with the bound of Homma and
Kim for plane curves. The parameters of several codes from rational surfaces
are computed. Among them, the codes defined by the evaluation of forms of
degree 3 on an elliptic quadric are studied. As far as we know, such codes have
never been treated before. Two other rational surfaces are studied and very
good codes are found on them. In particular, a [57,12,34] code over
$\mathbf{F}_7$ and a [91,18,53] code over $\mathbf{F}_9$ are discovered, these
codes beat the best known codes up to now.
|
1008.2386
|
Linear Precoding in Cooperative MIMO Cellular Networks with Limited
Coordination Clusters
|
cs.IT math.IT
|
In a cooperative multiple-antenna downlink cellular network, maximization of
a concave function of user rates is considered. A new linear precoding
technique called soft interference nulling (SIN) is proposed, which performs at
least as well as zero-forcing (ZF) beamforming. All base stations share channel
state information, but each user's message is only routed to those that
participate in the user's coordination cluster. SIN precoding is particularly
useful when clusters of limited sizes overlap in the network, in which case
traditional techniques such as dirty paper coding or ZF do not directly apply.
The SIN precoder is computed by solving a sequence of convex optimization
problems. SIN under partial network coordination can outperform ZF under full
network coordination at moderate SNRs. Under overlapping coordination clusters,
SIN precoding achieves considerably higher throughput compared to myopic ZF,
especially when the clusters are large.
|
1008.2410
|
Removing the Barrier to Scalability in Parallel FMM
|
cs.CE cs.NA physics.comp-ph
|
The Fast Multipole Method (FMM) is well known to possess a bottleneck arising
from decreasing workload on higher levels of the FMM tree [Greengard and Gropp,
Comp. Math. Appl., 20(7), 1990]. We show that this potential bottleneck can be
eliminated by overlapping multipole and local expansion computations with
direct kernel evaluations on the finest level grid.
|
1008.2412
|
Discover & eXplore Neural Network (DXNN) Platform, a Modular TWEANN
|
cs.NE cond-mat.dis-nn
|
In this paper I present a novel type of Topology and Weight Evolving
Artificial Neural Network (TWEANN) system called Modular Discover & eXplore
Neural Network (DXNN). Modular DXNN utilizes a hierarchical/modular topology
which allows for highly scalable and dynamically granular systems to evolve.
Among the novel features discussed in this paper is a simple and database
friendly encoding for hierarchical/modular NNs, a new selection method aimed at
producing highly compact and fit individuals within the population, a "Targeted
Tunning" system aimed at alleviating the curse of dimensionality, and a two
phase based neuroevolutionary approach which yields high population diversity
and removes the need for speciation algorithms. I will discuss DXNN's mutation
operators which are aimed at improving its efficiency, expandability, and
capabilities through a built in feature selection method that allows for the
evolved system to expand, discover, and explore new sensors and actuators.
Finally I will compare DXNN platform to other state of the art TWEANNs on a
control task to demonstrate its superior ability to produce highly compact
solutions faster than its competitors.
|
1008.2514
|
Epistemic irrelevance in credal nets: the case of imprecise Markov trees
|
cs.AI math.PR stat.ML
|
We focus on credal nets, which are graphical models that generalise Bayesian
nets to imprecise probability. We replace the notion of strong independence
commonly used in credal nets with the weaker notion of epistemic irrelevance,
which is arguably more suited for a behavioural theory of probability. Focusing
on directed trees, we show how to combine the given local uncertainty models in
the nodes of the graph into a global model, and we use this to construct and
justify an exact message-passing algorithm that computes updated beliefs for a
variable in the tree. The algorithm, which is linear in the number of nodes, is
formulated entirely in terms of coherent lower previsions, and is shown to
satisfy a number of rationality requirements. We supply examples of the
algorithm's operation, and report an application to on-line character
recognition that illustrates the advantages of our approach for prediction. We
comment on the perspectives, opened by the availability, for the first time, of
a truly efficient algorithm based on epistemic irrelevance.
