Algorithms for recognizing coordinates in two variables over UFD's We give an easy and efficient algorithm to check whether a given polynomial f in K[x, y] is a coordinate, where K be a commutative field of characteristic zero, and if so to compute a coordinate's mate of f . Then we treat the same problem replacing the ground field K by a unique factorization domain A of characteristic zero. A notable feature of our method is that it always produces a mate of minimum degree. . Deciding whether a given polynomial f is a coordinate is one of the most fundamental problems in the study of automorphisms of polynomial rings. To our knowledge this problem is still open for n ≥ 3. In the case of two variables it is solved by the famous AbhyankarMoh theorem [1] which states that f is a coordinate if and Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. only if I(∂xf, ∂yf ) = (1) and the curve C(f ) defined by f = 0 has one place at infinity. Since then, various and more or less explicit solutions have been given to this problem, see e.g. [4, 8, 5, 11, 3] . However, the closely related question of computing a coordinate's mate, i.e. a polynomial g such that K[f, g] = K [x, y] , is either not treated or solved in a more or less involved way, see [2] . For instance, in [5] an integral formula is given for computing a Jacobian mate, i.e. a polynomial g such that Jac(f, g) = 1, and as byproduct it solves the question of coordinate's mate. In [11] the same question is solved by keeping track of the so-called nonsingular Gröbner reductions performed to check whether f is a coordinate. In this work we build on the results of van den Essen [8] , so let us recall some of them. Given a polynomial f ∈ K[x, y] we let X f = ∂yf∂x −∂xf∂y be the Hamiltonian K-derivation associated to it. The main result of concern for our purpose states that f is a coordinate if and only if X f is locally nilpotent and I(∂xf, ∂yf ) = (1). Moreover, deciding whether X f is locally nilpotent reduces to check whether X d+1 f (x) = X d+1 f (y) = 0, where d is the total degree of f . Thus, deciding whether f is a coordinate reduces to explicit and well controlled algebraic computations. On the other hand, the question of computing a coordinate's mate for f is reduced to compute a slice of X f , i.e. an element s such that X f (s) = 1.. In this paper we show that the necessary computations performed to check whether X f is locally nilpotent, namely the computation of the iterates X i f (x) and X i f (y) up to the bound deg(f ) + 1, are enough for checking whether f is a coordinate and for computing a coordinate's mate in case it exists. We then extend the obtained result over fields to UFD's of characteristic zero, and as by-product we give an algorithm which allows to recognize coordinates in two variables over such rings.. The paper is structured as follows: in section 2 we give some basic results concerning locally nilpotent derivations and coordinates in two variables. Section 3 is devoted to the problem of algorithmically recognizing coordinates and computing mates over fields of characteristic zero. In section 4 we show that the method we describe always produces a younger mate. In section 5 we study coordinates in two variables over UFD's of characteristic zero. We give algorithmic solutions to both the recognition and the mate problems. In section 6 we give some details on implementations and we study some examples. In this section we give a pseudo-code description of the algorithm studied in the previous sections. The algorithm takes as input a polynomial f in two variables with coefficients in a UFD of characteristic zero and checks whether it is a coordinate, and if so it computes a coordinate's mate. Moreover it produces a mate of f of minimum degree. step 3: We check the condition iii) of theorem 5.1. For this, we use an algorithm called SEQ which corresponds to the routine described in theorem 5.3.

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Generalized vector complementarity-type problems in topological vector spaces In this paper, we introduced the generalized vector variational inequality-type problem and the generalized vector complementarity-type problem in the setting of topological vector space. By utilizing a modified version of the Fan-KKM theorem, we investigated the nonemptyness and compactness of solution sets of these problems without the demipseudomonotonicity assumption. Further, we prove that solution sets of both the problems are equivalent to each other under some suitable conditions. The results of this paper generalize and improve several results that appeared recently in the literature. As a useful and important branch of variational inequality theory, the vector variational inequality problem initially introduced and considered by Giannessi [1] , has been extensively studied in the last two decades because of its applications to vector optimization problems, vector complementarity problems, game theory, economics, etc; see for example [2] [3] [4] [5] 1, [6] [7] [8] [9] [10] [11] [12] [13] [14] and references therein. It is well known that the complementarity problems are closely related to variational inequality problems. Complementarity theory introduced by Lemke [12] , and Cottle and Dantzig [4] , has been extended and generalized in various directions to study a large class of problems arising in finance, optimization, mathematical and engineering sciences; see for example [3] [4] [5] 1, [6] [7] [8] [9] [10] [11] [12] [13] [14] .. There are many kinds of generalizations of monotonicity in the literature of recent years, such as pseudomonotonicity, quasi-monotonicity, etc. In 1999, Chen [2] introduced the concept of semimonotonicity for a single-valued mapping, which occurred in the study of nonlinear partial differential equations of divergence type. Motivated by Chen [2] , Zheng [14] introduced the concept of vector semi-monotone operator and investigated a class of vector variational inequality problems and obtained some existence results. Recently, vector complementarity problems and their relations with vector variational inequality problems have been investigated under pseudomonotone type conditions and positiveness type conditions; see for example [5, [7] [8] [9] 13] . In 2003, Fang and Huang [5] , introduced a class of demipseudomonotone mappings and considered the generalized vector variational inequality problems for a fixed cone and proved the existence of solutions of these problems under demipseudomonotonicity and hemicontinuity assumptions in the setting of reflexive Banach spaces. They have also provided applications of these problems to vector f -complementarity problems.. Inspired and motivated by the work of Chen [2] , Fang and Huang [5] and Zheng [14] , in this paper we introduced the generalized vector variational inequality-type problem and the generalized vector complementarity problem in the setting of topological vector space. Further, we investigate the nonemptyness and compactness of the solution set of the generalized vector variational inequality-type problem under P x -upper sign continuity in the setting of metrizable topological vector spaces but without the demipseudomonotonicity assumption. We use the modified version of the Fan-KKM theorem to extend and improve some results of Fang and Huang [5] . Furthermore we showed that solution sets of the generalized vector variational inequality-type problem and the generalized vector complementarity problem are equivalent to each other under suitable conditions.

