A signed graph is a pair $(G,\Sigma)$ where $G$ is a graph and $\Sigma$ is a subset of edges of $G$. A cycle $C$ of $G$ is a subset of edges of $G$ such that every vertex of the subgraph of $G$ induced by $C$ has an even degree. We say that $C$ is even in $(G,\Sigma)$ if $|C \cap \Sigma|$ is even; otherwise, $C$ is odd. A matroid $M$ is an even-cycle matroid if there exists a signed graph $(G,\Sigma)$ such that circuits of $M$ precisely corresponds to inclusion-wise minimal non-empty even cycles of $(G,\Sigma)$. For even-cycle matroids, two fundamental questions arise: (1) what is the relationship between two signed graphs representing the same even-cycle matroids? (2) how many signed graphs can an even-cycle matroid have? For (a), we characterize two signed graphs $(G_1,\Sigma_1)$ and $(G_2,\Sigma_2)$ where $G_1$ and $G_2$ are $4$-connected that represent the same even-cycle matroids. For (b), we introduce pinch-graphic matroids, which can generate exponentially many representations even when the matroid is $3$-connected. An even-cycle matroid is a pinch-graphic matroid if there exists a signed graph with a pair of vertices such that every odd cycle intersects with at least one of them. We prove that there exists a constant $c$ such that if a matroid is even-cycle matroid that is not pinch-graphic, then the number of representations is bounded by $c$. This is joint work with Bertrand Guenin and Irene Pivotto.

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줌정보 https://zoom.us/j/8456734198?pwd=d094SExIRW5HeElWSEVnampjdWZyZz09 회의 ID: 845 673 4198 암호: math

The Weighted $\mathcal F$-Vertex Deletion for a class $\mathcal F$ of graphs asks, given a weighted graph $G$, for a minimum weight vertex set $S$ such that $G-S\in\mathcal F$. The case when $\mathcal F$ is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for Weighted $\mathcal F$-Vertex Deletion. Only three cases of minor-closed $\mathcal F$ are known to admit constant-factor approximations, namely Vertex Cover, Feedback Vertex Set and Diamond Hitting Set. We study the problem for the class $\mathcal F$ of $\theta_c$-minor-free graphs, under the equivalent setting of the Weighted c-Bond Cover, and present a constant-factor approximation algorithm using the primal-dual method. For this, we leverage a structure theorem implicit in [Joret et al., SIDMA’14] which states the following: any graph $G$ containing a $\theta_c$-minor-model either contains a large two-terminal protrusion, or contains a constant-size $\theta_c$-minor-model, or a collection of pairwise disjoint constant-sized connected sets that can be contracted simultaneously to yield a dense graph. In the first case, we tame the graph by replacing the protrusion with a special-purpose weighted gadget. For the second and third case, we provide a weighting scheme which guarantees a local approximation ratio. Besides making an important step in the quest of (dis)proving a constant-factor approximation for Weighted $\mathcal F$-Vertex Deletion, our result may be useful as a template for algorithms for other minor-closed families. This is joint work with Euiwoong Lee and Dimitrios M. Thilikos.

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YouTube Live at https://youtube.com/ibsdimag

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줌정보 https://zoom.us/j/8456734198?pwd=d094SExIRW5HeElWSEVnampjdWZyZz09 회의 ID: 845 673 4198 암호: math

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줌정보 https://zoom.us/j/8456734198?pwd=d094SExIRW5HeElWSEVnampjdWZyZz09 회의 ID: 845 673 4198 암호: math

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자세한 내용은 아래 링크를 참고해주세요. https://saarc.kaist.ac.kr/boards/view/seminars/49

