arXiv subjects

Claudius Gros

Publications and source records attributed to Claudius Gros.

At least 91 records · Page 5Linked to original sources

arXiv2010

Tunnelling matrix elements with antiferromagnetic Gutzwiller wave functions

We use a generalized Gutzwiller Approximation (GA) elaborated to evaluate matrix elements with partially projected wave functions and formerly applied to homogeneous systems. In the present paper we consider projected single-particle (hole) excitations for electronic systems with antiferromagnetic (AFM) order and obtain the corresponding tunnelling probabilities. The accuracy and the reliability of our analytical approximation is tested using the Variational Monte Carlo (VMC). Possible comparisons with experimental results are also discussed.

cond-mat.str-el↗

arXiv2010

Self-organized chaos through polyhomeostatic optimization

The goal of polyhomeostatic control is to achieve a certain target distribution of behaviors, in contrast to polyhomeostatic regulation which aims at stabilizing a steady-state dynamical state. We consider polyhomeostasis for individual and networks of firing-rate neurons, adapting to achieve target distributions of firing rates maximizing information entropy. We show that any finite polyhomeostatic adaption rate destroys all attractors in Hopfield-like network setups, leading to intermittently bursting behavior and self-organized chaos. The importance of polyhomeostasis to adapting behavior in general is discussed.

cond-mat.dis-nn↗

arXiv2010

Interaction induced Fermi-surface renormalization in the $t_1{-}t_2$ Hubbard model close to the Mott-Hubbard transition

We investigate the nature of the interaction-driven Mott-Hubbard transition of the half-filled $t_1{-}t_2$ Hubbard model in one dimension, using a full-fledged variational Monte Carlo approach including a distance-dependent Jastrow factor and backflow correlations. We present data for the evolution of the magnetic properties across the Mott-Hubbard transition and on the commensurate to incommensurate transition in the insulating state. Analyzing renormalized excitation spectra, we find that the Fermi surface renormalizes to perfect nesting right at the Mott-Hubbard transition in the insulating state, with a first-order reorganization when crossing into the conducting state.

cond-mat.str-el↗

arXiv2010

Cognition and Emotion: Perspectives of a Closing Gap

The primary tasks of a cognitive system is to survive and to maximize a life-long utility function, like the number of offsprings. A direct computational maximization of life-long utility is however not possible in complex environments, especially in the context, of real-world time constraints. The central role of emotions is to serve as an intermediate layer in the space of policies available to agents and animals, leading to a large dimensional reduction of complexity. We review our current understanding of the functional role of emotions, stressing the role of the neuromodulators mediating emotions for the diffusive homeostatic control system of the brain. We discuss a recent proposal, that emotional diffusive control is characterized, in contrast to neutral diffusive control, by interaction effects, viz by interferences between emotional arousal and reward signaling. Several proposals for the realization of synthetic emotions are discussed in this context, together with key open issues regarding the interplay between emotional motivational drives and diffusive control.

q-bio.NC↗

arXiv2009

Spin-liquid and magnetic phases in the anisotropic triangular lattice: the case of $κ$-(ET)$_2$X

The two-dimensional Hubbard model on the anisotropic triangular lattice, with two different hopping amplitudes $t$ and $t^\prime$, is relevant to describe the low-energy physics of $κ$-(ET)$_2$X, a family of organic salts. The ground-state properties of this model are studied by using Monte Carlo techniques, on the basis of a recent definition of backflow correlations for strongly-correlated lattice systems. The results show that there is no magnetic order for reasonably large values of the electron-electron interaction $U$ and frustrating ratio $t^\prime/t = 0.85$, suitable to describe the non-magnetic compound with X=Cu$_2$(CN)$_3$. On the contrary, Néel order takes place for weaker frustrations, i.e., $t^\prime/t \sim 0.4 ÷0.6$, suitable for materials with X=Cu$_2$(SCN)$_2$, Cu[N(CN)$_2$]Cl, or Cu[N(CN)$_2$]Br.

cond-mat.str-el↗

arXiv2009

Vertex routing models

A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed by cyclic attractors, allowing to define a measure for the information centrality of a vertex given by the number of attractors passing through this vertex. We find the number of vertices having a non-zero information centrality to be extensive/sub-extensive for models with/without a memory trace in the thermodynamic limit. We evaluate the distribution of the number of cycles, of the cycle length and of the maximal basins of attraction, finding a complete scaling collapse in the thermodynamic limit for the latter. Possible implications of our results on the information flow in social networks are discussed.

physics.soc-ph↗

arXiv2009

Emotions, diffusive emotional control and the motivational problem for autonomous cognitive systems

All self-active living beings need to solve the motivational problem: The question what to do at any moment of their live. For humans and non-human animals at least two distinct layers of motivational drives are known, the primary needs for survival and the emotional drives leading to a wide range of sophisticated strategies, such as explorative learning and socializing. Part of the emotional layer of drives has universal facets, being beneficial in an extended range of environmental settings. Emotions are triggered in the brain by the release of neuromodulators, which are, at the same time, the agents for meta-learning. This intrinsic relation between emotions, meta-learning and universal action strategies suggests a central importance for emotional control for the design of artificial intelligences and synthetic cognitive systems. An implementation of this concept is proposed in terms of a dense and homogeneous associative network (dHan).

