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Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations, which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.

The paper deals with the recognition of symmetric three-dimensional (3D) bodies that can be rotated and translated. We provide a complete list of all existing combinations of rotation and reflection symmetries in 3D. We define 3D complex moments by means of spherical harmonics, and the influence of individual symmetry groups on complex moment values is studied. Each particular symmetry pre-defines certain moment values. These moments can no longer differentiate between two objects of the same symmetry, which decreases the recognition power of the feature set. They should not be included when constructing the invariants. Translation and rotation invariants up to the fourth order are presented and their performance is studied on both artificial and real data.

Improvements in networking technologies have provided users with useful information services. Such information services may bring convenience and efficiency, but might be accompanied by vulnerabilities to a variety of attacks. Therefore, a variety of research to enhance the security of the systems and get the services at the same time has been carried out. Especially, research on intrusion-tolerant systems (ITSs) has been conducted in order to survive against every intrusion, rather than to detect and prevent them. In this paper, an ITS based on effective resource conversion (ERC) is presented to achieve the goal of intrusion-tolerance. Instead of using the fixed number of virtual machines (VMs) to process requests and recover as in conventional approaches, the ITS based on ERC can transform the assigned resources depending on the system status. This scheme is proved to maintain a certain level of quality of service (QoS) and quality of security service (QoSS) in threatening environments. The performance of ERC is compared with previous studies on ITS by CSIM 20, and it is verified that the proposed scheme is more effective in retaining a specific level of QoS and QoSS.

In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of existing self-motions. Finally, we determine a new set of PSHs, which have so-called generalized Dietmaier self-motions. We close the paper with some comments on the self-mobility of hexapods with global/local symmetries.

Recently, due to the introduction of NFC (Near Field Communication), it has become possible to make easy electronic payments. Therefore, a secure communication method is necessary in these environments. NFC can be said to be relatively safe compared to other communication methods, because it carries out communications within 10 cm. However, it has made possible the risk of impersonation attacks by a disguised reader, leaving user information on the reader. In order to solve these problems, in this paper, we propose an authentication scheme that can reduce the weight of computation by using only a hash function and XOR (eXclusive OR) operation algorithms. This paper also shows that our method is safe, since it leaves no information with the other party.

Here we report on the issue of Advanced Persistent Threats (APT), which use malware for the purpose of leaking the data of large corporations and government agencies. APT attacks target systems continuously by utilizing intelligent and complex technologies. To overthrow the elaborate security network of target systems, it conducts an attack after undergoing a pre-reconnaissance phase. An APT attack causes financial loss, information leakage, etc. They can easily bypass the antivirus system of a target system. In this paper, we propose a Multi-Layer Defense System (MLDS) that can defend against APT. This system applies a reinforced defense system by collecting and analyzing log information and various information from devices, by installing the agent on the network appliance, server and end-user. It also discusses how to detect an APT attack when one cannot block the initial intrusion while continuing to conduct other activities. Thus, this system is able to minimize the possibility of initial intrusion and damages of the system by promptly responding through rapid detection of an attack when the target system is attacked.

Long-Term Evolution (LTE) is a fourth-generation mobile communication technology implemented throughout the world. It is the communication means of smartphones that send and receive all of the private date of individuals. M2M, IOT, etc., are the base technologies of mobile communication that will be used in the future cyber world. However, identification parameters, such as International Mobile Subscriber Identity (IMSI), Radio Network Temporary Identities (RNTI), etc., in the initial attach section for accessing the LTE network are presented with the vulnerability of being exposed as clear text. Such vulnerability does not end in a mere identification parameter, but can lead to a secondary attack using the identification parameter, such as replication of the smartphone, illegal use of the mobile communication network, etc. This paper proposes a security protocol to safely transmit identification parameters in different cases of the initial attach. The proposed security protocol solves the exposed vulnerability by encrypting the parameters in transmission. Using an OPNET simulator, it is shown that the average rate of delay and processing ratio are efficient in comparison to the existing process.

