Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
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There are at least 2 stands in this & issue debate.
**Scientific continuity is related to scientific change
Shebere & Kuhn are repredebtatives. The (alleged by S. ) problem of "incommensurability"(Kuhn, '60s) attempts to explain scientific change in terms of concepts of meaning and reference. Another way is through the concept of "reasons" and the issues of reasons.
The Gallilean paradigm broke meaning continuity from the Aristotelian & is inconsumerable i. E no comparison can be made between the 2
**Scientific Continuity as independent area
A more standard way, it providers factors such as mathematics continuity and causal continuity. GR for example deviated some how causal from Newtonian gravity but maintained mathematical cintinuity
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The issue of scientific continuity can be defined as the preservation of knowledge, research progress, and expertise in a field over time, despite changes in personnel, funding, and other factors. Scientific continuity is important because it ensures that research programs and projects can be continued over the long term, and that valuable knowledge and data are not lost or forgotten.
To assess the issue of scientific continuity, the following factors can be considered:
  1. Personnel stability: Assess the stability of the research team, including turnover, retirements, and other personnel changes, and their potential impact on scientific continuity.
  2. Funding stability: Evaluate the stability of funding sources and whether they are adequate to maintain the research program over the long term.
  3. Data management: Assess the quality of data management systems, including data archiving, sharing, and preservation.
  4. Collaborations: Evaluate the presence and strength of collaborations between researchers and institutions, which can help ensure scientific continuity by creating networks of expertise and resources.
  5. Documented procedures: Evaluate the existence and implementation of documented procedures for transferring knowledge, data, and expertise from one generation of researchers to the next.
By considering these factors, researchers and institutions can determine the level of scientific continuity in a field, and take steps to address any gaps or weaknesses to ensure that research progress is maintained over the long term.
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Hai,
I had worked with Dr. M. Azzedine,France member of MAA and proved unsolved Beals Conjecture, FLT directly, Collatz Conjecture & Goldbachs Conjecture.( All proofs in one article)Article will get published on April.
Can I expect any career / financial benefits from that work? I also developed Mathematical Theology to bring mathematics in humanity. I had investigated the thesis of some university level mathematics professors from Kerala State India.
What are the expectations on the person who proves Collatz Conjecture? I am an ordinary research scholar from a government college, Tamilnadu, India.
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Thank You Sir.
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Mathematics Teacher Educators (MTEs) best practices.
I'm interesting in research literature about Mathematics Teacher Educators (MTEs) best practices, especially on MTEs' practices for teaching to solve problems.
thank you.
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Thank you,
I am looking for accurate literature relating to core practices in teaching mathematics.
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I have 'N' number of inputs (which correspond to temperature) to calculate a specific output parameter. I'm getting 'N' number output data based on the inputs.
However, my goal is to select an optimum number from all the output data and use it in another calculation.
'N' number of input data --> Output parameter calculation --> Identification of an optimized output parameter --> Use that value for another calculation.
How to find an optimal value among 'N' "number of output data. Can we employ any algorithm or process?
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1. Choose an appropriate method of optimization such as linear programming, nonlinear programming, genetic algorithms, or simulated annealing.
2. Develop a model of the data set using the chosen method.
3. Use the model to find the optimal value among the data set.
4. Validate the results of the optimization using statistical tests and other methods.
5. Use the optimal value to make decisions or modify the data set as needed.
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We consider that R~Q, as valid for certain areas, and others not -- as in [1,2] and in the RG question:
See [Box 1], in the REFERENCES, taken from that previous question, where the discrete Weyl-Heisenberg group is explained in quantum information.
That said, the consequences, both illustrating and limiting the equivalence (~) relationship in a wider scope, are:
1. Differential and Integral Calculus (analysis) [1,2] work for R and Q, but are absolutely precise for the sets Q and Q*;
2. Fourier Transform (FT~FFT) [3] in the set Q*, contrary to well-known assumption using the set R over an infinite and "continuous" range of frequencies;
3. Existence of the new set Q* [4], allowing all calculations to be expressible numerically in the set Q*, absolutely accurate, as opposed to complex numbers (the sets C or G) that cannot even be numerically calculated;
4. Deprecation of the sets C and G (complex numbers) in numerical analysis [5], that is physically visualized and solved in the set Q*, for the equation x^2+1=0, and any other;
5. New applications in Physics [6-7];
6. Faster numerical calculations [8,9], without including hopeless approximations for the set R [1];
7. Problem of Closure [10] is solved in physics and mathematics;
[8] curvature representation of the inverse of the second derivative [11], instead of the second differential when it is not possible, or in the Schrödinger equation;
[9] According to [Box 1], in the REFERENCES,one cannot use mathematical real-numbers (the set R) in a "continuous" Weyl-Heisenberg group, in quantum information, but must use a discrete Weyl-Heisenberg group, which uses the set Q or Q*, and no infinitesimals are used;
[10] As provided by AO in this question, consider fractal functions. Fractal functions form the basis of a constructive approximation theory for non-differentiable functions,where "non-differentiable" is tainted by imposing a mythical continuity in mathematics [cf 1] in the set R, but linking to Q and Q*;
[11] As provided by RS in this question, consider Bayesian probability. The Bayesian methodology of updating beliefs (conditional probability) is cast in mathematical real-numbers R, but linking to Q, and Q*;
[12] The sets R, Q, and Q* look similar in a graph where the spacing between the points is small enough [1,2]; and
[13] particle diffraction uses stimulated emission with the set Q*, not waves using the set R, as explained in [13].
[+14] open in this question.
In addition, considering the wider scope of the points 1 and ff., above, can one consider R~Q in many cases as evidenced by those examples? But, in some cases, R cannot be used at all, even approximately, one has to use the sets Q or Q*.
The main consequences: Nature is ontically digital, quantum. Otherwise, R~Q is an approximation, to use R. Every effect in physical reality can be accomplished with Q or Q* only; none requires R, C, or G. Also, infinitesimals do not have to be used at all.
This also answers affirmatively two previous questions, confirming [BOX 1], and [5].
What is your qualified opinion?
REFERENCES
[Box 1] Although Weyl training was on these mythical aspects, the infinitesimal transformation and Lie algebra [7], he saw an application of groups in the many-electron atom, which must have a finite number of equations. The discrete Weyl-Heisenberg group comes from these discrete observations, and do not use infinitesimal transformations at all, with finite dimensional representations. Similarly, this is the same as someone trained in infinitesimal calculus, traditional, starting to use rational numbers in calculus, with DDF [1]. The similar previous training applies in both fields, from a "continuous" field to a discrete, quantum field. In that sense, R~Q and R~Q*; the results are the same formulas -- but now, absolutely accurate. This allows results foreseen in Chapter 7 of [8], and other new results in physics, but now on a firm, not self-contradictory mathematical "continuous" ground [1].
[3]
Preprint FT ~ FFT
[4]
[6[ Yuri Igorevich Ozhigov, “Constructive Physics (Physics Research and Technology).” Nova Science Pub Inc; UK ed., ISBN 1612095534, 2011.
[10] in print, see also [1].
]11] in print,see [12].
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Consequence number one: the numerical axis exhibits the properties of fractality not only through the Cantor fractal.
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It finally has occurred to me that there is a similarity between i = √-1 and √2. They are each linearized representations of essentially quadratic values. We use the former in complex numbers and include the latter in the real number system as an irrational number. Each has proved valuable and is part of accepted mathematics. However, an irrational number does not exist as a linear value because it is indeterminate – that is what non-ending, non-repeating decimal number means: it never can exist. Perhaps we need an irrational number system as well as a complex number system to be rigorous.
