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"Hartmann, Alexander"
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مدارس التحليل النفسي : التحليل النفسي في حركة مستمرة
ما هو دور الجمعية الدولية للتحليل النفسي؟ لماذا توجد مدارس واتجاهات متعددة تدعي اتباع تعاليم فرويد؟ هل إنكار الدور الأساسي للجنس الطفولي هو أصل كل الانشقاق؟ من المرجح أن تؤدي الاختلافات بين مدارس التحليل النفسي إلى إرباك القارئ الساذج في هذا المجال وتستمر في التسبب في مشاكل للمحللين النفسيين أنفسهم. في حين أنه من السهل إظهار كيف أن يونج أدلر. رايخ وغيره، منفصلين عن فرويد في النقاط النظرية الأساسية، وليس فقط في المسائل التفصيلية، فمن الصعب جدا الإجابة على هذا السؤال: هل هناك نظرية أفضل من غيرها، أم لا بد من أنه يعتقد أنه لا توجد نظرية في الوقت الحاضر.
Book
Large-deviations of disease spreading dynamics with vaccination
We numerically simulated the spread of disease for a Susceptible-Infected-Recovered (SIR) model on contact networks drawn from a small-world ensemble. We investigated the impact of two types of vaccination strategies, namely random vaccination and high-degree heuristics, on the probability density function (pdf) of the cumulative number C of infected people over a large range of its support. To obtain the pdf even in the range of probabilities as small as 10 −80 , we applied a large-deviation approach, in particular the 1/ t Wang-Landau algorithm. To study the size-dependence of the pdfs within the framework of large-deviation theory, we analyzed the empirical rate function. To find out how typical as well as extreme mild or extreme severe infection courses arise, we investigated the structures of the time series conditioned to the observed values of C .
Journal Article
Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks
A regime of coexistence of asynchronous and clustered dynamics is analysed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is based on accurate extensive simulations and complemented by a mean-field description in terms of low-dimensional next generation neural mass models for heterogeneously distributed synaptic couplings. The asynchronous regime is observable at low noise and becomes unstable via a sub-critical Hopf bifurcation at sufficiently large noise. This gives rise to a coexistence region between the asynchronous and the clustered regime. The clustered phase is characterised by population bursts in the γ -range (30–120 Hz), where neurons are split in two equally populated clusters firing in alternation. This clustering behaviour is quite peculiar: despite the global activity being essentially periodic, single neurons display switching between the two clusters due to heterogeneity and/or noise.
Journal Article
Time-dependent probability density function for partial resetting dynamics
Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage times to a target. Recently the concept of partial resetting, in which the particle is reset to a given fraction of the current value of the process, has been established and the associated search behaviour analysed. Here we go one step further and we develop a general technique to determine the time-dependent probability density function (PDF) for Markov processes with partial resetting. We obtain an exact representation of the PDF in the case of general symmetric Lévy flights with stable index 0 < α ⩽ 2 . For Cauchy and Brownian motions (i.e. α = 1 , 2 ), this PDF can be expressed in terms of elementary functions in position space. We also determine the stationary PDF. Our numerical analysis of the PDF demonstrates intricate crossover behaviours as function of time.
Journal Article
Phase transitions of the typical algorithmic complexity of the random satisfiability problem studied with linear programming
Here we study linear programming applied to the random K-SAT problem, a fundamental problem in computational complexity. The K-SAT problem is to decide whether a Boolean formula with N variables and structured as a conjunction of M clauses, each being a disjunction of K variables or their negations is satisfiable or not. The ensemble of random K-SAT attracted considerable interest from physicists because for a specific ratio αs = M/N it undergoes in the limit of large N a sharp phase transition from a satisfiable to an unsatisfiable phase. In this study we will concentrate on finding for linear programming algorithms \"easy-hard\" transitions between phases of different typical hardness of the problems on either side. Linear programming is widely applied to solve practical optimization problems, but has been only rarely considered in the physics community. This is a deficit, because those typically studied types of algorithms work in the space of feasible {0, 1}N configurations while linear programming operates outside the space of valid configurations hence gives a very different perspective on the typical-case hardness of a problem. Here, we demonstrate that the technique leads to one simple-to-understand transition for the well known 2-SAT problem. On the other hand we detect multiple transitions in 3-SAT and 4-SAT. We demonstrate that, in contrast to the previous work on vertex cover and therefore somewhat surprisingly, the hardness transitions are not driven by changes of any of various standard percolation or solution space properties of the problem instances. Thus, here a more complex yet undetected property must be related to the easy-hard transition.
