A Robust State Observer Using Multiple Integrators for Multivariable LTI Systems This paper proposes a robust state observer for multi-input multi-output LTI systems. Unknown inputs of polynomial form and highfrequency measurement noises are considered in the system model. The unknown inputs and the noises are not in the same form. Multiple integrations of both the observer error signal and the measurement output are used for the observer design. The existence condition of the proposed observer is shown to be the same as that of the proportional-integral (PI) observer. Computer simulations show the effectiveness of the proposed observer. key words: proportional integral observer, unknown input, measurement noise, multiple integrators This paper deals with how to estimate the states of systems with unknown disturbance inputs and measurement noises. We consider the multivariable linear time-invariant system ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ẋ = Ax + Bu + Nd y = Cx + w. where x ∈ R n is the state vector; u ∈ R m is the control input; d ∈ R q is the unknown disturbance input; y ∈ R p is the measurement output; w ∈ R p is the measurement noise, and A, B, N, C are the constant matrices of appropriate dimensions. We assume p ≥ q and, without loss of generality, rank{N} = q and rank{C} = p.. The unknown disturbance input vector is assumed to have the following polynomial function form:. where A i ∈ R q (i = 0, 1, ..., s − 1) are constant vectors, the values of which are unknown.. If the pair (C, A) is observable, the conventional observer is readily constructed aṡ. wherex ∈ R n is the estimation of the state x and L is the gain matrix such that (A − LC) is stable.. If we definex = x −x, then the error dynamics system is obtained bẏ When w = 0 and d is a constant vector (i.e. A i = 0 for i = 1, ..., s − 1), a proportional-integral (PI) observer was proposed in [1] under the following assumption. A robust observer using multiple integrators has been proposed for multi-variable LTI systems. Under the same existence condition as the PI observer the noise amplification problem can be avoided by replacing the measurement output with its r-times integration. The higher order r is employed, the more amount of noise is filtered out from the observer error dynamics. Moreover, with the integrations of the observer error signals upto s-times, the unknown disturbance input is estimated as well as the system states. A simple mechanical system and a multivariable numerical example have been considered to show the effectiveness of the proposed observer. For a mechanical example the proposed observer estimates the system state with less order than that of the previous observer in [7] . The noise reduction performance of the proposed observer can be more effective than the descriptor system approach [5] when r ≥ 2. Future study includes the design method (e.g. LTR technique) to select the observer gain for the proposed observer.

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 B I I B I B I 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 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 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


Incident Detection in Heavy Traffics in Tunnels by the Interlayer Feedback Algorithm Abstract In this paper, we developed video surveillance system to detect incidents from heavy traffics in tunnels. Incidents in tunnels may cause additional accidents or fires that may result in fatal disaster. Therefore, it is important to detect incidents as soon as possible to manage the traffics inside the tunnels by the officers. Generally, video images in the tunnels suffer from heavy occlusion due to the low position of camera settings. In particular, the problem of heavy occlusions would be more serious in the urban tunnels due to their heavy traffics. We developed a tracking algorithm to segment vehicles and estimate the precise vehicle trajectories against the heavy occlusions. Utilizing this tracking algorithm, dedicated algorithm to detect incidents from the traffic images was developed. For the experiments, video streams of three cameras for 6 months were investigated, and 32 incidents were examined to evaluate the developed algorithm. There are a lot of previous works on the vehicle tracking. Historical works of the vehicle tracking are as follows. A work by H. Kolling and H. Nagel [1] is widely known as successful by using vehicle shape model consisting of horizontal and vertical edges. Peterfreund [2] developed boundary extraction method by 'Snakes [3] ' for vehicle tracking. Smith [4] and Grimson [5] employed statistical analysis and clustering of optical flows for the tracking problem. Although those works do not deal with occlusion problem, some previous works deal with the problems. Leuck [6] and Gardner [7] employed 3D models of vehicle shape and developed a dedicated pattern matching algorithm to vehicle images. However, since this method requires various kinds of vehicle models, it would be difficult to be applied to a scene containing various kinds of vehicle traveling into various directions. Malik [8] tried to resolve occlusion problem by a dedicated reasoning method. Although, those methods achieved good performance in a sparse traffic with simple motion, they cannot deal with complicated traffics.. In recent years, the tracking algorithm has been restlessly improved [9] [10] [11] [12] [13] . Among them, Kanhere [10] tried to solve the occlusion problem at low camera angle by employing a 3-D perspective mapping from the scene to the image along with a plumb line projection. Zhang [12] applied multilayer framework to the occlusion problem. In this work, occlusion is detected by evaluating the compactness ratio and interior distance ratio of vehicles, and the detected occlusion is handled by removing a "cutting region" of the occluded vehicles. Ambai [13] developed the tracking method against occlusions consisting of feature point detection and clustering feature points. Gradient based feature detector was used for the feature point detection, and graph cut method was used for dividing the occluding objects.. A lot of researches on incident detection have been performed. Cuchira [14] applied traffic rule-based reasoning to images for simple traffic conditions on a single-lane straight road. Jung [15] tracked vehicle from traffic images for precise traffic monitoring. Zhang [16] , Srinivasan [17] , and Byun [18] employed Bayesian Network and Neural Network in order to distinguish incident from ordinary traffics. All the above algorithms do not consider about the effect of occlusion. Thus, they have some difficulties in being applied to complicated traffic situation such as congestion. Thomas [19] and Zheng [20] tried find outliers in the traffic flow statistics for the incident detection. Although their methods were successful, the methods require longer time for the detection than video analysis. Shehata [21] , Versavel [22] , and Austin [23] employed video surveillance for the incident detection. Although their methods were successful, they are focusing on relatively easier cases such as the detection of vehicles stalling at prohibited areas.. Incident detection in the heavy traffic is quite challenging because of heavy occlusions. The incident detections in the tunnel become more difficult due to the low angle condition of the camera settings. In this paper, we resolved the heavy occlusion problems by the interlayer feedback strategy, and developed a successful algorithm to detect incidents even in the congested traffic in the tunnel. The algorithm was examined using video images recorded in the tunnel at the Tokyo Metropolitan Expressway. In this paper, an algorithm for incident detection in the tunnel was developed. We developed the interlayer algorithm to combine the S-T MRF model and the algorithm in the Morphology layer, in order to resolve heavy occlusion problems in heavy traffic with the low angle image. The algorithm was proved to be effective for the segmentation of vehicles in the heavy occlusion images though the examinations using heavy occlusion images. Consequently, the algorithm could obtained precise trajectories of the vehicles, and contributed to the incident detections from the congested traffics in tunnels.. Since the incidents in tunnels may cause additional accidents or fires that may result in fatal disaster, it is important to detect them as soon as possible. The disaster would be rather serious in the heavy traffics of urban tunnels. The technology in this paper is expected to enhance the safety of tunnel traffics and the efficiency of tunnel operations.. Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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


