Page 1. Abstract Non-deterministic pitch scales observed in traditional Turkish music are viewed ... more Page 1. Abstract Non-deterministic pitch scales observed in traditional Turkish music are viewed as distributions along the pitch axis. This thesis contrasts with the conventional norm of using deterministic scales, where pitches ...
Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was... more Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached with the use of two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model that is capable of accommodating random variations in biological phenomena, as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model are replaced by probability distributions fitted into historical data from colony records. With the use of Crystal Ball (Decisioneering, Inc., Denver, CO) software, user-selected distributions are embedded in appropriate cells in the spreadsheet model. A Monte Carlo simulation scheme running within the spreadsheet draws (on each cycle) random values for input parameters from the distribution embedded in each relevant cell, and thus generates output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision-maker with a mathematical habitat for statistical analysis in a stochastic setting. In addition to providing standard statistical measures (e.g., mean, variance, and range) that describe the location and shape of the distribution, this approach offers the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.
An attempt is made to initiate an investigation into periodic, in-phase, extensional vibrations o... more An attempt is made to initiate an investigation into periodic, in-phase, extensional vibrations of flat plates with the purpose of characterizing those sub-domains of the elastic plane with constant tangential stresses along free boundaries at every *instant* of motion. For a flat plate in simple tension, it is shown that such vibrations are not possible.
A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pai... more A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pair elements separated by m steps. Allowing multiple values for m=1,2,…,k leads to a multiplicity of ordered pairs that function as building blocks in the construction of multi-layered feature vectors to represent the sequence. Index positions of the leading elements in each ordered pair serve as scalar components of the feature vector for capturing spatial/temporal structures at the local level. Such representation provides a fertile mathematical space in data mining for discovering potentially interesting patterns in sequential data. Experiments on the classification problem involving two classes, Eukaryota and Euglenozoa returned encouraging results, with 96% overall accuracy in identifying the class for each bio-sequence in the two groups.
Two taksims in the Hüzzam Makam by two Legendary Masters of Turkish Makam Music . . .
Nubar Tekya... more Two taksims in the Hüzzam Makam by two Legendary Masters of Turkish Makam Music . . . Nubar Tekyay (violin), Niyazi Sayın (Kız Ney). Recorded at different time frames; totally disconnected spiritual modes; and of different duration. Flow `synchronized`, for comparison, by using % as the unit of `time`. Objective: To explore mathematical patterns making up the acoustic architecture of, together with clues on admissible seyirs for the Hüzzam makam.
Two taksims - separate 78 rpm recordings - by the legendary master Cemil Bey on Tanbur in the Şed... more Two taksims - separate 78 rpm recordings - by the legendary master Cemil Bey on Tanbur in the Şed-di Araban makam. A comparative exploration of the two taksims might unlock clues on the *seyir* of this fundamental makam (courtesy, master Niyazi Sayın). Unequal durations were normalized by taking *flow* as the % of the taksim.
A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pai... more A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pair elements separated by m steps. Allowing multiple values for m=1,2,…,k leads to a multiplicity of ordered pairs that function as building blocks in the construction of multi-layered feature vectors to represent the sequence. Index positions of the leading elements in each ordered pair serve as scalar components of the feature vector for capturing spatial/temporal structures at the local level. Such representation provides a fertile mathematical space in data mining for discovering potentially interesting patterns in sequential data. Experiments on the classification problem involving two classes, Eukaryota and Euglenozoa returned encouraging results, with 96% overall accuracy in identifying the class for each bio-sequence in the two groups.
Geleneksel Türk Musikisi icralarında kullanılan ıskalaların "gezinirlik" gösteren nitelikleri, pe... more Geleneksel Türk Musikisi icralarında kullanılan ıskalaların "gezinirlik" gösteren nitelikleri, perdelerin frekans ekseni boyunca belirli bölgelerde kümeleşen "dağılımlar" olarak düşünülebileceği izlenimini vermektedir. Bu öneri şimdiye kadar alışılagelmiş ve perdelerin sayılar ekseni üzerinde belirli sayı dizileri ile gösterildiği - tuşlu veya perdeli sazlarda olduğu gibi - sabit ıskala modelleri ile ters düşmektedir. Bu çalışmada usta icracıların doğaçlama sırasında kullandıkları gerçek frekanslar Hertz cinsinden ölçülmüş ve modal ıskalaların dağılımlar şeklinde belirlenmesi amacına yönelik matematiksel analiz yöntemleri uygulanmıştır. Ses ölçüm sisteminin nitelikleri ile uygulanan matematiksel analiz yöntemlerinin olabilirliği iki seçkin usta icracının yaptıkları doğaçlamalar örnek alınarak gösterilmeğe çalışılmıştır.
