Accumulating evidence across multiple sensory modalities suggests that the thalamus does not simply relay information from the periphery to the cortex. Here we review recent findings showing that vestibular neurons wi...
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The availability and quality of channel state information heavily influences the performance of wireless communication systems. For perfect channel knowledge, optimal signal processing and coding schemes are well stud...
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ISBN:
(纸本)9781509066315
The availability and quality of channel state information heavily influences the performance of wireless communication systems. For perfect channel knowledge, optimal signal processing and coding schemes are well studied and often closed-form solutions are known. On the other hand, the case of imperfect channel information is much less understood and closed-form solutions remain unknown in general. This paper approaches this question from a fundamental, algorithmic point of view to study whether or not such optimal schemes can be found algorithmically in principle (without putting any constraints on the computational complexity of such algorithms). To this end, the compound channel is considered as a model for channel uncertainty and it is shown that although the compound channel itself is a computable channel, the corresponding capacity is not computable in general, i.e., there exists no algorithm or Turing machine that takes the channel as an input and computes the corresponding capacity. As an implication of this, it is then shown that for such compound channels, there are no effectively constructible optimal signal processing and coding schemes that achieve the capacity. This is particularly noteworthy as such schemes must exist (since the capacity is known), but they cannot be effectively, i.e., algorithmically, constructed.
It is a classic result in algorithmic information theory that every infinite binary sequence is computable from an infinite binary sequence which is random in the sense of Martin-Lof. If the computation of the first n...
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It is a classic result in algorithmic information theory that every infinite binary sequence is computable from an infinite binary sequence which is random in the sense of Martin-Lof. If the computation of the first n bits of a sequence requires n + g(n) bits of the random oracle, then g is the redundancy of the computation. We devise a new coding method that achieves optimal logarithmic redundancy. For any computable non-decreasing function g such that Sigma(i) 2(-g(i)) is bounded we show that there is a coding process that codes any given infinite binary sequence into a Martin-Lof random infinite binary sequence with redundancy g. This redundancy bound is known to be the best possible. (C) 2017 Elsevier Inc. All rights reserved.
Applying the method of optimal non-linear filtering and majorized algorithm, this paper discusses the optimal control of a generalized stochastic process;which yields two optimal control mathematical models and illust...
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ISBN:
(纸本)9781538669532
Applying the method of optimal non-linear filtering and majorized algorithm, this paper discusses the optimal control of a generalized stochastic process;which yields two optimal control mathematical models and illustrated how to establish the optimal coding and *** provides an effective and reliable approach for the optimal control of such a process.
Ion channels play essential roles toward determining how neurons respond to sensory input to mediate perception and behavior. Small conductance calcium-activated potassium (SK) channels are found ubiquitously througho...
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Ion channels play essential roles toward determining how neurons respond to sensory input to mediate perception and behavior. Small conductance calcium-activated potassium (SK) channels are found ubiquitously throughout the brain and have been extensively characterized both molecularly and physiologically in terms of structure and function. It is clear that SK channels are key determinants of neural excitability as they mediate important neuronal response properties such as spike frequency adaptation. However, the functional roles of the different known SK channel subtypes are not well understood. Here we review recent evidence from the electrosensory system of weakly electric fish suggesting that the function of different SK channel subtypes is to optimize the processing of independent but behaviorally relevant stimulus attributes. Indeed, natural sensory stimuli frequently consist of a fast time-varying waveform (i.e., the carrier) whose amplitude (i.e., the envelope) varies slowly and independently. We first review evidence showing how somatic SK2 channels mediate tuning and responses to carrier waveforms. We then review evidence showing how dendritic SK1 channels instead determine tuning and optimize responses to envelope waveforms based on their statistics as found in the organism's natural environment in an independent fashion. The high degree of functional homology between SK channels in electric fish and their mammalian orthologs, as well as the many important parallels between the electrosensory system and the mammalian visual, auditory, and vestibular systems, suggest that these functional roles are conserved across systems and species.
The article makes use of nonlinear filter theory and reviews the best control of being quadratic functional linear systems under the condition of incomplete number and continuous time and obtains two best control math...
