Finite geometries and diffractive orbits in isospectral billiards

Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective spaces; from the properties of these spaces, one can derive a relation between Green functions as well as a relation between diffractive orbits in isospectral billiards.Comment: 10 page

Micro-Textured Black Silicon Wick for Silicon Heat Pipe Array

Planar, semiconductor heat arrays have been previously proposed and developed; however, this design makes use of a novel, microscale black silicon wick structure that provides increased capillary pumping pressure of the internal working fluid, resulting in increased effective thermal conductivity of the device, and also enables operation of the device in any orientation with respect to the gravity vector. In a heat pipe, the efficiency of thermal transfer from the case to the working fluid is directly proportional to the surface area of the wick in contact with the fluid. Also, the primary failure mechanism for heat pipes operating within the temperature range of interest is inadequate capillary pressure for the return of fluid from the condenser to the wick. This is also what makes the operation of heat pipes orientation-sensitive. Thus, the two primary requirements for a good wick design are a large surface area and high capillary pressure. Surface area can be maximized through nanomachined surface roughening. Capillary pressure is largely driven by the working fluid and wick structure. The proposed nanostructure wick has characteristic dimensions on the order of tens of microns, which promotes menisci of very small radii. This results in the possibility of enormous pumping potential due to the inverse proportionality with radius. Wetting, which also enhances capillary pumping, can be maximized through growth of an oxide layer or material deposition (e.g. TiO2) to create a superhydrophilic surface

Silicon Heat Pipe Array

Improved methods of heat dissipation are required for modern, high-power density electronic systems. As increased functionality is progressively compacted into decreasing volumes, this need will be exacerbated. High-performance chip power is predicted to increase monotonically and rapidly with time. Systems utilizing these chips are currently reliant upon decades of old cooling technology. Heat pipes offer a solution to this problem. Heat pipes are passive, self-contained, two-phase heat dissipation devices. Heat conducted into the device through a wick structure converts the working fluid into a vapor, which then releases the heat via condensation after being transported away from the heat source. Heat pipes have high thermal conductivities, are inexpensive, and have been utilized in previous space missions. However, the cylindrical geometry of commercial heat pipes is a poor fit to the planar geometries of microelectronic assemblies, the copper that commercial heat pipes are typically constructed of is a poor CTE (coefficient of thermal expansion) match to the semiconductor die utilized in these assemblies, and the functionality and reliability of heat pipes in general is strongly dependent on the orientation of the assembly with respect to the gravity vector. What is needed is a planar, semiconductor-based heat pipe array that can be used for cooling of generic MCM (multichip module) assemblies that can also function in all orientations. Such a structure would not only have applications in the cooling of space electronics, but would have commercial applications as well (e.g. cooling of microprocessors and high-power laser diodes). This technology is an improvement over existing heat pipe designs due to the finer porosity of the wick, which enhances capillary pumping pressure, resulting in greater effective thermal conductivity and performance in any orientation with respect to the gravity vector. In addition, it is constructed of silicon, and thus is better suited for the cooling of semiconductor devices

Diffractive orbits in isospectral billiards

Isospectral domains are non-isometric regions of space for which the spectra of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean space, instances of such domains have been given. It has been proved for these examples that the length spectrum, that is the set of the lengths of all periodic trajectories, coincides as well. However there is no one-to-one correspondence between the diffractive trajectories. It will be shown here how the diffractive contributions to the Green functions match nevertheless in a ''one-to-three'' correspondence.Comment: 20 pages, 6 figure

An In Vivo Screen Identifies PYGO2 as a Driver for Metastatic Prostate Cancer

Advanced prostate cancer displays conspicuous chromosomal instability and rampant copy number aberrations, yet the identity of functional drivers resident in many amplicons remain elusive. Here, we implemented a functional genomics approach to identify new oncogenes involved in prostate cancer progression. Through integrated analyses of focal amplicons in large prostate cancer genomic and transcriptomic datasets as well as genes upregulated in metastasis, 276 putative oncogenes were enlisted into an in vivo gain-of-function tumorigenesis screen. Among the top positive hits, we conducted an in-depth functional analysis on Pygopus family PHD finger 2 (PYGO2), located in the amplicon at 1q21.3. PYGO2 overexpression enhances primary tumor growth and local invasion to draining lymph nodes. Conversely, PYGO2 depletion inhibits prostate cancer cell invasion in vitro and progression of primary tumor and metastasis in vivo In clinical samples, PYGO2 upregulation associated with higher Gleason score and metastasis to lymph nodes and bone. Silencing PYGO2 expression in patient-derived xenograft models impairs tumor progression. Finally, PYGO2 is necessary to enhance the transcriptional activation in response to ligand-induced Wnt/β-catenin signaling. Together, our results indicate that PYGO2 functions as a driver oncogene in the 1q21.3 amplicon and may serve as a potential prognostic biomarker and therapeutic target for metastatic prostate cancer.Significance: Amplification/overexpression of PYGO2 may serve as a biomarker for prostate cancer progression and metastasis. Cancer Res; 78(14); 3823-33. ©2018 AACR

Localization of the Grover walks on spidernets and free Meixner laws

A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of discrete-time quantum walks on graphs. We introduce the Grover walk on a spidernet and its one-dimensional reduction. We derive an integral representation of the $n$-step transition amplitude in terms of the free Meixner law which appears as the spectral distribution. As an application we determine the class of spidernets which exhibit localization. Our method is based on quantum probabilistic spectral analysis of graphs.Comment: 32 page

Molecular and functional characterization of an evolutionarily conserved CREB-binding protein in the Lymnaea CNS

In eukaryotes, CREB-binding protein (CBP), a coactivator of CREB, functions both as a platform for recruiting other components of the transcriptional machinery and as a histone acetyltransferase (HAT) that alters chromatin structure. We previously showed that the transcriptional activity of cAMP-responsive element binding protein (CREB) plays a crucial role in neuronal plasticity in the pond snail Lymnaea stagnalis. However, there is no information on the molecular structure and HAT activity of CBP in the Lymnaea central nervous system (CNS), hindering an investigation of its postulated role in long-term memory (LTM). Here, we characterize the Lymnaea CBP (LymCBP) gene and identify a conserved domain of LymCBP as a functional HAT. Like CBPs of other species, LymCBP possesses functional domains, such as the KIX domain, which is essential for interaction with CREB and was shown to regulate LTM. In-situ hybridization showed that the staining patterns of LymCBP mRNA in CNS are very similar to those of Lymnaea CREB1. A particularly strong LymCBP mRNA signal was observed in the cerebral giant cell (CGC), an identified extrinsic modulatory interneuron of the feeding circuit, the key to both appetitive and aversive LTM for taste. Biochemical experiments using the recombinant protein of the LymCBP HAT domain showed that its enzymatic activity was blocked by classical HAT inhibitors. Preincubation of the CNS with such inhibitors blocked cAMP-induced synaptic facilitation between the CGC and an identified follower motoneuron of the feeding system. Taken together, our findings suggest a role for the HAT activity of LymCBP in synaptic plasticity in the feeding circuitry