On optimal nonlinear associative recall

The problem of determining the nonlinear function (“blackbox”) which optimally associates (on given criteria) two sets of data is considered. The data are given as discrete, finite column vectors, forming two matricesX (“input”) andY (“output”) with the same numbers of columns and an arbitrary numbers of rows. An iteration method based on the concept of the generalized inverse of a matrix provides the polynomial mapping of degreek onX by whichY is retrieved in an optimal way in the least squares sense. The results can be applied to a wide class of problems since such polynomial mappings may approximate any continuous real function from the “input” space to the “output” space to any required degree of accuracy. Conditions under which the optimal estimate is linear are given. Linear transformations on the input key-vectors and analogies with the “whitening” approach are also discussed. Conditions of “stationarity” on the processes of whichX andY are assumed to represent a set of sample sequences can be easily introduced. The optimal linear estimate is given by a discrete counterpart of the Wiener-Hopf equation and, if the key-signals are noise-like, the holographic-like scheme of associative memory is obtained, as the optimal nonlinear estimator. The theory can be applied to the system identification problem. It is finally suggested that the results outlined here may be relevant to the construction of models of associative, distributed memory.     

Improving recall from an associative memory

The associative net as a model of biological associative memory is investigated. Calculating the output pattern retrieved from a partially connected associative net presented with noisy input cues involves several computations. This is complicated by variations in the dendritic sums of the output units due to errors in the cue and differences in input activity and unit usage. The possible implementation of these computations by biological neural machinery is unclear. We demonstrate that a relatively simple transformation can reduce variation in the dendritic sums. This leads to a winners-take-all type of strategy that produces increased recall performance which is equivalent to the more complicated optimal strategy proposed by others. We describe in detail the possible biological implications of our strategies, the novel feature of which ascribes a role to the NMDA and non-NMDA channels found in hippocampal pyramidal cells. Received: 13 April 1994 / Accepted: 25 October 1994     

Design of general bidirectional associative memories with improved recall capability

The concept of qth order Hamming ball for general bidirectional associative memories (GBAMs) is presented, which results in an enhanced recall capability. A technique based on the minimum overlap algorithm (MOA) is proposed to deal with the separability problem of the qth order Hamming balls. Simulation results show that the recall capability obtained by using the proposed method is indeed larger than that obtained by using the conventional method.     

On associative memory

The information storing capacity of certain associative and auto-associative memories is calculated. For example, in a 100×100 matrix of 1 bit storage elements more than 6,500 bits can be stored associatively, and more than 688,000 bits in a 1,000×1,000 matrix. Asymptotically, the storage capacity of an associative memory increases proportionally to the number of storage elements. The usefulness of associative memories, as opposed to conventional listing memories, is discussed — especially in connection with brain modelling.     

Balanced dopamine is critical for pattern completion during associative memory recall

Pattern completion, the ability to retrieve complete memories initiated by partial cues, is a critical feature of the memory process. However, little is known regarding the molecular and cellular mechanisms underlying this process. To study the role of dopamine in memory recall, we have analyzed dopamine transporter heterozygous knockout mice (DAT(+/-)), and found that while these mice possess normal learning, consolidation, and memory recall under full cue conditions, they exhibit specific deficits in pattern completion under partial cue condition. This form of memory recall deficit in the dopamine transporter heterozygous knockout mice can be reversed by a low dose of the dopamine antagonist haloperidol, further confirming that the inability to retrieve memory patterns is a result of dopamine imbalance. Therefore, our results reveal that a delicate control of the brain's dopamine level is critical for pattern completion during associative memory recall.     

NMDA receptors are not required for pattern completion during associative memory recall

Pattern completion, the ability to retrieve complete memories initiated by subsets of external cues, has been a major focus of many computation models. A previously study reports that such pattern completion requires NMDA receptors in the hippocampus. However, such a claim was derived from a non-inducible gene knockout experiment in which the NMDA receptors were absent throughout all stages of memory processes as well as animal's adult life. This raises the critical question regarding whether the previously described results were truly resulting from the requirement of the NMDA receptors in retrieval. Here, we have examined the role of the NMDA receptors in pattern completion via inducible knockout of NMDA receptors limited to the memory retrieval stage. By using two independent mouse lines, we found that inducible knockout mice, lacking NMDA receptor in either forebrain or hippocampus CA1 region at the time of memory retrieval, exhibited normal recall of associative spatial reference memory regardless of whether retrievals took place under full-cue or partial-cue conditions. Moreover, systemic antagonism of NMDA receptor during retention tests also had no effect on full-cue or partial-cue recall of spatial water maze memories. Thus, both genetic and pharmacological experiments collectively demonstrate that pattern completion during spatial associative memory recall does not require the NMDA receptor in the hippocampus or forebrain.     

