Outputs from health biological systems display complex fluctuations that are not random but display robust and often self-similar (fractal) temporal correlations at different time scales— scaling behaviors. The scaling behaviors in the fluctuations of biological outputs such as neural activities, cardiac dynamics, motor activity are believed to be originated from feedbacks within the complex biological networks, reflecting the system adaptability to internal and external inputs. Supporting this concept, our studies have demonstrated a mechanistic link between the scaling regulation of physiological fluctuations and the circadian control system— a result of evolutionary adaptation to daily environmental light-dark cycles on the earth. In this talk, I will discuss certain evidence for this ‘scaling-circadian’ link and its related implications. Moreover, I will review some recent studies, in which we examined how the scaling patterns of human motor activity fluctuations change with aging and in Alzheimer’s disease. Our results showed that (1) alterations in scaling activity patterns occur before the clinical manifestation of Alzheimer’s disease (i.e., cognitive impairment) and predict cognitive decline and the risk for Alzheimer’s dementia; and (2) the progression of Alzheimer’s disease accelerates the aging effect on the scaling activity patterns. Our work provides strong evidence that altered scaling activity patterns may also be a risk factor for neurodegeneration, playing a role in the development and progression of Alzheimer’s disease.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

In this talk, we will discuss a complete classification of proper holomorphic maps from the unit ball in complex two dimensional space into the Cartan’s classical domain of type IV in complex three dimensional space that extend smoothly to some boundary point. This classification (which is a consequence of a classification of CR maps from the 3-sphere into the tube over the future light cone) consists of 4 algebraic maps. Among them, two previously known maps are isometric with respect to the canonical Bergman metrics and two other maps give counterexamples to a recent conjecture of Xiao-Yuan for the case of maps from the complex 2-ball. This is a joint work with Michael Reiter.

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Zoom link https://zoom.us/j/91925812463?pwd=bnRWQnhQKzRsV1Q3VnJiRjZFMFVxQT09 ID: 919 2581 2463PW: 958065

We introduce an odd coloring of a graph, which was introduced very recently, motivated by parity type colorings of graphs. A proper vertex coloring of graph $G$ is said to be odd if for each non-isolated vertex $x \in V (G)$ there exists a color $c$ such that $c$ is used an odd number of times in the neighborhood of $x$. The recent work on this topic will be presented, and the work is based on Eun-Kyung Cho, Ilkyoo Choi, and Hyemin Kown.

Metastasis and therapy resistance cause over 90% of cancer-related deaths. Despite extensive ongoing efforts, no unique genetic or mutational signature has emerged for metastasis. Instead, the ability of genetically identical cells to adapt reversibly by exhibiting multiple phenotypes (phenotypic/non-genetic heterogeneity) and switch among them (phenotypic plasticity) is proposed as a hallmark of metastasis. Also, drug resistance can emerge from such non-genetic adaptive cellular changes. However, the origins of such non-genetic heterogeneity in most cancers are poorly understood. I will present our findings on a) how non-genetic heterogeneity emerges in a population of cancer, and b) what design principles underlie regulatory networks enabling non-genetic heterogeneity across multiple cancers. Our results unravel how systems-levels approaches integrating mechanistic mathematical modeling with in vitro and in vivo data can identify causes and consequences of such non-genetic heterogeneity.

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This talk will be presented online. Zoom link: 997 8258 4700 (pw: 1234)

