Events
Department of Mathematics and Statistics
Texas Tech University
Synergy and antagonism have been extensively studied in the context of the statistical analysis of drug combinations given to treat a disease. "Synergy" ("antagonism", resp.) in a drug combination occurs when the desirable effect of two drugs given together for treating a disease is greater than (less than, resp.) the effect of each drug given separately.
We, however, study "synergy" and "antagonism" in log-linear models. We also give a thorough review and extend several epidemiological definitions of synergy and antagonism for categorical data, and we connect these definitions to the definitions of synergy and antagonism in log-linear models.
In particular, we discuss in great detail Worcester's (1971) synergistic multiplicative model. Worcester's (1971) model was used to model "synergy" between the binary factors "smoking" and "use of oral contraceptive" in affecting the response variable "presence or absence of thromboembolism". We also provide asymptotic standard errors for a measure of synergy provided by Worcester. These allow us to perform tests of hypotheses and construct confidence intervals for this measure of synergy.
In a series of articles, Japanese statistician E. Funo (2002 to 2007) studied and generalized the log-linear versions of Worcester's (1971) models to multiway tables. We review Funo's nonstandard log-linear models and suggest generalizations of Worcester's measure of synergy that are appropriate for multiway contingency tables.
Please attend this week's Statistics seminar at 4 PM (UT-6) Monday via this Zoom link.
Meeting ID: 912 5320 6454
Passcode: 385154
We construct the smooth higher group of symmetries of any higher geometric structure on manifolds. Via a universal property, this classifies equivariant structures on the geometry. We present a general construction of moduli stacks of solutions in higher-geometric field theories and provide a criterion for when two such moduli stacks are equivalent. We then apply this to the study of generalised Ricci solitons, or NSNS supergravity: this theory has two different formulations, originating in higher geometry and generalised geometry, respectively. These formulations produce inequivalent field configurations and inequivalent symmetries. We resolve this discrepancy by showing that their moduli stacks are equivalent. This is joint work with C. Shahbazi.Understanding the volatility of speculative assets is critical for investment decisions. Given that Bitcoin is considered, at least by some, a potential alternative to fiat money, its volatility characteristics are of particular concern. It is, therefore, essential to comprehend and appropriately model the process governing Bitcoin's volatility.
In this presentation, we offer two perspectives for analyzing Bitcoin's volatility. First, we introduce a doubly subordinated Levy process called the Normal Double Inverse Gaussian to model the time series properties of the cryptocurrency Bitcoin. We also developed an arbitrage-free option pricing model based on the NDIG process, providing a fresh perspective on Bitcoin valuation.
Within this model, we derive two distinct measures of Bitcoin volatility. The first measure combines NDIG option pricing with the Chicago Board Options Exchange VIX model to compute an implied volatility measure that reflects the viewpoints of options traders. The second measure investigates implied volatility in the real world, considering the perspectives of spot traders and utilizing an intrinsic time formulation.
Both volatility measures are compared to a historical standard deviation-based volatility. With appropriate linear scaling, the NDIG process perfectly captures the observed in-sample volatility.
Please attend this week's Mathematical Finance seminar at 2 PM (UT-6) Wednesday via this Zoom link.
Meeting ID: 922 3009 8938
Passcode: 561572
See more information on this seminar at the Mathematical Finance webpage
Abstract. Reductions in computational expense are often achieved through low-fidelity surrogates using data from fine-scale dynamical models. This reliance on summarized information presents challenges for predictive simulation, however, since summarization generally fails to commute with fundamental model properties such as conservation or involution which guarantee stability of the fine-scale system. This talk explores consequences of this idea and presents some recent methods for ensuring that structural properties such as conservation laws and dissipation inequalities are respected by data-driven surrogate models independent of their predictive accuracy.
When: 4:00 pm (Lubbock's local time is CST)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 968 6501 7586
* Passcode: Applied
Math Circle Fall Poster
A stochastic differential equation model is derived for the evolution of mountain elevations. The derivation is based on several assumptions about tectonic and erosion processes in mountain elevation dynamics. At any given time, the model yields a CIR-type probability distribution for mountain heights. As data are often available for mountains of greatest elevation in a mountainous region, the tail of the CIR distribution is studied and compared with mountain height data for the highest mountains in the region. The stochastic model indicates that the tail distribution is proportional to the product of a power of height and an exponential function of height. Specifically, for mountain height h, the model tail density is proportional to $h^{b-1} exp(-a h)$ where a and b are constants. The resulting inverse distribution function of the tail probability density leads to a function that relates rank in height to the corresponding mountain height. This function indicates how mountain heights in a region are related and provides, for example, a decreasing sequence of theoretical mountain heights in the region. The derived inverse distribution function is tested against mountain height data sets for several mountainous regions in the British Isles, Continental Europe, Northern Africa, and North America. The derived inverse cumulative distribution function provides an excellent fit to the mountain height data ranked by height.
abstract noon CST (UT-6)
The AWM Raiders is hosting a series of "Meet the Professors" meetings throughout November, 2023. The professors from our department share their specialized knowledge of their research for a maximum of 7-10 minutes. The discussions range from Mathematical Physics to Biomath. This virtual event provides an opportunity for current and prospective students to know more about the ongoing research in the department from the professors themselves. Additionally, these events may foster collaboration between professors and graduate students.
The Meet the Professors meeting series is sponsored by the Raiders Chapter of AWM graduate student group and may be attended virtually at
3 PM (UT-6) via this Zoom link.
Meeting ID: 953 5112 5986
Passcode: AWM
The AWM Raiders is hosting a series of "Meet the Professors" meetings throughout November, 2023. The professors from our department share their specialized knowledge of their research for a maximum of 7-10 minutes. The discussions range from Mathematical Physics to Biomath. This virtual event provides an opportunity for current and prospective students to know more about the ongoing research in the department from the professors themselves. Additionally, these events may foster collaboration between professors and graduate students.
Today's schedule pdf
The Meet the Professors meeting series is sponsored by the Raiders Chapter of AWM graduate student group and may be attended virtually at
3 PM (UT-6) via this Zoom link.
Meeting ID: 953 5112 5986
Passcode: AWM