This paper aims to construct conservation laws for a Benjamin–Bona–Mahony equation with variable coefficients, which is a third-order partial differential equation. This equation does not have a Lagrangian and so we transform it to a fourth-order partial differential equation, which has a Lagrangian. The Noether approach is then employed to construct the conservation laws. It so happens that the derived conserved quantities fail to satisfy the divergence criterion and so one needs to make adjustments to the derived conserved quantities in order to satisfy the divergence condition. The conservation laws are then expressed in the original variable. Finally, a conservation law is used to obtain exact solution of a special case of the Benjamin–Bona–Mahony equation.

Pyranoindolizine is a tricyclic structure found in various biologically active compounds, such as camptothecin (CPT) and its derivatives. In the case of CPTs, the chirality at the α-position in the α-hydroxyl lactone moiety of pyranoindolizine is important for the antitumor activity. This paper deals with enantioselective oxidation of the α-position in pyranoindolizine lactone, which corresponds at C20 in CPT, with cumene hydroperoxide (CHP) in the presence of newly synthesized guanidine-bisurea bifunctional organocatalysts bearing chirality on both the inner and outer sides of the urea groups.

Machine learning is a very important approach to pattern classification. This paper provides a better insight into Incremental Attribute Learning (IAL) with further analysis as to why it can exhibit better performance than conventional batch training. IAL is a novel supervised machine learning strategy, which gradually trains features in one or more chunks. Previous research showed that IAL can obtain lower classification error rates than a conventional batch training approach. Yet the reason for that is still not very clear. In this study, the feasibility of IAL is verified by mathematical approaches. Moreover, experimental results derived by IAL neural networks on benchmarks also confirm the mathematical validation.

The idea of construction of twin buildings is as old as architecture itself, and yet there is hardly any study emphasizing their specificity. Most frequently there are two objects or elements in an architectural composition of “twins” in which there may be various symmetry relations, mostly bilateral symmetries. The classification of “twins” symmetry in this paper is based on the existence of bilateral symmetry, in terms of the perception of an observer. The classification includes both, 2D and 3D perception analyses. We start analyzing a pair of twin buildings with projection of the architectural composition elements in 2D picture plane (plane of the composition) and we distinguish four 2D keyframe cases based on the relation between the bilateral symmetry of the twin composition and the bilateral symmetry of each element. In 3D perception for each 2D keyframe case there are two sub-variants, with and without a symmetry plane parallel to the picture plane. The bilateral symmetry is dominant if the corresponding symmetry plane is orthogonal to the picture plane. The essence of the complete classification is relation between the bilateral (dominant) symmetry of the architectural composition and the bilateral symmetry of each element of that composition.

This paper describes the case study of applying projection-based augmented reality, especially for dynamic objects in live performing shows, such as plays, dancing, or musicals. Our study aims to project imagery correctly inside the silhouettes of flexible objects, in other words, live actors or the surface of actor’s costumes; the silhouette transforms its own shape frequently. To realize this work, we implemented a special projection system based on the real-time masking technique, that is to say real-time projection-based augmented reality system for dynamic objects in performing arts. We installed the sets on a stage for live performance, and rehearsed particular scenes of a musical. In live performance, using projection-based augmented reality technology enhances technical and theatrical aspects which were not possible with existing video projection techniques. The projected images on the surfaces of actor’s costume could not only express the particular scene of a performance more effectively, but also lead the audience to an extraordinary visual experience.

Numerous studies are currently being carried out on personalized services based on data analysis to find and provide valuable information about information overload. Furthermore, the number of studies on data analysis of teaching-learning activities for personalized services in the field of teaching-learning is increasing, too. This paper proposes a learning style recency-frequency-durability (LS-RFD) model for quantified analysis on the level of activities of learners, to provide the elements of teaching-learning activities according to the learning style of the learner among various parameters for personalized service. This is to measure preferences as to teaching-learning activity according to recency, frequency and durability of such activities. Based on the results, user characteristics can be classified into groups for teaching-learning activity by categorizing the level of preference and activity of the learner.

