This document summarizes a machine learning homework assignment with 4 problems:
1) Probability questions about constructing random variables.
2) Questions about Poisson generalized linear models (GLM) including log-likelihood, prediction, and regularization.
3) Questions comparing square loss and logistic loss for an outlier point.
4) Questions about batch normalization including its effect on model expressivity and gradients.
5.1 Defining and visualizing functions. A handout.Jan Plaza
This document introduces concepts related to functions including:
- Defining functions in terms of unique mappings between inputs and outputs
- Distinguishing between total, partial, and non-functions
- Specifying domains and ranges
- Using vertical line tests to identify functions from graphs
- Examples of functions defined by formulas or mappings
This document summarizes a machine learning homework assignment with 4 problems:
1) Probability questions about constructing random variables.
2) Questions about Poisson generalized linear models (GLM) including log-likelihood, prediction, and regularization.
3) Questions comparing square loss and logistic loss for an outlier point.
4) Questions about batch normalization including its effect on model expressivity and gradients.
5.1 Defining and visualizing functions. A handout.Jan Plaza
This document introduces concepts related to functions including:
- Defining functions in terms of unique mappings between inputs and outputs
- Distinguishing between total, partial, and non-functions
- Specifying domains and ranges
- Using vertical line tests to identify functions from graphs
- Examples of functions defined by formulas or mappings
Functions and its Applications in MathematicsAmit Amola
A function is a relation between a set of inputs and set of outputs where each input is related to exactly one output. An example is given of a function that relates shapes to colors, where each shape maps to one unique color. A function can be written as a set of ordered pairs, where the input comes first and the output second. The domain is the set of inputs, the codomain is the set of possible outputs, and the range is the set of outputs the function actually produces. A function is one-to-one if no two distinct inputs map to the same output, and onto if every element in the codomain is mapped to by at least one input.
This document discusses inverse functions and their derivatives. It defines inverse functions as switching the x- and y-values of a function to "undo" the original function. A function has an inverse only if it passes the horizontal line test. The derivative of an inverse function at a point equals the reciprocal of the derivative of the original function at the corresponding point.
This document discusses inverses of functions and their graphs. It provides an example of finding the inverse of a point (-4, 3) by reflecting it over the line y=x and switching the x and y values. It also gives an example function f(x)=4x+3 and explains how to write the inverse equation, draw the graph, and state the domain and range of both the function and its inverse. Finally, it provides two functions and explains how to determine algebraically if they are inverses of each other.
A function is a relation where each input is paired with exactly one output. Functions are commonly represented using function notation with an independent variable x and dependent variable y, written as f(x). Functions can be represented verbally, numerically in a table, visually in a graph, or algebraically with an explicit formula. The domain is the set of inputs, while the range is the set of outputs. Functions can be one-to-one, onto, many-to-one, or into. Operations like addition, subtraction, multiplication, and division can be performed on functions if they have overlapping domains. The composition of two functions is written as f(g(x)). Common functions include linear, square, cubic, and absolute
This document discusses functions and their properties. It defines a function as a relation where each input is paired with exactly one output. Functions can be represented numerically in tables, visually with graphs, algebraically with explicit formulas, or verbally. The domain is the set of inputs, the codomain is the set of all possible outputs, and the range is the set of actual outputs. Functions can be one-to-one (injective) if each input maps to a unique output, or onto (surjective) if each possible output is the image of some input.
The document discusses various types of functions including:
- Constant functions which assign the same real number to every element of the domain.
- Linear functions which have a degree of 1 and are defined by the equation f(x)=mx+b.
- Quadratic functions which are polynomial functions of degree 2.
- Cubic/power functions which are polynomial functions of degree 3.
It also briefly describes identity, absolute value, rational, and algebraic functions. The document concludes with instructions for a group activity on identifying different function types from graphs.
This document contains a mathematics exam for high school students in Greece. It is divided into 4 sections with multiple questions in each section. The questions cover topics related to functions, limits, derivatives, and integrals. Some questions ask students to prove statements, find domains of functions, determine if functions are injective or have critical points. The document is 3 pages long and aims to test students' understanding of key concepts in calculus and mathematical analysis.
The document discusses the Euler Phi function, which calculates the number of numbers less than n that are relatively prime to n. It provides examples of calculating phi(n) for different types of numbers n. For prime numbers, phi(n) = n-1. For numbers that are a power of a prime like 8, phi(n) = n - n/p, where n is the power of p. For numbers that can be expressed as a product of different primes, phi(n) is the product of phi(n) for each prime factor.
