title: Describing the stochastic dynamics of neurons using Hamilton’s equations of classical mechanics

authors: Wilson, Marcus T.

subjects: neurons

abstract: We consider the most likely behaviour of neuron models by formulating them in terms of Hamilton’s equations. Starting from a Lagrangian for a stochastic system, we describe how Hamilton’s equations of classical mechanics can be used to derive an equivalent description in terms of canonical co-ordinates and momenta. We give physical meaning to these generalized momenta; speciﬁcally they are linear combinations of the noise terms in the stochastic model. Pseudo-kinetic energy and potential energy terms are also derived. The conjugate momenta can be considered as growing modes, and by implication the most likely noise input to a system will grow exponentially at large times; this surprising prediction agrees with existing experimental work on a single neuron. For many-neuron models, multiple growing modes will exist, and the numerical analysis of these is more complicated; however, the approach may still provide insight on the more detailed dynamics of these systems.

text: Describing the stochastic dynamics of neurons using Hamilton’s equations of classical mechanics We consider the most likely behaviour of neuron models by formulating them in terms of Hamilton’s equations. Starting from a Lagrangian for a stochastic system, we describe how Hamilton’s equations of classical mechanics can be used to derive an equivalent description in terms of canonical co-ordinates and momenta. We give physical meaning to these generalized momenta; speciﬁcally they are linear combinations of the noise terms in the stochastic model. Pseudo-kinetic energy and potential energy terms are also derived. The conjugate momenta can be considered as growing modes, and by implication the most likely noise input to a system will grow exponentially at large times; this surprising prediction agrees with existing experimental work on a single neuron. For many-neuron models, multiple growing modes will exist, and the numerical analysis of these is more complicated; however, the approach may still provide insight on the more detailed dynamics of these systems.

year: 2008

title: Momentum returns, market states, and market dynamics: Are Islamic stocks different?

authors: Cheema, Muhammad A.

subjects: Islamic stocks

abstract: Recent studies suggest that momentum returns are conditioned by market states and market dynamics. We ask if Islamic stocks behave differently from Non-Islamic stocks. Using data from the Malaysian stock market from 1991 to 2015, we find no significant difference in Islamic versus Non-Islamic stocks either in their level of momentum returns or in the behaviour of momentum returns in response to market states and market dynamics, irrespective of whether we use time-series or cross-sectional momentum returns. Interestingly, we find that the behaviour of momentum returns in Malaysia is broadly consistent with that in the US market in that momentum returns are higher following UP markets compared with momentum returns following DOWN markets. We also find that momentum returns are larger when the market continues in same state than when it transitions to a different state, consistent with results in the US market and that the absence of momentum returns following DOWN market states is due to market dynamics. Our results suggest that investors in Islamic stocks can execute momentum strategies without loss of efficacy compared with Non-Islamic stocks.

text: Momentum returns, market states, and market dynamics: Are Islamic stocks different? Recent studies suggest that momentum returns are conditioned by market states and market dynamics. We ask if Islamic stocks behave differently from Non-Islamic stocks. Using data from the Malaysian stock market from 1991 to 2015, we find no significant difference in Islamic versus Non-Islamic stocks either in their level of momentum returns or in the behaviour of momentum returns in response to market states and market dynamics, irrespective of whether we use time-series or cross-sectional momentum returns. Interestingly, we find that the behaviour of momentum returns in Malaysia is broadly consistent with that in the US market in that momentum returns are higher following UP markets compared with momentum returns following DOWN markets. We also find that momentum returns are larger when the market continues in same state than when it transitions to a different state, consistent with results in the US market and that the absence of momentum returns following DOWN market states is due to market dynamics. Our results suggest that investors in Islamic stocks can execute momentum strategies without loss of efficacy compared with Non-Islamic stocks.

