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1 small number of important industrial metals (attractors).
2 ctions are greatly eased from that of a line attractor.
3 imulus information is not a fixed-point type attractor.
4 and the groups of nodes that determine each attractor.
5 with tumor grade, and a lymphocyte-specific attractor.
6 ctivity arises from a low-dimensional spiral attractor.
7 lls both as a plane attractor and as a point attractor.
8 f two species when the model has an interior attractor.
9 characteristics of the underlying dynamical attractor.
10 rticular node all models lead to an extended attractor.
11 t directional phase shifting around a cyclic attractor.
12 of preceding destabilization of a progenitor attractor.
13 sory cues (i.e. the landmarks) onto the ring attractor.
14 regulatory genes induced a jump to a nearby attractor.
15 of teaching is to make the content taught an attractor.
16 failed to correlate with either the NE or ML attractors.
17 ions, which we show are composed of discrete attractors.
18 esponse curves, tipping points and alternate attractors.
19 most probable transition paths between those attractors.
20 ction is limited by the demand for the major attractors.
21 works (GRNs) at the boundary between dynamic attractors.
22 duced switch between high-dimensional cancer attractors.
23 in computes using low-dimensional continuous attractors.
24 n the presence of latent "ghost" multistable attractors.
25 n of two networks that have adopted distinct attractors.
26 nearly instantaneously moving cells between attractors.
27 inct, stable, self-maintaining states called attractors.
28 ing rates of insects, thus creating multiple attractors.
29 r critical states, for instance, the network attractors.
30 point, instead of being obligatory resource attractors.
31 r fragment M12039 were identified as primary attractors.
32 repellors and decelerating costs may lead to attractors.
33 is driven to the respective, now accessible attractors.
34 run behavior of a BN is characterized by its attractors.
35 ttern separation and memory storage via bump attractors.
36 characterize the detailed structure of cell attractors.
37 onnective evolution end in non-modular local attractors.
38 urating neurons and their convergence toward attractors.
39 ed set of variables that control the size of attractors (a proxy for resilience), such as population
40 ecies may be drawn towards a single midpoint attractor - a unimodal gradient of environmental favoura
41 on attractor structure composed of singleton attractors, a control algorithm is derived by minimizing
42 ion D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate o
45 n transitions between a silent and an active attractor and assumed that neurons fired Poisson spike t
46 altered the transition rate into the silent attractor and reproduced the relation between correlatio
47 ition of each year in relation to the fitted attractors and assumed tipping points of the fold bifurc
49 dynamical systems theory and the concepts of attractors and repellors, we develop an understanding of
51 works, including analysis of the state space attractors and the basin of attraction of each attractor
52 be understood by finding stable steady-state attractors and the most probable transition paths betwee
54 These stable patterns function as 'dynamic attractors' and provide a feature that is characteristic
55 d as a ring attractor, grid cells as a plane attractor, and place cells both as a plane attractor and
56 non-additive modelling to estimate alternate attractors, and a quantitative resilience assessment to
57 nger doubling time than ones at the new pole attractor; and (5) the robust growth state identified by
58 o test experimentally whether any particular attractor architecture resides in any particular brain c
63 ed units express the spontaneous dynamics of attractor assemblies transitioning between distinct acti
66 dic memory [13-18], has been associated with attractor-based computations [5, 9], receiving support f
67 ene expression fluctuation occurs on or near attractor basin boundaries (the points of instability).
69 ives rise to a deep, smooth potential energy attractor basin that pulls toward the native structure.
70 etworks, such as being able to produce large attractor basins, can be useful for maintaining a stable
74 dify the network characteristics, especially attractors, by introducing a judicious change to the fun
76 demonstrate that the switching rate between attractors can be significantly influenced by the gene e
77 In case (iii), the dimension of the chaotic attractors can be very high, implying that the learning
80 These dynamics have led to the cancer cell attractor conceptual model, with implications for both c
81 t - a spiral - in which it behaved as a true attractor, converging to the same orbit when evoked, and
82 ssesses multiple metastable attractors, each attractor corresponding to a different spatial firing pa
83 his shape space predicts transitions between attractors corresponding to abrupt reversals in crawling
87 ess that converges to one of several precise attractors defining signatures representing biomolecular
88 ith the hypothesis that schizophrenia is an "attractor" disease and demonstrate that degraded neurona
89 be modeled using oscillatory interference or attractor dynamic mechanisms that perform path integrati
90 tive feedback loops, thereby elucidating the attractor (dynamic behavior) repertoire of the system an
91 on cognition by altering prefrontal cortical attractor dynamics according to an inverted U-shaped fun
92 whether human memory retrieval is driven by attractor dynamics and what neural mechanisms might unde
96 he hippocampal circuit and popular models of attractor dynamics in CA3 suggests a mechanistic explana
97 t is dramatically amplified by reverberating attractor dynamics in neural circuits for stimulus categ
99 n ambiguous novel context relate to putative attractor dynamics in the hippocampus, which support the
101 t, providing a concrete visualization of the attractor dynamics involved in language processing.
