Provably correct, asymptotically efficient, higher-order reverse-mode automatic differentiation

In this paper, we give a simple and efficient implementation of reverse-mode automatic differentiation, which both extends easily to higher-order functions, and has run time and memory consumption linear in the run time of the original program. In addition to a formal description of the translation, we also describe an implementation of this algorithm, and prove its correctness by means of a logical relations argument.

An improved Trapezoidal rule for numerical integration

Numerical Methods have attracted of research community for solving engineering problems. This interest is due to its practicality and the improvement of highspeed calculations done on current century processors. The increase in numerical method tools in engineering software, such as Matlab, is an example of the increased interest. In this paper, we are present a new improved numerical integration method, that is based on the well-known trapezoidal rule. The proposed method gives a great enhancement to the trapezoidal rule and overcomes the issue of the error value when dealing with some higher order functions even when solving for a single interval. After literature review, the proposed system is mathematically explained along with error analysis. Few examples are illustrated to prove improved accuracy of the proposed method over traditional trapezoidal method.

Reachability types: tracking aliasing and separation in higher-order functional programs

Ownership type systems, based on the idea of enforcing unique access paths, have been primarily focused on objects and top-level classes. However, existing models do not as readily reflect the finer aspects of nested lexical scopes, capturing, or escaping closures in higher-order functional programming patterns, which are increasingly adopted even in mainstream object-oriented languages. We present a new type system, λ * , which enables expressive ownership-style reasoning across higher-order functions. It tracks sharing and separation through reachability sets, and layers additional mechanisms for selectively enforcing uniqueness on top of it. Based on reachability sets, we extend the type system with an expressive flow-sensitive effect system, which enables flavors of move semantics and ownership transfer. In addition, we present several case studies and extensions, including applications to capabilities for algebraic effects, one-shot continuations, and safe parallelization.

Automatic migration from synchronous to asynchronous JavaScript APIs

The JavaScript ecosystem provides equivalent synchronous and asynchronous Application Programming Interfaces (APIs) for many commonly used I/O operations. Synchronous APIs involve straightforward sequential control flow that makes them easy to use and understand, but their "blocking" behavior may result in poor responsiveness or performance. Asynchronous APIs impose a higher syntactic burden that relies on callbacks, promises, and higher-order functions. On the other hand, their nonblocking behavior enables applications to scale better and remain responsive while I/O requests are being processed. While it is generally understood that asynchronous APIs have better performance characteristics, many applications still rely on synchronous APIs. In this paper, we present a refactoring technique for assisting programmers with the migration from synchronous to asynchronous APIs. The technique relies on static analysis to determine where calls to synchronous API functions can be replaced with their asynchronous counterparts, relying on JavaScript's async/await feature to minimize disruption to the source code. Since the static analysis is potentially unsound, the proposed refactorings are presented as suggestions that must be reviewed and confirmed by the programmer. The technique was implemented in a tool named Desynchronizer. In an empirical evaluation on 12 subject applications containing 316 synchronous API calls, Desynchronizer identified 256 of these as candidates for refactoring. Of these candidates, 244 were transformed successfully, and only 12 resulted in behavioral changes. Further inspection of these cases revealed that the majority of these issues can be attributed to unsoundness in the call graph.

Functions-as-constructors higher-order unification: extended pattern unification

Unification is a central operation in constructing a range of computational logic systems based on first-order and higher-order logics. First-order unification has several properties that guide its incorporation in such systems. In particular, first-order unification is decidable, unary, and can be performed on untyped term structures. None of these three properties hold for full higher-order unification: unification is undecidable, unifiers can be incomparable, and term-level typing can dominate the search for unifiers. The so-called pattern subset of higher-order unification was designed to be a small extension to first-order unification that respects the laws governing λ-binding (i.e., the equalities for α, β, and η-conversion) but which also satisfied those three properties. While the pattern fragment of higher-order unification has been used in numerous implemented systems and in various theoretical settings, it is too weak for many applications. This paper defines an extension of pattern unification that should make it more generally applicable, especially in proof assistants that allow for higher-order functions. This extension’s main idea is that the arguments to a higher-order, free variable can be more than just distinct bound variables. In particular, such arguments can be terms constructed from (sufficient numbers of) such bound variables using term constructors and where no argument is a subterm of any other argument. We show that this extension to pattern unification satisfies the three properties mentioned above.

