Indistinguishable Objects Research Articles

Physicalism and neo-Lockeanism about persons

The central objection to neo-Lockeanism about persons (NLP) is the too many thinkers problem: NLP ends up with an absurd multiplication of thinkers. Sydney Shoemaker attempts to solve this problem by arguing that the person and the animal do not share all of the same physical properties. This, according to him, leads to the idea that mental properties are realized in the person’s physical properties only. The project of this paper is to reject Shoemaker’s physicalist solution to the too many thinkers problem. I first argue that his physicalism fails to explain why two physically indistinguishable objects differ in their persistence conditions and physical properties. I then argue that Shoemaker illicitly treats the case of the person and the case of the animal differently, first in regard to cerebral function and its relation to mental properties, and second in regard to brainstem function and its relation to biological properties. This shows that Shoemaker’s solution actually undermines his entire argument.

Maximal limited similarity-based rough set model

Non-symmetric similarity relation-based rough set model (NS-RSM) is viewed as mathematical tool to deal with the analysis of imprecise and uncertain information in incomplete information systems with "?" values. NS-RSM relies on the concept of non-symmetric similarity relation to group equivalent objects and generate knowledge granules that are then used to approximate the target set. However, NS-RSM results in unpromising approximation space when addressing inconsistent data sets that have lots of boundary objects. This is because objects in the same similarity classes are not necessarily similar to each other and may belong to different target classes. To enhance NS-RSM capability, we introduce the maximal limited similarity-based rough set model (MLS-RSM) which describes the maximal collection of indistinguishable objects that are limited tolerance to each other in similarity classes. This allows accurate computation to be done for the approximation space. Furthermore, approximation accuracy comparisons have been conducted among NS-RSM and MLS-RSM. The results demonstrate that MLS-RSM model outperforms NS-RSM and can approximate the target set more efficiently.

Combinatorial Approach to Modeling Quantum Systems

Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers and unitarity in the formalism of quantum mechanics. In our approach, the quantum behavior can be explained by the fundamental impossibility to trace the identity of indistinguishable objects in their evolution. Any observation only provides information about the invariant relations between such objects. The trajectory of a quantum system is a sequence of unitary evolutions interspersed with observations -- non-unitary projections. We suggest a scheme to construct combinatorial models of quantum evolution. The principle of selection of the most likely trajectories in such models via the large numbers approximation leads in the continuum limit to the principle of least action with the appropriate Lagrangians and deterministic evolution equations.

Active Sensing System with In Situ Adjustable Sensor Morphology

BackgroundDespite the widespread use of sensors in engineering systems like robots and automation systems, the common paradigm is to have fixed sensor morphology tailored to fulfill a specific application. On the other hand, robotic systems are expected to operate in ever more uncertain environments. In order to cope with the challenge, it is worthy of note that biological systems show the importance of suitable sensor morphology and active sensing capability to handle different kinds of sensing tasks with particular requirements.MethodologyThis paper presents a robotics active sensing system which is able to adjust its sensor morphology in situ in order to sense different physical quantities with desirable sensing characteristics. The approach taken is to use thermoplastic adhesive material, i.e. Hot Melt Adhesive (HMA). It will be shown that the thermoplastic and thermoadhesive nature of HMA enables the system to repeatedly fabricate, attach and detach mechanical structures with a variety of shape and size to the robot end effector for sensing purposes. Via active sensing capability, the robotic system utilizes the structure to physically probe an unknown target object with suitable motion and transduce the arising physical stimuli into information usable by a camera as its only built-in sensor. Conclusions/SignificanceThe efficacy of the proposed system is verified based on two results. Firstly, it is confirmed that suitable sensor morphology and active sensing capability enables the system to sense different physical quantities, i.e. softness and temperature, with desirable sensing characteristics. Secondly, given tasks of discriminating two visually indistinguishable objects with respect to softness and temperature, it is confirmed that the proposed robotic system is able to autonomously accomplish them. The way the results motivate new research directions which focus on in situ adjustment of sensor morphology will also be discussed.

Reduce and Re-Lift: Bootstrapped Lifted Likelihood Maximization for MAP

By handling whole sets of indistinguishable objects together, lifted belief propagation approaches have rendered large, previously intractable, probabilistic inference problems quickly solvable. In this paper, we show that Kumar and Zilberstein's likelihood maximization (LM) approach to MAP inference is liftable, too, and actually provides additional structure for optimization. Specifically, it has been recognized that some pseudo marginals may converge quickly, turning intuitively into pseudo evidence. This additional evidence typically changes the structure of the lifted network: it may expand or reduce it. The current lifted network, however, can be viewed as an upper bound on the size of the lifted network required to finish likelihood maximization. Consequently, we re-lift the network only if the pseudo evidence yields a reduced network, which can efficiently be computed on the current lifted network. Our experimental results on Ising models, image segmentation and relational entity resolution demonstrate that this bootstrapped LM via "reduce and re-lift" finds MAP assignments comparable to those found by the original LM approach, but in a fraction of the time.

