A Multidimensional Szemer\'edi Theorem in the primes

Let $A$ be a subset of positive relative upper density of \PP^d, the $d$-tuples of primes. We prove that $A$ contains an affine copy of any finite set F\subs\Z^d, which provides a natural multi-dimensional extension of the theorem of Green and Tao on the existence of long arithmetic progressions in the primes. The proof uses the hypergraph approach by assigning a pseudo-random weight system to the pattern $F$ on a $d+1$-partite hypergraph; a novel feature being that the hypergraph is no longer uniform with weights attached to lower dimensional edges. Then, instead of using a transference principle, we proceed by extending the proof of the so-called hypergraph removal lemma to our settings, relying only on the linear forms condition of Green and Tao

Optimal Polynomial Recurrence

Let $P\in\Z[n]$ with $P(0)=0$ and \VE>0. We show, using Fourier analytic techniques, that if N\geq \exp\exp(C\VE^{-1}\log\VE^{-1}) and $A\subseteq\{1,\...,N\}$, then there must exist $n\in\N$ such that \frac{|A\cap (A+P(n))|}{N}>(\frac{|A|}{N})^2-\VE. In addition to this we also show, using the same Fourier analytic methods, that if $A\subseteq\N$, then the set of \emph{\VE-optimal return times} R(A,P,\VE)=\{n\in \N \,:\,\D(A\cap(A+P(n)))>\D(A)^2-\VE\} is syndetic for every \VE>0. Moreover, we show that R(A,P,\VE) is \emph{dense} in every sufficiently long interval, in the sense that there exists an L=L(\VE,P,A) such that |R(A,P,\VE)\cap I| \geq c(\VE,P)|I| for all intervals $I$ of natural numbers with $|I|\geq L$ and c(\VE,P)=\exp\exp(-C\,\VE^{-1}\log\VE^{-1}).Comment: Short remark added and typos fixe

Sodium-Assisted Formation of Binding and Traverse Conformations of the Substrate in a Neurotransmitter Sodium Symporter Model

Therapeutics designed to increase synaptic neurotransmitter levels by inhibiting neurotransmitter sodium sym- porters (NSSs) classify a strategic approach to treat brain disorders such as depression or epilepsy, however, the critical elementary steps that couple downhill flux of sodium to uphill transport of neurotransmitter are not disti nguished as yet. Here we present modelling of NSS member neuronal GAT1 with the substrate � -aminobutyric acid (GABA), the major inhibitory neurotransmitter. GABA binding is simulated with the occluded conformation of GAT1 homodimer in an ex- plicit lipid/water environment. Simulations performed in the 1-10 ns range of time elucidated persistent formation of half- extended minor and H-bridged major GABA conformations, referred to as binding and traverse conformations, respec- tively. The traverse GABA conformation was further stabilized by GAT1-bound Na + (1). We also observed Na + (1) trans- location to GAT1-bound Cl - as well as the appearance of water molecules at GABA and GAT1-bound Na + (2), conjectur- ing causality. Scaling dynamics suggest that the traverse GABA conformation may be valid for developing substrate in- hibitors with high efficacy. The potential for this finding is significant with impact not only in pharmacology but wherever understanding of the mechanism of neurotransmitter uptake is valuable

A fotoreceptor-fejlődés sejt- és molekuláris biológiája = Cell and molecular biology of photoreceptor development

Az opszinváltás szabályozása fajonként eltérő, tiroxin és TRbéta2 nélkülözhetetlen a zöld csapfejlődéshez. A receptormegoszlás időbeli és térbeli mintázatával igazoltuk a tiroxint mediáló TRbéta2 szerepét. Tenyésztő módszerünkkel a fotoreceptor-differenciálódás szérummentes környezetben is végbemegy, a világon először definitív médiumban vizsgálható. Más faktorok (A- és E-vitamin, BDNF) is hatnak a pigment-expresszióra. Szelektív neurotrophin antagonisták az opszin és a TrkB receptor kapcsoltságára utalnak. Az erythropoietin retinális expressziója HIF1-α szabályozás alatt áll és időben változik a fejlődés korai szakaszában. Szemnyitás után a retinában lecsökken a transzdukciós molekulák szintje, kivéve a fotoreceptorokat. A sejttestben szintetizálódnak, közös lipid rafton kerülnek a kültagba és játszanak szerepet a fejlődésben. Az STK38L gén homozigóta mutációja befolyásolja a fotoreceptor-fejlődést. Sejthalál és proliferáció egyaránt jelen van. Hibrid sejtek jelennek meg pálcika-, kisebb mértékben S-opszin termeléssel. A differenciált, mutáns sejtek a degenerációs gén hatására megőrzik osztódóképességüket. A melatonin éjszaka termelődik, éjjeli világítás a hormontermelés gátlásával patológiás folyamatokat (emlő és colorectalis carcinoma) okozhat. A pineális szerv emlősben elvesztette fotoreceptor működését és szimpatikus rostokon a retinából kap információt. Mivel a pineális melatoninképzést rövidhullámú fény gátolja, éjjeli műszakban hosszúhullámú megvilágítást kell használni. | Regulation of opsin-switch varies across species. Thyroxin and TRß2 receptor is essential for green cone development. Spatial and temporal receptor distribution proved the role of TRß2 mediating thyroxin. Photoreceptor differentiation is completed in our culture method in serum-free medium, allowing its examination in a definitive paradigm. Other factors such as Vitamins A and E, BDNF) also influence visual pigment expression. Selective neurotrophin antagonists reveal the close connection of opsin and Trkß. Retinal expression of erythropoietin is under the regulation of HIF1-α, and changes during development. Transduction molecule levels decrease after eye opening, except for photoreceptors. They are synthesized in the cell body, located and transported in the outer segment on common lipid rafts and play a developmental role. Homozygotic mutation of STK38L influences photoreceptor development. Cell death and proliferation are equally present. Hybrid photoreceptors appear that express rod and, to a lesser extent, S-opsin. The degenerated, hybrid mutants retain their capacity to divide. Melatonin is produced at night. Nocturnal light exposition inhibiting hormone production may generate pathological processes (e.g.: carcinomas). The pineal organ in mammals has lost its photoreceptor function and receives information from the retina via sympathetic fibers. Since short wave light inhibits melatonin production, long-wave illumination is recommended during night-shift