Haut PDF Functional programming and the logical variable

Functional programming and the logical variable

Functional programming and the logical variable

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Constrained variable clustering and the best basis problem in functional data analysis

Constrained variable clustering and the best basis problem in functional data analysis

There are well-known standard ways of extracting optimal features according to a given criterion. For instance in unsupervised problems, the first k principal components of a dataset give the best linear approximation of the original data in R k for the quadratic norm (see [13] for functional principal component analysis (PCA)). In regression problems, the partial least-squares approach extracts features with maximal correlation with a target variable (see also Sliced Inversion Regression methods [4]). The main drawback of those approaches is that they extract features that are not easy to interpret: while the link between the original features and the new ones is linear, it is seldom sparse; an extracted feature generally depends on many original features.
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Variable selection and estimation in multivariate functional linear regression via the Lasso

Variable selection and estimation in multivariate functional linear regression via the Lasso

our knowledge, the model has been first mentioned in the work of Cardot et al. (2007) under the name of multiple functional linear model. An estimator of β is defined with an iterative backfitting algorithm and applied to the ozone prediction dataset initially studied by Aneiros-P´erez et al. (2004). Variable selection is performed by testing all the possible models and selecting the one minimising the prediction error over a test sample. Let us also mention the work of Chiou et al. (2016) who consider a multivariate linear regression model with functional output. They define a consistent and asymptotically normal estimator based on the multivariate functional principal components initially proposed by Chiou et al. (2014).
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VARIABLE SELECTION AND ESTIMATION IN MULTIVARIATE FUNCTIONAL LINEAR REGRESSION VIA THE LASSO

VARIABLE SELECTION AND ESTIMATION IN MULTIVARIATE FUNCTIONAL LINEAR REGRESSION VIA THE LASSO

not possible if dim(H j ) = +∞ since b Γ j is a finite-rank operator. Without this condition, Equation (14) does not admit a closed-form solution and, hence, is not calculable. We then propose the GPD (Groupwise-Majorization-Descent) algorithm, initially proposed by Yang and Zou (2015), to compute the solution paths of the multivariate Group-Lasso penalized learning problem, without imposing the group-wise orthonormality condition. The GPD algorithm is also based on the principle of coordinate-wise descent but the minimisation problem (14) is modified in order to relax the group-wise orthonormality condition. We denote by b β (k) the value of the parameter at the end of iteration k. During iteration k + 1, we update sequentially each coordinate. Suppose that we have changed the j − 1 first coordinates (j = 1, ..., p), the current value of our estimator is ( b β 1 (k+1) , ..., b β j−1 (k+1) , b β j (k) , ..., b β p (k) ). We want to update the j-th coefficient and, ideally, we
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Static interpretation of higher-order modules in Futhark: functional GPU programming in the large

Static interpretation of higher-order modules in Futhark: functional GPU programming in the large

We have taken an extrinsic approach [ Benton et al. 2012 ], as opposed to an intrinsic one, to the representation of the core language, the module language, and the target language, which keeps our implementation close to the approach presented in the paper. The extrinsic encoding has an advantage of being more suitable for code extraction to obtain a certified implementation. That is, we have implemented the abstract syntax as simple inductive data types and given separate inductive definitions for relations such as elaboration, typing, and so on. The semantic objects of Figure 4 have been implemented as mutually defined inductive types using Coq’s with clause. The same approach is used for definitions of relations on environments. As described in Section 4, semantic objects are represented using finite maps and sets and indeed, the implementation makes use of Coq’s standard library implementations of such objects. Specifically, we use the FMapList and FSetList implementations of the FMap and FSet interfaces, respectively. Both FMapList and FSetList make use of the list data type together with a property that the list is ordered according to a strict order on the underlying data structure. The strict order for the underlying list allows us to prove an extensionality property for environments and sets (assuming proof irrelevance). That is, for any two environments 𝐸 1 and 𝐸 2 we have (∀𝑘, 𝐸 1 (𝑘) = 𝐸 2 (𝑘)) → 𝐸 1 = 𝐸 2 . The equal sign = refers to the Coq propositional equality, which means that we can use all the standard rewriting machinery instead of using setoid equality.
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Recursion Schemes and Logical Reflection