|
1008.2526
|
Low ML Decoding Complexity STBCs via Codes over GF(4)
|
cs.IT math.IT
|
In this paper, we give a new framework for constructing low ML decoding
complexity Space-Time Block Codes (STBCs) using codes over the finite field
$\mathbb{F}_4$. Almost all known low ML decoding complexity STBCs can be
obtained via this approach. New full-diversity STBCs with low ML decoding
complexity and cubic shaping property are constructed, via codes over
$\mathbb{F}_4$, for number of transmit antennas \mbox{$N=2^m$}, \mbox{$m \geq
1$}, and rates \mbox{$R>1$} complex symbols per channel use. When \mbox{$R=N$},
the new STBCs are information-lossless as well. The new class of STBCs have the
least known ML decoding complexity among all the codes available in the
literature for a large set of \mbox{$(N,R)$} pairs.
|
1008.2529
|
Quantum f-divergences and error correction
|
math-ph cs.IT math.IT math.MP quant-ph
|
Quantum f-divergences are a quantum generalization of the classical notion of
f-divergences, and are a special case of Petz' quasi-entropies. Many well known
distinguishability measures of quantum states are given by, or derived from,
f-divergences; special examples include the quantum relative entropy, the Renyi
relative entropies, and the Chernoff and Hoeffding measures. Here we show that
the quantum f-divergences are monotonic under the dual of Schwarz maps whenever
the defining function is operator convex. This extends and unifies all
previously known monotonicity results. We also analyze the case where the
monotonicity inequality holds with equality, and extend Petz' reversibility
theorem for a large class of f-divergences and other distinguishability
measures. We apply our findings to the problem of quantum error correction, and
show that if a stochastic map preserves the pairwise distinguishability on a
set of states, as measured by a suitable f-divergence, then its action can be
reversed on that set by another stochastic map that can be constructed from the
original one in a canonical way. We also provide an integral representation for
operator convex functions on the positive half-line, which is the main
ingredient in extending previously known results on the monotonicity inequality
and the case of equality. We also consider some special cases where the
convexity of f is sufficient for the monotonicity, and obtain the inverse
Holder inequality for operators as an application. The presentation is
completely self-contained and requires only standard knowledge of matrix
analysis.
|
1008.2565
|
Multigraph Sampling of Online Social Networks
|
cs.NI cs.DS cs.SI physics.data-an stat.ME
|
State-of-the-art techniques for probability sampling of users of online
social networks (OSNs) are based on random walks on a single social relation
(typically friendship). While powerful, these methods rely on the social graph
being fully connected. Furthermore, the mixing time of the sampling process
strongly depends on the characteristics of this graph. In this paper, we
observe that there often exist other relations between OSN users, such as
membership in the same group or participation in the same event. We propose to
exploit the graphs these relations induce, by performing a random walk on their
union multigraph. We design a computationally efficient way to perform
multigraph sampling by randomly selecting the graph on which to walk at each
iteration. We demonstrate the benefits of our approach through (i) simulation
in synthetic graphs, and (ii) measurements of Last.fm - an Internet website for
music with social networking features. More specifically, we show that
multigraph sampling can obtain a representative sample and faster convergence,
even when the individual graphs fail, i.e., are disconnected or highly
clustered.
|
1008.2571
|
Cooperative Secret Communication with Artificial Noise in Symmetric
Interference Channel
|
cs.IT math.IT
|
We consider the symmetric Gaussian interference channel where two users try
to enhance their secrecy rates in a cooperative manner. Artificial noise is
introduced along with useful information. We derive the power control and
artificial noise parameter for two kinds of optimal points, max-min point and
single user point. It is shown that there exists a critical value $P_c$ of the
power constraint, below which the max-min point is an optimal point on the
secrecy rate region, and above which time-sharing between single user points
achieves larger secrecy rate pairs. It is also shown that artificial noise can
help to enlarge the secrecy rate region, in particular on the single user
point.
|
1008.2579
|
Homotopy Perturbation Method for Image Restoration and Denoising
|
cs.CV cs.NA math.AP math.NA
|
The famous Perona-Malik (P-M) equation which was at first introduced for
image restoration has been solved via various numerical methods. In this paper
we will solve it for the first time via applying a new numerical method called
Homotopy Perturbation Method (HMP) and the correspondent approximated solutions
will be obtained for the P-M equation with regards to relevant error analysis.
