Biomanufacturing Harvest Optimization with Small Data
January 11, 2021
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Statistics
Computer Science
Machine Learning
Machine Learning
In biopharmaceutical manufacturing, fermentation processes play a critical
role in productivity and profit. A fermentation process uses living cells with
complex biological mechanisms, leading to high variability in the process
outputs, nam...
K-theory of admissible Zariski-Riemann spaces
January 11, 2021
Mathematics
Algebraic Geometry
K-Theory and Homology
We study relative algebraic K-theory of admissible Zariski-Riemann spaces and
prove that it is equivalent to G-theory and satisfies homotopy invariance.
Moreover, we provide an example of a non-noetherian abelian category whose
negative K-t...
The Proper Basis for Polynomial Ideals
January 10, 2021
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Mathematics
Computer Science
Commutative Algebra
Symbolic Computation
Algebraic Geometry
Commutative Algebra
Symbolic Computation
Algebraic Geometry
We define a new type of ideal basis called the proper basis that improves
both Gr\"obner basis and Buchberger's algorithm. Let x1 be the least
variable of a monomial ordering in a polynomial ring K[x1,…,xn] over a
field K. The...
New CP Phase and Exact Oscillation Probabilities of Dirac Neutrino
derived from Relativistic Equation
January 10, 2021
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Physics
High Energy Physics - Phenomenology
We present a new formulation for deriving neutrino oscillation probabilities
relativistically, based not on the Schr\"odinger equation but on the Dirac
equation. In the context of two generations, we calculate the oscillation
probabilities ...
Symplectic excision
January 10, 2021
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Mathematics
Symplectic Geometry
Differential Geometry
Dynamical Systems
We use time-independent incomplete Hamiltonian flows to excise interesting
closed subsets of positive codimension from symplectic manifolds. Examples of
such subsets include what we call a "Cantor brush", a "box with a tail", and --
more ge...
Torsors in super-symmetry
January 9, 2021
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Mathematics
Algebraic Geometry
Torsors under affine groups are generalized in the super context by
super-torsors under affine super-groups. We investigate those super-torsors by
using Hopf-algebra language and techniques. It is explicitly shown, under
suitable assumption...
Global existence of solutions of a loglog energy-supercritical
Klein-Gordon equation
January 8, 2021
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Mathematics
Analysis of PDEs
Analysis of PDEs
We prove global existence of solutions of a loglog energy-supercritical
Klein-Gordon equation for n=3,4,5. Assuming that blow-up occurs at a time of
maximal existence, we perform an analysis close to this time in order to find a
finite boun...
Random Unitary Representations of Surface Groups II: The large n limit
January 8, 2021
Mathematics
Physics
Representation Theory
Mathematical Physics
Geometric Topology
Mathematical Physics
Operator Algebras
Let Σg be a closed surface of genus g≥2 and Γg
denote the fundamental group of Σg. We establish a generalization of
Voiculescu's theorem on the asymptotic ∗-freeness of Haar unitary matrices
from free g...
Motivic Euler Characteristic of Nearby Cycles and a Generalized
Quadratic Conductor Formula
January 7, 2021
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Mathematics
Algebraic Geometry
Algebraic Topology
K-Theory and Homology
Algebraic Geometry
Algebraic Topology
K-Theory and Homology
We compute the motivic Euler characteristic of Ayoub's nearby cycles spectrum
in terms of strata of a semi-stable reduction, for a degeneration to multiple
semi-quasi-homogeneous singularities. This allows us to compare the local
picture at...
First-order algorithms for robust optimization problems via
convex-concave saddle-point Lagrangian reformulation
January 7, 2021
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Mathematics
Optimization and Control
Robust optimization (RO) is one of the key paradigms for solving optimization
problems affected by uncertainty. Two principal approaches for RO, the robust
counterpart method and the adversarial approach, potentially lead to
excessively lar...