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ISBN:
(纸本)9781509060610
The article makes use of nonlinear filter theory and reviews the best control of being quadratic functional linear systems under the condition of incomplete number and continuous time and obtains two best control mathematic models which contain quadratic boss functions under tow cases. It also provides another effective probability statistic method to the best statistic decision.
Here we sketch a new derivation of Zipf's law for word frequencies based on optimal coding. The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages ove...
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Here we sketch a new derivation of Zipf's law for word frequencies based on optimal coding. The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it starts from realistic cognitive pressures, (2) it does not require fine tuning of parameters, and (3) it sheds light on the origins of other statistical laws of language and thus can lead to a compact theory of linguistic laws. Our findings suggest that the recurrence of Zipf's law in human languages could originate from pressure for easy and fast communication. (c) 2016 Wiley Periodicals, Inc. Complexity 21: 409-411, 2016
The repertoire of lymphocyte receptors in the adaptive immune system protects organisms from diverse pathogens. A well-adapted repertoire should be tuned to the pathogenic environment to reduce the cost of infections....
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The repertoire of lymphocyte receptors in the adaptive immune system protects organisms from diverse pathogens. A well-adapted repertoire should be tuned to the pathogenic environment to reduce the cost of infections. We develop a general framework for predicting the optimal repertoire that minimizes the cost of infections contracted from a given distribution of pathogens. The theory predicts that the immune system will have more receptors for rare antigens than expected from the frequency of encounters;individuals exposed to the same infections will have sparse repertoires that are largely different, but nevertheless exploit cross-reactivity to provide the same coverage of antigens;and the optimal repertoires can be reached via the dynamics of competitive binding of antigens by receptors and selective amplification of stimulated receptors. Our results follow from a tension between the statistics of pathogen detection, which favor a broader receptor distribution, and the effects of cross-reactivity, which tend to concentrate the optimal repertoire onto a few highly abundant clones. Our predictions can be tested in high-throughput surveys of receptor and pathogen diversity.
A common computation in visual cortex is the divisive normalization of responses by a pooled signal of the activity of cells within its neighborhood From a geometrical point of view normalization constraints the popul...
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A common computation in visual cortex is the divisive normalization of responses by a pooled signal of the activity of cells within its neighborhood From a geometrical point of view normalization constraints the population response to high-contrast stimuli to lie on the surface of a high-dimensional sphere Here we study the implications this constraint imposes on the representation of a circular variable such as the orientation of a visual stimulus New results are derived for the infinite dimensional case of a homogeneous populations of neurons with identical tuning curves but different orientation preferences An important finding is that the ability of the population to discriminate between any two orientations depends exclusively on the Fourier amplitude spectrum of the orientation tuning curve We also study the problem of encoding by a finite set of neurons A central result is that under normalization optimal encoding can be achieved by a finite number of neurons with heterogeneous tuning curves In other words increasing the number of neurons in the population does not always allow for an improved population code These results are used to estimate the number of neurons involved in the coding of orientation at one position in the visual field If the cortex were to code orientation optimally we find that a small number (similar to 4) of neurons should suffice (C) 2010 Elsevier Ltd All rights reserved
The temporal pattern of amplitude modulations (AM) is often used to recognize acoustic objects. To identify objects reliably, intensity invariant representations have to be formed. We approached this problem within th...
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The temporal pattern of amplitude modulations (AM) is often used to recognize acoustic objects. To identify objects reliably, intensity invariant representations have to be formed. We approached this problem within the auditory pathway of grasshoppers. We presented AM patterns modulated at different time scales and intensities. Metric space analysis of neuronal responses allowed us to determine how well, how invariantly, and at which time scales AM frequency is encoded. We find that in some neurons spike-count cues contribute substantially (20-60%) to the decoding of AM frequency at a single intensity. However, such cues are not robust when intensity varies. The general intensity invariance of the system is poor. However, there exists a range of AM frequencies around 83 Hz where intensity invariance of local interneurons is relatively high. In this range, natural communication signals exhibit much variation between species, suggesting an important behavioral role for this frequency band. We hypothesize, just as has been proposed for human speech, that the communication signals might have evolved to match the processing properties of the receivers. This contrasts with optimal coding theory, which postulates that neuronal systems are adapted to the statistics of the relevant signals.
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