A note on palindromic δ\delta-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart $\delta$-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact.Comment: 4 page

A note on palindromic δ-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact

A note on palindromic δ-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact

A note on palindromic δ-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact

Immobilisation of electrochemically active bacteria on screen-printed electrodes for rapid in situ toxicity biosensing

Microbial biosensors can be an excellent alternative to classical methods for toxicity monitoring, which are time-consuming and not sensitive enough. However, bacteria typically connect to electrodes through biofllm formation, leading to problems due to lack of uniformity or long device production times. A suitable immobilisation technique can overcome these challenges. Still, they may respond more slowly than biofllm-based electrodes because bacteria gradually adapt to electron transfer during biofllm formation. In this study, we propose a controlled and reproducible way to fabricate bacteria-modified electrodes. The method consists of an immobilisation step using a cellulose matrix, followed by an electrode polarization in the presence of ferricyanide and glucose. Our process is short, reproducible and led us to obtain ready-to-use electrodes featuring a high-current response. An excellent shelf-life of the immobilised electrochemically active bacteria was demonstrated for up to one year. After an initial 50% activity loss in the first month, no further declines have been observed over the following 11 months. We implemented our bacteria-modified electrodes to fabricate a lateral flow platform for toxicity monitoring using formaldehyde (3%). Its addition led to a 59% current decrease approximately 20 min after the toxic input. The methods presented here offer the ability to develop a high sensitivity, easy to produce, and long shelf life bacteria-based toxicity detectors. (C) 2020 The Author(s). Published by Elsevier B.V. on behalf of Chinese Society for Environmental Sciences, Harbin Institute of Technology, Chinese Research Academy of Environmental Sciences

Influence of Alkali-Silica reaction (ASR) on aggregate interlock and shear-friction behavior of reinforced concrete members

Alkali-silica reaction (ASR) is one of the most damaging mechanisms affecting concrete structures worldwide. ASR effects on the durability and serviceability of damaged concrete are widely known and fairly well understood. However, the structural implications are still unclear, and a number of contradictory data are found in the literature, especially regarding shear behavior. The influence of ASR distressed reinforced concrete on aggregate interlock is presented in this paper. Push-off specimens having different transverse reinforcement ratios were fabricated with ASR reactive coarse aggregates. The specimens were monitored over time and displayed different levels of expansion. Results indicated that ASR-induced expansion and damage were affected by the transverse reinforcement ratio. However, little to no aggregate interlock reduction was observed on ASR-affected specimens up to moderate expansion levels (about 0.12%). It was found that there were two controlling and competing mechanisms that affected aggregate interlock for ASR-affected specimens: the beneficial effects of chemical prestressing and the detrimental ASR-induced damage

