Sequential Sparsening by Successive Adaptation in Neural Populations

In the principal cells of the insect mushroom body, the Kenyon cells (KC), olfactory information is represented by a spatially and temporally sparse code. Each odor stimulus will activate only a small portion of neurons and each stimulus leads to only a short phasic response following stimulus onset irrespective of the actual duration of a constant stimulus. The mechanisms responsible for the sparse code in the KCs are yet unresolved. Here, we explore the role of the neuron-intrinsic mechanism of spike-frequency adaptation (SFA) in producing temporally sparse responses to sensory stimulation in higher processing stages. Our single neuron model is defined through a conductance-based integrate-and-fire neuron with spike-frequency adaptation [1]. We study a fully connected feed-forward network architecture in coarse analogy to the insect olfactory pathway. A first layer of ten neurons represents the projection neurons (PNs) of the antenna lobe. All PNs receive a step-like input from the olfactory receptor neurons, which was realized by independent Poisson processes. The second layer represents 100 KCs which converge onto ten neurons in the output layer which represents the population of mushroom body extrinsic neurons (ENs). Our simulation result matches with the experimental observations. In particular, intracellular recordings of PNs show a clear phasic-tonic response that outlasts the stimulus [2] while extracellular recordings from KCs in the locust express sharp transient responses [3]. We conclude that the neuron-intrinsic mechanism is can explain a progressive temporal response sparsening in the insect olfactory system. Further experimental work is needed to test this hypothesis empirically. [1] Muller et. al., Neural Comput, 19(11):2958-3010, 2007. [2] Assisi et. al., Nat Neurosci, 10(9):1176-1184, 2007. [3] Krofczik et. al. Front. Comput. Neurosci., 2(9), 2009.Comment: 5 pages, 2 figures, This manuscript was submitted for review to the Eighteenth Annual Computational Neuroscience Meeting CNS*2009 in Berlin and accepted for oral presentation at the meetin

COMPARISON OF END-EXPIRATORY LUNG VOLUME MEASUREMENT BY ELECTRICAL IMPEDANCE TOMOGRAPHY AND NITROGEN WASHOUT METHOD IN PIGS

End-expiratory lung volume (EELV) can be determined using several methods that allow clinically accurate measurements, but it is difficult to apply these methods to the patient's bedside. Electrical impedance tomography (EIT) is offered as another method for measuring EELV. The aim of the study is to compare changes in EELV measured by nitrogen washout method with changes of EELV calculated from the change in end-expiratory lung impedance (EELI) measured by EIT and to determine whether changes in EELV calculated from changes in chest impedance can be used as one of the parameters for EIT data analysis and description. The prospective interventional animal study was performed on ten pigs. The animals received total intravenous anesthesia with muscle relaxation. Mechanical lung ventilation was conducted in the volume-controlled mode. 16-electrode EIT system was used for data acquisition. End-expiratory lung volume was measured by a modified nitrogen wash-in/wash-out technique developed by Olegard et al. The study protocol consisted of the baseline phase, two incremental PEEP steps, two decremental PEEP steps and from normal saline i. v. administration. For each animal, a reference frame (baseline frame) was selected from the initial baseline phase and was used for the reconstruction of EIT images and impedance waveforms. For each breath cycle, tidal variation image was calculated as a difference between the end-inspiratory and the previous end-expiratory EIT image. An equivalent end-expiratory volume change (ΔEELVequiv) was calculated from EELI. The values of ΔEELVequiv were compared with reference EELV data measured by a modified nitrogen wash-in/wash-out technique (ΔEELVmeas). The measured and the estimated changes in EELV were statistically compared and correlation between ΔEELVequiv and ΔEELVmeas was calculated. Statistically significant difference between ΔEELVequiv and ΔEELVmeas was observed only in administration of normal saline bolus. Pearson’s correlation coefficients were 0.29 for increase in PEEP, 0.45 for decrease in PEEP and -0.1 during administration of normal saline bolus. The study showed that during changes in PEEP in the porcine model, there was no linear relationship between ΔEELVequiv and ΔEELVmeas. Although there was no linear relationship between ΔEELVequiv and ΔEELVmeas with changes in PEEP, no statistically significant difference was demonstrated between these two methods, which justifies the use of ΔEELVequiv as a parameter suitable for description and evaluation of EIT data