102 pace and offer experimental support for bump attractor dynamics mediating cognitive tasks in the cort
103 We consider the stochastic long-timescale attractor dynamics of pairs of mutually inhibitory popul
104 k of interacting head direction neurons, but attractor dynamics predict a winner-take-all decision be
105 , to date, no demonstration exists that bump attractor dynamics underlies spatial working memory.
106 se results is that sensory cortex implements attractor dynamics, although this proposal remains contr
108 od reason to believe that the brain displays attractor dynamics, it has proven difficult to test expe
109 of general interest to neuroscience, such as attractor dynamics, temporal coding and multi-modal inte
117 twork dynamics possesses multiple metastable attractors, each attractor corresponding to a different
120 by Wang et al. corresponds to our predicted attractor for lineages harboring the maternal old pole.
122 We show that the critical state becomes an attractor for these networks, which points toward the on
123 loped a neural network model of the CA3 with attractors for both position and discrete contexts.
125 as barriers and locally cooler areas act as attractors for trajectories, creating source and sink ar
127 te the location and strength of the midpoint attractor from species occurrence data sampled along mou
128 and time-delay phase maps of low dimensional attractors graphically depict the sequence between perio
129 -direction cells have been modeled as a ring attractor, grid cells as a plane attractor, and place ce
130 e attractor state; (4) cells at the old pole attractor had a longer doubling time than ones at the ne
131 tractors and the basin of attraction of each attractor, has mainly focused on synchronous update of t
132 be equivalent to the existence of a positive attractor i.e. an attractor bounded away from extinction
133 me attractors that are unrelated to parental attractors, implying that cell fusion can create new cel
134 network models of GRNs and to compute their attractors impose specific assumptions that cannot be ea
137 st whether memories are stored as multimodal attractors in populations of place cells, recent experim
138 lity, i.e., the coexistence of two different attractors in the phase space of the system correspondin
142 ntly long delay times, the optimal number of attractors is less than the number of possible stimuli,
145 d, the stability of these states represents "attractor"-like states along a dynamic landscape that is
148 y cortex is organized into a small number of attractor-like neuronal assemblies, whose responses can
149 of a phase transition, and the emergence of attractor-like structure in the inferred energy landscap
150 ngle spatial map, position-dependent context attractors made transitions at different points along th
157 pure oscillatory interference and continuous attractor models, and provides testable predictions for
158 rid fields are produced by slow ramps, as in attractor models, whereas theta oscillations control spi
160 in PMd emerge from the coactivation of such attractor modules, heterogeneous in the strength of loca
161 nal transmission between a linked continuous attractor network and competitive network acts as a timi
162 ssociative memory model CA3 as a homogeneous attractor network because of its strong recurrent circui
163 t the head direction cells may be part of an attractor network bound more strongly to distal landmark
164 s of grid-like maps were proposed, including attractor network dynamics, interactions with theta osci
165 Third, although our decision model is an attractor network exhibiting winner-take-all competition
166 previously developed biophysically detailed attractor network exhibits spontaneous oscillations in t
167 iophysically informed model of a competitive attractor network for decision making, we found that dec
169 bservations, combined with simulations of an attractor network grid cell model, demonstrate that land
170 ort the conjecture of Hafting et al. that an attractor network in dMEC may be the source of path inte
175 g firing field traversals, whereas competing attractor network models predict slow depolarizing ramps
177 Here, we discuss evidence for continuous attractor network models that account for grid firing by
178 cue interactions are thought to occur on an attractor network of interacting head direction neurons,
181 l cortex, we simulated an integrate-and-fire attractor network taking decisions between competing inp
183 ly conflicting results are commensurate with attractor network theory, we developed a neural network
188 ippocampus has been postulated to be such an attractor network; however, the experimental evidence ha
189 natomical arrangement are suggestive of ring attractors, network structures that have been proposed t
192 diluted connectivity affects the dynamics of attractor networks in the cerebral cortex, we simulated
193 ions, associative synaptic modification, and attractor networks in which the storage capacity is in t
195 y derive how the stored memory in continuous attractor networks of probabilistically spiking neurons
196 mes in the sequence, suggesting that spiking attractor networks of this type can support an efficient
198 ty can be understood by considering cells as attractor networks whose basic property is to adopt a se
200 aracteristic of decision states in recurrent attractor networks, and its possible relevance to consci
201 ignificance in many processes represented by attractor networks, including biological, social, and po
202 ften crucial for the stability of the single attractor networks, we have uncovered that the funneled
204 scenario for modeling memory function is the attractor neural network scenario, whose prototype is th
206 decision-making, sharing a common recurrent (attractor) neural circuit mechanism with discrimination
207 diameter is proposed to be formed of a local attractor neuronal network with a capacity in the order
208 fferent mechanisms of escape from the stable attractors occur in the nonadiabatic, weakly adiabatic,
