oleh : smno@ub.ac.id

1. SISTEM DAN PEMODELAN SISTEM oleh: smno@ub.ac.id

2. MAKNA SUMBERDAYA ALAM “Semua benda hidup dan mati yg terdapat secara alamiah di bumi, Bermanfaat bagi manusia, Dapat dimanfaatkan oleh manusia, untuk memenuhi kebutuhan hidupnya Keberadaannya & ketersediaannya: 1. Sebaran geografisnya tdk merata 2. Pemanfaatannya tgt teknologi 3. Kalau diolah menghasilkan produk dan limbah

3. A Comprehensive Model Land (Resources) use = is a way of managing a large part of the human environment in order to obtain benefits for human. Resources use development The complex problems Systems theory is an interdisciplinary theory about the nature of complex systems in nature, society, and science, and is a framework by which one can investigate and/or describe any group of objects that work together to produce some result. The Comprehensive Model

4. FIVE GEOMETRIES IN RESOURCES USE SYSTEM Human demand geometry Natural resources geometry NATURAL RESOURCES USE GEOMETRY Resources Degradation Geometry Natural Resources Geometry

5. SISTEM sbg suatu pendekatan 1. Filosofis 2. Prosedural 3. Alat bantu analisis Systems thinking is the process of predicting, on the basis of anything at all, how something influences another thing. It has been defined as an approach to problem solving, by viewing "problems" as parts of an overall system, rather than reacting to present outcomes or events and potentially contributing to further development of the undesired issue or problem.

6. “Sistem”: Gugusanelemen-elemenygsalingberinteraksidanterorganisirperi-lakunyakearahtujuantertentu FILOSOFI Science systems thinkers consider that: A system is a dynamic and complex whole, interacting as a structured functional unit; Energy, material and information flow among the different elements that compose the system; A system is a community situated within an environment; energy, material and information flow from and to the surrounding environment via semi-permeable membranes or boundaries; Systems are often composed of entities seeking equilibrium but can exhibit oscillating, chaotic, or exponential behavior. “Tigaprasyarataplikasinya”: 1. Tujuandirumuskandenganjelas 2. Prosespengambilankeputusansentralisasilogis 3. Sekalawaktu -------- jangkapanjang

7. PROSEDUR “Tahapan Pokok”: 1. Analisis Kelayakan 2. Pemodelan Abstrak 3. Disain Sistem 4. Implementasi Sistem 5. Operasi Sistem A conceptual framework is used in research to outline possible courses of action or to present a preferred approach to a system analysis project. The framework is built from a set of concepts linked to a planned or existing system of methods, behaviors, functions, relationships, and objects. A conceptual framework might, in computing terms, be thought of as a relational model. For example a conceptual framework of accounting "seeks to identify the nature, subject, purpose and broad content of general-purpose financial reporting and the qualitative characteristics that financial information should possess". Need Assesment Tahapan Pokok: - - - Evaluasi Outcomes

8. ALAT -BANTU “Model Abstrak”: Perilaku esensialnya sama dengan dunia nyata “digunakandalam”: 1. Perancangan / DisainSistem 2. Menganalisis SISTEM ……………strukturnya INPUT …...…….. beragam STRUKTUR …….. fixed OUTPUT ……….. Diamatiperilakunya 3. Simulasi SISTEM untuksistem yang kompleks

9. SIMULASI SISTEM: OPERASINYA “Penggunaan Komputer ”: Simulasi Komputer: Disain Sistem Strategi Pengelolaan Sistem MODEL SISTEM • A model is a simplified abstract view of the complex reality. • A scientific model represents empirical objects, phenomena, and physical processes in a logical way. • Attempts to formalize the principles of the empirical sciences, use an interpretation to model reality, in the same way logicians axiomatize the principles of logic. • The aim of these attempts is to construct a formal system for which reality is the only interpretation. The world is an interpretation (or model) of these sciences, only insofar as these sciences are true. • For the scientist, a model is also a way in which the human thought processes can be amplified. • Models that are rendered in software allow scientists to leverage computational power to simulate, visualize, manipulate and gain intuition about the entity, phenomenon or process being represented. programming PROGRAM KOMPUTER