In cloud computing environments, user data are encrypted using numerous distributed servers before storing such data. Global Internet service companies, such as Google and Yahoo, recognized the importance of Internet service platforms and conducted self-research and development to create and utilize large cluster-based cloud computing platform technology based on low-priced commercial nodes. As diverse data services become possible in distributed computing environments, high-capacity distributed management is emerging as a major issue. Meanwhile, because of the diverse forms of using high-capacity data, security vulnerability and privacy invasion by malicious attackers or internal users can occur. As such, when various sensitive data are stored in cloud servers and used from there, the problem of data spill might occur because of external attackers or the poor management of internal users. Data can be managed through encryption to prevent such problems. However, existing simple encryption methods involve problems associated with the management of access to data stored in cloud environments. Therefore, in the present paper, a technique for data access management by user authority, based on Attribute-Based Encryption (ABE) and secret distribution techniques, is proposed.

Two principal methods are commonly employed for the estimation of developmental instability at the population level. Some studies use variances of morphological traits (σ2p), while others use fluctuating asymmetry (FA). In both cases, differences in the degree of developmental instability can be tested with an F-test, which is the most common way to compare variances. However, the variance is expected to scale proportionally to the square of the mean as there is a tendency in biological data for σ2p to scale proportionally to the square of the mean ( ): σ2p = Z ξ, where ξ is the scaling exponent, which is expected to be two for pure statistical reasons, is the mean of the trait and Z is a measure of individual-level variability. Because of this scaling effect, the fluctuating asymmetry will be affected, FA is estimated as the variance between the right and the left sides of a trait (σ2r − l = σ2r + σ2l − 2rσrσl), where σ2r and σ2l are the variances of the right and the left trait values, respectively. In this paper, we propose a novel method that allows an exact correction of the scaling effect, which will enable a proper comparison of the degree of fluctuating asymmetry for a trait. The problem of the scaling of the FA with the trait size is quite crucial if FA is to be considered an indicator of fitness or an indicator of environmental or genetic stress, as different stresses or fitness levels are typically accompanied by a change of the traits’ .

In order to prevent drug abuse or misuse cases and avoid over-prescriptions, it is necessary for medicine taker to be provided with detailed information about the medicine. In this paper, we propose a drug information system and develop an application to provide information through drug image recognition using a smartphone. We designed a contents-based drug image search algorithm using the color, shape and imprint of drug. Our convenient application can provide users with detailed information about drugs and prevent drug misuse.

Key-frame extracting technology has been widely used in the field of human motion synthesis. Efficient and accurate key frames extraction methods can improve the accuracy of motion synthesis. In this paper, we use an optimized t-Stochastic Neighbor Embedding (t-SNE for short) algorithm to reduce the data and on this basis extract the key frames. The experimental results show that the validity of this method is better than the existing methods under the same experimental data.

In this paper we present a novel unsupervised approach to detecting and segmenting objects as well as their constituent symmetric parts in an image. Traditional unsupervised image segmentation is limited by two obvious deficiencies: the object detection accuracy degrades with the misaligned boundaries between the segmented regions and the target, and pre-learned models are required to group regions into meaningful objects. To tackle these difficulties, the proposed approach aims at incorporating the pair-wise detection of symmetric patches to achieve the goal of segmenting images into symmetric parts. The skeletons of these symmetric parts then provide estimates of the bounding boxes to locate the target objects. Finally, for each detected object, the graphcut-based segmentation algorithm is applied to find its contour. The proposed approach has significant advantages: no a priori object models are used, and multiple objects are detected. To verify the effectiveness of the approach based on the cues that a face part contains an oval shape and skin colors, human objects are extracted from among the detected objects. The detected human objects and their parts are finally tracked across video frames to capture the object part movements for learning the human activity models from video clips. Experimental results show that the proposed method gives good performance on publicly available datasets.

