Universality Laws for Randomized Dimension Reduction
... Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. The question is how large the embedding dimension ...
... Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. The question is how large the embedding dimension ...
Guest lecture - Department of Mathematics & Statistics | McMaster
... • Write down equations that describe how the system works • Try to solve them • Fail • Do something else • Try to figure out what the results mean ...
... • Write down equations that describe how the system works • Try to solve them • Fail • Do something else • Try to figure out what the results mean ...
Department of Applied Mathematics and Physics Engineering
... In the highly advanced information society today, we encounter various situations that entail modeling, analysis, planning, control and operation of complex and large-scale systems. In these situations, it is extremely important to uncover common mathematical structures shared by those problems whic ...
... In the highly advanced information society today, we encounter various situations that entail modeling, analysis, planning, control and operation of complex and large-scale systems. In these situations, it is extremely important to uncover common mathematical structures shared by those problems whic ...
Chart of Course Options
... Required for APPM major. For full requirements see Undergraduate Advising Guide. ...
... Required for APPM major. For full requirements see Undergraduate Advising Guide. ...
Recent Advances in the Modelling of Renal Function
... permeabilities of the membranes in the various tubulär segments. For a realistic kidney model, both these parameters as the input and the predicted concentration profiles as the Output must be consistent with experimental results. Because of their biological nature, most of these input data can be m ...
... permeabilities of the membranes in the various tubulär segments. For a realistic kidney model, both these parameters as the input and the predicted concentration profiles as the Output must be consistent with experimental results. Because of their biological nature, most of these input data can be m ...
Uses and Abuses of Mathematics in Biology
... Darwin’s day saw offspring inherit a blend of parents’ characothers more formally in the design of teristics, here represented as the average of the two parental give so-called chaotic dynamics, where experiments to separate significant re- shadings. The result is that the variability diminishes in ...
... Darwin’s day saw offspring inherit a blend of parents’ characothers more formally in the design of teristics, here represented as the average of the two parental give so-called chaotic dynamics, where experiments to separate significant re- shadings. The result is that the variability diminishes in ...
Modelling Homeostatic Responses
... European Conference on Mathematical and Theoretical Biology 2011 Patricia Mostardinha University of Aveiro e-mail: [email protected] Fernão Vistulo de Abreu University of Aveiro ...
... European Conference on Mathematical and Theoretical Biology 2011 Patricia Mostardinha University of Aveiro e-mail: [email protected] Fernão Vistulo de Abreu University of Aveiro ...
Wolfram, Ch 12
... • Even with all information and rules there is irreducible amount of work to do. • “There are many common systems whose behavior cannot in the end be determined at all except by something like an explicit simulation” ??? • “the only way … just to run them” ...
... • Even with all information and rules there is irreducible amount of work to do. • “There are many common systems whose behavior cannot in the end be determined at all except by something like an explicit simulation” ??? • “the only way … just to run them” ...
THEMATIC SCHOOL ON MATHEMATICAL BIOLOGY, PARTICLE
... observed and the mathematical structures that arise in understanding them. Existence and stability of steady states. The systems with long-range attractive and shortrange repulsive interactions exhibit steady states of a variety of shapes and patterns. We will introduce sharp conditions on the exist ...
... observed and the mathematical structures that arise in understanding them. Existence and stability of steady states. The systems with long-range attractive and shortrange repulsive interactions exhibit steady states of a variety of shapes and patterns. We will introduce sharp conditions on the exist ...
2008-03 - International Mathematical Union
... Combinatorial structures. Enumeration: exact and asymptotic. Graph theory. Probabilistic and extremal combinatorics. Designs and finite geometries. Relations with linear algebra, representation theory and commutative algebra. Topological and analytical techniques in combinatorics. Combinatorial geom ...
... Combinatorial structures. Enumeration: exact and asymptotic. Graph theory. Probabilistic and extremal combinatorics. Designs and finite geometries. Relations with linear algebra, representation theory and commutative algebra. Topological and analytical techniques in combinatorics. Combinatorial geom ...
