Virtual reality (VR) research has provided overviews of locomotion techniques, how they work, their strengths and overall user experience. Considerable research has investigated new methodologies, particularly machine learning to develop redirection algorithms. To best support the development of redirection algorithms through machine learning, we must understand how best to replicate human navigation and behaviour in VR, which can be supported by the accumulation of results produced through live-user experiments. However, it can be difficult to identify, select and compare relevant research without a pre-existing framework in an ever-growing research field. Therefore, this work aimed to facilitate the ongoing structuring and comparison of the VR-based natural walking literature by providing a standardised framework for researchers to utilise. We applied thematic analysis to study methodology descriptions from 140 VR-based papers that contained live-user experiments. From this analysis, we developed the LoCoMoTe framework with three themes: navigational decisions, technique implementation, and modalities. The LoCoMoTe framework provides a standardised approach to structuring and comparing experimental conditions. The framework should be continually updated to categorise and systematise knowledge and aid in identifying research gaps and discussions.

We use integer programming (IP) and constraint programming (CP) to search for sets of mutually orthogonal latin squares (MOLS). We improve the performance of the solvers by formulating an extended symmetry breaking method and provide an alternative CP encoding which performs much better in practice. Using state-of-the-art solvers we are able to quickly find pairs of MOLS (or prove their nonexistence) in all orders up to and including eleven. We also analyze the effectiveness of using CP and IP solvers to search for triples of MOLS and estimate the running time of using this approach to resolve the longstanding open problem of determining the existence of a triple of MOLS of order ten.

We study the relation between near resolvable designs and ${\mathbb{F}_q}$ -linear codes over $\mathbb{F}_q^b$. We use the incidence matrix of a near resolvable design to construct a parity-check matrix of an ${\mathbb{F}_q}$-linear code. We show an equivalence between the construction of a new class of near resolvable designs NRB(rb + 1, r), that we call r-complete, and the well-known ${\mathbb{F}_q}$-linear codes over $\mathbb{F}_q^b$ with length n and dimension n – r which have the following good properties: (i) they are maximum distance separable (MDS), (ii) they are low-density, and (iii) they reach the maximum length of any MDS lowest density code.

Lévy flight is a type of random walk that characterizes the behaviour of many natural phenomena studied across a multiplicity of academic disciplines; within biology specifically, the behaviour of fish, birds, insects, mollusks, bacteria, plants, slime molds, t-cells, and human populations. The Lévy flight foraging hypothesis states that because Lévy flights can maximize an organism's search efficiency, natural selection should result in Lévy-like behaviour. Empirical and theoretical research has provided ample evidence of Lévy walks in both extinct and extant species, and its efficiency across models with a diversity of resource distributions. However, no model has addressed the maintenance of Lévy flight foraging through evolutionary processes, and existing models lack ecological breadth. We use numerical simulations, including lineage-based models of evolution with a distribution of move lengths as a variable and heritable trait, to test the Lévy flight foraging hypothesis. We include biological and ecological contexts such as population size, searching costs, lifespan, resource distribution, speed, and consider both energy accumulated at the end of a lifespan and averaged over a lifespan. We demonstrate that selection often results in Lévy-like behaviour, although conditional; smaller populations, longer searches, and low searching costs increase the fitness of Lévy-like behaviour relative to Brownian behaviour. Interestingly, our results also evidence a bet-hedging strategy; Lévy-like behaviour reduces fitness variance, thus maximizing geometric mean fitness over multiple generations.

In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometry—the long-standing problem of determining if a projective plane of order ten exists. Both the original search and an independent verification in 2011 discovered no such projective plane. However, these searches were each performed using highly specialized custom-written code and did not produce nonexistence certificates. In this paper, we resolve Lam's problem by translating the problem into Boolean logic and use satisfiability (SAT) solvers to produce nonexistence certificates that can be verified by a third party. Our work uncovered consistency issues in both previous searches—highlighting the difficulty of relying on special-purpose search code for nonexistence results.

We use integer programming (IP) and constraint programming (CP) to search for graeco-latin squares. We improve the performance of the solvers by formulating an extended symmetry breaking method and provide an alternative CP encoding which performs much better in practice. Using state-of-the-art solvers as black boxes we are able to quickly find graeco-latin squares (or prove their nonexistence) in all orders up to and including eleven.

In the 1970s and 1980s, searches performed by L. Carter, C. Lam, L. Thiel, and S. Swiercz showed that projective planes of order ten with weight 16 codewords do not exist. These searches required highly specialized and optimized computer programs and required about 2,000 hours of computing time on mainframe and supermini computers. In 2010, these searches were verified by D. Roy using an optimized C program and 16,000 hours on a cluster of desktop machines. We performed a verification of these searches by reducing the problem to the Boolean satisfiability problem (SAT). Our verification uses the cube-and-conquer SAT solving paradigm, symmetry breaking techniques using the computer algebra system Maple, and a result of Carter that there are ten nonisomorphic cases to check. Our searches completed in about 30 hours on a desktop machine and produced nonexistence proofs of about 1 terabyte in the DRAT (deletion resolution asymmetric tautology) format.