The sense of this observation is that some values are essentially quadratic. An example is the Schrödinger Equation which enables use of a linearized version of a particle wave function to calculate the probability of some future particle position, but only after multiplying the result by its complex conjugate to produce a real value. Complex number space is used to derive the result which must be made real to be real, i.e., a fundamentally quadratic value has been calculated using a linearized representation of it in complex number space.
Were we to consider √-1 and √2 as similarly non-rational we may find a companion space with √2 scaling to join the complex number space with √-1 scaling along a normal axis. For example, Development of the algebraic numbers a + b√2 could include coordinate points with a stretched normal axis (Harris Hancock, Foundations of the Theory of Algebraic Numbers).
A three-space with Rational – Irrational – Imaginary axes would clarify that linearization requires a closing operation to restore the result to the Rational number axis, where reality resides.
[Note: most people do not think like I do, and almost everyone is happy about that: please read openly, exploringly, as if there might be something here. (Yes, my request is based on experience!) Tens of thousands of pages in physics and mathematics literature from popular exposition to journal article lie behind this inquiry, should you wish to consider that.]
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Howdy Folks,
I am satisfied that mathematics and physics (science) have been well defined and described here. A couple movies are running in my mind's eye that I wish to pass along as afterwords - they are observations not insults.
In Ray Bradbury's work "Medicine for Melancholy" he includes a prose movie of Pablo Picasso sketching a mural in the moist sand of a long beach as the tide is coming in - just like the "then current" theories in science presented by academics as truth, the foaming edges of the waves wash the mural away - new paradigms replace old and the human creation of science is adjusted. It is not "nature" even now.
M. C. Escher's "Metamorphosis" is a great contribution to defined elements fitted together perfectly into a closed, consistent, unnatural whole. Rigorous, however independent of nature, EXCEPT FOR THE FACT that humans and their imagination are natural. I disagree with the separation of "artificial" from natural, except as a verbal convenience.
These are creations of human minds, not figments of human imagination. And I carefully avoided an observation that fresh ideas are not fertilizer and to bury them in a field will not benefit flowers there.
Great exchange, Thanks again, Happy Trails, Len
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Could any expert try to examine the new interesting methodology for multi-objective optimization?
A brand new conception of preferable probability and its evaluation were created, the book was entitled "Probability - based multi - objective optimization for material selection", and published by Springer, which opens a new way for multi-objective orthogonal experimental design, uniform experimental design, respose surface design, and robust design, etc.
It is a rational approch without personal or other subjective coefficients, and available at https://link.springer.com/book/9789811933509,
DOI: 10.1007/978-981-19-3351-6.
Best regards.
Yours
M. Zheng
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  1. Evolutionary Algorithms (EA): Evolutionary algorithms (EA) are a family of optimization algorithms that are inspired by the principles of natural evolution. These algorithms are widely used in multi-objective optimization because they can handle multiple objectives and constraints and can find a set of Pareto-optimal solutions that trade-off between the objectives.
  2. Particle Swarm Optimization (PSO): Particle Swarm Optimization (PSO) is a population-based optimization algorithm that is inspired by the social behavior of birds and fish. PSO has been applied to multi-objective optimization problems, and it has been shown to be effective in finding Pareto-optimal solutions.
  3. Multi-objective Artificial Bee Colony (MOABC): MOABC is a multi-objective optimization algorithm inspired by the foraging behavior of honeybees. MOABC has been applied to various multi-objective optimization problems and has been found to be efficient in finding the Pareto-optimal solutions
  4. Decomposition-based Multi-objective Optimization Algorithms (MOEA/D): Decomposition-based multi-objective optimization algorithms (MOEA/D) decompose the multi-objective problem into a set of scalar subproblems, then solve them by using a scalar optimization algorithm. MOEA/D has been found to be effective in solving multi-objective problems with high dimensionality and/or large numbers of objectives.
  5. Deep reinforcement learning (DRL) : DRL is a category of machine learning algorithm that allows the agent to learn by interacting with the environment and using the rewards as feedback. This approach has been used to optimize the decision-making process in multi-objective problems.
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My Awesomest Network, I am starting my Ph.D. studies and I have some questions and doubts concerning it. Could I write them down here, pleaswe? First of them is how can I join disciplines as sociology, management, economics, mathematics, informatics and other similaer items to make a complex holistic interdisciplinary analysis and coherent study of pointed fields.
Thank You very much for all in advance
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The first point is to read a lot from all of these fields. A good entry point are review articles which summarize large areas of a discipline and may point out open questions. Also, for a PhD, it is important to be aware of your personal, ongoing interests. Maybe these interests coincide with some open questions in the research domain. You can combine different fields in many ways, e.g. using methods from one discipline for problems in another one, or generalizing open questions into a more general question, or creating a new method by combining elements of an existing method, or transfering one model to another context, etc. It is up to your interests, your creativity, your questions! Always remember that each research discipline is simply a different perspective onto the world. Thus, you can pick any part of the world and look at it from all these different perspectives.
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Perception is not the ultimate guide for knowledge but as Gallileo captured the actual and empirical, not necessarily the real, similar concerns arise.
In general, the repercussions of Reduction arise because what is actual, i.e final instantiation of underlining process, is not all the story. Further omissions come from the empirical approach since sense means are not always valid projectors of the actual.
Gallilean approach has yielded a framework that empowered our comprehension & ability to define/describe phenomena in the realm of the actual& empirical. His treatise should not be considered more than this i.e descrining the nature of the real and its dynamics.
The reduction of change to motion has been noted but little has been argued about its shortfalls in epistemic practice. This reduction is part of the reduction of the real to the actual since it omits any need to refer to the real to make its claims functional. It also removes philosophical or anthropocentric notions of growth and ultimate ends which is good in one sense but in a pure "reductionist shortfalls" point of view is still a problem dimain restriction.
The description of motion with mathematics is another point neglected. Motion can be described qualitatively or conceptual but such a framework has not been devised.
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Thanks for your thoughts and wishes
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This question discusses the YES answer. We don't need the √-1.
The complex numbers, using rational numbers (i.e., the Gauss set G) or mathematical real-numbers (the set R), are artificial. Can they be avoided?
Math cannot be in ones head, as explains [1].
To realize the YES answer, one must advance over current knowledge, and may sound strange. But, every path in a complex space must begin and end in a rational number -- anything that can be measured, or produced, must be a rational number. Complex numbers are not needed, physically, as a number. But, in algebra, they are useful.
The YES answer can improve the efficiency in using numbers in calculations, although it is less advantageous in algebra calculations, like in the well-known Gauss identity.
For example, in the FFT [2], there is no need to compute complex functions, or trigonometric functions.
This may lead to further improvement in computation time over the FFT, already providing orders of magnitude improvement in computation time over FT with mathematical real-numbers. Both the FT and the FFT are revealed to be equivalent -- see [2].
I detail this in [3] for comments. Maybe one can build a faster FFT (or, FFFT)?
The answer may also consider further advances into quantum computing?
[2]
Preprint FT ~ FFT
[2]
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Many people write to me, and my mailbox is very accepting.
Some simple people assume that their questions are, somehow, special, worthy, or unique. They even may want to claim innovation!
But, we live in a fluid, and many of our thoughts are not even
original, or our own. Ego interferes.
Only correct living, like following the Dhrama and Jesus, can keep the laboratory of the mind clean and receptive to higher thoughts.
The complex numbers have been followed without deep questioning, and their justification, in medieval Italy, was to solve the equation x^2+1=0.
But, they actuall lead one astray from the actual solution.
