By Assad Ebrahim, on March 14th, 2023 (15,070 views) |
Topic: Maths--General Interest, Technology
Updated May 2024 (added non-banking financial sector), Updated March 2023 (added latest bank collapses in US/EU). First published July 5, 2010 (two years after the financial collapse triggered Great Recession).
Mathematical Finance is an area of applied mathematics that has developed rapidly during the late 80s and 90s after the deregulation of U.S. financial markets, and accelerated further in the 2000s concurrently with the rise of data science/’big data’ and computational platforms able to run complex models in close to real-time. For its financial models for risk and pricing, Mathematical Finance draws upon the partial differential equations of mathematical physics, stochastic calculus, probabilistic modeling, mathematical optimization, statistics, and numerical methods. The implementation of these often complex numerical mathematical models requires efficient algorithms and exploiting the state-of-the-art in software engineering (real-time and embedded development, low latency network programming) and computing hardware (FPGAs, GPUs, and parallel and distributed processing). Taken together, the technical aspects of mathematical finance and the software/hardware aspect of financial engineering lie at the intersection of business, economics, mathematics, computer science, physics, and electrical engineering. For the technologically inclined, there are ample opportunities to contribute.
But the relevance goes beyond mathematics. There is a kernel of core financial ideas that are at the heart of the global free market capitalist system that is in place across most of the world today. These ideas affect not only economics but also politics and society. Ideally, every citizen in a democracy should understand the essential mechanics of the modern financial world and how it has arisen, regardless of whether we agree with its principles or with the impact of the financial system on social structures.
This article presents a simplified account of the rise of the modern financial marketplace including some history, and contemporary financial context. Update (2012): A highly recommended graphic novel Economix, by Michael Goodwin has just been published that presents a panoramic yet highly accessible narrative.)
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TinyPhoto is a small rotating photobook embedded graphics project that uses the low-power ATtiny85 microcontroller (3mA) and a 128×64 pixel OLED display (c.5-10mA typical, 15mA max). This combination can deliver at least 20 hrs of continuous play on a 3V coin cell battery (225mAh capacity). TinyPhoto can be readily built from a handful of through-hole electronic components (12 parts, £5) organized to fit onto a 3cm x 7cm single-sided prototype PCB. The embedded software is c.150 lines of C code and uses less than 1,300 bytes of on-chip memory. TinyPhoto rotates through five user-selectable images using a total of 4,900 bytes (yes, bytes!) stored in the on-chip flash RAM. The setup produces crisp photos on the OLED display with a real-time display rate that is instantaneous to the human eye with the Tiny85 boosted to run at 8MHz. A custom device driver (200 bytes) sets up the OLED screen and enables pixel-by-pixel display. Custom Forth code converts a 0-1 color depth image into a byte-stream that can be written to the onboard flash for rapid display. It is a reminder of what can be accomplished with low-fat computing…
The magic, of course, is in the software. This article describes how this was done, and the software that enables it. Checkout the TinyPhoto review on Hackaday!
 Tiny Photo – 3cm x 7cm photo viewer powered by ATTiny85 8-bit microcontroller sending pixel level image data to OLED display (128×64 pixels), powered by 3V coin cell battery. Cycles through 5 images stored in 5kB of on-chip Flash RAM. (Note, this is 1 million times less memory than on a Windows PC with 8GB RAM). The magic is in the software. Continue reading this article…
This article explains how to use the Arduino toolchain to program microcontrollers from the Arduino IDE using their bootloaders, and also burning bootloaders directly onto bare microcontroller chips. It covers developing interactively with Forth (rapid prototyping), and moving your creations from a development board (Nano, Uno) to a standalone, low-cost, low-power, small footprint chip such as the ATMega328P or ATTiny85 or ATTiny84. Each of these microcontrollers is powerful, inexpensive, and allows using 3V batteries directly without the need to boost voltage to 5V. Additionally, we describe how to build an inexpensive (under £5), standalone 3-chip Atmel AVR universal bootloading programmer that you can use to program all of the chips above.
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Voice controlled hardware requires four capabilities: (1) vocal response to trigger events (sensors/calculations-to-brain), (2) speech generation (brain-to-mouth), (3) speech recognition (ear-to-brain), and (4) speech understanding (brain-to-database, aka learning). These capabilities can increasingly be implemented using off-the-shelf modules, due to progress in advanced low-cost silicon capable of digital signal processing (DSP) and statistical learning/machine learning/AI.