Recursion Schemes and Logical Reflection

I. I NTRODUCTION An old model of computation, recursion schemes were originally designed as a canonical programming calculus for studying program transformation and control structures. In recent years, higher-order recursion schemes (HORS) have received much attention as a method of constructing rich and robust classes of possibly infinite ranked trees (or sets of such trees) with strong algorithmic properties. The interest was sparked by the discovery of Knapik et al. [2] that HORSs which satisfy a syntactic constraint called safety generate the same class of trees as higher-order pushdown automata. Remarkably these trees have decidable monadic second-order (MSO) theories, subsuming earlier well-known MSO decidability results for regular (or order-0) trees [3] and algebraic (or order-1) trees [4]. We now know [5] that the modal µ-calculus (local) model checking problem for
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Logical equivalence for subtyping object and recursive types

Logical equivalence for subtyping object and recursive types

The third possibility is to forget about terms; then we interpret the judgement A :σ as: “the predicate σ makes sense of terms of type A”, namely σ ∈ L A for closed A. This logic of types, again inspired to domain logic, is our tool to treat object and recursive types. The formal system formalises the concept that both object and recursive types are some kind of fixed point, which is constructed starting with the trivial predicate ω, and iterating the proper rules determined by the structure of type expressions. We observe that this definition of the languages of object and recursive types is inductive, and that it makes sense without any consideration about the invariance of the object types nor (and more importantly) about the variance of the occurrences in A of the type variable X within the recursive type µX.A. The importance of the interplay between these assignment systems (actually integrated in a unique system) emerges when treating program equivalence. The system induces an
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Logical time @ work: the RT-Simex project

Logical time @ work: the RT-Simex project

The MARTE specification gives, in its Time sub- profile, a way to deal with logical and multiform time. Logical time relies on a relaxed form of time that supports causal (untimed) and chronological (timed) relationships between some events. In logical time, the ordering of events (causal relationships) is essential, albeit often partial. Multiform time supports metrics involving several time bases, not just the physical time (e.g., a car must stop before 100 ms or 2 m, which ever occur first). If needed, a metric to measure the distance in time between two instants may be added. The Time sub-profiles deals with logical time via Clocks . A clock is an ordered set of instants. MARTE also introduces clock constraints that specify relations between instants. A (logical) clock represents an event, its instants stand for the occurrences of the event, and an instant relation models a dependency between event occurrences. The Clock Constraint Specification Language (CCSL) is a model-based declarative language that allows handling of logical time and the associated constraints. As such, a CCSL specification characterizes the set of possible interactions and is suitable to describe the functional and real-time behavior of a system. CCSL has a formal semantics [1] that can be exploited to process a correct execution, if any, or to determine whether a candidate execution is valid (i.e., satisfies all the clock constraints) or not.
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Algebraic types and pattern matching in the logical language of the Why verification platform

Algebraic types and pattern matching in the logical language of the Why verification platform

Algebraic types and pattern matching in Why 3 1 Motivation This work was inspired by the recent experiments [1] with verification of floating- point computations in Why [2]. According to the IEEE Standard 754, which specifies the representation and operation for the floating-point numbers, at any point a programmer can choose: one of five different encodings (binary numbers of single, double, and quadruple precision and decimal numbers of double and quadruple precision); one of five rounding algorithms; a computation mode with or without overflows. Correspondingly, the logical annotations in a floating- point program must take into account the encoding of a particular variable or constant, as well as the current rounding algorithm and computation mode. This can be done, of course, with a number of appropriately chosen predicates and series of «if-then-else» expressions. However, a more elegant solution would be to use three enumerated types, namely:
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Exploring medical data using visual spaces with genetic programming and implicit functional mappings

Exploring medical data using visual spaces with genetic programming and implicit functional mappings