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Generalizations of the Hamming Associative Memory Abstract. This Letter reviews four models of associative memory which generalize the operation of the Hamming associative memory: the grounded Hamming memory, the cellular Hamming memory, the decoupled Hamming memory, and the two-level decoupled Hamming memory. These memory models offer high performance and allow for a more practical hardware realization than the Hamming net and other fully interconnected neural net architectures. Existing models of associative memory suffer from one or more of the following serious £aws:. . Limited capacity . Low or unquanti¢able error correction capability . Large number of spurious memories . Impractical hardware implementation.. In terms of hardware implementation, dif¢culties arise either from requiring complicated hardware or else requiring an excessive number of interconnection weights (for example, fully interconnected architectures). In this letter, we describe a class of associative memory models which can overcome some of these design £aws. These memory models generalize the operation of the Hamming associative memory by allowing for a ground state and local distance measures. Four different models are discussed:. (1) Grounded Hamming Memory (2) Cellular Hamming Memory (3) Decoupled Hamming Memory (4) Two-level decoupled Hamming Memory.. The grounded Hamming memory is similar to the Hamming associative memory, but allows for a ground state which will attracts all states with very low signal-to-noise ratio. The cellular Hamming memory utilizes local Hamming dis-tance measures rather than a global Hamming distance measure, leading to a cellular network architecture which is more amenable to VLSI hardware implementation and ¢ne-grained parallel implementations. The decoupled Hamming memory also uses local Hamming distance computations, but requires less hardware than the cellular Hamming memory because the local windows do not overlap. Finally, the two-level decoupled Hamming memory combines the decoupled Hamming distance computations with a higher-level decision making stage.. These associative memory models have been individually described and analyzed in the literature in recent years [1^7] . The purpose of this letter is to give a complete summary and comparison of the various models, highlighting their advantages and limitations in terms of memory capacity and hardware implementation.. In the following, we consider the binary autoassociative memory problem. In this case, the given fundamental memory set is of the form fx. i is an N-bit binary vector, i.e.. The task is to design a system which associates every fundamental pattern with itself. That is, when presented with x i as input, the system should produce x i at the output. In addition, when presented with a noisy version of x i at the input, the system should also produce x i at the output. Let the Hamming distance between two binary vectors x and y (of the same dimension) be denoted as dxY y.. The Hamming associative memory [2] is a static model, and operates as follows: For any memory key x P f0Y 1g N , the retrieved pattern is obtained by computing the Hamming distances d k dxY y k , selecting the minimum such distance d k Ã , and outputting the fundamental memory x k Ã (closest match). The most attractive feature of this model is its exponential capacity [8] and large error correction capability. There are two serious disadvantages of this model. First, there is no provision for a ground state. Second, the hardware implementation is cumbersome because the computation of the required Hamming distances is a global and sequential operation, and hence not immediately suitable to parallel and distributed processing systems. The following sections detail generalizations of the Hamming memory which overcome these limitations. In a template matching (Hamming network) approach to pattern recognition, the input image is compared (using a suitable metric) to each of the prototype images, and the output is simply the best match image. The sequential computation of comparing the input to each prototype is reminiscent of the serial processing that humans do when asked to identify people whom they do not know [15] . In a comparison between a feature based approach and a template matching approach for human face recognition problems, Poggio and Brunelei [16] found that template matching provided superior performance, and in fact, gave 100% recognition on their data set of face images.. The training time for template matching is O(1) complexity, and simply consists of storing all the images in memory. In other algorithms, such as neural net-based approaches, the training time is extremely long, but the retrieval time can be very quick.. An obvious advantage of template-based schemes is that it is easy to add new individuals by simply storing additional images or delete an individual by deleting the undesired prototype images. Another advantage is that template-based systems are not limited to producing just a single output, but can produce an ordered list containing the best matching, say k, individuals.. The main disadvantages of template-based methods were pointed out in Duda and Hart [17] :`. . . the complete set of samples must be stored, and must be searched each time a new feature vector is to be classi¢ed. ' Back in 1973 when this classic text was published, memory and processing speed were indeed serious constraints. In fact, it would take almost 10 years before PCs were developed with a clock speeds of a few MHz, 1 MB of RAM, and a few MB of hard disk space. Today, however, affordable PCs are available with clock speeds of 700 MHz, 384 MB of RAM, and 50 GB of hard disk storage. Clearly, the severity of the storage/speed dilemma has diminished in recent years with the availability these powerful and low cost computers, and hence the template matching approach of the Hamming network warrants further consideration.. As outlined in this paper, by combining the Hamming net computation with the parallel and distributed processing methods of neural networks, high performance associative memories can be designed. In future work, we will apply these generalized Hamming models to the practical problem of human face recognition.

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VISOR: Vast Independence System Optimization Routine Abstract. An algorithm is sketched that generates all K maximal independent sets and all M minimal dependent sets of an arbitrary independence system, based on a set of cardinality n having at most 2 n subsets, with access to an oracle that decides if a set is independent or not. Because the algorithm generates all those sets, it solves the problems of finding all maximum independent and minimum dependent sets. Those problems are known to be impossible to solve in general in time polynomial in n, K , and M, and they are N P hard. The algorithm proposed and used is efficient in the sense that it requires only O(nK + M) or O(K + nM) visits to the oracle, the nonpolynomial part is only related to bitstring comparisons and the like, which can be performed rather quickly and, to some degree, in parallel on a sequential machine. This complexity compares favorably with another algorithm that is O(n 2 K 2 ). The design of a computer routine that implements the algorithm in a highly optimized way is discussed. The routine behaves as expected, as is shown by numerical experiments on a range of randomly generated independence systems with n up to n = 34. Application on an engineering design problem with n = 28 shows the routine requires almost 10 6 times less visits to the oracle than an exhaustive search, while the time spent in visiting the oracle is still significantly larger than that spent for all other computations together.