Finite groups and quantum physics

Concepts of quantum theory are considered from the constructive “finite” point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution—only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers—a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories—in particular, within the Standard Model.

Classical and quantum discrete dynamical systems

We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for these concepts to physics as an empirical science. For a consistent description of the symmetries of dynamical systems at different times and the symmetries of the various parts of such systems, we introduce discrete analogs of the gauge connections. Gauge structures are particularly important to describe the quantum behavior. We show that quantum behavior is the result of a fundamental inability to trace the identity of indistinguishable objects in the process of evolution. Information is available only on invariant statements and values, relating to such objects. Using mathematical arguments of a general nature we can show that any quantum dynamics can be reduced to a sequence of permutations. Quantum interferences occur in the invariant subspaces of permutation representations of symmetry groups of dynamical systems. The observable values can be expressed in terms of permutation invariants. We also show that for the description of quantum phenomena, instead of a nonconstructive number system --- the field of complex numbers, it is enough to use cyclotomic fields --- the minimal extentions of natural numbers suitable for quantum mechanics. Finite groups of symmetries play a central role in this article. The interest in such groups has an additional motivation in physics. Numerous experiments and observations in particle physics point to an important role of finite groups of relatively low orders in a number of fundamental processes.

Permutation interpretation of quantum mechanics

We analyse quantum concepts in a constructive finite background. Introduction of continuum or other actual infinities into physics leads to non-constructivity without any need for them in description of empirical observations. We argue that quantum behavior is a natural consequence of symmetries of dynamical systems. It is a result of fundamental impossibility to trace identity of indistinguishable objects in their evolution — only information about invariant combinations of such objects is available. General mathematical arguments imply that any quantum dynamics can be reduced to a sequence of permutations. Quantum phenomena, such as interferences, arise in invariant subspaces of permutation representations of the symmetry group of a system. Observable quantities can be expressed in terms of the permutation invariants. We demonstrate that for description of quantum phenomena there is no need to use such non-constructive number system as complex numbers. It is sufficient to employ the cyclotomic numbers — a minimal extension of the natural numbers which is suitable for quantum mechanics.

3D segmentation of SBFSEM images of neuropil by a graphical model over supervoxel boundaries

The segmentation of large volume images of neuropil acquired by serial sectioning electron microscopy is an important step toward the 3D reconstruction of neural circuits. The only cue provided by the data at hand is boundaries between otherwise indistinguishable objects. This indistinguishability, combined with the boundaries becoming very thin or faint in places, makes the large body of work on region-based segmentation methods inapplicable. On the other hand, boundary-based methods that exploit purely local evidence do not reach the extremely high accuracy required by the application domain that cannot tolerate the global topological errors arising from false local decisions. As a consequence, we propose a supervoxel merging method that arrives at its decisions in a non-local fashion, by posing and approximately solving a joint combinatorial optimization problem over all faces between supervoxels. The use of supervoxels allows the extraction of expressive geometric features. These are used by the higher-order potentials in a graphical model that assimilate knowledge about the geometry of neural surfaces by automated training on a gold standard. The scope of this improvement is demonstrated on the benchmark dataset E1088 (Helmstaedter et al., 2011) of 7.5billionvoxels from the inner plexiform layer of rabbit retina. We provide C++ source code for annotation, geometry extraction, training and inference.

A Discussion on Finite Quasi-cardinals in Quasi-set Theory

Quasi-set theory Q is an alternative set-theory designed to deal mathematically with collections of indistinguishable objects. The intended interpretation for those objects is the indistinguishable particles of non-relativistic quantum mechanics, under one specific interpretation of that theory. The notion of cardinal of a collection in Q is treated by the concept of quasi-cardinal, which in the usual formulations of the theory is introduced as a primitive symbol, since the usual means of cardinal definition fail for collections of indistinguishable objects. In a recent work, Domenech and Holik have proposed a definition of quasi-cardinality in Q. They claimed their definition of quasi-cardinal not only avoids the introduction of that notion as a primitive one, but also that it may be seen as a first step in the search for a version of Q that allows for a greater representative power. According to them, some physical systems can not be represented in the usual formulations of the theory, when the quasi-cardinal is considered as primitive. In this paper, we discuss their proposal and aims, and also, it is presented a modification from their definition we believe is simpler and more general.