Freshwater Ecosystems, Modelling and Simulation, by
... informative graphics. This methods overview provides a background for the applications that follow, and is helpful in determining how the different methods can complement one another. The limitations of each method are also evaluated. Most of the book summarizes attempts to construct ecological mode ...
... informative graphics. This methods overview provides a background for the applications that follow, and is helpful in determining how the different methods can complement one another. The limitations of each method are also evaluated. Most of the book summarizes attempts to construct ecological mode ...
Chaos: A view of complexity in the physical sciences
... computer, and showed that even in this oversimplified case the system’s behavior was wonderfully rich and complex. In addition, he showed that its long-term behavior exhibited the kind of sensitivity to initial conditions that was described above for chaotic planetary systems. He made the point that ...
... computer, and showed that even in this oversimplified case the system’s behavior was wonderfully rich and complex. In addition, he showed that its long-term behavior exhibited the kind of sensitivity to initial conditions that was described above for chaotic planetary systems. He made the point that ...
Course Announcement
... ENEE 790 is NOT a prerequisite for this course. Description The course provides a comprehensive treatment of the mathematical theory and experimental methods used in nonlinear optics. It is intended for engineering or physics graduate students who are interested in learning about nonlinear optical e ...
... ENEE 790 is NOT a prerequisite for this course. Description The course provides a comprehensive treatment of the mathematical theory and experimental methods used in nonlinear optics. It is intended for engineering or physics graduate students who are interested in learning about nonlinear optical e ...
RECURRENCE AND TOPOLOGICAL ENTROPY Problem. Let T : X
... where hFi is the closed algebra in C(X) generated by F . Note that (2) is a generalization of the condition that every nite partition is measurable with respect to its past (or future), which for measure preserving systems implies 0-entropy. For measure preserving systems 0-entropy also implies tha ...
... where hFi is the closed algebra in C(X) generated by F . Note that (2) is a generalization of the condition that every nite partition is measurable with respect to its past (or future), which for measure preserving systems implies 0-entropy. For measure preserving systems 0-entropy also implies tha ...
Lecture 10 - Math TAMU
... Let f : R → R be a unimodal map, Λ be the set of all points x ∈ R such that Of+ (x) ⊂ [0, 1], and S : Λ → Σ{0,1} be the itinerary map. We know that S is a continuous semi-conjugacy of the restriction f |Λ with the shift. Theorem 1 The following conditions are equivalent: (i) Λ is a Cantor set; (ii) ...
... Let f : R → R be a unimodal map, Λ be the set of all points x ∈ R such that Of+ (x) ⊂ [0, 1], and S : Λ → Σ{0,1} be the itinerary map. We know that S is a continuous semi-conjugacy of the restriction f |Λ with the shift. Theorem 1 The following conditions are equivalent: (i) Λ is a Cantor set; (ii) ...
In The Name of Allah The Most Beneficent The
... Nonlinear models can be linearized. Linear models are most often used in analysis and design. ...
... Nonlinear models can be linearized. Linear models are most often used in analysis and design. ...
LMS Northern Meeting: Abstracts of Communications
... packing, twisting, and topological constraints on the structure of DNA present problems in carrying out the functions and processes necessary for life such as transcription, replication, and recombination. However, the actions of enzymes that make these functions possible–topologically cutting, past ...
... packing, twisting, and topological constraints on the structure of DNA present problems in carrying out the functions and processes necessary for life such as transcription, replication, and recombination. However, the actions of enzymes that make these functions possible–topologically cutting, past ...
Titles and Abstracts
... Abstract: I will describe some problems in the dynamics of PDEs for which numerically solving adjoint problems provides valuable insight. I will focus on the dynamics of spiral and scroll waves in excitable media. I will show how the computation of Response Functions (adjoints to Goldstone modes) al ...
... Abstract: I will describe some problems in the dynamics of PDEs for which numerically solving adjoint problems provides valuable insight. I will focus on the dynamics of spiral and scroll waves in excitable media. I will show how the computation of Response Functions (adjoints to Goldstone modes) al ...
