123 research outputs found
Response to Invasion by Antigen and Effects of Threshold in an Immune Network Dynamical System Model with a Small Number of Degrees of Freedom
We study a dynamical system model of an idiotypic immune network with a small
number of degrees of freedom, mainly focusing on the effect of a threshold
above which antibodies can recognise antibodies. The response of the system to
invasions by antigens is investigated in the both models with and without the
threshold and it turns out that the system changes in a desirable direction for
moderate magnitude of perturbation. direction for moderate magnitude of
perturbation. Also, the propagation of disturbance by an antigen is
investigated in the system of one-dimensionally connected basic units taking
the closed 3-clone system as a unit, and it is clarified that the threshold of
the system has effects to enhance the stability of the network and to localise
the immune response.Comment: 6 pages, 6 figures. Submitted to Prog. Theor. Phy
Diagonalization of replicated transfer matrices for disordered Ising spin systems
We present an alternative procedure for solving the eigenvalue problem of
replicated transfer matrices describing disordered spin systems with (random)
1D nearest neighbor bonds and/or random fields, possibly in combination with
(random) long range bonds. Our method is based on transforming the original
eigenvalue problem for a matrix (where ) into an
eigenvalue problem for integral operators. We first develop our formalism for
the Ising chain with random bonds and fields, where we recover known results.
We then apply our methods to models of spins which interact simultaneously via
a one-dimensional ring and via more complex long-range connectivity structures,
e.g. dimensional neural networks and `small world' magnets.
Numerical simulations confirm our predictions satisfactorily.Comment: 24 pages, LaTex, IOP macro
Hierarchical Self-Programming in Recurrent Neural Networks
We study self-programming in recurrent neural networks where both neurons
(the `processors') and synaptic interactions (`the programme') evolve in time
simultaneously, according to specific coupled stochastic equations. The
interactions are divided into a hierarchy of groups with adiabatically
separated and monotonically increasing time-scales, representing sub-routines
of the system programme of decreasing volatility. We solve this model in
equilibrium, assuming ergodicity at every level, and find as our
replica-symmetric solution a formalism with a structure similar but not
identical to Parisi's -step replica symmetry breaking scheme. Apart from
differences in details of the equations (due to the fact that here
interactions, rather than spins, are grouped into clusters with different
time-scales), in the present model the block sizes of the emerging
ultrametric solution are not restricted to the interval , but are
independent control parameters, defined in terms of the noise strengths of the
various levels in the hierarchy, which can take any value in [0,\infty\ket.
This is shown to lead to extremely rich phase diagrams, with an abundance of
first-order transitions especially when the level of stochasticity in the
interaction dynamics is chosen to be low.Comment: 53 pages, 19 figures. Submitted to J. Phys.
Statistical Mechanics of Soft Margin Classifiers
We study the typical learning properties of the recently introduced Soft
Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the
tools of Statistical Mechanics. We derive analytically the behaviour of the
learning curves in the regime of very large training sets. We obtain
exponential and power laws for the decay of the generalization error towards
the asymptotic value, depending on the task and on general characteristics of
the distribution of stabilities of the patterns to be learned. The optimal
learning curves of the SMCs, which give the minimal generalization error, are
obtained by tuning the coefficient controlling the trade-off between the error
and the regularization terms in the cost function. If the task is realizable by
the SMC, the optimal performance is better than that of a hard margin Support
Vector Machine and is very close to that of a Bayesian classifier.Comment: 26 pages, 12 figures, submitted to Physical Review
Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models
We present an analytically solvable random graph model in which the
connections between the nodes can evolve in time, adiabatically slowly compared
to the dynamics of the nodes. We apply the formalism to finite connectivity
attractor neural network (Hopfield) models and we show that due to the
minimisation of the frustration effects the retrieval region of the phase
diagram can be significantly enlarged. Moreover, the fraction of misaligned
spins is reduced by this effect, and is smaller than in the infinite
connectivity regime. The main cause of this difference is found to be the
non-zero fraction of sites with vanishing local field when the connectivity is
finite.Comment: 17 pages, 8 figure
Slowly evolving geometry in recurrent neural networks I: extreme dilution regime
We study extremely diluted spin models of neural networks in which the
connectivity evolves in time, although adiabatically slowly compared to the
neurons, according to stochastic equations which on average aim to reduce
frustration. The (fast) neurons and (slow) connectivity variables equilibrate
separately, but at different temperatures. Our model is exactly solvable in
equilibrium. We obtain phase diagrams upon making the condensed ansatz (i.e.
recall of one pattern). These show that, as the connectivity temperature is
lowered, the volume of the retrieval phase diverges and the fraction of
mis-aligned spins is reduced. Still one always retains a region in the
retrieval phase where recall states other than the one corresponding to the
`condensed' pattern are locally stable, so the associative memory character of
our model is preserved.Comment: 18 pages, 6 figure
Rapid land use conversion in the Cerrado has affected water transparency in a hotspot of ecotourism, Bonito, Brazil.
Abstract: Background: Brazil is the largest exporter of soybeans worldwide. Albeit its economic importance, soybean expansion has led to important land use and land cover changes. In this paper, we evaluate the impact of soybean expansion on ecotourism, using as a case study of the Prata River (Bonito), Brazil; tourist destination where over 30,000 tourists per year came to float in crystal waters. Methods: We first evaluated land cover and land use change in the region between 2010 and 2020, checking how and where soybean plantations have expanded. Second, based on monthly data of water transparency of the Prata River, Bonito, we created five possible models considering monthly rainfall and three categories of soybean expansion (slow, rapid and medium). The models were tested through generalized linear regression analysis and ranked through AIC and AIC weight. Results: Our results show that soybean expanded from occupying 4% of the river basin in 2010 to 23% in 2020, expanding mostly over pasture areas (31%) and native vegetation (12.9%). We also showed that while soybean plantation was expanding rapid between 2014 and 2016, it played a significant role in increasing the number of days the water in the Prata River was classified as very turbid. Conclusion: Our results emphasize the need for soybean expansion planning, considering better management of the soil (nontilling), common agreements between different stakeholders and the scale up of initiatives that are already in place in the region (e.g. planning of the locations of legal reserves in a way that complement the environmental protection areas (e.g. Aguas de Bonito), seting aside of conservation areas ("Area Priorit ´ aria Banhados") and payment for ecosystem service schemes) . Implications for conservation: Our research shows the importance of considering the different impacts soybean may have on the landscape. We present clear paths to reduce possible economic and environmental impacts, and present the importance to scale up innitiatives that are already in place in the region, such as payment for ecosystem services schemes and protection of watersheds
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