The Dangers of Mathematical Modeling

2002 ◽  
Vol 95 (2) ◽  
pp. 140-145
Author(s):  
Angela D. A. Köhler
Keyword(s):  
Mathematical Modeling ◽  
Mathematics Teachers ◽  
Real World ◽  
Real Life ◽  
Mathematical Language ◽  
Mathematical Skills ◽  
School Year ◽  
Or Economics ◽  
The Given

When setting long-term goals, mathematics teachers face a constant dilemma. Most of us realize that our students will need to be mathematically literate in their future jobs, be able to see the real world through mathematical eyes, and be ready to handle the huge quantities of numbers that will be presented to them in their company's reports and in the news. During most of the school year, however, we give our students problems that are already written in mathematical language. Even the socalled real-life applications often consist of just an equation from physics, medicine, or economics that students are expected to analyze algebraically or graphically. They do not learn how the equation was originally derived, and they can often solve such problems without giving any thought to the application. To truly connect their mathematical skills with the outside world, we need to confront them with problems that have not yet been translated into the language of mathematics. We should just say “Now what?” and give them the necessary time to try out several mathematical models for the given situation.

scholarly journals Computer simulation and mathematical modeling: a scientific review

2018 ◽  
Vol 6 (1) ◽  
Author(s):  
Rakesh Kumar Singh
Keyword(s):  
Mathematical Modeling ◽  
Computer Simulation ◽  
Dynamic Behaviour ◽  
Review Paper ◽  
Physical Phenomenon ◽  
Real Life ◽  
Process Models ◽  
Decision Making Process ◽  
Scientific Review

Computer simulation is used to study the dynamic behaviour of objects or systems in response to conditions that cannot be easily or safely applied in real life. Computer simulation in simple terms is a substitute for physical experimentation, in which computers are used to compute the results of some physical phenomenon by using mathematical description or mathematical models of a real system in the form of a computer program. Computer simulation and Mathematical modeling is often an integral part of the decision-making process. Models and simulations allow rapid and varied evaluation of causes and effects and the principal advantage is that they enable an analysis of even long-term actions with limited investment costs. This review paper is focused on major concepts, elements and practical areas of computer simulation and mathematical modeling.

scholarly journals Real-world comparison of the last generation balloon-expandable and self-expanding valves in patients undergoing TAVI

2021 ◽  
Vol 42 (Supplement_1) ◽  
Author(s):  
K Kalogeras ◽  
M Zuhair ◽  
T Kabir ◽  
R Jabbour ◽  
M Dalby ◽  
...  
Keyword(s):  
Real World ◽  
Real Life ◽  
Vascular Complications ◽  
The Self ◽  
Lv Function ◽  
Short Term ◽  
Term Outcome ◽  
Funding Sources ◽  
Transcatheter Aortic Valve

Abstract Background/Introduction The balloon expandable (BE) Edwards Sapien-S3/Ultra, and the self-expanding (SE) Medtronic Evolut-Pro represent the main volume of transcatheter aortic valve implantation (TAVI) procedures conducted worldwide. Purpose The present study represents the largest real-world comparison of periprocedural and short-term outcome between the aforementioned last generation devices. Methods Consecutive patients who had undergone TAVI with either the BE (S3/Ultra) or SE (Evolut-Pro/R-34mm if 34mm valve was required) device, in five centers were retrospectively studied. Periprocedural and short-term outcomes were recorded and compared. Results In total, 1341 patients (58.5% male) were treated with contemporary BE and SE valves (574 and 767pts with BE and SE respectively) and followed up for a median of 18.7 (IQR 30) months. Baseline demographics were similar between the two groups apart from severe left ventricle (LV) systolic impairment and extensive aorta calcification, being more prevalent amongst BE and SE groups respectively. Patients treated with the Evolut-Pro/R34mm device had significantly lower peak (16±9mmHg for SE vs 23.9±6mmHg for the BE valves, p=0.001) and mean (8.6±6mmHg SE vs 11.2±5.2mmHg BE, p=0.001) gradients at discharge. Conversely, the BE group demonstrated significantly lower rates of at least moderate residual aortic regurgitation (AR) post-operatively (0.7% vs 5.2% for BE and SE valves respectively, p<0.001). Interestingly, the rate of new permanent pacemaker (PPM) required after the implantation in initially pacemaker-free patients, was higher for the S3/Ultra cohort compared to the self-expanding valve group (14.4% vs 12.3% respectively, p=0.001). No statistical difference was recorded between valve groups regarding cerebrovascular events (3.4% vs. 2.7% for SE and BE respectively, p=0.466), major vascular complications (4.2% vs. 3.0% for SE and BE respectively, p=0.251) and death to hospital discharge (1.6% vs. 2.9% for SE and BE respectively, p=0.117). One-year Kaplan-Meier estimated survival was similar between the two groups (88.7% for BE vs. 91.4% for SE valves, plog-rank=0.093). When adjusting for age, extensive calcification of the aorta and baseline LV function all caused mortality hazard ratios were similar between patients treated with BE vs SE valves (HR 1.39; 95% CI 0.97 to 1.98, p=0.07). Conclusions Real life comparison of the last generation balloon expandable and self-expanding devices demonstrates superiority of the former in terms of residual PVL, at the expense of higher transvalvular gradients and higher need of new PPM implantation. The latter however may represent differences in center practices with regards to thresholds for permanent pacing. Long-term follow-up and future larger trials are required to establish any potential long-term difference in clinical outcomes and prognosis. FUNDunding Acknowledgement Type of funding sources: None.