10. SIMULASI SISTEM: METODOLOGI “Model dasar”: Model Matematik Model lain diformulasikan menjadi model matematik “tahapan”: 1. Identifikasi subsistem / komponen sistem 2. Peubah input ( U(t) ) ……….. Stimulus 3. Peubah internal = peubah keadaan = peubah struktural, X(t) 4. Peubah Output, Y(t) 5. Formulasi hubungan teoritik antara U(t), X(t), dan Y(t) 6. Menjelaskan peubah eksogen 7. Interaksi antar komponen ………… DIAGRAM LINGKAR 8. Verifikasi model …….. Uji ……. Revisi 9. Aplikasi Model ……. Problem solving A simulation is the implementation of a model over time. A simulation brings a model to life and shows how a particular object or phenomenon will behave. It is useful for testing, analysis or training where real-world systems or concepts can be represented by a model

11. “Pemodelan”: Serangkaian kegiatan pembuatan model MODEL: abstraksi dari suatu obyek atau situasi aktual PEMODELAN SISTEM: RUANG LINGKUP MODEL KONSEP 1. Hubungan Langsung 2. Hubungan tidak langsung 3. Keterkaitan Timbal-balik / Sebab-akibat / Fungsional 4. Peubah - peubah 5. Parameter MATEMATIKA Operasi Matematik: Formula, Tanda, Aksioma

12. “MODEL SIMBOLIK” : Simbol-simbol Matematik Angka Simbol “Persamaan” Rumus Ketidak-samaan Fungsi JENIS-JENIS MODEL “MODEL IKONIK” : Model Fisik 1. Peta-peta geografis 2. Foto, Gambar, Lukisan 3. Prototipe “MODEL ANALOG” : Model Diagramatik: 1. Hubungan-hubungan 2. …... 3. ….. • A system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole. • The concept of an 'integrated whole' can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and from relationships between an element of the set and elements not a part of the relational regime.

13. SIFAT MODEL PROBABILISTIK / STOKASTIK Teknik Peluang Memperhitungkan “uncertainty” “DETERMINISTIK”: Tidak memperhitungkan peluang kejadian Systems Engineering is an interdisciplinary approach and means for enabling the realization and deployment of successful systems. It can be viewed as the application of engineering techniques to the engineering of systems, as well as the application of a systems approach to engineering efforts. Systems Engineering integrates other disciplines and specialty groups into a team effort, forming a structured development process that proceeds from concept to production to operation and disposal. Systems Engineering considers both the business and the technical needs of all customers, with the goal of providing a quality product that meets the user needs

14. FUNGSI MODEL MODEL DESKRIPTIF Deskripsi matematik dari kondisi dunia nyata Scientific modelling is the process of generating abstract, conceptual, graphical and/or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling. Also a way to read elements easily which have been broken down to the simplest form “MODEL ALOKATIF” : Komparasi alternatif untuk mendapatkan “optimal solution”

15. TAHAPAN PEMODELAN 1. Seleksi Konsep 2. Konstruksi Model: a. Black Box b. Structural Approach 3. Implementasi Komputer 4. Validasi (keabsahan representasi) 5. Sensitivitas 6. Stabilitas 7. Aplikasi Model 1. Asumsi Model 2. Konsistensi Internal 3. Data Input ----- hitung parameter 4. Hubungan fungsional antar peubah-peubah 5. Uji Model vs kondisi aktual Scientific modelling is the process of generating abstract, conceptual, graphical and/or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling. Also a way to read elements easily which have been broken down to the simplest form

