On variables with few occurrences in conjunctive normal forms

We consider the question of the existence of variables with few occurrences in boolean conjunctive normal forms (clause-sets). Let mvd(F) for a clause-set F denote the minimal variable-degree, the minimum of the number of occurrences of variables. Our main result is an upper bound mvd(F) <= nM(surp(F)) <= surp(F) + 1 + log_2(surp(F)) for lean clause-sets F in dependency on the surplus surp(F). - Lean clause-sets, defined as having no non-trivial autarkies, generalise minimally unsatisfiable clause-sets. - For the surplus we have surp(F) <= delta(F) = c(F) - n(F), using the deficiency delta(F) of clause-sets, the difference between the number of clauses and the number of variables. - nM(k) is the k-th "non-Mersenne" number, skipping in the sequence of natural numbers all numbers of the form 2^n - 1. We conjecture that this bound is nearly precise for minimally unsatisfiable clause-sets. As an application of the upper bound we obtain that (arbitrary!) clause-sets F with mvd(F) > nM(surp(F)) must have a non-trivial autarky (so clauses can be removed satisfiability-equivalently by an assignment satisfying some clauses and not touching the other clauses). It is open whether such an autarky can be found in polynomial time. As a future application we discuss the classification of minimally unsatisfiable clause-sets depending on the deficiency.Comment: 14 pages. Revision contains more explanations, and more information regarding the sharpness of the boun

Multiple and plastic receptors mediate tonic GABAA receptor currents in the hippocampus

Persistent activation of GABAA receptors by extracellular GABA (tonic inhibition) plays a critical role in signal processing and network excitability in the brain. In hippocampal principal cells, tonic inhibition has been reported to be mediated by {alpha}5-subunit-containing GABAA receptors ({alpha}5GABAARs). Pharmacological or genetic disruption of these receptors improves cognitive performance, suggesting that tonic inhibition has an adverse effect on information processing. Here, we show that {alpha}5GABAARs contribute to tonic currents in pyramidal cells only when ambient GABA concentrations increase (as may occur during increased brain activity). At low ambient GABA concentrations, activation of {delta}-subunit-containing GABAA receptors predominates. In epileptic tissue, {alpha}5GABAARs are downregulated and no longer contribute to tonic currents under conditions of raised extracellular GABA concentrations. Under these conditions, however, the tonic current is greater in pyramidal cells from epileptic tissue than in pyramidal cells from nonepileptic tissue, implying substitution of {alpha}5GABAARs by other GABAA receptor subtypes. These results reveal multiple components of tonic GABAA receptor-mediated conductance that are activated by low GABA concentrations. The relative contribution of these components changes after the induction of epilepsy, implying an adaptive plasticity of the tonic current in the presence of spontaneous seizures

Perioperative infection prophylaxis and risk factor impact in colon surgery

Background: A prospective observational study was undertaken in 2,481 patients undergoing elective colon resection in 114 German centers to identify optimal drug and dosing modalities and risk factors for postoperative infection. Methods: Patients were pair matched using six risk factors and divided into 672 pairs (ceftriaxone vs, other cephalosporins, group A) and 400 pairs (ceftriaxone vs. penicillins, group B). End points were local and systemic postoperative infection and cost effectiveness. Results: Local infection rates were 6.0 versus 6.5% (group A) and 4.0 versus 10.5% (group B); systemic infection rates in groups A and B were 4.9 versus 6.3% and 3.3 versus 10.5%, respectively. Ceftriaxone was more effective than penicillins overall (6.8 vs. 17.8%, p < 0.001). Length of postoperative hospital stay was 16.2 versus 16.9 days (group A) and 15.8 versus 17.6 days (group B). Of the six risk factors, age and concomitant disease were significant for systemic infection, and blood loss, rectum resection and immunosuppressive therapy were significant for local infection. Penicillin was a risk factor compared to ceftriaxone (p < 0.0001). Ceftriaxone saved Q160.7 versus other cephalosporins and O416.2 versus penicillins. Conclusion: Clinical and microbiological efficacy are responsible for the cost effectiveness of ceftriaxone for perioperative prophylaxis in colorectal surgery. Copyright (C) 2000 S. Karger AG, Basel

Activity clamp provides insights into paradoxical effects of the anti-seizure drug carbamazepine