Minimalist counting in sensor networks (Noise helps)

We propose a novel algorithm for counting N indistinguishable objects, called targets, by a collection of sensors. We adopt a minimalist scenario where sensors are unaware of the (non-empty) intersections of sensing regions, and so simple addition of all sensor counts inflates estimates of the total number of targets. The multiple counting in intersections must be accounted for, but with nothing more than the sensor counts, this is clearly impossible. However, noise is typically present in the target counting of many, if not most, applications. We make the key observation that if there is a (target-dependent) noise source affecting all sensors simultaneously, then it couples those with non-empty intersections. Exploitation of this coupling allows us to extract multiple-counting statistics from stochastic correlation patterns, and hence to compute accurate estimates of N via the classical inclusion–exclusion formula. Cumulants are the correlation measures of choice. Our analysis brings out and resolves certain technicalities that arise in our statistical counting algorithm. Examples are worked out to show the potential of the new algorithm. The paper concludes with a discussion of alternative models and open problems.

Informed Lifting for Message-Passing

Lifted inference, handling whole sets of indistinguishable objects together, is critical to the effective application of probabilistic relational models to realistic real world tasks. Recently, lifted belief propagation (LBP) has been proposed as an efficient approximate solution of this inference problem. It runs a modified BP on a lifted network where nodes have been grouped together if they have — roughly speaking — identical computation trees, the tree-structured “unrolling” of the underlying graph rooted at the nodes. In many situations, this purely syntactic criterion is too pessimistic: message errors decay along paths. Intuitively, for a long chain graph with weak edge potentials, distant nodes will send and receive identical messages yet their computation trees are quite different. To overcome this, we propose iLBP, a novel, easy-to-implement, informed LBP approach that interleaves lifting and modified BP iterations. In turn, we can efficiently monitor the true BP messages sent and received in each iteration and group nodes accordingly. As our experiments show, iLBP can yield significantly faster more lifted network while not degrading performance. Above all, we show that iLBP is faster than BP when solving the problem of distributing data to a large network, an important real-world application where BP is faster than uninformed LBP.

Can indexes be voluntarily assigned in multiple object tracking?

In Multiple Object Tracking (MOT), an observer is able to track 4 – 5 objects in a group of otherwise indistinguishable objects that move independently and unpredictably about a display. According to the Visual Indexing Theory (Pylyshyn, 1989), successful tracking requires that target objects be indexed while they are distinct — before tracking begins. In the typical MOT task, the target objects are briefly flashed resulting in the automatic assignment of indexes. The question arises whether indexes are only assigned automatically or whether they can be assigned voluntarily in a top-down manner. This study compares several ways of specifying which of 8 items are the targets to be tracked. In the Flash condition the target items were flashed, in the Nonflash condition the targets were the items not flashed, and in the Number condition the targets were specified by number (e.g., items numbered 1–4). The results showed no difference between the three conditions, suggesting that tracking was possible with either voluntary or involuntary indexing. The second experiment tested the hypothesis that voluntary indexing is possible only if the target items are visited serially. The conditions were the same as experiment 1 except that the time available for index assignment was too short to allow targets to be visited serially. In this experiment, targets flashed only once (or, in the Numbers condition, remained visible for about 400 ms). The results showed a decrease in tracking performance for the Number condition, but the Flash and the Nonflash conditions did not differ, suggesting that as long as the designation of targets was done rapidly, the observer did not have to visit each target serially in order to index it. These results suggest that indexing can occur both automatically and voluntarily, and without serially visiting them, so long as the items are successfully specified.

Why quasi-sets?

Quasi-set theory was developed to deal with collections of indistinguishable objects. In standard mathematics, there are no such kind of entities, for indistinguishability (agreement with respect to all properties) entails numerical identity. The main motivation underlying such a theory is of course quantum physics, for collections of indistinguishable (’identical’ in the physicists’ jargon) particles cannot be regarded as ’sets’ of standard set theories, which are collections of distinguishable objects. In this paper, a rationale for the development of such a theory is presented, motivated by Heinz Post’s claim that indistinguishability of quantum entities should be attributed ’right at the start’.