This document discusses inverse functions including:
- Verifying that two functions are inverse functions by showing their compositions result in the identity function
- Determining whether a function has an inverse function using the horizontal line test
- Finding the derivative of an inverse function using the theorem that the derivative of the inverse is the reciprocal of the derivative of the original function
This document contains a mathematics exam with 4 problems (Themes A, B, C, D) involving functions, derivatives, monotonicity, convexity, extrema, asymptotes and limits.
Theme A involves properties of differentiable functions, the definition of the derivative, and Rolle's theorem. Theme B analyzes the monotonicity, convexity, asymptotes and graph of a given function.
Theme C proves properties of a continuous, monotonically increasing function and finds extrema of related functions. Theme D proves properties of a power function and its relation to a given line, defines a new function, and proves monotonicity and existence of a single real root for a polynomial equation.
This document discusses composite functions and the order of operations when combining functions.
It provides an example of a mother converting the temperature of her baby's bath water from Celsius to Fahrenheit using two separate functions. The first function converts the Celsius reading to Fahrenheit, and the second maps the Fahrenheit reading to whether the water is too cold, alright, or too hot. Together these functions form a composite function.
Algebraically, a composite function f∘g(x) is defined as applying the inner function f first to the input x, and then applying the outer function g to the output of f. The domain of the inner function must be contained within the range of the outer function. The order of
To have an inverse function, a function must be one-to-one and pass the horizontal line test. If a function fails either of these, the inverse is considered a relation instead of a function. The domain of the original function becomes the range of the inverse, and the range of the original becomes the domain of the inverse. An example given is reflecting points across the x or y-axis.
1) A function assigns each element of its domain to exactly one element of its codomain. The domain is the set of inputs and the codomain is the set of possible outputs.
2) A function can be represented by an equation, a mapping of inputs to outputs, or a graph. Properties of functions include being one-to-one, onto, bijective, increasing, decreasing.
3) The composition of two functions is the application of one function after the other. The inverse of a bijective function undoes the original mapping.
The document reports on a lesson about Wilson's theorem and the Chinese remainder theorem. It defines the two theorems, provides examples and proofs of them, and has students work on related activities and problems. It also has students evaluate their understanding of the lesson. Wilson's theorem relates to determining if a number is prime, while the Chinese remainder theorem addresses solving simultaneous congruences.
Lecture 20 fundamental theorem of calc - section 5.3njit-ronbrown
The document discusses indefinite integrals and introduces the notation used to represent them. It explains that an indefinite integral of a function f(x) is represented by ∫f(x) dx and denotes the general antiderivative of f(x), not a specific function. The document also provides an example of finding the indefinite integral of 10x4 - 2sec2x and explains how to check the answer.
Extreme values of a function & applications of derivativeNofal Umair
This document discusses key concepts related to finding extrema of functions, including:
- Absolute and relative extrema refer to the maximum and minimum values of a function over its entire domain or on a subinterval, respectively.
- Critical points, where the derivative is zero or undefined, and endpoints must be checked to find extrema.
- The Extreme Value Theorem states that continuous functions on closed intervals have both a maximum and minimum value.
- The first derivative determines whether a function is increasing or decreasing, and where it is zero may indicate relative extrema. The second derivative indicates concavity and points of inflection.
The document discusses techniques for calculating derivatives of functions, including:
- Using formulas and theorems to calculate derivatives more efficiently than using the definition of a derivative.
- Applying rules like the power rule, product rule, and quotient rule to take derivatives.
- Using derivatives to find equations of tangent lines and instantaneous rates of change.
This document defines metric spaces and discusses their basic properties. It begins by defining what a metric is and what constitutes a metric space. It provides some basic examples of metrics, such as the discrete metric and p-norm metrics. It then discusses metric topologies, defining open and closed balls and showing that the collection of open sets forms a topology. It also introduces the concept of topologically equivalent metrics.
Functions and its Applications in MathematicsAmit Amola
A function is a relation between a set of inputs and set of outputs where each input is related to exactly one output. An example is given of a function that relates shapes to colors, where each shape maps to one unique color. A function can be written as a set of ordered pairs, where the input comes first and the output second. The domain is the set of inputs, the codomain is the set of possible outputs, and the range is the set of outputs the function actually produces. A function is one-to-one if no two distinct inputs map to the same output, and onto if every element in the codomain is mapped to by at least one input.
