insights from a simple expression for linear fisher information in a recurrently connected population of spiking neurons a simple expression for a lower bound of fisher information is derived for a network of recurrently connected spiking neurons that have been driven to a noise perturbed steady state we call this lower bound linear fisher information as it corresponds to the fisher information that can be recovered by a locally optimal linear estimator unlike recent similar calculations the approach used here includes the effects of nonlinear gain functions and correlated input noise and yields a surprisingly simple and intuitive expression that offers substantial insight into the sources of information degradation across successive layers of a neural network here this expression is used to 1 compute the optimal i e information maximizing firing rate of a neuron 2 demonstrate why sharpening tuning curves by either thresholding or the action of recurrent connectivity is generally a bad idea 3 show how a single cortical expansion is sufficient to instantiate a redundant population code that can propagate across multiple cortical layers with minimal information loss and 4 show that optimal recurrent connectivity strongly depends on the covariance structure of the inputs to the network

definable relations and first order query languages over strings we study analogs of classical relational calculus in the context of strings we start by studying string logics taking a classical model theoretic approach we fix a set of string operations and look at the resulting collection of definable relations these form an algebra a class of n ary relations for every n closed under projection and boolean operations we show that by choosing the string vocabulary carefully we get string logics that have desirable properties computable evaluation and normal forms we identify five distinct models and study the differences in their model theory and complexity of evaluation we identify a subset of these models that have additional attractive properties such as finite vc dimension and quantifier elimination once you have a logic the addition of free predicate symbols gives you a string query language the resulting languages have attractive closure properties from a database point of view while sql does not allow the full composition of string pattern matching expressions with relational operators these logics yield compositional query languages that can capture common string matching queries while remaining tractable for each of the logics studied in the first part of the article we study properties of the corresponding query languages we give bounds on the data complexity of queries extend the normal form results from logics to queries and show that the languages have corresponding algebras expressing safe queries

electric discharge contour dynamics model the effects of curvature and finite conductivity in this paper we present the complete derivation of the effective contour model for electrical discharges which appears as the asymptotic limit of the minimal streamer model for the propagation of electric discharges when the electron diffusion is small it consists of two integro differential equations defined at the boundary of the plasma region one for the motion and a second equation for the net charge density at the interface we have computed explicit solutions with cylindrical symmetry and found the dispersion relation for small symmetry breaking perturbations in the case of finite resistivity we implement a numerical procedure to solve our model in general situations as a result we compute the dispersion relation for the cylindrical case and compare it with the analytical predictions comparisons with experimental data for a 2d positive streamers discharge are provided and predictions confirmed

the homomorphism problem for trace monoids it is proved to be decidable for any given finite subset f of x dependency alphabet y and mapping f y whether or not can be extended to a monoid homomorphism f m y this contrasts with the undecidability of the symmetric problem when we consider the dependency alphabet x instead some other particular cases of homomorphism and isomorphism problems among trace monoids are also discussed

output of a neuronal population code in the population coding framework we consider how the response distributions affect output distribution a general theory for the output of neuronal population code is presented when the spike train is a renewal process under a given condition on the response distribution the most probable value of the output distribution is the center of input preferred values whereas in the other cases the most improbable value of the output distribution is the center of input preferred values or there are no most probable states depending on the exact form of the response distributions the variance of the output distributions can either enlarge or reduce the tuning width of the tuning curves

radial fingering in a hele shaw cell a weakly nonlinear analysis abstract the saffman taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a hele shaw cell experiments in radial flow geometry form fan like patterns in which fingers of different lengths compete spread and split our weakly nonlinear analysis of the instability predicts these phenomena which are beyond the scope of linear stability theory finger competition arises through enhanced growth of sub harmonic perturbations while spreading and splitting occur through the growth of harmonic modes nonlinear mode coupling enhances the growth of these specific perturbations with appropriate relative phases as we demonstrate through a symmetry analysis of the mode coupling equations we contrast mode coupling in radial flow with rectangular flow geometry

how to decide continuity of rational functions on infinite words this paper presents a construction that computes the topological closure of a rational relation on infinite words besides showing that the closure is rational itself it also reduces the question of the continuity and the uniform continuity of a function to the question of the functionality of its closure which is known to be decidable in polynomial time

the equivalence problem of multitape finite automata abstract using a result of b h neumann we extend eilenberg s equality theorem to a general result which implies that the multiplicity equivalence problem of two nondeterministic multitape finite automata is decidable as a corollary we solve a long standing open problem in automata theory namely the equivalence problem for multitape deterministic finite automata the main theorem states that there is a finite test set for the multiplicity equivalence of finite automata over conservative monoids embeddable in a fully ordered group

multiscale codes in the nervous system the problem of noise correlations and the ambiguity of periodic scales encoding information about continuous variables using noisy computational units is a challenge nonetheless asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence of noise mathis herz and stemmler phys rev lett 109 018103 2012 indeed the cortex seems to use periodic multiscale grid codes to represent position accurately here we show how such codes can be read out without taking the long term limit even on short time scales the precision of such codes scales exponentially in the number n of neurons does this finding also hold for neurons that are not firing in a statistically independent fashion to assess the extent to which biological grid codes are subject to statistical dependences we first analyze the noise correlations between pairs of grid code neurons in behaving rodents we find that if the grids of two neurons align and have the same length scale the noise correlations between the neurons can reach values as high as 0 8 for increasing mismatches between the grids of the two neurons the noise correlations fall rapidly incorporating such correlations into a population coding model reveals that the correlations lessen the resolution but the exponential scaling of resolution with n is unaffected