Since the early 20th century, various theories have been advanced in order to mathematically expl... more Since the early 20th century, various theories have been advanced in order to mathematically explain and notate modes of Traditional Turkish music known as maqams. In this article, maqam scales according to various theoretical models based on different tunings are compared with pitch measurements obtained from select recordings of master Turkish performers in order to study their level of match with analysed data. Chosen recordings are subjected to a fully computerized sequence of signal processing algorithms for the automatic determination of the set of relative pitches for each maqam scale: f0 estimation, histogram computation, tonic detection + histogram alignment, and peak picking. For nine well-recognized maqams, automatically derived relative pitches are compared with scale tones defined by theoretical models using quantitative distance measures. We analyse and interpret histogram peaks based on these measures to find the theoretical models most conforming with all the recordi...
An attempt is made to initiate an investigation into periodic, in-phase, extensional vibrations o... more An attempt is made to initiate an investigation into periodic, in-phase, extensional vibrations of flat plates with the purpose of characterizing those sub-domains of the elastic plane with constant tangential stresses along free boundaries at every *instant* of motion. For a flat plate in simple tension, it is shown that such vibrations are not possible.
Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was... more Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached by two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model capable of accommodating random variations in biological phenomena as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model were replaced by probability distributions fitted into historical data from colony records. A software CRYSTAL BALL allows embedding user-selected distributions in appropriate cells in the spreadsheet model. On each cycle a Monte Carlo simulation scheme running within the spreadsheet itself draws random values for input parameters from the distribution embedded in each relevant cell, thus generating output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision maker a mathematical habitat for statistical analysis in a stochastic setting. In addition to standard statistical measures (mean, variance, range, etc.) describing the location and shape of the distribution, this approach presents the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.
Key words: deterministic modeling; stochastic modeling; probability distributions; Monte Carlo simulation; sensitivity analysis.
Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was... more Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached by two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model capable of accommodating random variations in biological phenomena as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model were replaced by probability distributions fitted into historical data from colony records. A software CRYSTAL BALL allows embedding user-selected distributions in appropriate cells in the spreadsheet model. On each cycle a Monte Carlo simulation scheme running within the spreadsheet itself draws random values for input parameters from the distribution embedded in each relevant cell, thus generating output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision maker a mathematical habitat for statistical analysis in a stochastic setting. In addition to standard statistical measures (mean, variance, range, etc.) describing the location and shape of the distribution, this approach presents the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.
Key words: deterministic modeling; stochastic modeling; probability distributions; Monte Carlo simulation; sensitivity analysis.
Page 1. Abstract Non-deterministic pitch scales observed in traditional Turkish music are viewed ... more Page 1. Abstract Non-deterministic pitch scales observed in traditional Turkish music are viewed as distributions along the pitch axis. This thesis contrasts with the conventional norm of using deterministic scales, where pitches ...
Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was... more Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached with the use of two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model that is capable of accommodating random variations in biological phenomena, as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model are replaced by probability distributions fitted into historical data from colony records. With the use of Crystal Ball (Decisioneering, Inc., Denver, CO) software, user-selected distributions are embedded in appropriate cells in the spreadsheet model. A Monte Carlo simulation scheme running within the spreadsheet draws (on each cycle) random values for input parameters from the distribution embedded in each relevant cell, and thus generates output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision-maker with a mathematical habitat for statistical analysis in a stochastic setting. In addition to providing standard statistical measures (e.g., mean, variance, and range) that describe the location and shape of the distribution, this approach offers the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.
An attempt is made to initiate an investigation into periodic, in-phase, extensional vibrations o... more An attempt is made to initiate an investigation into periodic, in-phase, extensional vibrations of flat plates with the purpose of characterizing those sub-domains of the elastic plane with constant tangential stresses along free boundaries at every *instant* of motion. For a flat plate in simple tension, it is shown that such vibrations are not possible.