A normalized basis for quintic Powell-Sabin splines We construct a suitable normalized B-spline representation for C 2 -continuous quintic Powell-Sabin splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction is based on the determination of a set of triangles that must contain a specific set of points. We are able to define control points and cubic control polynomials which are tangent to the spline surface. We also show how to compute the Bézier control net of such a spline in a stable way.Keywords : quintic Powell-Sabin splines, normalized B-splines, control points, control polynomials, Bézier control net MSC : Primary : 65D07, Secondary : 65D17, 68U07A normalized basis for quintic Powell-Sabin splinesDepartment of Computer Science, Katholieke Universiteit Leuven Celestijnenlaan 200A, B-3001 Leuven, BelgiumWe construct a suitable normalized B-spline representation for C 2 -continuous quintic PowellSabin splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction is based on the determination of a set of triangles that must contain a specific set of points. We are able to define control points and cubic control polynomials which are tangent to the spline surface. We also show how to compute the Bézier control net of such a spline in a stable way. Quadratic Powell-Sabin splines are defined on triangulations with a particular refinement. Each triangle in the triangulation is split into six subtriangles. These splines are C 1 -continuous, and they can be represented in a normalized basis [2] , in the sense that the basis functions B i , i = 1, . . . , N , form a convex partition of unity, i.e., for all points (x, y) in the domain. The construction of the basis allows us to define control triangles in a natural way. This normalized B-spline representation is effective in a wide range of application areas (see, e.g., [5, 8, 9, 13, 14] ).. Several authors considered C 2 -continuous quintic spline functions over triangulations of PowellSabin's type [10, 6, 1, 7] . In this paper we will follow the approach by Lai and Schumaker [7] , and we will construct a compact normalized basis for this spline space. Recently, a normalized basis was developed for reduced Clough-Tocher splines [12] .. The paper is organized as follows. In Section 2 we recall some general concepts of polynomials on triangles, and we define the quintic Powell-Sabin splines. Section 3 describes the construction of the normalized basis, which is based on determining a set of triangles that contain a specific set of points. In Section 4 we define control points and tangent control polynomials which are useful for computer aided geometric design. We also consider a stable computation of the Bézier ordinates of the spline. Finally, we show how the values of some spline coefficients can be determined from the other spline coefficients in an appropriate way. 2 Quintic Powell-Sabin splines

