math-phys-modern-world-march15-2011

Mathematics & Physics in the Real WorldDavid Quesada, Ph.D.

School of Science, Technology and EngineeringManagement, St. Thomas University.

Graduated from Moscow State University, M.V. Lomonosov, Russia 1990 M.S. in Physics and Mathematics – Suma Cum Laude – School of Physics

Graduated from Universidad de La Habana, Cuba 2000, Ph.D. in Physics, Best young scholar research of the year 2000 – School of Physics

CINVESTAV, Mexico DF

Dr. Rafael Baquero

Dr. Carlos Trallero-Giner

Some common misconceptions about Mathematics

1. Learning mathematics requires special and rare abilities. 2. Math in modern issues is too complex.3. Math makes you less sensitive, and is irrelevant to my life4. Math makes no allowance for creativity.5. Math provides exact answers.

What is Mathematics after all?The word mathematics is derived from the Greek word Mathematikos, which means “inclined to learn”. Thus, literally speaking, to be mathematical is to be curious, open-minded, and interested in always learning more !! Do you consider yourself to be either “ math phobic” (fear of mathematics) of “ math loathing” (dislike math )? Many adults harbor fear or loathing of mathematics and, unfortunately, these attitudes are often reinforced by classes that present mathematics as an obscure and sterile subject .

Mathematics also may be viewed as a tool forcreating models, or representations that allowus to study real phenomena

Applied Mathematics

Medicine and Physiology

Psychology and Sociology

Bioinformatics

Engineering

Biology and Ecology

Computer science andArtificial Intelligence

Physics and Chemistry

Economics Business Management

Atmospheric Physics or Meteorology

Actuarial Mathematics – Risk & Insurance

Strategic Management and Politics

Financial Analyst

What is Quantitative Literacy?Literacy is the ability to read and write, and it comes in varying degrees. Some people can recognize only a few words and write only their names; others read and write in many languages. Today, the abilities to interpret and reason with quantitative information - information that involves mathematical ideas or numbers – are crucial aspects of this literacy. This so called quantitative literacy is essential to understanding modern issues that appear in the news everyday. The process of interpreting and reasoning with quantitative information is called quantitative reasoning.

Level Language Skill Math Skill

1Recognizes 2500 two or three syllable words. Reads at a rate of 95-120 words per minute. Writes and speaks simple sentences.

Adds and subtracts two digit numbers. Does simple calculations with money, volume, length, and weight.

2Recognizes 5000-6000 words. Reads 190-125 words per minute. Read adventure stories and comic books, as well as instructions for assembling model cars. Writes compound and complex sentences.

Adds, subtracts, multiplies, and divides all units of measure. Compute ratio, rate, and percentage. Draws and interpret bar graphs.

3Read novels and magazines, as well as safety rules and equipment instructions. Writes reports with proper format and punctuation. Speak well before an audience.

Understand basic geometry and algebra. Calculates discount, interest, profit and loss, markup, and commissions.

4Reads novels, poems,newspapers, and manual. Prepares business letters, summaries, and reports. Participates in panel discussions and debates. Speaks extemporaneously on a variety of subjects.

Deals with complex algebra and geometry, including linear and quadratic equations, logarithmic functions, and axiomatic geometry.

5Reads literature, book and play reviews, scientific and technical journals, financial reports, and legal documents. Can write editorials, speeches, and critiques.

Knows calculus and statistics, able to deal with econometrics.

6 Same types of skills as level 5, but more advanced.Work with advanced calculus, modern algebra, and statistics.

Adapted from Education: The knowledge gap, supplement to The Wall Street Journal, February 9,1990

Occupation Language Level

Math Level Occupation Language Level

Math Level

Biochemist 6 6 Corporate executive 4 5

Computer Engineer 6 6 Computer sales agent 4 4

Mathematician 6 6 Management trainee 4 4

Cardiologist 6 5 Insurance sales agent 3 4

Social psychologist 6 5 Retail store manager 3 4

Lawyer 6 4 Cement mason 3 3

Tax Attorney 6 4 Dairy farm manager 3 3

Newspaper editor 6 4 Poultry farmer 3 3

Accountant 5 5 Tile setter 3 3

Personnel manager 5 5 Travel agent 3 3

Corporate president 5 5 Telephone operator 3 2

Weather forecaster 5 5 Janitor 3 2

Secondary teacher 5 5 Short-order cook 3 2

Elementary teacher 5 4 Assembly-line worker 2 2

Disc jockey 5 3 Toll collector 2 2

Financial analyst 4 5 Laundry worker 1 1

Adapted from Education: The knowledge gap, supplement to The Wall Street Journal, February 9,1990

http://casa.colorado.edu/~ajsh/wormbig_gif.html

Rocketry’s Club: The path from School to NASA

http://www.facebook.com/photo.php?pid=1604323&id=780758864


http://www.facebook.com/photo.php?pid=1862772&id=647571452&op=25&view=global&subj=780758864