A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pai... more A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pair elements separated by m steps. Allowing multiple values for m=1,2,…,k leads to a multiplicity of ordered pairs that function as building blocks in the construction of multi-layered feature vectors to represent the sequence. Index positions of the leading elements in each ordered pair serve as scalar components of the feature vector for capturing spatial/temporal structures at the local level. Such representation provides a fertile mathematical space in data mining for discovering potentially interesting patterns in sequential data. Experiments on the classification problem involving two classes, Eukaryota and Euglenozoa returned encouraging results, with 96% overall accuracy in identifying the class for each bio-sequence in the two groups.
Two taksims in the Hüzzam Makam by two Legendary Masters of Turkish Makam Music . . .
Nubar Tekya... more Two taksims in the Hüzzam Makam by two Legendary Masters of Turkish Makam Music . . . Nubar Tekyay (violin), Niyazi Sayın (Kız Ney). Recorded at different time frames; totally disconnected spiritual modes; and of different duration. Flow `synchronized`, for comparison, by using % as the unit of `time`. Objective: To explore mathematical patterns making up the acoustic architecture of, together with clues on admissible seyirs for the Hüzzam makam.
Two taksims - separate 78 rpm recordings - by the legendary master Cemil Bey on Tanbur in the Şed... more Two taksims - separate 78 rpm recordings - by the legendary master Cemil Bey on Tanbur in the Şed-di Araban makam. A comparative exploration of the two taksims might unlock clues on the *seyir* of this fundamental makam (courtesy, master Niyazi Sayın). Unequal durations were normalized by taking *flow* as the % of the taksim.
A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pai... more A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pair elements separated by m steps. Allowing multiple values for m=1,2,…,k leads to a multiplicity of ordered pairs that function as building blocks in the construction of multi-layered feature vectors to represent the sequence. Index positions of the leading elements in each ordered pair serve as scalar components of the feature vector for capturing spatial/temporal structures at the local level. Such representation provides a fertile mathematical space in data mining for discovering potentially interesting patterns in sequential data. Experiments on the classification problem involving two classes, Eukaryota and Euglenozoa returned encouraging results, with 96% overall accuracy in identifying the class for each bio-sequence in the two groups.
Geleneksel Türk Musikisi icralarında kullanılan ıskalaların "gezinirlik" gösteren nitelikleri, pe... more Geleneksel Türk Musikisi icralarında kullanılan ıskalaların "gezinirlik" gösteren nitelikleri, perdelerin frekans ekseni boyunca belirli bölgelerde kümeleşen "dağılımlar" olarak düşünülebileceği izlenimini vermektedir. Bu öneri şimdiye kadar alışılagelmiş ve perdelerin sayılar ekseni üzerinde belirli sayı dizileri ile gösterildiği - tuşlu veya perdeli sazlarda olduğu gibi - sabit ıskala modelleri ile ters düşmektedir. Bu çalışmada usta icracıların doğaçlama sırasında kullandıkları gerçek frekanslar Hertz cinsinden ölçülmüş ve modal ıskalaların dağılımlar şeklinde belirlenmesi amacına yönelik matematiksel analiz yöntemleri uygulanmıştır. Ses ölçüm sisteminin nitelikleri ile uygulanan matematiksel analiz yöntemlerinin olabilirliği iki seçkin usta icracının yaptıkları doğaçlamalar örnek alınarak gösterilmeğe çalışılmıştır.
Since the early 20th century, various theories have been advanced in order to mathematically expl... more Since the early 20th century, various theories have been advanced in order to mathematically explain and notate modes of Traditional Turkish music known as maqams. In this article, maqam scales according to various theoretical models based on different tunings are compared with pitch measurements obtained from select recordings of master Turkish performers in order to study their level of match with analysed data. Chosen recordings are subjected to a fully computerized sequence of signal processing algorithms for the automatic determination of the set of relative pitches for each maqam scale: f0 estimation, histogram computation, tonic detection + histogram alignment, and peak picking. For nine well-recognized maqams, automatically derived relative pitches are compared with scale tones defined by theoretical models using quantitative distance measures. We analyse and interpret histogram peaks based on these measures to find the theoretical models most conforming with all the recordi...
An attempt is made to initiate an investigation into periodic, in-phase, extensional vibrations o... more An attempt is made to initiate an investigation into periodic, in-phase, extensional vibrations of flat plates with the purpose of characterizing those sub-domains of the elastic plane with constant tangential stresses along free boundaries at every *instant* of motion. For a flat plate in simple tension, it is shown that such vibrations are not possible.
Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was... more Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached by two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model capable of accommodating random variations in biological phenomena as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model were replaced by probability distributions fitted into historical data from colony records. A software CRYSTAL BALL allows embedding user-selected distributions in appropriate cells in the spreadsheet model. On each cycle a Monte Carlo simulation scheme running within the spreadsheet itself draws random values for input parameters from the distribution embedded in each relevant cell, thus generating output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision maker a mathematical habitat for statistical analysis in a stochastic setting. In addition to standard statistical measures (mean, variance, range, etc.) describing the location and shape of the distribution, this approach presents the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.
Key words: deterministic modeling; stochastic modeling; probability distributions; Monte Carlo simulation; sensitivity analysis.
Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was... more Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached by two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model capable of accommodating random variations in biological phenomena as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model were replaced by probability distributions fitted into historical data from colony records. A software CRYSTAL BALL allows embedding user-selected distributions in appropriate cells in the spreadsheet model. On each cycle a Monte Carlo simulation scheme running within the spreadsheet itself draws random values for input parameters from the distribution embedded in each relevant cell, thus generating output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision maker a mathematical habitat for statistical analysis in a stochastic setting. In addition to standard statistical measures (mean, variance, range, etc.) describing the location and shape of the distribution, this approach presents the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.
Key words: deterministic modeling; stochastic modeling; probability distributions; Monte Carlo simulation; sensitivity analysis.
A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pai... more A finite sequence drawn from a finite alphabet is disassembled into m-step ordered pairs with pair elements separated by m steps. Allowing multiple values for m=1,2,…,k leads to a multiplicity of ordered pairs that function as building blocks in the construction of multi-layered feature vectors to represent the sequence. Positions of the leading elements in each ordered pair serve as scalar components of the feature vector for capturing spatial/temporal structures at the local level. Such representation provides a fertile mathematical space in data mining for classification and analysis at the micro/macro level. Furthermore, transparency and simplicity of the method allows the researcher to access the feature space for uncovering micro patterns embedded at various layers in this multi-layered vector space.
Experiments on the classification problem involving two classes, Eukaryota and Euglenozoa returned encouraging results, with 96% overall accuracy in identifying the class for each bio-sequence in the two groups.
Exploring the Mysteries of Turkish Makam Music
Can Akkoç (Jon Ahk-koch)
Middle East Technical U... more Exploring the Mysteries of Turkish Makam Music
Can Akkoç (Jon Ahk-koch)
Middle East Technical University (METU), Institute of Applied Mathematics (IAM), Ankara, Türkiye /
Abstract: Musical patterns in makam music are delicately intertwined between two fundamental elements; the ‘underlying scale’ made up of pitch clusters (perde), and (plausibly) an infinite collection of admissible, heavily stochastic ‘melody lines’, seyir (path) for each makam.
These two structures, with relative weights shifting between makams, make up the ‘genetic code’ (ID) for the makam on hand. Apparent short-term memory might be regulating the flow of microtonal intervals in the melody line to keep characteristic features of the host makam intact.
Underlying scales in the form of pitch clusters were determined through pitch measurements around the turn of the decade as developments in sound technology rendered them do’able. However, the problem of determining the set of all(?) admissible seyirs for a given makam is still a formidable task and a mystery , revealing its many faces in all sorts of awkward situations. The task called out here might demand all mining schemes known to men, possibly schemes yet to be invented, put to work in this musical habitat never experienced before./
We’re fortunate to host another visiting expert in Turkish Music, to discuss various mathematical models of the use of pitch and melodic sequence in the Turkish “makam” pitch system (https://en.wikipedia.org/wiki/Makam)./
Title: Exploring the Mysteries of Turkish Makam Music/
Time: Tuesday October 30, 2-3 pm (30- minutes lecture plus 30 minutes questions/discussion)/
The topology (architecture) of interlacing fiber structures in the process of weaving (carpets, r... more The topology (architecture) of interlacing fiber structures in the process of weaving (carpets, rugs, fabric, tapestry, etc.) has been inspirational in modeling, identifying, and uncovering the warp and woof of natural languages. Analysis of word patterns in written texts of large corpora on colloquial English-with reference to words of context vs. connecting terms/phrases-has presented a structure analogous to that of warp and woof in weaving patterns. The algorithm discussed in this article might carry the potential of uncovering the warp and woof of all natural languages on Earth, to pave the way for linguistic analysis, as well as deep-rooted schemes in foreign language acquisition.
