Automata and logics over finitely varying functions

We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or “signals”. In particular, we introduce a natural class of automata for generating finitely varying functions called View the MathML source’s, and show that it coincides in terms of language definability with a natural monadic second-order logic interpreted over finitely varying functions Rabinovich (2002) [15]. We also identify a “counter-free” subclass of View the MathML source’s which characterise the first-order definable languages of finitely varying functions. Our proofs mainly factor through the classical results for word languages. These results have applications in automata characterisations for continuously interpreted real-time logics like Metric Temporal Logic (MTL) Chevalier et al. (2006, 2007) [6] and [7].

Neuromagnetic studies on cortical somatosensory functions in infants and children : Normal development and effect of early brain lesions

Until recently, objective investigation of the functional development of the human brain in vivo was challenged by the lack of noninvasive research methods. Consequently, fairly little is known about cortical processing of sensory information even in healthy infants and children. Furthermore, mechanisms by which early brain insults affect brain development and function are poorly understood. In this thesis, we used magnetoencephalography (MEG) to investigate development of cortical somatosensory functions in healthy infants, very premature infants at risk for neurological disorders, and adolescents with hemiplegic cerebral palsy (CP). In newborns, stimulation of the hand activated both the contralateral primary (SIc) and secondary somatosensory cortices (SIIc). The activation patterns differed from those of adults, however. Some of the earliest SIc responses, constantly present in adults, were completely lacking in newborns and the effect of sleep stage on SIIc responses differed. These discrepancies between newborns and adults reflect the still developmental stage of the newborns’ somatosensory system. Its further maturation was demonstrated by a systematic transformation of the SIc response pattern with age. The main early adult­like components were present by age two. In very preterm infants, at term age, the SIc and SIIc were activated at similar latencies as in healthy fullterm newborns, but the SIc activity was weaker in the preterm group. The SIIc response was absent in four out of the six infants with brain lesions of the underlying hemisphere. Determining the prognostic value of this finding remains a subject for future studies, however. In the CP adolescents with pure subcortical lesions, contrasting their unilateral symptoms, the SIc responses of both hemispheres differed from those of controls: For example the distance between SIc representation areas for digits II and V was shorter bilaterally. In four of the five CP patients with cortico­subcortical brain lesions, no normal early SIc responses were evoked by stimulation of the palsied hand. The varying differences in neuronal functions, underlying the common clinical symptoms, call for investigation of more precisely designed rehabilitation strategies resting on knowledge about individual functional alterations in the sensorimotor networks.

Characterization of LRRTM and NGR gene families: Expression and functions

Some leucine-rich repeat (LRR) -containing membrane proteins are known regulators of neuronal growth and synapse formation. In this work I characterize two gene families encoding neuronal LRR membrane proteins, namely the LRRTM (leucine-rich repeat, transmembrane neuronal) and NGR (Nogo-66 receptor) families. I studied LRRTM and NGR family member's mRNA tissue distribution by RT-PCR and by in situ hybridization. Subcellular localization of LRRTM1 protein was studied in neurons and in non-neuronal cells. I discovered that LRRTM and NGR family mRNAs are predominantly expressed in the nervous system, and that each gene possesses a specific expression pattern. I also established that LRRTM and NGR family mRNAs are expressed by neurons, and not by glial cells. Within neurons, LRRTM1 protein is not transported to the plasma membrane; rather it localizes to endoplasmic reticulum. Nogo-A (RTN4), MAG, and OMgp are myelin-associated proteins that bind to NgR1 to limit axonal regeneration after central nervous system injury. To better understand the functions of NgR2 and NgR3, and to explore the possible redundancy in the signaling of myelin inhibitors of neurite growth, I mapped the interactions between NgR family and the known and candidate NgR1 ligands. I identified high-affinity interactions between RTN2-66, RTN3-66 and NgR1. I also demonstrate that Rtn3 mRNA is expressed in the same glial cell population of mouse spinal cord white matter as Nogo-A mRNA, and thus it could have a role in myelin inhibition of axonal growth. To understand how NgR1 interacts with multiple structurally divergent ligands, I aimed first to map in more detail the nature of Nogo-A:NgR1 interactions, and then to systematically map the binding sites of multiple myelin ligands in NgR1 by using a library of NgR1 expression constructs encoding proteins with one or multiple surface residues mutated to alanine. My analysis of the Nogo-A:NgR1 -interactions revealed a novel interaction site between the proteins, suggesting a trivalent Nogo-A:NgR1-interaction. Our analysis also defined a central binding region on the concave side of NgR1's LRR domain that is required for the binding of all known ligands, and a surrounding region critical for binding MAG and OMgp. To better understand the biological role of LRRTMs, I generated Lrrtm1 and Lrrtm3 knock out mice. I show here that reporter genes expressed from the targeted loci can be used for maping the neuronal connections of Lrrtm1 and Lrrtm3 expressing neurons in finer detail. With regard to LRRTM1's role in humans, we found a strong association between a 70 kb-spanning haplotype in the proposed promoter region of LRRTM1 gene and two possibly related phenotypes: left-handedness and schizophrenia. Interestingly, the responsible haplotype was linked to phenotypic variability only when paternally inherited. In summary, I identified two families of neuronal receptor-like proteins, and mapped their expression and certain protein-protein interactions. The identification of a central binding region in NgR1 shared by multiple ligands may facilitate the design and development of small molecule therapeutics blocking binding of all NgR1 ligands. Additionally, the genetic association data suggests that allelic variation upstream of LRRTM1 may play a role in the development of left-right brain asymmetry in humans. Lrrtm1 and Lrrtm3 knock out mice developed as a part of this study will likely be useful for schizophrenia and Alzheimer s disease research.