This was revealed by the FFT, that can now be entirely calculated with rational numbers, and without any trigonometric functions, as mentioned above.
Then, we conclude that FT ~ FFT, as the RG preprint briefly explains. For the savvy, a letter cn b a wrd!
There are no mathematical real-numbers either. Thus, the set C is deprecated and the set G is superfluous. They cannot be calculated (Gisin,Ozhigov, Gerck)with probability 1.
Mathematics gets simpler, and correct, accessible to natural processes, and accessing them in quantum mechanics.
Then, the Shor quantum algorithm of 1994, without any practical result since then, only theoretical results, opens the calculations of the FFT, to the components of numbers.
This reveas the prime numbers as "lumps", resonances in the number line, much in the same way that a physical chord has physical resonances. Easier to calculate, with such a physical model.
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We assume that in general probability and statistics belong to physics rather than mathematics.
The Normal/Gaussian Distribution:
f(x)={Exp(-x^2/2 sigm^2)}/sigma.Sqrt(2.Pie)
can be derived from the universal laws of physics for a given number n of randomly chosen data in less than five minutes.
Accuracy increases as n increases.
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In fact, and the meaning of the question is not understood.
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Mathematics abstracted and idealized concrete mathematics, exemplified in Euclid’s The Elements. Religion around the same time or earlier, abstracted the concrete representation of deities. Are there similarities in the problem solving approaches?
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There is certainly a similarity, but it is rather a property of inductive method of thinking, characteristic of human in general.
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I have a system of non-linear differential equations that explains the behaviour of some of the cancer cells.
Looking for help identifying the equilibrium points and eigenvalues of this model in order to determine the type of bifurcation present.
Thanks in advance.
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Well it's a good idea to find some of them, first. The first equation implies that y=0 is an equilibrium, so a class of equilibria is of the form (x,0,z). That reduces the problem. From the last equation it then should be possible to solve for z and, from the second, for x.
Then look at the other factor of the first equation; and so on.
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Mathematically, it is posited that the cosmic or local black hole singularity must someday become of infinite density and zero size. But this is unimaginable. If an infinite-density stuff should exist, it should already have existed.
Hence, in my opinion, this kind of mathematical necessities are to be the limiting cases of physics. IS THIS NOT THE STARTING POINT TO DETERMINE WHERE MATHEMATICS AND PHYSICAL SCIENCE MUST PART WAYS?
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Stam Nicolis, you have been telling me how the problem is being considered in GTR, Cosmology, etc. This is known already.
The question I have posed is for considerations towards new attempts to discuss the problem rationally and to come to possible further conclusions that might help us understand the very problems better
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In my current work on the theory of hyperbolic functions, I, as a completely extraneous observer of the turbulent debates relating to the subtlest intricacies of the Special Theory of Relativity (SRT), have drawn attention to the fact that hyperbolic functions are most used not in constructing bridges, aqueduct arches or describing complex cases of X-ray diffraction, but in those sections of the SRT that are related to the name of Professor Minkowski. Since my personal interest in SRT is essentially limited to the correct application of hyperbolic functions when describing moving physical realities, I would be grateful to the experts in the field of SRT for the most concise explanation of the deep essence of the theory of space-time patterns of surrounding me reality.
Naturally, my question in no way implies the translation into human language of the lecture of the Creator of the Theory, the honour of acquaintance with which in 1907 belongs to the academic/medical community of the city of Cologne and its surroundings. My level of development and my agreeableness have ensured that I not only managed to read independently the text underlying the concept of « Minkowski four-dimensional continuum », but also to formulate my question as follows:
Which of the options I propose is the most concise (i.e. non-emotional-linguistic) explanation of the essence of Minkowski’s theory:
1. The consequence of any relative movement of massive physical objects is that we are all bound to suffer the same fate as the dinosaurs and mammoths, i.e. extinction.
2. Understanding/describing the spatial movements of physical objects described by a^2-b^2=const type mathematical expression implies acquiring practical skills of constructing second-order curves called «hyperbolas».
3. All of us, including those who are in a state of careless ignorance, are compelled to exist in curved space.
4. Everything in our lives is relative, and only the interval between physical events is constant.
5. The products of the form ct (or zct), where c is the speed of light and z is some dimensionless mathematical quantity/number symbolizes not a segment of three-dimensional space, but a time interval (or time?) t between uniquely defined events.
6. The electromagnetic radiation generated by a moving massive object always propagates in a direction orthogonal to the velocity vector of the moving object.
Of course, I will be grateful for any adjustments to my options, or expert’s own formulations that have either eluded my attention or whose substance is far beyond my level of mathematical or general development.
Most respectfully
Sergey Sheludko
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Dear Azzam,
I was not talking about you. You know I have no problem to talk science with you. We were talking about some supporters of the theory of relativity, who don't accept the questioning of this theory. You know that.
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Our answer is YES. This question captured the reason of change: to help us improve. We, and mathematics, need to consider that reality is quantum [1-2], ontologically.
This affects both the microscopic (e.g., atoms) and the macroscopic (e.g., collective effects, like superconductivity, waves, and lasers).
Reality is thus not continuous, incremental, or happenstance.
That is why everything blocks, goes against, a change -- until it occurs, suddenly, taking everyone to a new and better level. This is History. It is not a surprise ... We are in a long evolution ...
As a consequence, tri-state, e.g., does not have to be used in hardware, just in design. Intel Corporation can realize this, and become more competitive. This is due to many factors, including 1^n = 1, and 0^n = 0, favoring Boolean sets in calculations.
This question is now CLOSED. Focusing on the discrete Weyl-Heisenberg group, as motivated by SN, this question has been expanded in a new question, where it was answered with YES in +12 areas:
[2]
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QM can have values unknown, but not uncertain. Likewise, RG questions. Please stay on topic, per question. Do not be uncertain yourself.
Opinions do not matter, every opinion is right and should be, therefore, not discussed.
But, facts? Mass is defined (not a choice or opinion) as the ratio of two absolutes: E/c^2. Then, mass is rest mass. There is no other mass.
This is consistent, which is the most that anyone can aspire. Not agreement, which depends on opinion. Science is not done by voting.
Everyone can, in our planet, reach consistency -- and the common basis is experiment, a fact. We know of other planets, and there consistency may be uncertain -- or ambivalent, and even obscure. A particle, there, may be defined, both, as the minimum amount of matter of a type, or the most amount of quantum particles of a type.
We can entertain such worlds in our minds, more or less formed by bodies of matter, and have fun with the consequences using physics. But, and there is my opinion (not lacking but not imposing objectivity) we all -- one day -- will be lead to abandon matter. What will we find? That life goes on. The quantum jump exists. Nature is quantum.
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If anyone knows of a conference on mathematics education to be held in Europe from April 2023 to March 2024, especially on mathematics education for elementary and junior high school students, please let me know.
As for the contents, it is even better if there are a textbook of mathematics, steam education, mathematics class and a computer.
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Please suggest some ML related research papers for Mathematics students.
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There are many research areas in machine learning that are well-suited for people with a strong background in math. Some of which are:
  1. Optimization: Machine learning often involves optimizing complex functions, and a strong background in math can be particularly helpful in this area.
  2. Theoretical machine learning: This subfield focuses on the mathematical foundations of machine learning, including the study of algorithms and their statistical properties.
  3. Deep learning: Deep learning is a subfield of machine learning that involves training artificial neural networks to perform tasks such as image and speech recognition. It requires a strong background in linear algebra and optimization.
  4. Reinforcement learning: This subfield focuses on developing algorithms that allow agents to learn through trial and error, and it requires a strong understanding of probability and decision theory.