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


A uniform approach to logic programming semantics Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more successful and acknowledged than others. The rationales behind those various semantics have been manifold, depending on one's point of view, which may be that of a programmer or inspired by commonsense reasoning, and consequently the constructions which lead to these semantics are technically very diverse, and the exact relationships between them have not yet been fully understood. In this paper, we present a conceptually new method, based on level mappings, which allows to provide uniform characterizations of different semantics for logic programs. We will display our approach by giving new and uniform characterizations of some of the major semantics, more particular of the least model semantics for definite programs, of the Fitting semantics, and of the well-founded semantics. A novel characterization of the weakly perfect model semantics will also be provided. Negation in logic programming differs from the negation of classical logic. Indeed, the quest for a satisfactory understanding of negation in logic programming is still inconclusive -although the issue has cooled down a bit recently -and has proved to be very stimulating for research activities in computational logic, and in particular amongst knowledge representation and reasoning researchers concerned with commonsense and nonmonotonic reasoning. During the last two decades, different interpretations of negation in logic programming have lead to the development of a variety of declarative semantics, as they are called. Some early research efforts for establishing a satisfactory declarative semantics for negation as failure and its variants, as featured by the resolution-based Prolog family of logic programming systems, have later on been merged with nonmonotonic frameworks for commonsense reasoning, culminating recently in the development of socalled answer set programming systems, like smodels or dlv (Eiter et al. 1997; Marek and Truszczyński 1999; Lifschitz 2002; Simons et al. 200x) .. Systematically, one can understand Fitting's proposal (Fitting 1985) of a KripkeKleene semantics -also known as Fitting semantics -as a cornerstone which plays a fundamental rôle both for resolution-based and nonmonotonic reasoning inspired logic programming. Indeed, his proposal, which is based on a monotonic semantic operator in Kleene's strong three-valued logic, has been pursued in both communities, for example by Kunen (Kunen 1987) for giving a semantics for pure Prolog, and by Apt and Pedreschi (Apt and Pedreschi 1993) in their fundamental paper on termination analysis of negation as failure, leading to the notion of acceptable program. On the other hand, however, Fitting himself (Fitting 1991a; Fitting 2002 ), using a bilattice-based approach which was further developed by Denecker, Marek, and Truszczynski (Denecker et al. 2000) , tied his semantics closely to the major semantics inspired by nonmonotonic reasoning, namely the stable model semantics due to Gelfond and Lifschitz (Gelfond and Lifschitz 1988) , which is based on a nonmonotonic semantic operator, and the well-founded semantics due to van Gelder, Ross, and Schlipf (van Gelder et al. 1991) , originally defined using a different monotonic operator in three-valued logic together with a notion of unfoundedness.. Another fundamental idea which was recognised in both communities was that of stratification, with the underlying idea of restricting attention to certain kinds of programs in which recursion through negation is prevented. Apt, Blair, and Walker (Apt et al. 1988 ) proposed a variant of resolution suitable for these programs, while Przymusinski (Przymusinski 1988) and van Gelder (van Gelder 1988) generalized the notion to local stratification. Przymusinski (Przymusinski 1988) developed the perfect model semantics for locally stratified programs, and together with Przymusinska (Przymusinska and Przymusinski 1990) generalized it later to a three-valued setting as the weakly perfect model semantics.. The semantics mentioned so far are defined and characterized using a variety of different techniques and constructions, including monotonic and nonmonotonic semantic operators in two-and three-valued logics, program transformations, level mappings, restrictions to suitable subprograms, detection of cyclic dependencies etc. Relationships between the semantics have been established, but even a simple comparison of the respective models in restricted cases could be rather tedious. So, in this paper, we propose a methodology which allows to obtain uniform characterizations of all semantics previously mentioned, and we believe that it will scale up well to most semantics based on monotonic operators, and also to some nonmonotonic operators, and to extensions of the logic programming paradigm including disjunctive conclusions and uncertainty. The characterizations will allow immediate comparison between the semantics, and once obtained we will easily be able to make some new and interesting observations, including the fact that the wellfounded semantics can formally be understood as a Fitting semantics augmented with a form of stratification. Indeed we will note that from this novel perspective the well-founded semantics captures the idea of stratification much better than the weakly perfect model semantics, thus providing a formal explanation for the historic fact that the latter has not received as much attention as the former.. The main tool which will be employed for our characterizations is the notion of level mapping. Level mappings are mappings from Herbrand bases to ordinals, i.e. they induce orderings on the set of all ground atoms while disallowing infinite descending chains. They have been a technical tool in a variety of contexts, including termination analysis for resolution-based logic programming as studied by Bezem (Bezem 1989) , Apt and Pedreschi (Apt and Pedreschi 1993) , Marchiori (Marchiori 1996) , Pedreschi, Ruggieri, and Smaus (Pedreschi et al. 2002) , and others, where they appear naturally since ordinals are well-orderings. They have been used for defining classes of programs with desirable semantic properties, e.g. by Apt, Blair, and Walker (Apt et al. 1988 ), Przymusinski (Przymusinski 1988) and Cavedon (Cavedon 1991) , and they are intertwined with topological investigations of fixed-point semantics in logic programming, as studied e.g. by Fitting (Fitting 1994; Fitting 2002) , and by Hitzler and Seda (Seda 1995; Seda 1997; Hitzler 2001; Hitzler and Seda 2003b) . Level mappings are also relevant to some aspects of the study of relationships between logic programming and artificial neural networks, as studied by Hölldobler, Kalinke, and Störr (Hölldobler et al. 1999 ) and by Hitzler and Seda (Hitzler and Seda 2000; Hitzler and Seda 2003a) . In our novel approach to uniform characterizations of different semantics, we will use them as a technical tool for capturing dependencies between atoms in a program.. The paper is structured as follows. Section 2 contains preliminaries which are needed to make the paper relatively self-contained. The subsequent sections contain the announced uniform characterizations of the least model semantics for definite programs and the stable model semantics in Section 3, of the Fitting semantics in Section 4, of the well-founded semantics in Section 5, and of the weakly perfect model semantics in Section 6. Related work will be discussed in Section 7, and we close with conclusions and a discussion of further work in Section 8.. Part of this paper was presented at the 25th German Conference on Artificial Intelligence, KI2002, Aachen, Germany, September 2002 (Hitzler and Wendt 2002) .. A (normal) logic program is a finite set of (universally quantified) clauses of the form ∀(A ← A 1 ∧ . . . ∧ A n ∧ ¬B 1 ∧ . . . ∧ ¬B m ), commonly written as A ← A 1 , . . . , A n , ¬B 1 , . . . , ¬B m , where A, A i , and B j , for i = 1, . . . , n and j = 1, . . . , m, are atoms over some given first order language. A is called the head of the clause, while the remaining atoms make up the body of the clause, and depending on context, a body of a clause will be a set of literals (i.e. atoms or negated atoms) or the conjunction of these literals. Care will be taken that this identification does not cause confusion. We allow a body, i.e. a conjunction, to be empty, in which case it always evaluates to true. A clause with empty body is called a unit clause or a fact. A clause is called definite, if it contains no negation symbol. A program is called definite if it consists only of definite clauses. We will usually denote atoms with A or B , and literals, which may be atoms or negated atoms, by L or K .. Given a logic program P , we can extract from it the components of a first order language. The corresponding set of ground atoms, i.e. the Herbrand base of the program, will be denoted by B P . For a subset I ⊆ B P , we set ¬I = {¬A | A ∈ I }. The set of all ground instances of P with respect to B P will be denoted by ground(P ). For I ⊆ B P ∪ ¬B P we say that A is true with respect to (or in) I if A ∈ I , we say that A is false with respect to (or in) I if ¬A ∈ I , and if neither is the case, we say that A is undefined with respect to (or in) I . A (three-valued or partial) interpretation I for P is a subset of B P ∪ ¬B P which is consistent, i.e. whenever A ∈ I then ¬A ∈ I . A body, i.e. a conjunction of literals, is true in an interpretation I if every literal in the body is true in I , it is false in I if one of its literals is false in I , and otherwise it is undefined in I . For a negative literal L = ¬A we will find it convenient to write ¬L ∈ I if A ∈ I and say that L is false in I etc. in this case. By I P we denote the set of all (three-valued) interpretations of P . It is a complete partial order (cpo) via set-inclusion, i.e. it contains the empty set as least element, and every ascending chain has a supremum, namely its union. A model of P is an interpretation I ∈ I P such that for each clause A ← body we have that body true in I implies A true in I , and body undefined in I implies A true or undefined in I . A total interpretation is an interpretation I such that no A ∈ B P is undefined in I .. For an interpretation I and a program P , an I -partial level mapping for P is a partial mapping l : B P → α with domain dom(l ) = {A | A ∈ I or ¬A ∈ I }, where α is some (countable) ordinal. We extend every level mapping to literals by setting l (¬A) = l (A) for all A ∈ dom(l ). A (total) level mapping is a total mapping l : B P → α for some (countable) ordinal α.. Given a normal logic program P and some I ⊆ B P ∪¬B P , we say that U ⊆ B P is an unfounded set (of P ) with respect to I if each atom A ∈ U satisfies the following condition: For each clause A ← body in ground(P ) (at least) one of the following holds.. (Ui) Some (positive or negative) literal in body is false in I . (Uii) Some (non-negated) atom in body occurs in U .. Given a normal logic program P , we define the following operators on B P ∪ ¬B P . T P (I ) is the set of all A ∈ B P such that there exists a clause A ← body in ground(P ) such that body is true in I . F P (I ) is the set of all A ∈ B P such that for all clauses A ← body in ground(P ) we have that body is false in I . Both T P and F P map elements of I P to elements of I P . Now define the operator Φ P : I P → I P by Φ P (I ) = T P (I ) ∪ ¬F P (I )· This operator is due to Fitting (Fitting 1985) and is monotonic on the cpo I P , hence has a least fixed point by the Tarski fixed-point theorem, and we can obtain this fixed point by defining, for each monotonic operator F , that F ↑ 0 = ∅, F ↑ (α + 1) = F (F ↑ α) for any ordinal α, and F ↑ β = γ<β F ↑ γ for any limit ordinal β, and the least fixed point lfp(F ) of F is obtained as F ↑ α for some ordinal α. The least fixed point of Φ P is called the Kripke-Kleene model or Fitting model of P , determining the Fitting semantics of P .. Example 2.1 Let P be the program consisting of the two clauses p ← p and q ← ¬r . Then Φ P ↑ 1 = {¬r }, and Φ P ↑ 2 = {q, ¬r } = Φ P ↑ 3 is the Fitting model of P . Now, for I ⊆ B P ∪ ¬B P , let U P (I ) be the greatest unfounded set (of P ) with respect to I , which always exists due to van Gelder, Ross, and Schlipf (van Gelder et al. 1991) . Finally, define. for all I ⊆ B P ∪ ¬B P . The operator W P , which operates on the cpo B P ∪ ¬B P , is due to van Gelder et al. (van Gelder et al. 1991) and is monotonic, hence has a least fixed point by the Tarski fixed-point theorem, as above for Φ P . It turns out that W P ↑ α is in I P for each ordinal α, and so the least fixed point of W P is also in I P and is called the well-founded model of P , giving the well-founded semantics of P .. Example 2.2 Let P be the program consisting of the following clauses.. Then {p} is the largest unfounded set of P with respect to ∅ and we obtain W P ↑ 1 = {¬p}, W P ↑ 2 = {¬p, q}, and. Given a program P , we define the operator T + P on subsets of B P by T + P (I ) = T P (I ∪¬(B P \I )). It is well-known that for definite programs this operator is monotonic on the set of all subsets of B P , with respect to subset inclusion. Indeed it is Scott-continuous (Lloyd 1988; Abramsky and Jung 1994; Stoltenberg-Hansen et al. 1994) and, via Kleene's fixed-point theorem, achieves its least fixed point M as the supremum of the iterates T + P ↑ n for n ∈ N. So M = lfp(T + P ) = T + P ↑ ω is the least two-valued model of P . In turn, we can identify M with the total interpretation M ∪ ¬(B P \ M ), which we will call the definite (partial) model of P .. Example 2.3 Let P be the program consisting of the clauses. where X denotes a variable and 0 a constant symbol. Write s n (0) for the term s(· · · s(0) · · ·) in which the symbol s appears n times. Then. for all n ∈ N and {p(s n (0)) | n ∈ N} is the least two-valued model of P .. In order to avoid confusion, we will use the following terminology: the notion of interpretation will by default denote consistent subsets of B P ∪ ¬B P , i.e. interpretations in three-valued logic. We will sometimes emphasize this point by using the notion partial interpretation. By two-valued interpretations we mean subsets of B P . Given a partial interpretation I , we set I + = I ∩ B P and I − = {A ∈ B P | ¬A ∈ I }. Each two-valued interpretation I can be identified with the partial interpretation I ′ = I ∪¬(B P \I ). Both, interpretations and two-valued interpretations, are ordered by subset inclusion. We note however, that these two orderings differ: If I ⊆ B P , for example, then I ′ is always a maximal element in the ordering for partial interpretations, while I is in general not maximal as a two-valued interpretation. The two orderings correspond to the knowledge-and the truth-ordering due to Fitting (Fitting 1991a) .. There is a semantics using two-valued logic, the stable model semantics due to Gelfond and Lifschitz (Gelfond and Lifschitz 1988) , which is intimately related to the well-founded semantics. Let P be a normal program, and let M ⊆ B P be a set of atoms. Then we define P /M to be the (ground) program consisting of all clauses A ← A 1 , . . . , A n for which there is a clause A ← A 1 , . . . , A n , ¬B 1 , . . . , ¬B m in ground(P ) with B 1 , . . . , B m ∈ M . Since P /M does no longer contain negation, it has a least two-valued model T + P /M ↑ ω. For any two-valued interpretation I we can therefore define the operator GL P (I ) = T + P /I ↑ ω, and call M a stable model of the normal program P if it is a fixed point of the operator GL P , i.e. if M = GL P (M ) = T + P /M ↑ ω. As it turns out, the operator GL P is in general not monotonic for normal programs P . However it is antitonic, i.e. whenever I ⊆ J ⊆ B P then GL P (J ) ⊆ GL P (I ). As a consequence, the operator GL 2 P , obtained by applying GL P twice, is monotonic and hence has a least fixed point L P and a greatest fixed point G P . Van Gelder (van Gelder 1989) has shown that GL P (L P ) = G P , L P = GL P (G P ), and that L P ∪ ¬(B P \ G P ) coincides with the well-founded model of P . This is called the alternating fixed point characterization of the well-founded semantics.. Example 2.4 Consider the program P from Example 2.2. The subprogram Q consisting of the first three clauses of the program P has stable model M = {s, q}, which can be verified by noting that Q /M consists of the clauses. and has M as its least two-valued model.. For the program P we obtain. So L P = {q, s} while G P = {q, s, r }, and L P ∪ ¬(B P \ G P ) = {q, s, ¬p} is the well-founded model of P . As already mentioned in the introduction, level mappings have been used for studying semantic aspects of logic programs in a number of different ways. Our presentation suggests a novel application of level mappings, namely for providing uniform characterizations of different fixed-point semantics for logic programs with negation. Although we believe our perspective to be new in this general form, there nevertheless have been results in the literature which are very close in spirit to our characterizations.. A first noteable example of this is Fages' characterization of stable models (Fages 1994 ), which we have stated in Theorem 3.3. Another result which uses level mappings to characterize a semantics is by Lifschitz, Przymusinski, Stärk, and McCain (Lifschitz et al. 1995, Lemma 3) . We briefly compare their characterization of the well-founded semantics and ours. In fact, this discussion can be based upon two different characterizations of the least fixed point of a monotonic operator F . On the one hand, this least fixed point is of course the least of all fixed points of F , and on the other hand, this least fixed point is the limit of the sequence of powers (F ↑ α) α , and in this latter sense is the least iterate of F which is also a fixed point. Our characterizations of definite, Fitting, well-founded, and weakly stratified semantics use the latter approach, which is reflected in our general proof scheme, which defines level mappings according to powers, or iterates, of the respective operators. The results by Fages (Fitting 1994) and Lifschitz et al. (Lifschitz et al. 1995) hinge upon the former approach, i.e. they are based on the idea of characterizing the fixed points of an operator -GL P , respectively Ψ P (Przymusinski 1989; Bonnier et al. 1991) -and so the sought fixed point turns out to be the least of those. Consequently, as can be seen in the proof of Theorem 3.3, the level mapping in Fages' characterization, and likewise in the result by Lifschitz et al., arises only indirectly from the operator -GL P , respectively Ψ P -whose fixed point is sought. Indeed, the level mapping by Fages is defined according to iterates of T P /I , which is the operator for obtaining GL P (I ), for any I . The result by Lifschitz et al. is obtained similarly based on a three-valued operator Ψ P .. Unforunately, these characterizations by Fages, in Theorem 3.3, respectively by Lifschitz et al. (Lifschitz et al. 1995) , seem to be applicable only to operators which are defined by least fixed points of other operators, as is the case for GL P and Ψ P , and it seems that the approach by Lifschitz et al. is unlikely to scale to other semantics. For example, we attempted a straightforward characterization of the Fitting semantics in the spririt of Lifschitz et al. which failed.. On a more technical level, a difference between our result, Theorem 5.2, and the characterization by Lifschitz et al. (Lifschitz et al. 1995) of the well-founded semantics is this: In our characterization, the model is described using conditions on atoms which are true or false (i.e. not undefined) in the well-founded model, whereas in theirs the conditions are on those atoms which are true or undefined (i.e. not false) in the well-founded model. The reason for this is that we consider iterates of W P , where W P ↑ 0 = ∅, while they use the fact that each fixed point of Ψ P is a least fixed point of Φ P /I with respect to the truth ordering on interpretations (note that in this case P /I denotes a three-valued generalization of the GelfondLifschitz transformation due to Przymusinski (Przymusinski 1989) ). In this ordering we have Φ P /I ↑ 0 = ¬B P . It is nevertheless nice to note that in the special case of the well-founded semantics there exist two complementary characterizations using level mappings.. Since our proposal emphasizes uniformity of characterizations, it is related to the large body of work on uniform approaches to logic programming semantics, of which we will discuss two in more detail: the algebraic approach via bilattices due to Fitting, and the work of Dix.. Bilattice-based semantics has a long tradition in logic programming theory, starting out from the four-valued logic of Belnap (Belnap 1977) . The underlying set of truth values, a four-element lattice, was recognized to admit two ordering relations which can be interpreted as truth-and knowledge-order. As such it has the structure of a bilattice, a term due to Ginsberg (Ginsberg 1986) , who was the first to note the importance of bilattices for inference in artificial intelligence (Ginsberg 1992 ).. This general approach was imported into logic programming theory by Fitting (Fitting 1991a) . Although multi-valued logics had been used for logic programming semantics before (Fitting 1985) , bilattices provided an interesting approach to semantics as they are capable of incorporating both reasoning about truth and reasoning about knowledge, and, more technically, because they have nice algebraic behaviour. Using this general framework Fitting was able to show interesting relationships between the stable and the well-founded semantics (Fitting 1991b; Fitting 1993; Fitting 2002) .. Without claiming completeness we note two current developments in the bilatticebased approach to logic programming: Fitting's framework has been extended to an algebraic approach for approximating operators by Denecker, Marek, and Truszczynski (Denecker et al. 2000) . The inspiring starting point of this work was the noted relationship between the stable model semantics and the well-founded semantics, the latter approximating the former. The other line of research was pursued mainly by Arieli and Avron (Arieli and Avron 1994; Arieli and Avron 1998; Arieli 2002) , who use bilattices for paraconsistent reasoning in logic programming. The above outline of the historical development of bilattices in logic programming theory suggests a similar kind of uniformity as we claim for our approach. The exact relationship between both approaches, however, is still to be investigated. On the one hand, bilattices can cope with paraconsistency -an issue of logic programming and deductive databases, which is becoming more and more important -in a very convenient way. On the other hand, our approach can deal with semantics based on multi-valued logics, whose underlying truth structure is not a bilattice. A starting point for investigations in this direction could be the obvious meeting point of both theories: the well-founded semantics for which we can provide a characterization and which is a special case of the general approximation theory of Denecker et al. (Denecker et al. 2000) .. Another very general, and uniform, approach to logic programming pursues a different point of view, namely logic programming semantics as nonmonotonic inference. The general theory of nonmonotonic inference and a classification of properties of nonmonotonic operators was developed by Kraus, Lehmann, and Magidor (Kraus et al. 1990 ), leading to the notion KLM-axioms for these properties, and developed further by Makinson (Makinson 1994) . These axioms were adopted to the terminology of logic programming and extended to a general theory of logic programming semantics by Dix (Dix 1995a; Dix 1995b) . In this framework, different known semantics are classified according to strong properties -the KLM-axioms which hold for the semantics -and weak properties -specific properties which deal with the irregularities of negation-as-failure. As such Dix' framework is indeed a general and uniform approach to logic programming, its main focus being on semantic properties of logic programs. Our approach in turn could be called semisyntactic in that definitions that employ level mappings naturally take the structure of the logic program into account. As in the case of the bilattice-based approaches, it is not yet completely clear whether these two approaches can be amalgamated in the sense of a correspondence between properties of level mappings, e.g. strict or semi-strict descent of the level, etc., on the one hand, and KLM-properties of the logic program on the other. However, we believe that it is possible to develop a proof scheme for nonmonotonic properties of logic programs in the style of the proof scheme presented in the paper, which can be used to cast semantics based on monotonic operators into level mapping form.. We finally mention the work by Hitzler and Seda (Hitzler and Seda 1999) , which was the root and starting point for our investigations. This framework aims at the characterization of program classes, such as (locally) stratified programs (Apt et al. 1988; Przymusinski 1988) , acceptable programs (Apt and Pedreschi 1993) , or Φ-accessible programs (Hitzler and Seda 1999) . Such program classes appear naturally whenever a semantics is not defined for all logic programs. In these cases one tries to characterize those programs, for which the semantics is well-defined or well-behaved. Their main tool were monotonic operators in three-valued logic, in the spirit of Fitting's Φ P , rather than level mappings. With each operator comes a least fixed point, hence a semantics, and it is easily checked that these semantics can be characterized using our approach, again by straightforward application of our proof scheme. Indeed, preliminary steps in this direction already led to an independent proof of a special case of Corollary 6.7 (Hitzler and Seda 2001) .