Identifying optimal incomplete phylogenetic data sets from sequence databases

We introduce a new method for identifying optimal incomplete data sets from large sequence databases based on the graph theoretic concept of alpha-quasi-bicliques. The quasi-biclique method searches large sequence databases to identify useful phylogenetic data sets with a specified amount of missing data while maintaining the necessary amount of overlap among genes and taxa. The utility of the quasi-biclique method is demonstrated on large simulated sequence databases and on a data set of green plant sequences from GenBank. The quasi-biclique method greatly increases the taxon and gene sampling in the data sets while adding only a limited amount of missing data. Furthermore, under the conditions of the simulation, data sets with a limited amount of missing data often produce topologies nearly as accurate as those built from complete data sets. The quasi-biclique method will be an effective tool for exploiting sequence databases for phylogenetic information and also may help identify critical sequences needed to build large phylogenetic data sets.     

On the non-existence of an optimal migration rate

 We show that an optimal migration rate may not exist in a population distributed over an infinite number of individual living sites if empty sites occur. This is the case when the mean number of offspring per individual μ is finite. We make the assumption of uniform migration to other sites whose rate is determined by the parent’s genotype or the offspring’s genotype at a single locus in a diploid hermaphrodite population undergoing random mating. In both cases, for μ small enough, any population at fixation would go to extinction. Moreover, in the latter case, for intermediate values of μ, the only fixation state that could resist the invasion of any mutant would lead the population to extinction. These are the two conditions for the non-existence of an optimal migration rate. They become less stringent as the cost for migration expressed by a coefficient of selection 1−β becomes larger, that is, closer to 1. The results are obtained assuming that the allele at fixation is either nondominant or dominant. Although the optimal migration rate is the same in both cases when it exists, the optimality properties may differ. Received 14 December 1995; received in revised form 5 April 1996     

Visual homing using an associative memory

Homing is the process by which an autonomous system guides itself to a particular location on the basis of sensory input. In this paper, a method of visual homing using an associative memory based on a simple pattern classifier is described. Homing is accomplished without the use of an explicit world model by utilizing direct associations between learned visual patterns and system motor commands. The method is analyzed in terms of a pattern space and conditions obtained that allow the system performance to be predicted on the basis of statistical measurements on the environment. Results of experiments utilizing the method to guide a robot-mounted camera in a three-dimensional environment are presented.     

On the storage capacity of an associative memory with randomly distributed storage elements

In an associative memory with randomly distributed storage elements at least 0.05 bit per storage element can be stored.     

Remembering visual motion: neural correlates of associative plasticity and motion recall in cortical area MT

The pictorial content of visual memories recalled by association is embodied by neuronal activity at the highest processing stages of primate visual cortex. This activity is elicited by top-down signals from the frontal lobe and recapitulates the bottom-up pattern normally obtained by the recalled stimulus. To explore the generality and mechanisms of this phenomenon, we recorded motion-sensitive neurons at an early stage of cortical processing. After monkeys learned to associate directions of motion with static shapes, these neurons exhibited unprecedented selectivity for the shapes. This emergent shape selectivity reflects activation of neurons representing the motion stimuli recalled by association, and it suggests that recall-related activity may be a general feature of neurons in visual cortex.     

Experimental influenza caused by an incomplete form of the agent]

Incomplete form of the influenza virus obtained in accordance with Nayak's method was administered intranasally to mice CBA and C57BL. From the lung tissue of the infected mice the causative agent could be isolated for 45 days, and from the other internal organs--the first hours after the infection only. In morphological investigation of the lungs of animals infected with an incomplete form of the influenza virus a prevalence of the proliferative component against the background of inflammatory changes was noted. Three months after the infection limited lymphoid formations consisting of monomorphic cells with hyperchromic nuclei were defined in the lung tissue. Marked proliferation of the alveolar and bronchial epithelium was observed later; considerable anaplasia of the cells was noted in the papillomatous structure of the alveolar and bronchial epithelium. Glomangioma of the mesentery was observed among affections of other internal organs in 18.7% of mice CBA.     

Host range limitation caused by incomplete host regulation in an aphid parasitoid

Defining host ranges in parasitoid insects is important both from a theoretical and an applied point of view. Based on the literature, some species seem able to use a wide range of hosts, while field studies indicate possible local host specialization. In koinobiont endoparasitoid species, such specialization could involve physiological processes. We tested the ability of two strains of the cosmopolitan and polyphagous parasitoid Diaeretiella rapae, to develop in three of its recorded aphid host species. Both strains produced high parasitism rates on the cabbage aphid Brevicoryne brassicae and the green peach aphid Myzus persicae but almost no progeny on the cherry-oat aphid Rhopalosiphum padi. This last species was less attacked by female parasitoids. Moreover, parasitoid eggs and larvae were smaller than in the two other host aphid species and their development was delayed. This abnormal development appeared to be due to an incomplete host regulation process, probably related to the low number and the size of teratocytes produced by D. rapae in R. padi individuals. Such a failure as far as gaining control of the host's metabolism is concerned could play an important role in shaping the host range of parasitoid insects, leading to local variation of the host spectrum in populations from various geographical areas.     