The paper presents the group theory of optimally-localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all of the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into optimally-localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M or to a subgroup of G or M. In this context, the paper considers usual, as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors (Ekkehard Krüger) in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the optimally-localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly-correlated localized electrons makes clear predictions of whether or not the system can possess superconducting or magnetic eigenstates.

Future communication networks would be required to deliver data on a far greater scale than is known to us today, thus mandating the maximal utilization of the available radio spectrum using cognitive radios. In this paper, we have proposed a novel cooperative spectrum sensing approach for cognitive radios. In cooperative spectrum sensing, the fusion center relies on reports of the cognitive users to make a global decision. The global decision is obtained by assigning weights to the reports received from cognitive users. Computation of such weights requires prior information of the probability of detection and the probability of false alarms, which are not readily available in real scenarios. Further, the cognitive users are divided into reliable and unreliable categories based on their weighted energy by using some empirical threshold. In this paper, we propose a method to classify the cognitive users into reliable, neutral and unreliable categories without using any pre-defined or empirically-obtained threshold. Moreover, the computation of weights does not require the detection, or false alarm probabilities, or an estimate of these probabilities. Reliable cognitive users are assigned the highest weights; neutral cognitive users are assigned medium weights (less than the reliable and higher than the unreliable cognitive users’ weights); and unreliable users are assigned the least weights. We show the performance improvement of our proposed method through simulations by comparing it with the conventional cooperative spectrum sensing scheme through different metrics, like receiver operating characteristic (ROC) curve and mean square error. For clarity, we also show the effect of malicious users on detection probability and false alarm probability individually through simulations.

We present three types of polyhedral surfaces, which are continuously flexible and have not only an initial pose, where all faces are coplanar, but pass during their self-motion through another pose with coplanar faces (“flat pose”). These surfaces are examples of so-called rigid origami, since we only admit exact flexions, i.e., each face remains rigid during the motion; only the dihedral angles vary. We analyze the geometry behind Miura-ori and address Kokotsakis’ example of a flexible tessellation with the particular case of a cyclic quadrangle. Finally, we recall Bricard’s octahedra of Type 3 and their relation to strophoids.

At the center of core technologies for a future cyber world, such as Internet of Things (IoT) or big data, is a context-rich system that offers services by using situational information. The field where context-rich systems were first introduced is near-field communication (NFC)-based electronic payments. Near-field Communication (NFC) integrated payment services collect the payment information of the credit card and the location information to generate patterns in the user’s consumption or movement through big data technology. Based on such pattern information, tailored services, such as advertisement, are offered to users. However, there is difficulty in controlling access to personal information, as there is a collaborative relationship focused on the trusted service manager (TSM) that is close knit to shared personal information. Moreover, in the case of Hadoop, among the many big data analytical technologies, it offers access control functions, but not a way to authorize the processing of personal information, making it impossible to grant authority between service providers to process information. As such, this paper proposes a key generation and distribution method, as well as a secure communication protocol. The analysis has shown that the efficiency was greater for security and performance compared to relation works.

In this paper, we study a generalized Zakharov–Kuznetsov equation in three variables, which has applications in the nonlinear development of ion-acoustic waves in a magnetized plasma. Conservation laws for this equation are constructed for the first time by using the new conservation theorem of Ibragimov. Furthermore, new exact solutions are obtained by employing the Lie symmetry method along with the simplest equation method.

Recently, the hospital information system environment using IT communication technology and utilization of medical information has been increasing. In the medical field, the medical information system only supports the transfer of patient information to medical staff through an electronic health record, without information about patient status. Hence, it needs a method of real-time monitoring for the patient. Also, in this environment, a secure method in approaching healthcare through various smart devices is required. Therefore, in this paper, in order to classify the status of the patients, we propose a dynamic approach of the medical information system in a hospital information environment using the dynamic access control method. Also, we applied the symmetric method of AES (Advanced Encryption Standard). This was the best encryption algorithm for sending and receiving biological information. We can define usefulness as the dynamic access application service based on the final result of the proposed system. The proposed system is expected to provide a new solution for a convenient medical information system.