Exploring the post-genomic world: Differing explanatory and manipulatory functions of post-genomic sciences

Richard Lewontin proposed that the ability of a scientific field to create a narrative for public understanding garners it social relevance. This article applies Lewontin's conceptual framework of the functions of science (manipulatory and explanatory) to compare and explain the current differences in perceived societal relevance of genetics/genomics and proteomics. We provide three examples to illustrate the social relevance and strong cultural narrative of genetics/genomics for which no counterpart exists for proteomics. We argue that the major difference between genetics/genomics and proteomics is that genomics has a strong explanatory function, due to the strong cultural narrative of heredity. Based on qualitative interviews and observations of proteomics conferences, we suggest that the nature of proteins, lack of public understanding, and theoretical complexity exacerbates this difference for proteomics. Lewontin's framework suggests that social scientists may find that omics sciences affect social relations in different ways than past analyses of genetics.

Guessing based on length functions

Close relationships between guessing functions and length functions are established. Good length functions lead to good guessing functions. In particular, guessing in the increasing order of Lempel-Ziv lengths has certain universality properties for finite-state sources. As an application, these results show that hiding the parameters of the key-stream generating source in a private key crypto-system may not enhance the privacy of the system, the privacy level being measured by the difficulty in brute-force guessing of the key stream.

New rational interpolation functions for finite element analysis of rotating beams

A rotating beam finite element in which the interpolating shape functions are obtained by satisfying the governing static homogenous differential equation of Euler–Bernoulli rotating beams is developed in this work. The shape functions turn out to be rational functions which also depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. These rational functions yield the Hermite cubic when rotation speed becomes zero. The new element is applied for static and dynamic analysis of rotating beams. In the static case, a cantilever beam having a tip load is considered, with a radially varying axial force. It is found that this new element gives a very good approximation of the tip deflection to the analytical series solution value, as compared to the classical finite element given by the Hermite cubic shape functions. In the dynamic analysis, the new element is applied for uniform, and tapered rotating beams with cantilever and hinged boundary conditions to determine the natural frequencies, and the results compare very well with the published results given in the literature.

Novel window functions for digital filters

Window technique is one of the simplest methods to design Finite Impulse Response (FIR) filters. It uses special functions to truncate an infinite sequence to a finite one. In this paper, we propose window techniques based on integer sequences. The striking feature of the proposed work is that it overcomes all the problems posed by floating point numbers and inaccuracy, as the sequences are made of only integers. Some of these integer window sequences, yield sharp transition, while some of them result in zero ripple in passband and stopband.

Stiff-String Basis Functions for Vibration Analysis of High Speed Rotating Beams

A new rotating beam finite element is developed in which the basis functions are obtained by the exact solution of the governing static homogenous differential equation of a stiff string, which results from an approximation in the rotating beam equation. These shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. Using this new element and the Hermite cubic finite element, a convergence study of natural frequencies is performed, and it is found that the new element converges much more rapidly than the conventional Hermite cubic element for the first two modes at higher rotation speeds. The new element is also applied for uniform and tapered rotating beams to determine the natural frequencies, and the results compare very well with the published results given in the literature.