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B I 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 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 B I O O O 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Future clinical uses of neurophysiological biomarkers to predict and monitor treatment response for schizophrenia © 2015 New York Academy of Sciences. Advances in psychiatric neuroscience have transformed our understanding of impaired and spared brain functions in psychotic illnesses. Despite substantial progress, few (if any) laboratory tests have graduated to clinics to inform diagnoses, guide treatments, and monitor treatment response. Providers must rely on careful behavioral observation and interview techniques to make inferences about patients' inner experiences and then secondary deductions about impacted neural systems. Development of more effective treatments has also been hindered by a lack of translational quantitative biomarkers that can span the brain-behavior treatment knowledge gap. Here, we describe an example of a simple, low-cost, and translatable electroencephalography (EEG) measure that offers promise for improving our eScholarship provides open access, scholarly publishing services to the University of California and delivers a dynamic research platform to scholars worldwide. understanding and treatment of psychotic illnesses: mismatch negativity (MMN). MMN is sensitive to and/or predicts response to some pharmacologic and nonpharmacologic interventions and accounts for substantial portions of variance in clinical, cognitive, and psychosocial functioning in schizophrenia (SZ). This measure has recently been validated for use in large-scale multisite clinical studies of SZ. Finally, MMN greatly improves our ability to forecast which individuals at high clinical risk actually develop a psychotic illness. These attributes suggest that MMN can contribute to personalized biomarker-guided treatment strategies aimed at ameliorating or even preventing the onset of psychosis. Biomarkers are objective measures that can provide information on a variety of different clinical characteristics, such as an individual's normal biology, pathology, including the trajectory of illness, or the response to a therapeutic intervention. While it is clear that symptom-based diagnostic schema can distinguish patients in a manner that predicts their trajectory and therapeutic sensitivity (e.g., in the parsing of a primary anxiety versus psychotic disorder), it is equally apparent that these schema have reached their limits of resolution with respect to pathophysiology and the development of novel and individualized therapeutics.. Biomarkers offer the hope that, despite great heterogeneity and multivariate interactions in the pathogenesis of brain disorders, objective measures will identify clusters of individuals that can then be reliably stratified on the basis of the cause, course, and/or treatment sensitivity of a given disorder. Of course, this hope is neither new-the search for biomarkers for mental illness can be traced back decades and perhaps centuries-nor is it a hope fulfilled, as we presently lack biomarkers that contribute in a meaningful way to our treatment of any major psychiatric syndrome.. In this paper, we provide an overview of biomarkers and their potential utility for improving our understanding and treatment of psychotic disorders. Many neurophysiological biomarkers have already undergone extensive validation and may contribute to the development of next-generation therapeutics, potentials (ERPs), 5 and electroencephalography (EEG) measures of oscillatory dynamics, 6-11,a as well as prepulse inhibition (PPI) of the acoustic startle response. 12, 13 Here, we focus on MMN as an example of a simple, low-cost, translatable, and automatically elicited EEG biomarker. This measure has provided valuable insights into impaired and spared sensory processing in schizophrenia (SZ), with robust relationships to important domains of functioning. We also discuss a strategy for a rational coupling of biomarker performance with cognitive therapies for personalized assignment to treatments that alter the course or even prevent the development of psychosis in children at ultrahigh clinical risk. One of the challenges facing the use of biomarkers in SZ patient populations is that, for the most part, biomarkers are being applied after the fact. In other words, if we acknowledge that SZ is a neurodevelopmental disorder (or set of disorders), likely reflecting perturbations of in utero neural development, then the events (genetic, environmental, or otherwise) that lead to the late-adolescent/early-adult manifestations of the disorder have come and gone, decades before biomarker data are measured. The number of variations in the expression of these early eventsfor example, variable neuronal migratory routes and the adjustments of the surrounding developing brain to them, the consequent alterations in premorbid behavior, and the reflected impact of environmental responses onto brain development-from in utero causative events to adult manifestation is substantial if not limitless. Unlike disorders of adult onset in which an anatomically or neurochemically constrained lesion is superimposed on a normally developed brain, in SZ, the absent connections lost to cells that did not arrive, and the aberrant connections formed in their place, are infused throughout the matrix of a very complex forebrain circuitry. Making sense of right and wrong in this circuit context, as a basis for understanding the biology of SZ and its courses or treatments, may not be feasible or even productive in the foreseeable future. While awaiting this more comprehensive understanding of SZ, we propose further development of biomarkers for predicting treatment response in a manner that is consistent both with the therapeutic goals of personalized medicine and the scientific strategies of experimental medicine. 110 Individuals are characterized by measures of brain activity that are associated with neurocognition and function, and areas of healthy or normal-range performance are identified. In this process, drugs or other experimental manipulations and designs can be used as clinical probes to identify targets of residual neuroplasticity. Treatments are then identified that leverage the intact neural circuit or neurocognitive resources so that the individual patient can utilize their capacities to reap the gains of the therapeutic intervention. In truth, the basic principles of the biomarkers-of-health approach are simple ones, long espoused by disciplines ranging from childhood education to career counseling: a successful outcome is best achieved by matching residual strengths-areas of resiliency-with task demands. In the frenzied search for the genetic and molecular markers and mechanisms of that which is wrong in SZ patients, the field and its treatments may not have fully appreciated and leveraged all that is right.. One key to the successful use of biomarkers in this model is the ability to link a healthy biomarker with a positive response to a specific therapy. For example, as alluded to in the introduction, some forms of cognitive training put demands on processes requiring healthy WM and attention 15 and thus would be best pursued in patients with biomarker evidence of relatively intact WM and attentional capacity. Alternatively, evidence that WM and attentional performance could be enhanced in that patient by a psychostimulant challenge might predict benefits of psychostimulant augmentation of cognitive training. Different biomarkers of neurocognitive and neural circuit strengths might predict optimal responses of SZ patients to cognitive behavioral therapy, computerized cognitive training, social skills training, medications such as the proextinction drug d-cycloserine 111 or the prosocial drug oxytocin, 112, 113 or even neurostimulation. 114 While there is substantial evidence that baseline cognitive deficits generally predict poor outcomes in cognitive interventions, 115-118 we are not yet at a point where we can apply specific algorithms other than clinical intuition to match biomarkers of intact neural function in a SZ patient with treatment response to different types of therapies (Fig. 6) . 52 Developing such algorithms will be advanced by incorporating informative biomarkers, such as MMN, and detailed neurocognitive assessments, into the designs of trials of cognitive interventions for SZ patients.. Importantly, the fidelity and optimal methods for many potential biomarkers have already been established in multisite studies, where deficits in these measures have been used as endophenotypes to identify risk genes for SZ. 3, 4, 12 In the figure-ground reversal proposed here, these biomarkers are used not to predict a risk of illness, but rather they are used to predict a likelihood of recovery.. Thus, we can envision a future in which biomarkers, used in conjunction with demographic, clinical, and genetic predictors, improve the identification of individuals at clinical risk for developing psychosis, inform individual assignment to beneficial interventions, and help quantify response to treatments. 3, 5, 52 Such an approach could contribute to the development of next-generation, precise, personalized, and even preemptive interventions.