Communication Templates have been extracted from a corpus of 300,000 sentences drawn from written... more Communication Templates have been extracted from a corpus of 300,000 sentences drawn from written communications, in English, in the European Union (EU). The idea behind such a choice was to establish reference to English used in the International arena, as opposed to forms used exclusively in English-speaking countries around the Globe (UK, USA, Canada, Australia, UK colonies,. . .).
A novel algorithmic approach based on internalizing 'communication templates' from the target 2nd... more A novel algorithmic approach based on internalizing 'communication templates' from the target 2nd language is introduced with a premise of training learners not too distant in command of the foreign language from that of native speakers. It is conjectured that a fundamental difference between a native speaker and a 2nd language learner plausibly lies in the way thoughts are put into words, most notably usage and positioning of 'connective terms' (communication templates) used in the discourse linking context phrases. Communication templates are context-free skeletal structures made up of stationary connective terms, to be fitted with words of context for building a verbal discourse. A training scheme centered on the usage of communication templates is proposed in this article, hopefully to alleviate the frustration of 2nd language learners feeling uneasy about communicating like, or close to that of native speakers. The methodology is currently being implemented in an experimental setting, measurable results yet to be determined. It is suggested that this algorithmic scheme is likely to work for all written languages on Earth if it works for ESL.
The author is to present his personal ESL experience over the course of the past 70 years, focusi... more The author is to present his personal ESL experience over the course of the past 70 years, focusing on (a) Sequential order of elements of the English language presented in ESL programs, (b) Redundancies, (c) ‘Absurdities’ in ESL programs. A new born baby is exposed to her/his native tongue from the moment of delivery. The child picks up the vocabulary and, most importantly, the templates on the street during childhood years through constant exposure. Grammar structures are not on the radar screen, fortunately(!), until school starts with secondary education. What is demanded of an adult learner in ESL is basically the simulation of the childhood experience of a native speaker, combined with grammar rules in full bloom, all tucked into one same program within a finite time frame. This description might sound like ‘mission impossible’, and it certainly is. Whereas the human intellect is incredibly smart in capturing patterns in any setting, such as learning a new language, this feature of the human mind is completely ignored, tacitly, in the current teaching strategy by mercilessly uploading the beginner with every conceivable grammar structure under the sun for the new target language. If beginners in ESL were allowed breathing room to exercise their pattern recognition capabilities, they could go a long way, on their own, in uncovering some of the patterns making up the language, even some of the grammar structures, at least at an intuitive level.
Two taksims - separate 78 rpm recordings - by the legendary master Cemil Bey on Tanbur in the Şed... more Two taksims - separate 78 rpm recordings - by the legendary master Cemil Bey on Tanbur in the Şed-di Araban makam; might unlock clues on the *seyir* of this fundamental makam (courtesy, master Niyazi Sayın). Durations normalized by taking *flow* as the % of the taksim.
3 Saba Taksims by 3 Legendary Masters of Turkish Makam Music . . .
Cemil Bey (kemençe), Niyazi S... more 3 Saba Taksims by 3 Legendary Masters of Turkish Makam Music . . .
Cemil Bey (kemençe), Niyazi Sayın (Mansur Ney), İhsan Özgen (kemençe).
Recorded in different time frames; totally disconnected(?) spiritual modes; of different duration.
Flow `synchronized`, for comparison, by using % as the unit of `time`.
Objective: to explore mathematical patterns making up admissible seyirs for the Saba makam.
Communication Templates have been extracted from a corpus of 300,000 sentences drawn from written... more Communication Templates have been extracted from a corpus of 300,000 sentences drawn from written communications, in English, in the European Union (EU). The idea behind such a choice was to establish reference to English used in the International arena, as opposed to forms used exclusively in English-speaking countries around the Globe (UK, USA, Canada, Australia, UK colonies,. . .).
Addition Table_
Starting with (an) Addition Table, as opposed to the usual Multiplication Ta... more Addition Table_
Starting with (an) Addition Table, as opposed to the usual Multiplication Table, for beginning little girls and boys . . .
It is suggested that little girls and boys start with an Addition Table in learning Arithmetic_
Rationale:
The author has observed young adults using their fingers, inadvertently under the table, to add numbers in the order of 10. Unlike the well-established practice of learning the Multiplication Table ASAP in elementary school, this embarrassing situation with Addition is probably due to not having been exposed to a regimented approach in learning addition of small numbers around 10.
