Strategic polymorphism requires just two combinators!

In previous work, we introduced the notion of functional strategies: first-class generic functions that can traverse terms of any type while mixing uniform and type-specific behaviour. Functional strategies transpose the notion of term rewriting strategies (with coverage of traversal) to the functional programming paradigm. Meanwhile, a number of Haskell-based models and combinator suites were proposed to support generic programming with functional strategies. In the present paper, we provide a compact and matured reconstruction of functional strategies. We capture strategic polymorphism by just two primitive combinators. This is done without commitment to a specific functional language. We analyse the design space for implementational models of functional strategies. For completeness, we also provide an operational reference model for implementing functional strategies (in Haskell). We demonstrate the generality of our approach by reconstructing representative fragments of the Strafunski library for functional strategies.Comment: A preliminary version of this paper was presented at IFL 2002, and included in the informal preproceedings of the worksho

The path of a scholar

“The path of a scholar” is the introduction to Production, Distribution and Trade: Alternative Perspectives, a volume of essays in honour of Sergio Parrinello (edited by Adriano Birolo, Duncan Foley, Heinz Kurz, Bertram Schefold and Ian Steedman, published by Routledge, 2010). The author traces out the scientific career of Sergio Parrinello in context of the italian market for economists of the sixties and seventies of the twentieth century and critically discusses his most significant works, specially those have resulted as seminal contributions for the later development of the neo-Ricardian theory. This discussion inevitably evolves in a tentative appraisal of the meaning of the neo-Ricardian theory in the recent history of political economy.neo-Ricardian; capital controversy; history of political economy

Algorithms for Galois group computations over multivariate function fields

In this thesis, two separate algorithms are described to determine the Galois group of a polynomial f defined over a function field of the form Q(w1,...,wa), both of which use Stauduhar’s method for polynomials over Q, with various techniques used to make them compatible for function fields as the base field. In particular, both algorithms construct the resolvent of f. The first algorithm uses a special form of Hensel lifting to express the roots as a multivariate power series of sufficient precision to determine the resolvent exactly. This precision is derived through the use of Newton polygons and by obtaining a bound on the size of the coefficients of the resolvent. The second algorithm constructs the resolvents of a set of specialisations of f, which are then interpolated. Computational complexity and timing of implementations in MAGMA for polynomials of degree up to 8 are compared and discussed

Characterization of the Community Structure of Large Scale Functional Brain Networks During Ketamine-Medetomidine Anesthetic Induction

One of the central questions in neuroscience is to understand the way communication is organized in the brain, trying to comprehend how cognitive capacities or physiological states of the organism are potentially related to brain activities involving interactions of several brain areas. One important characteristic of the functional brain networks is that they are modularly structured, being this modular architecture regarded to account for a series of properties and functional dynamics. In the neurobiological context, communities may indicate brain regions that are involved in one same activity, representing neural segregated processes. Several studies have demonstrated the modular character of organization of brain activities. However, empirical evidences regarding to its dynamics and relation to different levels of consciousness have not been reported yet. Within this context, this research sought to characterize the community structure of functional brain networks during an anesthetic induction process. The experiment was based on intra-cranial recordings of neural activities of an old world macaque of the species Macaca fuscata during a Ketamine-Medetomidine anesthetic induction process. Networks were serially estimated in time intervals of five seconds. Changes were observed within about one and a half minutes after the administration of the anesthetics, revealing the occurrence of a transition on the community structure. The awake state was characterized by the presence of large clusters involving frontal and parietal regions, while the anesthetized state by the presence of communities in the primary visual and motor cortices, being the areas of the secondary associative cortex most affected. The results report the influence of general anesthesia on the structure of functional clusters, contributing for understanding some new aspects of neural correlates of consciousness.Comment: 24 pages, 8 figures. arXiv admin note: text overlap with arXiv:1604.0000

On the reality of spectra of Uq(sl2)\boldsymbol{U_q(sl_2)}-invariant XXZ Hamiltonians

A new inner product is constructed on each standard module over the Temperley-Lieb algebra $\mathsf{TL}_n(\beta)$ for $\beta\in \mathbb R$ and $n \ge 2$. On these modules, the Hamiltonian $h = -\sum_i e_i$ is shown to be self-adjoint with respect to this inner product. This implies that its action on these modules is diagonalisable with real eigenvalues. A representation theoretic argument shows that the reality of spectra of the Hamiltonian extends to all other Temperley-Lieb representations. In particular, this result applies to the celebrated $U_q(sl_2)$-invariant XXZ Hamiltonian, for all $q+q^{-1}\in \mathbb R$.Comment: 30 page

Dynamics of continued fractions and distribution of modular symbols

We formulate a thermodynamical approach to the study of distribution of modular symbols, motivated by the work of Baladi-Vall\'ee. We introduce the modular partitions of continued fractions and observe that the statistics for modular symbols follow from the behavior of modular partitions. We prove the limit Gaussian distribution and residual equidistribution for modular partitions as a vector-valued random variable on the set of rationals whose denominators are up to a fixed positive integer by studying the spectral properties of transfer operator associated to the underlying dynamics. The approach leads to a few applications. We show an average version of conjectures of Mazur-Rubin on statistics for the period integrals of an elliptic newform. We further observe that the equidistribution of mod $p$ values of modular symbols leads to mod $p$ non-vanishing results for special modular $L$-values twisted by a Dirichlet character.Comment: 42 page

Incentives and Human Resource Management in the Design of Public Sector Reform

We, in Pakistan, should be very happy that the global development community has finally accepted the centrality of public sector reform (also known as improved governance) in the quest for improved living standards in poor countries. Development economics is a subject that is based on the interpretation and observation of some Western academics and Western donor-based agencies. We should have some sympathy for these leaders of development thought and policy for they have struggled with integrating the prevailing theme (fad) in Western thought and philanthropy with learning about the societies and economies that they were supposed to be prescribing for. Using the principle of “ends justifying the means”, they defend their reliance on the current “fad” as well as on the only clearly visible, organised and powerful actor—the government, no matter how inefficient—they would. The result is that this approach led to a long era of government-led development, which centralised policy- and decision-making, initiated planning, and created a wide range of public-sector institutions. The role of the government was thus extended into areas that were conceptually indefensible. In this manner, the public servant grew into her new much more lustrous and looser robes. A bloated, over-centralised, and a private sector inhibiting government was created to be the observation and implementation outpost of the development word. This was the first step in the transformation of the public sector in the direction of misgovernance.