16. PHASES OF SYSTEMS ANALYSIS Recognition…. Definition and bounding of the PROBLEM Identification of goals and objectives Generation of solutions MODELLING Evaluation of potential courses of action Implementation of results

17. Mengapa kita gunakan Analisis Sistem? 1. Kompleksitas obyek / fenomena /substansi penelitian Multi-atribute Multi fungsional Multi dimensional Multi-variabel 2. Interaksi rumit yg melibatkan banyak hal Korelasional Pathways Regresional Struktural 3. Interaksi dinamik: Time-dependent , and Constantly changing 4. Feed-back loops Negative effects vs. Positive effects ProsesAbstraksi & Simplifikasi

18. PROSES PEMODELAN INTRODUCTION SISTEM - MODEL - PROSES Bounding - Word Model Alternatives: Separate - Combination DEFINITION Relevansi : Indikator - variabel - subsistem Proses : Linkages - Impacts Hubungan : Linear - Non-linear - interaksi Decision table: HYPOTHESES MODELLING Data : Plotting - outliers Analisis : Test - Estimation Choice : Verifikasi: Subyektif - reasonable Uji Kritis: Eksperiment - Analisis/Simulasi Sensitivity: Uncertainty - Resources - - Interaksi VALIDATION Communication Conclusions INTEGRATION

19. Proses Pemodelan SISTEM: Approach SimulasiSistem AnalisisSistem Model vs. Pemodelan Mathematical models: An exact science, Its Practical Application: 1. A high degree of intuition 2. Practical experiences 3. Imagination 4. “Flair” 5. Problem define & bounding Modelling refers to the process of generating a model as a conceptual representation of some phenomenon. Typically a model will refer only to some aspects of the phenomenon in question, and two models of the same phenomenon may be essentially different, that is in which the difference is more than just a simple renaming. This may be due to differing requirements of the model's end users or to conceptual or aesthetic differences by the modellers and decisions made during the modelling process. Aesthetic considerations that may influence the structure of a model might be the modeller's preference for a reduced ontology, preferences regarding probabilistic models vis-a-vis deterministic ones, discrete vs continuous time etc. For this reason users of a model need to understand the model's original purpose and the assumptions of its validity

20. DEFINITION & BOUNDING IDENTIFIKASI dan PEMBATASAN Masalah penelitian 1. Alokasi sumberdaya penelitian 2. Aktivitas penelitian yang relevan 3. Kelancaran pencapaian tujuan Proses pembatasan masalah: 1. Bersifat iteratif, tidak mungkin “sekali jadi” 2. Make a start in the right direction 3. Sustain initiative and momentum System bounding: SPACE - TIME - SUB-SYSTEMS Sample vs. Population THE WHOLE SYSTEMS vs. SETS OF SUB-SYSTEMS

21. COMPLEXITY AND MODELS The real system sangat kompleks The hypotheses to be tested MODEL Sub-systems Trade-off: complexity vs. simplicity Proses Pengujian Model Hipotetik

22. WORD MODEL Masalah penelitian dideskripsikan secara verbal, dengan meng-gunakan kata (istilah) yang relevan dan simple Simbolisasi kata-kata atau istilah Setiap simbol (simbol matematik) harus dapat diberi deskripsi penjelasan maknanya secara jelas A conceptual schema or conceptual data model is a map of concepts and their relationships. This describes the semantics of an organization and represents a series of assertions about its nature. Specifically, it describes the things of significance to an organization (entity classes), about which it is inclined to collect information, and characteristics of (attributes) and associations between pairs of those things of significance (relationships). Pengembangan Model simbolik Hubungan-hubunganverbal dipresentasikandengansimbol-simbol yang relevan

23. GENERATION OF SOLUTION Alternatif “solusi” jawaban permasalahan , berapa banyak? Pada awalnya diidentifikasi sebanyak mungkin alternatif jawaban yang mungkin Penggabunganbeberapaalternatifjawaban yang mungkindigabungkan A conceptual schema or conceptual data model is a map of concepts and their relationships. This describes the semantics of an organization and represents a series of assertions about its nature. Specifically, it describes the things of significance to an organization (entity classes), about which it is inclined to collect information, and characteristics of (attributes) and associations between pairs of those things of significance (relationships). A conceptual schema or conceptual data model is a map of concepts and their relationships. This describes the semantics of an organization and represents a series of assertions about its nature. Specifically, it describes the things of significance to an organization (entity classes), about which it is inclined to collect information, and characteristics of (attributes) and associations between pairs of those things of significance (relationships).