Phantom limb pain is a neuropathic condition in which a person feels pain in a limb that is not present. Cognitive treatments that visually recreate the limb in an attempt to create a cross modal interaction between vision, and touch/proprioception have shown to be effective at alleviating this pain. With improvements in technology, Virtual Mirror Therapy is starting to gain favor, however, there are currently no applications that utilize passive touch in the same way non-virtual reality applications do. This paper investigates whether a visual stimulus can relocate a tactile stimulus to a different location using principles from the rubber hand illusion and mirror therapy. We demonstrate that a displaced visual stimulus in virtual reality can disrupt accurate spatial perception of a physical vibrotactile sensation however the effects are small and require further investigation.

The qtx(q+1)tordered orthogonal arrays (OOAs) of strength t over the alphabet Fq were constructed using linear feedback shift register sequences (LFSRs) defined by primitive polynomials in Fq[x]. In this paper, we extend this result to all polynomials in Fq[x] which satisfy some fairly simple restrictions, i.e., the restrictions that are automatically satisfied by primitive polynomials. While these restrictions sometimes reduce the number of columns produced from (q + 1)t to a smaller multiple oft, in many cases, we still obtain the maximum number of columns in the constructed OOA when using non-primitive polynomials. For 2 ≤ q ≤ 9 and small t, we generate OOAs in this manner for all permissible polynomials of degree t in Fq[x] and compare the results to the ones produced in [2], [16], and [17] showing how close the arrays are to being “full” orthogonal arrays. Unusually for the finite fields, our arrays based on the non-primitive irreducible and even reducible polynomials are closer to the orthogonal arrays than those built from the primitive polynomials.

We present a new construction of ordered orthogonal arrays (OOAs) of strength t with (q + 1)t columns over a finite field Fqusing linear feedback shift register sequences (LFSRs). OOAs are naturally related to (t, m, s)-nets, linear codes, and MDS codes. Our construction selects suitable columns from the array formed by all subintervals of length (qt-1)/(q-1) of an LFSR sequence generated by a primitive polynomial of degree t over Fq. We prove properties about the relative positions of runs in an LFSR, which guarantee that the constructed OOA has strength t. The set of parameters of our OOAs are the same as the ones given by Rosenbloom and Tsfasman (1997) and Skriganov (2002), but the constructed arrays are different. We experimentally verify that our OOAs are stronger than the Rosenbloom-Tsfasman-Skriganov OOAs in the sense that ours are “closer” to being a “full” orthogonal array. We also discuss how our OOA construction relates to previous techniques to build OOAs from a set of linearly independent vectors over Fq, as well as to hypergraph homomorphisms.

Local binary pattern on three orthogonal planes (LBP-TOP) is one of the most popular method for dynamic texture analysis and has been successfully applied to facial expression analysis. Yet an effective LBP-TOP operator highly relies on preprocessing. And, like many appearance-based approaches, this approach reserves more identity-related cues rather than expression. In this work, we propose a fully automatic approach for facial expression recognition based on points registration, localized patch extraction and LBP-TOP feature representation. The efficiency of this method is evaluated on CK+ database. Results show that the proposed method has achieved a better performance compared with existing methods.

The concepts of ambiguity and deficiency for a bijection on a finite Abelian group were recently introduced. In this paper, we present some further fundamental results on the ambiguity and deficiency of functions; in particular, we note that they are invariant under the well-known Carlet-Charpin-Zinoviev-equivalence, we obtain upper and lower bounds on the ambiguity and deficiency of differentially k-uniform functions, and we give a lower bound on the nonlinearity of functions that achieve the lower bound of ambiguity and deficiency. In addition, we provide an explicit formula in terms of the ranks of matrices on the ambiguity and deficiency of a Dembowski-Ostrom (DO) polynomial, and using this technique, we find exact values for known cases of DO permutations with few terms. We also derive exact values for the ambiguities and deficiencies of DO permutations obtained from trace functions. The key relationship between the above polynomials is that they all have linearized difference map.

Complex and natural social interaction between artificial agents (computer-generated or robotic) and humans necessitates the display of rich emotions in order to be believable, socially relevant, and accepted, and to generate the natural emotional responses that humans show in the context of social interaction, such as engagement or empathy. Whereas some robots use faces to display (simplified) emotional expressions, for other robots such as Nao, body language is the best medium available given their inability to convey facial expressions. Displaying emotional body language that can be interpreted whilst interacting with the robot should significantly improve naturalness. This research investigates the creation of an affect space for the generation of emotional body language to be displayed by humanoid robots. To do so, three experiments investigating how emotional body language displayed by agents is interpreted were conducted. The first experiment compared the interpretation of emotional body language displayed by humans and agents. The results showed that emotional body language displayed by an agent or a human is interpreted in a similar way in terms of recognition. Following these results, emotional key poses were extracted from an actor's performances and implemented in a Nao robot. The interpretation of these key poses was validated in a second study where it was found that participants were better than chance at interpreting the key poses displayed. Finally, an affect space was generated by blending key poses and validated in a third study. Overall, these experiments confirmed that body language is an appropriate medium for robots to display emotions and suggest that an affect space for body expressions can be used to improve the expressiveness of humanoid robots.