Through implementation of our algorithm we will access some effective results
which are deserved to be considered as worthy as the other solutions issued by
the other methods.
|
1008.2581
|
The LASSO risk for gaussian matrices
|
math.ST cs.IT math.IT stat.TH
|
We consider the problem of learning a coefficient vector x_0\in R^N from
noisy linear observation y=Ax_0+w \in R^n. In many contexts (ranging from model
selection to image processing) it is desirable to construct a sparse estimator
x'. In this case, a popular approach consists in solving an L1-penalized least
squares problem known as the LASSO or Basis Pursuit DeNoising (BPDN).
For sequences of matrices A of increasing dimensions, with independent
gaussian entries, we prove that the normalized risk of the LASSO converges to a
limit, and we obtain an explicit expression for this limit. Our result is the
first rigorous derivation of an explicit formula for the asymptotic mean square
error of the LASSO for random instances. The proof technique is based on the
analysis of AMP, a recently developed efficient algorithm, that is inspired
from graphical models ideas.
Simulations on real data matrices suggest that our results can be relevant in
a broad array of practical applications.
|
1008.2613
|
Joint maximum likelihood estimation of carrier and sampling frequency
offsets for OFDM systems
|
cs.IT math.IT
|
In orthogonal-frequency division multiplexing (OFDM) systems, carrier and
sampling frequency offsets (CFO and SFO, respectively) can destroy the
orthogonality of the subcarriers and degrade system performance. In the
literature, Nguyen-Le, Le-Ngoc, and Ko proposed a simple maximum-likelihood
(ML) scheme using two long training symbols for estimating the initial CFO and
SFO of a recursive least-squares (RLS) estimation scheme. However, the results
of Nguyen-Le's ML estimation show poor performance relative to the Cramer-Rao
bound (CRB). In this paper, we extend Moose's CFO estimation algorithm to joint
ML estimation of CFO and SFO using two long training symbols. In particular, we
derive CRBs for the mean square errors (MSEs) of CFO and SFO estimation.
Simulation results show that the proposed ML scheme provides better performance
than Nguyen-Le's ML scheme.
|
1008.2626
|
Mining tree-query associations in graphs
|
cs.DB cs.AI
|
New applications of data mining, such as in biology, bioinformatics, or
sociology, are faced with large datasetsstructured as graphs. We introduce a
novel class of tree-shapedpatterns called tree queries, and present algorithms
for miningtree queries and tree-query associations in a large data graph. Novel
about our class of patterns is that they can containconstants, and can contain
existential nodes which are not counted when determining the number of
occurrences of the patternin the data graph. Our algorithms have a number of
provableoptimality properties, which are based on the theory of conjunctive
database queries. We propose a practical, database-oriented implementation in
SQL, and show that the approach works in practice through experiments on data
about food webs, protein interactions, and citation analysis.
|
1008.2743
|
PMOG: The projected mixture of Gaussians model with application to blind
source separation
|
stat.ML cs.AI stat.ME
|
We extend the mixtures of Gaussians (MOG) model to the projected mixture of
Gaussians (PMOG) model. In the PMOG model, we assume that q dimensional input
data points z_i are projected by a q dimensional vector w into 1-D variables
u_i. The projected variables u_i are assumed to follow a 1-D MOG model. In the
PMOG model, we maximize the likelihood of observing u_i to find both the model
parameters for the 1-D MOG as well as the projection vector w. First, we derive
an EM algorithm for estimating the PMOG model. Next, we show how the PMOG model
can be applied to the problem of blind source separation (BSS). In contrast to
conventional BSS where an objective function based on an approximation to
differential entropy is minimized, PMOG based BSS simply minimizes the
differential entropy of projected sources by fitting a flexible MOG model in
the projected 1-D space while simultaneously optimizing the projection vector
w. The advantage of PMOG over conventional BSS algorithms is the more flexible
fitting of non-Gaussian source densities without assuming near-Gaussianity (as
in conventional BSS) and still retaining computational feasibility.
