Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit

Information heat engine: converting information to energy by feedback control

In 1929, Leo Szilard invented a feedback protocol in which a hypothetical intelligence called Maxwell's demon pumps heat from an isothermal environment and transduces it to work. After an intense controversy that lasted over eighty years; it was finally clarified that the demon's role does not contradict the second law of thermodynamics, implying that we can convert information to free energy in principle. Nevertheless, experimental demonstration of this information-to-energy conversion has been elusive. Here, we demonstrate that a nonequilibrium feedback manipulation of a Brownian particle based on information about its location achieves a Szilard-type information-energy conversion. Under real-time feedback control, the particle climbs up a spiral-stairs-like potential exerted by an electric field and obtains free energy larger than the amount of work performed on it. This enables us to verify the generalized Jarzynski equality, or a new fundamental principle of "information-heat engine" which converts information to energy by feedback control.Comment: manuscript including 7 pages and 4 figures and supplementary material including 6 pages and 8 figure

Localized Nanoresonator Mode in Plasmonic Microcavities.

Submicron-thick hexagonal boron nitride crystals embedded in noble metals form planar Fabry-Perot half-microcavities. Depositing Au nanoparticles on top of these microcavities forms previously unidentified angle- and polarization-sensitive nanoresonator modes that are tightly laterally confined by the nanoparticle. Comparing dark-field scattering with reflection spectroscopies shows plasmonic and Fabry-Perot-like enhancements magnify subtle interference contributions, which lead to unexpected redshifts in the dark-field spectra, explained by the presence of these new modes

Bargaining with Optimism

Excessive optimism is a prominent explanation for bargaining delays. Recent results demonstrate that optimism plays a subtle role in bargaining, and its careful analysis may shed valuable insights into negotiation behavior. This article reviews some of these results, focusing on the following findings. First, when there is a nearby deadline, optimistic players delay the agreement to the last period before the deadline, replicating a broad empirical regularity known as the deadline effect. Second, there cannot be a substantial delay under persistent optimism; i.e., excessive optimism alone cannot explain delays. Third, when optimistic players are expected to learn during the negotiation, they delay the agreement in order to persuade their opponents. The delays in these results can be quite costly, Pareto inefficient, and common knowledge at the beginning of the game

Spontaneous expectoration of pulmonary metastases in a child with osteogenic sarcoma

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148355/1/pbc27611.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148355/2/pbc27611_am.pd

Tissue Localization and Extracellular Matrix Degradation by PI, PII and PIII Snake Venom Metalloproteinases: Clues on the Mechanisms of Venom-Induced Hemorrhage

20 páginas, 4 figuras, 3 tablas y 7 tablas en material suplementario.Snake venom hemorrhagic metalloproteinases (SVMPs) of the PI, PII and PIII classes were compared in terms of tissue localization and their ability to hydrolyze basement membrane components in vivo, as well as by a proteomics analysis of exudates collected in tissue injected with these enzymes. Immunohistochemical analyses of co-localization of these SVMPs with type IV collagen revealed that PII and PIII enzymes co-localized with type IV collagen in capillaries, arterioles and post-capillary venules to a higher extent than PI SVMP, which showed a more widespread distribution in the tissue. The patterns of hydrolysis by these three SVMPs of laminin, type VI collagen and nidogen in vivo greatly differ, whereas the three enzymes showed a similar pattern of degradation of type IV collagen, supporting the concept that hydrolysis of this component is critical for the destabilization of microvessel structure leading to hemorrhage. Proteomic analysis of wound exudate revealed similarities and differences between the action of the three SVMPs. Higher extent of proteolysis was observed for the PI enzyme regarding several extracellular matrix components and fibrinogen, whereas exudates from mice injected with PII and PIII SVMPs had higher amounts of some intracellular proteins. Our results provide novel clues for understanding the mechanisms by which SVMPs induce damage to the microvasculature and generate hemorrhage.This work was performed in partial fulfillment of the requirements for the PhD degree for Cristina Herrera at Universidad de Costa Rica.Peer reviewe

Functional near infrared spectroscopy (fNIRS) to assess cognitive function in infants in rural Africa

Cortical mapping of cognitive function during infancy is poorly understood in low-income countries due to the lack of transportable neuroimaging methods. We have successfully piloted functional near infrared spectroscopy (fNIRS) as a neuroimaging tool in rural Gambia. Four-to-eight month old infants watched videos of Gambian adults perform social movements, while haemodynamic responses were recorded using fNIRS. We found distinct regions of the posterior superior temporal and inferior frontal cortex that evidenced either visual-social activation or vocally selective activation (vocal > non-vocal). The patterns of selective cortical activation in Gambian infants replicated those observed within similar aged infants in the UK. These are the first reported data on the measurement of localized functional brain activity in young infants in Africa and demonstrate the potential that fNIRS offers for field-based neuroimaging research of cognitive function in resource-poor rural communities

Tuning ultrafast electron thermalization pathways in a van der Waals heterostructure

Ultrafast electron thermalization - the process leading to Auger recombination, carrier multiplication via impact ionization and hot carrier luminescence - occurs when optically excited electrons in a material undergo rapid electron-electron scattering to redistribute excess energy and reach electronic thermal equilibrium. Due to extremely short time and length scales, the measurement and manipulation of electron thermalization in nanoscale devices remains challenging even with the most advanced ultrafast laser techniques. Here, we overcome this challenge by leveraging the atomic thinness of two-dimensional van der Waals (vdW) materials in order to introduce a highly tunable electron transfer pathway that directly competes with electron thermalization. We realize this scheme in a graphene-boron nitride-graphene (G-BN-G) vdW heterostructure, through which optically excited carriers are transported from one graphene layer to the other. By applying an interlayer bias voltage or varying the excitation photon energy, interlayer carrier transport can be controlled to occur faster or slower than the intralayer scattering events, thus effectively tuning the electron thermalization pathways in graphene. Our findings, which demonstrate a novel means to probe and directly modulate electron energy transport in nanoscale materials, represent an important step toward designing and implementing novel optoelectronic and energy-harvesting devices with tailored microscopic properties.Comment: Accepted to Nature Physic