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 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 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 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 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 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 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 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


Battery-Aware Task Mapping for Coarse-Grained Reconfigurable Architecture Coarse-grained Reconfigurable Architecture (CGRA) is a parallel computing platform that provides both high performance of hardware and high flexibility of software. It is becoming a promising platform for embedded and mobile applications. Since the embedded and mobile devices are usually battery-powered, improving battery lifetime becomes one of the primary design issues in using CGRAs. In this paper, we propose a battery-aware task-mapping method to optimize energy consumption and improve battery lifetime. The proposed method mainly addresses two problems: task partitioning and task scheduling when mapping applications onto CGRA. The task partitioning and scheduling are formulated as a joint optimization problem of minimizing the energy consumption. The nonlinear effects of real battery are taken into account in problem formulation. Using the insights from the problem formulation, we design the task-mapping algorithm. We have used several real-world benchmarks to test the effectiveness of the proposed method. Experiment results show that our method can dramatically lower the energy consumption and prolong the battery-life. Coarse-grained Reconfigurable Architecture (CGRA) is a kind of parallel computing platform combining high performance of hardware and high flexibility of software. It is becoming a promising platform for embedded and mobile applications. During past decade, a large number of CGRAs [1] - [3] have been developed which demonstrated the high performance, flexibility and energy-efficiency.. Since the embedded and mobile devices are usually battery-powered, improving battery lifetime becomes one of the primary design issues in using CGRAs. Recent research results show that the real battery has the nonlinear characteristics: rate capacity effect and recovery effect [5] . The rate capacity effect shows that higher discharge current will bring lower energy conversion efficiency, and recovery effect indicates that inserting idle time into discharge procedure will increase the effective charge that the battery can provide. These effects indicate that the battery lifetime is sensitive to the discharge current distribution. In [5] , Rakhmatov proposed an analytical battery model. This model describes the battery charge loss as a function of the profile of discharge currents, which takes into account both the rate capacity effect and the recovery effect. And this model indicates that the battery charge loss can be optimized by adjusting the profile of discharge currents. For a CGRA, the energy consumption is from the execution of application. A typical CGRA is composed of a host controller and a 2-D processing element (PE) array. For implementing a given application on CGRA, the application is partitioned to several tasks and the tasks are scheduled and executed on PE array. The host controller would controls the PE array to be reconfigured several times for executing these tasks. Therefore, the discharge current distribution is closely correlated with the task partitioning and scheduling. More specifically, the different task partitioning will cause the different number of operators in each task. When these tasks are mapped onto PE array, it will cause different number of active PEs, which results in different working current of PE array. Thus, how to partition the application into tasks determines the working current of each task. The task scheduling determines the task executing order and start time of each task. It also affects the profile of discharge currents.. Since the energy consumption of battery is determined by the profile of discharge currents, the most rational way to optimize the battery lifetime of CGRA is to find the proper task partitioning and scheduling, resulting in the profile of discharge currents that causes minimum battery charge loss. In this paper, we formulate the task partitioning and scheduling as a joint optimization problem of minimizing the battery charge loss. Using the insights from the problem formulation, we design the battery-aware task-mapping algorithm.. The remainder of this paper is structured as follows: we will introduce the background of battery model and CGRA in Sect. 2. In Sect. 3 we will give some related works about energy-efficient task partitioning and scheduling. We will formulate the task mapping problem in Sect. 4. And we will present the battery-aware task mapping method in Sect. 5. Some experiment results are shown in Sect. 6. Finally, we will conclude in Sect. 7. In this paper, we proposed a battery-aware task mapping method for battery-powered reconfigurable computing system. The battery nonlinear characteristics are taken into account. The proposed method optimizes task partitioning and scheduling jointly to minimize the energy consumption. Experiment results show that the proposed task mapping method can reduce the energy consumption and improve the battery lifetime greatly. Low-power design is the fundamental theme pervading the embedded system and mobile computing research. Voltage and frequency scaling has been extensively used on singleprocessor and multi-processor platform. However, in most of the published work, an ideal power source is assumed. In [7] , the authors proposed an energy-efficient scheduling algorithm. Their method is aimed at sporadic real-time tasks in multiprocessor, by hiring LRE-TL scheduling algorithm [16] , it can minimize energy consumption by adjust the voltage and frequency of processors. An energyaware partitioned fixed-priority scheduling method is proposed in [8] . This method can optimize the energy cost by adjusting the clock frequency. In [9] , an energy-efficient scheduling method for real-time tasks is given. This method is cluster-based, by controlling active-island and frequency assignment, it can minimize energy consumption. In [10] the authors proposed an energy-efficient scheduling method for lightly loaded multicore processors. They let the overfull cores work on low frequency and lock down idle cores. A task scheduling method for dual-core system is proposed in [11] . It employs DVS (Dynamic Voltage Scaling) for each subtask and match them to certain processor. This method shows good result in energy optimization. A priority-based scheduling method to optimize energy consumption is proposed in [6] . Firstly, it partitions the input task by priority, and then chooses different strategy for different priority. By controlling the power threshold of each processor, they could balance the load and reduce energy consumption. Since the nonideal battery properties play an important role in effective utilization of the battery capacity, the actual performance of all the above methods is overestimated.. Our work is different to the voltage and frequency scaling methods. Those methods find the proper supply voltage and frequency to reduce energy consumption, while we focus on how to partition and schedule the tasks from a given applications.. Recently, since the reconfigurable architecture is becoming more and more popular, some issues about energy optimization for reconfigurable computing platform have been investigated. In [12] , the authors proposed a task-scheduling algorithm to manage energy consumption for FPGA. This algorithm schedules the tasks based on Rakhmatov battery model. This method works well on fine-grained reconfigurable architecture. An interconnect optimization method is proposed in [13] . It achieves optimized energy consumption by shutting down connections that is not in use. However it does not take into account the nonlinear effects of battery, which limits its effect. In [14] , the authors proposed a task-mapping algorithm for CGRA. This method takes the architectural features of CGRA into account; it can get less power consumption and shorter execution cycles. However, an ideal power source is assumed. A power centric mapping method for reconfigurable processor with dual V dd and dual V th is shown in [15] . But its target architecture is different from ours and they don't consider the battery nonlinear features either.. Our work is also quite different to the above methods for reconfigurable computing platform. First, less of them consider the battery nonlinear features, while our proposed method is based on nonlinear battery model. Second, most existing methods only consider task-scheduling problem, such as the algorithm in [12] . However, task partitioning determines the profile of working current of tasks, which cannot be neglected. In our work, we deal with task partitioning and scheduling jointly.