210 egafauna are arguably considered the primary attractor of ecotourists to sub-Saharan African protecte
211 oreceptor cells, ketocholesterol is a potent attractor of macrophages and induces macrophages to expr
213 wo pure strategies; this polymorphism is the attractor of the standard replicator dynamics operating
221 en viewed as coming from transitions between attractors on an epigenetic landscape that governs the d
222 ions predicted that the network settles into attractors, or TF expression patterns, that correlate wi
223 erate a BN possessing the selected states as attractors, perhaps with some added requirements such as
224 pped as dynamical states clustered around an attractor point in gene expression space, owing to a bal
226 gree distribution and the number of periodic attractors produced determine the relative complexity of
229 In particular we focus on when evolutionary attractors, repellors and branching points occur and how
230 ronments made of different materials creates attractor representations for both shapes: Place cells a
232 el that demonstrates that alternative stable attractors, representing the ictal and postictal states,
234 he boundary between the two lineage-specific attractors; second, the cell is driven to the respective
235 athematical model to capture such biological attractor selection and derive a generic, adaptive and d
236 We show that the proposed scheme based on attractor selection can not only promote the balance of
238 nd provides a deep understanding of adaptive attractor selection-based control formation that is usef
239 with similar preferred directions as a ring attractor, so that their relative phases remain constant
240 increases in monoamine efflux would enhance attractor stability, whereas high frontal monoamine leve
242 he destabilization of their high-dimensional attractor state, such that differentiating cells undergo
243 ed to that of the median cells, revealing an attractor state, they lasted long enough to confer a gre
246 the maternal old pole converged to a stable attractor state; (3) lineages receiving sequentially the
247 pole converged to an equivalent but separate attractor state; (4) cells at the old pole attractor had
248 unless it was switched to its "pathological" attractor state; thus, although the underlying pathology
249 to calculate rates of switching between two attractor states and enables an accurate simulation of t
250 back inhibition, which not only instantiates attractor states for forming categorical choices but als
254 eterogeneity can be specified dynamically by attractor states of a master regulatory TF network.
255 scuss these results in the light of possible attractor states of gene expression and how this would a
256 tive responses, as well as the robustness of attractor states of networks of neurons performing memor
258 rithm; and check the concordance between the attractor states of the designed network and the data st
262 ble, both in time and space, indicating that attractor states were still present despite the lack of
263 w inward current that allowed for two stable attractor states, one corresponding to quiescence and th
267 mor stage, a mitotic chromosomal instability attractor strongly associated with tumor grade, and a ly
268 fined in all cases: a mesenchymal transition attractor strongly associated with tumor stage, a mitoti
269 mily of Boolean networks possessing a common attractor structure composed of singleton attractors, a
272 a under the constraint that they all possess attractor structures matching the data states, which are
273 I propose an alternate mechanism to a line attractor that allows the network to hold the value of a
274 directed motion mode resembles a limit cycle attractor that is independent of its initial condition.
275 ate during a trial suggests that the type of attractor that is responsible for holding the stimulus i
276 le the probability of the system being in an attractor that lies within prescribed boundaries decreas
277 We find that the hybrid networks can assume attractors that are unrelated to parental attractors, im
278 this structure is a situation of alternative attractors that remain qualitatively robust over a signi
279 m offers a substantial advantage over a line attractor: The tuning requirements of cell to cell conne
280 ctuations orthogonal to the persistent state attractor, thereby causing minimal stochastic drift.
281 continuously changed states within their own attractor, thus driving the repopulation, as shown by fl
282 er perturbation to drive the system from one attractor to another, assuming that the former is undesi
283 ceptualized as automatic, bottom-up resource attractors to on-beat times-preparatory neural activity
284 lity of their gene expression configuration (attractor) to exit the attractor in one direction remain
285 is proposed in which meta-stable sequential attractor transitions are learned through changes to syn
287 ulating Boolean network models and obtaining attractors under different assumptions by successfully r
288 the mechanisms that move the system between attractors using both the quasipotential and the probabi
289 the impact on network state transitions and attractors via analytical approaches or identify a pertu
290 s should be related to switches in ecosystem attractors; we present a new spectral density ratio indi
291 hybrid networks are prone to assume spurious attractors, which are emergent and sporadic network stat
292 ll cases strongly accelerating costs lead to attractors while strongly decelerating ones lead to repe
293 be equivalent to permanence i.e. a positive attractor whose basin of attraction includes all positiv
294 networks asymptotically either approaches an attractor with fixed waveform and amplitude, or fails to
297 memory can be supported by overlapping local attractors within a spatial map of CA3 place cells.
299 biological diversity and that the number of attractors within the phase space exponentially increase
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