Pseudo and Quasi Random Number GenerationAshwin Rao
Talk given at Morgan Stanley on efficient Monte Carlo simulation using Pseudo random numbers and low-discrepancy sequences (i.e., Quasi random numbers)
The second Fundamental Theorem of Calculus makes calculating definite integrals a problem of antidifferentiation!
(the slideshow has extra examples based on what happened in class)
Pseudo and Quasi Random Number GenerationAshwin Rao
Talk given at Morgan Stanley on efficient Monte Carlo simulation using Pseudo random numbers and low-discrepancy sequences (i.e., Quasi random numbers)
The second Fundamental Theorem of Calculus makes calculating definite integrals a problem of antidifferentiation!
(the slideshow has extra examples based on what happened in class)
We define the definite integral as a limit of Riemann sums, compute some approximations, then investigate the basic additive and comparative properties
At times it is useful to consider a function whose derivative is a given function. We look at the general idea of reversing the differentiation process and its applications to rectilinear motion.
Lesson 14: Derivatives of Logarithmic and Exponential Functions (slides)Matthew Leingang
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
We define the definite integral as a limit of Riemann sums, compute some approximations, then investigate the basic additive and comparative properties
At times it is useful to consider a function whose derivative is a given function. We look at the general idea of reversing the differentiation process and its applications to rectilinear motion.
Lesson 14: Derivatives of Logarithmic and Exponential Functions (slides)Matthew Leingang
The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.
There are various reasons why we would want to find the extreme (maximum and minimum values) of a function. Fermat's Theorem tells us we can find local extreme points by looking at critical points. This process is known as the Closed Interval Method.
Careers outside Academia - USC Computer Science Masters and Ph.D. StudentsAshwin Rao
Talk given at USC CS Colloquium to grad students (http://viterbi.usc.edu/news/events/?event=10265). The topic was - Prospective Careers outside Academia.
IIT Bombay - First Steps to a Successful CareerAshwin Rao
Career-Advice for IIT Bombay students. Emphasis on Quant Finance Jobs. Decisions-making on Tech versus Finance, Startups versus Large Firms. Introduction to ZLemma.com to help students identify the right jobs/careers.
z-Transform is for the analysis and synthesis of discrete-time control systems.The z transform in discrete-time systems play a similar role as the Laplace transform in continuous-time systems
High-dimensional polytopes defined by oracles: algorithms, computations and a...Vissarion Fisikopoulos
The processing and analysis of high dimensional geometric data plays a fundamental role in disciplines of science and engineering. A systematic framework to study these problems has been developing in the research area of discrete and computational geometry. This Phd thesis studies problems in this area. The fundamental geometric objects of our study are high dimensional convex polytopes defined byan oracle.The contribution of the thesis is threefold. First, the design and analysis of geometric algorithms for problems concerning high-dimensional convex polytopes, such as convex hull and volume computation and their applications to computational algebraic geometry and optimization. Second, the establishment of combinatorial characterization results for essential polytope families. Third, the implementation and experimental analysis of the proposed algorithms and methods
Transformations in OpenGL are not drawing
commands. They are retained as part of the
graphics state. When drawing commands are issued, the
current transformation is applied to the points
drawn. Transformations are cumulative.
Bartosz Milewski, “Re-discovering Monads in C++”Platonov Sergey
Once you know what a monad is, you start seeing them everywhere. The std::future library of C++11 was an example of an incomplete design, which stopped short of recognizing the monadic nature of futures. This is now being remedied in C++17, and there are new library additions, like std::expected and the range library, that are much more monad-conscious. I’ll explain what a monad is using copious C++ examples.
I am Bing Jr. I am a Signal Processing Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab Deakin University, Australia. I have been helping students with their assignments for the past 9 years. I solve assignments related to Signal Processing.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com. You can also call on +1 678 648 4277 for any assistance with Signal Processing Assignments.
Stochastic Control/Reinforcement Learning for Optimal Market MakingAshwin Rao
Optimal Market Making is the problem of dynamically adjusting bid and ask prices/sizes on the Limit Order Book so as to maximize Expected Utility of Gains. This is a stochastic control problem that can be tackled with classical Dynamic Programming techniques or with Reinforcement Learning (using a market-learnt simulator)
Understanding Dynamic Programming through Bellman OperatorsAshwin Rao
Policy Iteration and Value Iteration algorithms are best understood by viewing them from the lens of Bellman Policy Operator and Bellman Optimality Operator
A.I. for Dynamic Decisioning under Uncertainty (for real-world problems in Re...Ashwin Rao
Slides from the Research Seminar talk I gave at Nvidia. The topic was: A.I. for Dynamic Decisioning under Uncertainty (for Real-World problems in Retail and in Financial Trading)
Overview of Stochastic Calculus FoundationsAshwin Rao
This is a quick refresher/overview of Stochastic Calculus Foundations. This assumes you have done a Stochastic Calculus course previously and now want to review/revise the material to prepare for a course that lists Stochastic Calculus as a pre-req. In these 11 slides, I list the key content you must be familiar with within Stochastic Calculus.
