Intelligent systems with deep learning have emerged as a key technique for a wide range of different applications including vision processing, autonomous driving and robot navigation. SoC implementations in deep learning-based intelligent systems give us higher performance and low-power operations in many applications.

Title: Explicit constructions of Curves Ⅱ

Speaker: Prof. Frank O. Schreyer (U. of Saarlands & KAIST)

Date: 29 September, 2016

Time: 17:10 - 18:10

Place: Rm. 1409, Natural Sciences B/D E6-1

 We continue with differential calculus on infinite jet bundle. After introducing variational bicomplex, we discuss Lagrangian field theory in this framework. We omit chapter 9, but we will make some comments on a bihamiltonian structure of KdV equation.

The pharmacometrics (PM) is originated from roots of pharmacokinetics and pharmacodynamics through population and physiological based pharmacokinetics to pharmacometrics. PM is developing science that how to apply and use mathematical and statistical methods to understand a drug's behavior in body, quantify uncertainty of information, and make rational for data-driven decision in the drug discovery and pharmacotherapy.

Improvements in drug discovery is necessarily require to enhance translational research from pre-clinical to clinical stages. According to this stream, PM are occurring to powerful and efficient skill to unify divided knowledge. Nowadays, it is hard to imagine a more efficient, powerful and informative drug development process without the expansion of the role of PM. Pharmacotherapy is also in great need of improved dosing strategy selection for the avoidance of adverse events and the improvement in efficacy. This will get through the development of pragmatic PM models that provide knowledge about drug behavior and how the drug can be optimally used. As more pragmatic PM models are developed, optimal dosing strategies based can be implemented.

In recent, paradigm of PM is going to be more wider than now to cover biological process, as system pharmacology. Therefore, the importance of PM is not able to be overemphasized in whole process for drug discovery and clinical application.

Keywords

Pharmacometrics, Drug discovery, Clinical application

In this talk, we will survey the book "Vertex operator algebras and the monster- I.Frankel, J. Lepowsky and A. Meurman (1988)".

Speaker: Jinhyung Park (KIAS)

Title: A bound for Castelnuovo-Mumford regularity by double point divisor

Date: Friday, Sep. 23

Time: 15:00 - 15:50

Place: Rm. 1409, Natural Sciences B/D E6-1

Hilbert syzygy theorem says that any finitely generated graded module $M$ over the standard graded polynomial ring $S=K[x_1,ldots,x_n]$ has a finite free resolution

$$

0 leftarrow M leftarrow F_0 leftarrow F_1 leftarrow ldots leftarrow F_c leftarrow 0

$$

with $F_i = oplus_j S(-i)^{beta_{ij}}$ a free module with $beta_{ij}$ generators

in degree $j$. Hilbert proved his syzygy theorem to exhibit the polynomial nature of the Hilbert series:

$$

H_M(t) = sum_k dim M_k t^k = frac{sum_i (-1)^i sum_j beta_{ij}t^j}{(1-t)^n}

$$

In the talk I will report on the  question, what kind of more information about $M$

is encoded in the graded Betti numbers $beta_{ij}(M)$, what are the possible values

of these numbers, and, what can be said about extremal cases.

자유경계문제는 물질의 상태변화, American Option Pricing 등 Financial Problems, Geometric Application등에서 

The ideas of Lagrangian and Hamiltonian field theories from Physics can be precisely formulated using the formalisms of infinite jet bundles and polysymplectic manifolds, respectively. Moreover, the classical stages of their BRST quantization procedures can also be described on simple extensions of them involving Grassmann variables. We plan to follow chapters 1, 2, 9, 3, 4 of "Advanced classical field theory" by Giachetta-Mangiarotti-Sardanashvily (http://www.worldscientific.com/worldscibooks/10.1142/7189) in four lectures, in the order as indicated. We assume some experience with differential forms on smooth manifolds. In the first lecture, we cover chapter 1, that reviews geometry of fiber bundles and introduces infinite jet formalism.

Suppose that a rational map between two projective spaces over a field is defined by a set of homogeneous polynomials of the same degree. It is interesting and important to study if such a map is birational onto its image. In this talk, we present an algebraic characterization under some assumptions on the ideal. Our result is obtained by analyzing the defining ideal of the special fiber ring. This is joint work with Vivek Mukundan.