On optimal predator search

Search tactics are explored for animals hunting randomly distributed prey in two-dimensional habitats. The predator chooses between two modes of search: continuous travel and alternating pause-travel. A model based on renewal processes is derived for the predator's net rate of energy intake. The model is used to explore the optimal mode of search, search height, pause duration (“giving-up time”) and move length. Energy expenditure for search is assumed to increase from perchtravel over continuous travel to hover-travel. Prey detectability is assumed to be higher for the pausing than for the travelling predator. The following predictions emerge: The relative merits of the different search modes are mainly determined by the relative magnitudes of energy consumption rates and prey detection efficiencies at pausing and travelling. The energetically cheaper among two search modes reaches its highest relative merit at low prey density and detectability. As either increases, a more expensive search tactic may become superior. If the rate of energy expenditure increases considerably at locomotion, pause-travel tactics may be superior to continuous travel. This requires that the search can be performed from sufficient height, because net energy gain decreases rapidly below the optimum search height. It is greater for pause-travel than for continuous travel, and it increases slightly with decreasing prey density, and markedly with increasing prey detectability. With perch-travel or hover-travel tactics, the optimal giving-up time decreases with increasing prey density and detectability. The optimal move length increases with detectability. Empirical evidence coincides qualitatively with several predictions. Possibilities for further tests of the model are discussed, as are observed behavioural and morphological features on which the search model may shed light.     

An algebraic model of an associative noise-like coding memory

A mathematical model of an associative memory is presented, sharing with the optical holography memory systems the properties which establish an analogy with biological memory. This memory system-developed from Gabor's model of memoryis based on a noise-like coding of the information by which it realizes a distributed, damage-tolerant, equipotential storage through simultaneous state changes of discrete substratum elements. Each two associated items being stored are coded by each other by means of two noise-like patterns obtained from them through a randomizing preprocessing. The algebraic braic transformations operating the information storage and retrieval are matrix-vector products involving Toeplitz type matrices. Several noise-like coded memory traces are superimposed on a common substratum without crosstalk interference; moreover, extraneous noise added to these memory traces does not injure the stored information. The main performances shown by this memory model are: i) the selective, complete recovering of stored information from incomplete keys, both mixed with extraneous information and translated from the position learnt; ii) a dynamic recollection where the information just recovered acts as a new key for a sequential retrieval process; iii) context-dependent responses. The hypothesis that the information is stored in the nervous system through a noise-like coding is suggested. The model has been simulated on a digital computer using bidimensional images.     

Modeling the acquisition of counting with an associative network

In the acquision of counting by children, there are three interesting phenomena (Fuson et al. 1982): (1) the number word sequence produced by children can be divided into three distinct portions, called the conventional, stable nonconventional, and unstable portions; (2) irregular number words such as fifteen are omitted more often than regular ones such as fourteen, sixteen, and seventeen; and (3) initially the number word sequence is in a recitation form, rather than in the form of an associative chain of separable serial elements. Our paper at first analyzes these phenomena from the viewpoint of associative memory by assuming the number word sequences are made up of many associative relationships between the number words. This assumption is not contradictory to the third phenomenon described above, because the associative relationships are not confined only to those between the serial number words. On the basis of these anaylses, an associative network model, HAPS proposed by one of the authors (Hirai 1983), is extended so that it can mimic some aspects of the learning of sequence which involves the above three phenomena. The learning and production of sequence by the network are simulated on a digital computer, and the results show that the three phenomena can be observed in the performance of the network.     

Linking neuronal ensembles by associative synaptic plasticity

Synchronized activity in ensembles of neurons recruited by excitatory afferents is thought to contribute to the coding information in the brain. However, the mechanisms by which neuronal ensembles are generated and modified are not known. Here we show that in rat hippocampal slices associative synaptic plasticity enables ensembles of neurons to change by incorporating neurons belonging to different ensembles. Associative synaptic plasticity redistributes the composition of different ensembles recruited by distinct inputs such as to specifically increase the similarity between the ensembles. These results show that in the hippocampus, the ensemble of neurons recruited by a given afferent projection is fluid and can be rapidly and persistently modified to specifically include neurons from different ensembles. This linking of ensembles may contribute to the formation of associative memories.