General anesthesia, sleep and coma

In the United States, nearly 60,000 patients per day receive general anesthesia for surgery.1 General anesthesia is a drug-induced, reversible condition that includes specific behavioral and physiological traits — unconsciousness, amnesia, analgesia, and akinesia — with concomitant stability of the autonomic, cardiovascular, respiratory, and thermoregulatory systems.2 General anesthesia produces distinct patterns on the electroencephalogram (EEG), the most common of which is a progressive increase in low-frequency, high-amplitude activity as the level of general anesthesia deepens3,4 (Figure 1Figure 1Electroencephalographic (EEG) Patterns during the Awake State, General Anesthesia, and Sleep.). How anesthetic drugs induce and maintain the behavioral states of general anesthesia is an important question in medicine and neuroscience.6 Substantial insights can be gained by considering the relationship of general anesthesia to sleep and to coma. Humans spend approximately one third of their lives asleep. Sleep, a state of decreased arousal that is actively generated by nuclei in the hypothalamus, brain stem, and basal forebrain, is crucial for the maintenance of health.7,8 Normal human sleep cycles between two states — rapid-eye-movement (REM) sleep and non-REM sleep — at approximately 90-minute intervals. REM sleep is characterized by rapid eye movements, dreaming, irregularities of respiration and heart rate, penile and clitoral erection, and airway and skeletal-muscle hypotonia.7 In REM sleep, the EEG shows active high-frequency, low-amplitude rhythms (Figure 1). Non-REM sleep has three distinct EEG stages, with higher-amplitude, lower-frequency rhythms accompanied by waxing and waning muscle tone, decreased body temperature, and decreased heart rate. Coma is a state of profound unresponsiveness, usually the result of a severe brain injury.9 Comatose patients typically lie with eyes closed and cannot be roused to respond appropriately to vigorous stimulation. A comatose patient may grimace, move limbs, and have stereotypical withdrawal responses to painful stimuli yet make no localizing responses or discrete defensive movements. As the coma deepens, the patient's responsiveness even to painful stimuli may diminish or disappear. Although the patterns of EEG activity observed in comatose patients depend on the extent of the brain injury, they frequently resemble the high–amplitude, low-frequency activity seen in patients under general anesthesia10 (Figure 1). General anesthesia is, in fact, a reversible drug-induced coma. Nevertheless, anesthesiologists refer to it as “sleep” to avoid disquieting patients. Unfortunately, anesthesiologists also use the word “sleep” in technical descriptions to refer to unconsciousness induced by anesthetic drugs.11 (For a glossary of terms commonly used in the field of anesthesiology, see the Supplementary Appendix, available with the full text of this article at NEJM.org.) This review discusses the clinical and neurophysiological features of general anesthesia and their relationships to sleep and coma, focusing on the neural mechanisms of unconsciousness induced by selected intravenous anesthetic drugs.Massachusetts General Hospital. Dept. of Anesthesia and Critical Care, and Pain MedicineNational Institutes of Health (NIH) (Director’s Pioneer Award DP1OD003646)University of Michigan. Dept. of AnesthesiologyNational Institutes of Health (U.S.) (grant HL40881)National Institutes of Health (U.S.) (grant HL65272)James S. McDonnell FoundationNational Institutes of Health (U.S.) (grant HD51912

Prospective object search in dogs: mixed evidence for knowledge of What and Where

We investigated whether two dogs that had been specially trained to retrieve objects by their names were able to integrate information about the identity (What) as well as the location (Where) of those objects so that they could plan their search accordingly. In a first study, two sets of objects were placed in two separate rooms and subjects were asked to retrieve the objects, one after the other. Both dogs remembered the identity of the objects as they reliably retrieved the correct objects. One of the dogs was also able to integrate information about the object’s location as he chose the correct location in which the object had been placed. Further investigation of the second dog’s behavior revealed that she followed a more stereotyped search strategy. Despite this variation in performance, this study provides evidence for the memory of What and Where in a domestic dog and shows the prospective use of such information in a search task

Deuteron life-time in hot and dense nuclear matter near equilibrium

We consider deuteron formation in hot and dense nuclear matter close to equilibrium and evaluate the life-time of the deuteron fluctuations within the linear response theory. To this end we derive a generalized linear Boltzmann equation where the collision integral is related to equilibrium correlation functions. In this framework we then utilize finite temperature Green functions to evaluate the collision integrals. The elementary reaction cross section is evaluated within the Faddeev approach that is suitably modified to reflect the properties of the surrounding hot and dense matter.Comment: 15 pages, 5 figure

Culture shapes how we look at faces

Background: Face processing, amongst many basic visual skills, is thought to be invariant across all humans. From as early as 1965, studies of eye movements have consistently revealed a systematic triangular sequence of fixations over the eyes and the mouth, suggesting that faces elicit a universal, biologically-determined information extraction pattern. Methodology/Principal Findings: Here we monitored the eye movements of Western Caucasian and East Asian observers while they learned, recognized, and categorized by race Western Caucasian and East Asian faces. Western Caucasian observers reproduced a scattered triangular pattern of fixations for faces of both races and across tasks. Contrary to intuition, East Asian observers focused more on the central region of the face. Conclusions/Significance: These results demonstrate that face processing can no longer be considered as arising from a universal series of perceptual events. The strategy employed to extract visual information from faces differs across cultures