Brain systems engage in what are generally considered to be among the most complex forms of information processing. In the present study, we investigated the functional complexity of anuran auditory processing using t...Brain systems engage in what are generally considered to be among the most complex forms of information processing. In the present study, we investigated the functional complexity of anuran auditory processing using the approximate entropy（Ap En） protocol for electroencephalogram（EEG） recordings from the forebrain and midbrain while male and female music frogs（Babina daunchina） listened to acoustic stimuli whose biological significance varied. The stimuli used were synthesized white noise（reflecting a novel signal）, conspecific male advertisement calls with either high or low sexual attractiveness（reflecting sexual selection） and silence（reflecting a baseline）. The results showed that 1） Ap En evoked by conspecific calls exceeded Ap En evoked by synthesized white noise in the left mesencephalon indicating this structure plays a critical role in processing acoustic signals with biological significance; 2） Ap En in the mesencephalon was significantly higher than for the telencephalon, consistent with the fact that the anuran midbrain contains a large well-organized auditory nucleus（torus semicircularis） while the forebrain does not; 3） for females Ap En in the mesencephalon was significantly different than that of males, suggesting that males and females process biological stimuli related to mate choice differently.展开更多
Based on a graph-theoretic analysis,we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m,p,n),and describe the irreducible subsystems of all possible types in the root...Based on a graph-theoretic analysis,we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m,p,n),and describe the irreducible subsystems of all possible types in the root system R(m,p,n)of G(m,p,n).展开更多
Kostka functions K_(λ,μ)~±(t), indexed by r-partitions λ and μ of n, are a generalization of Kostka polynomials K_(λ,μ)(t) indexed by partitions λ,μ of n. It is known that Kostka polynomials have an inter...Kostka functions K_(λ,μ)~±(t), indexed by r-partitions λ and μ of n, are a generalization of Kostka polynomials K_(λ,μ)(t) indexed by partitions λ,μ of n. It is known that Kostka polynomials have an interpretation in terms of Lusztig's partition function. Finkelberg and Ionov(2016) defined alternate functions K_(λ,μ)(t) by using an analogue of Lusztig's partition function, and showed that K_(λ,μ)(t) ∈Z≥0[t] for generic μ by making use of a coherent realization. They conjectured that K_(λ,μ)(t) coincide with K_(λ,μ)^-(t). In this paper, we show that their conjecture holds. We also discuss the multi-variable version, namely, r-variable Kostka functions K_(λ,μ)~±(t_1,…,t_r).展开更多
基金supported by the grants from the National Natural Science Foundation of China (No. 31372217 and No. 31672305) to Guangzhan Fang
文摘Brain systems engage in what are generally considered to be among the most complex forms of information processing. In the present study, we investigated the functional complexity of anuran auditory processing using the approximate entropy（Ap En） protocol for electroencephalogram（EEG） recordings from the forebrain and midbrain while male and female music frogs（Babina daunchina） listened to acoustic stimuli whose biological significance varied. The stimuli used were synthesized white noise（reflecting a novel signal）, conspecific male advertisement calls with either high or low sexual attractiveness（reflecting sexual selection） and silence（reflecting a baseline）. The results showed that 1） Ap En evoked by conspecific calls exceeded Ap En evoked by synthesized white noise in the left mesencephalon indicating this structure plays a critical role in processing acoustic signals with biological significance; 2） Ap En in the mesencephalon was significantly higher than for the telencephalon, consistent with the fact that the anuran midbrain contains a large well-organized auditory nucleus（torus semicircularis） while the forebrain does not; 3） for females Ap En in the mesencephalon was significantly different than that of males, suggesting that males and females process biological stimuli related to mate choice differently.
基金supported by National Natural Science Foundation of China(Grant Nos.10631010,10971138)the General Research Project of Shanghai Normal University(Grant No.SK200702)+2 种基金the Science Foundation of University Doctoral Project of China(Grant No.20060269011)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.41192803)Shanghai Leading Academic Discipline Project(Grant No.B407)
文摘Based on a graph-theoretic analysis,we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m,p,n),and describe the irreducible subsystems of all possible types in the root system R(m,p,n)of G(m,p,n).
文摘Kostka functions K_(λ,μ)~±(t), indexed by r-partitions λ and μ of n, are a generalization of Kostka polynomials K_(λ,μ)(t) indexed by partitions λ,μ of n. It is known that Kostka polynomials have an interpretation in terms of Lusztig's partition function. Finkelberg and Ionov(2016) defined alternate functions K_(λ,μ)(t) by using an analogue of Lusztig's partition function, and showed that K_(λ,μ)(t) ∈Z≥0[t] for generic μ by making use of a coherent realization. They conjectured that K_(λ,μ)(t) coincide with K_(λ,μ)^-(t). In this paper, we show that their conjecture holds. We also discuss the multi-variable version, namely, r-variable Kostka functions K_(λ,μ)~±(t_1,…,t_r).