Logic-based interpretation of geometrically observable changes occurring in dynamic scenes

The work presented here is about employing a theory of updates to study geometrically observable changes that occur in spatial information about image sequences of a dynamic scene. The logical framework consists of a formalism for specifying the geometrical content of a scene, as well as the changes that occur in this geometry, and an algorithm for constructing a description for such changes from logical deductions. In this approach, a database state represents the available sensor data at a particular time instant. Transitions in sensor data are modeled by changes in the database and interpreted based on axioms encoding commonsense spatial reasoning. The main contribution of this work is that it provides the theoretical foundations for symbolically interpreting long sequences of sensor data transitions. For testing the framework and its implementation, the problem of interpreting rotational movements of objects in a sequence of images was used. Our experiments show that the system correctly interprets rotational movements for objects of different colors and provides satisfactory results for interpreting such movements from perceptually indistinguishable objects.

Logical and Philosophical Remarks on Quasi-Set Theory

Quasi-set theory is a theory for dealing with collections of indistinguishable objects. In this paper we discuss some logical and philosophical questions involved with such a theory. The analysis of these questions enable us to provide the first grounds of a possible new view of physical reality, founded on an ontology of non-individuals, to which quasi-set theory may constitute the logical basis.

Improving Discrete Model Representations via Symmetry Considerations

In this paper, we focus on a useful modeling concept that is frequently ignored while formu lating discrete optimization problems. Very often, there exists a natural symmetry inherent in the problem itself that, if propagated to the model, can hopelessly mire a branch-and-bound solver by burdening it to explore and eliminate such alternative symmetric solutions. We discuss three applications where such a symmetry arises: a telecommunications network design problem, a noise pollution problem, and a machine procurement and operation problem. For each case, we identify the indistinguishable objects in the model that create the problem symmetry and show how imposing certain decision hierarchies within the model significantly enhances its solvability, while using a popular modern-day commercial branch-and-cut software (CPLEX 6.5).

Exchanges of "Quanta" Among Distinguishable and Indistinguishable Objects

Beginning with a physical problem of exchange of n indistinguishable "quanta" of energy in an ensemble of k oscillators we define a new wide class of combinatorial problems, which also contains statistics intermediate between Fermi–Dirac and Bose–Einstein. One such problem is related to the number theoretic problem of computing the partitions of positive integers. After establishing such a connection, we give explicit formulas for the partitions M(n,k) of an integer n into k parts with k ≤ 4. Moreover, we derive a recursion relation for fixed n and varying k which is valid for any k. A formula which relates partitions to the cardinality of the partition set taking order into account is also derived. The leading asymptotic behavior for n large is obtained for any k. A suggestive interpretation of this formulas is proposed in terms of simplicial lattices. Recursive formulas at fixed k and varying n are then written for k ≤ 5 using the concept of factorial triangle, which is amenable for generalizations to larger k's. The problem of distinct partitions is mapped onto the probability problem of ball removal with replacement, for which we give again recursive solution formulas. Finally, the method of generalized Tartaglia triangle allows the derivation of recursive formulas for limited partitions which take order into account. This latter result is related to the problem of finding the number of distinct ways of dividing n indistinguishable objects into k distinguishable groups, for which explicit summations had been previously found.

Violent Relaxation of Indistinguishable Objects and Neutrino Hot Dark Matter in Clusters of Galaxies

The statistical mechanical investigation of violent relaxation (first introduced by Lynden-Bell in 1967) is extended to indistinguishable objects. It is found that, coincidentally, the equilibrium distribution is the same as that obtained for classical objects. For massive neutrinos, the phase-space bound published by Tremaine & Gunn in 1979 is revisited and reinterpreted as the limit indicating the onset of degeneracy related to the coarse-grained phase-space distribution. In the context of one of the currently most popular cosmological models, the cold and hot dark matter (CHDM) model (published by Primack et al. in 1995), the onset of degeneracy may be of importance in the core region of clusters of galaxies. Degeneracy allows the neutrino HDM density to exceed the limit imposed by the Tremaine & Gunn bound while accounting for the phase-space bound.

Institutions of Art: Reconsiderations of George Dickie's Philosophy

Contents Preface 1. Reconsidering the Institutional Theory Noel Carroll/Identifying Art Jeffrey Wieand/Perceptually Indistinguishable Objects Susan Feagin/Valuing the Artworld 2. Reconsidering the Evaluation of Art Bohdan Dziemidok/On the Need to Distinguish Between Aesthetic and Artistic Evaluations of Art Peggy Zeglin Brand/Evaluating Art: A Feminist Case for Dickie's Matrix System Marcia Muelder Eaton/Evaluating More Than Art 3. Reconsidering the History of Aesthetics Peter Kivy/From Literature as Imagination to Literature as Memory: A Historical Sketch Ted Cohen/Partial Enchantments of the Quixote Story in Hume's Essay on Taste Robert J. Yanal/Kant on Aesthetic Ideas and Beauty George Dickie: A Biography and Bibliography