A Note on Easily Testable Realizations for Logic Functions

It is shown that at most, n + 3 tests are required to detect any single stuck-at fault in an AND gate or a single faulty EXCLUSIVE OR (EOR) gate in a Reed-Muller canonical form realization of a switching function.

An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on $$\left( {{{\frac{{dk}}{{dt}}} \mathord{\left/ {\vphantom {{\frac{{dk}}{{dt}}} k}} \right. \kern-\nulldelimiterspace} k}} \right)$$ is less restrictive than earlier criteria.

ORP1L, a new Rab7 effector and regulator of late endosome functions

Oxysterol binding protein (OSBP) homologues have been found in eukaryotic organisms ranging from yeast to humans. These evolutionary conserved proteins have in common the presence of an OSBP-related domain (ORD) which contains the fully conserved EQVSHHPP sequence motif. The ORD forms a barrel structure that binds sterols in its interior. Other domains and sequence elements found in OSBP-homologues include pleckstrin homology domains, ankyrin repeats and two phenylalanines in an acidic tract (FFAT) motifs, which target the proteins to distinct subcellular compartments. OSBP homologues have been implicated in a wide range of intracellular processes, including vesicle trafficking, lipid metabolism and cell signaling, but little is known about the functional mechanisms of these proteins. The human family of OSBP homologues consists of twelve OSBP-related proteins (ORP). This thesis work is focused on one of the family members, ORP1, of which two variants were found to be expressed tissue-specifically in humans. The shorter variant, ORP1S contains an ORD only. The N-terminally extended variant, ORP1L, comprises a pleckstrin homology domain and three ankyrin repeats in addition to the ORD. The two ORP1 variants differ in intracellular localization. ORP1S is cytosolic, while the ankyrin repeat region of ORP1L targets the protein to late endosomes/lysosomes. This part of ORP1L also has profound effects on late endosomal morphology, inducing perinuclear clustering of late endosomes. A central aim of this study was to identify molecular interactions of ORP1L on late endosomes. The morphological changes of late endosomes induced by overexpressed ORP1L implies involvement of small Rab GTPases, regulators of organelle motility, tethering, docking and/or fusion, in generation of the phenotype. A direct interaction was demonstrated between ORP1L and active Rab7. ORP1L prolongs the active state of Rab7 by stabilizing its GTP-bound form. The clustering of late endosomes/lysosomes was also shown to be linked to the minus end-directed microtubule-based dynein-dynactin motor complex through the ankyrin repeat region of ORP1L. ORP1L, Rab7 and the Rab7-interacting lysosomal protein (RILP) were found to be part of the same effector complex recruiting the dynein-dynactin complex to late endosomes, thereby promoting minus end-directed movement. The proteins were found to be physically close to each other on late endosomes and RILP was found to stabilize the ORP1L-Rab7 interaction. It is possible that ORP1L and RILP bind to each other through their C-terminal and N-terminal regions, respectively, when they are bridged by Rab7. With the results of this study we have been able to place a member of the uncharacterized OSBP-family, ORP1L, in the endocytic pathway, where it regulates motility and possibly fusion of late endosomes through interaction with the small GTPase Rab7.

A Note on Minimal Reed-Muller Canonical Forms of Switching Functions

A nonexhaustive procedure for obtaining minimal Reed-Muller canonical (RMC) forms of switching functions is presented. This procedure is a modification of a procedure presented earlier in the literature and enables derivation of an upper bound on the number of RMC forms to be derived to choose a minimal one. It is shown that the task of obtaining minimal RMC forms is simplified in the case of symmetric functions and self-dual functions.