24. HYPOTHESES Tigamacamhipotesis: 1. Hypotheses of relevance: mengidentifikasi & mendefinisikanfaktor, variabel, parameter, ataukomponensistem yang relevan dg permasalahan 2. Hypotheses of processes: merangkaikanfaktor-faktorataukomponen-komponensistemygrelevandenganproses / perilakusistemdanmengidentifikasidampaknyathdsistem 3. Hypotheses of relationship: hubunganantarfaktor, danrepresentasihubungantersebutdengan formula-formula matematikaygrelevan, linear, non linear, interaktif. A conceptual system is a system that is composed of non-physicalobjects, i.e. ideas or concepts. In this context a system is taken to mean "an interrelated, interworking set of objects". A conceptual system is simply a . There are no limitations on this kind of model whatsoever except those of human imagination. If there is an experimentally verified correspondence between a conceptual system and a physical system then that conceptual system models the physical system. "values, ideas, and beliefs that make up every persons view of the world": that is a model of the world; a conceptual system that is a model of a physical system (the world). The person who has that model is a physical system. Penjelasan / justifikasiHipotesis Justifikasisecarateoritis Justifikasiberdasarkanhasil-hasilpenelitian yang telahada

25. KONSTRUKSI MODEL Manipulasimatematis Data dikumpulkandandiperiksa dg seksamauntukmengujipenyimpangannyaterhadaphipotesis. Grafikdibuatdandigambarkanuntukmenganalisishubungan yang adadanbagaimanasifat / bentukhubunganitu Ujistatistikdilakukanuntukmengetahuitingkatsignifikasinya Simulation is the imitation of some real thing, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system. Simulation is used in many contexts, including the modeling of natural systems or human systems in order to gain insight into their functioning. Other contexts include simulation of technology for performance optimization, safety engineering, testing, training and education. Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Proses seleksi / uji alternatif yang ada

26. VERIFICATION & VALIDATION VERIFIKASI MODEL 1. Menguji apakah “general behavior of a MODEL” mampu mencerminkan “the real system” 2. Apakah mekanisme atau proses yang di “model” sesuai dengan yang terjadi dalam sistem 3. Verifikasi: subjective assessment of the success of the modelling 4. Inkonsistensi antara perilaku model dengan real-system harus dapat diberikan penjelasannya VALIDASI MODEL 1. Sampai seberapa jauh output dari model sesuai dengan perilaku sistem yang sesungguhnya 2. Uji prosedur pemodelan 3. Uji statistik untuk mengetahui “adequacy of the model” 4. ProsesPemodelan

27. SENSITIVITY ANALYSIS Perubahan input variabel dan perubahan parameter menghasilkan variasi kinerja model (diukur dari solusi model) ……… analisis sensitivitas Variabel atau parameter yang sensitif bagi hasil model harus dicermati lebih lanjut untuk menelaah apakah proses-proses yg terjadi dalam sistem telah di “model” dengan benar Validasi MODEL Model validation is possibly the most important step in the model building sequence. It is also one of the most overlooked. Often the validation of a model seems to consist of nothing more than quoting the R2 statistic from the fit (which measures the fraction of the total variability in the response that is accounted for by the model).