In this article we look at the value chain involved in building voice control into hardware. We cover highlights in the history of artificial speech. And we show how to convert an ordinary sensor into a talking sensor for less than £5. We demonstrate this by building a Talking Passive Infra-Red (PIR) motion sensor deployed as part of an April Fool’s Day prank (jump to the design video and demonstration video).
The same design pattern can be used to create any talking sensor, with applications abounding around home, school, work, shop, factory, industrial site, mass-transit, public space, or interactive art/engineering/museum display.
 Bringing Junk Model Robots to life with Talking Motion Sensors (April Fools Prank, 2021) Continue reading this article…
By Assad Ebrahim, on April 12th, 2021 (1,427 views) | Enter your password to view comments.
Topic: Building Technology, Education, Electronics, Personal File, Technology
Abstract This brief note explores the use of fuzzy classifiers, with membership functions chosen using a statistical heuristic (quantile statistics), to monitor time-series metrics. The time series can arise from environmental measurements, industrial process control data, or sensor system outputs. We demonstrate implementation using the R language on an example dataset (ozone levels in New York City). Click here to skip straight to the coded solution), or read on for the discussion.
 Fuzzy classification into 5 classes using p10 and p90 levels to achieve an 80-20 rule in the outermost classes and graded class membership in the inner three classes. Comparison with crisp classifier using the same 80-20 rule is shown in the bottom panel of the figure. Continue reading this article…
This article looks at Propositional Logic, also called Statement Calculus, from a combinatorial and algebraic point of view (Sections 3-6), its implementation in software (Section 7), and its application to digital electronics (Section 10). Historical sections cover the shift in viewpoint from classical logic based on Aristotle’s syllogism to modern symbolic logic (Section 2) and the axiomatization of logic (Section 9). (See logic sourcebook for the original source papers (1830-1881) that drove this shift.)
In Section 7, we implement the grammar of the statement calculus in the Symbolic Logic Simulator (SLS), a program written in 28 lines of Forth code, that allows computer-aided verification of any theorem in Propositional Logic (see Appendix 1 for source code). The program makes it straight-forward to explore non-obvious logical identities, and verify any propositional logic theorem or conjecture, in particular see Appendix 2 for key identities in the statement calculus (duality, algebraic, and canonical identities).
The concept of linguistic adequacy is developed in Section 8 and the NAND Adequacy Theorem is proved showing that NAND can generate all logical operations. A corollary is that any digital logic circuit can be built up entirely using NAND gates, illustrated using the free Digital Works software.
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In this article we look at the ideas of George Peacock whose 700-page opus A Treatise on Algebra (1830) transformed classical algebra into its modern form as an abstract symbolic science, free from the physical interpretation of quantity that had previously restricted it.
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By Assad Ebrahim, on March 18th, 2020 (11,723 views) |
Topic: Maths--General Interest
Revised Nov 2022, Jan 2023
In this article we look at the evolution of logic from its earliest form in the demonstration of truths to the rapid development of mathematical logic in the 1800s at the start of the “golden century” of logic (1850-1950). We also look at the rise and surprising dashing of hopes for the formalist program.
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By Assad Ebrahim, on February 18th, 2020 (3,819 views) |
Topic: Maths--History
This is Part 3 in the Ancient Mathematics series. (To read earlier parts: Part 1: Prehistoric Origins of Mathematics, Part 2: The Mathematics of Uruk and Susa).
This article explores what the people of Mesopotamia wrote about, counted and produced in the last part of the fourth millenium BCE. It does so by examining the frequency of signs in the proto-cuneiform tablets from the period c.3500-3000 BCE. For those wishing to build up experiential understanding of life in the Neolithic and early Bronze Age near east, this article provides suitable references as well as practical explorations of the economic and productive activities of the people: rope-making from grass, basket-weaving from reads, baking, weaving of cloth from linen, breaking ground, sowing, reaping, making flour, etc.
The first part of the article look closely at the collection of artifacts in each period that are associated with the evolution of writing and mathematics in ancient Mesopotamia, examining noteworthy individual artifacts that showcase a key development.
The study uses the CDLI database of cuneiform documents, and software I’ve written that parse the files in the CDLI database, extracting counts, parsing signs, generating frequency distributions of signs, creating a proto-cuneiform glossary, and assisting in the quantitative analysis of artifacts and semi-automated translation (see CDLI parser software library written in Ruby).
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