Colon Cancer GP-GEP (8 functions) 0.002874 FRPR 0.024015 It is impossible to represent a VR space on hard media. Snapshots of the visual spaces computed over the Breast Cancer data set using GP-GEP (Fig. 4(b), Fig. 5(a)) and FRPR (Fig. 5(b)) show the similarity structure and the orig- inal classes (benign and malignant tumors). In addition, the classes are wrapped with transparent membranes as an aid and Fig. 4(a) may be compared to Fig. 4(b) to appreciate the enhancement. Both algorithms, GP-GEP and FRPR, succeeded in showing the benign class (light objects) more densely packed and homogeneous than the malignant class. In addition, it can be observed that both classes have an important intersection making it difficult to expect perfect classification of this data with machine learning techniques. The same class structure is exhibited by the FRPR space (Fig. 5(b)) despite its lower mapping error.
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Asymptotic observers and integer programming for functional classification of a microbial community in a chemostat

Asymptotic observers and integer programming for functional classification of a microbial community in a chemostat

grated omics for the identification of key functionalities in biological wastewater treatment microbial communities,” Microbial Biotechnol- ogy, 2015. [3] S. Widder, R. J. Allen, T. Pfeiffer, T. P. Curtis, C. Wiuf, W. T. Sloan, O. X. Cordero, S. P. Brown, B. Momeni, W. Shou, H. Kettle, H. J. Flint, A. F. Haas, B. Laroche, J. U. Kreft, P. B. Rainey, S. Freilich, S. Schuster, K. Milferstedt, J. R. Van Der Meer, T. Grobkopf, J. Huisman, A. Free, C. Picioreanu, C. Quince, I. Klapper, S. Labarthe, B. F. Smets, H. Wang, O. S. Soyer, S. D. Allison, J. Chong, M. C. Lagomarsino, O. A. Croze, J. Hamelin, J. Harmand, R. Hoyle, T. T. Hwa, Q. Jin, D. R. Johnson, V. de Lorenzo, M. Mobilia, B. Murphy, F. Peaudecerf, J. I. Prosser, R. A. Quinn, M. Ralser, A. G. Smith, J. P. Steyer, N. Swainston, C. E. Tarnita, E. Trably, P. B. Warren, and P. Wilmes, “Challenges in microbial ecology: Building predictive understanding of community function and dynamics,” 2016. [4] M. J. Wade, J. Harmand, B. Benyahia, T. Bouchez, S. Chaillou,
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On the Versatility of Open Logical Relations

On the Versatility of Open Logical Relations

Abstract. Logical relations are one among the most powerful tech- niques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differen- tiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no apparent good definition for a base case (i.e. for closed terms of ground types). To overcome this is- sue, we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in sev- eral contexts in which the property of interest is about expressions of first-order type. Our setting is a simply-typed λ-calculus enriched with real numbers and real-valued first-order functions from a given set, such as the one of continuous or differentiable functions. We first prove a containment theorem stating that for any collection of real-valued first- order functions including projection functions and closed under function composition, any well-typed term of first-order type denotes a function belonging to that collection. Then, we show by way of open logical re- lations the correctness of the core of a recently published algorithm for forward automatic differentiation. Finally, we define a refinement-based type system for local continuity in an extension of our calculus with con- ditionals, and prove the soundness of the type system using open logical relations.
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Navigating the Semantic Web with Logical Information Systems

Navigating the Semantic Web with Logical Information Systems

4 Discussion and Conclusion The contribution of this paper is not about a new query language, but about an interactive navigation process that guides users from query to query, along the LIS principles. The query language proposed here has been driven by LIS constraints (a query denotes a complex class), and the wish to have queries as concise and natural as possible. However, it is interesting to discuss further its expressivity compared to SPARQL [PAG06]. The missing graph patterns are the OPTIONAL, UNION, and FILTER patterns. In our case, the OPTIONAL pattern is useless because the SELECT clause has only one variable. Our prototype has already UNION patterns through an or operator but we do not have consistency and completeness results yet about their navigation. It also has negation, and some limited forms of FILTER patterns as predefined classes of literals. For instance, the class match "regexp" denotes the set of all strings that match a regular expression. Similarly, we have classes for intervals and inequalities over numbers and dates. The most important restriction in our queries is the one-variable SELECT clause. However, the index alleviates this restriction to some extent. Suppose the SPARQL query SELECT ?x ?y WHERE { ?x rdf:type gen:man . ?x gen:mother ?y }. By setting the query to a man, and by expanding mother : ?, the index gives for each mother, how many male children she has. A highlighting mechanism allows to select a man in the extension to discover who is his mother; and alternately, to select a mother in the index to discover which are her children. The index is an inverted view over the table of SPARQL results. Each subtree of the index (with count annotation) is a histogram of the values from a column of the table. The highlighting mechanism enables to retrieve the associations between the values of the different columns, i.e., the result tuples.
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Improvement of Functional Performance of Spatial Parallel Manipulators Using Mechanisms of Variable Structure