In order to recognize outstanding papers that have been published in Symmetry, the Editorial Board established an annual “Symmetry Best Paper Award”. We are pleased to announce the first “Symmetry Best Paper Award” for 2015. Nominations were selected by the Editorial Board Office, with all research articles published in 2013 and 2014 eligible for consideration. Following review and voting by the Symmetry Best Paper Award Committee, the following three papers have won Symmetry Best Paper Awards for 2015:

Virtual simulation technology has been considered as a highly efficient and cost-effective solution for a soldier training system, and evolved into diverse combinations of hardware and software. To maximize the virtual reality effect within a restricted space, a locomotion interface such as an omni-directional treadmill is introduced as a major component of a virtual simulator, therefore real time interaction between human and the virtual simulator becomes very important. Displacement and heading changes of the trainee are crucial information to control the virtual simulator when we implement highly reactive motion control for the omni-directional treadmill and interaction control of the virtual contents. This paper proposes a control parameter estimation algorithm for the virtual training simulator by using two types of motion capture sensors and presents the experimental results. Kinematic joint positions are analyzed to estimate the trainee’s location and velocity for feedback and feedforward control of the omni-directional treadmill. The accuracy of two approaches is evaluated by comparing with the reference system, which gives a ground truth value.

This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges and internal symmetries provide a plethora of information as to further symmetries of the Lagrangian. Several of these symmetries are calculated to second order. It is hoped that investigations such as these may yield avenues to help solve the auxiliary field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2 Fayet-Hypermultiplet, without using an infinite number of auxiliary fields.

This paper presents a novel hierarchical clustering method using support vector machines. A common approach for hierarchical clustering is to use distance for the task. However, different choices for computing inter-cluster distances often lead to fairly distinct clustering outcomes, causing interpretation difficulties in practice. In this paper, we propose to use a one-class support vector machine (OC-SVM) to directly find high-density regions of data. Our algorithm generates nested set estimates using the OC-SVM and exploits the hierarchical structure of the estimated sets. We demonstrate the proposed algorithm on synthetic datasets. The cluster hierarchy is visualized with dendrograms and spanning trees.

Big data refers to informationalization technology for extracting valuable information through the use and analysis of large-scale data and, based on that data, deriving plans for response or predicting changes. With the development of software and devices for next generation sequencing, a vast amount of bioinformatics data has been generated recently. Also, bioinformatics data based big-data technology is rising rapidly as a core technology by the bioinformatician, biologist and big-data scientist. KEGG pathway is bioinformatics data for understanding high-level functions and utilities of the biological system. However, KEGG pathway analysis requires a lot of time and effort because KEGG pathways are high volume and very diverse. In this paper, we proposed a network analysis and visualization system that crawl user interest KEGG pathways, construct a pathway network based on a hierarchy structure of pathways and visualize relations and interactions of pathways by clustering and selecting core pathways from the network. Finally, we construct a pathway network collected by starting with an Alzheimer’s disease pathway and show the results on clustering and selecting core pathways from the pathway network.

Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schrödinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schrödinger–Hirota–Maxwell–Bloch equations, along with their Lax pairs.

This research is a natural continuation of the recent paper “Exact solutions of the simplified Keller–Segel model” (Commun Nonlinear Sci Numer Simulat 2013, 18, 2960–2971). It is shown that a (1+2)-dimensional Keller–Segel type system is invariant with respect infinite-dimensional Lie algebra. All possible maximal algebras of invariance of the Neumann boundary value problems based on the Keller–Segel system in question were found. Lie symmetry operators are used for constructing exact solutions of some boundary value problems. Moreover, it is proved that the boundary value problem for the (1+1)-dimensional Keller–Segel system with specific boundary conditions can be linearized and solved in an explicit form.