TBA

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

Tuberculosis (TB) is one of the world’s deadliest infectious diseases. Caused by the pathogen Mycobacterium tuberculosis (Mtb), the standard regimen for treating TB consists of treatment with multiple antibiotics for at least six months. There are a number of complicating factors that contribute to the need for this long treatment duration and increase the risk of treatment failure. The structure of granulomas, lesions forming in lungs in response to Mtb infection, create heterogeneous antibiotic distributions that limit antibiotic exposure to Mtb. We can use a systems biology approach pairing experimental data from non-human primates with computational modeling to represent and predict how factors impact antibiotic regimen efficacy and granuloma bacterial sterilization. We utilize an agent-based, computational model that simulates granuloma formation, function and treatment, called GranSim. A goal in improving antibiotic treatment for TB is to find regimens that can shorten the time it takes to sterilize granulomas while minimizing the amount of antibiotic required. We also created a whole host model, called HOSTSIM, to study Mtb dynamics within a human host. Overall, we use these models to help better understand TB treatment and strengthen our ability to predict regimens that can improve clinical treatment of TB.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

Extension problems through a small singular set appear throughout complex analysis. After a short reminder of some classical results we shall focus on problems of extending (pluri)subharmonic functions. In particular we shall focus on new techniques coming from PDEs that lead to resolutions of several questions in the field. The talk is partially based on joint works with Zywomir Dinew.

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https://us06web.zoom.us/j/82764115688?pwd=N2NzWjFDQ2FpQXJnRGdGNnFacnl2Zz09 ID: 827 6411 5688 PW: wrEH3p

In 1975, Szemerédi proved that for every real number $\delta > 0 $ and every positive integer $k$, there exists a positive integer $N$ such that every subset $A$ of the set $\{1, 2, \cdots, N \}$ with $|A| \geq \delta N$ contains an arithmetic progression of length $k$. There has been a plethora of research related to Szemerédi's theorem in many areas of mathematics. In 1990, Cameron and Erdős proposed a conjecture about counting the number of subsets of the set $\{1,2, \dots, N\}$ which do not contain an arithmetic progression of length $k$. In the talk, we study a natural higher dimensional version of this conjecture, and also introduce recent extremal problems related to Szemerédi's theorem.

A macroscopic theory for cellular states with steady-growth is presented, based on consistency between cellular growth and molecular replication, together with robustness of phenotypes against perturbations. Adaptive changes in high-dimensional phenotypes are shown to be restricted within a low-dimensional slow manifold, from which a macroscopic law for cellular states is derived, as is confirmed by adaptation experiments of bacteria under stress. The theory is extended to phenotypic evolution, leading to proportionality between phenotypic responses against genetic evolution and by environmental adaptation, which explains the evolutionary fluctuation-response relationship previously uncovered.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

We will discuss hormone circuits and their dynamics using new models that take into account timescales of weeks due to growth of the hormone glands. This explains some mysteries in diabetes and autoimmune disease.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

We investigate in depth the behaviour of Monge-Ampère volumes of quasi-psh functions on a given compact hermitian manifold. We prove that the property for these Monge-Ampère volumes to stay bounded away from zero or infinity is a bimeromorphic invariant. We show in particular that a conjecture of Demailly-Paun holds true if and only if such Monge-Ampère volumes stay bounded away from infinity. This is a joint work with Vincent Guedj.

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https://us06web.zoom.us/j/83876347559?pwd=SVZoUzZkUkMyZno0Vk1pS0pkTEdZQT09 ID: 838 7634 7559 PW: 8XahHQ

Suppose that $E$ is a subset of $\mathbb{F}_q^n$, so that each point is contained in $E$ with probability $\theta$, independently of all other points. Then, what is the probability that there is an $m$-dimensional affine subspace that contains at least $\ell$ points of $E$? What is the probability that $E$ intersects all $m$-dimensional affine subspaces? We give Erdős-Renyi threshold functions for these properties, in some cases sharp thresholds. Our results improve previous work of Chen and Greenhill. This is joint work with Jeong Han Kim, Thang Pham, and Semin Yoo.