  5. Natural language processing: This subfield involves using machine learning to process and understand human language. It requires a strong background in linguistics and statistical modeling.
You can search and explore more areas and choose one best suited to you
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Right now, in 2022, we can read with perfect understanding mathematical articles and books
written a century ago. It is indeed remarkable how the way we do mathematics has stabilised.
The difference between the mathematics of 1922 and 2022 is small compared to that between the mathematics of 1922 and 1822.
Looking beyond classical ZFC-based mathematics, a tremendous amount of effort has been put
into formalising all areas of mathematics within the framework of program-language implementations (for instance Coq, Agda) of the univalent extension of dependent type theory (homotopy type theory).
But Coq and Agda are complex programs which depend on other programs (OCaml and Haskell) and frameworks (for instance operating systems and C libraries) to function. In the future if we have new CPU architectures then
Coq and Agda would have to be compiled again. OCaml and Haskell would have to be compiled again.
Both software and operating systems are rapidly changing and have always been so. What is here today is deprecated tomorrow.
My question is: what guarantee do we have that the huge libraries of the current formal mathematics projects in Agda, Coq or other languages will still be relevant or even "runnable" (for instance type-checkable) without having to resort to emulators and computer archaeology 10, 20, 50 or 100 years from now ?
10 years from now will Agda be backwards compatible enough to still recognise
current Agda files ?
Have there been any organised efforts to guarantee permanent backward compatibility for all future versions of Agda and Coq ? Or OCaml and Haskell ?
Perhaps the formal mathematics project should be carried out within a meta-programing language, a simpler more abstract framework (with a uniform syntax) comprehensible at once to logicians, mathematicians and programers and which can be converted automatically into the latest version of Agda or Coq ?
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The engineering philosophy behind Coq and the Coq kernel is well worth careful consideration:
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Greeting,
When I tried to remotely accessed the scopus database by login into my institution id, it kept bring me back to the scopus preview. I tried cleaning the cache, reinstall the browser, using other internet and etc. But, none of it is working. As you can see in the image. It kept appeared in scopus preview.
Please help..
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To reach the Scopus document search module, you should use academic IPs. If your institute has been listed in the Scopus database, you have permission to search documents in Scopus. It is not free of charge, and your university should pay its share to Scopus to provide this service for its academic researchers.
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How to write formally within the context of mathematics that: "given two series S1 and S2 and they are subtracted each other coming from a proved identity that is true and the result of this subtraction is a known finite number (real number) (which is valid) the two series S1 and S2 are convergent necessarily because the difference could not be divergent as it would contradict the result of convergence? I need that definition within a pure mathematical scenario ( I am engineer).
" Given S1- S2 = c , if c is a finite and real number, and the expression S1-S2 = c comes from a valid deduction, then, S1 and S2 are both convergent as mandatory."
Best regards
Carlos
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Cite:
Mark Gritter
No. Consider the series ... in the above link example/ answer by Mark Gritter.
Both are divergent series, but the difference between the series is ... a convergent series.
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I'm trying to write a java programme that will solve the system of ordinary differential equations using the Runge-Kutta fourth-order (RK4) technique. I need to solve a system of five equations. Those are not linear.
And determining all of the equilibrium solutions to this system of differential equations also requires.
Can someone help me? Thank you in advance.
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Hereby attached is a system of three Ordinary Differential Equations (ODE). We have to use numerical methods such as RK4 and Euler to obtain the results using Java. I think RK4 is better for this kind of problem. In this thread, Dudley J Benton has already mentioned C programming for this. It is really amazing.
For the parameter values, you can use your own values for your convenience.
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Which are the implications in mathematics if the Irrationality Measure bound of "Pi" is proved to be Less than or equal to 2.5?
How can be understood the number pi within this context?
Thanks,
Carlos
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Many thanks Jack Don McLovin
I have evidence that that is the upper bound... today it has been proved. But I reserve my ideas to publish them by a proper article. I just hope that journals can accept so clear ideas behind of this problem is a fundamental basis but not complicated to understand as it is believed. Many thanks.
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I am working on meta-heuristic optimization algorithms. I would like to solve Image segmentation using Otsu’s method and my algorithm. I could not understand how to use meta-heuristic in image segmentation. Please help me in this regard. I am from maths back ground. If anybody have matlab code for the same, please share with me. I will be grateful to you.
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Thank you very much Madam @Shima Shafiee
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Irrational numbers are uncomputable with probability one. In that sense, numerical, they do not belong to nature. Animals cannot calculate it, nor humans, nor machines.
But algebra can deal with irrational numbers. Algebra deals with unknowns and indeterminates, exactly.
This would mean that a simple bee or fish can do algebra? No, this means, given the simple expression of their brains, that a higher entity is able to command them to do algebra. The same for humans and machines. We must be able also to do quantum computing, and beyond, also that way.
Thus, no one (animals, humans, extraterrestrials in the NASA search, and machines) is limited by their expressions, and all obey a higher entity, commanding through a network from the top down -- which entity we call God, and Jesus called Father.
This means that God holds all the dice. That also means that we can learn by mimicking nature. Even a wasp can teach us the medicinal properties of a passion fruit flower to lower aggression. Animals, no surprise, can self-medicate, knowing no biology or chemistry.
There is, then, no “personal” sense of algebra. It just is a combination of arithmetic operations.There is no “algebra in my sense” -- there is only one sense, the one mathematical sense that has made sense physically, for ages. I do not feel free to change it, and did not.
But we can reveal new facets of it. In that, we have already revealed several exact algebraic expressions for irrational numbers. Of course, the task is not even enumerable, but it is worth compiling, for the weary traveler. Any suggestions are welcome.
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We need to be optimistic, because that is the lesson from nature. An animal can self-medicate, obeying natural laws in chemistry that are unknown to animals. A tree grows when pruned, so we can see this pandemic as an opportunity. Let's grow, nature is not a zero-sum game!
Irrational numbers and mathematical real-numbers are uncomputable, with probability 1.
But irrational numbers can be calculated exactly in algebra a and that is how animals are able to calculate-- in a network of thoughts.
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I'm interested in the intersection of mathematics and social sciences, and I'm looking for expert opinions on ethical content in mathematical history.
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One of the most important features that distinguish mathematics from other sciences is abstraction, so some of them think that mathematics is abstract concepts. Abstraction is simply (a mental process based on separating one of the properties from something, and considering it independent of others).
(The Link Between Mathematics and Ethics) was built on the basis of the new view of man in contemporary psychology, as this view tends towards the primacy of the mind. In other words, this is consistent with the new scientific view that began with the theory of relativity and quantum mechanics, which proved the centrality of the mind. After World War II, many psychologists pointed out that the abolition of the role of the mind in human behavior and the subjection of the mind to instinct in the method of psychoanalysis led to the dehumanization of man. Therefore, psychology in the new view considers reason and determination as the highest human faculties, and they distinguish man from animals. (And the mind and the will not only control the body, but they also control the emotions and nullify them when necessary. By subordinating the emotions to the mind, harmony and happiness become within the reach of man). (And the old view of science considers that the human mind cannot choose freely because matter does not act except by mechanical necessity. This is the reason why the old view tended to explain human actions in the language of instinct). In short, this study comes within this framework, that is, we proceed here from the fact that man is a conscious force, and what mathematics does is that it creates what can be called a “moral authority” with mental foundations, meaning that the ethics generated by mathematics are based on the authority of the mind, not fear. (According to Dr. Mahmoud Bakir's opinion).