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


rpartOrdinal: An R Package for Deriving a Classification Tree for Predicting an Ordinal Response This paper describes an R package, rpartOrdinal, that implements alternative splitting functions for fitting a classification tree when interest lies in predicting an ordinal response. This includes the generalized Gini impurity function, which was introduced as a method for predicting an ordinal response by including costs of misclassification into the impurity function, as well as an alternative ordinal impurity function due to ? that does not require the assignment of misclassification costs. The ordered twoing splitting method, which is not defined as a decrease in node impurity, is also included in the package. Since, in the ordinal response setting, misclassifying observations to adjacent categories is a less egregious error than misclassifying observations to distant categories, this package also includes a function for estimating an ordinal measure of association, the gamma statistic. For many high-throughput genomic studies, the phenotype to be predicted is ordinal. Some examples of ordinal responses include the more recently advocated method for evaluating response to treatment in target tumor lesions, known as the response evaluation criteria in solid tumors (RECIST) method, with ordinal outcomes defined as complete response > partial response > stable disease > progressive disease. Moreover, most histopathological measures are ordinal, such as scoring methods for liver biopsy specimens from patients with chronic hepatitis, including the Knodell hepatic activity index, the Ishak score, and the METAVIR score. Statistical methods such as adjacent category, proportional odds, and continuation ratio models (?) are traditionally used when modeling an ordinal response, though they fail for high-throughput genomic datasets when the number of covariates, , exceeds the number of observations, .. An alternative class prediction method, classification trees (CTs), is capable of predicting a response when the << (?). Suppose independent observations to be classified are characterized by a -dimensional vector of predictors = ( 1 , 2 , . . . , ) and each observation falls into one of classes. Let denote the class with = 1 representing observations in class 1, = 2 representing class 2,. . ., and = representing class . When deriving a CT, all observations start together in the root node, . Then, for predictors 1, 2, . . . , , the optimal split is determined, where optimality is defined as that split resulting in the largest decrease in node impurity.. For node , the optimal split divides the observations to the left and right descendent nodes, and , respectively, and the proportion of cases in each of the classes within these nodes are called the node proportions, that is, ( | ) for = 1, . . . , such that ( 1 | ) + ( 2 | ) + . . . + ( | ) = 1. For nominal response classification, the within-node impurity measure most commonly used is the Gini criterion (?), defined as. This is the default impurity function in the R programming environment rpart package (??) for predicting a nominal class response. However, use of this impurity function does not take advantage of the additional information present when the response is ordinal. To that end, the generalized Gini impurity function (?),. which factors in ( | ), the cost of misclassifying a class observation as belonging to class , has been proposed for ordinal response prediction.. Another proposed ordinal impurity function for deriving an ordinal response classification tree based on a measure of nominal-ordinal association (?) that does not require the assignment of costs of misclassification is. where ( | ) = ∑ =1 ( | ) (?). A splitting method for ordinal response prediction that is not impurity-based is the ordered twoing method (?). Though this method was described in the seminal book by ? and has been implemented in the CART Software by Salford Systems (??), it has not yet been implemented in R. Ordered twoing proceeds by reformulating the ordinal response as a vector of dichotomous responses, where for each observation , the ℎ dichotomous response is taken to be. For node and dichotomous response , the split that maximizes. over the covariates is taken to be the best split for that dichotomous response . Subsequently, the split associated with the dichotomous response * = arg max ( , , ). is then selected for splitting node . In this paper, we describe the rpartOrdinal R package, which implements ordered twoing, the generalized Gini, and the ordinal impurity splitting 1 bwt > 3500 2 3000 < bwt ≤ 3500 3 2500 < bwt ≤ 3000 4 bwt ≤ 2500 Table 1 : Ordinal response levels for low birthweight (Category).. methods. These splitting methods should be considered for use when deriving an ordinal response classification tree.. For nominal response prediction, misclassification rates are often examined as a means for assessing the performance of the classifier. For ordinal response prediction problems, it may be of more interest to estimate the gamma statistic as an ordinal measure of association between the observed and predicted responses as a means for gauging the success of ordinal classification. Briefly, the association between two ordinal variables and can be estimated by the gamma statistic (?), where given the cross-tabulation matrix of and having rows and columns, the number of concordant pairs for cells (1, 1) to ( − 1, − 1) is given by. Similarly, the number of discordant pairs for cells (1, 2) to ( − 1, ) is given by. We then let =. such that the gamma statistic of ordinal association is defined asˆ. An R package, rpartOrdinal, that implements the described ordinal splitting methods as well as a function for estimating the gamma statistic as an ordinal measure of association is available for download from the Comprehensive R Archive Network at http://cran.r-project. org/package=rpartOrdinal. Herein we have described the rpartOrdinal package which works in conjuction with the rpart package in the R programming environment. The package provides methods for fitting a CT when the response is ordinal. We note that another R package, party (?), can also be used to derive an ordinal conditional inference tree, where the variable selected for splitting a given node is determined using an inferential test (?). These methods may prove useful when the dataset to be analyzed includes an ordinal response and the number of covariates exceeds the sample size. In such situations, traditional ordinal response methods such as proportional odds models cannot be fit. Secondary data analyses are a natural and desirable by-product from publicly available databases such as Gene Expression Omnibus. In the high-throughput genomic setting, most attention has been focused on classification algorithms for dichotomous responses. We believe analysts will find the rpartOrdinal useful particularly when modeling ordinal responses for high-dimensional datasets. The rpartOrdinal package was written in the R programming environment (?) and depends on the rpart package (?). Currently, rpart includes methods for deriving regression, classification, and survival trees. Due to the method= option in rpart, users can define their own splitting methods for use in conjunction with the rpart function. A user defined method passed to the method= option must be a list consisting of three functions named eval, split, and init. Since previous research comparing the ordinal splitting methods to traditional methods for single trees and for bootstrap aggregating classification trees has demonstrated that when the response to be predicted is ordinal, an ordinal splitting method is usually preferred (??), we have implemented three ordinal splitting methods, namely, ordered twoing, ordinal impurity, and generalized Gini for use in conjunction with rpart.