wavelength selection in hele shaw flows a maximum amplitude criterion as in most interfacial flow problems the standard theoretical procedure to establish wavelength selection in the viscous fingering instability is to maximize the linear growth rate however there are important discrepancies between previous theoretical predictions and existing experimental data in this work we perform a linear stability analysis of the radial hele shaw flow system that takes into account the combined action of viscous normal stresses and wetting effects most importantly we introduce an alternative selection criterion for which the selected wavelength is determined by the maximum of the interfacial perturbation amplitude the effectiveness of such a criterion is substantiated by the significantly improved agreement between theory and experiments

synchronized rational relations of finite and infinite words abstract the purpose of this paper is a comprehensive study of a family of rational relations both of finite and infinite words namely those that are computable by automata where the reading heads move simultaneously on the n input tapes and that we thus propose to call synchronized rational relations

fisher information and temporal correlations for spiking neurons with stochastic dynamics population coding accuracy can be studied using fisher information here the fisher information and correlation functions are determined analytically for a network of coupled spiking neurons with a more general than poisson stochastic dynamics it is shown that stimulus driven temporal correlations between neurons always increase the fisher information whereas stimulus independent correlations need not do so additionally we find that for subthreshold stimuli there is some nonzero level of noise for which network coding is optimal we also find that the fisher information is larger for purely excitatory than for purely inhibitory networks but only in a limited range of values of synaptic coupling strengths in most cases the dependence of the fisher information on time is linear except for excitatory networks with strong synaptic couplings and for strong stimuli in the latter case this dependence shows two distinct regimes fast and slow for excitatory networks short term synaptic depression can improve the coding accuracy significantly whereas short term facilitation can lower the coding accuracy for inhibitory networks coding accuracy is insensitive to short term synaptic dynamics

representational accuracy of stochastic neural populations fisher information is used to analyze the accuracy with which a neural population encodes d stimulus features it turns out that the form of response variability has a major impact on the encoding capacity and therefore plays an important role in the selection of an appropriate neural model in particular in the presence of baseline firing the reconstruction error rapidly increases with d in the case of poissonian noise but not for additive noise the existence of limited range correlations of the type found in cortical tissue yields a saturation of the fisher information content as a function of the population size only for an additive noise model we also show that random variability in the correlation coefficient within a neural population as found empirically considerably improves the average encoding quality finally the representational accuracy of populations with inhomogeneous tuning properties either with variability in the tuning widths or fragmented into specialized subpopulations is superior to the case of identical and radially symmetric tuning curves usually considered in the literature

fundamental limits on persistent activity in networks of noisy neurons neural noise limits the fidelity of representations in the brain this limitation has been extensively analyzed for sensory coding however in short term memory and integrator networks where noise accumulates and can play an even more prominent role much less is known about how neural noise interacts with neural and network parameters to determine the accuracy of the computation here we analytically derive how the stored memory in continuous attractor networks of probabilistically spiking neurons will degrade over time through diffusion by combining statistical and dynamical approaches we establish a fundamental limit on the network s ability to maintain a persistent state the noise induced drift of the memory state over time within the network is strictly lower bounded by the accuracy of estimation of the network s instantaneous memory state by an ideal external observer this result takes the form of an information diffusion inequality we derive some unexpected consequences despite the persistence time of short term memory networks it does not pay to accumulate spikes for longer than the cellular time constant to read out their contents for certain neural transfer functions the conditions for optimal sensory coding coincide with those for optimal storage implying that short term memory may be co localized with sensory representation

on the decidability of the equivalence problem for partially commutative rational power series abstract starting from an idea of harju and karhumaki 1991 we prove the decidability of the equivalence problem for partially commutative power series and unambiguous rational sets of the free partially commutative monoids

the equal last letter predicate for words on infinite alphabets and classes of multitape automata we consider the first order theory of the free infinitely generated monoid with the usual predicates prefix and equal length along with the predicate equal last letter the associated definable relations are related to the algebras of relations recognized by different types of multitape automata which are natural extensions of the famous rabin scott multitape automata and the synchronous automata we investigate these classes of automata and solve decision issues concerning them

fuzzy spatial relation ontology for image interpretation the semantic interpretation of images can benefit from representations of useful concepts and the links between them as ontologies in this paper we propose an ontology of spatial relations in order to guide image interpretation and the recognition of the structures it contains using structural information on the spatial arrangement of these structures as an original theoretical contribution this ontology is then enriched by fuzzy representations of concepts which define their semantics and allow establishing the link between these concepts which are often expressed in linguistic terms and the information that can be extracted from images this contributes to reducing the semantic gap and it constitutes a new methodological approach to guide semantic image interpretation this methodological approach is illustrated on a medical example dealing with knowledge based recognition of brain structures in 3d magnetic resonance images using the proposed fuzzy spatial relation ontology

on the representation of finite deterministic 2 tape automata this paper presents properties of relations between words that are realized by deterministic finite 2 tape automata it has been made as complete as possible and is structured by the systematic use of the matrix representation of automata it is first shown that deterministic 2 tape automata are characterized as those which can be given a prefix matrix representation schutzenberger construct on representations the one that gives semi monomial representations for rational functions of words is then applied to this prefix representation in order to obtain a new proof of the fact that the lexicographic selection of a deterministic rational relation on words is a rational function

on finite complete rewriting systems finite derivation type and automaticity for homogeneous monoids this paper investigates the class of finitely presented monoids defined by homogeneous length preserving relations from a computational perspective the properties of admitting a finite complete rewriting system having finite derivation type being automatic and being biautomatic are investigated for this class of monoids the first main result shows that for any consistent combination of these properties and their negations there is a homogeneous monoid with exactly this combination of properties we then introduce the new concept of abstract rees commensurability an analogue of the notion of abstract commensurability for groups in order to extend this result to show that the same statement holds even if one restricts attention to the class of n ary homogeneous monoids where every side of every relation has fixed length n we then introduce a new encoding technique that allows us to extend the result partially to the class of n ary multihomogenous monoids