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Real Emission and Virtual Exchange of Gravitons and Unparticles in Pythia8 Models with large extra dimensions as well as unparticle models could give rise to new phenomena at collider experiments due to real emission or virtual exchange of gravitons or unparticles. In this paper we present the common implementation of these processes in the Monte Carlo generator Pythia8, using relations between the parameters of the two models. The program offers several options related to the treatment of the UV region of the effective theories, including the possibility of using a form factor for the running gravitational coupling. Characteristic results obtained with Pythia8 have been used to validate the implementations as well as to illustrate the key features and effects of the model parameters. The results presented in this paper are focused on mono-jet, di-photon and di-lepton final states at the LHC. Models with large extra dimensions (LED) are popular extensions of the Standard Model (SM) and studies of LED phenomena are usually based on the so-called ADD scenario [1] , where gravity alone has access to the extra dimensions. The large size of the extra dimensions gives rise to dense Kaluza-Klein (KK) mass modes which appear as a continuous graviton mass spectrum. Due to the large number of contributing mass states graviton processes could obtain sufficiently large cross sections to be observed at collider experiments, where the new processes involve real emission or virtual exchange of gravitons. These processes have been studied in great detail [2] , however, no signs of new physics have been indicated at existing experiments.. More recently so-called unparticle models [3] have also gained a large interest. These models relate to physics originating from a scale invariant new sector which is coupled to the SM through a connector sector with a high mass scale. Unparticle models can often, at least from a phenomenological point of view, be associated with extra dimension models and the particular case addressed here would result in phenomena very similar to the scenario of LED gravity. Having access to processes with the same final state from more than one model can be helpful to generalise the experimental analysis as well as for studying differences in the measured observables. The latter, in turn, could also be of value after a discovery to characterise the observed signal.. This paper describes the processes involving real emission or virtual exchange of unparticles (U ) or LED gravitons (G) as implemented in Pythia8 [4] . The corresponding processes are:. • Mono-jets (U /G + jet): gg → U /G + g, qg → U /G + q, qq → U /G + g;. • Mono-Z/γ (U /G + Z/γ): ff → U /G + Z, ff → U /G + γ;. • Di-photons (γγ): ff → U * /G * → γγ, gg → U * /G * → γγ;. • Di-leptons (ℓl): ff → U * /G * → ℓl, gg → U * /G * → ℓl.. Because of the large similarities both models can be covered by a common implementation [5] , where only a simple translation of a few model related constants is required to change between the models. In addition to technical advantages, this common description makes comparisons between the processes both consistent and transparent. The effective theory description of these processes behaves poorly in the UV limit and several related options are available in the program. These include a form factor [6] for the graviton processes which represents a realistic alternative of the behaviour at high energies due to the running of the gravitational coupling.. The Pythia8 implementations have been validated against the original theory papers and we present here some of these results. Besides providing reference results for the Pythia8 program, the results illustrate different characteristic effects of the model parameters and various key features 1 . All results are produced with respect to the nominal LHC conditions (pp-collisions at a centre-of-mass energy of √ s = 14 TeV), unless explicitly stated otherwise.. This paper is organised as follows. The first section starts with a description of the model parameters and different conventions. It is followed by a description of the implementation of the processes and the relations between the two models. This section also describes the available options for treating the UV region of the effective theories. Sec. 3 to 5 present the different program options in Pythia8 together with results related to the individual processes: U /G + jet, γγ, and ℓl production. In addition, Sec. 5 draws special attention to possibile effects on the forward-backward asymmetry in lepton pair production from spin-1 unparticle exchange. The U /G + Z/γ processes are not addressed here since they were already presented in a previous paper [5] . A complete list of the process and model parameter names used in the Pythia8 program can be found in the appendix. The appendix also contains complementary information used for the scalar unparticle process, ff → ZU , which is not available in the literature.. This paper presents results obtained with Pythia version 8.125 and all parameters not explicitly mentioned in the text have been kept at the default values of this version. During the work a few minor corrections have been made 2 , which all are included in the following version 8.130. In order to produce results comparable to what is available in the literature, only the hard part of the process has been considered 3 and the MRST2001 parton distribution functions (PDF) of the proton have been used unless stated otherwise. Both large extra dimensions as well as unparticle models have become very popular among possible extensions of the SM. Many of the main processes related to LED searches have analogous processes in the unparticle scenario, which are often more general in terms of model parameters. A common way to implement the similar processes has been found within the Monte Carlo generator Pythia8, where only a few translations of model dependent constants are necessary. In addition to technical benefits, the common implementation makes comparisons between the processes from the two models consistent and simplifies studies of how differences at the process level for a certain final state can affect the measured observables. The processes can be used together with several options for the treatment of the UV region of the effective theory. In this paper, the options related to the individual processes have been discussed together with results obtained by Pythia8. In addition to providing references for the Pythia8 program, the results

O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Data harvesting with mobile elements in wireless sensor networks The sensor nodes may have unalike data cohort rates, which pointers to theMobile Portion Scheduling Problem. In this paper, we proposed a Partitioning-Based Scheduling (PBS) procedure to report this problem. We comparedourprocedure with Least Weighted Sum Firstalgorithm and showed that our PBS algorithm provides higher performance in terms of decreasing lossrate, dipping the leastcompulsory speed, andproviding high predictability. Our future workincludes investigation of methods to utilize morethan one mobile element for data collection and tocater to the needs of vital real-time announcement events.

O O O O O O O B I O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O


Bias and pathology in minimax search This article presents the results of experiments designed to gain insight into the effect of the minimax algorithm on the error of a heuristic evaluation function. Two types of effect of minimax are considered: (a) evaluation accuracy (are the minimax backed-up values more accurate than the heuristic values themselves?), and (b) decision accuracy (are moves played by deeper minimax search better than those by shallower search?). The experiments were performed in the KRK chess endgame and in randomly generated game trees. The results show that, counter-intuitively, evaluation accuracy may decline with search depth, whereas at the same time decision accuracy improves with depth. In the article, this is explained by the fact that minimax in combination with a noisy evaluation function introduces a bias into the backed-up evaluations, which masks the evaluation effectiveness of minimax, but this bias still permits decision accuracy to improve with depth. This observed behaviour of minimax in the KRK endgame is discussed in the light of previous studies of pathology in minimax. It is shown that explaining the behaviour of minimax in an actual chess endgame in terms of previously known results requires special care. Over twenty years ago Beal [4] 2 and Nau [11, 12] independently of one another set out to analyze whether and why values backed up from minimax search are more trustworthy than the heuristic values themselves. Beal constructed a simple mathematical model to analyze the minimax algorithm. To his surprise, the analysis of the model showed that the backed-up values were actually somewhat less trustworthy than the heuristic values themselves. He then wrote: "This result is disappointing. It was hoped that the analysis would show that the probability of error reduced with backing-up." A couple of years later two articles [5, 8] simultaneously conducted further analysis into why minimax does yield good results in practical game-playing while apparently backed-up values seem less reliable; both articles independently reached the same conclusion. They argued that the true values of sibling nodes in a game tree are not independent of one another. This clustering of similar values is a major feature in practical games and it was this phenomenon that Beal's original mathematical model (1980) did not account for. The problem with the minimax paradigm under the assumption of independence of sibling values was also found by Nau [11, 12, 13, 14] , who called this a search-depth pathology in game trees.