Thus, we propose exposing the little guys in grade school, first to an Addition Table (sample shown below), for them to begin to grasp, not brutal rote(!) memorization, the patterns involved in the addition operation.
The table conceals all arithmetic properties of the addition operation, to be uncovered before the little guys by an observant teacher, or better yet, to be discovered by the exuberant learner herself/himself:
_ Numerals, in red, along the main diagonal are all EVEN numbers, equal to the sum of their identical ‘components’, in blue, top row and left-most column,
_ Every element of the table, in black, is equal to the sum of its respective components along the top row and left-most column,
_ Layout of black numbers display a *symmetric* pattern - like a mirror image - with respect to the main diagonal in red,
_ The said symmetry is a visual proof of the, so called, *commutative* property of the addition operation, A + B = B + A.
This much exposure to addition should keep the little guy happy and, most of all, confident for the rest of her/his life, while keeping out their little fingers away from arithmetic operations . . .
Can Akkoç,
Middle East Technical University (METU),
Institute of Applied Mathematics (IAM),
Ankara, Turkey
An Algebra is a mathematical “structure” over a *set of mathematical objects*, together with a se... more An Algebra is a mathematical “structure” over a *set of mathematical objects*, together with a set of (algebraic) operations defined on the elements of the underlying set, satisfying certain properties.
The author is to present his personal ESL experience over the course of the past 70 years, focusi... more The author is to present his personal ESL experience over the course of the past 70 years, focusing on (a) Sequential order of elements of the English language presented in ESL programs, (b) Redundancies, (c) ‘Absurdities’ in ESL programs. A new born baby is exposed to her/his native tongue from the moment of delivery. The child picks up the vocabulary and, most importantly, the templates on the street during childhood years through constant exposure. Grammar structures are not on the radar screen, fortunately(!), until school starts with secondary education. What is demanded of an adult learner in ESL is basically the simulation of the childhood experience of a native speaker, combined with grammar rules in full bloom, all tucked into one same program within a finite time frame. This description might sound like ‘mission impossible’, and it certainly is. Whereas the human intellect is incredibly smart in capturing patterns in any setting, such as learning a new language, this feature of the human mind is completely ignored, tacitly, in the current teaching strategy by mercilessly uploading the beginner with every conceivable grammar structure under the sun for the new target language. If beginners in ESL were allowed breathing room to exercise their pattern recognition capabilities, they could go a long way, on their own, in uncovering some of the patterns making up the language, even some of the grammar structures, at least at an intuitive level.
Uploads
Papers by Can C Akkoç
Nubar Tekyay (violin), Niyazi Sayın (Kız Ney).
Recorded at different time frames; totally disconnected spiritual modes; and of different duration.
Flow `synchronized`, for comparison, by using % as the unit of `time`.
Objective: To explore mathematical patterns making up the acoustic architecture of, together with clues on admissible seyirs for the Hüzzam makam.
Key words: deterministic modeling; stochastic modeling; probability distributions; Monte Carlo simulation; sensitivity analysis.
Key words: deterministic modeling; stochastic modeling; probability distributions; Monte Carlo simulation; sensitivity analysis.
Nubar Tekyay (violin), Niyazi Sayın (Kız Ney).
Recorded at different time frames; totally disconnected spiritual modes; and of different duration.
Flow `synchronized`, for comparison, by using % as the unit of `time`.
Objective: To explore mathematical patterns making up the acoustic architecture of, together with clues on admissible seyirs for the Hüzzam makam.
Key words: deterministic modeling; stochastic modeling; probability distributions; Monte Carlo simulation; sensitivity analysis.
Key words: deterministic modeling; stochastic modeling; probability distributions; Monte Carlo simulation; sensitivity analysis.
Experiments on the classification problem involving two classes, Eukaryota and Euglenozoa returned encouraging results, with 96% overall accuracy in identifying the class for each bio-sequence in the two groups.
Can Akkoç (Jon Ahk-koch)
Middle East Technical University (METU), Institute of Applied Mathematics (IAM), Ankara, Türkiye /
Abstract: Musical patterns in makam music are delicately intertwined between two fundamental elements; the ‘underlying scale’ made up of pitch clusters (perde), and (plausibly) an infinite collection of admissible, heavily stochastic ‘melody lines’, seyir (path) for each makam.
