From Sensory Signals to Modality-Independent Conceptual Representations: A Probabilistic Language of Thought Approach

People learn modality-independent, conceptual representations from modality-specific sensory signals. Here, we hypothesize that any system that accomplishes this feat will include three components: a representational language for characterizing modality-independent representations, a set of sensory-specific forward models for mapping from modality-independent representations to sensory signals, and an inference algorithm for inverting forward models—that is, an algorithm for using sensory signals to infer modality-independent representations. To evaluate this hypothesis, we instantiate it in the form of a computational model that learns object shape representations from visual and/or haptic signals. The model uses a probabilistic grammar to characterize modality-independent representations of object shape, uses a computer graphics toolkit and a human hand simulator to map from object representations to visual and haptic features, respectively, and uses a Bayesian inference algorithm to infer modality-independent object representations from visual and/or haptic signals. Simulation results show that the model infers identical object representations when an object is viewed, grasped, or both. That is, the model’s percepts are modality invariant. We also report the results of an experiment in which different subjects rated the similarity of pairs of objects in different sensory conditions, and show that the model provides a very accurate account of subjects’ ratings. Conceptually, this research significantly contributes to our understanding of modality invariance, an important type of perceptual constancy, by demonstrating how modality-independent representations can be acquired and used. Methodologically, it provides an important contribution to cognitive modeling, particularly an emerging probabilistic language-of-thought approach, by showing how symbolic and statistical approaches can be combined in order to understand aspects of human perception.     

Statistical Object Data Analysis of Taxonomic Trees from Human Microbiome Data

Human microbiome research characterizes the microbial content of samples from human habitats to learn how interactions between bacteria and their host might impact human health. In this work a novel parametric statistical inference method based on object-oriented data analysis (OODA) for analyzing HMP data is proposed. OODA is an emerging area of statistical inference where the goal is to apply statistical methods to objects such as functions, images, and graphs or trees. The data objects that pertain to this work are taxonomic trees of bacteria built from analysis of 16S rRNA gene sequences (e.g. using RDP); there is one such object for each biological sample analyzed. Our goal is to model and formally compare a set of trees. The contribution of our work is threefold: first, a weighted tree structure to analyze RDP data is introduced; second, using a probability measure to model a set of taxonomic trees, we introduce an approximate MLE procedure for estimating model parameters and we derive LRT statistics for comparing the distributions of two metagenomic populations; and third the Jumpstart HMP data is analyzed using the proposed model providing novel insights and future directions of analysis.     

A hierarchical probabilistic model for rapid object categorization in natural scenes

Humans can categorize objects in complex natural scenes within 100-150 ms. This amazing ability of rapid categorization has motivated many computational models. Most of these models require extensive training to obtain a decision boundary in a very high dimensional (e.g., ～6,000 in a leading model) feature space and often categorize objects in natural scenes by categorizing the context that co-occurs with objects when objects do not occupy large portions of the scenes. It is thus unclear how humans achieve rapid scene categorization.To address this issue, we developed a hierarchical probabilistic model for rapid object categorization in natural scenes. In this model, a natural object category is represented by a coarse hierarchical probability distribution (PD), which includes PDs of object geometry and spatial configuration of object parts. Object parts are encoded by PDs of a set of natural object structures, each of which is a concatenation of local object features. Rapid categorization is performed as statistical inference. Since the model uses a very small number (～100) of structures for even complex object categories such as animals and cars, it requires little training and is robust in the presence of large variations within object categories and in their occurrences in natural scenes. Remarkably, we found that the model categorized animals in natural scenes and cars in street scenes with a near human-level performance. We also found that the model located animals and cars in natural scenes, thus overcoming a flaw in many other models which is to categorize objects in natural context by categorizing contextual features. These results suggest that coarse PDs of object categories based on natural object structures and statistical operations on these PDs may underlie the human ability to rapidly categorize scenes.     

Parameter inference for biochemical systems that undergo a Hopf bifurcation

The increasingly widespread use of parametric mathematical models to describe biological systems means that the ability to infer model parameters is of great importance. In this study, we consider parameter inferability in nonlinear ordinary differential equation models that undergo a bifurcation, focusing on a simple but generic biochemical reaction model. We systematically investigate the shape of the likelihood function for the model's parameters, analyzing the changes that occur as the model undergoes a Hopf bifurcation. We demonstrate that there exists an intrinsic link between inference and the parameters’ impact on the modeled system's dynamical stability, which we hope will motivate further research in this area.     

