Events
Department of Mathematics and Statistics
Texas Tech University
Configuration space integrals and graph complexes have been used to study a number of problems in topology. We will discuss the application to cohomology of spaces of embeddings, which directly generalizes their application to Vassiliev knot invariants. In joint work with Komendarczyk and Volić, we showed that such integrals describe the whole cohomology of spaces of 1-dimensional pure braids in any Euclidean space of dimension at least 4. We related them to Chen’s iterated integrals and showed that the inclusion of 1-dimensional pure braids into 1-dimensional long links induces a surjection in cohomology. This motivated further work of ours on the relationship between higher-dimensional pure braids and string links. In work in progress, I have been using these integrals to relate classes of long links to classes of long knots in various dimensions.Trolls use fake personas and distribute disinformation through multiple social media streams. Given the increased frequency of this social media misuse, understanding those operations is paramount in combating their influence. Building on existing scholarship on the inner functions within those influence networks on social media, we suggest a new approach to map those types of operations. Using Twitter content identified as part of the Russian influence network, we created a predictive model to map the network operations. We classify accounts type based on their authenticity function for a sub-sample of accounts and trained AI to identify similar behavior patterns across the network. Our model attains 88% prediction accuracy for the test set. Validation is done by comparing the similarities with a couple of publicly available troll datasets. The prediction and validation results suggest that our proposed model adequately understands the complexity of the network from different perspectives. On the other hand, visualization of activities allows us to understand the structure of the Russian troll network. The geometry of the network shows that there are noticeable isolations and activity trends regardless of the classification.
Please virtually attend this week's Statistics seminar at 3:00 PM Wednesday the 13th via this zoom link
Meeting ID: 942 0486 6435
Passcode: 909439
The regulation and interpretation of transcription factor levels is critical in spatiotemporal regulation of gene expression in development biology. However, concentration-dependent transcriptional regulation, and the spatial regulation of transcription factor levels are poorly studied in plants. WUSCHEL, a stem cell-promoting homeodomain transcription factor was found to activate and repress transcription at lower and higher levels respectively. The differential accumulation of WUSCHEL in adjacent cells is critical for spatial regulation on the level of CLAVATA3, a negative regulator of WUSCHEL transcription, to establish the overall gradient. However, the roles of extrinsic spatial cues in maintaining differential accumulation of WUSCHEL are not well understood. We have developed a 3D cell-based computational model which integrates sub-cellular partition with cellular concentration across the spatial domain to analyze the regulation of WUS. By using this model, we investigate the machinery of the maintenance of WUS gradient within the tissue. We also developed a stochastic model to study the binding and unbinding of WUS to cis-elements regulating CLV3 expression to understand the concentration dependent manner mechanistically. The robustness mechanism and the concentration-dependent machinery discovered by the modeling analysis can be general principles for stem cell homeostasis in different biological systems.
Please virtually attend the Applied Math seminar via this Zoom link Wednesday the 20th at 4 PM -- meeting ID: 937 2431 1192
It is well-known in number theory that some of the deepest results
come in connecting complex analysis in the form of $L$-functions with
algebra/geometry in the form of Galois representations/motives. In
this talk we will consider this for a particular case. Let $f$ be a
newform of weight $k$ and full level. Associated to $f$ one has the
adjoint Galois representation and the symmetric square $L$-function.
The Bloch-Kato conjecture predicts a precise relationship between
special values of the symmetric square $L$-function of $f$ with size
of the Selmer groups of twists of the adjoint Galois representation.
We will outline a result providing evidence for this conjecture by
lifting $f$ to a Klingen Eisenstein series and producing a congruence
between the Klingen Eisenstein series and a Siegel cusp form with
irreducible Galois representation. This is joint work with Kris
Klosin.
One criticism of the classical Black-Scholes-Merton option pricing formulation
is its use of a Gaussian price process for the asset underlying the option.
As a result, various observed (“stylized”) facts of financial price processes
remain uncaptured by the BSM model.
These behaviors, which are observed in the return process
(fractional change in price over time) and in the distribution of those returns over time,
include volatility clustering, skewness and heavy tails.
Going beyond a Gaussian model presents challenges,
for example existing formalisms for option pricing cannot accommodate distributions
with power-law tails such as Student’s t.
In this talk I discuss the use of double subordinated Levy processes within
established option pricing formalisms.
In particular, inverse Gauss processes
(https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution)
are used to capture five stylized behaviors: the mean, volatility,
skewness and kurtosis of the distribution of asset returns,
as well as to capture the fact that information driving asset prices arrives at discrete,
random intervals.
This work will be presented in the context of European call and put options
whose underlying asset is a portfolio.
The specific portfolio consists of holdings in real estate investment trusts (REITs).
A by-product of the use of subordinated methods is the natural definition of a
new measure for the volatility of asset returns.We will discuss how to define the AKSZ theory as a fully extended functorial field theory using the geometric cobordism hypothesis.The Generalized Hyperbolic (GH) distribution is a multivariate heavy tailed distribution that has been widely used in finance.
In this presentation we review its properties and show that some popular techniques based on Gaussian
distribution (i) shrinkage estimator, (ii) online parameter updating, (iii) portfolio optimization via quadratic programming,
and (iv) measuring portfolio diversification can be extended to the GH distribution as well.