Improvement of Functional Performance of Spatial Parallel Manipulators Using Mechanisms of Variable Structure

At first the calculation of the pressure angles in the joints along the trajectory for all possible structures of the parallel mechanism with variable architecture must be accomplished, then the best structure must be chosen for which the maximum value of the pressure angle along the trajectory is always less than the limit value. If there is no structure satisfying this condition, the given trajectory must be decomposed in several parts and the generation of the motion must be carried out by different structures. It is obvious that in this case it would be desirable that the trajectory can be realized by minimal structural changes.
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Biosignals for driver's stress level assessment : functional variable selection and fractal characterization

Biosignals for driver's stress level assessment : functional variable selection and fractal characterization

Abstract Thanks to the rise of new wearable and non-intrusive sensor tech- nology, Internet of Things (IoT) contributes in human daily life improve- ment. In the context of smart vehicles, human affective monitoring should be based on a context-aware system in order to consider the interactions be- tween the driver, his vehicle and his ambient environment. In this chapter, we propose AffectiveROAD platform, that sense the human physiological changes, the ambient environment inside the vehicle, and the vehicle speed. The proposed sensor-based solutions are not only providing real-time phys- iological monitoring, but also enriching the tools for human affective and cognitive states tracking. Thanks to this platform, several driver’s state in- dicators such as stress and arousal may be developed and validated. Two types of wireless physiological sensors are used to monitor the electrodermal activity, the heart rate, the skin temperature, the respiration, and the motion of the driver. Moreover, we developed a sensor network allowing to capture the ambient temperature, humidity, pressure, and luminosity. The vehicle speed is extracted from the Global Position System (GPS) data captured using a smartphone. Two GoPro devices are used to capture the internal and external scenes. The purpose of this chapter is to describe a real-world driving protocol to collect data using the proposed IoT-based materials and to announce the publication of a database for driver’s state monitoring re- search. We propose 13 datasets related to drives in different road types: city and highway. A part of the database concerning the physiological and the environmental data is released for public use.
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Computation by interaction for space-bounded functional programming

Computation by interaction for space-bounded functional programming

of exponentials, which are responsible for size increases in message passing. In order to obtain space bounds, the exponentials must therefore be restricted. The difficulty is to do so without the programming language becoming too weak. In this paper we argue that intml with its subexponentials represents a good solution to this problem. Subexponentials make intml an expressive higher-order language. For example, we show that it can type the Kierstead terms, which cannot be typed in similar linear type systems, such as [14]. Moreover, the proof of flogspace- completeness in this paper is completely straightforward. In earlier work, such as [36, 42], the completeness proofs were more involved. The expressiveness of intml is further illustrated by the programming examples, such as in Section 4. Subexponentials not only give us control over space usage, they also afford an efficient treatment of controlled duplication. For example, Ghica and Smith [15] treat copying in the language by actual duplication of terms. Here we show how to allow copying by sharing without the need to duplicate parts of the program. Finally, the language intml presented in this paper is the first higher-order language with logarithmic space bounds that allows one to use (and define!) higher-order combinators such as for tail recursion and call with current continuation.
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Reasoning on the response of logical signaling networks with Answer Set Programming

Reasoning on the response of logical signaling networks with Answer Set Programming