These two structures, with relative weights shifting between makams, make up the ‘genetic code’ (ID) for the makam on hand. Apparent short-term memory might be regulating the flow of microtonal intervals in the melody line to keep characteristic features of the host makam intact.
Underlying scales in the form of pitch clusters were determined through pitch measurements around the turn of the decade as developments in sound technology rendered them do’able. However, the problem of determining the set of all(?) admissible seyirs for a given makam is still a formidable task and a mystery , revealing its many faces in all sorts of awkward situations. The task called out here might demand all mining schemes known to men, possibly schemes yet to be invented, put to work in this musical habitat never experienced before./
We’re fortunate to host another visiting expert in Turkish Music, to discuss various mathematical models of the use of pitch and melodic sequence in the Turkish “makam” pitch system (https://en.wikipedia.org/wiki/Makam)./
Title: Exploring the Mysteries of Turkish Makam Music/
Time: Tuesday October 30, 2-3 pm (30- minutes lecture plus 30 minutes questions/discussion)/
Place: Stanford University, CCRMA Classroom (Knoll 217)/
Presenter: Can Akkoç ("Jon Ahk-koch”)
Institute of Applied Mathematics (IAM), Middle East Technical University (METU), Ankara, Türkiye (TURKEY)/
http://metu.academia.edu/CanAkko%C3%A7 = http://metu.academia.edu/CanAkkoç
Video at: https://www.youtube.com/watch?v=f17hqxP8wZo&feature=em-share_video_user
İletişim: can1936@gmail.com
Video: http://notist.org/incelemeler.html
A new born baby is exposed to her/his native tongue from the moment of delivery. The child picks up the vocabulary and, most importantly, the templates on the street during childhood years through constant exposure. Grammar structures are not on the radar screen, fortunately(!), until school starts with secondary education.
What is demanded of an adult learner in ESL is basically the simulation of the childhood experience of a native speaker, combined with grammar rules in full bloom, all tucked into one same program within a finite time frame. This description might sound like ‘mission impossible’, and it certainly is.
Whereas the human intellect is incredibly smart in capturing patterns in any setting, such as learning a new language, this feature of the human mind is completely ignored, tacitly, in the current teaching strategy by mercilessly uploading the beginner with every conceivable grammar structure under the sun for the new target language.
If beginners in ESL were allowed breathing room to exercise their pattern recognition capabilities, they could go a long way, on their own, in uncovering some of the patterns making up the language, even some of the grammar structures, at least at an intuitive level.
Cemil Bey (kemençe), Niyazi Sayın (Mansur Ney), İhsan Özgen (kemençe).
Recorded in different time frames; totally disconnected(?) spiritual modes; of different duration.
Flow `synchronized`, for comparison, by using % as the unit of `time`.
Objective: to explore mathematical patterns making up admissible seyirs for the Saba makam.
Starting with (an) Addition Table, as opposed to the usual Multiplication Table, for beginning little girls and boys . . .
It is suggested that little girls and boys start with an Addition Table in learning Arithmetic_
Rationale:
The author has observed young adults using their fingers, inadvertently under the table, to add numbers in the order of 10. Unlike the well-established practice of learning the Multiplication Table ASAP in elementary school, this embarrassing situation with Addition is probably due to not having been exposed to a regimented approach in learning addition of small numbers around 10.
Thus, we propose exposing the little guys in grade school, first to an Addition Table (sample shown below), for them to begin to grasp, not brutal rote(!) memorization, the patterns involved in the addition operation.
The table conceals all arithmetic properties of the addition operation, to be uncovered before the little guys by an observant teacher, or better yet, to be discovered by the exuberant learner herself/himself:
_ Numerals, in red, along the main diagonal are all EVEN numbers, equal to the sum of their identical ‘components’, in blue, top row and left-most column,
_ Every element of the table, in black, is equal to the sum of its respective components along the top row and left-most column,
_ Layout of black numbers display a *symmetric* pattern - like a mirror image - with respect to the main diagonal in red,
_ The said symmetry is a visual proof of the, so called, *commutative* property of the addition operation, A + B = B + A.
This much exposure to addition should keep the little guy happy and, most of all, confident for the rest of her/his life, while keeping out their little fingers away from arithmetic operations . . .
Can Akkoç,
Middle East Technical University (METU),
Institute of Applied Mathematics (IAM),
Ankara, Turkey