Simplifying transformations for type-alpha certificates

This paper presents an algorithm for simplifying NDL deductions. An array of simplifying transformations are rigorously defined. They are shown to be terminating, and to respect the formal semantis of the language. We also show that the transformations never increase the size or complexity of a deduction---in the worst case, they produce deductions of the same size and complexity as the original. We present several examples of proofs containing various types of "detours", and explain how our procedure eliminates them, resulting in smaller and cleaner deductions. All of the given transformations are fully implemented in SML-NJ. The complete code listing is presented, along with explanatory comments. Finally, although the transformations given here are defined for NDL, we point out that they can be applied to any type-alpha DPL that satisfies a few simple conditions.

Programming Examples Needing Polymorphic Recursion

Inferring types for polymorphic recursive function definitions (abbreviated to polymorphic recursion) is a recurring topic on the mailing lists of popular typed programming languages. This is despite the fact that type inference for polymorphic recursion using for all-types has been proved undecidable. This report presents several programming examples involving polymorphic recursion and determines their typability under various type systems, including the Hindley-Milner system, an intersection-type system, and extensions of these two. The goal of this report is to show that many of these examples are typable using a system of intersection types as an alternative form of polymorphism. By accomplishing this, we hope to lay the foundation for future research into a decidable intersection-type inference algorithm. We do not provide a comprehensive survey of type systems appropriate for polymorphic recursion, with or without type annotations inserted in the source language. Rather, we focus on examples for which types may be inferred without type annotations.

Examples of Network Flow Verification Using TRAFFIC(X)

In our previous work, we developed TRAFFIC(X), a specification language for modeling bi-directional network flows featuring a type system with constrained polymorphism. In this paper, we present two ways to customize the constraint system: (1) when using linear inequality constraints for the constraint system, TRAFFIC(X) can describe flows with numeric properties such as MTU (maximum transmission unit), RTT (round trip time), traversal order, and bandwidth allocation over parallel paths; (2) when using Boolean predicate constraints for the constraint system, TRAFFIC(X) can describe routing policies of an IP network. These examples illustrate how to use the customized type system.

A Type System For Safe SN Resource Allocation

snBench is a platform on which novice users compose and deploy distributed Sense and Respond programs for simultaneous execution on a shared, distributed infrastructure. It is a natural imperative that we have the ability to (1) verify the safety/correctness of newly submitted tasks and (2) derive the resource requirements for these tasks such that correct allocation may occur. To achieve these goals we have established a multi-dimensional sized type system for our functional-style Domain Specific Language (DSL) called Sensor Task Execution Plan (STEP). In such a type system data types are annotated with a vector of size attributes (e.g., upper and lower size bounds). Tracking multiple size aspects proves essential in a system in which Images are manipulated as a first class data type, as image manipulation functions may have specific minimum and/or maximum resolution restrictions on the input they can correctly process. Through static analysis of STEP instances we not only verify basic type safety and establish upper computational resource bounds (i.e., time and space), but we also derive and solve data and resource sizing constraints (e.g., Image resolution, camera capabilities) from the implicit constraints embedded in program instances. In fact, the static methods presented here have benefit beyond their application to Image data, and may be extended to other data types that require tracking multiple dimensions (e.g., image "quality", video frame-rate or aspect ratio, audio sampling rate). In this paper we present the syntax and semantics of our functional language, our type system that builds costs and resource/data constraints, and (through both formalism and specific details of our implementation) provide concrete examples of how the constraints and sizing information are used in practice.

Type Inference For Recursive Definitions

We consider type systems that combine universal types, recursive types, and object types. We study type inference in these systems under a rank restriction, following Leivant's notion of rank. To motivate our work, we present several examples showing how our systems can be used to type programs encountered in practice. We show that type inference in the rank-k system is decidable for k ≤ 2 and undecidable for k ≥ 3. (Similar results based on different techniques are known to hold for System F, without recursive types and object types.) Our undecidability result is obtained by a reduction from a particular adaptation (which we call "regular") of the semi-unification problem and whose undecidability is, interestingly, obtained by methods totally different from those used in the case of standard (or finite) semi-unification.

Applied type system

We present a type system that can effectively facilitate the use of types in capturing invariants in stateful programs that may involve (sophisticated) pointer manipulation. With its root in a recently developed framework Applied Type System (ATS), the type system imposes a level of abstraction on program states by introducing a novel notion of recursive stateful views and then relies on a form of linear logic to reason about such views. We consider the design and then the formalization of the type system to constitute the primary contribution of the paper. In addition, we mention a prototype implementation of the type system and then give a variety of examples that attests to the practicality of programming with recursive stateful views.

Extracting S-matrix poles for resonances from numerical scattering data: Type-II Pade reconstruction

We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S-matrix element is performed by constructing a type-II Pade approximant from given physical values (Bessis et al. (1994) [421: Vrinceanu et al. (2000) [24]; Sokolovski and Msezane (2004) [23]). The algorithm involves iterative 'preconditioning' of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select 'true' physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package (Bailey (1993) [451) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + H-2 -> HE + H, F + HD : HE + D, Cl + HCI CIH + Cl and H + D-2 -> HD + D reactions. Some detailed examples are given in the text.