This document discusses inverse functions and their derivatives. It defines inverse functions as switching the x- and y-values of a function to "undo" the original function. A function has an inverse only if it passes the horizontal line test. The derivative of an inverse function at a point equals the reciprocal of the derivative of the original function at the corresponding point.
This document discusses inverses of functions and their graphs. It provides an example of finding the inverse of a point (-4, 3) by reflecting it over the line y=x and switching the x and y values. It also gives an example function f(x)=4x+3 and explains how to write the inverse equation, draw the graph, and state the domain and range of both the function and its inverse. Finally, it provides two functions and explains how to determine algebraically if they are inverses of each other.
A function is a relation where each input is paired with exactly one output. Functions are commonly represented using function notation with an independent variable x and dependent variable y, written as f(x). Functions can be represented verbally, numerically in a table, visually in a graph, or algebraically with an explicit formula. The domain is the set of inputs, while the range is the set of outputs. Functions can be one-to-one, onto, many-to-one, or into. Operations like addition, subtraction, multiplication, and division can be performed on functions if they have overlapping domains. The composition of two functions is written as f(g(x)). Common functions include linear, square, cubic, and absolute
This document discusses functions and their properties. It defines a function as a relation where each input is paired with exactly one output. Functions can be represented numerically in tables, visually with graphs, algebraically with explicit formulas, or verbally. The domain is the set of inputs, the codomain is the set of all possible outputs, and the range is the set of actual outputs. Functions can be one-to-one (injective) if each input maps to a unique output, or onto (surjective) if each possible output is the image of some input.
The document discusses various types of functions including:
- Constant functions which assign the same real number to every element of the domain.
- Linear functions which have a degree of 1 and are defined by the equation f(x)=mx+b.
- Quadratic functions which are polynomial functions of degree 2.
- Cubic/power functions which are polynomial functions of degree 3.
It also briefly describes identity, absolute value, rational, and algebraic functions. The document concludes with instructions for a group activity on identifying different function types from graphs.
This document contains a mathematics exam for high school students in Greece. It is divided into 4 sections with multiple questions in each section. The questions cover topics related to functions, limits, derivatives, and integrals. Some questions ask students to prove statements, find domains of functions, determine if functions are injective or have critical points. The document is 3 pages long and aims to test students' understanding of key concepts in calculus and mathematical analysis.
The document discusses the Euler Phi function, which calculates the number of numbers less than n that are relatively prime to n. It provides examples of calculating phi(n) for different types of numbers n. For prime numbers, phi(n) = n-1. For numbers that are a power of a prime like 8, phi(n) = n - n/p, where n is the power of p. For numbers that can be expressed as a product of different primes, phi(n) is the product of phi(n) for each prime factor.
This document discusses inverse functions including:
- Verifying that two functions are inverse functions by showing their compositions result in the identity function
- Determining whether a function has an inverse function using the horizontal line test
- Finding the derivative of an inverse function using the theorem that the derivative of the inverse is the reciprocal of the derivative of the original function
This document contains a mathematics exam with 4 problems (Themes A, B, C, D) involving functions, derivatives, monotonicity, convexity, extrema, asymptotes and limits.
Theme A involves properties of differentiable functions, the definition of the derivative, and Rolle's theorem. Theme B analyzes the monotonicity, convexity, asymptotes and graph of a given function.
Theme C proves properties of a continuous, monotonically increasing function and finds extrema of related functions. Theme D proves properties of a power function and its relation to a given line, defines a new function, and proves monotonicity and existence of a single real root for a polynomial equation.
This document discusses composite functions and the order of operations when combining functions.
It provides an example of a mother converting the temperature of her baby's bath water from Celsius to Fahrenheit using two separate functions. The first function converts the Celsius reading to Fahrenheit, and the second maps the Fahrenheit reading to whether the water is too cold, alright, or too hot. Together these functions form a composite function.
Algebraically, a composite function f∘g(x) is defined as applying the inner function f first to the input x, and then applying the outer function g to the output of f. The domain of the inner function must be contained within the range of the outer function. The order of
To have an inverse function, a function must be one-to-one and pass the horizontal line test. If a function fails either of these, the inverse is considered a relation instead of a function. The domain of the original function becomes the range of the inverse, and the range of the original becomes the domain of the inverse. An example given is reflecting points across the x or y-axis.