Theoretical Computer Science provides the sound foundation

and rigorous concepts underlying contemporary algorithm

design and software development -- for discrete problems:

Problems in the continuous realm commonly considered in Numerical Engineering are largely treated by 'recipes' and 'methods'

whose correctness and efficiency is usually shown empirically.

We extend and apply the theory of computation over discrete structures

to continuous domains: It turns out that famous complexity classes like

P, NP, #P, and PSPACE naturally re-emerge in the setting of real numbers,

sequences, continuous functions, operators, and Euclidean subsets

(including a reformulation of a Millennium Prize Problem as a numerical one).

We currently work towards a rigorous computability and complexity

classification for partial differential equations, namely over

Sobolev spaces that their solutions naturally 'live' in.

In this talk, I will review energy momentum fields and conformal weights of vertex operator algebras (VOAs). I will show conformal weight decompositions of VOAs with some examples. If time allows, I will introduce relations between vertex algebras and Poisson vertex algebras. 

In this talk we review some of the recent progresses on the mathematical theory of the surface superconducting states of type 2 superconductors and of the surface smectic states of liquid crystals, including the recent work with S. Fournais and A. Kachmar on the conjecture of surface smectic states. We discuss the effects of domain geometry and physical parameters to the characterization of the phase transitions with emphasis on the analogies between the mathematical descriptions of superconductors and liquid crystals. Some observations and questions on the related topics will also be presented.

   In this talk, we would like to discuss about an algorithm to numerically solve a normal

ow equation in level set method on a polyhedron mesh in 3D. The equation has been
extensively used in image processing and surface evolution. Unlike to commonly used a
structured mesh in level set method, it is very challenging to obtain a high order scheme in
a polyhedron mesh. We propose a cell-centered gradient dened by
ux signs to design a
robust scheme considered as an extension of well-known Rouy-Tourin scheme into 3D with
the second order upwind dierence. A high order of convergence, performance in parallel
computation, and a recovery of signed distance function from a sparse data are illustrated
in numerical examples.


I have pioneered a couple of mathematical and computational approaches for free
boundary problems and optimization; 1) The immersed boundary (IB) method for
advection-electrodiffusion, 2) an IB method for non-Newtonian two-phase viscoelastic
fluids and gels, 3) an extended finite element method for phonon Boltzmann transport
and shape/topology optimization by adjoint method, 4) minimum attention in motor
control by one shot method.
Let us galvanize a couple of applications in mechanobiology; 1) Cardiac differentiation
and dendritic spine motility by the IB methods, 2) collective cell migration of wound
healing and cancer metastasis, 3) the mechanics of pulmonary arterial hypertension from
micro CT image-segmented vascular network, ventricular-vascular interaction in
coronary impedance matching, and renal peristaltic concentration.

Siegel pioneered the generalization of the theory of elliptic modular functions to the modular functions in several variables, which are called Siegel modular functions. Siegel modular functions are of fundamental importance in number theory and algebraic geometry. However, we know relatively little about Siegel modular functions until now because it is difficult to find attractive examples that can be handled. In this talk, we construct explicit generators of Siegel modular function field of higher genus and level in terms of multi-variable theta constants. 

In this talk, I will review various constructions of vertex algebras. Also, I will talk about an energy momentum field and corresponding conformal weights of a vertex operator algebra.

This is a joint work with Dale Rolfsen (University of British Columbia).
Let G be a group with a strict total ordering <  of the elements of G.
If < is invariant under the left-multiplication,
(i.e, g < h implies fg < fh  for all elements f, g and h in G)
 then we call (G, <) a  left-ordered group.
 If the ordering < is also invariant under the right-multiplication, we call
(G,<) a  bi-ordered group.
In this talk, we consider which groups of links in the 3-sphere
(that is the fundamental groups of the complements of links) are  bi-orderable.
We focus on the links obtained from braids together with the braid axis.
We prove that groups of some of interesting links are bi-orderable. 

Our examples include the minimally twisted 4- and 5-chain links, the Whitehead link.
We also prove that the group of the (-2,3,8)-pretzel link can not be bi-orderable.