Risk-Aversion, Risk-Premium and Utility TheoryAshwin Rao
This lecture helps understand the concepts of Risk-Aversion and Risk-Premium viewed from the lens of Utility Theory. These are foundational economic concepts used widely in Financial applications - Portfolio problems and Pricing problems, to name a couple.
To make Reinforcement Learning Algorithms work in the real-world, one has to get around (what Sutton calls) the "deadly triad": the combination of bootstrapping, function approximation and off-policy evaluation. The first step here is to understand Value Function Vector Space/Geometry and then make one's way into Gradient TD Algorithms (a big breakthrough to overcome the "deadly triad").
Stanford CME 241 - Reinforcement Learning for Stochastic Control Problems in ...Ashwin Rao
I am pleased to introduce a new and exciting course, as part of ICME at Stanford University. I will be teaching CME 241 (Reinforcement Learning for Stochastic Control Problems in Finance) in Winter 2019.
HJB Equation and Merton's Portfolio ProblemAshwin Rao
Deriving the solution to Merton's Portfolio Problem (Optimal Asset Allocation and Consumption) using the elegant formulation of Hamilton-Jacobi-Bellman equation.
A Quick and Terse Introduction to Efficient Frontier MathematicsAshwin Rao
A Quick and Terse Introduction to Efficient Frontier Mathematics. Only a basic background in Linear Algebra, Probability and Optimization is expected to cover this material and gain a reasonable understanding of this topic within one hour.
Recursive Formulation of Gradient in a Dense Feed-Forward Deep Neural NetworkAshwin Rao
Recursive Formulation of Gradient in a Dense Feed-Forward Deep Neural Network. Derived for a fairly general setting where the supervisory variable has a conditional probability density modeled as an arbitrary Generalized Linear Model's "normal-form" probability density, and whose output layer activation function is the GLM canonical link function.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Epistemic Interaction - tuning interfaces to provide information for AI support
Abstract Algebra in 3 Hours
1. ABSTRACT ALGEBRA IN 3 HOURS!
Ashwin Rao
Meant to be a quick preparation
for learning Category Theory
2. Overview of Preliminaries
• Set: unordered and unique elements
• Cartesian Product of Sets
• Relation: A subset of a cartesian product
• Reflexive, Symmetric, Transitive Relation on a set ó Equivalence Classes (Partition)
• Partially Ordered Set: Reflexive, Anti-symmetric and Transitive
• Function: Just a relation on A x B with every a in A mapped to a single b in B
• Domain, Codomain, Range, Injective, Surjective, Bijective functions
• Inverse and Composition of functions
3. Semigroup
• A set with an operation (*) under which the set is closed, along with associativity.
• Associativity: a * (b * c) = (a * b) * c
• Commutativity a * b = b * a is fairly common, but not part of semigroup definition.
• Canonical Example: Positive Integers Z+ with operation as + or *
• Funky Example: Integers with Min or Max operation.
• Example: Free semigroup of an alphabet (List[T] except empty list, with concat)
• Or, List[T] of length n, for any n in Z+
• Eg: Set of Functions f : X -> X with composition (think “shrinking” functions)
• Sub-Semigroup example: nZ+, for n in Z+
• Semigroup homomorphism (structure-preserving) f: G -> H : f(a *G b) = f(a) *H f(b)
4. Monoid
• Semigroup together with an identity element (call it “1”)
• Canonical Example: Natural numbers N with + as * , 0 as 1
• or, Z+ with * as * and 1 as 1
• Example: Free monoid of an alphabet (List[T] with concat)
• Or, List[T] of length n, for any n in N.