We call an induced cycle of length at least four a hole. The parity of a hole is the parity of its length. Forbidding holes of certain types in a graph has deep structural implications. In 2006, Chudnovksy, Seymour, Robertson, and Thomas famously proved that a graph is perfect if and only if it does not contain an odd hole or a complement of an odd hole. In 2002, Conforti, Cornuéjols, Kapoor, and Vuškovíc provided a structural description of the class of even-hole-free graphs. I will describe the structure of all graphs that contain only holes of length $\ell$ for every $\ell \geq 7$ (joint work with Jake Horsfield, Myriam Preissmann, Paul Seymour, Ni Luh Dewi Sintiari, Cléophée Robin, Nicolas Trotignon, and Kristina Vuškovíc. Analysis of how holes interact with graph structure has yielded detection algorithms for holes of various lengths and parities. In 1991, Bienstock showed it is NP-Hard to test whether a graph G has an even (or odd) hole containing a specified vertex $v \in V(G)$. In 2002, Conforti, Cornuéjols, Kapoor, and Vuškovíc gave a polynomial-time algorithm to recognize even-hole-free graphs using their structure theorem. In 2003, Chudnovsky, Kawarabayashi, and Seymour provided a simpler and slightly faster algorithm to test whether a graph contains an even hole. In 2019, Chudnovsky, Scott, Seymour, and Spirkl provided a polynomial-time algorithm to test whether a graph contains an odd hole. Later that year, Chudnovsky, Scott, and Seymour strengthened this result by providing a polynomial-time algorithm to test whether a graph contains an odd hole of length at least $\ell$ for any fixed integer $\ell \geq 5$. I will present a polynomial-time algorithm (joint work with Paul Seymour) to test whether a graph contains an even hole of length at least $\ell$ for any fixed integer $\ell \geq 4$.

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YouTube Live at https://youtube.com/ibsdimag

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자세한 내용은 아래 링크를 참고해주세요. https://saarc.kaist.ac.kr/boards/view/seminars/49

We show that for pairs (Q,R) and (S,T) of disjoint subsets of vertices of a graph G, if G is sufficiently large, then there exists a vertex v in V(G)−(Q∪R∪S∪T) such that there are two ways to reduce G by a vertex-minor operation while preserving the connectivity between Q and R and the connectivity between S and T. Our theorem implies an analogous theorem of Chen and Whittle (2014) for matroids restricted to binary matroids. Joint work with Sang-il Oum.

(전체일정: 7/28, 7/29, 8/3, 8/5) In 2d first-passage percolation, we let (t_e) be a family of i.i.d. weights associated to the edges of the square lattice, and let T = T(x,y) be the induced weighted graph metric on Z^2. If we let p be the probability that a weight takes the value 0, then there is a transition in the large-scale behavior of T depending on the value of p. Specifically, when p < 1/2, T grows linearly, but when p > 1/2, T is stochastically bounded. In these lectures, I will describe some of the standard questions of FPP in the case p < 1/2, and then focus on the "critical" case, where p = 1/2. Regarding this case, I will show some of my work over the last few years including exact asymptotics for T, universality results, and recent work on a dynamical version of the model. The work I will present was done in collaboration with J. Hanson, D. Harper, W.-K. Lam, P. Tang, and X. Wang. Lec 4: Critical FPP: the general case

(전체일정: 7/26, 7/27, 8/2, 8/4) Lec 4: Information Percolation In this final lecture, we discuss the celebrated technique known as the information percolation introduced by Lubetzky and Sly. Then, we explain the application of this technique to Glauber dynamics of the Ising model on lattice, and of the Random cluster model. The last result is a joint work with Shirshendu Ganguly.

(전체일정: 7/28, 7/29, 8/3, 8/5) In 2d first-passage percolation, we let (t_e) be a family of i.i.d. weights associated to the edges of the square lattice, and let T = T(x,y) be the induced weighted graph metric on Z^2. If we let p be the probability that a weight takes the value 0, then there is a transition in the large-scale behavior of T depending on the value of p. Specifically, when p < 1/2, T grows linearly, but when p > 1/2, T is stochastically bounded. In these lectures, I will describe some of the standard questions of FPP in the case p < 1/2, and then focus on the "critical" case, where p = 1/2. Regarding this case, I will show some of my work over the last few years including exact asymptotics for T, universality results, and recent work on a dynamical version of the model. The work I will present was done in collaboration with J. Hanson, D. Harper, W.-K. Lam, P. Tang, and X. Wang. Lec 3: Critical FPP: the Bernoulli case

(전체일정: 7/26, 7/27, 8/2, 8/4) Lec 3: Cut-off phenomenon for mean-field spin systems In this third lecture, we explain the cut-off phenomenon for the Glauber dynamics of the mean-field Ising or Potts model and general strategy to prove it.