Most of the Hurricanes follow a parabolic path that can be a motivation for Algebra

Project 1.3: Hurricane’s Science

Feature Range (English)

Accuracy (English)

Range(Metric)

Accuracy(Metric)

Temperature -55F – 150F +/- 1F -45C – 60C +/- 0.5C

Relative Humidity 0 – 100% +/- 2% 0 – 100% +/- 2%

Wind Speed 0 – 125 mph +/- 2 mph 0 – 275 kph +/- 4 kph

Wind Direction 0 – 360 deg +/- 3 deg 0 – 360 deg +/- 3 deg

Barometric Pressure 28 – 32” Hg +/- 0.05”Hg 900 – 1100 mbar +/- 5 mbar

Rainfall Unlimited +/- 2% Unlimited +/- 2%

Light Intensity 0 – 100% N/A 0 – 100% N/A

Auxiliary Temperature -55F – 150F +/- 2F -45C – 60C +/- 1C

The WeatherBug Network is the largest weather network in the world. More than 8000 schools across the U.S. operate WeatherBug Tracking Stations, including Saint Thomas University, to integrate live, local weather data and technology into classroom learning. This is accomplished through WeatherBug Achieve, an online teaching tool that automatically embeds live weather readings and images from any source on the WeatherBug Network into lessons.

Data collected by the weather tracking station in campus. It is interesting to notice; how many parameters may be correlated at once by looking at these graphics.

Hail storm took place on May 26, 2005 in the area of Miami Gardens and Opa-Locka. Hails of size an inch and a half were collected that day.

Visits to the National Hurricane Center




Slopes, Trigonometric Functions, Average Values, and Global Warming

It is worth to notice the periodicity (24 hrs) of these peaks; however itis clear the irregular shape of all these peaks too – Why?

Range of variation

Cloudiness and Random Fluctuations in the weather are responsible for these irregularities

Ongoing research project # 1.1: Climate and Weather Variability

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Periodic Patterns in Nature and its Graphical Representation

DCBxAy )sin(

Daily variations – Days and Nights Period = T = 24 hr

Daily, monthly, and yearly variations - three periods T1= 24 hr, T2= 90 days, T3= 365 days

Time Series Analysis

Maximum

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More complicated behaviors are indicators of hidden dynamical processes to be studied

wavelength

speedswaveTPeriod

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Ongoing research project # 1: Climate and Weather Variability

How far weather variability influences seasonal asthma episodes: Three years of correlations in Miami Dade, Florida

David QuesadaSchool of Science, Technology and Engineering Management,

St. Thomas University, Miami Gardens FL 33054

Climatic and environmental changes occurring since the middle of the Twentieth Century as well as the aggravating pollution levels in megacities are exacerbating asthma episodes and the number of hospitalizations due to this disease. Since 1999, in Miami Dade County the hospitalization rates were doubling the Healthy People 2010 objectives in every age group. A comprehensive weather database including outdoor temperature (T), humidity (H), barometric pressure (P), wind direction (θw) and speed (vw) as well as the values of maximum and minimum and the range of all these variables has been created. As a result, a seasonal pattern emerged, with a maximum appearing around the middle of December and a minimum around the middle of March every year for the three years of analysis.

Florida Academy of Sciences, 75th Anniversary Meeting, FIT - Melbourne FL March 2011

Asthma Statistics Worldwide

Number of people diagnosed: more than 150 MEurope: the # of cases has doubledUSA: the number of cases has increased more than 60%India: between 15 and 20 MAfrica: between 11 and 18% populationNumber of deaths yearly: around 180,000

Miami Dade County , Florida

7.1% Middle and HS children were reported with asthmaThe number of hospitalizations due to asthma has doubled.The number 1 cause of school absences and 35 % of parents missed work

Why to study Asthma? How far Bio-Meteorology may help with?