B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Measurement

of

disproportionality

in

proportional

representation

systems

Nineteen

indices

characterizing

the

disproportionality

in

a

parliament

are

studied.

A

classification

of

these

indices

is

suggested,

and

computational

experiments

and

an

axiomatic

approach

are

used

to

study

their

properties.

Effects

of

the

number

of

parties

and

the

degree

of

disproportionality

are

considered.

The

indices

are

evaluated

for

parliamentary

elections

(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)

in

Russia.

In

the

century,

the

wide

appearance

of

proportional

representation

(PR)

systems

was

one

of

the

reasons

for

the

development

of

various

methods

for

measuring

the

quality

of

electoral

systems.

Balinski

and

Young

gained

one

of

the

main

results.

They

proved

the

impossibility

of

constructing

a

PR

system

that

allocates

seats

in

an

exactly

proportional

way..

The

impossibility

of

creating

an

ideal

electoral

system

forced

researchers

to

search

for

quantitative

indices

that

would

reflect

the

degree

to

which

the

system

satisfies

certain

conditions.

Such

indices

contain

quantitative

information

and

allow

researchers

to

conduct

empirical

research

and

compare

various

electoral

systems.

One

of

the

most

extensive

investigations

of

this

sort

was

conducted

by

Detailed

study

of

implementing

PR

by

minimizing

misrepresentation

is

given

in

pp.

Up

to

now,

many

indices

describing

disproportionality

have

been

constructed.

Some

of

them

were

developed

for

studying

some

particular

electoral

system,

while

others

were

adapted

from

other

areas

of

science.

Thus,

there

is

no

agreement

concerning

what

indices

are

better

in

a

particular

situation.

A

survey

of

such

indices

can

be

found

in

Until

now,

there

has

been

almost

no

research

that

studies

the

properties

of

disproportionality

indices..

This

paper

studies

the

properties

of

disproportionality

indices.

It

is

organized

as

follows.

Section

introduces

the

main

concepts.

Sections

describe

the

main

indices.

Section

presents

an

axiomatic

approach.

Section

concludes

with

the

results

of

calculating

indices

for

the

parliament

elections

in

Russia

from

to

Each

index

creates

a

unique

ordering

on

the

election

results

set.

We

can

measure

the

distance

between

orderings

using

rank

correlations

between

sets

of

the

index

values,

which

are

calculated

for

random

vote

and

seat

vectors.

The

Spearman

rank

correlation

coefficient

is

used

for

this

purpose..

The

values

of

the

Spearman

correlation

coefficient

are

given

in

Table

The

Loosmore-Hanby

index

is

not

reported,

since

it

gives

an

ordering

that

is

equivalent

to

that

given

by

the

Rae

index..

High

rank

correlations

reflect

considerable

similarity

and

homogeneity

among

the

group

of

absolute

deviation

indices.

Figs.

and

demonstrate

the

means

and

standard

deviations

for

various

numbers

of

parties

at

degree

of

disproportionality

σ

The

mean

of

the

majority

of

the

indices

decreases

with

an

increase

in

n,

since

the

average

size

of

the

parties

and

of

their

deviations

are

also

decreasing..

In

the

given

experiment,

an

increase

in

the

number

of

parties

can

be

viewed

as

a

party

split.

There

are

more

parties

with

a

similar

rule

for

the

distribution

of

seats.

The

behavior

of

the

indices

that

satisfy

the

property

of

independence

from

split

significantly

differs

from

the

others.

The

means

of

the

first

group

of

indices

increase,

while

the

means

of

the

others

decrease..

Standard

deviation

decreases

considerably.

This

makes

the

ordering

more

random

and

weakens

rank

correlations.

An

increase

in

disproportionality

has

a

reverse

effect..

The

choice

of

index

is

less

important

when

the

degree

of

disproportionality

is

high.

Orderings

became

closer

in

terms

of

rank-order

correlations.

The

mean

and

standard

deviation

increase

for

degree

of

disproportionality..

The

second

group

of

indices

demonstrates

a

closer

relationship

in

terms

of

Spearman

rank

correlations

(Table

Modifications

of

the

Gallagher

index

do

not

result

in

noteworthy

changes.

The

Gatev

and

Ryabtsev

indices

differ

insignificantly,

as

could

be

expected

given

the

similarity

in

their

analytical

form.

The

Monroe

index,

which

was

not

The

number

of

parties

is

n

and

the

degree

of

disproportionality

is

σ

considered

in

the

experiment,

would

be

very

close

to

the

indices

given

in

Table

The

Szalai

index

demonstrates

a

markedly

different

behavior

and

will

be

considered

in

more

detail

(see

Figs.

and

The

means

of

Lsq

and

H

k

diminish,

because

the

average

differences

between

vote

and

seat

share

are

reduced.

The

Gatev,

Ryabtsev,

and

Szalai

indices

are

higher

for

a

higher

number

of

parties,

because

they

are

more

sensitive

to

small

parties.

This

property

was

considered

above

in

the

analysis

of

their

analytical

form.

We

again

notice

that

indices

that

satisfy

the

property

of

independence

from

split

differ

from

the

others..

The

histograms

of

index

values

in

most

cases

are

very

similar.

They

are

asymmetric

one-peaked

distributions..

For

the

degree

of

disproportionality

σ

and

the

number

of

parties

n

the

Gallagher

index

histogram

is

shown

in

Fig.

For

the

degree

of

disproportionality

σ

the

value

of

the

Gallagher

index

drops,

but

the

histogram's

shape

does

not

change.

Almost

all

indices

have

similar

distributions..

The

Szalai

index

histogram

looks

like

the

histogram

given

above

at

σ

Parties

that

have

no

seats

appear

for

larger

degrees

of

disproportionality.

This

has

considerable

impact

on

the

value

of

the

index,

and

therefore

on

the

shape

of

the

histogram

as

well.

There

are

two

separate

groups

of

elections

results.

On

the

one

hand,

there

are

election

results

with

parties

that

did

not

win

any

seats,

and

on

the

other

hand

there

are

election

results

without

any

such

parties.