l a l b decidability results from complete formal systems abstract the equivalence problem for deterministic pushdown automata is shown to be decidable we exhibit a complete formal system for deducing equivalent pairs of deterministic rational boolean series on the alphabet associated with a dpda m we then extend the result to deterministic pushdown transducers from a free monoid into an abelian group a general algebraic and logical framework inspired by harrison et al theoret comput sci 9 1979 173 205 conrcelle theoret comput sci 6 1978 255 279 and meitus kybernetika 5 1989 14 25 in russian is developed

the symbol grounding problem there has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling this paper describes the symbol grounding problem how can the semantic interpretation of a formal symbol system be made intrinsic to the system rather than just parasitic on the meanings in our heads how can the meanings of the meaningless symbol tokens manipulated solely on the basis of their arbitrary shapes be grounded in anything but other meaningless symbols the problem is analogous to trying to learn chinese from a chinese chinese dictionary alone a candidate solution is sketched symbolic representations must be grounded bottom up in nonsymbolic representations of two kinds 1 iconic representations which are analogs of the proximal sensory projections of distal objects and events and 2 categorical representations which are learned and innate feature detectors that pick out the invariant features of object and event categories from their sensory projections elementary symbols are the names of these object and event categories assigned on the basis of their nonsymbolic categorical representations higher order 3 symbolic representations grounded in these elementary symbols consist of symbol strings describing category membership relations e g an x is a y that is z connectionism is one natural candidate for the mechanism that learns the invariant features underlying categorical representations thereby connecting names to the proximal projections of the distal objects they stand for in this way connectionism can be seen as a complementary component in a hybrid nonsymbolic symbolic model of the mind rather than a rival to purely symbolic modeling such a hybrid model would not have an autonomous symbolic module however the symbolic functions would emerge as an intrinsically dedicated symbol system as a consequence of the bottom up grounding of categories names in their sensory representations symbol manipulation would be governed not just by the arbitrary shapes of the symbol tokens but by the nonarbitrary shapes of the icons and category invariants in which they are grounded

analytical investigation of the effects of lateral connections on the accuracy of population coding we studied how lateral connections affect the accuracy of a population code by using a model of orientation selectivity in the primary visual cortex investigating the effects of lateral connections on population coding is a complex problem because these connections simultaneously change the shape of tuning curves and correlations between neurons both of these changes caused by lateral connections have to be taken into consideration to correctly evaluate their effects we propose a theoretical framework for analytically computing the fisher information which measures the accuracy of a population code in stochastic spiking neuron models with refractory periods within our framework we accurately evaluated both the changes in tuning curves and correlations caused by lateral connections and their effects on the fisher information we found that their effects conflicted with each other and the answer to whether or not the lateral connections increased the fisher information strongly depended on the intrinsic properties of the model neuron by systematically changing the coupling strengths of excitations and inhibitions we found the parameter regions of lateral connectivities where sharpening of tuning curves through mexican hat connectivities led to an increase in information which is in contrast to some previous findings

the growth ratio of synchronous rational relations is unique we introduce a synchronous relations for a rational number a we show that if a rational relation is both a and a synchronous for two different numbers a and a then it is recognizable we give a synchronization algorithm for a synchronous transducers we also prove the closure under boolean operations and composition of a synchronous relations

population coding and the labeling problem extrinsic versus intrinsic representations current population coding methods including weighted averaging and bayesian estimation are based on extrinsic representations these require that neurons be labeled with response parameters such as tuning curve peaks or noise distributions which are tied to some external world based metric scale firing rates alone without this external labeling are insufficient to represent a variable however the extrinsic approach does not explain how such neural labeling is implemented a radically different and perhaps more physiological approach is based on intrinsic representations which have access only to firing rates because neurons are unlabeled intrinsic coding represents relative rather than absolute values of a variable we show that intrinsic coding has representational advantages including invariance categorization and discrimination and in certain situations it may also recover absolute stimulus values

on decision problems for parameterized machines in this paper we investigate various decision problems concerning parameterized versions of some classes of machines let c s m t be the class of nondeterministic multitape turing machine tm acceptors with a two way read only input at most s states at most m read write worktapes and at most t symbols in the worktape alphabet where s m t are fixed positive integers there is no restriction on the cardinality of the input alphabet we are able to show the emptiness disjointness and universe also called universality problems to be decidable for c s m t for the class consisting of machines in c s m t that always halt or whose minimal time accepting computations can be bounded by some recursive function f n where n is the input length the containment and equivalence problems are decidable these results hold for other machines e g when the worktapes are pushdown stacks where on every step each pushdown can only pop the top of the stack or replace the top of the stack by at most two symbols or when stacks are counters where on every step a counter can be incremented by 1 decremented by 1 or remain unchanged and can be tested for zero our results are the best possible in the sense that not parameterizing one of s m t or in the case of counter machines allowing the counters to increment by arbitrary integers that may change from machines to machines makes the universe problem undecidable we also give a simple characterization of the languages defined by c s m t finally we investigate the applicability of our techniques to machines with multiple input heads or multiple input tapes

geometric learning algorithms abstract emergent computation in the form of geometric learning is central to the development of motor and perceptual systems in biological organisms and promises to have a similar impact on emerging technologies including robotics vision speech and graphics this paper examines some of the trade offs involved in different implementation strategies focusing on the tasks of learning discrete classifications and smooth nonlinear mappings the trade offs between local and global representations are discussed a spectrum of distributed network implementations are examined and an important source of computational inefficiency is identified efficient algorithms based on k d trees and the delaunay triangulation are presented and the relevance to biological networks is discussed finally extensions of both the tasks and the implementations are given