year: 2016

title: Te Kauwhanganui o Tāwhiao

authors: Teinakore, Tiare Kata

abstract: Wiremu Tarapīpipi Te Waharoa Tamihana: Kaiwhakawahi Kīngi

I te tau 1892 i kite a Tāwhiao i te hinga mai o te iwi Māori i te rau o te patu a te Pākehā, ka whakatūngia mai ko tōna whare pāremata a Te Kauwhanganui hei pīkau i ēnei taumahatanga. He whare pāremata tēnei i whakatūngia mai i te rohe tonu o Ngāti Hauā, he whare pāremata mō ngā iwi Māori puta noa i Aotearoa, he whare whakatau nawe, he whare whakature kaupapa, he punanga tēnei mō te iwi Māori. Ko Te Kauwhanganui te tāhuhu o tēnei tuhinga whakapae, engari, ko te aronga nui, ko te takenga mai o Te Kauwhanganui i tēwhea ao, te ao Māori, te ao Pākehā rānei? I konei mahuta mai ai ko te kaupapa matua o tēnei tuhinga.
“I pūtake mai Te Kauwhanganui o Tāwhiao i te ao Māori tūturu, i ngā whakaaweawe rānei o te mana whakahaere o te Pākehā?”
Ko tēnei kaupapa ka rukuhia atu mā te huri kōaro ki te rangahau i te mana whakahaere o te ao Māori tūturu. Ka rangahautia ko te mana whakahaere o te iwi Māori i mua i te taenga mai o te Pākehā, kia mahea ai te kite he aha rā ngā tikanga o te ao Māori tūturu. Ka hūpeke atu ki te taenga mai o te Pākehā ki Aotearoa, ka whakaatu i ngā whakaaweawe mana whakahaere o te Pākehā i tōia mai e te Pākehā, ko Te Tiriti o Waitangi, ko Te Kawenata motuhake o Aotearoa ēnei. Ka whakaatu hoki i te pānga o ēnei whakaaweawe ki ngā kōkiritanga, ki ngā whakahoki a te Māori ki Te Tiriti o Waitangi me Te Kawenata motuhake o Aotearoa. Kātahi ka whakamāramahia ngā tikanga o Te Kauwhanganui me te tautoko o ngā pou kōrero i ēnei whakamārama. Ka whakamutua ake me te tātari i ngā hua o ēnei kimihanga, kia taea te kite ko tēwhea te ao ka pūtake mai Te Kauwhanganui, mai i te ao Māori tūturu, mai i ngā whakaaweawe rānei o te mana whakahaere o te Pākehā.

text: Te Kauwhanganui o Tāwhiao Wiremu Tarapīpipi Te Waharoa Tamihana: Kaiwhakawahi Kīngi

I te tau 1892 i kite a Tāwhiao i te hinga mai o te iwi Māori i te rau o te patu a te Pākehā, ka whakatūngia mai ko tōna whare pāremata a Te Kauwhanganui hei pīkau i ēnei taumahatanga. He whare pāremata tēnei i whakatūngia mai i te rohe tonu o Ngāti Hauā, he whare pāremata mō ngā iwi Māori puta noa i Aotearoa, he whare whakatau nawe, he whare whakature kaupapa, he punanga tēnei mō te iwi Māori. Ko Te Kauwhanganui te tāhuhu o tēnei tuhinga whakapae, engari, ko te aronga nui, ko te takenga mai o Te Kauwhanganui i tēwhea ao, te ao Māori, te ao Pākehā rānei? I konei mahuta mai ai ko te kaupapa matua o tēnei tuhinga.
“I pūtake mai Te Kauwhanganui o Tāwhiao i te ao Māori tūturu, i ngā whakaaweawe rānei o te mana whakahaere o te Pākehā?”
Ko tēnei kaupapa ka rukuhia atu mā te huri kōaro ki te rangahau i te mana whakahaere o te ao Māori tūturu. Ka rangahautia ko te mana whakahaere o te iwi Māori i mua i te taenga mai o te Pākehā, kia mahea ai te kite he aha rā ngā tikanga o te ao Māori tūturu. Ka hūpeke atu ki te taenga mai o te Pākehā ki Aotearoa, ka whakaatu i ngā whakaaweawe mana whakahaere o te Pākehā i tōia mai e te Pākehā, ko Te Tiriti o Waitangi, ko Te Kawenata motuhake o Aotearoa ēnei. Ka whakaatu hoki i te pānga o ēnei whakaaweawe ki ngā kōkiritanga, ki ngā whakahoki a te Māori ki Te Tiriti o Waitangi me Te Kawenata motuhake o Aotearoa. Kātahi ka whakamāramahia ngā tikanga o Te Kauwhanganui me te tautoko o ngā pou kōrero i ēnei whakamārama. Ka whakamutua ake me te tātari i ngā hua o ēnei kimihanga, kia taea te kite ko tēwhea te ao ka pūtake mai Te Kauwhanganui, mai i te ao Māori tūturu, mai i ngā whakaaweawe rānei o te mana whakahaere o te Pākehā.

year: 2013