Time and Energy Complexity of Distributed Computation of a Class of Functions in Wireless Sensor Networks

We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in the work of Giridhar and Kumar, 2005), of which max, min, and indicator functions are important examples: our discussions are couched in terms of the max function. We view the problem as one of message-passing distributed computation over a geometric random graph. The network is assumed to be synchronous, and the sensors synchronously measure values and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (1) the communication topology assumed and (2) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralized contention-free scheduling of packet transmissions. First, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one-time maximum computation. We show that for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Theta(radicn/log n) and Theta(n) asymptotically as the number of sensors n rarr infin. Second, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the tree algorithm, multihop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n rarr infin. In particular, we show that the computation time for these algorithms scales as Theta(radicn/lo- g n), Theta(n), and Theta(radicn log n), respectively, whereas the energy expended scales as , Theta(n), Theta(radicn/log n), and Theta(radicn log n), respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling. The simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler, and hence, our results can be viewed as providing bounds for the performance with practical distributed schedulers.

Augustine and the functions of concupiscence

This study analyses Augustine s concept of concupiscentia, or evil desire (together with two cognate terms, libido and cupiditas) in the context of his entire oeuvre. By the aid of systematic analysis, the concept and its development is explored in four distinct ways. It is claimed that Augustine used the concept of concupiscentia for several theological purposes, and the task of the study is to represent these distinct functions, and their connections to Augustine s general theological and philosophical convictions. The study opens with a survey on terminology. A general overview of the occurrences of the negatively connoted words for desire in Latin literature precedes a corresponding examination of Augustine s own works. In this introductory chapter it is shown that, despite certain preferences in the uses of the words, a sufficient degree of synonymy reigns so as to allow an analysis of the concept without tightly discriminating between the terms. The theological functions of concupiscentia with its distinct contexts are analysed in separate chapters. The function of concupiscentia as a divine punishment is explored first (Ch 3). It is seen how Augustine links together concupiscentia and ideas about divine justice, and finally suggests that in the inordinate, psychologically experienced sexual desire, the original theological disobedience of Adam and Eve can be perceived. Augustine was criticized for this solution already in his own times, and the analysis of the function of concupiscentia as a divine punishment ends in a discussion on the critical response of punitive concupiscentia by Julian of Aeclanum. Augustine also attached to concupiscentia another central theological function by viewing evil desire as an inward originating cause for all external evil actions. In the study, this function is analysed by surveying two formally distinct images of evil desire, i.e. as the root (radix) of all evil, and as a threefold (triplex) matrix of evil actions (Ch 4). Both of these images were based on a single verse of the Bible (1 Jn 2, 16 and 1 Tim 6, 10). This function of concupiscentia was formed both parallel to, and in answer to, Manichaean insights into concupiscentia. Being familiar with the traditional philosophical discussions on the nature and therapy of emotions, Augustine situated concupiscentia also into this context. It is acknowledged that these philosophical traditions had an obvious impact into his way of explaining psychological processes in connection with concupiscentia. Not only did Augustine implicitly receive and exploit these traditions, but he also explicitly moulded and criticized them in connection with concupiscentia. Eventually, Augustine conceives the philosophical traditions of emotions as partly useful but also partly inadequate to deal with concupiscentia (Ch 5). The role of concupiscentia in connection to divine grace and Christian renewal is analysed in the final chapter of the study. Augustine s gradual development in internalizing the effects of concupiscentia also into the life of a baptized Christian are elucidated, as are the strong limitations and mitigations Augustine makes to the concept when attaching it into the life under grace (sub gratia). A crucial part in the development of this function is played by Augustine s changing interpretation of Rom 7, and the way concupiscentia appears in Augustine s readings of this text is therefore also analysed. As a result of the analysis of these four distinct functions and contexts of concupiscentia, it is concluded that Augustine s concept of concupiscentia is fairly tightly and coherently connected to his views of central theological importance. Especially the functions of concupiscentia as a punishment and the function of concupiscentia in Christian renewal were both tightly interwoven into Augustine s view of God s being and God s grace. The study shows the importance of reading Augustine s discussions on evil desire with a constant awareness of their role in their larger context, that is, of their function in each situation. The study warns against too simplistic and unifying readings of Augustine s concupiscentia, emphasizing the need to acknowledge both the necessitating, sinful aspects of concupiscentia, and the domesticated features of concupiscentia during Christian renewal.