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• Asthma seasonal variations confirmed• Larger seasonal variation associated with a decrease in age.

Seasonal Variations in Asthma Hospital Admissions in the United States

Aichatou Hassane, UNH; Robert Woodward, PhD, UNH; Ross Gittell, PhD, UNH - May 27, 2004


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Areas of major incidence


Zip codes patients came from

WeatherBug Mesonet stations

NWS stations, MIA & Tamiami

Year Total Patients

Total Respiratory

Total Asthma % of asthma

2008 5172 2950 2222 43

2009 6981 4301 2680 38

2010 7813 4960 2853 37

Year White White Hispanic

Non White Hispanic

African American

2008 490 505 820 510

2009 350 256 650 525

2010 528 495 605 657

Seasonal Variations of Asthma diagnosed cases by the Kendall Medical Group in Miami Dade, FL

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Seasonal Variations of Asthma diagnosed cases in standard units Z = (N – Nave)/S

by the Kendall Medical Group in Miami Dade, FL

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Correlations between the number of cases and the given set of variables (IBM-SPSS-19)

Tmax Tmin ΔT Tmean dT/dt ΔT/Tmean

Pearson (r) - 0.524 - 0.529 0.357 - 0.531 - 0.122 0.487

P - value 0.000 0.000 0.002 0.000 0.306 0.000

Kendall - τ - 0.325 - 0.301 0.159 - 0.311 - 0.122 0.264

P - value 0.000 0.000 0.048 0.000 0.132 0.002

Spearman - ρ - 0.485 - 0.463 0.224 - 0.475 - 0.148 0.375

P - value 0.000 0.000 0.059 0.000 0.215 0.001

ΔP Pmean dP/dt ΔP/Pmean ΔH Hmean dH/dt ΔH/Hmean

Pearson (r) 0.367 - 0.021 0.082 0.42 0.452 - 0.213 - 0.015 0.445

P - value 0.002 0.862 0.491 0.000 0.000 0.073 0.899 0.000

Kendall - τ 0.269 0.008 0.045 0.291 0.282 - 0.052 0.006 0.264

P - value 0.001 0.922 0.579 0.000 0.000 0.521 0.938 0.001

Spearman - ρ 0.388 0.001 0.063 0.415 0.402 -0.091 0.003 0.373

P - value 0.001 0.996 0.600 0.000 0.000 0.445 0.979 0.001



Factors affecting respiratory gas exchange

Concentration Gradient == CGTemperature == TSurface Area == SMolecular size == MSDistance == dDiffusion Rate == DD = [CG x T x S] / [MS x d]Ventilation – Perfusion ratio == V/QV/Q < 1 hypoventilation

Systems Theory and System Biology MacroscopicDynamics ofbreathing

MesoscopicImmune cells populationdynamics

MicroscopicGenes

Cooperative effect – Emergent properties

• Mathematical modeling of the episode of Asthma by using dynamical system theory

Macroscopic Mechanical Description of Breathing

Mathematical expressions appealing to basic laws of aerodynamics describe the basics of breathing and disorders within the lung functioning.

Bronchial Hyper-responsiveness: Excessive constriction of smooth muscle that surrounds bronchi and bronchioles, resulting in narrowed airway passage and airflow limitation.

Atopy: A genetically determined state of hypersensitivity to environmental allergens that is detected by increased serum immunoglobulin E and/or positive dermal allergen tests

Mesoscopic immune description of an asthma episodeA system of differential equations describes the population dynamics of each one of the cells involved in an asthma episode.

A very complicated Network of cells (IL4, IL3, IL5, IL13- Cytokines, IgE – Immunoglobuline) Interacting and Competing.

In asthmatic individuals, antigen presentation is thought to results in the polarization of T-cells towards a Th2 patterns whereas T cells from non atopic, non-asthmatic individuals show the opposing Th1 (interferon-γ and IL2) pattern of cytokine secretion

Microscopic genetic analysis of asthma incidence Bio-informatics of Asthma

The multigenic nature of asthma has greatly hampered efforts to identify the specific genes involved. Genetic heterogeneity across populations, variability in disease expression, phenocopies and uncontrolled environmental influences confound the analysis of asthma and other complex genetic disorders.

90th Annual Meeting of AMS, Atlanta 2010





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