A Transcriptome Community-and-Module Approach of the Human Mesoconnectome

Graph analysis allows exploring transcriptome compartments such as communities and modules for brain mesostructures. In this work, we proposed a bottom-up model of a gene regulatory network to brain-wise connectome workflow. We estimated the gene communities across all brain regions from the Allen Brain Atlas transcriptome database. We selected the communities method to yield the highest number of functional mesostructures in the network hierarchy organization, which allowed us to identify specific brain cell functions (e.g., neuroplasticity, axonogenesis and dendritogenesis communities). With these communities, we built brain-wise region modules that represent the connectome. Our findings match with previously described anatomical and functional brain circuits, such the default mode network and the default visual network, supporting the notion that the brain dynamics that carry out low- and higher-order functions originate from the modular composition of a GRN complex network

Footvector Representation of Curves and Surfaces

This paper proposes a foot mapping-based representation of curves and surfaces which is a geometric generalization of signed distance functions. We present a first-order characterization of the footvector mapping in terms of the differential geometric invariants of the represented shape and quantify the dependence of the spatial partial derivatives of the footvector mapping with respect to the principal curvatures at the footpoint. The practical applicability of foot mapping representations is highlighted by several fast iterative methods to compute the exact footvector mapping of the offset surface of CSG trees. The set operations for footpoint mappings are higher-order functions that map a tuple of functions to a single function, which poses a challenge for GPU implementations. We propose a code generation framework to overcome this that transforms CSG trees to the GLSL shader code.

Effects of general anesthetics on synaptic transmission and plasticity

: General anesthetics depress excitatory and/or enhance inhibitory synaptic transmission principally by modulating the function of glutamatergic or GABAergic synapses, respectively, with relative anesthetic agent-specific mechanisms. Synaptic signaling proteins, including ligand- and voltage-gated ion channels, are targeted by general anesthetics to modulate various synaptic mechanisms including presynaptic neurotransmitter release, postsynaptic receptor signaling, and dendritic spine dynamics to produce their characteristic acute neurophysiological effects. As synaptic structure and plasticity mediate higher-order functions such as learning and memory, long-term synaptic dysfunction following anesthesia may lead to undesirable neurocognitive consequences depending on specific anesthetic agent and the vulnerability of population. Here we review the cellular and molecular mechanisms of transient and persistent general anesthetic alterations of synaptic transmission and plasticity.

Isogeometric Analysis for Tire Simulations: From Mesh Generation to High Precision Results

ABSTRACT Isogeometric analysis (IGA) has become an alternative to standard finite element analysis (FEA) in many areas of engineering. Its powerful tools for model generation and flexibility of basis functions make this relatively new approach attractive for tire analysis and its computational challenges. This contribution summarizes the benefits of IGA for complex tire simulations starting from model generation and the subsequent transition to the environment of numerical analysis without losing accuracy at the parametrizing stage. It presents results of further development work on earlier pioneering examples of the application of IGA in pneumatic tire analysis. In addition to the analysis of vertical stiffness, for the first time, velocity and acceleration fields are addressed and compared with experimental results and standard FEA simulations, with a focus on benefits of the continuity of basis functions within the contact patch. The numerical issues that arise in IGA at the enforcement of contact and the application of inelastic materials with inclusions of reinforcing layers are studied. Moreover, the important advantages of the possibility to use higher order functions for simulations of tire maneuvers are addressed within the steady-state framework. Numerical examples are provided to illustrate the capabilities of IGA. Concluding remarks on the results close the publication.