28. PLANNING & INTEGRATION PLANNING Integrasiberbagaimacamaktivitas, formulasimasalah, hipotesis, pengumpulan data, penyusunanalternatifrencanadanimplementasirencana. Kegagalanintegrasiiniberdampakpadahilangnyakomunikasi : 1. Antara data eksperimentasidan model development 2. Antarasimulasi model denganimplementasi model 3. Antarahasilprediksi model denganimplementasi model 4. Antara management practices denganpengembangan hipotesis yang baru 5. Implementasihasilujicobadenganhipotesisygbaru DEVELOPMENT of MODEL 1. Kualitas data danpemahamanterhadapfenomenasebab- akibat (proses yang di model) umumnya POOR 2. Analisissistemdanpengumpulan data harusdilengkapi denganmekanismeumpan-balik 3. Pelatihandalamanalisissistemsangatdiperlukan 4. Model sistemhanyadapatdiperbaikidenganjalanmengatasi kelemahannya 5. Tim analisissistemseyogyanyainterdisiplin

29. PEMODELAN KUANTITATIF : MATEMATIKA DAN STATISTIKA MODEL STATISTIKA: FENOMENA STOKASTIK MODEL MATEMATIKA: FENOMENA DETERMINISTIK

30. WHAT IS SYSTEM MODELLING ? Worthwhile Recognition Problems Amenable Compromise Complexity Definitions Simplification Bounding Objectives Hierarchy Identification Goals Priorities Generality Solution Family Generation Selection Modelling Inter-relationship Feed-back Stopping rules Evaluation Sensitivity & Assumptions Implementation

31. PHASES OF SYSTEM MODELLING Recognition Definition and bounding of the problems Identification of goals and objectives Generation of solution MODELLING Evaluation of potential courses of action Implementation of results Model evaluation A crucial part of the modelling process is the evaluation of whether or not a given mathematical model describes a system accurately. This question can be difficult to answer as it involves several different types of evaluation.

32. Fit to empirical data Usually the easiest part of model evaluation is checking whether a model fits experimental measurements or other empirical data. In models with parameters, a common approach to test this fit is to split the data into two disjoint subsets: training data and verification data. The training data are used to estimate the model parameters. An accurate model will closely match the verification data even though this data was not used to set the model's parameters. This practice is referred to as cross-validation in statistics. Defining a metric to measure distances between observed and predicted data is a useful tool of assessing model fit. In statistics, decision theory, and some economic models, a loss function plays a similar role. While it is rather straightforward to test the appropriateness of parameters, it can be more difficult to test the validity of the general mathematical form of a model. In general, more mathematical tools have been developed to test the fit of statistical models than models involving Differential equations. Tools from nonparametric statistics can sometimes be used to evaluate how well data fits a known distribution or to come up with a general model that makes only minimal assumptions about the model's mathematical form.

33. Scope of the model Assessing the scope of a model, that is, determining what situations the model is applicable to, can be less straightforward. If the model was constructed based on a set of data, one must determine for which systems or situations the known data is a "typical" set of data. The question of whether the model describes well the properties of the system between data points is called interpolation, and the same question for events or data points outside the observed data is called extrapolation. As an example of the typical limitations of the scope of a model, in evaluating Newtonian classical mechanics, we can note that Newton made his measurements without advanced equipment, so he could not measure properties of particles travelling at speeds close to the speed of light. Likewise, he did not measure the movements of molecules and other small particles, but macro particles only. It is then not surprising that his model does not extrapolate well into these domains, even though his model is quite sufficient for ordinary life physics.

34. Philosophical considerations Many types of modelling implicitly involve claims about causality. This is usually (but not always) true of models involving differential equations. As the purpose of modelling is to increase our understanding of the world, the validity of a model rests not only on its fit to empirical observations, but also on its ability to extrapolate to situations or data beyond those originally described in the model. One can argue that a model is worthless unless it provides some insight which goes beyond what is already known from direct investigation of the phenomenon being studied. An example of such criticism is the argument that the mathematical models of Optimal foraging theory do not offer insight that goes beyond the common-sense conclusions of evolution and other basic principles of ecology.