In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597), (2013, J. Math. Phys. 54, 072901), where the extended Lie symmetry analysis is performed in the Fourier space. Here, we introduce a method to perform the extended Lie symmetry analysis in the physical space where we have to deal with the transformation of the integration variable in the appearing integral terms. The method is based on the transformation of the product y(x)dx appearing in the integral terms and applied to the functional formulation of the viscous Burgers equation. The extended Lie symmetry analysis furnishes all known symmetries of the viscous Burgers equation and is able to provide new symmetries associated with the Hopf formulation of the viscous Burgers equation. Hence, it can be employed as an important tool for applications in continuum mechanics.

In this paper we propose a novel algorithm that enables online actions segmentation and classification. The algorithm enables segmentation from an incoming motion capture (MoCap) data stream, sport (or karate) movement sequences that are later processed by classification algorithm. The segmentation is based on Gesture Description Language classifier that is trained with an unsupervised learning algorithm. The classification is performed by continuous density forward-only hidden Markov models (HMM) classifier. Our methodology was evaluated on a unique dataset consisting of MoCap recordings of six Oyama karate martial artists including multiple champion of Kumite Knockdown Oyama karate. The dataset consists of 10 classes of actions and included dynamic actions of stands, kicks and blocking techniques. Total number of samples was 1236. We have examined several HMM classifiers with various number of hidden states and also Gaussian mixture model (GMM) classifier to empirically find the best setup of the proposed method in our dataset. We have used leave-one-out cross validation. The recognition rate of our methodology differs between karate techniques and is in the range of 81% ± 15% even to 100%. Our method is not limited for this class of actions but can be easily adapted to any other MoCap-based actions. The description of our approach and its evaluation are the main contributions of this paper. The results presented in this paper are effects of pioneering research on online karate action classification.

Aiming to effectively recognize train center plate bolt loss faults, this paper presents an improved fault detection method. A multi-scale local binary pattern operator containing the local texture information of different radii is designed to extract more efficient discrimination information. An improved teaching-learning-based optimization algorithm is established to optimize the classification results in the decision level. Two new phases including the worst recombination phase and the cuckoo search phase are incorporated to improve the diversity of the population and enhance the exploration. In the worst recombination phase, the worst solution is updated by a crossover recombination operation to prevent the premature convergence. The cuckoo search phase is adopted to escape the local optima. Experimental results indicate that the recognition accuracy is up to 98.9% which strongly demonstrates the effectiveness and reliability of the proposed detection method.

This paper addresses the problem of computing the family of two-filiform Lie algebra laws of dimension nine using three Lie algebra properties converted into matrix form properties: Jacobi identity, nilpotence and quasi-filiform property. The interest in this family is broad, both within the academic community and the industrial engineering community, since nilpotent Lie algebras are applied in traditional mechanical dynamic problems and current scientific disciplines. The conditions of being quasi-filiform and nilpotent are applied carefully and in several stages, and appropriate changes of the basis are achieved in an iterative and interactive process of simplification. This has been implemented by means of the development of more than thirty Maple modules. The process has led from the first family formulation, with 64 parameters and 215 constraints, to a family of 16 parameters and 17 constraints. This structure theorem permits the exhaustive classification of the quasi-filiform nilpotent Lie algebras of dimension nine with current computational methodologies.

In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.

Asymmetry of brain function is known to be widespread amongst vertebrates, and it seems to have appeared very early in their evolution. In fact, recent evidence of functional asymmetry in invertebrates suggests that even small brains benefit from the allocation of different functions to the left and right sides. This paper discusses the differing functions of the left and right sides of the brain, including the roles of the left and right antennae of bees (several species) in both short- and long-term recall of olfactory memories and in social behaviour. It considers the likely advantages of functional asymmetry in small and large brains and whether functional asymmetry in vertebrates and invertebrates is analogous or homologous. Neural or cognitive capacity can be enhanced both by the evolution of a larger brain and by lateralization of brain function: a possible reason why both processes occur side-by-side is offered.