Resolution in Focused Electron- and Ion-Beam Induced Chemical Vapor Deposition

The key physical processes governing resolution of focused electron-beam and ion-beam-assisted chemical vapor deposition are analyzed via an adsorption rate model. We quantify for the first time how the balance of molecule depletion and replenishment determines the resolution inside the locally irradiated area. Scaling laws are derived relating the resolution of the deposits to molecule dissociation, surface diffusion, adsorption, and desorption. Supporting results from deposition experiments with a copper metalorganic precursor gas on a silicon substrate are presented and discussed.Comment: 4 pages, 4 figures, 1 tabl

Feasibly constructive proofs of succinct weak circuit lower bounds

We ask for feasibly constructive proofs of known circuit lower bounds for explicit functions on bit strings of length n. In 1995 Razborov showed that many can be proved in PV1, a bounded arithmetic formalizing polynomial time reasoning. He formalized circuit lower bound statements for small n of doubly logarithmic order. It is open whether PV1 proves known lower bounds in succinct formalizations for n of logarithmic order. We give such proofs in APC1, an extension of PV1 formalizing probabilistic polynomial time reasoning: for parity and AC0, for mod q and AC0[p] (only for n slightly smaller than logarithmic), and for k-clique and monotone circuits. We also formalize Razborov and Rudich’s natural proof barrier. We ask for short propositional proofs of circuit lower bounds expressed succinctly by propositional formulas of size nO(1) or at least much smaller than the 2O(n) size of the common “truth table” formula. We discuss two such expressions: one via feasible functions witnessing errors of circuits, and one via the anticheckers of Lipton and Young 1994. Our APC1 formalizations yield conditional upper bounds for the succinct formulas obtained by witnessing: we get short Extended Frege proofs from general circuit lower bounds expressed by the common “truth-table” formulas. We also show how to construct in quasipolynomial time propositional proofs of quasipolynomial size tautologies expressing AC0[p] quasipolynomial size lower bounds; these proofs are in Jerábek’s system WF.Peer ReviewedPostprint (author's final draft

Polynomial time ultrapowers and the consistency of circuit lower bounds

A polynomial time ultrapower is a structure given by the set of polynomial time computable functions modulo some ultrafilter. They model the universal theory ∀PV of all polynomial time functions. Generalizing a theorem of Hirschfeld (Israel J Math 20(2):111–126, 1975), we show that every countable model of ∀PV is isomorphic to an existentially closed substructure of a polynomial time ultrapower. Moreover, one can take a substructure of a special form, namely a limit polynomial time ultrapower in the classical sense of Keisler (in: Bergelson, V., Blass, A., Di Nasso, M., Jin, R. (eds.) Ultrafilters across mathematics, contemporary mathematics vol 530, pp 163–179. AMS, New York, 1963). Using a polynomial time ultrapower over a nonstandard Herbrand saturated model of ∀PV we show that ∀PV is consistent with a formal statement of a polynomial size circuit lower bound for a polynomial time computable function. This improves upon a recent result of Krajíček and Oliveira (Logical methods in computer science 13 (1:4), 2017).Peer ReviewedPostprint (author's final draft

Automating Resolution is NP-hard

We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatizable unless P = NP. Indeed, we show that it is NP-hard to distinguish between formulas that have Resolution refutations of polynomial length and those that do not have subexponential length refutations. This also implies that Resolution is not automatizable in subexponential time or quasi-polynomial time unless~NP is included in SUBEXP or QP, respectively.Peer ReviewedPostprint (author's final draft

Sustained maintenance of somatotopic information in brain regions recruited by tactile working memory

To adaptively guide ongoing behavior, representations in working memory (WM) often have to be modified in line with changing task demands. We used event-related potentials (ERPs) to demonstrate that tactile WM representations are stored in modality-specific cortical regions, that the goal-directed modulation of these representations is mediated through hemispheric-specific activation of somatosensory areas, and that the rehearsal of somatotopic coordinates in memory is accomplished by modality-specific spatial attention mechanisms. Participants encoded two tactile sample stimuli presented simultaneously to the left and right hands, before visual retro-cues indicated which of these stimuli had to be retained to be matched with a subsequent test stimulus on the same hand. Retro-cues triggered a sustained tactile contralateral delay activity component with a scalp topography over somatosensory cortex contralateral to the cued hand. Early somatosensory ERP components to task-irrelevant probe stimuli (that were presented after the retro-cues) and to subsequent test stimuli were enhanced when these stimuli appeared at the currently memorized location relative to other locations on the cued hand, demonstrating that a precise focus of spatial attention was established during the selective maintenance of tactile events in WM. These effects were observed regardless of whether participants performed the matching task with uncrossed or crossed hands, indicating that WM representations in this task were based on somatotopic rather than allocentric spatial coordinates. In conclusion, spatial rehearsal in tactile WM operates within somatotopically organized sensory brain areas that have been recruited for information storage