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Hello,
I am looking for mathematical formulas that calculate the rigid body movement of an element based on the nodal displacements. Can anyone give a brief explanation and recommend some materials to read? Thanks a lot.
Best,
Chen
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Ignoring the displacements due to strain in the element, the rigid body translation equals the average of the nodal displacements of the elements and the rigid body rotations equal the average rotations of the nodes of the element. I believe this would offer high accuracy for elements away from the regions of constraints.
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Why is it necessary to study the History of Mathematics?
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History of mathematics can offer students a window into the processes of developing new mathematics, and the ways in which this knowledge is accepted and circulated within different communities. Especially pertinent to the question of decolonising the curriculum, turning to the history of the discipline offers a window into the role played by mathematics and mathematicians in settler colonialism, and how the mathematics we use today was in turn shaped by colonialism.
A new project at The Open University will produce an interactive online database of original sources, selected to demonstrate the global nature of mathematics. Original sources – such as letters, calculation aids, khipu or clay tablets – enable students to see beyond the final results explicated in their university textbooks to the work that went into uncovering these results in the first place...
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Which software is best for making high-quality graphs? Origin or Excel? Thank you
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origin
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How long does it take to a journal indexed in the "Emerging Sources Citation Index" get an Impact Factor? What is the future of journals indexed in Emerging Sources Citation Index?
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Clarivate announced that starting with 2023 ESCI-indexed journals will also be assigned an impact factor. See: https://clarivate.com/blog/clarivate-announces-changes-to-the-2023-journal-citation-reports-release/
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Lockdowns due to the COVID pandemic in last three years (2020-22) has played a significant role in the widespread of online based classrooms using applications like Zoom, MS teams, Webex and Google Meet. While substantial amount of the students were happy to complete their semester classes in due time without getting hampered by the lockdowns, thanks to the online based classrooms, there are also notable amount of students and parents who were complained regarding the online based classrooms that they have drastically distracted the academic performance of students.
Overall, I would like to leave it as an open-ended question. Dear researchers, what you think regarding the online based classroom? Is it an advantage for students or a disadvantage?
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Online-based classrooms are necessary for circumstances where the learners and teachers feel that the knowledge can be catered to without meeting in person. It is an opportunity for learners to learn at their doorsteps. Nonetheless, online classes are not as effective as offline classes for many learners who take education as a social process where peer learning, group dynamics, and interpersonal relationship are of high importance. Online class doesn't provide the experience of personal interaction while learning.
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My Awesomest Network, I am starting my Ph.D. studies and I have some questions and doubts concerning it. Could I write them down here, please? First of them is how can I join disciplines as sociology, management, economics, mathematics, informatics and other similar items to make a complex holistic interdisciplinary analysis and coherent study of pointed fields. I think personally that linking or joining et cetera aspects of artificial intelligence and computational social sciences would be interesting area of considerations. What are Your opinions?
Thank You very much for all in advance
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There is even such a discipline called "COmputational Social Sciences"...
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I am a post graduate student presently writing my thesis in the department of curriculum and instructional designs.
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I recommend research results from authors of the French group of Didactis of Mathematics as: Vergnaud, Bideaud, Meljac, Fischer, Brun. Also, from Oxford University Peter Bryant and Terezinha Nunes.
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I need mathematical full solution.. Can anyone please help me..
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Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100.
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What is infinite? does this have any value? must there be an end or is it just our thoughts it can't imagine that there is no end to infinity! Aren't all things part of infinity? we too? is God an infinity that cannot be imagined but felt? is an infinity an energy that binds us and all things (reality and thought) together? Is there a physical explanation for infinity? Is the limitation by (infinity -1) or (-infinity + 1) legitimate or just a need to calculate it mathematically?
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We can imagine any finite quantity to be halved, and then each half to be halved again, and so on, without end. You can then say the finite quantity has infinitely many parts. It's just a conceptual distinction.
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We see many theories in physics, mathematics, etc. becoming extremely axiomatic and rigorous. But are comparisons between mathematics, physics, and philosophy? Can the primitive notions (categories) and axioms of mathematics, physics and philosophy converge? Can they possess a set of primitive notions, from which the respective primitive notions and axioms of mathematics, physics, and philosophy may be derived?
Raphael Neelamkavil
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Raphael Neelamkavil , you said, "But in your paper "The zero-dimensional physical theory (V): information, energy, efficiency, and intelligence" you exhibit enough awareness of the above facts. Hence, I do not understand what else you meant by the question at the end of your comment!".
The title of this forum topic is, "Can the Primitive Notions (Categories) and Axioms of Mathematics, Physics and Philosophy Converge?". When I said, "This is all a good question and debate, yet what is deliberate misinformation and ignorance, what is the drive for it, and can it be written about in a way so as not to promote it as being useful?" I am essentially asking whether or not the primitive notions are already granted by the contemporary ideas of mathematics, physics, and philosophy. My work highlights they are not, so a clear issue in this debate is all about what is assumed and what is not. My work with zero-dimensionality assumes nothing, and thence creates a new spectrum of ideas for mathematics, physics, and philosophy which has been, is, and perhaps still will be for most.
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I suppose so, it's true that physics is the special case of mathematics.
In physics, the existence and the uniqueness of the solution are ensured whereas in mathematics, it is the general case of physics, the existence and the uniqueness of the solution pass before all.
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In Leon Lederman's wonderful book, "The God Particle" he comments about a pecking order in physics. It goes something like, "the experimental physicists only defer to the theoretical physicists who in turn only defer to the mathematician and the mathematician only defer to God..."
Physics is not mathematics. The role of physics like all sciences is to understand the universe. The theoretical physicists' role is to develop theories that explains all the experiments from the past plus allows predictions to be made to test the and potentially falsify the theory. The role of the experimental physics is to develop and perform those experiments. There is often as much deep mathematics used by an experimental physicists as a theoretical physicists.
The role of the mathematician is simple to expend the understanding of mathematics through rigorous logical reasoning. If a physicists or any other scientist finds these tools useful - then great.
Arguably the greatest theoretical physicists of the second half of the 20 Century was Richard Feynman. Here is what he said about physics.
"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
I would suggest for a better understanding of physics - what it is and isn't - a read of "The God Particle" would be recommended
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Assume we have a program with different instructions. Due to some limitations in the field, it is not possible to test all the instructions. Instead, assume we have tested 4 instructions and calculated their rank for a particular problem.
the rank of Instruction 1 = 0.52
the rank of Instruction 2 = 0.23
the rank of Instruction 3 = 0.41
the rank of Instruction 4 = 0.19
Then we calculated the similarity between the tested instructions using cosine similarity (after converting the instructions from text form to vectors- machine learning instruction embedding).
Question ... is it possible to create a mathematical formula considering the values of rank and the similarity between instructions, so that .... given an un-tested instruction ... is it possible to calculate, estimate, or predict the rank of the new un-tested instruction based on its similarity with a tested instruction?
For example, we measure the similarity between instruction 5 and instruction 1. Is it possible to calculate the rank of instruction 5 based on its similarity with instruction 1? is it possible to create a model or mathematical formula? if yes, then how?
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As far as I understand your problem, you first need a mathematical relation between the instructions and rank. For instance, Rank x should correspond to some instruction value as y and vice versa; it means you require a mathematical function.
So there are various methods/tools to find a suitable (as accurate as you want) to find mathematical function based on given discrete values like curve fitting methods or the use of ML.
Further, Once you obtain the mathematical function, run your code a few times, and you will get a set for various combinations of (instruction, rank). These set values will work as the feedback for your derived function. Make changes based on the feedback, and you will get a much more accurate function.