(전체일정: 7/28, 7/29, 8/3, 8/5) In 2d first-passage percolation, we let (t_e) be a family of i.i.d. weights associated to the edges of the square lattice, and let T = T(x,y) be the induced weighted graph metric on Z^2. If we let p be the probability that a weight takes the value 0, then there is a transition in the large-scale behavior of T depending on the value of p. Specifically, when p < 1/2, T grows linearly, but when p > 1/2, T is stochastically bounded. In these lectures, I will describe some of the standard questions of FPP in the case p < 1/2, and then focus on the "critical" case, where p = 1/2. Regarding this case, I will show some of my work over the last few years including exact asymptotics for T, universality results, and recent work on a dynamical version of the model. The work I will present was done in collaboration with J. Hanson, D. Harper, W.-K. Lam, P. Tang, and X. Wang. Lec 2: Phase transition and the shape theorem

Analyzing group behavior of systems of interacting variables is a ubiquitous problem in many fields including probability, combinatorics, and dynamical systems. This problem also naturally arises when one tries to learn essential features (dictionary atoms) from large and structured data such as networks. For instance, independently sampling some number of nodes in a sparse network hardly detects any edges between adjacent nodes. Instead, we may perform a random walk on the space of connected subgraphs, which will produce more meaningful but correlated samples. As classical results in probability were first developed for independent variables and then gradually generalized for dependent variables, many algorithms in machine learning first developed for independent data samples now need to be extended to correlated data samples. In this talk, we discuss some new results that accomplish this including some for online nonnegative matrix and tensor factorization for Markovian data. A unifying technique for handling dependence in data samples we develop is to condition on the distant past, rather than the recent history. As an application, we present a new approach for learning "basis subgraphs" from network data, that can be used for network denoising and edge inference tasks. We illustrate our method using several synthetic network models as well as Facebook, arXiv, and protein-protein interaction networks, that achieve state-of-the-art performance for such network tasks when compared to several recent methods.

Certain zero range processes on a finite set exhibits metastability. Most of the time nearly all particles of the zero range process are at one single site, and the site of condensate asymptotically behaves as a Markov chain. In this talk, we prove the metastability of zero range processes on a finite set with an approach using the Poisson equation. This approach doesn't need precise estimates of capacities and can be applied for both reversible and non-reversible cases. This talk is based on the joint work with F. Rezakhanlou.

(전체일정: 7/28, 7/29, 8/3, 8/5) In 2d first-passage percolation, we let (t_e) be a family of i.i.d. weights associated to the edges of the square lattice, and let T = T(x,y) be the induced weighted graph metric on Z^2. If we let p be the probability that a weight takes the value 0, then there is a transition in the large-scale behavior of T depending on the value of p. Specifically, when p < 1/2, T grows linearly, but when p > 1/2, T is stochastically bounded. In these lectures, I will describe some of the standard questions of FPP in the case p < 1/2, and then focus on the "critical" case, where p = 1/2. Regarding this case, I will show some of my work over the last few years including exact asymptotics for T, universality results, and recent work on a dynamical version of the model. The work I will present was done in collaboration with J. Hanson, D. Harper, W.-K. Lam, P. Tang, and X. Wang. Lec 1: Introduction and the passage time to infinity

Most organisms exhibit various endogenous oscillating behaviors, which provides crucial information about how the internal biochemical processes are connected and regulated. Along with physical experiments, studying such periodicity of organisms often utilizes computer experiments relying on ordinary differential equations (ODE) because configuring the internal processes is difficult. Simultaneously utilizing both experiments, however, poses a significant statistical challenge due to its ill behavior in high dimension, identifiability, and numerical instability. This article devises a new Bayesian calibration strategy for oscillating biochemical models. The proposed methodology can efficiently estimate the computer experiments’ (ODE) parameters that match the physical experiments. The proposed framework is illustrated with circadian oscillations observed in a model filamentous fungus, Neurospora crassa.

TBA

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This talk will be presented online. Zoom link: 709 120 4849 (pw: 1234)

(전체일정: 7/26, 7/27, 8/2, 8/4) Lec 2: Introduction to cut-off phenomenon In this second lecture, we introduce the so-called cut-off phenomenon and look at several examples exhibiting this phenomenon. Then, we rigorously prove the cut-off phenomenon for the simplest possible model, the lazy random walk on hypergraphs.

Lec 1: Introduction to Markov chain mixing theory In this lecture, we introduce the Markov chain mixing theory by assuming that the attendances have no background on this field. The precise definition of the mixing time and several basic techniques estimating mixing time will be discussed.