35. MODEL & MATEMATIK: Term Tipe Konstante Variabel Parameter Likelihood Dependent Populasi Probability Analitik Independent Maximum Sampel Simulasi Regressor Modelling and Simulation One application of scientific modelling is the field of "Modelling and Simulation", generally referred to as "M&S". M&S has a spectrum of applications which range from concept development and analysis, through experimentation, measurement and verification, to disposal analysis. Projects and programs may use hundreds of different simulations, simulators and model analysis tools.

36. JENIS VARIABEL Intervening (Mediating) Moderator Independent Dependent INTRANEOUS EXTRANEOUS Confounding Control Concomitant

37. Variabeltergantungadalahvariabel yang tercakupdalamhipotesispenelitian, keragamannyadipengaruhiolehvariabel lain Variabelbebasadalahvariabel yang yangtercakupdalamhipotesispenelitiandanberpengaruhataumempengaruhivariabeltergantung Variabelantara (intervene variables) adalahvariabel yang bersifatmenjadiperantaradarihubunganvariabelbebaskevariabeltergantung. Variabel Moderator adalahvariabel yang bersifatmemperkuatataumemperlemahpengaruhvariabelbebasterhadapvariabeltergantung

38. Variabelpembaur (confounding variables) adalahsuatuvariabel yang tercakupdalamhipotesispenelitian, akantetapimunculdalampenelitiandanberpengaruhterhadapvariabeltergantungdanpengaruhtersebutmencampuriatauberbaurdenganvariabelbebas Variabelkendali (control variables) adalahvariabelpembaur yang dapatdikendalikanpadasaatriset design. Pengendaliandapatdilakukandengancaraeksklusi (mengeluarkanobyek yang tidakmemenuhikriteria) daninklusi (menjadikanobyek yang memenuhikriteriauntukdiikutkandalamsampelpenelitian) ataudenganblocking, yaitumembagiobyekpenelitianmenjadikelompok-kelompok yang relatifhomogen. Variabelpenyerta (concomitant variables) adalahsuatuvariabelpembaur (cofounding) yang tidakdapatdikendalikansaatriset design. Variabelinitidakdapatdikendalikan, sehinggatetapmenyertai (terikut) dalamprosespenelitian, dengankonsekuensiharusdiamatidanpengaruhbaurnyaharusdieliminirataudihilanggkanpadasaatanalisis data.

39. MODEL & MATEMATIK: Definition Preliminary Goodall Mathematical Mapping Rules Formal Expression Maynard-Smith Representational Predicted values Words Homomorph Model Comparison Physical Symbolic Simulation Mathematical Data values Simplified Model adalah rencana, representasi, atau deskripsi yang menjelaskan suatu objek, sistem, atau konsep, yang seringkali berupa penyederhanaan atau idealisasi. Bentuknya dapat berupa model fisik (maket, bentuk prototipe), model citra (gambar rancangan, citra komputer), atau rumusan matematis.

40. MODEL & MATEMATIK: Relatives Advantages Disadvantages Distortion Precise Opaqueness Abstract Complexity Transfer Replacement Communication Eykhoff (1974) defined a mathematical model as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'. Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures

41. MODEL & MATEMATIK: Families Basis Choices Types A mathematical model uses mathematical language to describe a system. Mathematical models are used not only in the natural sciences and engineering disciplines (such as physics, biology, earth science, meteorology, and engineering) but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively. The process of developing a mathematical model is termed 'mathematical modelling' (also modeling). Dynamics Compartment Stochastic Multivariate Network