PS1-10afx at z = 1.388: Pan-STARRS1 Discovery of a New Type of Superluminous Supernova

We present the Pan-STARRS1 discovery of PS1-10afx, a unique hydrogen-deficient superluminous supernova (SLSN) at redshift z = 1.388. The light curve peaked at z P1 = 21.7 mag, making PS1-10afx comparable to the most luminous known SNe, with Mu = -22.3 mag. Our extensive optical and near-infrared observations indicate that the bolometric light curve of PS1-10afx rose on the unusually fast timescale of ~12 days to the extraordinary peak luminosity of 4.1 × 1044 erg s-1 (M bol = -22.8 mag) and subsequently faded rapidly. Equally important, the spectral energy distribution is unusually red for an SLSN, with a color temperature of ~6800 K near maximum light, in contrast to previous hydrogen-poor SLSNe, which are bright in the ultraviolet (UV). The spectra more closely resemble those of a normal SN Ic than any known SLSN, with a photospheric velocity of ~11, 000 km s-1 and evidence for line blanketing in the rest-frame UV. Despite the fast rise, these parameters imply a very large emitting radius (gsim 5 × 1015 cm). We demonstrate that no existing theoretical model can satisfactorily explain this combination of properties: (1) a nickel-powered light curve cannot match the combination of high peak luminosity with the fast timescale; (2) models powered by the spindown energy of a rapidly rotating magnetar predict significantly hotter and faster ejecta; and (3) models invoking shock breakout through a dense circumstellar medium cannot explain the observed spectra or color evolution. The host galaxy is well detected in pre-explosion imaging with a luminosity near L*, a star formation rate of ~15 M ⊙ yr-1, and is fairly massive (~2 × 1010 M ⊙), with a stellar population age of ~108 yr, also in contrast to the young dwarf hosts of known hydrogen-poor SLSNe. PS1-10afx is distinct from known examples of SLSNe in its spectra, colors, light-curve shape, and host galaxy properties, suggesting that it resulted from a different channel than other hydrogen-poor SLSNe.

Using Effective Teaching Strategies and Personality Type to Enhance the Mathematics Classroom: A Handbook for Intermediate Math Teachers

This project addressed the need for more insightful, current, and applicable resources for intermediate math teachers in Canadian classrooms. A need for a handbook in this division seemed warranted by a lack of government resource support. Throughout an extensive review of the literature, themes and topics for the handbook emerged. The handbook was designed to not only provide educators with examples of effective teaching strategies within the mathematics classroom but to also inform them about the ways in which their personal characteristics and personality type could affect their students and their own pedagogical practices. Three teaching professionals who had each taught in an intermediate math class within the past year evaluated the handbook. The feedback received from these educators was directly applied to the first draft of the handbook in order to make it more accessible and applicable to other math teachers. Although the handbook was written with teachers in mind, the language and format used throughout the manual also make it accessible to parents, tutors, preservice education students, and educational administrators. Essentially, any individual who is hoping to inspire and educate intermediate math students could make use of the content within the handbook.

Fast Learning by Bounding Likelihoods in Sigmoid Type Belief Networks

Sigmoid type belief networks, a class of probabilistic neural networks, provide a natural framework for compactly representing probabilistic information in a variety of unsupervised and supervised learning problems. Often the parameters used in these networks need to be learned from examples. Unfortunately, estimating the parameters via exact probabilistic calculations (i.e, the EM-algorithm) is intractable even for networks with fairly small numbers of hidden units. We propose to avoid the infeasibility of the E step by bounding likelihoods instead of computing them exactly. We introduce extended and complementary representations for these networks and show that the estimation of the network parameters can be made fast (reduced to quadratic optimization) by performing the estimation in either of the alternative domains. The complementary networks can be used for continuous density estimation as well.

Small time Chung-type LIL for Lévy processes

We prove Chung-type laws of the iterated logarithm for general Lévy processes at zero. In particular, we provide tools to translate small deviation estimates directly into laws of the iterated logarithm. This reveals laws of the iterated logarithm for Lévy processes at small times in many concrete examples. In some cases, exotic norming functions are derived.

Sheet Metal Examples

A wall in the Sheet Metal Department at the New York Trade School shows many examples of duct work, pipe, and decorative metal work that students learn to produce. Black and white photograph that is starting to fade.

Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems

We associate to an arbitrary Z-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer-Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.

BORN-INFELD ELECTRODYNAMICS and EULER-HEISENBERG-LIKE MODEL: OUTSTANDING EXAMPLES of THE LACK of COMMUTATIVITY AMONG QUANTIZED TRUNCATED ACTIONS and TRUNCATED QUANTIZED ACTIONS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A MODEL OF THE DEUTERON BASED ON A BREIT TYPE EQUATION

A relativistic treatment of the deuteron and its observables based on a two-body Dirac (Breit) equation, with phenomenological interactions, associated to one-boson exchanges with cutoff masses, is presented. The 16-component wave function for the deuteron (J(pi) = 1+) solution contains four independent radial functions which obey a system of four coupled differential equations of first order. This radial system is numerically integrated, from infinity to the origin, by fixing the value of the deuteron binding energy and using appropriate boundary conditions at infinity. Specific examples of mixtures containing scalar, pseudoscalar and vector like terms are discussed in some detail and several observables of the deuteron are calculated. Our treatment differs from more conventional ones in that nonrelativistic reductions of the order c-2 are not used.