q-bio.NC↗

arXiv2009

Cognitive computation with autonomously active neural networks: an emerging field

The human brain is autonomously active. To understand the functional role of this self-sustained neural activity, and its interplay with the sensory data input stream, is an important question in cognitive system research and we review here the present state of theoretical modelling. This review will start with a brief overview of the experimental efforts, together with a discussion of transient vs. self-sustained neural activity in the framework of reservoir computing. The main emphasis will be then on two paradigmal neural network architectures showing continuously ongoing transient-state dynamics: saddle point networks and networks of attractor relics. Self-active neural networks are confronted with two seemingly contrasting demands: a stable internal dynamical state and sensitivity to incoming stimuli. We show, that this dilemma can be solved by networks of attractor relics based on competitive neural dynamics, where the attractor relics compete on one side with each other for transient dominance, and on the other side with the dynamical influence of the input signals. Unsupervised and local Hebbian-style online learning then allows the system to build up correlations between the internal dynamical transient states and the sensory input stream. An emergent cognitive capability results from this set-up. The system performs online, and on its own, a non-linear independent component analysis of the sensory data stream, all the time being continuously and autonomously active. This process maps the independent components of the sensory input onto the attractor relics, which acquire in this way a semantic meaning.

q-bio.NC↗

arXiv2008

Evolving complex networks with conserved clique distributions

We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We evaluate the statistical properties of the graphs generated, such as the degree distribution and network diameters, and compare them to some real-world graphs.

physics.soc-ph↗

arXiv2008

Proposed low energy model Hamiltonian for spin-gapped system CuTe2O5

Using first-principles electronic structure calculations based on the Nth order muffin tin orbital (NMTO)-downfolding technique, we derived the low-energy spin model for CuTe2O5. Our study reveals that this compound is a 2D coupled spin-dimer system with the strongest Cu-Cu interaction mediated by two O-Te-O bridges. We checked the goodness of our model by computing the magnetic susceptibility with the Quantum Monte Carlo technique and by comparing it with available experimental data. We also present magnetization and specific heat results which may be compared with future experimental investigations. Our derived model is in disagreement with a recently proposed model for this compound [J. Deisenhofer et al, Phys. Rev. B,74 (2006) 174421]. The situation needs to be settled in terms of further experimental investigations.

cond-mat.mtrl-sci↗

arXiv2008

Learning in cognitive systems with autonomous dynamics

The activity patterns of highly developed cognitive systems like the human brain are dominated by autonomous dynamical processes, that is by a self-sustained activity which would be present even in the absence of external sensory stimuli. During normal operation the continuous influx of external stimuli could therefore be completely unrelated to the patterns generated internally by the autonomous dynamical process. Learning of spurious correlations between external stimuli and autonomously generated internal activity states needs therefore to be avoided. We study this problem within the paradigm of transient state dynamics for the internal activity, that is for an autonomous activity characterized by a infinite time-series of transiently stable attractor states. We propose that external stimuli will be relevant during the sensitive periods, the transition period between one transient state and the subsequent semi-stable attractor. A diffusive learning signal is generated unsupervised whenever the stimulus influences the internal dynamics qualitatively. For testing we have presented to the model system stimuli corresponding to the bar-stripes problem and found it capable to perform the required independent-component analysis on its own, all the time being continuously and autonomously active.

q-bio.NC↗

arXiv2007

Neural networks with transient state dynamics

We investigate dynamical systems characterized by a time series of distinct semi-stable activity patterns, as they are observed in cortical neural activity patterns. We propose and discuss a general mechanism allowing for an adiabatic continuation between attractor networks and a specific adjoined transient-state network, which is strictly dissipative. Dynamical systems with transient states retain functionality when their working point is autoregulated; avoiding prolonged periods of stasis or drifting into a regime of rapid fluctuations. We show, within a continuous-time neural network model, that a single local updating rule for online learning allows simultaneously (i) for information storage via unsupervised Hebbian-type learning, (ii) for adaptive regulation of the working point and (iii) for the suppression of runaway synaptic growth. Simulation results are presented; the spontaneous breaking of time-reversal symmetry and link symmetry are discussed.

cond-mat.dis-nn↗

arXiv2007

Self-Sustained Thought Processes in a Dense Associative Network

Several guiding principles for thought processes are proposed and a neural-network-type model implementing these principles is presented and studied. We suggest to consider thinking within an associative network built-up of overlapping memory states. We consider a homogeneous associative network as biological considerations rule out distinct conjunction units between the information (the memories) stored in the brain. We therefore propose that memory states have a dual functionality: They represent on one side the stored information and serve, on the other side, as the associative links in between the different dynamical states of the network which consists of transient attractors. We implement these principles within a generalized winners-take-all neural network with sparse coding and an additional coupling to local reservoirs. We show that this network is capable to generate autonomously a self-sustained time-series of memory states which we identify with a thought process. Each memory state is associatively connected with its predecessor. This system shows several emerging features, it is able (a) to recognize external patterns in a noisy background, (b) to focus attention autonomously and (c) to represent hierarchical memory states with an internal structure.

