58 research outputs found
A statistical mechanics approach to autopoietic immune networks
The aim of this work is to try to bridge over theoretical immunology and
disordered statistical mechanics. Our long term hope is to contribute to the
development of a quantitative theoretical immunology from which practical
applications may stem. In order to make theoretical immunology appealing to the
statistical physicist audience we are going to work out a research article
which, from one side, may hopefully act as a benchmark for future improvements
and developments, from the other side, it is written in a very pedagogical way
both from a theoretical physics viewpoint as well as from the theoretical
immunology one.
Furthermore, we have chosen to test our model describing a wide range of
features of the adaptive immune response in only a paper: this has been
necessary in order to emphasize the benefit available when using disordered
statistical mechanics as a tool for the investigation. However, as a
consequence, each section is not at all exhaustive and would deserve deep
investigation: for the sake of completeness, we restricted details in the
analysis of each feature with the aim of introducing a self-consistent model.Comment: 22 pages, 14 figur
Nonstandard analysis, deformation quantization and some logical aspects of (non)commutative algebraic geometry
This paper surveys results related to well-known works of B. Plotkin and V.
Remeslennikov on the edge of algebra, logic and geometry. We start from a brief
review of the paper and motivations. The first sections deal with model theory.
In Section 2.1 we describe the geometric equivalence, the elementary
equivalence, and the isotypicity of algebras. We look at these notions from the
positions of universal algebraic geometry and make emphasis on the cases of the
first order rigidity. In this setting Plotkin's problem on the structure of
automorphisms of (auto)endomorphisms of free objects, and auto-equivalence of
categories is pretty natural and important. Section 2.2 is dedicated to
particular cases of Plotkin's problem. Section 2.3 is devoted to Plotkin's
problem for automorphisms of the group of polynomial symplectomorphisms. This
setting has applications to mathematical physics through the use of model
theory (non-standard analysis) in the studying of homomorphisms between groups
of symplectomorphisms and automorphisms of the Weyl algebra. The last two
sections deal with algorithmic problems for noncommutative and commutative
algebraic geometry. Section 3.1 is devoted to the Gr\"obner basis in
non-commutative situation. Despite the existence of an algorithm for checking
equalities, the zero divisors and nilpotency problems are algorithmically
unsolvable. Section 3.2 is connected with the problem of embedding of algebraic
varieties; a sketch of the proof of its algorithmic undecidability over a field
of characteristic zero is given.Comment: In this review we partially used results of arXiv:1512.06533,
arXiv:math/0512273, arXiv:1812.01883 and arXiv:1606.01566 and put them in a
new contex
Interacting String Multi-verses and Holographic Instabilities of Massive Gravity
Products of large-N conformal field theories coupled by multi-trace
interactions in diverse dimensions are used to define quantum multi-gravity
(multi-string theory) on a union of (asymptotically) AdS spaces. One-loop
effects generate a small O(1/N) mass for some of the gravitons. The boundary
gauge theory and the AdS/CFT correspondence are used as guiding principles to
study and draw conclusions on some of the well known problems of massive
gravity - classical instabilities and strong coupling effects. We find examples
of stable multi-graviton theories where the usual strong coupling effects of
the scalar mode of the graviton are suppressed. Our examples require a fine
tuning of the boundary conditions in AdS. Without it, the spacetime background
backreacts in order to erase the effects of the graviton mass.Comment: 51 pages, 3 figures; v2 typos corrected, version published in NPB; v3
added appendix E on general class of fixed points in multi-trace deformation
Quantum information with continuous variables
Quantum information is a rapidly advancing area of interdisciplinary
research. It may lead to real-world applications for communication and
computation unavailable without the exploitation of quantum properties such as
nonorthogonality or entanglement. We review the progress in quantum information
based on continuous quantum variables, with emphasis on quantum optical
implementations in terms of the quadrature amplitudes of the electromagnetic
field.Comment: accepted for publication in Reviews of Modern Physic
Tight informationally complete quantum measurements
We introduce a class of informationally complete positive-operator-valued
measures which are, in analogy with a tight frame, "as close as possible" to
orthonormal bases for the space of quantum states. These measures are
distinguished by an exceptionally simple state-reconstruction formula which
allows "painless" quantum state tomography. Complete sets of mutually unbiased
bases and symmetric informationally complete positive-operator-valued measures
are both members of this class, the latter being the unique minimal rank-one
members. Recast as ensembles of pure quantum states, the rank-one members are
in fact equivalent to weighted 2-designs in complex projective space. These
measures are shown to be optimal for quantum cloning and linear quantum state
tomography.Comment: 20 pages. Final versio
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