Page 1 2017610 .: SCIENPRESS LTD :. https://www.scienpress.com
... Theoretical Mathematics and Applications (TMA) is a refereed journal devoted to the publication of original research papers and review articles in all areas of theoretical mathematics. The journal also is concerned with high‐level mathematical investigations of certain applications in other fields o ...
... Theoretical Mathematics and Applications (TMA) is a refereed journal devoted to the publication of original research papers and review articles in all areas of theoretical mathematics. The journal also is concerned with high‐level mathematical investigations of certain applications in other fields o ...
7302 (Analytical Dynamics)
... Course Description and Objectives Analytical dynamics develops Newtonian mechanics to the stage where powerful mathematical techniques can be used to determine the behaviour of many physical systems. The mathematical framework also plays a role in the formulation of modern quantum and relativity the ...
... Course Description and Objectives Analytical dynamics develops Newtonian mechanics to the stage where powerful mathematical techniques can be used to determine the behaviour of many physical systems. The mathematical framework also plays a role in the formulation of modern quantum and relativity the ...
current new course name 18.135
... Representations of Lie Groups Topics in Lie Theory Graduate Topology Seminar Topics in Geometry ...
... Representations of Lie Groups Topics in Lie Theory Graduate Topology Seminar Topics in Geometry ...
- Center for Quantum Science and Engineering
... Motivated by the baryon chiral perturbation theory for QCD, using the symmetries as well as other relevant properties of the underlying microscopic t-J model, we have constructed a low-energy effective field theory for the t-J model on the square and honeycomb lattices. The effective field theory is ...
... Motivated by the baryon chiral perturbation theory for QCD, using the symmetries as well as other relevant properties of the underlying microscopic t-J model, we have constructed a low-energy effective field theory for the t-J model on the square and honeycomb lattices. The effective field theory is ...
Comparing Two Evolutionary Algorithms for Inducing Chaos in a
... The homeostatic process in a cell adapts the internal state to a changing environment by adjusting the concentrations of proteins related to expression genes. The changes in the concentrations of proteins in the cell can be represented like a dynamical system, particularly by means of a system of or ...
... The homeostatic process in a cell adapts the internal state to a changing environment by adjusting the concentrations of proteins related to expression genes. The changes in the concentrations of proteins in the cell can be represented like a dynamical system, particularly by means of a system of or ...
Department of Mathematics Research Colloquia 1998 – 2000 Dec 8 2000
... Mar 12 1999 Steve Alpern (LSE) Chaos is Generic when Volume is Preserved Chaotic dynamical systems usually `live' on fairly exotic, often fractal, domains. However it is possible to show that they can `live' on such ordinary sets as the unit square. We outline a combinatorial construction which defi ...
... Mar 12 1999 Steve Alpern (LSE) Chaos is Generic when Volume is Preserved Chaotic dynamical systems usually `live' on fairly exotic, often fractal, domains. However it is possible to show that they can `live' on such ordinary sets as the unit square. We outline a combinatorial construction which defi ...
Theoretical Foundation for Jung`s "Mandala Symbolism" Based on
... As it is well known thermodynamics is not analyzing the dynamical changes in time of constituents, but giving us equations for calculation of final distribution of elements composing systems (just one point in concentration space when oc). The next step in constructing adequate calculus to the livin ...
... As it is well known thermodynamics is not analyzing the dynamical changes in time of constituents, but giving us equations for calculation of final distribution of elements composing systems (just one point in concentration space when oc). The next step in constructing adequate calculus to the livin ...
Chaos theory
Chaos theory is the field of study in mathematics that studies the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as:Chaos: When the present determines the future, but the approximate present does not approximately determine the future.Chaotic behavior exists in many natural systems, such as weather and climate. This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Chaos theory has applications in several disciplines, including meteorology, sociology, physics, engineering, economics, biology, and philosophy.