scholarly journals P504 Effectiveness and safety of ustekinumab maintenance therapy in 103 patients with real-world ulcerative colitis: A GETAID multicentre cohort study

2021 ◽  
Vol 15 (Supplement_1) ◽  
pp. S486-S487
Author(s):  
M Fumery ◽  
J Filippi ◽  
V Abitbol ◽  
A Biron ◽  
D Laharie ◽  
...  
Keyword(s):  
Ulcerative Colitis ◽  
Cohort Study ◽  
Adverse Events ◽  
Real World ◽  
Clinical Remission ◽  
Real Life ◽  
Phase Iii ◽  
Phase Iii Trials ◽  
One Year

Abstract Background Phase III trials have demonstrated the efficacy and safety of ustekinumab in moderate-to-severe ulcerative colitis (UC), but no real-life long-term data is currently available. Methods From January to September 2019, all consecutive patients with active UC treated with ustekinumab in a GETAID centre were included. Patients were evaluated at week 52. Remission was defined by a partial Mayo Clinic score ≤ 2. The aim of the present study was to assess long-term effectiveness and safety of ustekinumab in UC. Results 103 UC patients (62 men; mean age: 41.2 ± 16.2 years; 52% pancolitis E3) were included in 21 centres. History of immunomodulator, anti-TNF and vedolizumab therapies was noted in 84.5%, 99.0% and 85.4% of the cases, respectively. At week 54, 44 (43%) patients discontinued ustekinumab, for lack of efficacy (n=41), pregnancy (n=1), persistence of eczematiform lesions (n=1) or personal decision (n=1). Cumulative probabilities of ustekinumab persistence were 96.1%, 81.6%, 71.7%, and 58.4% after 3, 6, 9, and 12 months, respectively. In multivariate analysis, a CRP>5 mg/L at week 0 (OR=2.91, CI95%[1.15–7.36]; p=0.02) and concomitant steroids at week 0 (OR=3.05, CI95%[1.30–7.14]; p=0.01) were significantly associated with ustekinumab discontinuation within one year. The overall rate of steroid-free clinical remission at week 52 was 32% of whom 71% had null rectal bleeding and stool frequency subscores. Ten patients (9.7%) underwent colectomy within a median of 6.7 [4.3–10.6] months. Adverse events were observed in 15 (16.9%) patients, of whom 4 (4.5%) had severe adverse events including three patients with exacerbation of UC leading to hospitalization, and a 62 years-old men who died from a myocardial infarction four months after ustekinumab initiation. Conclusion In this real-world cohort study that included patients with refractory ulcerative colitis to multiple therapies, more than one-half of patients were still treated by ustekinumab and one-third were in steroid-free clinical remission, after 52 weeks.

scholarly journals Alemtuzumab in a Large Real-Life Cohort: Interim Baseline Data of the TREAT-MS Study