42. BEBERAPA PENGERTIAN MODEL DETERMINISTIK: Nilai-nilai yang diramal (diestimasi, diduga) dapat dihitung secara eksak. MODEL STOKASTIK: Model-model yang diramal (diestimasi, diduga) tergantung pada distribusi peluang POPULASI: Keseluruhan individu-individu (atau area, unit, lokasi dll.) yang diteliti untuk mendapatkan kesimpulan. SAMPEL: sejumlah tertentu individu yang diambil dari POPULASI dan dianggap nilai-nilai yang dihitung dari sampel dapat mewakili populasi secara keseluruhan PARAMETER: Nilai-nilai karakteristik dari populasi KONSTANTE, KOEFISIEAN: nilai-nilai karakteristik yang dihitung dari SAMPEL VARIABEL DEPENDENT: Variabel yang diharapkan berubah nilainya disebabkan oleh adanya perubahan nilai dari variabel lain VARIABEL INDEPENDENT: variabel yang dapat menyebabkan terjadinya perubahan VARIABEL DEPENDENT.

43. BEBERAPA PENGERTIAN MODEL FITTING: Proses pemilihan parameter (konstante dan/atau koefisien yang dapat menghasilkan nilai-nilai ramalan paling mendekati nilai-nilai sesungguhnya ANALYTICAL MODEL: Model yang formula-formulanya secara eksplisit diturunkan untuk mendapatkan nilai-nilai ramalan, contohnya: MODEL REGRESI MODEL MULTIVARIATE EXPERIMENTAL DESIGN STANDARD DISTRIBUTION, etc SIMULATION MODEL: Model yang formula-formulanya diturunkan dengan serangkaian operasi arithmatik, misal: Solusi persamaan diferensial Aplikasi matrix Penggunaan bilangan acak, dll.

44. DYNAMIC MODEL MODELLING SIMULATION Equations Dynamics Computer FORMAL Language ANALYSIS Special General DYNAMO CSMP CSSL BASIC

45. DYNAMIC MODEL DIAGRAMS SYMBOLS RELATIONAL AUXILIARY VARIABLES LEVELS MATERIAL FLOW PARAMETER RATE EQUATIONS SINK INFORMATION FLOW

46. DYNAMIC MODEL: ORIGINS Abstraction Equations Steps Computers Hypothesis Discriminant Function Simulation Undestanding Other functions Exponentials Logistic

47. MATRIX MODEL MATHEMATICS Eigen value Matrices Operations Dominant Elements Additions Substraction Multiplication Inversion Types Eigen vector Square Rectangular Diagonal Identity Vectors Scalars Row Column

48. MATRIX MODEL DEVELOPMENT Interactions Groups Stochastic Size Markov Models Materials cycles Development stages The term matrix model may refer to one of several concepts: In theoretical physics, a matrix model is a system (usually a quantum mechanical system) with matrix-valued physical quantities. See, for example, Lax pair. The "old" matrix models are relevant for string theory in two spacetime dimensions. The "new" matrix model is a synonym for Matrix theory. Matrix population models are used to model wildlife and human population dynamics. The Matrix Model of substance abuse treatment was a model developed by the Matrix Institute in the 1980's to treat cocaine and methamphetamine addiction. A concept from Algebraic logic.

49. STOCHASTIC MODEL STOCHASTIC Probabilities History Other Models Dynamics Statistical method Stability A statistical model is a set of mathematical equations which describe the behavior of an object of study in terms of random variables and their associated probability distributions. If the model has only one equation it is called a single-equation model, whereas if it has more than one equation, it is known as a multiple-equation model. In mathematical terms, a statistical model is frequently thought of as a pair (Y,P) where Y is the set of possible observations and P the set of possible probability distributions on Y. It is assumed that there is a distinct element of P which generates the observed data. Statistical inference enables us to make statements about which element(s) of this set are likely to be the true one.

50. STOCHASTIC MODEL Spatial patern Distribution Example Negative Binomial Pisson Poisson Binomial Negative Binomial Others Fitting Test In statistics, spatial analysis or spatial statistics includes any of the formal techniques which study entities using their topological, geometric, or geographic properties. The phrase properly refers to a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of 'place and route' algorithms to build complex wiring structures.