arXiv subjects

Giovanni Feverati

Publications and source records attributed to Giovanni Feverati.

12 recordsLinked to original sources

arXiv2011

Mutation-selection dynamics and error threshold in an evolutionary model for Turing Machines

We investigate the mutation-selection dynamics for an evolutionary computation model based on Turing Machines that we introduced in a previous article. The use of Turing Machines allows for very simple mechanisms of code growth and code activation/inactivation through point mutations. To any value of the point mutation probability corresponds a maximum amount of active code that can be maintained by selection and the Turing machines that reach it are said to be at the error threshold. Simulations with our model show that the Turing machines population evolve towards the error threshold. Mathematical descriptions of the model point out that this behaviour is due more to the mutation-selection dynamics than to the intrinsic nature of the Turing machines. This indicates that this result is much more general than the model considered here and could play a role also in biological evolution.

q-bio.PE↗

arXiv2011

Quantum integrable systems. Quantitative methods in biology

Quantum integrable systems have very strong mathematical properties that allow an exact description of their energetic spectrum. From the Bethe equations, I formulate the Baxter "T-Q" relation, that is the starting point of two complementary approaches based on nonlinear integral equations. The first one is known as thermodynamic Bethe ansatz, the second one as Klümper-Batchelor-Pearce-Destri- de Vega. I show the steps toward the derivation of the equations for some of the models concerned. I study the infrared and ultraviolet limits and discuss the numerical approach. Higher rank integrals of motion can be obtained, so gaining some control on the eigenvectors. After, I discuss the Hubbard model in relation to the N = 4 supersymmetric gauge theory. The Hubbard model describes hopping electrons on a lattice. In the second part, I present an evolutionary model based on Turing machines. The goal is to describe aspects of the real biological evolution, or Darwinism, by letting evolve populations of algorithms. Particularly, with this model one can study the mutual transformation of coding/non coding parts in a genome or the presence of an error threshold. The assembly of oligomeric proteins is an important phenomenon which interests the majority of proteins in a cell. I participated to the creation of the project "Gemini" which has for purpose the investigation of the structural data of the interfaces of such proteins. The objective is to differentiate the role of amino acids and determine the presence of patterns characterizing certain geometries.

math-ph↗

arXiv2010

Introduction to Quantum Integrability

In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary Yang-Baxter equations depending on the choice of boundary conditions. The relation between the aforementioned equations and the braid group is briefly discussed. A short review on quantum groups as well as the quantum inverse scattering method (algebraic Bethe ansatz) is also presented.

math-ph↗

arXiv2009

Physical Combinatorics and Quasiparticles

We consider the physical combinatorics of critical lattice models and their associated conformal field theories arising in the continuum scaling limit. As examples, we consider A-type unitary minimal models and the level-1 sl(2) Wess-Zumino-Witten (WZW) model. The Hamiltonian of the WZW model is the $U_q(sl(2))$ invariant XXX spin chain. For simplicity, we consider these theories only in their vacuum sectors on the strip. Combinatorially, fermionic particles are introduced as certain features of RSOS paths. They are composites of dual-particles and exhibit the properties of quasiparticles. The particles and dual-particles are identified, through an energy preserving bijection, with patterns of zeros of the eigenvalues of the fused transfer matrices in their analyticity strips. The associated (m,n) systems arise as geometric packing constraints on the particles. The analyticity encoded in the patterns of zeros is the key to the analytic calculation of the excitation energies through the Thermodynamic Bethe Ansatz (TBA). As a by-product of our study, in the case of the WZW or XXX model, we find a relation between the location of the Bethe root strings and the location of the transfer matrix 2-strings.

hep-th↗

arXiv2007

Generalised integrable Hubbard models

We construct the XX and Hubbard-like models based on unitary superalgebras gl(N|M) generalizing Shastry's and Maassarani's approach. We introduce the R-matrix of the gl(N|M) XX-type model; the one of the Hubbard-like model is defined by "coupling" two independent XX models. In both cases, we show that the R-matrices satisfy the Yang-Baxter equation. We derive the corresponding local Hamiltonian in the transfer matrix formalism and we determine its symmetries. A perturbative calculation "à la Klein and Seitz" is performed. Some explicit examples are worked out. We give a description of the two-particle scattering.

