nikola popovic | University of Belgrade (original) (raw)

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Papers by nikola popovic

Research paper thumbnail of A geometric approach to bistable front propagation in scalar reaction–diffusion equations with cut-off

Physica D-nonlinear Phenomena, 2010

Research paper thumbnail of Rigorous Asymptotic Expansions for Critical Wave Speeds in a Family of Scalar Reaction-Diffusion Equations

Journal of Dynamics and Differential Equations, 2006

Research paper thumbnail of The critical wave speed for the Fisher Kolmogorov Petrowskii Piscounov equation with cut-off

Research paper thumbnail of The asymptotic critical wave speed in a family of scalar reaction–diffusion equations

Journal of Mathematical Analysis and Applications, 2007

Research paper thumbnail of Mixed-Mode Oscillations in Three TimeScale Systems: A Prototypical Example

Siam Journal on Applied Dynamical Systems, 2008

Research paper thumbnail of Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron

Research paper thumbnail of Homozygous mutations incaveolin-3 cause a severe form of rippling muscle disease

Annals of Neurology, 2003

Heterozygous missense mutations in the caveolin-3 gene (CAV3) cause different muscle disorders. M... more Heterozygous missense mutations in the caveolin-3 gene (CAV3) cause different muscle disorders. Most patients with CAV3 alterations present with rippling muscle disease (RMD) characterized by signs of increased muscle irritability without muscle weakness. In some patients, CAV3 mutations underlie the progressive limb-girdle muscular dystrophy type 1C (LGMD1C). Here, we report two unrelated patients with novel homozygous mutations (L86P and A92T) in CAV3. Both presented with a more severe clinical phenotype than usually seen in RMD. Immunohistochemical and immunoblot analyses of muscle biopsies showed a strong reduction of caveolin-3 in both homozygous RMD patients similar to the findings in heterozygous RMD. Electron microscopy studies showed a nearly complete absence of caveolae in the sarcolemma in all RMD patients analyzed. Additional plasma membrane irregularities (small plasmalemmal discontinuities, subsarcolemmal vacuoles, abnormal papillary projections) were more pronounced in homozygous than in heterozygous RMD patients. A stronger activation of nitric oxide synthase was observed in both homozygous patients compared with heterozygous RMD. Like in LGMD1C, dysferlin immunoreactivity is reduced in RMD but more pronounced in homozygous as compared with heterozygous RMD. Thus, we further extend the phenotypic variability of muscle caveolinopathies by identification of a severe form of RMD associated with homozygous CAV3 mutations. Ann Neurol 2003

Research paper thumbnail of Rippling Muscle Disease in Childhood

Journal of Child Neurology, 2002

Rippling muscle disease is a rare autosomal dominant disorder first described in 1975. Recently, ... more Rippling muscle disease is a rare autosomal dominant disorder first described in 1975. Recently, it could be classified as a caveolinopathy; in European families, mutations in the caveolin-3 gene were revealed as causing this disease. Although clinical symptoms were almost all described in adulthood, we are now reporting clinical data of seven children with rippling muscle disease owing to mutations in the caveolin-3 gene. Initial symptoms were frequent falls, inability to walk on heels, tiptoe walking with pain and a warm-up phenomenon, calf hypertrophy, and an elevated serum creatine kinase level. Percussion-/pressure-induced rapid contractions, painful muscle mounding, and rippling could be observed even in early childhood. The diagnosis can be confirmed by molecular genetic analysis. Muscle biopsy must be considered in patients without muscle weakness or mechanical hyperirritability to differentiate between rippling muscle disease and limb-girdle muscular dystrophy 1C.

Research paper thumbnail of A geometric analysis of logarithmic switchback phenomena

Journal of Physics: Conference Series, 2005

One common characteristic of many classical singular perturbation problems is the occurrence of l... more One common characteristic of many classical singular perturbation problems is the occurrence of logarithmic (switchback) terms in the corresponding asymptotic expansions. We discuss two such problems well known to give rise to logarithmic switchback: first, Lagerstrom's equation, a model related to the asymptotic treatment of low Reynolds number flow from fluid mechanics, and second, the Evans function approach to the stability of degenerate shock waves in (scalar) reaction-diffusion equations. We show how asymptotic expansions for these two problems can be obtained by means of methods from dynamical systems theory as well as of the blow-up technique. We identify the structure of these expansions and demonstrate that the occurrence of the logarithmic switchback terms therein is in fact caused by a resonance phenomenon.

