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I am studying Noether’s theorem in field theory and I am not understanding what spacelike-surfaces mean. I will reproduce the bit of the argument below that contains the term “spacelike-sufaces” in the context I am not understanding.

There will be a conserved ccurrent for each group generator $a$. Each will result in a conserved charge (that is, an integral of motion). To see this, take in spacetime a volume unbounded in the space-like direction, but limited in time by two space-like surfaces $w_1$ and $w_2$. Integrating $\partial_{\mu} J^{\mu}_a=0$ over this volume, we get an integral over the boundary surface, composed of $w_1$, $w_2$ and the time-like boundaries supposed to be at infinity. If we now suppose the current to be zero at infinity on these boundaries, we remain with.

$$\int_{w_1}d\sigma_{\mu} J^{\mu}_a=\int_{w_2}d\sigma_{\mu} J^{

Genome editing is a powerful breeding technique that introduces mutations into specific gene sequences in genomes. For genome editing in higher plants, nucleotides for artificial nuclease (e.g. TALEN or CRISPR-Cas9) are transiently or stably introduced into the plant cells. After the introduction of mutations by artificial nucleases, it is necessary to select lines that do not contain the foreign nucleotides to overcome GMO regulation; however, there is still no widely legally authorized and approved method for detecting foreign genes in genome-edited crops. Recently, k-mer analysis based on next-generation sequencing (NGS) was proposed as a new method for detecting foreign DNA in genome-edited agricultural products. Compared to conventional methods, such as PCR and Southern hybridization, in principle, this method can detect short DNA fragments with high accuracy.

The classic film “Alien” was once promoted with the tagline “In space, no one can hear you scream.” Physicists Zhuoran Geng and Ilari Maasilta from the Nanoscience Center at the University of Jyväskylä, Finland, have demonstrated that, on the contrary, in certain situations, sound can be transmitted strongly across a vacuum region.

In a recent article published in Communications Physics they show that in some cases, a can jump or “tunnel” fully across a vacuum gap between two solids if the materials in question are piezoelectric. In such materials, vibrations (sound waves) produce an electrical response as well, and since an can exist in vacuum, it can transmit the .

The requirement is that the size of the gap is smaller than the wavelength of the sound wave. This effect works not only in audio range of frequencies (Hz–kHz), but also in ultrasound (MHz) and hypersound (GHz) frequencies, as long as the vacuum gap is made smaller as the frequencies increase.

Recent research published in Nature Communications has used machine learning algorithms to find new compounds that can eliminate senescent cells [1].

Senolytics are molecules that destroy senescent cells. Only a small number of such molecules have been identified, and only two have shown efficacy in clinical trials: dasatinib and quercetin in combination [2]. One of the biggest challenges is that senolytics often only work against specific types of cells. Additionally, some senolytics may work well for one cell type while being toxic to other, non-senescent cell types [3].

There is also a group of senolytics that are used in cancer therapies. However, most of them target pathways that are mutated in cancer. Therefore, they cannot be used as therapeutic agents in different contexts.

Researchers have long thought that rewards like food or money encourage learning in the brain by causing the release of the “feel-good” hormone dopamine, known to reinforce storage of new information. Now, a new study in rodents describes how learning still occurs in the absence of an immediate incentive.

Led by researchers at NYU Grossman School of Medicine, the study explored the relationship between dopamine and the brain chemical acetylcholine, also known to play a role in learning and memory. Past research had shown that these two hormones compete with one another, so that a boost in one causes a decline in the other. Rewards were thought to promote learning by simultaneously triggering an increase in dopamine and a decrease in acetylcholine.

This sudden hormone imbalance is believed to open a window of opportunity for brain cells to adjust to new circumstances and form memories for later use. Known as neuroplasticity, this process is a major feature of learning as well as recovery after injury. However, the question had remained whether food and other external rewards are the only drivers for this memory system, or whether our brains instead are able to create the same conditions that are favorable to learning without outside help.

The discipline of systems chemistry deals with the analysis and synthesis of various autocatalytic systems and is therefore closely related to the study of the origin of life, since it investigates systems that can be considered as a transition between chemical and biological evolution: more complex than simple molecules, but simpler than living cells.

Tibor Gánti described the theory of self-replicating microspheres as early as 1978. These still lacked , but concealed within their membranes an autocatalytic metabolic network of small molecules, isolated (compartmentalized) within their membranes.

As the autocatalytic process takes place, the membrane-building material is also produced, leading to the division of the sphere. This system may appear to be a , and although it lacks genetic material, this can only be verified experimentally. These microspheres can be considered as “infrabiological” , since they do not reach the level of biological organization, but they exceed the complexity of normal chemical reactions.