1) A function assigns each element of its domain to exactly one element of its codomain. The domain is the set of inputs and the codomain is the set of possible outputs.
2) A function can be represented by an equation, a mapping of inputs to outputs, or a graph. Properties of functions include being one-to-one, onto, bijective, increasing, decreasing.
3) The composition of two functions is the application of one function after the other. The inverse of a bijective function undoes the original mapping.
The document reports on a lesson about Wilson's theorem and the Chinese remainder theorem. It defines the two theorems, provides examples and proofs of them, and has students work on related activities and problems. It also has students evaluate their understanding of the lesson. Wilson's theorem relates to determining if a number is prime, while the Chinese remainder theorem addresses solving simultaneous congruences.
Lecture 20 fundamental theorem of calc - section 5.3njit-ronbrown
The document discusses indefinite integrals and introduces the notation used to represent them. It explains that an indefinite integral of a function f(x) is represented by ∫f(x) dx and denotes the general antiderivative of f(x), not a specific function. The document also provides an example of finding the indefinite integral of 10x4 - 2sec2x and explains how to check the answer.
Extreme values of a function & applications of derivativeNofal Umair
This document discusses key concepts related to finding extrema of functions, including:
- Absolute and relative extrema refer to the maximum and minimum values of a function over its entire domain or on a subinterval, respectively.
- Critical points, where the derivative is zero or undefined, and endpoints must be checked to find extrema.
- The Extreme Value Theorem states that continuous functions on closed intervals have both a maximum and minimum value.
- The first derivative determines whether a function is increasing or decreasing, and where it is zero may indicate relative extrema. The second derivative indicates concavity and points of inflection.
The document discusses techniques for calculating derivatives of functions, including:
- Using formulas and theorems to calculate derivatives more efficiently than using the definition of a derivative.
- Applying rules like the power rule, product rule, and quotient rule to take derivatives.
- Using derivatives to find equations of tangent lines and instantaneous rates of change.
This document defines metric spaces and discusses their basic properties. It begins by defining what a metric is and what constitutes a metric space. It provides some basic examples of metrics, such as the discrete metric and p-norm metrics. It then discusses metric topologies, defining open and closed balls and showing that the collection of open sets forms a topology. It also introduces the concept of topologically equivalent metrics.
This document contains a lecture on functions, λ-calculus, and Peano arithmetic. It defines functions, injections, surjections, bijections, function composition, and identity functions. It introduces λ-calculus, including β-reduction and shows how Church numerals can represent numbers. It then covers Peano arithmetic, defining numbers, addition, multiplication, and exponentiation recursively using λ-terms.
This document provides an overview and agenda for a master's level course on probability and statistics. It covers key topics like statistical models, probability distributions, conditional distributions, convergence theorems, sampling, confidence intervals, decision theory, and testing procedures. Examples of common probability distributions and functions are also presented, including the cumulative distribution function, probability density function, independence, and conditional independence. Additional references for further reading are included.
The document discusses key concepts related to limits, continuity, and differentiation. It defines what it means for a variable x to approach a finite number a or infinity, and provides the formal definitions of one-sided limits and two-sided limits. It also discusses indeterminate forms when limits take on forms like 0/0, infinity/infinity, or infinity - infinity. The document outlines several properties of limits, including limits of even and odd functions. It distinguishes between the limit of a function as x approaches a, denoted limx→af(x), versus the function value at that point, f(a). Finally, it states standard theorems about limits, such as the sum and product of two functions whose limits exist
This document summarizes a talk given by Yoshihiro Mizoguchi on developing a Coq library for relational calculus. The talk introduces relational calculus and its applications. It describes implementing definitions and proofs about relations, Boolean algebras, relation algebras, and Dedekind categories in Coq. The library provides a formalization of basic notions in relational theory and can be used to formally verify properties of relations and prove theorems automatedly.
This document discusses graphs of polynomial functions. It defines a polynomial function as a function of the form f(x) = anxn + an-1xn-1 + ... + a1x + a0, where n is a nonnegative integer and each ai is a real number. The degree of the polynomial is n and the leading coefficient is an. Polynomial graphs are continuous and smooth without breaks or cusps. The behavior of graphs as x approaches positive or negative infinity depends on the sign of the leading coefficient and whether the degree is odd or even. Polynomials can have real zeros where they intersect the x-axis. Their graphs may have up to n turning points and n zeros.
