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

Can One Hear the Shape of a Graph?

We show that the spectrum of the Schrodinger operator on a finite, metric graph determines uniquely the connectivity matrix and the bond lengths, provided that the lengths are non-commensurate and the connectivity is simple (no parallel bonds between vertices and no loops connecting a vertex to itself). That is, one can hear the shape of the graph! We also consider a related inversion problem: A compact graph can be converted into a scattering system by attaching to its vertices leads to infinity. We show that the scattering phase determines uniquely the compact part of the graph, under similar conditions as above.Comment: 9 pages, 1 figur

Isospectral domains with mixed boundary conditions

We construct a series of examples of planar isospectral domains with mixed Dirichlet-Neumann boundary conditions. This is a modification of a classical problem proposed by M. Kac.Comment: 9 figures. Statement of Theorem 5.1 correcte

Quantum graphs with singular two-particle interactions

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that the interaction is provided by boundary conditions. In order to find such Hamiltonians closed and semi-bounded quadratic forms are constructed, from which the associated self-adjoint operators are extracted. We provide a general characterisation of such operators and, furthermore, produce certain classes of examples. We then consider identical particles and project to the bosonic and fermionic subspaces. Finally, we show that the operators possess purely discrete spectra and that the eigenvalues are distributed following an appropriate Weyl asymptotic law

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

Class I and Class II methanol masers in high-mass star forming regions

Among the tracers of the earliest phases in the massive star formation process, methanol masers have gained increasing importance. The phenomenological distinction between Class I and II methanol masers is based on their spatial association with objects such as jets, cores, and ultracompact HII regions, but is also believed to correspond to different pumping mechanisms: radiation for Class II masers, collisions for Class I masers. In this work, we have surveyed a large sample of massive star forming regions - 296 objects divided into two groups named 'High' and 'Low' according to their [25-12] and [60-12] IRAS colours - in Class I and II methanol masers. Previous studies indicate that the High sources are likely more evolved. Therefore, the sample can be used to assess the existence of a sequence for the occurrence of Class I and II methanol masers during the evolution of a massive star forming region. We observed the 6 GHz (Class II) CH3OH maser with the Effelsberg 100-m telescope, and the 44 GHz and 95 GHz (Class I) CH3OH masers with the Nobeyama 45-m telescope. We have detected: 55 sources in the Class II line (12 new detections); 27 sources in the 44 GHz Class I line (17 new detections); 11 sources in the 95 GHz Class I line (all except one are new detections). Our statistical analysis shows that the ratio between the detection rates of Class II and Class I methanol masers is basically the same in High and Low sources. Therefore, both masers are equally associated with each evolutionary phase. In contrast, all maser species have about 3 times higher detection rates in High than in Low sources. This might indicate that the phenomena that originate all masers become progressively more active with time, during the earliest evolutionary phases of a high-mass star forming region.Comment: 30 pages including Appendices, 11 figures, accepted for publication in Astronomy & Astrophysic

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

A ring laser gyroscope without lock-in phenomenon

We theoretically and numerically study the effect of backscattering on rotating ring lasers by employing the Maxwell-Bloch equations. We show that frequency shifts due to the Sagnac effect incorporating the effect of backscattering can be observed without lock-in phenomenon, if the strength of backscattering originating in the bumps of the refractive index is larger than a certain value. It is also shown that the experimental results corresponding to the theoretical ones can actually be obtained by using a semiconductor fiber-optic ring laser gyroscope.Comment: 9 pages, 6figure