A computer model for reshaping of cells in epithelia due to in-plane deformation and annealing

Although cell reshaping is fundamental to the mechanics of epithelia, technical barriers have prevented the methods of mechanics from being used to investigate it. These barriers have recently been overcome by the cell-based finite element formulation of Chen and Brodland. Here, parameters to describe the fabric of an epithelium in terms of cell shape and orientation and cell edge density are defined. Then, rectangular "patches" of model epithelia having various initial fabric parameters are generated and are either allowed to anneal or are subjected to one of several patterns of in-plane deformation. The simulations show that cell reshaping lags the deformation history, that it is allayed by cell rearrangement and that it causes the epithelium as a whole to exhibit viscoelastic mechanical properties. Equations to describe changes in cell shape due to annealing and in-plane deformation are presented.     

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

In order to quantitatively study object perception, be it perception by biological systems or by machines, one needs to create objects and object categories with precisely definable, preferably naturalistic, properties¹. Furthermore, for studies on perceptual learning, it is useful to create novel objects and object categories (or object classes) with such properties².Many innovative and useful methods currently exist for creating novel objects and object categories^3-6 (also see refs. 7,8). However, generally speaking, the existing methods have three broad types of shortcomings.First, shape variations are generally imposed by the experimenter^5,9,10, and may therefore be different from the variability in natural categories, and optimized for a particular recognition algorithm. It would be desirable to have the variations arise independently of the externally imposed constraints.Second, the existing methods have difficulty capturing the shape complexity of natural objects^11-13. If the goal is to study natural object perception, it is desirable for objects and object categories to be naturalistic, so as to avoid possible confounds and special cases.Third, it is generally hard to quantitatively measure the available information in the stimuli created by conventional methods. It would be desirable to create objects and object categories where the available information can be precisely measured and, where necessary, systematically manipulated (or ''tuned''). This allows one to formulate the underlying object recognition tasks in quantitative terms.Here we describe a set of algorithms, or methods, that meet all three of the above criteria. Virtual morphogenesis (VM) creates novel, naturalistic virtual 3-D objects called ''digital embryos'' by simulating the biological process of embryogenesis¹⁴. Virtual phylogenesis (VP) creates novel, naturalistic object categories by simulating the evolutionary process of natural selection^9,12,13. Objects and object categories created by these simulations can be further manipulated by various morphing methods to generate systematic variations of shape characteristics^15,16. The VP and morphing methods can also be applied, in principle, to novel virtual objects other than digital embryos, or to virtual versions of real-world objects^9,13. Virtual objects created in this fashion can be rendered as visual images using a conventional graphical toolkit, with desired manipulations of surface texture, illumination, size, viewpoint and background. The virtual objects can also be ''printed'' as haptic objects using a conventional 3-D prototyper.We also describe some implementations of these computational algorithms to help illustrate the potential utility of the algorithms. It is important to distinguish the algorithms from their implementations. The implementations are demonstrations offered solely as a ''proof of principle'' of the underlying algorithms. It is important to note that, in general, an implementation of a computational algorithm often has limitations that the algorithm itself does not have.Together, these methods represent a set of powerful and flexible tools for studying object recognition and perceptual learning by biological and computational systems alike. With appropriate extensions, these methods may also prove useful in the study of morphogenesis and phylogenesis.     

A Computer Model for Reshaping of Cells in Epithelia Due to In-plane Deformation and Annealing

Although cell reshaping is fundamental to the mechanics of epithelia, technical barriers have prevented the methods of mechanics from being used to investigate it. These barriers have recently been overcome by the cell-based finite element formulation of Chen and Brodland. Here, parameters to describe the fabric of an epithelium in terms of cell shape and orientation and cell edge density are defined. Then, rectangular "patches" of model epithelia having various initial fabric parameters are generated and are either allowed to anneal or are subjected to one of several patterns of in-plane deformation. The simulations show that cell reshaping lags the deformation history, that it is allayed by cell rearrangement and that it causes the epithelium as a whole to exhibit viscoelastic mechanical properties. Equations to describe changes in cell shape due to annealing and in-plane deformation are presented.     