A major challenge in experimental epilepsy research is to reconcile the effects of anti-epileptic drugs (AEDs) on individual neurons with their network-level actions. Highlighting this difficulty, it is unclear why carbamazepine (CBZ), a front-line AED with a known molecular mechanism, has been reported to increase epileptiform activity in several clinical and experimental studies. We confirmed in an in vitro mouse model (both sexes) that the frequency of interictal bursts increased following CBZ perfusion. To address the underlying mechanisms we developed a method, activity clamp, to distinguish the response of individual neurons from network-level actions of CBZ. We first recorded barrages of synaptic conductances from neurons during epileptiform activity, and then replayed them in pharmacologically isolated neurons under control conditions and in the presence of CBZ. CBZ consistently decreased the reliability of the second action potential in each burst of activity. Conventional current clamp recordings using excitatory ramp or square step current injections failed to reveal this effect. Network modelling showed that a CBZ-induced decrease of neuron recruitment during epileptic bursts can lead to an increase in burst frequency at the network level, by reducing the refractoriness of excitatory transmission. By combining activity clamp with computer simulations, the present study provides a potential explanation for the paradoxical effects of CBZ on epileptiform activity.SIGNIFICANCE STATEMENTThe effects of anti-epileptic drugs on individual neurons are difficult to separate from their network-level actions. Although carbamazepine has a known anti-epileptic mechanism, it has also been reported to paradoxically increase epileptiform activity in clinical and experimental studies. To investigate this paradox during realistic neuronal epileptiform activity we developed a method, activity clamp, to distinguish effects of carbamazepine on individual neurons from network-level actions. We demonstrate that carbamazepine consistently decreases the reliability of the second action potential in each burst of epileptiform activity. Network modelling shows that this effect on individual neuronal responses could explain the paradoxical effect of carbamazepine at the network level

The mass of odd-odd nuclei in microscopic mass models

Accurate estimates of the binding energy of nuclei far from stability that cannot be produced in the laboratory are crucial to our understanding of nuclear processes in astrophysical scenarios. Models based on energy density functionals have shown that they are capable of reproducing all known masses with root-mean-square error better than 800 keV, while retaining a firm microscopic foundation. However, it was recently pointed out in [M. Hukkanen et al., arXiv:2210.10674] that the recent BSkG1 model fails to account for a contribution to the binding energy that is specific to odd-odd nuclei, and which can be studied by using appropriate mass difference formulas. We analyse here the (lacking) performance of three recent microscopic mass models with respect to such formulas and examine possibilities to remedy this deficiency in the future.Comment: 6 pages, 2 figures; Contribution to the proceedings of INPC 2022, Cape Town, South Afric

Dysfunction of the CaV2.1 calcium channel in cerebellar ataxias

Mutations in the CACNA1A gene are associated with episodic ataxia type 2 (EA2) and spinocerebellar ataxia type 6 (SCA6). CACNA1A encodes the α-subunit of the P/Q-type calcium channel or CaV2.1, which is highly enriched in the cerebellum. It is one of the main channels linked to synaptic transmission throughout the human central nervous system. Here, we compare recent advances in the understanding of the genetic changes that underlie EA2 and SCA6 and what these new findings suggest about the mechanism of the disease

Macrostate Data Clustering

We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to the metastable macroscopic states (macrostates) of a diffusive system. A "minimum uncertainty criterion" determines the linear transformation from eigenvectors to cluster-defining window functions. Eigenspectrum gap and cluster certainty conditions identify the proper number of clusters. The physically motivated fuzzy representation and associated uncertainty analysis distinguishes macrostate clustering from spectral partitioning methods. Macrostate data clustering solves a variety of test cases that challenge other methods.Comment: keywords: cluster analysis, clustering, pattern recognition, spectral graph theory, dynamic eigenvectors, machine learning, macrostates, classificatio

LISA Metrology System - Final Report

Gravitational Waves will open an entirely new window to the Universe, different from all other astronomy in that the gravitational waves will tell us about large-scale mass motions even in regions and at distances totally obscured to electromagnetic radiation. The most interesting sources are at low frequencies (mHz to Hz) inaccessible on ground due to seismic and other unavoidable disturbances. For these sources observation from space is the only option, and has been studied in detail for more than 20 years as the LISA concept. Consequently, The Gravitational Universe has been chosen as science theme for the L3 mission in ESA's Cosmic Vision program. The primary measurement in LISA and derived concepts is the observation of tiny (picometer) pathlength fluctuations between remote spacecraft using heterodyne laser interferometry. The interference of two laser beams, with MHz frequency difference, produces a MHz beat note that is converted to a photocurrent by a photodiode on the optical bench. The gravitational wave signal is encoded in the phase of this beat note. The next, and crucial, step is therefore to measure that phase with µcycle resolution in the presence of noise and other signals. This measurement is the purpose of the LISA metrology system and the subject of this report

Evolving networks with disadvantaged long-range connections

We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at distance $d$ is proportional to $d^{-\alpha}$, where $\alpha$ is a tunable parameter of the model. We show that the properties of the networks grown with $\alpha <1$ are close to those of the genuine scale-free construction, while for $\alpha >1$ the structure of the network is vastly different. Thus, in this regime, the node degree distribution is no more a power law, and it is well-represented by a stretched exponential. On the other hand, the small-world property of the growing networks is preserved at all values of $\alpha$.Comment: REVTeX, 6 pages, 5 figure