Efficient end-to-end learning for quantizable representationsNAVER Engineering
발표자: 정연우(서울대 박사과정)
발표일: 2018.7.
유사한 이미지 검색을 위해 neural network를 이용해 이미지의 embedding을 학습시킨다. 기존 연구에서는 검색 속도 증가를 위해 binary code의 hamming distance를 활용하지만 여전히 전체 데이터 셋을 검색해야 하며 정확도가 떨어지는 다는 단점이 있다. 이 논문에서는 sparse한 binary code를 학습하여 검색 정확도가 떨어지지 않으면서 검색 속도도 향상시키는 해쉬 테이블을 생성한다. 또한 mini-batch 상에서 optimal한 sparse binary code를 minimum cost flow problem을 통해 찾을 수 있음을 보였다. 우리의 방법은 Cifar-100과 ImageNet에서 precision@k, NMI에서 최고의 검색 정확도를 보였으며 각각 98× 와 478×의 검색 속도 증가가 있었다.
This document provides an overview of integral calculus concepts including:
1) The definition of an indefinite integral as the function whose derivative is the integrand plus a constant term.
2) Notation used in integral calculus including the integral sign and limits of integration for definite integrals.
3) Examples of integrating basic functions like 4x and the integral of sin(x) from 0 to π.
4) A table of common integration formulas for integrating functions like 1/x, e^x, sin(x), tan(x), and more.
5) An explanation of the integration by parts formula and examples of using it to integrate functions like xe^x and sin(
This document discusses random variables and their probability distributions. It defines different types of random variables such as real, complex, discrete, continuous, and mixed. It also defines key concepts such as sample space, cumulative distribution function (CDF), and probability density function (PDF) for both discrete and continuous random variables. Examples are provided to illustrate how to calculate the CDF and PDF for different random variables. Properties of CDFs and PDFs are also covered.
A Generalized Metric Space and Related Fixed Point TheoremsIRJET Journal
This document presents a new concept of generalized metric spaces and establishes some fixed point theorems in these spaces. It begins with defining generalized metric spaces, which generalize standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces with the Fatou property. It then proves some properties of generalized metric spaces, including conditions for convergence. Finally, it establishes an extension of the Banach contraction principle to generalized metric spaces, proving the existence and uniqueness of a fixed point under certain assumptions.
1) The document reviews concepts from probability and statistics including discrete and continuous random variables, their distributions (e.g. binomial, Poisson, normal), and multivariate distributions.
2) It then discusses key properties of multivariate normal distributions including their probability density function and how marginal and conditional distributions can be derived from the joint distribution.
3) Concepts like independence, mean vectors, covariance matrices, and their implications are also covered as they relate to multivariate normal distributions.
This document provides an introduction to functions and their key concepts. It defines a function as a rule that assigns each element in one set to a unique element in another set. Functions can be represented graphically and algebraically. Common types of functions discussed include polynomial, linear, constant, rational, trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions. Examples are provided to illustrate domain, range, and graphing of different function types.
This document provides an overview of linear equations and functions. It defines what makes an equation linear and explains that a linear equation can be written in the form of y=mx+b. Examples are provided to demonstrate how to identify the x-intercept and y-intercept of a linear equation and graph it. Students are introduced to the concept that a linear function satisfies a linear equation and can be written as f(x)=mx+b. The document concludes by providing practice problems for students to evaluate linear functions and find intercepts of a linear equation graph.
This document provides an introduction to radial basis function (RBF) interpolation of scattered data. It discusses how RBFs choose basis functions centered at data points to guarantee a well-posed interpolation problem. Common RBF kernels include the multiquadric, inverse multiquadric, and Gaussian functions. While RBF interpolation is guaranteed to have a unique solution, it can still be ill-conditioned depending on the shape parameter choice. Considerations for using RBFs include that the interpolation matrix is dense, requiring optimization of the shape parameter, and interpolation error increases near boundaries.
This document provides an introduction to functions and limits. It defines key concepts such as domain, range, and different types of functions including algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions. Examples are provided to illustrate how to find the domain and range of functions, evaluate functions, and draw graphs of functions. Function notation and the concept of a function as a rule that assigns each input to a single output are also explained.
