769 research outputs found
Critical thermodynamics of the two-dimensional +/-J Ising spin glass
We compute the exact partition function of 2d Ising spin glasses with binary
couplings. In these systems, the ground state is highly degenerate and is
separated from the first excited state by a gap of size 4J. Nevertheless, we
find that the low temperature specific heat density scales as exp(-2J/T),
corresponding to an ``effective'' gap of size 2J; in addition, an associated
cross-over length scale grows as exp(J/T). We justify these scalings via the
degeneracy of the low-lying excitations and by the way low energy domain walls
proliferate in this model
Video augmentation to support video-based learning
Multimedia content and video-based learning are expected to take a central role in the post-pandemic world. Thus, providing new advanced interfaces and services that further exploit their potential becomes of paramount importance. A challenging area deals with developing intelligent visual interfaces that integrate the knowledge extracted from multimedia materials into educational applications. In this respect, we designed a web-based video player that is aimed to support video consumption by exploiting the knowledge extracted from the video in terms of concepts explained in the video and prerequisite relations between them. This knowledge is used to augment the video lesson through visual feedback methods. Specifically, in this paper we investigate the use of two types of visual feedback, i.e. an augmented transcript and a dynamic concept map (map of concept's flow), to improve video comprehension in the first-watch learning context. Our preliminary findings suggest that both the methods help the learner to focus on the relevant concepts and their related contents. The augmented transcript has an higher impact on immediate comprehension compared to the map of concepts' flow, even though the latter is expected to be more powerful to support other tasks such as exploration and in-depth analysis of the concepts in the video
Gauge and Poincare' Invariant Regularization and Hopf Symmetries
We consider the regularization of a gauge quantum field theory following a
modification of the Polchinski proof based on the introduction of a cutoff
function. We work with a Poincare' invariant deformation of the ordinary
point-wise product of fields introduced by Ardalan, Arfaei, Ghasemkhani and
Sadooghi, and show that it yields, through a limiting procedure of the cutoff
functions, to a regularized theory, preserving all symmetries at every stage.
The new gauge symmetry yields a new Hopf algebra with deformed co-structures,
which is inequivalent to the standard one.Comment: Revised version. 14 pages. Incorrect statements eliminate
A generalized Kac-Ward formula
The Kac-Ward formula allows to compute the Ising partition function on a
planar graph G with straight edges from the determinant of a matrix of size 2N,
where N denotes the number of edges of G. In this paper, we extend this formula
to any finite graph: the partition function can be written as an alternating
sum of the determinants of 2^{2g} matrices of size 2N, where g is the genus of
an orientable surface in which G embeds. We give two proofs of this generalized
formula. The first one is purely combinatorial, while the second relies on the
Fisher-Kasteleyn reduction of the Ising model to the dimer model, and on
geometric techniques. As a consequence of this second proof, we also obtain the
following fact: the Kac-Ward and the Fisher-Kasteleyn methods to solve the
Ising model are one and the same.Comment: 23 pages, 8 figures; minor corrections in v2; to appear in J. Stat.
Mech. Theory Ex
IL DIVIETO DI MATRIMONIO MISTO NEI DIRITTI RELIGIOSI:DIRITTO CANONICO E DIRITTO EBRAICO A CONFRONTO
Starting from an analysis of the discipline of the prohibition of mixed marriages in canon law and in jewish law, this research aims to clarify if, how and under what conditions the religious laws taken into consideration exceed the prohibition of mixed marriages and show characters of flexibility/dynamism and openness in attitude towards the followers of other faiths, and towards the followers of own faith, balancing authority and freedom
Error threshold in the evolution of diploid organisms
The effects of error propagation in the reproduction of diploid organisms are
studied within the populational genetics framework of the quasispecies model.
The dependence of the error threshold on the dominance parameter is fully
investigated. In particular, it is shown that dominance can protect the
wild-type alleles from the error catastrophe. The analysis is restricted to a
diploid analogue of the single-peaked landscape.Comment: 9 pages, 4 Postscript figures. Submitted to J. Phy. A: Mat. and Ge
Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution
In the theoretical biology framework one fundamental problem is the so-called
error catastrophe in Darwinian evolution models. We reexamine Eigen's
fundamental equations by mapping them into a polymer depinning transition
problem in a ``genotype'' space represented by a unitary hypercubic lattice.
The exact solution of the model shows that error catastrophe arises as a direct
consequence of the equations involved and confirms some previous qualitative
results. The physically relevant consequence is that such equations are not
adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors.
[email protected] (e-mail address
On measurement-based quantum computation with the toric code states
We study measurement-based quantum computation (MQC) using as quantum
resource the planar code state on a two-dimensional square lattice (planar
analogue of the toric code). It is shown that MQC with the planar code state
can be efficiently simulated on a classical computer if at each step of MQC the
sets of measured and unmeasured qubits correspond to connected subsets of the
lattice.Comment: 9 pages, 5 figure
Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants
We continue the discussion of the fermion models on graphs that started in
the first paper of the series. Here we introduce a Graphical Gauge Model (GGM)
and show that : (a) it can be stated as an average/sum of a determinant defined
on the graph over (binary) gauge field; (b) it is equivalent
to the Monomer-Dimer (MD) model on the graph; (c) the partition function of the
model allows an explicit expression in terms of a series over disjoint directed
cycles, where each term is a product of local contributions along the cycle and
the determinant of a matrix defined on the remainder of the graph (excluding
the cycle). We also establish a relation between the MD model on the graph and
the determinant series, discussed in the first paper, however, considered using
simple non-Belief-Propagation choice of the gauge. We conclude with a
discussion of possible analytic and algorithmic consequences of these results,
as well as related questions and challenges.Comment: 11 pages, 2 figures; misprints correcte
The Tangled Nature model as an evolving quasi-species model
We show that the Tangled Nature model can be interpreted as a general
formulation of the quasi-species model by Eigen et al. in a frequency dependent
fitness landscape. We present a detailed theoretical derivation of the mutation
threshold, consistent with the simulation results, that provides a valuable
insight into how the microscopic dynamics of the model determine the observed
macroscopic phenomena published previously. The dynamics of the Tangled Nature
model is defined on the microevolutionary time scale via reproduction, with
heredity, variation, and natural selection. Each organism reproduces with a
rate that is linked to the individuals' genetic sequence and depends on the
composition of the population in genotype space. Thus the microevolutionary
dynamics of the fitness landscape is regulated by, and regulates, the evolution
of the species by means of the mutual interactions. At low mutation rate, the
macro evolutionary pattern mimics the fossil data: periods of stasis, where the
population is concentrated in a network of coexisting species, is interrupted
by bursts of activity. As the mutation rate increases, the duration and the
frequency of bursts increases. Eventually, when the mutation rate reaches a
certain threshold, the population is spread evenly throughout the genotype
space showing that natural selection only leads to multiple distinct species if
adaptation is allowed time to cause fixation.Comment: Paper submitted to Journal of Physics A. 13 pages, 4 figure
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