Exact dynamics of two ultra-cold bosons confined in a one-dimensional
double-well potential
March 17, 2016
|
Physics
Quantum Gases
The dynamics of two ultra-cold bosons confined in a one-dimensional
double-well potential is studied. We compare the exact dynamics governed by a
full two-body Hamiltonian with the dynamics obtained in a two-mode model
approximation. We sho...
The Helstrom Bound
March 15, 2016
Physics
Quantum Physics
Quantum state discrimination between two wave functions on a ring is
considered. The optimal minimum-error probability is known to be given by the
Helstrom bound. A new strategy is introduced by inserting instantaneously two
impenetrable ba...
A Primer on the Signature Method in Machine Learning
March 11, 2016
| | |
Statistics
Computer Science
Machine Learning
Machine Learning
Methodology
Machine Learning
Machine Learning
Methodology
We provide an introduction to the signature method, focusing on its
theoretical properties and machine learning applications. Our presentation is
divided into two parts. In the first part, we present the definition and
fundamental propertie...
Calibrar: an R package for fitting complex ecological models
March 9, 2016
|
Quantitative Biology
Mathematics
Statistics
Quantitative Methods
Optimization and Control
Computation
The fitting or parameter estimation of complex ecological models is a
challenging optimisation task, with a notable lack of tools for fitting
complex, long runtime or stochastic models. calibrar is an R package that is
dedicated to the fitt...
On the link between binomial theorem and discrete convolution
March 8, 2016
Mathematics
Number Theory
Let Pbm(x) be a 2m+1-degree polynomial in x and b∈RPbm(x)=k=0∑b−1r=0∑mAm,rkr(x−k)r where Am,r are real coefficients. In this man...
Quasi-isometry classification of right-angled Artin groups II: several
infinite out cases
March 7, 2016
|
Mathematics
Geometric Topology
Group Theory
Geometric Topology
Group Theory
We are motivated by the question that for which class of right-angled Artin
groups (RAAG's), the quasi-isometry classification coincides with
commensurability classification. This is previously known for RAAG's with
finite outer automorphis...
Posterior Consistency for Gaussian Process Approximations of Bayesian
Posterior Distributions
March 7, 2016
|
Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
We study the use of Gaussian process emulators to approximate the
parameter-to-observation map or the negative log-likelihood in Bayesian inverse
problems. We prove error bounds on the Hellinger distance between the true
posterior distribut...
Existence and uniqueness theorems for solutions of McKean--Vlasov
stochastic equations
March 7, 2016
|
Mathematics
Probability
New weak and strong existence and weak and strong uniqueness results for
multi-dimensional stochastic McKean--Vlasov equations are established under
relaxed regularity conditions. Weak existence is a variation of Krylov's weak
existence for...
Generalizations of local bijectivity of Keller maps and a proof of
2-dimensional Jacobian conjecture
March 6, 2016
Mathematics
Physics
Algebraic Geometry
Mathematical Physics
Commutative Algebra
Mathematical Physics
Rings and Algebras
Using the local bijectivity of Keller maps, we give a proof of
two-dimensional Jacobian conjecture....
Solution of Hypergraph Turan problem
March 1, 2016
Mathematics
Combinatorics
Using original {\it Symmetrical Smoothing Method} we solve (3,k)-
hypergraph Turan problem...