decidability and syntactic control of interference we investigate the decidability of observational equivalence and approximation in reynolds syntactic control of interference sci a prototypical functional imperative language in which covert interference between functions and their arguments is prevented by the use of an affine typing discipline by associating denotations of terms in a fully abstract relational model of finitary basic sci due to reddy with multitape finite state automata we show that observational approximation is not decidable even at first order but that observational equivalence is decidable for all terms we then consider the same problems for basic sci extended with non local control in the form of backwards jumps we show that both observational approximation and observational equivalence are decidable in this observably sequential version of the language by describing a fully abstract games model in which strategies are regular languages

on factors of synchronized sequences let k 2 be an integer a sequence of natural numbers is k synchronized if its graph is represented in base k by a right synchronized rational relation we show that the factor complexity and the palindromic complexity of a k synchronized sequence are k regular sequences we derive that the palindromic complexity of a k automatic sequence is k automatic

hamiltonian formulation towards minimization of viscous fluid fingering a variational approach has been recently employed to determine the ideal time dependent injection rate q t that minimizes fingering formation when a fluid is injected in a hele shaw cell filled with another fluid of much greater viscosity however such a calculation is approximate in nature since it has been performed by assuming a high capillary number regime in this work we go one step further and utilize a hamiltonian formulation to obtain an analytical exact solution for q t now valid for arbitrary values of the capillary number moreover this hamiltonian scheme is applied to calculate the corresponding injection rate that minimizes fingering formation in a uniform three dimensional porous media an analysis of the improvement offered by these exact injection rate expressions in comparison with previous approximate results is also provided

stability study of a constant volume thin film flow we study the stability of a constant volume of fluid spreading down an incline in contrast to the commonly considered flow characterized by constant fluid flux in the present problem the base flow is time dependent we present a method to carry out consistently linear stability analysis based on simultaneously solving the time evolution of the base flow and of the perturbations the analysis is performed numerically by using a finite difference method supplemented with an integral method developed here the computations show that after a short transient stage imposed perturbations travel with the same velocity as the leading contact line the spectral analysis of the modes evolution shows that their growth rates are in general time dependent the wavelength of maximum amplitude ensuremath lambda max decreases with time until it reaches an asymptotic value which is in good agreement with experimental results we also explore the dependence of ensuremath lambda max on the cross sectional fluid area a and on the inclination angle ensuremath alpha of the substrate for considered small a s corresponding to small bond numbers we find that the dependence of ensuremath lambda max on a is in good agreement with experimental data this dependence differs significantly from the one observed for the films characterized by much larger a s and bond numbers we also predict the dependence of ensuremath lambda max on the inclination angle ensuremath alpha

the inclusion problem for some classes of deterministic multitape automata abstract a natural and sufficiently large class of deterministic one way multitape automa is defined with decidable inclusion problem this class is also the largest with decidable equivalence problem at this moment

on size reduction techniques for multitape automata we present a method for size reduction of two way multitape automata our algorithm applies local transformations that change the order in which transitions concerning different tapes occur in the automaton graph and merge suitable states into a single state our work is motivated by implementation of a language for string manipulation in database systems where string predicates are compiled into two way multitape automata additionally we present a one tape nfa reduction algorithm that is based on a method proposed for dfa minimization by kameda and weiner and apply this algorithm combined with the multitape automata reduction algorithm on our multitape automata empirical results on the performance of our method when applied on some multitape automata originating from string predicates are reported

finite grobner shirshov bases for plactic algebras and biautomatic structures for plactic monoids this paper shows that every plactic algebra of finite rank admits a finite grobner shirshov basis the result is proved by using the combinatorial properties of young tableaux to construct a finite complete rewriting system for the corresponding plactic monoid which also yields the corollaries that plactic monoids of finite rank have finite derivation type and satisfy the homological finiteness properties left and right fp fp also answering a question of zelmanov we apply this rewriting system and other techniques to show that plactic monoids of finite rank are biautomatic

uniform strategies rational relations and jumping automata a general concept of uniform strategies has recently been proposed as a relevant notion in game theory for computer science which subsumes various notions from the literature it relies on properties involving sets of plays in two player turn based arenas equipped with arbitrary binary relations between plays these properties are expressed in a language based on ctl with a quantifier over related plays there are two semantics for our quantifier a strict one and a full one that we study separately regarding the strict semantics the existence of a uniform strategy is undecidable for rational binary relations but introducing jumping tree automata and restricting attention to recognizable relations allows us to establish a 2 exptime complete complexity and still capture a class of two player imperfect information games with epistemic temporal objectives regarding the full semantics relying on information set automata we establish that the existence of a uniform strategy is decidable for rational relations and we provide a nonelementary synthesis procedure we also exhibit an essentially optimal subclass of rational relations for which the problem becomes 2 exptime complete considering rich classes of relations makes the theory of uniform strategies powerful it directly entails various results in logics of knowledge and time some of them already known and others new

optimal population codes for space grid cells outperform place cells rodents use two distinct neuronal coordinate systems to estimate their position place fields in the hippocampus and grid fields in the entorhinal cortex whereas place cells spike at only one particular spatial location grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice we study how to best construct place and grid codes taking the probabilistic nature of neural spiking into account which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal s position from the neuronal population response a priori estimating a spatial position from a grid code could be ambiguous as regular periodic lattices possess translational symmetry the solution to this problem requires lattices for grid cells with different spacings the spatial resolution crucially depends on choosing the right ratios of these spacings across the population we compute the expected error in estimating the position in both the asymptotic limit using fisher information and for low spike counts using maximum likelihood estimation achieving high spatial resolution and covering a large range of space in a grid code leads to a trade off the best grid code for spatial resolution is built of nested modules with different spatial periods one inside the other whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed first short lattice spacings should outnumber long lattice spacings second the grid code should be self similar across different lattice spacings so that the grid field always covers a fixed fraction of the lattice period if these conditions are satisfied and the spatial tuning curves for each neuron span the same range of firing rates then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons

