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Non-Hermitian systems give rise to distinct topological phenomena, yet their manifestations at temporal interfaces characterized by abrupt changes in system parameters remain largely unex plored. Upon an abrupt alteration of the Hamiltonian…
A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function.…
One of the main challenges in the study of time-varying networks is the interplay of memory effects with structural heterogeneity. In particular, different nodes and dyads can have very different statistical properties in terms of both link…
Evolution in changing environments is an important, but little studied aspect of the theory of evolution. The idea of adaptive walks in fitness landscapes has triggered a vast amount of research and has led to many important insights about…
Metazoans are capable of gathering information from their environments and respond in predictable ways. These computational tasks are achieved by means of more or less complex networks of neurons. Task performance must be reliable over an…
Interface migration governs microstructural evolution during phase transformations and grain growth thereby dictating those material properties that depend on microstructure. Recent work continues to highlight the rich range of behaviors…
We report short-term memory formation in a nonlinear dynamical system with many degrees of freedom. The system ``remembers'' a sequence of impulses for a transient period, but it coarsens and eventually ``forgets'' nearly all of them. The…
Collective motion of cells is critical to some of the most vital tasks including wound healing, development, and immune response [Friedl and Gilmour 2009; Tokarski et al. 2012; Lee et al. 2012; Beltman et al. 2009], and is common to many…
We explore the connection between evolution and large-deviation theory. To do so, we study evolutionary dynamics in which individuals experience mutations, reproduction, and selection using variants of the Moran model. We show that, in the…
Emergent behavior in active systems is a complex byproduct of local, often pairwise, interactions. One such interaction is self-avoidance, which experimentally can arise as a response to self-generated environmental signals; such…
Learning and memory relies on synapses changing their strengths in response to neural activity. However there is a substantial gap between the timescales of neural electrical dynamics (1-100 ms) and organism behaviour during learning…
Time-calibrated species phylogenies are critical for addressing a wide range of questions in evolutionary biology, such as those that elucidate historical biogeography or uncover patterns of coevolution and diversification. Because…
Information gathered along a path is inherently submodular; the incremental amount of information gained along a path decreases due to redundant observations. In addition to submodularity, the incremental amount of information gained is a…
Evolutionary dynamics on graphs can lead to many interesting and counterintuitive findings. We study the Moran process, a discrete time birth-death process, that describes the invasion of a mutant type into a population of wild-type…
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the…
Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and…
Despite contending with constraints imposed by the environment, morphology, and physiology, animals move well by physically interactingwith the environment to use and transition between modes such as running, climbing, and self-righting. By…
Neural correlations during a cognitive task are central to study brain information processing and computation. However, they have been poorly analyzed due to the difficulty of recording simultaneous single neurons during task performance.…
Organisms may respond to local stimuli that benefit or threaten their fitness. The adaptive movement behaviour may allow individuals to adjust their speed to maximise the chances of being in comfort zones, where death risk is minimal. We…
A central problem in open quantum systems is the characterization of non-Markovian processes, where an environment retains the memory of its interaction with the system. A key distinction is whether or not this memory can be simulated…