Journal Article
Non-analytic behaviour in large-deviations of the susceptible-infected-recovered model under the influence of lockdowns
We numerically investigate the dynamics of an SIR model with infection level-based lockdowns on Small-World networks. Using a large-deviation approach, namely the Wang–Landau algorithm, we study the distribution of the cumulative fraction of infected individuals. We are able to resolve the density of states for values as low as 10 −85 . Hence, we measure the distribution on its full support giving a complete characterization of this quantity. The lockdowns are implemented by severing a certain fraction of the edges in the Small-World network, and are initiated and released at different levels of infection, which are varied within this study. We observe points of non-analytical behaviour for the pdf and discontinuous transitions for correlations with other quantities such as the maximum fraction of infected and the duration of outbreaks. Further, empirical rate functions were calculated for different system sizes, for which a convergence is clearly visible indicating that the large-deviation principle is valid for the system with lockdowns.
Journal Article
Distribution of the Number of Paths in Two-Dimensional Directed Percolation
In a percolating system, there are typically exponentially many spanning paths. Here, we study numerically, for a two-dimensional L×L diluted system, restricted to percolating realizations, the number N of directed percolating paths. First, we study the average entropy ⟨S⟩=⟨logN⟩ as a function of the occupation density p and compare with mathematical results from the literature. Furthermore, we investigate the distribution P(S). By using large-deviation approaches, we are able to obtain P(S) down to the very low-probability tail reaching probabilities as small as 10−300. We consider the percolating phase, the (typically) non-percolating phase, and the critical point. Finally, we also analyze the structure of the realizations for some values of S and p.
Journal Article
Large-deviation properties of the largest biconnected component for random graphs
Abstract We study the size of the largest biconnected components in sparse Erdős–Rényi graphs with finite connectivity and Barabási–Albert graphs with non-integer mean degree. Using a statistical-mechanics inspired Monte Carlo approach we obtain numerically the distributions for different sets of parameters over almost their whole support, especially down to the rare-event tails with probabilities far less than 10−100. This enables us to observe a qualitative difference in the behavior of the size of the largest biconnected component and the largest 2-core in the region of very small components, which is unreachable using simple sampling methods. Also, we observe a convergence to a rate function even for small sizes, which is a hint that the large deviation principle holds for these distributions. Graphical abstract
Journal Article
Large-deviation properties of resilience of power grids
We study the distributions of the resilience of power flow models against transmission line failures via a so-called backup capacity. We consider three ensembles of random networks, and in addition, the topology of the British transmission power grid. The three ensembles are Erd s-Rényi random graphs, Erd s-Rényi random graphs with a fixed number of links, and spatial networks where the nodes are embedded in a two-dimensional plane. We numerically investigate the probability density functions (pdfs) down to the tails to gain insight into very resilient and very vulnerable networks. This is achieved via large-deviation techniques, which allow us to study very rare values that occur with probability densities below 10−160. We find that the right tail of the pdfs towards larger backup capacities follows an exponential with a strong curvature. This is confirmed by the rate function, which approaches a limiting curve for increasing network sizes. Very resilient networks are basically characterized by a small diameter and a large power sign ratio. In addition, networks can be made typically more resilient by adding more links.
Journal Article
Easy-hard phase transition in parameter estimation for optical waveguides
The determination of the parameters of cylindrical optical waveguides, e.g. the diameters
d
→
=
(
d
1
,
…
,
d
r
)
of
r
layers of (semi-) transparent optical fibres, can be executed by inverse evaluation of the scattering intensities that emerge under monochromatic illumination. The inverse problem can be solved by optimising the mismatch
R
(
d
→
)
between the measured and simulated scattering patterns. The global optimum corresponds to the correct parameter values. The mismatch
R
(
d
→
)
can be seen as an
energy landscape
as a function of the diameters. In this work, we study the structure of the energy landscape for different values of the complex refractive indices
n
→
, for
r
=
1
and
r
=
2
layers. We find that for both values of
r
, depending on the values of
n
→
, two very different types of energy landscapes exist, respectively. One type is dominated by one global minimum and the other type exhibits a multitude of local minima. From an algorithmic viewpoint, this corresponds to
easy
and
hard
phases, respectively. Our results indicate that the two phases are separated by sharp phase-transition lines and that the shape of these lines can be described by one “critical” exponent
b
, which depends slightly on
r
. Interestingly, the same exponent also describes the dependence of the number of local minima on the diameters. Thus, our findings are comparable to previous theoretical studies on easy-hard transitions in basic combinatorial optimisation or decision problems like
Travelling Salesperson
and
Satisfiability
. To our knowledge our results are the first indicating the existence of easy-hard transitions for a real-world optimisation problem of technological relevance.
Journal Article