hep-th↗

arXiv2007

An evolutionary model with Turing machines

The development of a large non-coding fraction in eukaryotic DNA and the phenomenon of the code-bloat in the field of evolutionary computations show a striking similarity. This seems to suggest that (in the presence of mechanisms of code growth) the evolution of a complex code can't be attained without maintaining a large inactive fraction. To test this hypothesis we performed computer simulations of an evolutionary toy model for Turing machines, studying the relations among fitness and coding/non-coding ratio while varying mutation and code growth rates. The results suggest that, in our model, having a large reservoir of non-coding states constitutes a great (long term) evolutionary advantage.

q-bio.QM↗

arXiv2006

A Renormalisation group for TCSA

We discuss the errors introduced by level truncation in the study of boundary renormalisation group flows by the Truncated Conformal Space Approach. We show that the TCSA results can have the qualitative form of a sequence of RG flows between different conformal boundary conditions. In the case of a perturbation by the field phi(13), we propose a renormalisation group equation for the coupling constant which predicts a fixed point at a finite value of the TCSA coupling constant and we compare the predictions with data obtained using TBA equations.

hep-th↗

arXiv2006

Hubbard's Adventures in ${\cal N}=4$ SYM-land? Some non-perturbative considerations on finite length operators

As the Hubbard energy at half filling is believed to reproduce at strong coupling (part of) the all loop expansion of the dimensions in the SU(2) sector of the planar $ {\cal N}=4$ SYM, we compute an exact non-perturbative expression for it. For this aim, we use the effective and well-known idea in 2D statistical field theory to convert the Bethe Ansatz equations into two coupled non-linear integral equations (NLIEs). We focus our attention on the highest anomalous dimension for fixed bare dimension or length, $L$, analysing the many advantages of this method for extracting exact behaviours varying the length and the 't Hooft coupling, $λ$. For instance, we will show that the large $L$ (asymptotic) expansion is exactly reproduced by its analogue in the BDS Bethe Ansatz, though the exact expression clearly differs from the BDS one (by non-analytic terms). Performing the limits on $L$ and $λ$ in different orders is also under strict control. Eventually, the precision of numerical integration of the NLIEs is as much impressive as in other easier-looking theories.

hep-th↗

arXiv2006

On the finite size corrections of anti-ferromagnetic anomalous dimensions in ${\cal N}=4$ SYM

Non-linear integral equations derived from Bethe Ansatz are used to evaluate finite size corrections to the highest (i.e. {\it anti-ferromagnetic}) and immediately lower anomalous dimensions of scalar operators in ${\cal N}=4$ SYM. In specific, multi-loop corrections are computed in the SU(2) operator subspace, whereas in the general SO(6) case only one loop calculations have been finalised. In these cases, the leading finite size corrections are given by means of explicit formulæand compared with the exact numerical evaluation. In addition, the method here proposed is quite general and especially suitable for numerical evaluations.

hep-th↗

arXiv2004

Exact (d)->(+)&(-) boundary flow in the tricritical Ising model

The integrable perturbation of the degenerate boundary condition (d) by the $ϕ_{1,3}$ boundary field generates a renormalization group flow down to the superposition of Cardy boundary states (+)&(-). Exact Thermodynamic Bethe Ansatz (TBA) equations for all the excited states are derived here extending the results of a previous paper to this case. As an intermediate step, the non-Cardy boundary conformal sector (+)&(-) is also described as the scaling limit of an A_4 lattice model with appropriate integrable boundary conditions and produces the first example of superposition of finitized Virasoro characters.

hep-th↗

arXiv2002

Critical RSOS and Minimal Models I: Paths, Fermionic Algebras and Virasoro Modules

We consider sl(2) minimal conformal field theories on a cylinder from a lattice perspective. To each allowed one-dimensional configuration path of the A_L Restricted Solid-on-Solid (RSOS) models we associate a physical state |h> and a monomial in a finite fermionic algebra. The orthonormal states produced by the action of these monomials on the primary states generate finite Virasoro modules with dimensions given by the finitized Virasoro characters $χ^{(N)}_h(q)$. These finitized characters are the generating functions for the double row transfer matrix spectra of the critical RSOS models. We argue that a general energy-preserving bijection exists between the one-dimensional configuration paths and the eigenstates of these transfer matrices and exhibit this bijection for the critical and tricritical Ising models in the vacuum sector. Our results extend to Z_{L-1} parafermion models by duality.

hep-th↗

arXiv2002

Lattice Approach to Excited TBA Boundary Flows: Tricritical Ising Model

We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering the continuum scaling limit of the A4 lattice model with integrable boundaries. Fixing the bulk weights to their critical values, the integrable boundary weights admit two boundary fields $ξ$ and $η$ which play the role of the perturbing boundary fields $ϕ_{1,3}$ and $ϕ_{1,2}$ inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations.

hep-th↗