Two

distributions

will

result.

The

first

distribution

will

have

one

peak;

the

second

distribution

will

depend

on

the

number

of

unrepresented

parties.

Joint

distributions

have

many

peaks.

The

Figs.

show

histograms

of

the

Szalai

index

with

the

various

numbers

of

parties..

At

σ

the

Szalai

index

distribution

is

bimodal,

because

parties

without

any

representation

appear.

This

can

be

explained

using

the

analytical

form

of

the

index:.

If

s

i

the

sum

will

include

this

considerably

increases

the

index,

because

the

other

values

are

rather

small.

This

effect

is

more

significant

for

a

small

number

of

parties.

At

n

the

histogram

demonstrates

a

sharp

increase

after

the

value

I

Szalai

At

n

the

values

and

more

are

reached

when

there

are

parties

that

did

not

obtain

a

seat,

and

therefore

this

effect

is

less

evident.

It

is

therefore

incorrect

to

compare

the

election

results

with

a

different

number

of

parties

that

received

no

seats..

Inequality

indices

and

objective

functions

greatly

differ

in

analytical

form.

Therefore,

they

have

smaller

rank-order

correlations.

The

D'Hondt

index

has

the

smallest

Spearman

correlation

coefficient,

at

about

The

D'Hondt

index

measures

the

maximum

discrepancy,

but

the

other

indices

are

closer

to

measuring

the

average

dissimilarity.

The

rank

correlations

for

the

Atkinson

index

and

for

generalized

entropy

significantly

depend

on

the

parameters

ε

and

α,

respectively.

The

disproportionality

indices

describe

the

quality

of

apportionment.

They

are

strongly

correlated,

though

they

provide

different

results.

This

experiment

can

be

used

to

consider

the

unique

features

of

the

indices

and

explain

how

the

values

of

the

indices

change

in

real

situations.

This

understanding

of

the

structure

of

the

indices

and

of

their

properties

improves

the

analysis

of

the

election

results.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Calculation of delay characteristics for multiserver queues with constant service times We consider a discrete-time infinite-capacity queueing system with a general uncorrelated arrival process, constant-length service times of multiple slots, multiple servers and a first-come-first-served queueing discipline. Under the assumption that the queueing system can reach a steady state, we first establish a relationship between the steady-state probability distributions of the system content and the customer delay. Next, by means of this relationship, an explicit expression for the probability generating function of the customer delay is obtained from the known generating function of the system content, derived in previous work. In addition, several characteristics of the customer delay, namely the mean value, the variance and the tail distribution of the delay, are derived through some mathematical manipulations. The analysis is illustrated by means of some numerical examples.Editor: Artalejo In this paper, we have studied the delay characteristics of a discrete-time infinite-capacity queueing system with multiple servers, constant service times of arbitrary length and a general independent arrival process. The study is an extension of previous work ( [3] ), which was concerned with the analysis of the system content for this type of multiserver queueing system. In the present paper, we have established a relationship between the PGFs of the customer delay and the system content, using an analytical technique based on generating functions. Then from the result for the PGF of the system content, known from [3] , we have obtained an explicit expression for the PGF of the customer delay, as well as closed-form expressions for the mean value, the variance and the tail distribution of the customer delay. The obtained analytical results are easy to evaluate numerically.. Some numerical results have been presented to illustrate the analysis and the usefulness of the results.. The analyzed queueing model has practical applications in the domain of digital communication networks, such as circuit-switched TDMA systems, switching elements and traffic concentrators. We note that besides the characteristics of the system content studied in [3] for the considered model, the derived results for the customer delay (i.e., performance measures like the mean delay, the delay jitter and the probability that the customer delay exceeds a given threshold) are also very important for a network designer to guarantee the quality of service of the network.

