The human brain contains an estimated 100 billion neurons that must be systematically organized into functional neural circuits for it to function properly.These circuits range from short-range local signaling network...The human brain contains an estimated 100 billion neurons that must be systematically organized into functional neural circuits for it to function properly.These circuits range from short-range local signaling networks between neighboring neurons to long-range networks formed between various brain regions.Compelling converging evidence indicates that alterations in neural circuits arising from abnormalities during early neuronal development or neurodegeneration contribute significantly to the etiology of neurological disorders.Supporting this notion,efforts to identify genetic causes of these disorders have uncovered an over-representation of genes encoding proteins involved in the processes of neuronal differentiation,maturation,synaptogenesis and synaptic function.Fasciculation and elongation protein zeta-1,a Kinesin-1 adapter,has emerged as a key central player involved in many of these processes.Fasciculation and elongation protein zeta-1-dependent transport of synaptic cargoes and mitochondria is essential for neuronal development and synapse establishment.Furthermore,it acts downstream of guidance cue pathways to regulate axo-dendritic development.Significantly,perturbing its function causes abnormalities in neuronal development and synapse formation both in the brain as well as the peripheral nervous system.Mutations and deletions of the fasciculation and elongation protein zeta-1 gene are linked to neurodevelopmental disorders.Moreover,altered phosphorylation of the protein contributes to neurodegenerative disorders.Together,these findings strongly implicate the importance of fasciculation and elongation protein zeta-1 in the establishment of neuronal circuits and its maintenance.展开更多
The purpose for this research was to investigate the Riemann zeta function at odd integer values, because there was no simple representation for these results. The research resulted in the closed form expression <i...The purpose for this research was to investigate the Riemann zeta function at odd integer values, because there was no simple representation for these results. The research resulted in the closed form expression <img src="Edit_909dc64a-717a-4477-a9f8-a3b94ab4008e.bmp" alt="" /> for representing the zeta function at the odd integer values 2<em>n</em>+1 for <em>n</em> a positive integer. The above representation shows the zeta function at odd positive integers can be represented in terms of the Euler numbers <em>E</em><sub>2<em>n</em></sub> and the polygamma functions <em>ψ</em><sup>(2<em>n</em>)</sup>(3/4). This is a new result for this study area. For completeness, this paper presents a review of selected properties of the Riemann zeta function together with how these properties are derived. This paper will summarize how to evaluate zeta (n) for all integers n different from 1. Also as a result of this research, one can obtain a closed form expression for the Dirichlet beta series evaluated at positive even integers. The results presented enable one to construct closed form expressions for the Dirichlet eta, lambda and beta series evaluated at odd and even integers. Closed form expressions for Apéry’s constant zeta (3) and Catalan’s constant beta (2) are also presented.展开更多
基金the Singapore Ministry of Education(T1-2015 Apr-03)the National University of SingaporeInstitute for Health Innovation and Technology to JJEC.
文摘The human brain contains an estimated 100 billion neurons that must be systematically organized into functional neural circuits for it to function properly.These circuits range from short-range local signaling networks between neighboring neurons to long-range networks formed between various brain regions.Compelling converging evidence indicates that alterations in neural circuits arising from abnormalities during early neuronal development or neurodegeneration contribute significantly to the etiology of neurological disorders.Supporting this notion,efforts to identify genetic causes of these disorders have uncovered an over-representation of genes encoding proteins involved in the processes of neuronal differentiation,maturation,synaptogenesis and synaptic function.Fasciculation and elongation protein zeta-1,a Kinesin-1 adapter,has emerged as a key central player involved in many of these processes.Fasciculation and elongation protein zeta-1-dependent transport of synaptic cargoes and mitochondria is essential for neuronal development and synapse establishment.Furthermore,it acts downstream of guidance cue pathways to regulate axo-dendritic development.Significantly,perturbing its function causes abnormalities in neuronal development and synapse formation both in the brain as well as the peripheral nervous system.Mutations and deletions of the fasciculation and elongation protein zeta-1 gene are linked to neurodevelopmental disorders.Moreover,altered phosphorylation of the protein contributes to neurodegenerative disorders.Together,these findings strongly implicate the importance of fasciculation and elongation protein zeta-1 in the establishment of neuronal circuits and its maintenance.
文摘The purpose for this research was to investigate the Riemann zeta function at odd integer values, because there was no simple representation for these results. The research resulted in the closed form expression <img src="Edit_909dc64a-717a-4477-a9f8-a3b94ab4008e.bmp" alt="" /> for representing the zeta function at the odd integer values 2<em>n</em>+1 for <em>n</em> a positive integer. The above representation shows the zeta function at odd positive integers can be represented in terms of the Euler numbers <em>E</em><sub>2<em>n</em></sub> and the polygamma functions <em>ψ</em><sup>(2<em>n</em>)</sup>(3/4). This is a new result for this study area. For completeness, this paper presents a review of selected properties of the Riemann zeta function together with how these properties are derived. This paper will summarize how to evaluate zeta (n) for all integers n different from 1. Also as a result of this research, one can obtain a closed form expression for the Dirichlet beta series evaluated at positive even integers. The results presented enable one to construct closed form expressions for the Dirichlet eta, lambda and beta series evaluated at odd and even integers. Closed form expressions for Apéry’s constant zeta (3) and Catalan’s constant beta (2) are also presented.