The concepts of ambiguity and deficiency for a given bijection on a finite Abelian group were recently introduced [13]. In this work we investigate the ambiguity and deficiency of some well-known polynomials which satisfy Dn(x+y, xy) = xn+ynfor every x, y ϵ Fqand n ϵ N, as well as linearized polynomials and Dembowski-Ostrom polynomials (DO polynomials). For some specific values of n (related to q) these polynomials generate permutations on Fq. We derive explicitly the ambiguity and deficiency of some of them. Numerical results on the ambiguity and deficiency of the others are also provided. Some of these polynomials are almost perfect nonlinear (APN) functions.

We introduce the concepts of weighted ambiguity and deficiency for a mapping between two finite Abelian groups of the same size. Then, we study the optimum lower bounds of these measures for permutations of an Abelian group. A construction of permutations, by modifying some permutation functions over finite fields, is given. Their ambiguity and deficiency is investigated; most of these functions are APN permutations. We show that, when they are not optimal, the Möbius function in the multiplicative group of \BBFqis closer to being optimal in ambiguity than the inverse function in the additive group of \BBFq. We note that the inverse function over \BBF28is used in AES. Finally, we conclude that a twisted permutation polynomial of a finite field is again closer to being optimal in ambiguity than the APN function employed in the SAFER cryptosystem.

In this paper, we define and study error locating arrays (ELAs), which can be used in software testing for locating faulty interactions among parameters or components in a system. We give constructions of ELAs for arbitrary strength t, based on covering arrays. We show that the number of tests given by ELAs grows as $O(\log k)$, where k is the number of parameters/components in the system, assuming other quantities (the number g of values per parameter, the strength t of faulty interactions, and the number d of faulty interactions) are bounded by a constant. We then give a series of results for the case of pairwise interactions ($t=2$). We study the computational complexity of deciding whether a graph describing the faulty pairwise interactions is “locatable.” We characterize the locatable graphs for the binary case ($g=2$). We design and analyze efficient algorithms that locate errors under certain assumptions on the structure of the faulty pairwise interactions. Under the assumption of known “safe values,” our algorithm performs a number of tests that is polynomial in $\log k$ and d, where k is the number of parameters in the system and d is an upper bound on the number of faulty pairwise interactions. For the binary alphabet case, we provide an algorithm that does not require safe values and runs in expected polynomial time in $\log k$ whenever $d\in O(\log\log k)$.

Given a set V of active components in charge of a distributed execution, a storage scheme is a sequence B0, B1,..., Bb-1of subsets of V, where successive global states are recorded. The subsets, also called blocks, have the same size and are scheduled according to some fixed and cyclic calendar of b steps. During the ith step, block Biis selected. Each component takes a copy of its local state and sends it to one of the components in Bi, in such a way that each component stores (approximately) the same number of local states. Afterward, if a component of Bicrashes, all of its stored data is lost and the computation cannot continue. If there exists a block with no failed components in it, then a recent global state can be retrieved and the computation does not need to start over from the very beginning. The goal is to design storage schemes that tolerate as many crashes as possible, while trying to have each component participating in as few blocks as possible and, at the same time, working with large blocks (so that a component in a block stores a small number of local states). In this paper, several such schemes are described and compared in terms of these measures

A projection augmented model (PA model) is a type of projection based haptic augmented reality display. It consists of a real physical model, onto which a computer image is projected to create a realistic looking object. Users can physically touch the surface of a PA model with their bare hands, which has clear experiential value for the types of applications for which they are being developed. However, the majority of PA models are front-projected and do not provide haptic feedback for material properties (e.g. temperature and physical texture), which suggests a user's sense of object-presence will be reduced when this type of PA model is touched. (object-presence measures the subjective feeling that the object the PA model represents exists in a person's environment, as opposed to a white physical model and a projected computer image.) Alternatively, if people consider PA models to be essentially computer generated objects (i. e. it is the projected image that gives the 'dummy' physical model meaning), then the act of being able to touch computer generated information may increase object-presence. The empirical investigation reported in this paper found that object-presence was lower when this type of PA model was touched. The implications these results have for both PA models and other types of displays, are discussed.

This paper reports on a study that investigated the effect touching a projection augmented model, and interacting with it using a spatially-coincident device, has on the perception of size. It was found that touching increased the accuracy of size estimates, however interaction using a spatially-coincident device did not.