Refinement Types for Logical Frameworks and Their Interpretation as Proof Irrelevance

Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical forms are well-typed. Both the usual LF rules and the rules for type refinements are bidirectional, leading to a straightforward proof of decidability of typechecking even in the presence of intersection types. Because we insist on canonical forms, structural rules for subtyping can now be derived rather than being assumed as primitive. We illustrate the expressive power of our system with examples and validate its design by demonstrating a precise correspondence with traditional presentations of subtyping. Proof irrelevance provides a mechanism for selectively hiding the identities of terms in type theories. We show that LF refinement types can be interpreted as predicates using proof irrelevance, establishing a uniform relationship between two previously studied concepts in type theory. The interpretation and its correctness proof are surprisingly complex, lending support to the claim that refinement types are a fundamental construct rather than just a convenient surface syntax for certain uses of proof irrelevance

Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity

In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity

A Type Checker for a Logical Framework with Union and Intersection Types

We present the syntax, semantics, and typing rules of Bull, a prototype theorem prover based on the Delta-Framework, i.e. a fully-typed lambda-calculus decorated with union and intersection types, as described in previous papers by the authors. Bull also implements a subtyping algorithm for the Type Theory Xi of Barbanera-Dezani-de'Liguoro. Bull has a command-line interface where the user can declare axioms, terms, and perform computations and some basic terminal-style features like error pretty-printing, subexpressions highlighting, and file loading. Moreover, it can typecheck a proof or normalize it. These terms can be incomplete, therefore the typechecking algorithm uses unification to try to construct the missing subterms. Bull uses the syntax of Berardi's Pure Type Systems to improve the compactness and the modularity of the kernel. Abstract and concrete syntax are mostly aligned and similar to the concrete syntax of Coq. Bull uses a higher-order unification algorithm for terms, while typechecking and partial type inference are done by a bidirectional refinement algorithm, similar to the one found in Matita and Beluga. The refinement can be split into two parts: the essence refinement and the typing refinement. Binders are implemented using commonly-used de Bruijn indices. We have defined a concrete language syntax that will allow the user to write Delta-terms. We have defined the reduction rules and an evaluator. We have implemented from scratch a refiner which does partial typechecking and type reconstruction. We have experimented Bull with classical examples of the intersection and union literature, such as the ones formalized by Pfenning with his Refinement Types in LF. We hope that this research vein could be useful to experiment, in a proof theoretical setting, forms of polymorphism alternatives to Girard's parametric one

Activity of nAChRs containing α9 subunits modulates synapse stabilization via bidirectional signaling programs

Although the synaptogenic program for cholinergic synapses of the neuromuscular junction is well known, little is known of the identity or dynamic expression patterns of proteins involved in non-neuromuscular nicotinic synapse development. We have previously demonstrated abnormal presynaptic terminal morphology following loss of nicotinic acetylcholine receptor (nAChR) α9 subunit expression in adult cochleae. However, the molecular mechanisms underlying these changes have remained obscure. To better understand synapse formation and the role of cholinergic activity in the synaptogenesis of the inner ear, we exploit the nAChR α9 subunit null mouse. In this mouse, functional acetylcholine (ACh) neurotransmission to the hair cells is completely silenced. Results demonstrate a premature, effusive innervation to the synaptic pole of the outer hair cells in α9 null mice coinciding with delayed expression of cell adhesion proteins during the period of effusive contact. Collapse of the ectopic innervation coincides with an age-related hyperexpression pattern in the null mice. In addition, we document changes in expression of presynaptic vesicle recycling/trafficking machinery in the α9 null mice that suggests a bidirectional information flow between the target of the neural innervation (the hair cells) and the presynaptic terminal that is modified by hair cell nAChR activity. Loss of nAChR activity may alter transcriptional activity, as CREB binding protein expression is decreased coincident with the increased expression of N-Cadherin in the adult α9 null mice. Finally, by using mice expressing the nondesensitizing α9 L90T point mutant nAChR subunit, we show that increased nAChR activity drives synaptic hyperinnervation. © 2009 Wiley Periodicals, Inc.Fil: Murthy, Vidya. Tufts University School of Medicine; EslovaquiaFil: Taranda, Julian. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; Argentina. Tufts University School of Medicine; EslovaquiaFil: Elgoyhen, Ana Belen. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; Argentina. Universidad de Buenos Aires. Facultad de Medicina. Departamento de Farmacología; ArgentinaFil: Vetter, Douglas E.. Tufts University School of Medicine; Eslovaqui

High-Resolution Shape Completion Using Deep Neural Networks for Global Structure and Local Geometry Inference

We propose a data-driven method for recovering miss-ing parts of 3D shapes. Our method is based on a new deep learning architecture consisting of two sub-networks: a global structure inference network and a local geometry refinement network. The global structure inference network incorporates a long short-term memorized context fusion module (LSTM-CF) that infers the global structure of the shape based on multi-view depth information provided as part of the input. It also includes a 3D fully convolutional (3DFCN) module that further enriches the global structure representation according to volumetric information in the input. Under the guidance of the global structure network, the local geometry refinement network takes as input lo-cal 3D patches around missing regions, and progressively produces a high-resolution, complete surface through a volumetric encoder-decoder architecture. Our method jointly trains the global structure inference and local geometry refinement networks in an end-to-end manner. We perform qualitative and quantitative evaluations on six object categories, demonstrating that our method outperforms existing state-of-the-art work on shape completion.Comment: 8 pages paper, 11 pages supplementary material, ICCV spotlight pape

Large-Scale Light Field Capture and Reconstruction

This thesis discusses approaches and techniques to convert Sparsely-Sampled Light Fields (SSLFs) into Densely-Sampled Light Fields (DSLFs), which can be used for visualization on 3DTV and Virtual Reality (VR) devices. Exemplarily, a movable 1D large-scale light field acquisition system for capturing SSLFs in real-world environments is evaluated. This system consists of 24 sparsely placed RGB cameras and two Kinect V2 sensors. The real-world SSLF data captured with this setup can be leveraged to reconstruct real-world DSLFs. To this end, three challenging problems require to be solved for this system: (i) how to estimate the rigid transformation from the coordinate system of a Kinect V2 to the coordinate system of an RGB camera; (ii) how to register the two Kinect V2 sensors with a large displacement; (iii) how to reconstruct a DSLF from a SSLF with moderate and large disparity ranges. To overcome these three challenges, we propose: (i) a novel self-calibration method, which takes advantage of the geometric constraints from the scene and the cameras, for estimating the rigid transformations from the camera coordinate frame of one Kinect V2 to the camera coordinate frames of 12-nearest RGB cameras; (ii) a novel coarse-to-fine approach for recovering the rigid transformation from the coordinate system of one Kinect to the coordinate system of the other by means of local color and geometry information; (iii) several novel algorithms that can be categorized into two groups for reconstructing a DSLF from an input SSLF, including novel view synthesis methods, which are inspired by the state-of-the-art video frame interpolation algorithms, and Epipolar-Plane Image (EPI) inpainting methods, which are inspired by the Shearlet Transform (ST)-based DSLF reconstruction approaches