In the context of logic-based models, the inference of Boolean (genetic) networks from time-series gene expression data has been addressed by several authors under dif- ferent hypotheses and methods [LIA 98, AKU 00, IDE 00, LÄH 03]. Recently, a brief review and evaluation of these methods has been published in [BER 13]. Importantly, methods for reverse engineering of biological systems are highly dependent on avail- able (amount of) data, prior knowledge and modeling hypotheses. In particular, re- verse engineering of Boolean logic models by confronting prior knowledge on causal interactions with phosphorylation activities has been first described in [SAE 09]. A genetic algorithm implementation was proposed to solve the underlying optimization problem, and a software was provided, CellNOpt [TER 12]. Nonetheless, stochastic search methods cannot characterize the models precisely: they are intrinsically unable not just to provide a complete set of solutions, but also to guarantee that an optimal so- lution is found. To overcome some of this shortcomings, mathematical programming approaches were presented in [MIT 09, SHA 12]. Notably, authors in [SAE 09] have shown that the model is very likely to be non-identifiable when we consider the experi- mental error from measurements. Hence, rather than looking for the optimum Boolean model, one is interested in finding (nearly) optimal models within certain tolerance. Interestingly, in the context of quantitative modeling, authors in [CHE 09] have elabo- rated upon the same argument. Clearly, an exhaustive enumeration of (nearly) optimal solutions would allow for identifying admissible Boolean logic models without any methodological bias. Importantly, previous methods, namely stochastic search and mathematical programming, are not able to cope with this question. Moreover, all sub- sequent analysis will certainly profit from having such a complete characterization of feasible models. For example, finding “key-players” in
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Reasoning on the response of logical signaling networks with answer set programming

Reasoning on the response of logical signaling networks with answer set programming

Chapter 1. Introduction obtain the most plausible models for certain environmental conditions or specific cell type. This is normally achieved by defining an objective fitness function to be optimized [Banga, 2008]. Optimization over quantitative modeling leads to continuous optimization problems. On the other hand, reverse engineering considering qualitative models typically give rise to combinatorial (discrete) optimization problems. Notably, this subject represents a very active area of research as illustrated by the successive “DREAM” challenges [Stolovitzky et al., 2007]. Importantly, methods for reverse engineering of biological systems are highly depen- dent on available (amount of) data, prior knowledge and modeling hypotheses. For instance, an inference method from gene expression data collected by DNA microarrays, may not be applicable to biochemical data like phosphorylation assays collected using xMAP Luminex technology. In particular, reverse engineering of logical models for signaling networks by confronting prior knowledge on causal interactions with phosphorylation activities has been first addressed in [Saez-Rodriguez et al., 2009]. Therein, authors have shown that the model is non-identifiable as soon as we consider the experimental error from measurements. Hence, rather than looking for the optimum logical model, one aims at finding (nearly) optimal mod- els within certain tolerance. Interestingly, in the context of mathematical modeling, authors in [Chen et al., 2009] have elaborated upon the same argument. Clearly, an exhaustive enu- meration of (nearly) optimal solutions would allow for identifying admissible logical models without any methodological bias. Furthermore, all subsequent analysis will certainly profit from having such a complete characterization of feasible models. That is, being able to ad- dress a given problem but considering an ensemble of logical models may lead to more robust solutions. In fact, this is in line with recent work showing that an ensemble of models often yields more robust predictions than each model in isolation [Kuepfer et al., 2007, Marbach et al., 2012]. Importantly, existing approaches, namely stochastic search and mathematical programming, are not well-suited to cope with this question in an exhaustive manner. Hence, there is an increasing demand of more powerful computational methods in order to achieve robust discoveries in the context of logic-based modeling.
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The Robot Programming Network

The Robot Programming Network

In this paper, we present a system that allows users of a Virtual Learning Environment to seamlessly work with web-based laboratories consisting of real robots or 2D/3D simulators. User programs consist of fully-functional source code written on any of the supported programming languages (Python, Lisp, Matlab). The code is executed in the remote laboratory, thus it can access all the available information and services, without any additional remote communication overhead during execution. Upon finishing, the output of the process is returned back to the user’s browser, and the generated data is readily available to download for further analysis.
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Aggregate production scheduling by linear programming with variable planning interval

Aggregate production scheduling by linear programming with variable planning interval

Issues Raised by the Use of LP at Peerless Procurement, Provisioning, and Production at Peerless What the Provisioner Needs General Philosophy The Ideal System: The Ideal System: Data Ge[r]

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