Research paper thumbnail of A geometric approach to bistable front propagation in scalar reaction–diffusion equations with cut-off

Physica D-nonlinear Phenomena, 2010

Research paper thumbnail of Rigorous Asymptotic Expansions for Critical Wave Speeds in a Family of Scalar Reaction-Diffusion Equations

Journal of Dynamics and Differential Equations, 2006

Research paper thumbnail of The critical wave speed for the Fisher Kolmogorov Petrowskii Piscounov equation with cut-off

Research paper thumbnail of The asymptotic critical wave speed in a family of scalar reaction–diffusion equations

Journal of Mathematical Analysis and Applications, 2007

Research paper thumbnail of Mixed-Mode Oscillations in Three TimeScale Systems: A Prototypical Example

Siam Journal on Applied Dynamical Systems, 2008

Research paper thumbnail of Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron

Research paper thumbnail of Homozygous mutations incaveolin-3 cause a severe form of rippling muscle disease

Annals of Neurology, 2003

Heterozygous missense mutations in the caveolin-3 gene (CAV3) cause different muscle disorders. M... more Heterozygous missense mutations in the caveolin-3 gene (CAV3) cause different muscle disorders. Most patients with CAV3 alterations present with rippling muscle disease (RMD) characterized by signs of increased muscle irritability without muscle weakness. In some patients, CAV3 mutations underlie the progressive limb-girdle muscular dystrophy type 1C (LGMD1C). Here, we report two unrelated patients with novel homozygous mutations (L86P and A92T) in CAV3. Both presented with a more severe clinical phenotype than usually seen in RMD. Immunohistochemical and immunoblot analyses of muscle biopsies showed a strong reduction of caveolin-3 in both homozygous RMD patients similar to the findings in heterozygous RMD. Electron microscopy studies showed a nearly complete absence of caveolae in the sarcolemma in all RMD patients analyzed. Additional plasma membrane irregularities (small plasmalemmal discontinuities, subsarcolemmal vacuoles, abnormal papillary projections) were more pronounced in homozygous than in heterozygous RMD patients. A stronger activation of nitric oxide synthase was observed in both homozygous patients compared with heterozygous RMD. Like in LGMD1C, dysferlin immunoreactivity is reduced in RMD but more pronounced in homozygous as compared with heterozygous RMD. Thus, we further extend the phenotypic variability of muscle caveolinopathies by identification of a severe form of RMD associated with homozygous CAV3 mutations. Ann Neurol 2003

Research paper thumbnail of Rippling Muscle Disease in Childhood

Journal of Child Neurology, 2002

Rippling muscle disease is a rare autosomal dominant disorder first described in 1975. Recently, ... more Rippling muscle disease is a rare autosomal dominant disorder first described in 1975. Recently, it could be classified as a caveolinopathy; in European families, mutations in the caveolin-3 gene were revealed as causing this disease. Although clinical symptoms were almost all described in adulthood, we are now reporting clinical data of seven children with rippling muscle disease owing to mutations in the caveolin-3 gene. Initial symptoms were frequent falls, inability to walk on heels, tiptoe walking with pain and a warm-up phenomenon, calf hypertrophy, and an elevated serum creatine kinase level. Percussion-/pressure-induced rapid contractions, painful muscle mounding, and rippling could be observed even in early childhood. The diagnosis can be confirmed by molecular genetic analysis. Muscle biopsy must be considered in patients without muscle weakness or mechanical hyperirritability to differentiate between rippling muscle disease and limb-girdle muscular dystrophy 1C.

Research paper thumbnail of A geometric analysis of logarithmic switchback phenomena

Journal of Physics: Conference Series, 2005

One common characteristic of many classical singular perturbation problems is the occurrence of l... more One common characteristic of many classical singular perturbation problems is the occurrence of logarithmic (switchback) terms in the corresponding asymptotic expansions. We discuss two such problems well known to give rise to logarithmic switchback: first, Lagerstrom's equation, a model related to the asymptotic treatment of low Reynolds number flow from fluid mechanics, and second, the Evans function approach to the stability of degenerate shock waves in (scalar) reaction-diffusion equations. We show how asymptotic expansions for these two problems can be obtained by means of methods from dynamical systems theory as well as of the blow-up technique. We identify the structure of these expansions and demonstrate that the occurrence of the logarithmic switchback terms therein is in fact caused by a resonance phenomenon.

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