A cost-aware logical framework

We present calf , a c ost- a ware l ogical f ramework for studying quantitative aspects of functional programs. Taking inspiration from recent work that reconstructs traditional aspects of programming languages in terms of a modal account of phase distinctions , we argue that the cost structure of programs motivates a phase distinction between intension and extension . Armed with this technology, we contribute a synthetic account of cost structure as a computational effect in which cost-aware programs enjoy an internal noninterference property: input/output behavior cannot depend on cost. As a full-spectrum dependent type theory, calf presents a unified language for programming and specification of both cost and behavior that can be integrated smoothly with existing mathematical libraries available in type theoretic proof assistants. We evaluate calf as a general framework for cost analysis by implementing two fundamental techniques for algorithm analysis: the method of recurrence relations and physicist’s method for amortized analysis . We deploy these techniques on a variety of case studies: we prove a tight, closed bound for Euclid’s algorithm, verify the amortized complexity of batched queues, and derive tight, closed bounds for the sequential and parallel complexity of merge sort, all fully mechanized in the Agda proof assistant. Lastly we substantiate the soundness of quantitative reasoning in calf by means of a model construction.

Algebras for weighted search

Weighted search is an essential component of many fundamental and useful algorithms. Despite this, it is relatively under explored as a computational effect, receiving not nearly as much attention as either depth- or breadth-first search. This paper explores the algebraic underpinning of weighted search, and demonstrates how to implement it as a monad transformer. The development first explores breadth-first search, which can be expressed as a polynomial over semirings. These polynomials are generalised to the free semimodule monad to capture a wide range of applications, including probability monads, polynomial monads, and monads for weighted search. Finally, a monad transformer based on the free semimodule monad is introduced. Applying optimisations to this type yields an implementation of pairing heaps, which is then used to implement Dijkstra's algorithm and efficient probabilistic sampling. The construction is formalised in Cubical Agda and implemented in Haskell.

Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions

In this article, an analytical reliable treatment based on the concept of residual error functions is employed to address the series solution of the differential logistic system in the fractional sense. The proposed technique is a combination of the generalized Taylor series and minimizing the residual error function. The solution methodology depends on the generation of a fractional expansion in an effective convergence formula, as well as on the optimization of truncated errors, Resqjt, through the use of repeated Caputo derivatives without any restrictive assumptions of system nature. To achieve this, some logistic patterns are tested to demonstrate the reliability and applicability of the suggested approach. Numerical comparison depicts that the proposed technique has high accuracy and less computational effect and is more efficient.

A Fuzzy Set Based Approach for Rating Bias

In recommender systems, the user uncertain preference results in unexpected ratings. This paper makes an initial attempt in integrating the influence of user uncertain degree into the matrix factorization framework. Specifically, a fuzzy set of like for each user is defined, and the membership function is utilized to measure the degree of an item belonging to the fuzzy set. Furthermore, to enhance the computational effect on sparse matrix, the uncertain preference is formulated as a side-information for fusion. Experimental results on three real-world datasets show that the proposed approach produces stable improvements compared with others.

A specific role for serotonin in overcoming effort cost

Serotonin is implicated in many aspects of behavioral regulation. Theoretical attempts to unify the multiple roles assigned to serotonin proposed that it regulates the impact of costs, such as delay or punishment, on action selection. Here, we show that serotonin also regulates other types of action costs such as effort. We compared behavioral performance in 58 healthy humans treated during 8 weeks with either placebo or the selective serotonin reuptake inhibitor escitalopram. The task involved trading handgrip force production against monetary benefits. Participants in the escitalopram group produced more effort and thereby achieved a higher payoff. Crucially, our computational analysis showed that this effect was underpinned by a specific reduction of effort cost, and not by any change in the weight of monetary incentives. This specific computational effect sheds new light on the physiological role of serotonin in behavioral regulation and on the clinical effect of drugs for depression.Clinical trial Registration: ISRCTN75872983

A COMPUTATIONAL EFFICIENCY PRINCIPLE IN ACTION IN THE PROCESSING OF RECURSIVELY EMBEDDED PPS IN BRAZILIAN PORTUGUESE AND IN KARAJÁ

This paper presents and discusses two eye-tracking experiments comparing the processing of coordination and embedding of Prepositional Phrases in Brazilian Portuguese (BP) and of Postpositional Phrases in Karajá. Experiment 1 compares the processing of sentences containing Prepositional Phrases which may be self-embedded or conjoined in Brazilian Portuguese. Experiment 2 compares the processing of sentences containing Postpositional Phrases which may be self-embedded or conjoined in Karajá. 20 Brazilian Portuguese (BP) and 20 Karajá subjects had their eye movements monitored as they performed a sentence/picture matching task including sentences in BP and in Karajá, respectively. Based on previous studies reported in Maia et al (to appear), two hypotheses were formulated, both for BP and Karajá, namely, (i) launching the self- embedding of PPs would be more costly to process than launching the conjoining of PPs; (ii) after launching, the subsequent self-embedding of a third PP would be less costly than the previous PP. Results confirmed these predictions and are analyzed in terms of a third factor computational effect learning algorithm.---Original in English.

AN INFEASIBLE SSLE FILTER ALGORITHM FOR GENERAL CONSTRAINED OPTIMIZATION WITHOUT STRICT COMPLEMENTARITY

In this paper, we propose a new sequential systems of linear equations (SSLE) filter algorithm, which is an infeasible QP-free method. The new algorithm needs to solve a few reduced systems of linear equations with the same nonsingular coefficient matrix, and after finitely many iterations, only two linear systems need to be solved. Furthermore, the nearly active set technique is used to improve the computational effect. Under the linear independence condition, the global convergence is proved. In particular, the rate of convergence is proved to be one-step superlinear without assuming the strict complementarity condition. Numerical results and comparison with other algorithms indicate that the new algorithm is promising.

On stabilization of the node-based smoothed finite element method for free vibration problems

The node-based smoothed finite element method (NS-FEM) has been recently proposed by Liu et al to enhance the computational effect for solid mechanics problems. However, it is evident that the NS-FEM behaves "overly-soft" and so it may lead to instability for dynamic problems. The instability can be clearly shown as spurious non-zero energy modes in free vibration analysis. In this paper, we present a stabilization of the node-based smoothed finite element method (SN-FEM) that is stable (no spurious non-zero energy modes) and more effective than the standard finite element method (FEM). Three numerical illustrations are given to evince the high reliability of the proposed formulation.