many aspects of defect theorems we give a survey and a unified presentation of the defect theorem its generalizations and recent aspects of interest in its basic form the defect theorem states that if a set of n words satisfies a nontrivial relation then these words can be expressed simultaneously as products of at most n 1 words in other words dependency of words causes a defect effect there does not exist just one defect theorem but several ones depending on the restrictions that are put to the n 1 words the defect theorem is closely related to equations of words and in this way to the compactness theorem for systems of word equations

multidimensional encoding strategy of spiking neurons neural responses in sensory systems are typically triggered by a multitude of stimulus features using information theory we study the encoding accuracy of a population of stochastically spiking neurons characterized by different tuning widths for the different features the optimal encoding strategy for representing one feature most accurately consists of narrow tuning in the dimension to be encoded to increase the single neuron fisher information and broad tuning in all other dimensions to increase the number of active neurons extremely narrow tuning without sufficient receptive field overlap will severely worsen the coding this implies the existence of an optimal tuning width for the feature to be encoded empirically only a subset of all stimulus features will normally be accessible in this case relative encoding errors can be calculated that yield a criterion for the function of a neural population based on the measured tuning curves

a general formulation of conceptual spaces as a meso level representation representing cognitive processes remains one of the great research challenges many important application areas such as clinical diagnosis operate in an environment of relative magnitudes counts shapes colours etc which are not well captured by current representational approaches this paper presents conceptual spaces as a meso level representation for cognitive systems between the high level symbolic representations and the subconceptual connectionist representations which have dominated ai conceptual spaces emphasize orders and measures and therefore naturally represent counts magnitudes and volumes taking grdenfors decade long investigation of conceptual spaces grdenfors conceptual spaces the geometry of thought mit press 2000 as start point the paper presents a formal foundation for conceptual spaces shows how they are theoretically and practically linked to higher and lower representational levels and develops dynamics which allow the orbits of states in the space to solve appropriate meso level reasoning tasks interpretations of conceptual spaces are given to illustrate the formal definitions and show the flexibility of the representation

computing with continuous attractors stability and online aspects two issues concerning the application of continuous attractors in neural systems are investigated the computational robustness of continuous attractors with respect to input noises and the implementation of bayesian online decoding in a perfect mathematical model for continuous attractors decoding results for stimuli are highly sensitive to input noises and this sensitivity is the inevitable consequence of the system s neutral stability to overcome this shortcoming we modify the conventional network model by including extra dynamical interactions between neurons these interactions vary according to the biologically plausible hebbian learning rule and have the computational role of memorizing and propagating stimulus information accumulated with time as a result the new network model responds to the history of external inputs over a period of time and hence becomes insensitive to short term fluctuations also since dynamical interactions provide a mechanism to convey the prior knowledge of stimulus that is the information of the stimulus presented previously the network effectively implements online bayesian inference this study also reveals some interesting behavior in neural population coding such as the trade off between decoding stability and the speed of tracking time varying stimuli and the relationship between neural tuning width and the tracking speed

optimal signal estimation in neuronal models we study optimal estimation of a signal in parametric neuronal models on the basis of interspike interval data fisher information is the inverse asymptotic variance of the best estimator its dependence on the parameter value indicates accuracy of estimation our models assume that the input signal is estimated from neuronal output interspike interval data where the frequency transfer function is sigmoidal if the coefficient of variation of the interspike interval is constant with respect to the signal the fisher information is unimodal and its maximum for the most estimable signal can be found we obtain a general result and compare the signal producing maximal fisher information with the inflection point of the sigmoidal transfer function in several basic neuronal models

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

efficient neural codes that minimize lp reconstruction error the efficient coding hypothesis assumes that biological sensory systems use neural codes that are optimized to best possibly represent the stimuli that occur in their environment most common models use information theoretic measures whereas alternative formulations propose incorporating downstream decoding performance here we provide a systematic evaluation of different optimality criteria using a parametric formulation of the efficient coding problem based on the reconstruction error of the maximum likelihood decoder this parametric family includes both the information maximization criterion and squared decoding error as special cases we analytically derived the optimal tuning curve of a single neuron encoding a one dimensional stimulus with an arbitrary input distribution we show how the result can be generalized to a class of neural populations by introducing the concept of a meta tuning curve the predictions of our framework are tested against previously measured characteristics of some early visual systems found in biology we find solutions that correspond to low values of suggesting that across different animal models neural representations in the early visual pathways optimize similar criteria about natural stimuli that are relatively close to the information maximization criterion

a construction on finite automata that has remained hidden abstract we show how a construction on matrix representations of two tape automata proposed by schutzenberger to prove that rational functions are unambiguous can be given a central role in the theory of relations and functions realized by finite automata in such a way that the other basic results such as the cross section theorem its dual the theorem of rational uniformisation or the decomposition theorem of rational functions into sequential functions appear as direct and formal consequences of it

equations over finite sets of words and equivalence problems in automata theory abstract several observations concerning equations over monoids of finite sets of words are made monoids considered are the monoid of finite prefix codes the monoid of all finite sets and the monoid of all finite multisets as well as some others as an application some known decidability results in automata theory are extended finally several open questions are raised