I will give an introduction to topological data analysis (TDA), in which one uses ideas from algebraic topology to study the “shape” of data. I will focus on persistent homology (PH), which is the most common approach in TDA.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

From the venation patterns of leaves to spider webs, roads in cities, social networks, and the spread of COVID-19 infections and vaccinations, the structure of many systems is influenced significantly by space. In this talk, I will discuss the application of topological data analysis (specifically, persistent homology) to spatial systems. I will present a few examples, such as voting in presidential elections, city street networks, spatiotemporal dynamics of COVID-19 infections and vaccinations, and webs that were spun by spiders under the influence of various drugs.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains a copy of $F$ or its complement contains $H$. Burr in 1981 proved a pleasingly general result that for any graph $H$, provided $n$ is sufficiently large, a natural lower bound construction gives the correct Ramsey number involving cycles: $R(C_n,H)=(n-1)(\chi(H)-1)+\sigma(H)$, where $\sigma(H)$ is the minimum possible size of a colour class in a $\chi(H)$-colouring of $H$. Allen, Brightwell and Skokan conjectured that the same should be true already when $n\geq |H|\chi(H)$. We improve this 40-year-old result of Burr by giving quantitative bounds of the form $n\geq C|H|\log^4\chi(H)$, which is optimal up to the logarithmic factor. In particular, this proves a strengthening of the Allen-Brightwell-Skokan conjecture for all graphs $H$ with large chromatic number. This is joint work with John Haslegrave, Joseph Hyde and Hong Liu

It is known that the rank- and tree-width of the random graph G(n,p) undergo a phase transition at p=1/n; whilst for subcritical p, the rank- and tree-width are bounded above by a constant, for supercritical p, both parameters are linear in n. The known proofs of these results use as a black box an important theorem of Benjamini, Kozma, and Wormald on the expansion of supercritical random graphs. We give a new, short, and direct proof of these results, leading to more explicit bounds on these parameters, and also consider the rank- and tree-width of supercritical random graphs closer to the critical point, showing that this phase transition is smooth. This is joint work with Joshua Erde and Mihyun Kang.

This talk follows on from the recent talk of Pascal Gollin in this seminar series, but will aim to be accessible for newcomers. Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. By relaxing `packing’ to `half-integral packing’, Reed obtained an analogous result for odd cycles, and gave a structural characterisation of when the (integral) packing version fails. We prove some far-reaching generalisations of these theorems. First, we show that if the edges of a graph are labelled by finitely many abelian groups, then the cycles whose values avoid a fixed finite set for each abelian group satisfy the half-integral Erdős-Pósa property. Similarly to Reed, we give a structural characterisation for the failure of the integral Erdős-Pósa property in this setting. This allows us to deduce the full Erdős-Pósa property for many natural classes of cycles. We will look at applications of these results to graphs embedded on surfaces, and also discuss some possibilities and obstacles for extending these results. This is joint work with Kevin Hendrey, Ken-ichi Kawarabayashi, O-joung Kwon, Sang-il Oum, and Youngho Yoo.

Cells make fate decisions in response to dynamic environments and multicellular structure emerges from interplays among cells in space and time. The recent single-cell genomics technology provides an unprecedented opportunity to profile cells. However, those measurements are taken as snapshots for groups of individual cells with only static information. Can one infer interactions among cells from such datasets? Is it possible to recover spatial information from non-spatial datasets? How to obtain temporal relationships of cells from the static measurements? In this talk I will present our newly developed computational tools that reconstruct interactions and spatiotemporal relationships for cells using single-cell RNA-seq, ATAC-seq, and spatial transcriptomics datasets. Through applications of those methods to systems in development and regeneration, we show the discovery power of such methods and identify areas for further development in spatiotemporal reconstruction.

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This talk will be presented online. ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: 1234)

I present a version of the Moser-Trudinger inequality in the setting of complex geometry. As a very particular case, the result already gives a new Moser-Trudinger inequality for functions in the Sobolev space W1,2 of a domain in R2. As an application, we deduce a new necessary condition for the complex Monge-Ampere equation for a given measure on a compact Kahler manifold to admit a Holder continuous solution. This is a joint work with Tien-Cuong Dinh and George Marinescu.