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Continuous strategy replicator dynamics for multi-agent Q-learning The problem of multi-agent learning and adaptation has attracted a great deal of attention in recent years. It has been suggested that the dynamics of multi agent learning can be studied using replicator equations from population biology. Most existing studies so far have been limited to discrete strategy spaces with a small number of available actions. In many cases, however, the choices available to agents are better characterized by continuous spectra. This paper suggests a generalization of the replicator framework that allows to study the adaptive dynamics of Q-learning agents with continuous strategy spaces. Instead of probability vectors, agents' strategies are now characterized by probability measures over continuous variables. As a result, the ordinary differential equations for the discrete case are replaced by a system of coupled integral-differential replicator equations that describe the mutual evolution of individual agent strategies. We derive a set of functional equations describing the steady state of the replicator dynamics, examine their solutions for several two-player games, and confirm our analytical results using simulations. The notion of autonomous agents that learn by interacting with the environment, and possibly with other agents, is a central concept in modern distributed AI [23] . Of particular interests are systems where multiple agents learn concurrently and independently by interacting with each other. This multi-agent learning problem has attracted a great deal of attention due to a number of important applications. Among existing approaches, multi-agent reinforcement learning (MARL) algorithms have become increasingly popular due to their generality A. Galstyan (B) Information Sciences Institute, University of Southern California, Los Angeles, CA, USA e-mail: galstyan@isi.edu [1, 4, 5, 9, 10, 17, 22] . Although MARL does not hold the same convergence guarantees as in single-agent case, it has been shown to work well in practice (for a recent survey, see [2] ).. From the analysis standpoint, MARL represents a complex dynamical system, where the learning trajectories of individual agents are coupled with each other via a collective reward mechanism. Thus, it is desirable to know what are the possible long-term behaviors of those trajectories. Specifically, one is usually interested whether, for a particular game structure, those trajectories converge to a desirable steady state (called fixed points), or oscillate indefinitely between many (possibly infinite) meta-stable states. While answering this question has proven to be very difficult in the most general settings, there has been some limited progress for specific scenarios. In particular, it has been established that for simple, stateless Q-learning with a finite number of actions, the learning dynamics can be examined using the so called replicator equations from population biology [8] . Namely, if one associates a particular biological trait with each pure strategy, then the adaptive learning of (possibly mixed) strategies in multi-agent settings is analogous to competitive dynamics of mixed population, where the species evolve according to their relative fitness in the population. This framework has been used successfully to study various interesting features of adaptive dynamics of learning agents [7, 16, 20, 19, 27, 24, 25] .. With a few exceptions (e.g., see [18, 26] ), most existing studies so far have focused on discrete action spaces, which has limited the full analysis of the learning dynamics to games with very few actions. On the other hand, in many practical scenarios, strategic interactions between agents are better characterized by continuous spectra of possible choices. For instance, modeling an agent's bid in an auction with a continuous rather than discrete variable is more natural. In such situations, agents' strategies are represented as probability density functions defined over a continuous set of actions. Of course, in reality all the decisions are made over a discretized subset. However, the rationale for using the continuous approximation is that it makes the dynamics more amenable to mathematical analysis.. In this paper we consider simple Q-learning agents that play repeated continuous-strategy games. The agents use Boltzmann action-selection mechanism that controls the exploration/exploitation tradeoff through a single temperature-like parameter. The reward functions for the agents are assumed to be functions of continuous variables instead of tensors, and the agent strategies are represented as probability distribution over those variables. In contrast to the finite strategy spaces where the learning dynamics is captured by a set of coupled ordinary differential equations, the replicator dynamics for the continuous-strategy games are described by functional-differential equations for each agent, with coupling across different agents/equations. The long-term behavior of those equations define the steady state, or equilibrium, profiles of the agent strategies. It is shown that, in general, the steady state strategy profiles of the replicator dynamics do not correspond to the Nash equilibria of the game. This discrepancy can be attributed to the limited rationality of the agents due to exploration. In particular, for the Boltzmann action-selection mechanism studied here, exploration results in adding an entropic term to the agents' payoff function, with a coefficient governed by the exploration rate (temperature). Thus, when one decreases the exploration rate, the relative importance of this term diminishes and one is able to gradually recover the correspondence with the Nash equilibria. Furthermore, for games that allow uniformly mixed Nash equilibrium, the steady state solution of the replicator equation is identical with this uniform Nash equilibrium for any exploration rate. This is because the uniform distribution already maximizes the entropic term. And example of such a game if provided in Sect. 4.4.. The rest of this paper is organized as follows: In the next section we provide a brief overview of relevant literature. In Sect. 3 we introduce our model, derive the replicator equations for the continuous strategy spaces, and a set of coupled non-linear functional equations that describe the steady state strategy profile. In Sect. 4 we illustrate the framework on several examples of two-agent games, and provide some detailed results for general bi-linear and quadratic payoffs. Finally, we conclude the paper with a discussion of our results and possible future directions in Sect. 5. In this paper we presented a generalization of the replicator dynamics framework to study the dynamics of multi-agent reinforcement learning with continuous strategy spaces. We presented a set of differential-functional equations that describe the adaptive learning dynamics in multi-agent settings. We also derived a set of equations that characterize the steady state strategy profile of the learning agents. We demonstrated the analytical framework on several examples, and obtained an excellent agreement with the simulations results.. It was shown, both theoretically and through simulations, that for the Boltzmann exploration mechanism, the long-term limit of the replicator dynamics does not necessarily correspond to the Nash equilibria of the corresponding game-theoretical system. The reason for this is the bounded rationality of the agents as characterized by the exploration noise in their strategies. Specifically, the replicator dynamics at non-zero temperature minimizes an objective function that is related to the thermodynamic concept of free energy. We demonstrated on examples that the Nash equilibrium is recovered from the replicator dynamics in the zero temperature limit β → ∞. Finally, note that for the investment game considered in Sect. 4.4, the steady state of the replicator dynamics coincides with the Nash equilibria for arbitrary β: The underlying reason for this is the strategy profile that minimizes the energy (NE) also happens to maximize the entropy, so that the the same strategy profile minimizes both energy and free energy. More generally, one can say that any uniform Nash equilibrium also serves as a steady state for the replicator dynamics.. There are several important directions to pursue this work further. First of all, it will be worthwhile to perform more formal analysis of the steady state equations, and examine the issues of existence and uniqueness of the solutions depending on particular payoff structures. Furthermore, we intend to extend our analysis beyond two-player games, and specifically, consider games with a very large number of agents, N 1, where statisticalmechanical approaches for analyzing the solution structure might be appropriate. Finally, another direction of further research is to generalize the stateless Q-learning model considered here to a more general model which will account for different states and probabilistic transitions between them. We believe that such generalization will be possible by complementing the replicator equations with equations that describe the Markovian evolution of the states.. Next, let us define δ = dx xε(x, t), which describes the shift in the mean due to the perturbation. We multiply Eq. 39 by x and integrate over x to obtain. Thus, for T < a/12, or alternatively, β > 12/a ≡ β c , any perturbation that shifts the mean of the uniform solution will be amplified, indicating that the uniform steady state profile is unstable.

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Towards historical document indexing: extraction of drop cap letters Abstract This paper deals with the difficult problem of indexing ancient graphic images. It tackles the particular case of indexing drop caps (also called Lettrines) and specifically, considers the problem of letter extraction from this complex graphic images. Based on an analysis of the features of the images to be indexed, an original strategy is proposed. This approach relies on filtering the relevant information, on the basis of Meyer decomposition. Then, in order to accommodate the variability of representation of the information, a Zipf's law modeling enables detection of the regions belonging to the letter, what allows it to be segmented. The overall process is evaluated using a relevant set of images, which shows the relevance of the approach. As mentioned, in the Meyer-based segmentation part, the shape layer issuing from this stage has to be considered for extraction of the letter. For this purpose, since component extraction is not adapted, we propose to use a complementary Zipf's law based segmentation stage in order to extract large and homogeneous regions which correspond to the letter.. In order to become robust with respect to noisy conditions and detail changes, we chose a statistical approach based on the frequency of the patterns. The variety of colors involved in drop caps is considerable and never known. Besides, the letter is more than often in a single tone within an image. We then looked for a model to approximate the distribution of patterns present in the drop caps. This model is Zipf's law.. In this section, we will review Zipf's law and its application to images, in particular to drop caps; in fact, a mixture of laws is observed. We then compare the results according to the nature of the image. In this paper, we consider the problem of extracting letters from drop-cap images. Our strategy consists of decomposing the information into several layers, as a function of the identified features for each of these layers. Based on the frequency properties of the information, the Meyer-based decomposition allows a separation of the various layers, in which the information can be more easily analyzed. Then, based on the use of a Zipf modeling, which enables the extraction of areas First column corresponds to the image regularized, the second column corresponds to image after applying the Zipf algorithm, and the third column corresponds to letter extracted. Each row presents the result for each approach tested, and the difference between two results explains differences in recognition rates Fig. 15 An example of very difficult letter extraction. The first line corresponds to the original image and the last line to the letter extracted potentially corresponding to the letter, a letter extraction can be performed. Evaluation of the overall process highlights the relevance of the approach, by enabling the extraction of letters from a significant set of data. Further development of this work may require the use of other layers (textures and noise), in order to complete the indexing process. In addition, we will consider the use of visual keywords for the various layers, in order to achieve a comprehensive and practical indexing process.