deciding word neighborhood with universal neighborhood automata given some form of distance between words a fundamental operation is to decide whether the distance between two given words w and v is within a given bound in earlier work we introduced the concept of a universal levenshtein automaton for a given distance bound n this deterministic automaton takes as input a sequence g of bitvectors computed from w and v the sequence g is accepted iff the levenshtein distance between w and v does not exceed n the automaton is called universal since the same automaton can be used for arbitrary input words w and v regardless of the underlying input alphabet here we extend this picture after introducing a large abstract family of generalized word distances we exactly characterize those members where word neighborhood can be decided using universal neighborhood automata similar to universal levenshtein automata our theoretical results establish several bridges to the theory of synchronized finite state transducers and dynamic programming for small neighborhood bounds universal neighborhood automata can be held in main memory this leads to very efficient algorithms for the above decision problem evaluation results show that these algorithms are much faster than those based on dynamic programming

rational equivalence relations rational relations finite transductions which are equivalence relations are discussed after establishing a containment hierarchy the complexity of canonical function computation and a number of class membership decision problems are studied the following classes are considered

population coding and decoding in a neural field a computational study this study uses a neural field model to investigate computational aspects of population coding and decoding when the stimulus is a single variable a general prototype model for the encoding process is proposed in which neural responses are correlated with strength specified by a gaussian function of their difference in preferred stimuli based on the model we study the effect of correlation on the fisher information compare the performances of three decoding methods that differ in the amount of encoding information being used and investigate the implementation of the three methods by using a recurrent network this study not only rediscovers main results in existing literatures in a unified way but also reveals important new features especially when the neural correlation is strong as the neural correlation of firing becomes larger the fisher information decreases drastically we confirm that as the width of correlation increases the fisher information saturates and no longer increases in proportion to the number of neurons however we prove that as the width increases further wider than 2 times the effective width of the turning function the fisher information increases again and it increases without limit in proportion to the number of neurons furthermore we clarify the asymptotic efficiency of the maximum likelihood inference mli type of decoding methods for correlated neural signals it shows that when the correlation covers a nonlocal range of population excepting the uniform correlation and when the noise is extremely small the mli type of method whose decoding error satisfies the cauchy type distribution is not asymptotically efficient this implies that the variance is no longer adequate to measure decoding accuracy

feasible reductions to kolmogorov loveland stochastic sequences for every binary sequence a there is an infinite binary sequence s such that a ttp s and s is stochastic in the sense of kolmogorov and loveland

direct and dual laws for automata with multiplicities we present here theoretical results coming from the implementation of the package called amult automata with multiplicities we show that classical formulas are optimal for the bounds especially they are almost everywhere optimal for the fields r and c we characterize the dual laws preserving rationality and examine compatibility between the geometry of the k automata andthese laws copyright 2001 elsevier science b v

fibonacci representations and finite automata finite state automata are used as a simple model of computation since only a finite memory is needed the problem of passing from any representation to the normal representation of an integer within the fibonacci numeration system which is called the process of normalization is addressed it is shown that the normalization can be realized by means of infinite automata more precisely this function can be obtained by the composition of two subsequential transducers that are simply obtained from the linear recurrence definition of the basis of the fibonacci system one processing words from left to right and the other from right to left the normalization although not a sequential process can be obtained in two sequential passes it is proved that it is possible to add to integers written in the fibonacci numeration system of order m by means of a finite state automaton the conversion from a fibonacci representation to the standard binary representation cannot be realized by a finite state automaton

on lindenmayerian algebraic sequences abstract we define and study lindenmayerian algebraic sequences these sequences are a generalization of algebraic sequences k regular sequences and automatic sequences

some decisional problems on rational relations abstract in this paper we prove that the problem of deciding whether a deterministic rational relation is star free is recursively solvable although the same problem for any rational relation is undecidable we also prove that a rational relation is star free if and only if it is aperiodic and deterministic

characterizing the neural coding of symbolic quantities how the brain encodes abstract numerical symbols is a fundamental question in philosophy and cognitive neuroscience alike here we probe the nature of symbolic number representation in the brain by characterizing the neural similarity space for symbolic quantities in regions sensitive to their semantic content in parietal and occipital regions the similarity space of number symbols was positively predicted by the lexical frequency of numerals in parietal and occipital areas and was unrelated to numerical ratio these results are more consistent with a categorical frequency based account of symbolic quantity encoding in contrast the similarity space of analog quantities was positively predicted by ratio in prefrontal parietal and occipital regions we thus provide an explanation for why previous work has indicated that symbolic and analog quantities are distinct number symbols operate primarily like discrete categories sensitive to input frequency while analog quantities operate more like approximate perceptual magnitudes in addition we find substantial evidence for related patterns of activity across formats in prefrontal parietal and occipital regions crucially however between format relations were not specific to individual quantities indicating common processing as opposed to common representation moreover evidence for between format processing was strongest for quantities that could be represented as exact discrete values in both systems quantities in the subitizing range 1 4 in sum converging evidence presented here indicates that symbolic quantities are coded in the brain as discrete categories sensitive to input frequency and largely independent of approximate analog quantities