In this talk, we will introduce some applications of currents. Thanks to results of Demailly--Paun or Collins--Tosatti, we have a decent understanding of how (cohomology class of) currents are found to be nef and big, the positivity notions that succeed Kahler-ness. With the K3 surface example, where its intersection theory is well-known, we then sketch on how all these machinery are applied to give some result (of Filip--Tosatti) on dynamical rigidity on K3 surfaces.

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Zoom 회의 참가 https://zoom.us/j/92837213232?pwd=Y1RTODFITGFHQWNRbTRTeTlNakZsQT09 회의 ID: 928 3721 3232 암호: barH1Y

In this talk, we will introduce the notion of currents, a generalization of differential forms, allowing distributions (dual of smooth compactly supported functions) as coefficients. With this, we introduce their examples, derivatives, cohomology, "de Rham" type groups, and how they interplay with divisors of complex varieties.

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Zoom 회의 참가 https://zoom.us/j/92837213232?pwd=Y1RTODFITGFHQWNRbTRTeTlNakZsQT09 회의 ID: 928 3721 3232 암호: barH1Y

The studies on the fibers of the Hitchin map are equivalent to those on spectral data for Higgs bundles. In this talk, I will introduce spectral data for SL(2, C)- Higgs bundles over a smooth curve and then discuss how to describe spectral data for SL(2, C)-Higgs bundles over an irreducible nodal curve.

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Zoom ID: 352 730 6970, PW: 9999.

Organisms have evolved an internal biological clock which allows them to temporally regulate and organize their physiological and behavioral responses to cope in an optimal way with the fundamentally periodic nature of the environment. It is now well established that the molecular genetics of such rhythms within the cell consist of interwoven transcriptional-translational feedback loops involving about 15 clock genes, which generate circa 24-h oscillations in many cellular functions at cell population or whole organism levels. We will present statistical methods and modelling approaches that address newly emerging large circadian data sets, namely spatio-temporal gene expression in SCN neurons and rest-activity actigraph data obtained from non-invasive e-monitoring, both of which provide unique opportunities for furthering progress in understanding the synchronicity of circadian pacemaking and address implications for monitoring patients in chronotherapeutic healthcare.

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This talk will be presented online. Zoom link: 709 120 4849 (pw: 1234)

TBA

MUltiple SIgnal Classification (MUSIC) is a well-known, non-iterative imaging technique in inverse scattering problem. Throughout various researches, it has been confirmed that MUSIC is very fast, effective, and stable. Due to this reason MUSIC has been applied to various inverse scattering problems however, it has not yet been designed and used to identify unknown anomalies from measured scattering parameters (S-parameters) in microwave imaging. In this presentation, we apply MUSIC in microwave imaging for a fast identification of arbitrary shaped anomalies from real-data and establish a mathematical theory for illustrating the feasibilities and limitations of MUSIC. Simulations results with real-data are shown for supporting established theoretical results. Meeting ID: 873 9069 4743 Passcode: 728543

Gromov-Witten invariants are some rational numbers roughly counting curves inside a Calabi-Yau manifold. These numbers have some recurvsive structure on the genus of the curve. I will explain how to study this recursive structure throughholomorphic anomaly equation. For a semi-simple Gromov-Witten theory, I will explain the method of proof of holomorphic anomaly equation for several examples using Givental-Teleman's classification thoerem.If I have more time, I will discuss how to generalize this method to a non-semi simple Gromov-Witten theory.

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Zoom ID: 352 730 6970, Password: 9999

Abstract: We consider the problem of nonparametric imputation using neural network models. Neural network models can capture complex nonlinear trends and interaction effects, making it a powerful tool for predicting missing values under minimum assumptions on the missingness mechanism. Statistical inference with neural network imputation, including variance estimation, is challenging because the basis for function estimation is estimated rather than known. In this paper, we tackle the problem of statistical inference with neural network imputation by treating the hidden nodes in a neural network as data-driven basis functions. We prove that the uncertainty in estimating the basis functions can be safely ignored and hence the linearization method for neural network imputation can be greatly simplified. A simulation study confirms that the proposed approach results in efficient and well-calibrated confidence intervals even when classic approaches fail due to severe nonlinearity and complicated interactions.