Description of the deformation of the left ventricle by a kinematic model.

A model of left ventricular (LV) kinematics is essential to identify the fundamental physiological modes of LV deformation during a complete cardiac cycle as observed from the motion of a finite number of markers embedded in the LV wall. Kinematics can be described by a number of modes of motion and deformation in succession. An obvious mode of LV deformation is the ejection of cavity volume while the wall thickens. In the more sophisticated model of LV kinematics developed here, seven time-dependent parameters were used to describe not only volume change but also torsion and shape changes throughout the cardiac cycle. Rigid-body motion required another six parameters. The kinematic model employed a deformation field that had no singularities within the myocardium, and all parameters describing the modes of deformation were dimensionless. Note that torsion, volume and symmetric shape changes all require the definition of a cardiac coordinate system, which has generally been related to the measured cardiac geometry by reference to approximate anatomical landmarks. However, in the present study the coordinate system was positioned objectively by a least-squares fit of the kinematic model to the measured motion of markers. Theoretically, at least five markers are needed to find a unique set of parameters.(ABSTRACT TRUNCATED AT 250 WORDS)     

The effects of simple objects on the electric field of Apteronotus

How might electric fish determine, from patterns of transdermal voltage changes, the size, shape, location, and impedance of a nearby object? I have investigated this question by measuring and simulating electric images of spheres and ellipsoids near an Apteronotus leptorhynchus. Previous studies have shown that this fish's electric field magnitude, and perturbations of the field due to objects, are complicated nonliner functions of distance from the fish. These functions become much simpler when distance is measured from the axes of symmetry of the fish and the object, instead of their respective edges. My analysis suggests the following characteristics of high frequency electric sense and electric images. 1. The shape of electric images on the fish's body is relatively independent of a spherical object's radius, conductivity, and rostrocaudal location. 2. An image's relative width increases linearly with lateral distance, and might therefore unambiguously encode object distance. 3. Only objects with very large dielectric constants cause appreciable phase shifts, and the degree of shift depends strongly on water conductivity. 4. Several parameters, such as the range of electric sense, may depend on the rostrocaudal location of an object. Large objects may be detectable further from the head than the tail, and conversely, small objects may be detectable further from the tail than head. 5. Asymmetrical objects produce different electric images, correlated with their cross-sections, for different orientations and phases of the electric field. 6. The steep attenuation with distance of the field magnitude causes spatial distortions in electric images, somewhat analogous to the perspective distortion inherent in wide angle optical lenses.     

Particle detection,number estimation,and feature measurement in gene transfer studies: optical fractionator stereology integrated with digital image processing and analysis

Assessing the efficacy of in vivo gene transfer often requires a quantitative determination of the number, size, shape, or histological visualization characteristics of biological objects. The optical fractionator has become a choice stereological method for estimating the number of objects, such as neurons, in a structure, such as a brain subregion. Digital image processing and analytic methods can increase detection sensitivity and quantify structural and/or spectral features located in histological specimens. We describe a hardware and software system that we have developed for conducting the optical fractionator process. A microscope equipped with a video camera and motorized stage and focus controls is interfaced with a desktop computer. The computer contains a combination live video/computer graphics adapter with a video frame grabber and controls the stage, focus, and video via a commercial imaging software package. Specialized macro programs have been constructed with this software to execute command sequences requisite to the optical fractionator method: defining regions of interest, positioning specimens in a systematic uniform random manner, and stepping through known volumes of tissue for interactive object identification (optical dissectors). The system affords the flexibility to work with count regions that exceed the microscope image field size at low magnifications and to adjust the parameters of the fractionator sampling to best match the demands of particular specimens and object types. Digital image processing can be used to facilitate object detection and identification, and objects that meet criteria for counting can be analyzed for a variety of morphometric and optical properties.     