|
1008.2750
|
On BICM receivers for TCM transmission
|
cs.IT math.IT
|
Recent results have shown that the performance of bit-interleaved coded
modulation (BICM) using convolutional codes in nonfading channels can be
significantly improved when the interleaver takes a trivial form (BICM-T),
i.e., when it does not interleave the bits at all. In this paper, we give a
formal explanation for these results and show that BICM-T is in fact the
combination of a TCM transmitter and a BICM receiver. To predict the
performance of BICM-T, a new type of distance spectrum for convolutional codes
is introduced, analytical bounds based on this spectrum are developed, and
asymptotic approximations are also presented. It is shown that the minimum
distance of the code is not the relevant optimization criterion for BICM-T.
Optimal convolutional codes for different constrain lengths are tabulated and
asymptotic gains of about 2 dB are obtained. These gains are found to be the
same as those obtained by Ungerboeck's one-dimensional trellis coded modulation
(1D-TCM), and therefore, in nonfading channels, BICM-T is shown to be
asymptotically as good as 1D-TCM.
|
1008.2857
|
Bidirectional multi-pair network with a MIMO relay: Beamforming
strategies and lack of duality
|
cs.IT math.IT
|
We address the problem of a multi-user relay network, where multiple
single-antenna node pairs want to exchange information by using a multiple
antenna relay node. Due to the half-duplex constraint of the relay, the
exchange of information takes place in two steps. In the first step, the nodes
transmit their data to the relay, while in the second step, the relay is
broadcasting the data by using linear and non-linear precoding strategies. We
focus on the second step in this paper. We first consider the problem of
maximizing the overall rate achievable using linear and dirty-paper type
precoding strategies at the relay. Then, we consider minimizing the total power
at the relay subject to individual SINR constraints using the same strategies
at the relay. We show that the downlink-uplink duality does not hold for the
setup considered here, which is a somewhat surprising result. We also show that
the beamforming strategy which is optimal in the single-pair case performs very
well in the multi-pair case for practically relevant SNR. The results are
illustrated by numerical simulations.
|
1008.2873
|
Compressive Channel Estimation for Two-way Relay Network in a
Frequency-Selective Channel with Compressed Sensing
|
cs.IT math.IT
|
Two-way relay network (TWRN) was introduced to realize high-data rate
transmission over the wireless frequency-selective channel. However, TWRC
requires the knowledge of channel state information (CSI) not only for coherent
data detection but also for the self-data removal. This is partial accomplished
by training sequence-based linear channel estimation. However, conventional
linear estimation techniques neglect anticipated sparsity of multipath channel.
Unlike the previous methods, we propose a compressive channel estimation method
which exploit the sparse structure and provide significant improvements in MSE
performance when compared with traditional LSbased linear channel probing
strategies. Simulation results confirm the proposed methods.
|
1008.2972
|
Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for
Polynomial Transforms Based on Induction
|
cs.IT math.IT math.RA
|
A polynomial transform is the multiplication of an input vector $x\in\C^n$ by
a matrix $\PT_{b,\alpha}\in\C^{n\times n},$ whose $(k,\ell)$-th element is
defined as $p_\ell(\alpha_k)$ for polynomials $p_\ell(x)\in\C[x]$ from a list
$b=\{p_0(x),\dots,p_{n-1}(x)\}$ and sample points $\alpha_k\in\C$ from a list
$\alpha=\{\alpha_0,\dots,\alpha_{n-1}\}$. Such transforms find applications in
the areas of signal processing, data compression, and function interpolation.