I hope you are looking for the same.
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Hi frds,
Need a good weather probability calculator. Would like to calculate the probability of e.g. 10 degrees Celsius on a day above the average. Has anybody got good research/formulas?
Which distribution is assumed in the probability calculation? Normal one?
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One possible approach is presented in the attached word document
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Hi all, I want to solve a system of simultaneous equations in which some equations are cubic and some are quadratic. How to solve such a system. The solution should consist of combinations of all solutions i.e., the positive as well as the negative solutions.
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And this:
"Theoretically, such a system can be solved exactly; i.e. it can be determined whether the system has real solutions or not, and if it has, its solutions can be calculated exactly." is exactly what CAS-systems like Maple and Mathematica do. Good for Dudley J Benton to have a perpetual subscription. My experience is: the Maple syntax is simpler - and the sysmbolic solution of partial differential equations is better in Maple than in Mathematica. But for people wthout a license Mathematica is easier to rech - via wolframaplha.com. And there you need not to adhere to the syntax rules.
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Physics is a game of looking at physical phenomena, analyzing how physical phenomena changes with a hypothetical and yet mathematical arrow of time in 3D space, namely by plotting that physical phenomena with a mathematical grid model (typically cartesian based) assuming that physical phenomena can be plotted with points, and then arriving at a theory describing that physical phenomenon and phenomena under examination. The success of those physical models (mathematical descriptions of physical phenomena) is predicting new phenomena by taking that mathematics and predicting how the math of one phenomenon can link with the math of another phenomenon without any prior research experience with that connection yet based on the presumption of the initial mathematical model of physical phenomena being undertaken.
Everyone in physics, professional and amateur, appears to be doing this.
Does anyone see a problem with that process, and if so what problems do you see?
Is the dimension of space, such as a point in space, a physical thing? Is the dimension of time, such as a moment in time, a physical thing? Can a moment in time and a point of space exist as dimensions in the absence of what is perceived as being physical?
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A point in space is given always by two points:
- coordinates of the point
- coordinates of origin of coordinates
Between those two points there is a "length" (physical dimension) with a physical Unit (Meters)
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I am thinking of the vector as a point in multidimensional space. The Mean would be the location of a vector point with the minimum squared distances from all of the other vector points in the sample. Similarly, the Median would be the location of the vector point with the minimum absolute distance from all the other vector points.
Conventional thinking would have me calculate the Mean vector as the vector formed from the arithmetic mean of all the vector elements. However, there is a problem with this method. If we are working with a set of unit vectors the result of this method would not be a unit vector. So conventional thinking would have me normalize the result into a unit vector. But how would that method apply to other, non-unit, vectors? Should we divide by the arithmetic mean of the vector magnitudes? When calculating the Median, should we divide by the median of the vector magnitudes?
Do these methods produce a result that is mathematically correct? If not, what is the correct method?
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For vectors X1=[x1,1;x2,1;..,xn,1]; X2=[x1,2;x2,2;..,xn,2];,.., Xn=[x1,n;x2,n;..,xn,n]
M=[m1,m2,..mn] - vector median,
where
m1=med(x1,1; x2,1;..,xn,1)
m2=med(x1,2; x2,2;..,xn,2)
- - - - - - - - - - - - -
mn=med(x1,n; x2,n;..,xn,n)
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Any idea why the solution of the attached equation is always zero at r=0? It seems simple at first look, however, when you start solving, you will see a black hole-like sink which makes the solution zero at r=0 (should not be). I used the variable separation method, I will be happy if you suggest another method or discuss the reasons.
I also attached the graph of the solution, showing the black hole-like sink.
Thanks
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I did give a physical explanation for why your boundary condition enforces the function f to become zero at r=0. In at least one physical interpretation, it models a system with infinite emission/absorption rate at r=0. This forces the temperature at this point to immediately become equal to the environmental temperature. In this interpretation f is (proportional to) the difference between body and environment temperatures. When you define a physcally unreasonable it is only fair that it provides you with physically unreasonable results ;-D
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I have no mathematical experience and no statistician to help me.
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Thank you, Anton Vrdoljak.
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Is it possible to decompose a conditional probability with three or more elements (i.e. events) into conditional probability of only two elements or the marginal probability of one element? Knowing this decomposition, it would help to solve higher order Markov Chain mathematically. I also know that this decomposition can be solved if we add assumption of conditional independent.
To make it concrete here is a negative example:
P(c│a,b)=(P(a,b│c)∙P(c))/(P(a│b)∙P(b) ).
Notice that the RHS still contains a conditional probability with three elements P(a,b│c).
Assuming conditional independent on c, we have P(a,b│c)=P(a│c)∙P(b│c). Thus, the conditional probability decomposition becomes
P(c│a,b)≅(P(a│c)∙P(b│c)∙P(c))/(P(a│b)∙P(b) )
My question is whether this type of conditional probability decomposition into one or two element is possible without making assumption. If it is really unsolvable problem, then at least we know that the assumption of conditional independent is a must.
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For my opinion we can use any product formulas only under condition of independence. For example the formula that you used P(a,b│c)=P(a│c)∙P(b│c) is valid if a and b are independent each from other. Both may be dependent from c. But it can be the case of so called "false dependence". For example a is the usage of energy, b is sale of warm clothes, c is decreasing of tempetature.
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During the lecture, the lecturer mentioned the properties of Frequentist. As following
Unbiasedness is only one of the frequentist properties — arguably, the most compelling from a frequentist perspective and possibly one of the easiest to verify empirically (and, often, analytically).
There are however many others, including:
1. Bias-variance trade-off: we would consider as optimal an estimator with little (or no) bias; but we would also value ones with small variance (i.e. more precision in the estimate), So when choosing between two estimators, we may prefer one with very little bias and small variance to one that is unbiased but with large variance;
2. Consistency: we would like an estimator to become more and more precise and less and less biased as we collect more data (technically, when n → ∞).
3. Efficiency: as the sample size incrases indefinitely (n → ∞), we expect an estimator to become increasingly precise (i.e. its variance to reduce to 0, in the limit).
Why Frequentist has these kinds of properties and can we prove it? I think these properties can be applied to many other statistical approach.
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Sorry, Jianhing. But I think you have misunderstood something in the lecture. Frequentist statistics, which is an interpretation of probability to be assigned on the basis of many random experiments.
In this setting, on designs functions of the data (also called statistics) which estimate certain quantities from data. For example, the probability p of a coin to land heads is given from n independent trials with the same coin and just counting the fraction of heads. This is then an estimator for the parameter p.
Each estimator should have desirable properties, as unbiasedness, consistency, efficiency and low variance and so on. Not every estimator has these properties. But, in principle one can proof, whether a given estimator has these properties.
So, it is not a characteristics of frequentist statistics, but a property of an individual estimator based on frequentist statistics.
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Provide me the detail mathematical calculation for the measurement of uranium, thorium and potassium with their daughter progenies.
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The solution is not a mathematical formula!
The question can be approached by two ways:
a) experimental: prepare homogenous standards having the same density and geometry as your samples, #1 material with low K,Th,U content, #2 same as #1 with known amount of K added, #3 same as #1 with known amount of Th added ,and #4 same as #1 with known amount of U added.
From the differences between measurements #N-#1 you may deduce the contribution of each of the three elements to the spectrum and, more specifically, the contribution of each of them to three regions of interest corresponding to strong peaks of each element, usually 1.46 MeV for 40K, 2.61 MeV for Tl208 (progeny of Th) and 609 keV for Bi214 (progeny of U), assuming secular equilibrium in Th and U families, or at least the same disequilibrium conditions in sample and standards.