Three-dimensional analysis of object properties during active electrolocation in mormyrid weakly electric fishes (Gnathonemus petersii)

Weakly electric fishes are nocturnal and orientate in the absence of vision by using their electrical sense. This enables them not only to navigate but also to perceive and recognize objects in complete darkness. They create an electric field around their bodies by producing electric signals with specialized electric organs. Objects within this field alter the electric current at electroreceptor organs, which are distributed over almost the entire body surface. During active electrolocation, fishes detect, localize and analyse objects by monitoring their self-produced electric signals. We investigated the ability of the mormyrid Gnathonemus petersii to perceive objects three-dimensionally in space. Within a range of about 12 cm, G. petersii can perceive the distance of objects. Depth perception is independent of object size, shape and material. The mechanism for distance determination through electrolocation involves calculating the ratio between two parameters (maximal slope and maximal amplitude) of the electrical image which each object projects onto the fish's skin. During active electrolocation, electric fishes cannot only locate objects in space but in addition can determine the three-dimensional shape of an object. Up to certain limits, objects are spontaneously categorized according to their shapes, but not according to their sizes or the materials of which they are made.     

Depth perception in disparity-defined objects: finding the balance between averaging and segregation

Deciding what constitutes an object, and what background, is an essential task for the visual system. This presents a conundrum: averaging over the visual scene is required to obtain a precise signal for object segregation, but segregation is required to define the region over which averaging should take place. Depth, obtained via binocular disparity (the differences between two eyes’ views), could help with segregation by enabling identification of object and background via differences in depth. Here, we explore depth perception in disparity-defined objects. We show that a simple object segregation rule, followed by averaging over that segregated area, can account for depth estimation errors. To do this, we compared objects with smoothly varying depth edges to those with sharp depth edges, and found that perceived peak depth was reduced for the former. A computational model used a rule based on object shape to segregate and average over a central portion of the object, and was able to emulate the reduction in perceived depth. We also demonstrated that the segregated area is not predefined but is dependent on the object shape. We discuss how this segregation strategy could be employed by animals seeking to deter binocular predators.This article is part of the themed issue ‘Vision in our three-dimensional world’.     

Growth Based Morphogenesis of Vertebrate Limb Bud

Many genes and their regulatory relationships are involved in developmental phenomena. However, by chemical information alone, we cannot fully understand changing organ morphologies through tissue growth because deformation and growth of the organ are essentially mechanical processes. Here, we develop a mathematical model to describe the change of organ morphologies through cell proliferation. Our basic idea is that the proper specification of localized volume source (e.g., cell proliferation) is able to guide organ morphogenesis, and that the specification is given by chemical gradients. We call this idea “growth-based morphogenesis.” We find that this morphogenetic mechanism works if the tissue is elastic for small deformation and plastic for large deformation. To illustrate our concept, we study the development of vertebrate limb buds, in which a limb bud protrudes from a flat lateral plate and extends distally in a self-organized manner. We show how the proportion of limb bud shape depends on different parameters and also show the conditions needed for normal morphogenesis, which can explain abnormal morphology of some mutants. We believe that the ideas shown in the present paper are useful for the morphogenesis of other organs.     

Size does not matter: size-invariant echo-acoustic object classification

Echolocating bats can not only extract spatial information from the auditory analysis of their ultrasonic emissions, they can also discriminate, classify and identify the three-dimensional shape of objects reflecting their emissions. Effective object recognition requires the segregation of size and shape information. Previous studies have shown that, like in visual object recognition, bats can transfer an echo-acoustic object discrimination task to objects of different size and that they spontaneously classify scaled versions of virtual echo-acoustic objects according to trained virtual-object standards. The current study aims to bridge the gap between these previous findings using a different class of real objects and a classification—instead of a discrimination paradigm. Echolocating bats (Phyllostomus discolor) were trained to classify an object as either a sphere or an hour-glass shaped object. The bats spontaneously generalised this classification to objects of the same shape. The generalisation cannot be explained based on similarities of the power spectra or temporal structures of the echo-acoustic object images and thus require dedicated neural mechanisms dealing with size-invariant echo-acoustic object analysis. Control experiments with human listeners classifying the echo-acoustic images of the objects confirm the universal validity of auditory size invariance. The current data thus corroborate and extend previous psychophysical evidence for sonar auditory-object normalisation and suggest that the underlying auditory mechanisms following the initial neural extraction of the echo-acoustic images in echolocating bats may be very similar in bats and humans.     