Important examples include the discrete Fourier and cosine transforms. In this
paper we introduce a novel technique to derive fast algorithms for polynomial
transforms. The technique uses the relationship between polynomial transforms
and the representation theory of polynomial algebras. Specifically, we derive
algorithms by decomposing the regular modules of these algebras as a stepwise
induction. As an application, we derive novel $O(n\log{n})$ general-radix
algorithms for the discrete Fourier transform and the discrete cosine transform
of type 4.
|
1008.2996
|
Sparsity-Cognizant Total Least-Squares for Perturbed Compressive
Sampling
|
cs.IT math.IT
|
Solving linear regression problems based on the total least-squares (TLS)
criterion has well-documented merits in various applications, where
perturbations appear both in the data vector as well as in the regression
matrix. However, existing TLS approaches do not account for sparsity possibly
present in the unknown vector of regression coefficients. On the other hand,
sparsity is the key attribute exploited by modern compressive sampling and
variable selection approaches to linear regression, which include noise in the
data, but do not account for perturbations in the regression matrix. The
present paper fills this gap by formulating and solving TLS optimization
problems under sparsity constraints. Near-optimum and reduced-complexity
suboptimum sparse (S-) TLS algorithms are developed to address the perturbed
compressive sampling (and the related dictionary learning) challenge, when
there is a mismatch between the true and adopted bases over which the unknown
vector is sparse. The novel S-TLS schemes also allow for perturbations in the
regression matrix of the least-absolute selection and shrinkage selection
operator (Lasso), and endow TLS approaches with ability to cope with sparse,
under-determined "errors-in-variables" models. Interesting generalizations can
further exploit prior knowledge on the perturbations to obtain novel weighted
and structured S-TLS solvers. Analysis and simulations demonstrate the
practical impact of S-TLS in calibrating the mismatch effects of contemporary
grid-based approaches to cognitive radio sensing, and robust
direction-of-arrival estimation using antenna arrays.
|
1008.3035
|
Achievable Rates in Two-user Interference Channels with Finite Inputs
and (Very) Strong Interference
|
cs.IT math.IT
|
For two-user interference channels, the capacity is known for the case where
interference is stronger than the desired signal. Moreover, it is known that if
the interference is above a certain level, it does not reduce the capacity at
all. To achieve this capacity, the channel inputs need to be Gaussian
distributed. However, Gaussian signals are continuous and unbounded. Thus, they
are not well suited for practical applications. In this paper, we investigate
the achievable rates if the channel inputs are restricted to finite
constellations. Moreover, we will show by numerical simulations that rotating
one of these input alphabets in the complex plane can increase the achievable
rate region. Finally, we show that the threshold at which the single-user rates
are achieved also depends on this rotation.
|
1008.3043
|
Learning Functions of Few Arbitrary Linear Parameters in High Dimensions
|
math.NA cs.CC cs.LG stat.ML
|
Let us assume that $f$ is a continuous function defined on the unit ball of
$\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix
and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m
\in \mathbb N$ of possible point evaluations $f(x_i)$, $i=1,...,m$, of $f$,
which we are allowed to query in order to construct a uniform approximating
function. Under certain smoothness and variation assumptions on the function
$g$, and an {\it arbitrary} choice of the matrix $A$, we present in this paper
1. a sampling choice of the points $\{x_i\}$ drawn at random for each
function approximation;
2. algorithms (Algorithm 1 and Algorithm 2) for computing the approximating
function, whose complexity is at most polynomial in the dimension $d$ and in
the number $m$ of points.