The biological functions of mouse twinfilin isoforms

The actin cytoskeleton is essential for many cellular processes, including motility, morphogenesis, endocytosis and signal transduction. Actin can exist in monomeric (G-actin) or filamentous (F-actin) form. Actin filaments are considered to be the functional form of actin, generating the protrusive forces characteristic for the actin cytoskeleton. The structure and dynamics of the actin filament and monomer pools are regulated by a large number of actin-binding proteins in eukaryotic cells. Twinfilin is an evolutionarily conserved small actin monomer binding protein. Twinfilin is composed of two ADF/cofilin-like domains, separated by a short linker and followed by a C-terminal tail. Twinfilin forms a stable, high affinity complex with ADP-G-actin, inhibits the nucleotide exchange on actin monomers, and prevents their assembly into filament ends. Twinfilin was originally identified from yeast and has since then been found from all organisms studied except plants. Not much was known about the role of twinfilin in the actin dynamics in mammalian cells before this study. We set out to unravel the mysteries still covering twinfilins functions using biochemistry, cell biology, and genetics. We identified and characterized two mouse isoforms for the previously identified mouse twinfilin-1. The new isoforms, twinfilin-2a and -2b, are generated from the same gene through alternative promoter usage. The three isoforms have distinctive expression patterns, but are similar biochemically. Twinfilin-1 is the major isoform during development and is expressed in high levels in almost all tissues examined. Twinfilin-2a is also expressed almost ubiquitously, but at lower levels. Twinfilin-2b turned out to be a muscle-specific isoform, with very high expression in heart and skeletal muscle. It seems all mouse tissues express at least two twinfilin isoforms, indicating that twinfilins are important regulators of actin dynamics in all cell and tissue types. A knockout mouse line was generated for twinfilin-2a. The mice homozygous for this knockout were viable and developed normally, indicating that twinfilin-2a is dispensable for mouse development. However, it is important to note that twinfilin-2a shows similar expression pattern to twinfilin-1, suggesting that these proteins play redundant roles in mice. All mouse isoforms were shown to be able to sequester actin filaments and have higher affinity for ADP-G-actin than ATP-G-actin. They are also able to directly interact with heterodimeric capping protein and PI(4,5)P2 similar to yeast twinfilin. In this study we also uncovered a novel function for mouse twinfilins; capping actin filament barbed ends. All mouse twinfilin isoforms were shown to possess this function, while yeast and Drosophila twinfilin were not able to cap filament barbed ends. Twinfilins localize to the cytoplasm but also to actin-rich regions in mammalian cells. The subcellular localizations of the isoforms are regulated differently, indicating that even though twinfilins biochemical functions in vitro are very similar, in vivo they can play different roles through different regulatory pathways. Together, this study show that twinfilins regulate actin filament assembly both by sequestering actin monomers and by capping filament barbed ends, and that mammals have three biochemically similar twinfilin isoforms with partially overlapping expression patterns.

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].

Kinetic characterization of rat brain type IIA sodium channel alpha-subunit stably expressed in a somatic cell line

1. The rat brain type IIA Na+ channel alpha-subunit was stably expressed in Chinese hamster ovary (CHO) cells. Current through the expressed Na+ channels was studied using the whole-cell configuration of the patch clamp technique. The transient Na+ current was sensitive to TTX and showed a bell-shaped peak current vs. membrane potential relation. 2. Na+ current inactivation was better described by the sum of two exponentials in the potential range -30 to +40 mV, with. a dominating fast component and a small slower component. 3. The steady-state inactivation, h(infinity), was related to potential by a Boltzmann distribution, underlying thr ee states of the inactivation gate. 4. Recovery of the channels from inactivation at different potentials in the range -70 to -120 mV were characterized by al? initial delay which decreased with hyperpolarization. The time course was well fitted by the sum of two exponentials. In this case the slower exponential was the major component, and both time constants decreased with hyperpolarization. 5. For a working description of the Na+ channel inactivation in this preparation, with a minimal deviation from the Hodgkin-Huxley model, a three-state scheme of the form O reversible arrow I-1 reversible arrow I-2 was proposed, replacing the original two-state scheme of the Hodgkin-Huxley model, and the rate constants are reported. 6. The instantaneous current-voltage relationship showed marked deviation from linearity and was satisfactorily fitted by the constant-field equation. 7. The time course of activation was described by an m(x) model. However, the best-fitted value of x varied with the membrane potential and had a mean value of 2. 8. Effective gating charge was determined to be 4.7e from the slope of the activation plot, plotted on a logarithmic scale. 9. The rate constants of activation, alpha(m) and beta(m), were determined. Their functional dependence on the membrane potential was investigated.

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.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.