It is then possible to calculate a matrix relating the measurements in the 3 ROIs to the three activities.
b) Monte Carlo simulation. The NaI detector is usually quite simple and can be simulated with a good accuracy. Experimental measurements are still necessary to evaluate the gaussian broadening of the peaks at the different energies, and an experimental validation of the MC model is always desirable.
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Hello,
For correlation analysis between body composition variables and blood hormone levels,
I have data from two different blood analysis methods but the same units; ECLIA & CLIA.
I wonder if there is any statistical and mathematical error when I run correlation analysis using the data together.
If it cannot,
Is there any suggestion for using these data together for statistical analysis?
Thank you very much.
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If the methods are different, it is likely that there is no correlation ...
However, it would help a lot to know the datasets and the processing you say you have done.
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Mathematics is a subject most pupils love to hate; how did your journey into the world of mathematics proper begin?
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My predisposition to mull with numbers and mathematical equations consistently, even though I do not specialize in the math field as a professional, is due to having FUN filled mentors early in life. They were so creative to attach images and anecdotes to math problems that my sense of wonder and fun was constantly tickled as I trundle along mathematical mines and problems. Missing the correct answer was not occasion for embarrassment but for more opportunities to discover funny and creative ways to approach math problems with new, innovative, and fun-filled attempts. My mentors showed me the short-cut methods, the winding methods, and the funny but sure fire methods. I do not believe I ever hated math. Math is FUN!
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Famous mathematicians are failing each day to prove the Riemann's Hypothesis even if Clay Mathematics Institute proposes a prize of One Million Dollars for the proof.
The proof of Riemann's Hypothesis would allow us to understand better the distribution of prime numbers between all numbers and would also allow its official application in Quantics. However, many famous scientists still refuse the use of Riemann's Hypothesis in Quantics as I read in an article of Quanta Magazine.
Why is this Hypothesis so difficult to prove? And is the Zeta extension really useful for Physics and especially for Quantics ? Are Quantics scientists using the wrong mathematical tools when applying Riemann's Hypothesis ? Is Riemann's Hypothesis announcing "the schism" between abstract mathematics and Physics ? Can anyone propose a disproof of Riemann's Hypothesis based on Physics facts?
Here is the link to the article of Natalie Wolchover:
The zeros of the Riemann zeta function can also be caused by the use of rearrangements when trying to find an image by the extension since the Lévy–Steinitz theorem can happen when fixing a and b.
Suppositions or axioms should be made before trying to use the extension depending on the scientific field where it is demanded, and we should be sure if all the possible methods (rearrangements of series terms) can give the same image for a known s=a+ib.
You should also know that the Lévy–Steinitz theorem was formulated in 1905 and 1913, whereas, the Riemann's Hypothesis was formulated in 1859. This means that Riemann who died in 1866 and even the famous Euler never knew the Lévy–Steinitz theorem.
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I thought it would be better to type my work. Here is a link to the acceptable version of the article : https://www.researchgate.net/publication/364357359_A_contradiction_in_the_formula_of_Poisson_which_destroys_Riemann's_Hypothesis
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Everybody is eager to see the New winner of the Millenium Prize. Please share all your incomplete works about the Millenium Prize problems of Clay Mathematics Institute in order to collaborate for the solutions.
I am actually using the different nabla operator which I demonstrated mathematically in my published work: " A thesis about Newtonian mechanics rotations and about differential operators ".
This demonstrated differential tool enables to deal differently with the millenium problem about Navier-Stokes equation.
I also suggest that P=NP if the problem can be translated to a differential equation that has a solution. If your lucky friend finds and gives you an easy solution, than that solution leads directly to the general solution of the differential equation.
I will be waiting for your collaborations.
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I thought it would be better to type my work. Here is a link to the acceptable version of the article : https://www.researchgate.net/publication/364357359_A_contradiction_in_the_formula_of_Poisson_which_destroys_Riemann's_Hypothesis
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Say I have a satellite image of known dimensions. I also know the size of each pixel. The coordinates of some pixels are given to me, but not all. How can I calculate the coordinates for each pixel, using the known coordinates?
Thank you.
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Therefore, you have 20x20 = 400 control points. If you do georeferencing in Qgis, you can use all control points or some of them, like every 5 Km (16-points). During resampling, all pixels have coordinates in the ground system.
If you do not do georeferencing (no resampling), then you could calculate the coordinates of unknown pixels by interpolation. Suppose a pixel size a [m], then in one km, you have p = 1000/a pixels, and therefore known coordinates have the first(x1,y1) and the last(x2,y2) pixel. The slope angle between the first and last pixel is:
s = arc-tan[(x2-x1)/(y2-y1)]. Therefore, a pixel of a distance d from the first pixel has coordinates x = x1 + d.sin(s) and y = y1 +d.cos(s). You can do either row of column interpolation or both and take the average.
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Hello Friends and Colleagues,
Can anyone suggest a mathematical book that helps me to build my own mathematical equations and functions? I want to convert real-life problems(natural sciences) into mathematical formulations.
Note that I have basic knowledge of mathematics.
Thanks in advance,
Hadi
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For me the following book is very useful
Functional Equations and How to Solve Them (Problem Books in Mathematics)
Springer
Christopher G. Small
Year:
2006
Language:
English
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Plz share if yes . I want to know how to get patent in vedic maths.
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WO 2017/037729 A1: Concurrent architecture of Vedic multiplier-an accelerator scheme for high speed computing
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Applying mathematical knowledge in research models: This question has been in my mind for a long time. Can advance mathematics and applied mathematics solve all the problems in modeling research? Especially the formula derivation in the theoretical model part, can the analysis conclusion be obtained through multiple derivations or other methods? You have also read some mathematics-related publications yourself, and you have to admire the mystery of mathematics.
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Mathematics is essentially one of the professional tools of science, including for physicists.
Admire the tool... If the cook says "Miracle saucepan", then the food will not get better...
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didactics of mathematics
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Students should be shown the application of mathematics from a practical point of view. On the other hand, it is necessary to respect the theoretical side of mathematics, which is not easy for everyone to learn.@Peter Kepp Rickardo Gomes
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Hello everyone,
I would like to know how to locate mathematically a damage on a blade.
Usually a frequency analysis of the blade and a comparison with a similar healthy one helps to determine a default or damage on a blade. However, how could someone locate that damage?
Thank you for your time.
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Hi fellow researcher,
I think the answer depends on what kind of equipment you have on your disposition and what is your purpose. The simpler way is to have a model blade and compare it to the blade you want to determine the integrity using the physical properties of the blade.
For example, if you have an accurate sound sensor and a device that produces an specific sound profile in the model blade you can use this device to produce a similar sound in the test blade. Comparing the Fourier decomposition of frequencies of the sound produced by the test blade will give you information of cracks and non-uniformity in density produced by the forging process or even if the material the blade was made is of quality or not.
You can do a similar approach with thermodynamics. you can heat Specific spots on the test blade. As cracked regions do not conduct heat as well as non-cracked regions you will observe anomalies in the heat map of the blade.
Notice you don't really have to calculate something, but just know what to expect with a model blade data.
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for different approach
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I'm struggling to understand the method followed in the following analysis. Can someone please explain how the author got the values of Δ_1 and K_1 that justify its analysis?
I have tried to isolate "Δ" and "K" by setting Equation (B8) equal to zero. but I have failed to get similar conditions.
P.S: I'm new to mathematical modelling, so I really need to understand what's going on here. Thanks
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The RHS is a fraction, whose numerator and denominator are quadratic expressions in Δ. Therefore the fraction takes positive values when numerator and denominator are of the same sign...
