We develop a new approach to construction of Br\`{e}gman relative entropies
over nonreflexive Banach spaces, based on nonlinear mappings into reflexive
Banach spaces. We apply it to derive few families of Br\`{e}gman relative
entropies over...
Change Acceleration and Detection
October 2, 2017
|
Mathematics
Statistics
Statistics Theory
Methodology
Statistics Theory
A novel sequential change detection problem is proposed, in which the goal is
to not only detect but also accelerate the change. Specifically, it is assumed
that the sequentially collected observations are responses to treatments
selected i...
Black holes have more states than those giving the Bekenstein-Hawking
entropy: a simple argument
September 30, 2017
|
Physics
General Relativity and Quantum Cosmology
High Energy Physics - Theory
General Relativity and Quantum Cosmology
High Energy Physics - Theory
It is often assumed that the maximum number of independent states a black
hole may contain is NBH=eSBH, where SBH=A/4 is the
Bekenstein-Hawking entropy and A the horizon area in Planck units. I present
a simple and straigh...
Notes on rate equations in nonlinear continuum mechanics
September 28, 2017
Physics
Computer Science
Classical Physics
Computational Engineering, Finance, and Science
The paper gives an introduction to rate equations in nonlinear continuum
mechanics which should obey specific transformation rules. Emphasis is placed
on the geometrical nature of the operations involved in order to clarify the
different co...
Valued fields, Metastable groups
September 25, 2017
|
Mathematics
Logic
We introduce a class of theories called metastable, including the theory of
algebraically closed valued fields (ACVF) as a motivating example. The key
local notion is that of definable types dominated by their stable part. A
theory is metas...
A Practical Quantum Algorithm for the Schur Transform
September 20, 2017
|
Physics
Quantum Physics
We describe an efficient quantum algorithm for the quantum Schur transform.
The Schur transform is an operation on a quantum computer that maps the
standard computational basis to a basis composed of irreducible representations
of the unita...
Two resonant quantum electrodynamics models of quantum measuring systems
September 20, 2017
Physics
Quantum Physics
A quantum measurement scheme is suggested in two resonant models of quantum
electrodynamics. The first model is the brain, where, for the propagation of
its action potentials, the free electron laser-like coherence mechanism
recently invest...
Dependent randomized rounding for clustering and partition systems with
knapsack constraints
September 20, 2017
| | |
Computer Science
Data Structures and Algorithms
Clustering problems are fundamental to unsupervised learning. There is an
increased emphasis on fairness in machine learning and AI; one representative
notion of fairness is that no single demographic group should be
over-represented among ...
Relative completed cohomologies and modular symbols
September 17, 2017
| | |
Mathematics
Number Theory
Number Theory
Generalizing Emerton's completed cohomologies, we define relative completed
cohomologies of arithmetic manifolds. We also define modular symbols for them,
and show that the relative completed cohomology spaces interpolate the ``nearly
ordin...
A priori bounds for geodesic diameter. Part III. A Sobolev-Poincar\'e
inequality and applications to a variety of geometric variational problems
September 16, 2017
|
Mathematics
Differential Geometry
Analysis of PDEs
Classical Analysis and ODEs
Based on a novel type of Sobolev-Poincar\'e inequality (for generalised
weakly differentiable functions on varifolds), we establish a finite upper
bound of the geodesic diameter of generalised compact connected
surfaces-with-boundary of arb...