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Improving FPGA Placement With Dynamically Adaptive Stochastic Tunneling Abstract-This paper develops a dynamically adaptive stochastic tunneling (DAST) algorithm to avoid the "freezing" problem commonly found when using simulated annealing for circuit placement on field-programmable gate arrays (FPGAs). The main objective is to reduce the placement runtime and improve the quality of final placement. We achieve this by allowing the DAST placer to tunnel energetically inaccessible regions of the potential solution space, adjusting the stochastic tunneling schedule adaptively by performing detrended fluctuation analysis, and selecting move types dynamically by a multi-modal scheme based on Gibbs sampling. A prototype annealing-based placer, called DAST, was developed as part of this paper. It targets the same computer-aided design flow as the standard versatile placement and routing (VPR) but replaces its original annealer with the DAST algorithm. Our experimental results using the benchmark suite and FPGA architecture file which comes with the Toronto VPR5 software package have shown a 18.3% reduction in runtime and a 7.2% improvement in critical-path delay over that of conventional VPR.Index Terms-Field-programmable gate array (FPGA), placement, simulated annealing, stochastic tunneling. This paper presented a DAST algorithm which improves the quality of FPGA placement while reducing the placement runtime. Three key ingredients of the DAST algorithm are: 1) a detection scheme for local minima entrapment based on DFA; 2) a dynamically adaptive annealing schedule based on stochastic tunneling; and 3) a heuristic to automatically select move types based on Gibbs sampling.. DAST can readily be incorporated into existing FPGA placement software and benefit from other research work specifically targeting FPGA placement improvement. We hope that this paper will motivate the FPGA community to systematically evaluate the many newly developed and promising optimization techniques, such as stochastic tunneling, parallel tempering, and particle swarm optimization. As a versatile algorithm, DAST may also be applied to other global optimization problems, such as protein folding, and has the potential to yield significant performance improvements there as well.

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An Efficient Rearrangement of Wavelet Packet Coefficients for Embedded Image Coding Based on SPIHT Algorithm In this paper, we propose an efficient method for rearranging the wavelet packet coefficients of an image to form hierarchical trees, by which the well known SPIHT algorithm can be applied. For images with textures, the high frequency wavelet coefficients are likely to become significant after several code passes of SPIHT, which degrades substantially the coding performance. As a result, the high frequency wavelet coefficients representing most of the high detail content of images need to be decomposed into wavelet packet coefficients for a further exploitation. The proposed rearrangement scheme has been applied to the highest frequency wavelet packet coefficients of images. Experimental results show that the performance of SPIHT can be improved, especially for fingerprint images. With the rapid growth of modern communications, multimedia applications and computer technologies, image compression continues to be in great demand [1] - [4] . The discrete cosine transform (DCT) based coder known as Joint Photographic Experts Group (JPEG) shows good compression results at moderate to high rates of bits per pixel [5] . Wavelet transform has drawn a lot of attention to the image compression applications [6] . It provides many desirable properties including multiresolution analysis, progressive transmission and embedded coding, and therefore has been adopted by JPEG2000 [7] , [8] . The wavelet based multiresolution analysis matches the characteristics of Human Visual System [9] . Specifically, the higher detailed information is projected onto the shorter basis function with higher spatial resolution; the lower detailed information is projected onto the larger basis function with higher spectral resolution. Progressive transmission with successive approximations is required for the Internet streaming and database browsing. By embedded coding, an image can be coded into a single code stream, from which the decoded image at any rate of bits per pixel can be obtained. In many cases, the embedded code stream of an image is organized in decreasing order of information importance for progressive transmission. By wavelet transform, images can be decomposed into subbands with orientation selectivity. If a wavelet coefficient is insignificant with respective to a given threshold, all the spatially related wavelet coefficients in the higher frequency subbands are likely to be insignificant with respective to the same threshold. Shapiro first introduced this property known as the self similarity of wavelet transform and developed an efficient embedded zerotree wavelet (EZW) coding algorithm [10] . Its improved version known as set partitioning in hierarchical trees (SPIHT) proposed by Said and Pearlman has been considered a benchmark [11] . In SPIHT, the wavelet transform coefficients of an image are examined against a sequence of successively smaller thresholds to locate significant coefficients. Su proposed a hybrid coder by combining SPIHT with vector quantization [12] . In which, the so-called high frequency trees with a large number of significant coefficients in the high frequency subbands are first identified and then coded using a different, more suitable method instead of SPIHT. Mukherjee and Mitra developed a vector extension of SPIHT called VSPIHT, in which wavelet coefficients are first grouped into small vectors and then coded using SPIHT [13] . Both EZW and SPIHT are quad-tree algorithms, in which the spatially related wavelet coefficients taken from all the subbands of the same orientation are arranged to form hierarchical trees. Whereas quad-tree coders are based on the self similarity of wavelet transform, there are some coders based on block coding in wavelet domain. The basic idea behind the block coding strategy is to exploit the energy clustering of wavelet coefficients within each subband. The amplitude and group partitioning (AGP) algorithm divides a region of high energy wavelet coefficients into small blocks through quadtree partitioning [14] . The SWEET algorithm takes octaveband partitioning to exploit the pyramid structure of wavelet transform [15] . Pearlman et al. developed the set partitioning embedded block (SPECK) algorithm [16] . In which, both quad-tree partitioning and octave-band partitioning are utilized to divide the wavelet transform coefficients of an image into blocks of different sizes. The embedded block coding with optimized truncation (EBCOT) algorithm proposed by Taubman [17] has been adopted by JPEG2000, which is preferable to JPEG [18] . However, the complexity of JPEG2000 is much more intense than JPEG. EBCOT is a two-tier algorithm: tier-1 performs embedded block coding followed by arithmetic coding; tier-2 takes charge of rate distortion control by using the post compression rate distortion (PCRD) algorithm, which requires a large amount of Copyright c 2007 The Institute of Electronics, Information and Communication Engineers memory space to store all the code streams of code blocks and their respective rate distortion information. In addition, every code block must be processed in the tier-1 of EBCOT before PCRD, however, some code blocks may not be needed to reconstruct the optimal decoded image at a given bit rate, which surely leads to waste of computation power. In [19] , Fang et al. proposed a pre-compression rate distortion optimization algorithm to avoid unnecessary computation and reduce memory space by ignoring unused code blocks.. For images with high detail textures, lots of wavelet coefficients are found significant in the high frequency subbands. Thus, the detailed information of an image represented by the significant wavelet coefficients in the high frequency subbands demands a further decomposition. Whereas wavelet transform only decomposes the low frequency subband in the iterative manner, wavelet packet transform decomposes both the low and high frequency subbands and therefore provides a much larger family of subband decompositions [20] , [21] . In this paper, an efficient method for rearranging the wavelet packet coefficients of an image is proposed to construct hierarchical wavelet packet trees, based on which images can be coded by using an efficient quad-tree based algorithm, e.g. SPIHT.. The remainder of this paper proceeds as follows. In Sect. 2, wavelet transform, wavelet packet transform and SPIHT are reviewed briefly. Section 3 describes the proposed scheme to construct the wavelet packet trees of images for embedded coding. Experimental results are presented in Sect. 4. Conclusion is given in Sect. 5. Wavelet transform provides an efficient multi-resolution analysis with many desirable properties. The wavelet tree based SPIHT algorithm is a well known image coder and has been considered a benchmark. The coding strategy of SPIHT is based on the so-called self similarity property of wavelet transform. Specifically, if a node in a wavelet tree is insignificant with respective to a given threshold, all the descendants are likely to be insignificant with respective to the same threshold. However, for images with high detail textures, many wavelet coefficients in the high frequency subbands are likely to become significant after several code passes of SPIHT. To improve the coding performance, the high frequency wavelet coefficients of an image need to be decomposed further into wavelet packet coefficients. To incorporate with the framework of SPIHT, an efficient scheme has been proposed to rearrange the high frequency wavelet packet coefficients, together with the low frequency wavelet coefficients, the called wavelet packet trees of images are thus constructed. As the proposed hierarchical wavelet packet tree is still a quad tree, the coding performance can be improved at no extra cost of coding complexity. Experimental results show that the proposed method is suitable for images with textures, especially for coding fingerprint images, which is one of the most demanding tasks.