Due to the arbitrariness of $A$, the choice of the sampling points will be
according to suitable random distributions and our results hold with
overwhelming probability. Our approach uses tools taken from the {\it
compressed sensing} framework, recent Chernoff bounds for sums of
positive-semidefinite matrices, and classical stability bounds for invariant
subspaces of singular value decompositions.
|
1008.3056
|
On the Performance of Spectrum Sensing Algorithms using Multiple
Antennas
|
cs.IT math.IT stat.AP
|
In recent years, some spectrum sensing algorithms using multiple antennas,
such as the eigenvalue based detection (EBD), have attracted a lot of
attention. In this paper, we are interested in deriving the asymptotic
distributions of the test statistics of the EBD algorithms. Two EBD algorithms
using sample covariance matrices are considered: maximum eigenvalue detection
(MED) and condition number detection (CND). The earlier studies usually assume
that the number of antennas (K) and the number of samples (N) are both large,
thus random matrix theory (RMT) can be used to derive the asymptotic
distributions of the maximum and minimum eigenvalues of the sample covariance
matrices. While assuming the number of antennas being large simplifies the
derivations, in practice, the number of antennas equipped at a single secondary
user is usually small, say 2 or 3, and once designed, this antenna number is
fixed. Thus in this paper, our objective is to derive the asymptotic
distributions of the eigenvalues and condition numbers of the sample covariance
matrices for any fixed K but large N, from which the probability of detection
and probability of false alarm can be obtained. The proposed methodology can
also be used to analyze the performance of other EBD algorithms. Finally,
computer simulations are presented to validate the accuracy of the derived
results.
|
1008.3136
|
MIMO Precoding Using Rotating Codebooks
|
cs.IT math.IT
|
Next generation wireless communications rely on multiple input multiple
output (MIMO) techniques to achieve high data rates. Feedback of channel
information can be used in MIMO precoding to fully activate the strongest
channel modes and improve MIMO performance. Unfortunately, the bandwidth of the
control channel via which the feedback is conveyed is severely limited. An
important issue is how to improve the MIMO precoding performance with minimal
feedback. In this letter, we present a method that uses a rotating codebook
technique to effectively improve the precoding performance without the need of
increasing feedback overhead. The basic idea of the rotating codebook precoding
is to expend the effective precoding codebook size via rotating multiple
codebooks so that the number of feedback bits remains unchanged. Simulation
results are presented to show the performance gain of the proposed rotating
codebook precoding over the conventional precoding.
|
1008.3146
|
Exact Localization and Superresolution with Noisy Data and Random
Illumination
|
cs.IT math.IT math.PR physics.data-an physics.optics
|
This paper studies the problem of exact localization of sparse (point or
extended) objects with noisy data. The crux of the proposed approach consists
of random illumination. Several recovery methods are analyzed: the Lasso, BPDN
and the One-Step Thresholding (OST). For independent random probes, it is shown
that both recovery methods can localize exactly $s=\cO(m)$, up to a logarithmic
factor, objects where $m$ is the number of data. Moreover, when the number of
random probes is large the Lasso with random illumination has a performance
guarantee for superresolution, beating the Rayleigh resolution limit. Numerical
evidence confirms the predictions and indicates that the performance of the
Lasso is superior to that of the OST for the proposed set-up with random
illumination.
|
1008.3147
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Proceedings First Workshop on Applications of Membrane computing,
Concurrency and Agent-based modelling in POPulation biology
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cs.CE cs.MA
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This volume contains the papers presented at the first International Workshop
on Applications of Membrane Computing, Concurrency and Agent-based Modelling in
Population Biology (AMCA-POP 2010) held in Jena, Germany on August 25th, 2010
as a satellite event of the 11th Conference on Membrane Computing (CMC11).
The aim of the workshop is to investigate whether formal modelling and
analysis techniques could be applied with profit to systems of interest for
population biology and ecology. The considered modelling notations include
membrane systems, Petri nets, agent-based notations, process calculi,
automata-based notations, rewriting systems and cellular automata. Such
notations enable the application of analysis techniques such as simulation,
model checking, abstract interpretation and type systems to study systems of
interest in disciplines such as population biology, ecosystem science,
epidemiology, genetics, sustainability science, evolution and other disciplines
in which population dynamics and interactions with the environment are studied.
Papers contain results and experiences in the modelling and analysis of systems
of interest in these fields.
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