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why to quantize a Hamilton-Jacobi theory with fractional derivatives?, what are the physical or mathematical advantages?
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Also, Hamilton-Jacobi theory can be applied with not only fractional derivatives but also, definition of fractional derivatives and integrals on time scale Yazen Alawaideh
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How to people propose a new optimization algorithm. I mean what is the baseline? Is there any intuition or mathematical foundation behind it?
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The question is too general. To generate the basic idea of the algorithm, you need to know the detailed statement of the problem. Typically, the process of developing an algorithm starts with the identification of your problem complexity class. If there is no evidence or clear feeling that the problem is NP-hard, then it is reasonable to try to develop a polynomial algorithm for solving it. Such algorithms are usually based on the use of specific properties of the problem. Sometimes it is possible to construct a polynomial algorithm based on the general scheme of dynamic programming, taking into account the specific properties of the problem.
If the problem is known to be NP-hard, then branch-and-bound methods, dynamic programming, and their modifications often work well for a relatively small problem dimension. Sometimes it is possible to build a successful formulation of the problem in the form of an integer programming model, followed by the use of appropriate methods or ready-made software. For high-dimensional problems, you can either use well-known metaheuristics, or develop your own approximate algorithm. In the latter case, success is usually based on the use of the problem properties. As you can see, in any case, it is useful to start by studying the specific properties of your particular problem.
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When solving mathematical equations or system of equations there are things that are considerable; such as the Universe or domains...
Because, some equations may have no solutions or impossible to solve., at all. If a solution or some solutions exist for an equation or systems of equations, there are regions or intervals containing the solution(s). Such considerations may be important when applying numerical methods.
What are basins of attractions?
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Dear, Tekle Gemechu basins of attraction comes from the dynamical system and chaos theory. It is related with systems behavior. There are several example of basins of attraction. Therefore, definition and examples of basins of attraction are given in scholarpedia. Below scholarpedia's link:
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The physical constants (G, h, c, e, me, kB), can be considered fundamental only if the units they are measured in (kg, m, s ...) are independent. However there are anomalies which occur in certain combinations of these constants which suggest a mathematical (unit number) relationship. By assigning a unit number θ (kg -> 15, m -> -13, s -> -30, A -> 3, K -> 20) to each unit we can define the relationship between the units.
In order for the dimensioned physical constants to be fundamental, as noted above, the units must be independent of each other, there cannot be any unit number relationship, however these anomalies (listed below) question this fundamental assumption. In every combination predicted by the model they give an answer consistent with CODATA precision. Statistically therefore, can these anomalies be dismissed as coincidence?
The anomalies are listed on this wiki site (adapted from the article)
The diagram shows the relationship linking the constants according to their unit number.
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Some general background to the physical constants.
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Hi Hieram, youre welcome! Imho fun should be induced by fruitful scientific research supported by open commenting one other’s ideas (opposed to endless fruitless repeating discussions what presumingly not cannot ever workuntil it does) like iSpace („integer-Space„ or „complex-Space“ when treating the i as the one for a complex number) able to derive and decipher inter-relationships, dependencies and calculate exact arbitrary precision numerical values for most but all constants of nature.
Also recently a new true quantum geometric iSpace-IQ unit system has been developed, able to directly represent native quantum relations of contants while keeping strictly compatible to MKSA/SI system showing a single *time* based conversion factor, effective predicting quantization of time itself.
So - no - being a true long time Apple expert consultant i’d say we do not need to fear to be sued for (at least not in the foreseeable future ;-) ). And please all take the time to read thru the very short yet imho rreally convincing math of both of my newest papers to be found on my RG home.
Here is a link to RG summary of my iSpace project:
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I am aware of the facts that every totally bounded metric space is separable and a metric space is compact iff it is totally bounded and complete but I wanted to know, is every totally bounded metric space is locally compact or not. If not, then give an example of a metric space that is totally bounded but not locally compact.
Follow this question on the given link
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Metric space A is said to be a totally bounded if every Cauchy sequence in A has convergent sub sequence
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What are the areas where mathematics are been applied medically.
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Fertility rate, mortality rate, menstrual period, gestation of the fetus week per week compare to the physiological and patological symptoms, body weight and body height to determine the healthyness, the length of conjugata vera, conjugata diagonale, etc to assest the passage for labour the baby need sectio caesarea or not. Count the weeks of gestation to know the maturity of embrio or fetus organ systems, mengukur tinggi fundus uteri dengan meteran untuk menaksir masa kehamilan, ukur jarak dari symphisis pubis dan proccesus xyphoideus sebagai patokan, ukur lingkar lengan atas dengan meteran, menentukan masa subur untuk fertilisasi dengan perhitungan penanggalan, dll.
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Does nature understand mathematics?
A connected question is -- How are theory, theorem, and truth related?
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Theories and Theories of Truth | SpringerLink
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I am trying to model a business scenario mathematically for my research paper but I do not have the required skillset. What is a legitimate way to find and get help. Are there any online sources or paid services. Do I need to add the expert a co-author? What type of solutions exists.
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I have many times served as an applied mathematician on a multi-disciplinary team, including, for instance, biologists, meteorologists, geologists, hydrologists, etc. The other team members possessed essential knowledge to the success of the project but not the math skills. This is good for you to recognize in the study of business because nobody knows everything. A diverse team can solve problems that a single individual cannot. I would have the biologists explain over and over again that part they understood (like fish behavior or metabolic needs) and I would create a model. Then we would run the model and ask, "Is it responding the way you expect it to?" One of these interesting projects considered production of peanut butter crackers and cheese crackers sold in vending machines manufactured on the same assembly line at a factory on the road from my house to the school. Walk over to the Mathematics Department and find a graduate student studying applied mathematics who is looking for a project. You can help each other.
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Why use metaheuristic algorithms when there are so many mathematical optimization tools available, like GAMS?
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Ankur Maheshwari I agree with Ben Cardoen that a heuristic/partial search algorithm may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity where commercial solvers may struggle. But the key issue of heuristics is that they do not guarantee that a globally optimal solution can be found on some class of problems when compared with commercial solvers such as Ipopt, Cplex, Mosek, Gurobi,..., for NLP or LP or MILP or MINLP problems.
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1) What's the difference between SCILAB and MATLAB?
2) Which one would you recommend?
3) Which one is the most friendly user?
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Hi Sunday Emmanuel Fadugba I have no experience with SCILAB (and very little with MATLAB). What I can recommend is using Mathematica (if you can afford it; or maybe you can use the free version on Raspberry Pi) or Julia (free). Hope it helps.
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Dear Colleagues, a recent trend in Fractional Calculus is in introducing more and more new fractional derivatives and integrals and considering classical equations and models with these operators. Thus, we have to think about and to answer questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. These and similar questions have remained mostly unanswered until now. To provide an independent platform for discussion of these trends in the current development of FC, the SI “Fractional Integrals and Derivatives: “True” versus “False””( https://www.mdpi.com/journal/mathematics/special_issues/Fractional_Integrals_Derivatives2021) has been initiated. In this SI, some important papers have been already published. However, you are welcome to share with the scientific community your viewpoint. Contributions to this SI devoted both to the new fractional integrals and derivatives and their justification and those containing constructive criticism of these concepts are welcome.
Best regards
Yuri Luchko
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I like this new thinking. But for me it is difficult to say "true" or "false" since everyone has his own standard. I feel interested in the definition convenient both in the application and mathematical analysis.
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How can we analyze the propagation constant in slab waveguides? Is there a mathematical formula for this parameter?
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