q-bio.NC↗

arXiv2007

Autonomous Dynamics in Neural networks: The dHAN Concept and Associative Thought Processes

The neural activity of the human brain is dominated by self-sustained activities. External sensory stimuli influence this autonomous activity but they do not drive the brain directly. Most standard artificial neural network models are however input driven and do not show spontaneous activities. It constitutes a challenge to develop organizational principles for controlled, self-sustained activity in artificial neural networks. Here we propose and examine the dHAN concept for autonomous associative thought processes in dense and homogeneous associative networks. An associative thought-process is characterized, within this approach, by a time-series of transient attractors. Each transient state corresponds to a stored information, a memory. The subsequent transient states are characterized by large associative overlaps, which are identical to acquired patterns. Memory states, the acquired patterns, have such a dual functionality. In this approach the self-sustained neural activity has a central functional role. The network acquires a discrimination capability, as external stimuli need to compete with the autonomous activity. Noise in the input is readily filtered-out. Hebbian learning of external patterns occurs coinstantaneous with the ongoing associative thought process. The autonomous dynamics needs a long-term working-point optimization which acquires within the dHAN concept a dual functionality: It stabilizes the time development of the associative thought process and limits runaway synaptic growth, which generically occurs otherwise in neural networks with self-induced activities and Hebbian-type learning rules.

q-bio.NC↗

arXiv2006

Spontaneous breaking of the Fermi surface symmetry in the t-J model: a numerical study

We present a variational Monte Carlo (VMC) study of spontaneous Fermi surface symmetry breaking in the t-J model. We find that the variational energy of a Gutzwiller projected Fermi sea is lowered by allowing for a finite asymmetry between the x- and the y-directions. However, the best variational state remains a pure superconducting state with d-wave symmetry, as long as the underlying lattice is isotropic. Our VMC results are in good overall agreement with slave boson mean field theory (SBMFT) and renormalized mean field theory (RMFT), although apparent discrepancies do show up in the half-filled limit, revealing some limitations of mean field theories. VMC and complementary RMFT calculations also confirm the SBMFT predictions that many-body interactions can enhance any anisotropy in the underlying crystal lattice. Thus, our results may be of consequence for the description of strongly correlated superconductors with an anisotropic lattice structure.

cond-mat.str-el↗

arXiv2006

The Mott-Hubbard Transition on the D=infinity Bethe Lattice

In view of a recent controversy we investigated the Mott-Hubbard transition in D=infinity with a novel cluster approach. i) We show that any truncated Bethe lattice of order n can be mapped exactly to a finite Hubbard-like cluster. ii) We evaluate the self-energy numerically for n=0,1,2 and compare with a series of self-consistent equation-of-motion solutions. iii) We find the gap to open continously at the critical U_c~2.5t* (t = t* / sqrt{4d}). iv) A low-energy theory for the Mott-Hubbard transition is developed and relations between critical exponents are presented.

cond-mat.str-el↗

arXiv2006

Determining the underlying Fermi surface of strongly correlated superconductors

The notion of a Fermi surface (FS) is one of the most ingenious concepts developed by solid state physicists during the past century. It plays a central role in our understanding of interacting electron systems. Extraordinary efforts have been undertaken, both by experiment and by theory, to reveal the FS of the high temperature superconductors (HTSC), the most prominent strongly correlated superconductors. Here, we discuss some of the prevalent methods used to determine the FS and show that they lead generally to erroneous results close to half filling and at low temperatures, due to the large superconducting gap (pseudogap) below (above) the superconducting transition temperature. Our findings provide a perspective on the interplay between strong correlations and superconductivity and highlight the importance of strong coupling theories for the characterization as well as the determination of the underlying FS in ARPES experiments.

cond-mat.supr-con↗

arXiv2006

Electronic structure of strongly correlated d-wave superconductors

We study the electronic structure of a strongly correlated d-wave superconducting state. Combining a renormalized mean field theory with direct calculation of matrix elements, we obtain explicit analytical results for the nodal Fermi velocity, v_F, the Fermi wave vector, k_F, and the momentum distribution, n_k, as a function of hole doping in a Gutzwiller projected d-wave superconductor. We calculate the energy dispersion, E_k, and spectral weight of the Gutzwiller-Bogoliubov quasiparticles, and find that the spectral weight associated with the quasiparticle excitation at the antinodal point shows a non monotonic behavior as a function of doping. Results are compared to angle resolved photoemission spectroscopy (ARPES) of the high temperature superconductors.

cond-mat.supr-con↗