O O O O B O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O B O O O O O O O O O O O B O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O B O O O B O O O O O O O O O O O O B O O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O B O O O O O O O B O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O


Model checking conditional CSL for continuous-time Markov chains We consider the model-checking problem of continuous-time Markov chains (CTMCs) with respect to Conditional Continuous Stochastic Logic (CCSL). CCSL extends the logic CSL introduced in [1] with a conditional probabilistic operator, which allows us to express a richer class of properties for CTMCs. Based on a parameterized product construction, we propose an approximate model checking algorithm with complexity analysis. CTMCs have received considerable attentions in network performance analysis, model checking, and system biology. In [1] , Continuous Stochastic Logic (CSL) has been introduced, that has been widely used to specify properties over CTMCs.. In the paper [1] , Aziz et al. focused on the decidability of the model-checking of CSL. Later, Baier et al. [2] presented an approximate model checking algorithm for the case restricted to binary until formulas. Recently, the approximate algorithm has been extended to handle nested until formulas in [3] . The main idea is to exploit the notion of stratified CTMCs, which are a subclass of CTMCs that have the nice feature allowing one to obtain the desired probability using a sequence of transient analysis. Then, the product of the CTMC and a deterministic finite automaton (DFA) obtained from the nested until formula is constructed, which is guaranteed to be stratified by construction. The product CTMC can then be analyzed efficiently, in a similar manner as the approach in [2] .. In this paper, we propose the conditional continuous stochastic logic (CCSL), an extension of CSL with a conditional probabilistic operator. CCSL allows one to express a richer class of properties, such as:. The probability is at least 0.1, that the number of proteins is more than 5 and the gene becomes inactive within time interval [10, 20) , under the condition that the proteins increasingly accumulated from 0 to k within the same time interval [10, 20) .. Such property can be expressed as a state formula of the form P ≥0.1 (3 [10, 20) f ∧ g | f 1 U [10, 20) f 2 U [10, 20) . where f, g, f 1 , . . . , f k are atomic propositions. We believe that such conditional properties are an important extension because of the important role of conditional probabilities in stochastic models [4] . Essentially, the model checking for the conditional probabilistic operator deals with binary conjunction of CCSL path formulas, which is not allowed in the classical CSL, see [1, 2] . Thus, in this paper, we extend the logic CSL with binary conjunction and disjunction operators for the path formulas.. We discuss how to compute the probability of a conjunctive path formula, and then present an approximate model checking algorithm, following the approach in [3] . First, a DFA A ψ is constructed for a CCSL path formula ψ. The next step is to construct the DFA A i ψ i for the conjunction from the automata A ψ i . The first challenging step is to construct the product of the CTMC and the automaton A i ψ i . A plain product construction turns out to be insufficient: We have to pay special attention to whether some conjuncts of the formula have been satisfied. We propose a notion of parameterized product construction. The probability is then computed on this product. The size of the automaton could be exponential in the number of binary operators in the path formulas, arising from the product construct, and the approximation calculation for the transient probability is linear in the size of the product.. Related Work There is a rich literature on model checking techniques for CTMCs, see [1, 2, 5, 6, 7, 8] . In [5, 6 ], deterministic timed automata (DTA) are used for specifying path properties. As discussed in [9] , nested until CSL path formulas can be expressed in DTA as well, however with a much larger number of states. Real-time is considered in [8] , with exponential complexity both in the size of the formula and in the time bound appearing in it. In this paper, we extend CSL path formulas by allowing conjunction and disjunction, then accordingly extend state formulas by introducing the conditional probabilistic operator.. The conditional probabilistic operator is directly inspired by the paper [10] , in which the conditional probabilistic operator is introduced and analyzed for Markov decision processes (MDP). Path formulas considered there are restricted binary path operators, and the challenge for MDPs is to study the scheduler class guaranteeing the extreme (maximal or minimal) probabilities.

O O O O O B I I O O O O O O B I I O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O