Preferences for familiarity and novelty: a model for the simultaneous development of both

Many developing animals show an increasing preference for familiar companions and objects. They may also come to prefer things which are slightly different from the familiar. A model which shows how both processes can occur simultaneously is developed with particular reference to imprinting in birds. It shows how a biphasic curve would be obtained if preferences were measured in choice tests during the course of familiarization. The model predicts that shape of the preference curve will depend on the difference between the familiar and unfamiliar objects. It also predicts that the shape will be altered if inexperienced animals show a preference for one object over the other.     

Fringe-scan flow cytometry

We describe the development of a scanning flow cytometer capable of measuring the distribution of fluorescent dye along objects with a spatial resolution of 0.7 micron. The heart of this instrument, called a fringe-scan flow cytometer, is an interference field (i.e., a series of intense planes of illumination) produced by the intersection of two laser beams. Fluorescence profiles (i.e., records showing the intensity of fluorescence measured at 20 ns intervals) are recorded during the passage of objects through the fringe field. The shape of the fringe field is determined by recording light scatter profiles as 0.25 micron diameter microspheres traverse the field. The distribution of the fluorescent dye along each object passing through the fringe field is estimated from the recorded fluorescence profile using Fourier deconvolution. We show that the distribution of fluorescent dye along microsphere doublets and along propidium iodide stained human chromosomes can be determined accurately using fringe-scan flow cytometry. The accuracy of fringe-scan shape analysis was determined by comparing fluorescence profiles estimated from fringe-scan profiles for microspheres and chromosomes with fluorescence profiles for the same objects measured using slit-scan flow cytometry.     

The Time Course of Activation of Object Shape and Shape+Colour Representations during Memory Retrieval

Little is known about the timing of activating memory for objects and their associated perceptual properties, such as colour, and yet this is important for theories of human cognition. We investigated the time course associated with early cognitive processes related to the activation of object shape and object shape+colour representations respectively, during memory retrieval as assessed by repetition priming in an event-related potential (ERP) study. The main findings were as follows: (1) we identified a unique early modulation of mean ERP amplitude during the N1 that was associated with the activation of object shape independently of colour; (2) we also found a subsequent early P2 modulation of mean amplitude over the same electrode clusters associated with the activation of object shape+colour representations; (3) these findings were apparent across both familiar (i.e., correctly coloured – yellow banana) and novel (i.e., incorrectly coloured - blue strawberry) objects; and (4) neither of the modulations of mean ERP amplitude were evident during the P3. Together the findings delineate the timing of object shape and colour memory systems and support the notion that perceptual representations of object shape mediate the retrieval of temporary shape+colour representations for familiar and novel objects.     

Simulation of deformable models with the Poisson equation

In this paper, we present a new methodology for the deformation of soft objects by drawing an analogy between the Poisson equation and elastic deformation from the viewpoint of energy propagation. The potential energy stored due to a deformation caused by an external force is calculated and treated as the source injected into the Poisson system, as described by the law of conservation of energy. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. An autonomous cellular neural network (CNN) model is established by using the analogy between the Poisson equation and CNN to solve the Poisson model for the real-time requirement of soft object deformation. A method is presented to derive the internal forces from the potential energy distribution. The proposed methodology models non-linear materials with the non-linear Poisson equation and thus non-linear CNN, rather than geometric non-linearity. It not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying constitutive coefficients. A haptic virtual reality system has been developed for deformation simulation with force feedback. Examples are presented to demonstrate the efficiency of the proposed methodology.     

Simulation of deformable models with the Poisson equation

In this paper, we present a new methodology for the deformation of soft objects by drawing an analogy between the Poisson equation and elastic deformation from the viewpoint of energy propagation. The potential energy stored due to a deformation caused by an external force is calculated and treated as the source injected into the Poisson system, as described by the law of conservation of energy. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. An autonomous cellular neural network (CNN) model is established by using the analogy between the Poisson equation and CNN to solve the Poisson model for the real-time requirement of soft object deformation. A method is presented to derive the internal forces from the potential energy distribution. The proposed methodology models non-linear materials with the non-linear Poisson equation and thus non-linear CNN, rather than geometric non-linearity. It not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying constitutive coefficients. A haptic virtual reality system has been developed for deformation simulation with force feedback. Examples are presented to demonstrate the efficiency of the proposed methodology.