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


Program Equivalence in Linear Contexts Abstract. Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at contextual equivalence in the usual (non-linear) functional languages, and fail in capturing non-trivial equivalent programs in linear contexts, particularly when non-determinism is present. We propose the notion of linear contextual equivalence to formally characterize such program equivalence, as well as a novel and general approach to studying it in higher-order languages, based on labeled transition systems specifically designed for functional languages. We show that linear contextual equivalence indeed coincides with trace equivalence. We illustrate our technique in both deterministic (a linear version of PCF) and non-deterministic (linear PCF in Moggi's framework) functional languages. Contextual equivalence is an important concept in programming languages and can be used to formalize and reason about many interesting properties of computing systems. For functional languages, there are many techniques that can help to prove contextual equivalence. Among others, applicative bisimulations [1, 14] and logical relations [25, 28] are particularly successful.. On the other side, linear logic (and its term correspondence often known as linear λ-calculus) has seen significant applications in computer science ever since its birth, due to its native mechanism of describing restricted use of resources. For example, the linear λ-calculus provides the core of a functional programming language with an expressive type system, in which statements like "this resource will be used exactly once" can be formally expressed and checked. Such properties become useful when introducing imperative concepts into functional programming [13] , structural complexity theory [12] , or analyzing memory allocation [30] . Moreover, linear λ-calculus, when equipped with dependent types, can serve as a representation language within a logical framework, a general meta-language for the formalization of deductive systems [6] .. Introducing linearity also leads to novel observation over program equivalences. In particular, if we consider a special sort of contexts where candidate programs must be used linearly (we call these contexts linear contexts), program equivalence with respect to these contexts should be a coarser relation than the usual notion of contextual equivalence, especially when non-determinism is present. For instance, take Moggi's language for non-determinism [19] , where we have a primitive ⊓ for non-deterministic choice (same as the internal choice in CSP [11] ), and consider the following two functions:. = val(λx . val(0)) ⊓ val(λx . val (1)).. Existing techniques such as bisimulation or logical relations distinguish these two functions. In fact, it is easy to show that they are not equivalent in arbitrary contexts, by considering, e.g., the context bind f = [_] in bind x = f (0) in bind y = f (0) in val(x = y).. The context makes a double evaluation of the function by applying it to concrete arguments (noticing that Moggi's language enforces a call-by-value evaluation of nondeterministic computations): with the first function f 1 , the two evaluation of f (0) can return different values since the non-deterministic choice is inside the function body; with the second function f 2 , the non-deterministic choice is made before both evaluations of f (0) and computation inside the function is deterministic, so the two evaluations always return the same value. But if we consider only linear contexts, where programs will be evaluated exactly once, then the two functions must be equivalent. However, no existing technique, at least to the best of our knowledge, can characterize such an equivalence relation with respect to linear contexts. We have presented a novel approach for characterizing program equivalence in linear contexts, via trace equivalence in appropriate labeled transition systems. The technique is both sound and complete, and as we have shown in the paper, is general enough to be adapted for languages with linear type systems. Linear contextual equivalence is indeed a restricted notion of program equivalence and one may question its use in practice. As we have explained in the beginning of the paper, it does have application in security since we can use linearity to limit adversaries' behaviour. We also believe that such a notion of program equivalence can be useful in reasoning about programs in systems where only restricted access to resources is allowed, particularly when side effects are present. The result in non-deterministic languages already enables us to prove linear contextual equivalence between non-trivial programs. The motivation of the work first comes from the second author's work on building a logic (namely CSLR) for reasoning about computational indistinguishability, which is an essential concept in complexity-theoretic cryptography and helps to define many important security criteria [32, 8] . The CSLR logic is based on a functional langage which characterizes probabilistic polynomial-time computations by typing, where linearity plays an important role. A rule that can identify program equivalence in linear contexts 3 can help to simplify many proofs, e.g., the IND-CPA proof of the El-Gamal encryption, which is currently in the form of so-called game-based proofs [20] . Although the language of the CSLR logic is probabilistic, a general proof technique of linear contextual equivalence is missing from the literature, particularly in the setting of purely non-determinism where there exist programs that are equivalent in linear contexts but not in general, as we described previously.. Program equivalence with respect to non-linear contexts has been widely investigated. Logical relations are one of the powerful tools for proving contextual equivalence in typed lambda-calculi, in both operational [22, 23, 5] and denotational settings [25, 18, 10] . They are defined by induction on types, hence are relatively easy to use. But it is known that completeness of (strict) logical relations are often hard to achieve, especially for higher-order types. It is even worse for monadic types, particularly when non-determinism is present [17] .. Characterization in terms of simulation relation has been studied in functional languages [14, 9, 21, 16] , as well as languages with linear type systems [4] . Due to the higher-order features of the languages, it is difficult to directly prove the precongruence property of similarity. A common feature crucial to this line of research is then to follow Howe's approach [14] , which requires to first define a precongruence candidate, a precongruence relation by construction, and then to show the coincidence of that relation with simulation. An alternative approach, such as environmental bisimulation proposed in [27] , has a built-in congruence property, but then the definition itself has very complex conditions.

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


Minimum Phase Noise of an LC oscillator: Determination of the optimal operating point of the active part In this paper, we describe an original method for determining the optimal operating point of the active part (transistor) of an LC oscillator leading to the minimum phase noise for given specifications in terms of power consumption, oscillation frequency and for given devices (i.e., transistor and resonator). The key point of the proposed method is based on the use of a proper LC oscillator architecture providing a fixed loaded quality factor for different operating points of the active part within the oscillator. The feedback network of this architecture is made of an LC resonator with coupling transformers. In these conditions, we show that it is possible to easily change the operating point of the amplifier, through the determination of the turns ratio of those transformers, and observe its effect on phase noise without modifying the loaded quality factor of the resonator. The optimal operating point for minimum phase noise is then extracted from nonlinear simulations. Once this optimal behaviour of the active part known and by associating the previous LC resonator, a design of an LC oscillator or VCO with an optimal phase noise becomes possible. The conclusions of the presented simulation results have been widely used to design and implement a fully integrated, LC differential VCO on a 0.35 µm BiCMOS SiGe process. Mobile communication system evolution demands continuous efforts toward the improvement of RadioFrequency (RF) circuit performances. Concerning the oscillators and voltage-controlled oscillators (VCOs), the phase noise requirements are even more stringent. Indeed, the carrier rejection and the transmission quality of any systems depend on the phase noise of the signals applied to the modulator. Furthermore, from the designer point of view, pressure is growing as design time is getting shorter and shorter. In this context, it seems to be very interesting to know rapidly if the specification required in terms of phase noise and consumption are consistent with the technology provided. Due to these considerations, this paper describes a method for determining the optimal operating point of the active part of an LC oscillator leading to the minimum phase noise for given specifications in terms of power consumption, oscillation frequency and for given devices.. Email address: david.cordeau@univ-poitiers.fr (David Cordeau) Section 2 is a brief review of some of the existing phase noise models giving important key points for phase noise minimization. Section 3 presents the theoretical analysis of the chosen LC oscillator topology and concludes with the sequence to be carried out to obtain the oscillation at a frequency f 0 for a given operating point of the amplifier. Section 4 describes the simulations leading to the optimal operating point of a SiGe HBT LC oscillator. Finally, section 5 presents the design and implementation of a fully integrated differential VCO optimized in phase noise using the conclusions of the previous section. An original method for determining the optimal operating point of the active part of an LC oscillator leading to a minimum phase noise for given specifications in terms of power consumption, oscillation frequency and for given devices (i.e., transistor and resonator) is presented in this paper. To achieve this optimal operating point, a proper LC oscillator topology, which provides a fixed loaded quality factor for different operating points of the active part, is studied and simulated. The presented simulation results clearly show that the optimal operating point, for the power consumption, oscillation frequency and the BiCMOS SiGe technology chosen, leading to the minimum phase noise is the class-C operation of the active part within the oscillator with a maximum voltage swing across the resonator for a given loaded quality factor. From this conclusion, a fully integrated, LC differential VCO has been designed and implemented on the same 0.35 µm BiCMOS SiGe process. The fabricated VCO is tuned over two frequency bands from 1.5 to 2 GHz with a tuning voltage varying from 0 to 2.7 V . The optimized measured best case phase noise is −98 dBc/Hz and −104 dBc/Hz at 50 kHz and 10 100 kHz frequency offset respectively under 2.7 V supply voltage with only 7 mA current consumption.

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 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 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 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 B 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 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 B I 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 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 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 B I 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