2021 ◽  
Vol 12 ◽  
Author(s):  
Tjalf Ziemssen ◽  
Frank Hoffmann ◽  
Stephan Richter ◽  
Ulrich Engelmann ◽  
Robin White
Keyword(s):  
Multiple Sclerosis ◽  
Real World ◽  
Disease Duration ◽  
Real Life ◽  
Surface Glycoprotein ◽  
Cell Surface Glycoprotein ◽  
Long Term Study ◽  
Relapsing Remitting ◽  
Treatment Sequences

The non-interventional long-Term study foR obsErvAtion of Treatment with alemtuzumab in active relapsing–remitting MS (TREAT-MS) study collects the so far largest real-life cohort regarding utilization, long-term effectiveness, and safety of alemtuzumab, a humanized monoclonal antibody directed against the cell surface glycoprotein CD52, in adult patients with active relapsing–remitting multiple sclerosis (RRMS). An interim analysis of baseline parameters at inclusion of a non-interventional real-world study about alemtuzumab in Germany including previous multiple sclerosis (MS) medication utilization, MS activity, severity, and duration, as well as comorbidities was performed. Of the 883 patients, 71.6% were women. Mean age was 35.7 ± 9.2 years, time since first MS symptoms (=disease duration) is 8.0 ± 6.8 years, and Expanded Disability Status Scale (EDSS) is 2.7 ± 1.8 points (range, 0.0–7.5 points). The number of relapses in the 12 and 24 months prior to inclusion were 1.6 ± 1.2 and 2.2 ± 1.8, respectively. Of the patients, 14.4% were treatment naive, while for the majority, a wide spectrum of MS disease-modifying treatments (DMTs) and treatment sequences were documented. Overall, interferon beta (IFN-beta) was reported most frequently (52.4%), followed by fingolimod (35.2%), natalizumab (34.9%), and glatiramer acetate (28.9%). Patients with longer disease duration and higher EDSS had a higher number of previous DMTs. Compared to the pivotal phase 2/3 studies, RRMS patients starting alemtuzumab treatment had a longer disease duration in real-world conditions. There was variety of different treatment sequences before the final switch to alemtuzumab. In the future, linking these treatment sequences or other baseline characteristics with effectiveness and safety outcomes might be useful to support treatment decisions. Registered at Paul-Ehrlich-Institut under NIS 281.

Parabolic Sound Reflectors–History and Modeling

2019 ◽  
Vol 112 (5) ◽  
pp. 330-337
Author(s):  
Elaine M. Purvinis ◽  
Joshua B. Fagan
Keyword(s):  
Mathematical Modeling ◽  
Mathematics Teachers ◽  
Real Life ◽  
Conceptual Basis ◽  
Time Intervals ◽  
Mathematical Concepts ◽  
Quadratic Equations ◽  
Novel Approach ◽  
Life Challenges ◽  
Second Year

In first- and second-year algebra classrooms, the all-too-familiar whine of “when are we ever going to use this in real life?” challenges mathematics teachers to find new, engaging ways to present mathematical concepts. The introduction of quadratic equations is typically modeled by describing the motion of a moving object with respect to time, and typical lessons include uninspiring textbook practice problems that portray dropping or shooting objects from given distances or at particular time intervals. For a novel approach to exploring quadratics, we chose to step outside the classroom to look at some phenomena in the field of acoustics. Our activity incorporates mathematical modeling to provide a multirepresentational view of the math behind the physics and to provide a conceptual basis for analyzing and understanding a real-world quadratic situation.

Neuropsychology in the Real World

2014 ◽  
Vol 25 (4) ◽  
pp. 233-238 ◽  
Author(s):  
Martin Peper ◽  
Simone N. Loeffler
Keyword(s):  
Neuropsychological Assessment ◽  
Real World ◽  
Ecological Validity ◽  
Real Life ◽  
Emotional States ◽  
Context Sensitive ◽  
Traditional Assessment ◽  
Life Data ◽  
Real Life Data ◽  
Assessment And Treatment

Current ambulatory technologies are highly relevant for neuropsychological assessment and treatment as they provide a gateway to real life data. Ambulatory assessment of cognitive complaints, skills and emotional states in natural contexts provides information that has a greater ecological validity than traditional assessment approaches. This issue presents an overview of current technological and methodological innovations, opportunities, problems and limitations of these methods designed for the context-sensitive measurement of cognitive, emotional and behavioral function. The usefulness of selected ambulatory approaches is demonstrated and their relevance for an ecologically valid neuropsychology is highlighted.

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