This document provides an introduction to functions and their key concepts. It defines what a function is, using examples to illustrate functions that relate variables. Functions have a domain and range, and can be represented graphically. Common types of functions are discussed, including algebraic functions like polynomials and rational functions, as well as trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions. Methods for determining a function's domain and range and drawing its graph are presented.
This document presents a mathematical theory on weak contractions in cone metric spaces. It begins by introducing concepts such as cone metric spaces, C-contractions, weak C-contractions, and f-contractions. It then defines a new concept of a C-f weak contraction, which generalizes previous weak contraction definitions. The main result proved is a coincidence point and common fixed point theorem for C-f weak contractions in complete cone metric spaces under certain conditions on the mappings. Examples and remarks are provided to show how the new C-f weak contraction definition generalizes previous contraction definitions.
This document introduces equivalence relations and partitions. It defines an equivalence relation as a binary relation that is reflexive, symmetric, and transitive. Equivalence relations partition a set into disjoint equivalence classes that cover the entire set. The quotient set of a set by an equivalence relation consists of the equivalence classes. Every equivalence relation determines a partition, and every partition determines an equivalence relation. Examples are provided to illustrate these concepts using the equivalence relation of congruence modulo 3 on the integers.
6.2 Reflexivity, symmetry and transitivity (dynamic slides)Jan Plaza
This document introduces basic concepts of set theory including definitions of reflexive, symmetric and transitive relations. It provides examples of relations between lines that are parallel or perpendicular. It also discusses relations between people like siblings and ancestors. The document proves properties of congruence relations and discusses counting relations with certain properties over sets with a given number of elements. It addresses a claim about relations that are symmetric and transitive necessarily being reflexive, finding a counterexample.
This document provides an introduction to permutations. It begins by defining a permutation as a bijection from a set to itself. It then gives examples of permutations of small sets. The document proves several properties of permutations, including that the number of permutations of a set with n elements is n!. It introduces the concept of powers of permutations and proves related properties. It concludes by proving additional properties of permutations using an algebraic approach that relies on basic properties like associativity of composition.
This document introduces the concept of an inverse relation. It defines an inverse relation R-1 as the set containing all pairs (b,a) such that (a,b) is in R. It provides examples of inverse relations and shows how inverse relations can be defined using formulas, tuples, truth tables, and visual representations like graphs. The document also presents exercises for identifying inverse relations and propositions about inverse relations and their properties.
This document introduces concepts from set theory including families of sets ordered by inclusion, Hasse diagrams, smallest, largest, minimal and maximal sets. It defines these terms and provides examples to illustrate the concepts. Properties of families are proved, including that there can only be one smallest set, two minimal sets must be incomparable, and a finite non-empty family always has at least one minimal set. It is shown that the smallest set is also the intersection of all sets in the family.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
1. Introduction to set theory and to methodology and philosophy of
mathematics and computer programming
Basic functions
An overview
by Jan Plaza
c 2017 Jan Plaza
Use under the Creative Commons Attribution 4.0 International License
Version of November 6, 2017
2. Definition
1. The identity function on X , idX , is the function on X s.t.
idX(x)=x for every x ∈ X.
2. Let X ⊆ Y . The inclusion function from X to Y , X → Y , is idX.
3. f is a constant function on X if f is a function on X, and there is c such that
f(x) = c for every x ∈ X.
4. The empty function is the empty relation; ∅ : ∅ −→ X.
5. Let X ⊆ U. The characteristic function of X with respect to U is the
function from U to {0, 1} defined as follows:
x → 1 if x ∈ X,
x → 0 if x ∈ X.
3. True or false?
χA∩B(x) = χA(x) · χB(x),
True
True or false?
χA∪B(x) = χA(x) + χB(x)
False
Find a counter-example!
4. Definition
Let X1 and X2 be sets.
The 1-st projection from X1 × X2 is the function
π1 : X1 × X2 −→ X1 defined as π1 : x1, x2 → x1.
The 2-nd projection from X1 × X2 is the function
π2 : X1 × X2 −→ X2 defined as π2 : x1, x2 → x2.
Proposition
For every set Y and f1 : Y −→ X1 and f2 : Y −→ X2, there exists a unique function
f : Y −→ X1 × X2 such that π1 ◦ f = f1 and π2 ◦ f = f2.
Y
f1
zz
! f
f2
$$
X1 X1 × X2π1
oo
π2
// X2