sample skewness as a statistical measurement of neuronal tuning sharpness we propose using the statistical measurement of the sample skewness of the distribution of mean firing rates of a tuning curve to quantify sharpness of tuning for some features like binocular disparity tuning curves are best described by relatively complex and sometimes diverse functions making it difficult to quantify sharpness with a single function and parameter skewness provides a robust nonparametric measure of tuning curve sharpness that is invariant with respect to the mean and variance of the tuning curve and is straightforward to apply to a wide range of tuning including simple orientation tuning curves and complex object tuning curves that often cannot even be described parametrically because skewness does not depend on a specific model or function of tuning it is especially appealing to cases of sharpening where recurrent interactions among neurons produce sharper tuning curves that deviate in a complex manner from the feedforward function of tuning since tuning curves for all neurons are not typically well described by a single parametric function this model independence additionally allows skewness to be applied to all recorded neurons maximizing the statistical power of a set of data we also compare skewness with other nonparametric measures of tuning curve sharpness and selectivity compared to these other nonparametric measures tested skewness is best used for capturing the sharpness of multimodal tuning curves defined by narrow peaks maximum and broad valleys minima finally we provide a more formal definition of sharpness using a shape based information gain measure and derive and show that skewness is correlated with this definition

a mixture model for population codes of gabor filters population coding is a coding scheme which is ubiquitous in neural systems and is also of more general use in coding stimuli for example in vision problems a population of responses to a stimulus can be used to represent not only the value of some variable in the environment but a full probability distribution for that variable the information is held in a distributed and encoded form which may in some situations be more robust to noise and failures than conventional representations gabor filters are a popular choice for detecting edges in the visual field for several reasons they are easily tuned for a variety of edge widths and orientations and are considered a close model of the edge filters in the human visual system in this paper we consider population codes of gabor filters with different orientations a probabilistic model of gabor filter responses is presented based on the analytically derived orientation tuning function and a parametric mixture model of the filter responses in the presence of local edge structure with single or multiple orientations a probability density function pdf of the local orientation in any point x y can be extracted through a parameter estimation procedure the resulting pdf of the local contour orientation captures not only angular information at edges corners or t junctions but also describes the certainty of the measurement which can be characterized in terms of the entropy of the individual mixture components

deterministic synchronization of automations with bounded delay resume nous montrons qu un automate a delai borne sous sequentiel i e deterministe sur les entrees est equivalent a un automate en ligne c est a dire lettre a lettre apres une periode transitoire fixe ou l automate lit le debut de l entree sans rien sortir et sous sequentiel les resultats de synchronisation etablis anterieurement pour les automates a delai borne ne preservaient pas la sous sequentialite

topology of finite graphs this paper derives from a course in group theory which i gave at berkeley in 1982 i wanted to prove the standard theorems on free groups and discovered that after a few preliminaries the notion of locally injective map or immersion of graphs was very useful this enables one to see in an effective easy algorithmic way just what happens with finitely generated free groups one can understand in this way 1 howson s theorem that if a and b are finitely generated subgroups of a free group then a b is finitely generated and 2 m hall s theorem that finitely generated subgroups of free groups are closed in the profinite topology during this course s m gersten came up with a simple proof of h neumann s inequality on the ranks in howson s theorem one of the ideas in gersten s proof was to use core graphs graphs with no trees hanging on subsequently i found that some consequences of a paper of greenberg s could be proved using core graphs and covering translations of immersions the most striking such result is that if a and b are finitely generated subgroups of a free group and if a c b is of finite index in both a and b then a b is of finite index in a v b the subgroup generated by a ub

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

parameter extraction from population codes a critical assessment in perceptual systems a stimulus parameter can be extracted by determining the center of gravity of the response profile of a population of neural sensors likewise at the motor end of a neural system center of gravity decoding also known as vector decoding generates a movement direction from the neural activation profile we evaluate these schemes from a statistical perspective by comparing their statistical variance with the minimum variance possible for an unbiased parameter extraction from the noisy neuronal ensemble activation profile center of gravity decoding can be statistically optimal this is the case for regular arrays of sensors with gaussian tuning profiles that have an output described by poisson statistics and for arrays of sensors with a sinusoidal tuning profile for the angular parameter estimated however there are also many cases in which center of gravity decoding is highly inefficient this includes the important case where sensor positions are very irregular finally we study the robustness of center of gravity decoding against response nonlinearities at different stages of an information processing hierarchy we conclude that in neural systems instead of representing a parameter explicitly it is safer to leave the parameter coded implicitly in a neuronal ensemble activation profile

cosine tuning minimizes motor errors cosine tuning is ubiquitous in the motor system yet a satisfying explanation of its origin is lacking here we argue that cosine tuning minimizes expected errors in force production which makes it a natural choice for activating muscles and neurons in the final stages of motor processing our results are based on the empirically observed scaling of neuromotor noise whose standard deviation is a linear function of the mean such scaling predicts a reduction of net force errors when redundant actuators pull in the same direction we confirm this prediction by comparing forces produced with one versus two hands and generalize it across directions under the resulting neuromotor noise model we prove that the optimal activation profile is a possibly truncated cosine for arbitrary dimensionality of the workspace distribution of force directions correlated or uncorrelated noise with or without a separate cocontraction command the model predicts a negative force bias truncated cosine tuning at low muscle cocontraction levels and misalignment of preferred directions and lines of action for nonuniform muscle distributions all predictions are supported by experimental data

neuronal tuning to sharpen or broaden sensory and motor variables are typically represented by a population of broadly tuned neurons a coarser representation with broader tuning can often improve coding accuracy but sometimes the accuracy may also improve with sharper tuning the theoretical analysis here shows that the relationship between tuning width and accuracy depends crucially on the dimension of the encoded variable a general rule is derived for how the fisher information scales with the tuning width regardless of the exact shape of the tuning function the probability distribution of spikes and allowing some correlated noise between neurons these results demonstrate a universal dimensionality effect in neural population coding