• Eg: {True, False} with AND as *, True as 1 (or with OR as *, False as 1)
• Eg: All subsets of a set S with Union as *, Empty as 1 (or Intersect as *, S as 1)
• Note: Cartesian product of monoids is a monoid
• Note: All functions from a set to a monoid form a monoid (pointwise operation)
• Eg: All Functions f: X -> X for any set X, with composition as * and identity function as 1
5. Monoid (continued)
• Submonoid example: nN
• Monoid homomorphism f: G -> H : f(a *G b) = f(a) *H f(b) and f(1G) = 1H
• Example: f(x) = 2x from (N,+,0) to (N,*,1)
• Isomorphism is when we have homomorphisms f: G -> H and g: H -> G such that g . f
= idG and f . g = idH
• Isomorphism means the two monoids are “basically the same”
• Kernel(f) = {a in G | f(a) = 1H} is a monoid
• Isomorphism can also be defined as a homomorphism f with Kernel(f) = {1G}
• Note: The f(x) = 2x example is an isomorphism
6. Group
• Monoid together with an inverse a-1 for every a such that a * a-1 = a-1 * a = 1
• Canonical Example: Z
• Eg: Bijective functions f : X -> X for any set X with {func composition, identity func, inverse func}
• Great Example: All Permutations of a finite set of size n (refered to as Sn)
• Eg: n-th complex root of unity zn and its powers (zn is called the generator of the group)
• Example of subgroup: nZ for any n in Z+
• Homomorphism f: G -> H: f(a *G b) = f(a) *H f(b), f(1G) = f(1H), f(a-1) = f(a)-1, eg: Z -> nZ
• Coseta,H for any a in G and any subgroup H if defined as: {a + h: h in H}
• Quotient Group: G/H is a group consisting of all the cosets of H (H becomes identity element)
• Canonical Example of Quotient Group: Z / nZ = Zn (Integers modulo n for any n in Z+)
• Isomorphism is same as defined for a monoid (isomorphism means “basically the same group“)
• First Isomorphism Theorem: Homomorphism f: G -> H, Kernel(f) is a subgroup of G, Range(f) is a
subgroup of H, G/Kernel(f) is isomorphic to Range(f)
7. Semiring and Ring
• Semiring has two monoid operations (*,1) and (+,0) with a * (b + c) = (a * b) + (a *
c), (a + b) * c = (a * c) + (b * c), and 0 * a = a * 0 = 0. Moreover, + is commutative.
• Canonical Example: N
• Ring is a semiring with + operation having an inverse (i.e., a group under +)
• Ring Homomorphism means homomorphism under both + and *
• Canonical Example: Z
• Another Canonical Example: Polynomials over R
• Ideal I is a subset of Ring R s.t. for any x, y in I and r in R, x + y and r * x are in I
• Canonical Example of Ideal: nZ
• R / I is a ring (Quotient Ring) consisting of all the cosets of I s.t. (a+I)+(b+I) =
(a+b)+I and (a+I)*(b+I) = (ab)+I
8. Field
• Field is a ring with an inverse for *, and * commutative.
• Canonical Example: Rational Numbers Q or Real Numbers R
• Finite Field Example: Zp for any prime p
• Every finite field is isomorphic to the set of polynomials over the finite field Zp
modulo an irreducible polynomial (over Zp)
• Hence, finite fields are of size pr (r is the degree of the irreducible polynomial)
9. Vector Space and Linear Map
• Vector Space V (associated with scalar Field F) is a commutative group under vector addition,
together with scalar multiplication, and the following properties:
o a(bv) = (ab)v
o 1(v) = v
o a(u+v) = au + av
o (a+b)v = av + bv
• Canonical Example: Rn
• Eg: Complex numbers and other field extensions
• Eg: Functions from a set X to a field F (pointwise addition and pointwise scalar multiplication)
• Linear Map f: V -> W has property f(v+w) = f(v) + f(w) and f(a.x) = a.f(x)
• Canonical Example: m by n Matrix M: Rn -> Rm
• Linear maps V -> W forms a vector space L(V,W)
• Linear maps V -> F (F the scalar Field) is called the Dual Vector Space V*
10. Fundamental Theorem of Linear Algebra
• Consider a linear map expressed as a m x n matrix M : Rn -> Rm
• Column Space (Range): Subspace of Rm consisting of all Mx (over all x in Rn)
• Row Space (CoRange): Subspace of Rn consisting of all MTy (over all y in Rm)
• Kernel Space: Subspace of Rn mapping (through M) to 0 in Rm
• CoKernel Space: Subspace of Rm mapping (through MT) to 0 in Rn
• Rank r is defined as the dimension of Column Space(= Dimension of Row Space)
• Kernel Space is orthogonal to Row Space and has rank n – r (a.k.a. Nullity)
• CoKernel Space is orthogonal to Column Space and has rank m – r (a.k.a. CoRank)
• More generally, we know from the First Isomorphism Theorem (on Groups) that the
Kernel Quotient (i.e., Row Space) and Range (i.e., Column Space) are isomorphic.