efficiency characterization of a large neuronal network a causal information approach abstract when inhibitory neurons constitute about 40 of neurons they could have an important antinociceptive role as they would easily regulate the level of activity of other neurons we consider a simple network of cortical spiking neurons with axonal conduction delays and spike timing dependent plasticity representative of a cortical column or hypercolumn with a large proportion of inhibitory neurons each neuron fires following a hodgkin huxley like dynamics and it is interconnected randomly to other neurons the network dynamics is investigated estimating bandt and pompe probability distribution function associated to the interspike intervals and taking different degrees of interconnectivity across neurons more specifically we take into account the fine temporal structures of the complex neuronal signals not just by using the probability distributions associated to the interspike intervals but instead considering much more subtle measures accounting for their causal information the shannon permutation entropy fisher permutation information and permutation statistical complexity this allows us to investigate how the information of the system might saturate to a finite value as the degree of interconnectivity across neurons grows inferring the emergent dynamical properties of the system

wavenumber selection and eckhaus instability in couette taylor flow abstract we review a number of experimental results which pertain to pattern selection in couette taylor flow they include measurements of the harmonic contents of taylor vortices of the location of the eckhaus boundary of wavenumber selection by a spatial ramp of the reynolds number and of the axial variation of the wavenumber in the finite system we show that many of the results can be understood quantitatively in terms of the ginzburg landau amplitude equation

on the definition of word hyperbolic groups formal languages based on multiplication tables of finitely generated groups are investigated and used to give a linguistic characterization of word hyperbolic groups

a rescaling scheme with application to the long time simulation of viscous fingering in a hele shaw cell in this paper we present a time and space rescaling scheme for the computation of moving interface problems the idea is to map time space such that the interfaces can evolve exponentially fast in the new time scale while the area volume enclosed by the interface remains unchanged the rescaling scheme significantly reduces the computation time especially for slow growth and enables one to accurately simulate the very long time dynamics of moving interfaces we then implement this scheme in a hele shaw problem examine the dynamics for a number of different injection fluxes and present the largest and most pronounced viscous fingering simulations to date

optimal short term population coding when fisher information fails efficient coding has been proposed as a first principle explaining neuronal response properties in the central nervous system the shape of optimal codes however strongly depends on the natural limitations of the particular physical system here we investigate how optimal neuronal encoding strategies are influenced by the finite number of neurons n place constraint the limited decoding time window length t time constraint the maximum neuronal firing rate fmax power constraint and the maximal average rate f max energy constraint while fisher information provides a general lower bound for the mean squared error of unbiased signal reconstruction its use to characterize the coding precision is limited analyzing simple examples we illustrate some typical pitfalls and thereby show that fisher information provides a valid measure for the precision of a code only if the dynamic range fmint fmaxt is sufficiently large in particular we demonstrate that the optimal width of gaussian tuning curves depends on the available decoding time t within the broader class of unimodal tuning functions it turns out that the shape of a fisher optimal coding scheme is not unique we solve this ambiguity by taking the minimum mean square error into account which leads to fiat tuning curves the tuning width however remains to be determined by energy constraints rather than by the principle of efficient coding

difficulty of singularity in population coding fisher information has been used to analyze the accuracy of neural population coding this works well when the fisher information does not degenerate but when two stimuli are presented to a population of neurons a singular structure emerges by their mutual interactions in this case the fisher information matrix degenerates and the regularity condition ensuring the cramer rao paradigm of statistics is violated an animal shows pathological behavior in such a situation we present a novel method of statistical analysis to understand information in population coding in which algebraic singularity plays a major role the method elucidates the nature of the pathological case by calculating the fisher information we then suggest that synchronous firing can resolve singularity and show a method of analyzing the binding problem in terms of the fisher information our method integrates a variety of disciplines in population coding such as nonregular statistics bayesian statistics singularity in algebraic geometry and synchronous firing under the theme of fisher information

efficient sensory encoding and bayesian inference with heterogeneous neural populations the efficient coding hypothesis posits that sensory systems maximize information transmitted to the brain about the environment we develop a precise and testable form of this hypothesis in the context of encoding a sensory variable with a population of noisy neurons each characterized by a tuning curve we parameterize the population with two continuous functions that control the density and amplitude of the tuning curves assuming that the tuning widths vary inversely with the cell density this parameterization allows us to solve in closed form for the information maximizing allocation of tuning curves as a function of the prior probability distribution of sensory variables for the optimal population the cell density is proportional to the prior such that more cells with narrower tuning are allocated to encode higher probability stimuli and that each cell transmits an equal portion of the stimulus probability mass we also compute the stimulus discrimination capabilities of a perceptual system that relies on this neural representation and find that the best achievable discrimination thresholds are inversely proportional to the sensory prior we examine how the prior information that is implicitly encoded in the tuning curves of the optimal population may be used for perceptual inference and derive a novel decoder the bayesian population vector that closely approximates a bayesian least squares estimator that has explicit access to the prior finally we generalize these results to sigmoidal tuning curves correlated neural variability and a broader class of objective functions these results provide a principled embedding of sensory prior information in neural populations and yield predictions that are readily testable with environmental physiological and perceptual data

contour dynamics model for electric discharges we present an effective contour model for electrical discharges deduced as the asymptotic limit of the minimal streamer model for the propagation of electric discharges in the limit of small electron diffusion the incorporation of curvature effects to the velocity propagation and not to the boundary conditions is a feature and makes it different from the classical laplacian growth models the dispersion relation for a nonplanar two dimensional discharge is calculated the development and propagation of fingerlike patterns are studied and their main features quantified

fingering instabilities in adhesive failure we study the fingering instabilities that occur in the debonding of model adhesives we perform a linear analysis of the instability in the lifting hele shaw cell relevant for the failure of soft adhesives the analysis is done for a newtonian fluid but can be extended to shear thinning fluids without any problem when compared to experiment significant differences are found between the linear theory and the experimental results we therefore discuss three dimensional effects that are found to improve the agreement nevertheless significant differences between theory and experiment persist