A Note on the HRT Conjecture and a New Uncertainty Principle for the Short-Time Fourier Transform

In this note we provide a negative answer to a question raised by Kreisel concerning a condition on the short-time Fourier transform that would imply the HRT conjecture. In particular we provide a new type of uncertainty principle for the short-time Fourier transform which forbids the arrangement of an arbitrary “bump with fat tail” profile

On Exceptional Times for Pointwise Convergence of Integral Kernels in Feynman–Trotter Path Integrals

In the first part of the paper we provide a survey of recent results concerning the problem of pointwise convergence of integral kernels in Feynman path integrals, obtained by means of time-frequency analysis techniques. We then focus on exceptional times, where the previous results do not hold, and we show that weaker forms of convergence still occur. In conclusion we offer some clues about possible physical interpretation of exceptional times

On heat equations associated with fractional harmonic oscillators

We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator e−t Hβ , t,β > 0, associated with the harmonic oscillator H = − + |x| 2. We then prove some local and global wellposedness results for nonlinear fractional heat equation

Multi-Targeting Bioactive Compounds Extracted from Essential Oils as Kinase Inhibitors

Essential oils (EOs) are popular in aromatherapy, a branch of alternative medicine that claims their curative effects. Moreover, several studies reported EOs as potential anti-cancer agents by inducing apoptosis in different cancer cell models. In this study, we have considered EOs as a potential resource of new kinase inhibitors with a polypharmacological profile. On the other hand, computational methods offer the possibility to predict the theoretical activity profile of ligands, discovering dangerous off-targets and/or synergistic effects due to the potential multi-target action. With this aim, we performed a Structure-Based Virtual Screening (SBVS) against X-ray models of several protein kinases selected from the Protein Data Bank (PDB) by using a chemoinformatics database of EOs. By evaluating theoretical binding affinity, 13 molecules were detected among EOs as new potential kinase inhibitors with a multi-target profile. The two compounds with higher percentages in the EOs were studied more in depth by means Induced Fit Docking (IFD) protocol, in order to better predict their binding modes taking into account also structural changes in the receptor. Finally, given its good binding affinity towards five different kinases, cinnamyl cinnamate was biologically tested on different cell lines with the aim to verify the antiproliferative activity. Thus, this work represents a starting point for the optimization of the most promising EOs structure as kinase inhibitors with multi-target feature

FHIT gene therapy prevents tumor development in Fhit-deficient mice

The tumor suppressor gene FHIT spans a common fragile site and is highly susceptible to environmental carcinogens. FHIT inactivation and loss of expression is found in a large fraction of premaligant and malignant lesions. In this study, we were able to inhibit tumor development by oral gene transfer, using adenoviral or adenoassociated viral vectors expressing the human FHIT gene, in heterozygous Fhit+/- knockout mice, that are prone to tumor development after carcinogen exposure. We therefore suggest that FHIT gene therapy could be a novel clinical approach not only in treatment of early stages of cancer, but also in prevention of human cancer

Hipk2 cooperates with p53 to suppress γ-ray radiation-induced mouse thymic lymphoma

A genome-wide screen for genetic alterations in radiation-induced thymic lymphomas generated from p53+/− and p53−/− mice showed frequent loss of heterozygosity (LOH) on chromosome 6. Fine mapping of these LOH regions revealed three non-overlapping regions, one of which was refined to a 0.2 Mb interval that contained only the gene encoding homeobox-interacting protein kinase 2 (Hipk2). More than 30% of radiation-induced tumors from both p53+/− and p53−/− mice showed heterozygous loss of one Hipk2 allele. Mice carrying a single inactive allele of Hipk2 in the germline were susceptible to induction of tumors by γ-radiation, but most tumors retained and expressed the wild-type allele, suggesting that Hipk2 is a haploinsufficient tumor suppressor gene for mouse lymphoma development. Heterozygous loss of both Hipk2 and p53 confers strong sensitization to radiation-induced lymphoma. We conclude that Hipk2 is a haploinsufficient lymphoma suppressor gene

VE-PTP controls blood vessel development by balancing Tie-2 activity

Vascular endothelial protein tyrosine phosphatase (VE-PTP) is an endothelial-specific receptor-type tyrosine phosphatase that associates with Tie-2 and VE-cadherin. VE-PTP gene disruption leads to embryonic lethality, vascular remodeling defects, and enlargement of vascular structures in extraembryonic tissues. We show here that antibodies against the extracellular part of VE-PTP mimic the effects of VE-PTP gene disruption exemplified by vessel enlargement in allantois explants. These effects require the presence of the angiopoietin receptor Tie-2. Analyzing the mechanism we found that anti–VE-PTP antibodies trigger endocytosis and selectively affect Tie-2–associated, but not VE-cadherin–associated VE-PTP. Dissociation of VE-PTP triggers the activation of Tie-2, leading to enhanced endothelial cell proliferation and enlargement of vascular structures through activation of Erk1/2. Importantly, the antibody effect on vessel enlargement is also observed in newborn mice. We conclude that VE-PTP is required to balance Tie-2 activity and endothelial cell proliferation, thereby controlling blood vessel development and vessel size

Overexpression of HMGA1 promotes anoikis resistance and constitutive Akt activation in pancreatic adenocarcinoma cells

HMGA1 proteins are architectural transcription factors that are overexpressed by pancreatic adenocarcinomas. Roles of HMGA1 in mediating the malignant phenotype of this cancer are poorly understood. We tested the hypothesis that overexpression of HMGA1 promotes resistance to anoikis (apoptosis induced by anchorage deprivation) in pancreatic cancer cells. HMGA1 cDNA was stably transfected into MiaPaCa2 human pancreatic adenocarcinoma cells (which have low baseline expression levels of HMGA1). Cells were grown in suspension on PolyHEMA-coated plates and their susceptibility to anoikis was assayed using flow cytometry. Overexpression of HMGA1 was associated with marked reductions in susceptibility to anoikis in concert with increases in Akt phosphorylation (Ser473) and in Akt kinase activity and with reductions in caspase 3 activation. Inhibition of phosphoinositidyl-3 (PI3-K)/Akt pathway with either the small molecule inhibitor LY294002 or dominant-negative Akt resulted in reversal of anoikis resistance induced by HMGA1 overexpression. Further, RNA interference-mediated HMGA1 silencing in MiaPaCa2 and BxPC3 (a human pancreatic adenocarcinoma cell line with high baseline levels of HMGA1 expression) cells resulted in significant increases in susceptibility to anoikis. Our findings suggest HMGA1 promotes anoikis resistance through a PI3-K/Akt-dependent mechanism. Given the putative associations between anoikis resistance and metastatic potential, HMGA1 represents a potential therapeutic target in pancreatic adenocarcinoma

Protein tyrosine phosphatases expression during development of mouse superior colliculus

Protein tyrosine phosphatases (PTPs) are key regulators of different processes during development of the central nervous system. However, expression patterns and potential roles of PTPs in the developing superior colliculus remain poorly investigated. In this study, a degenerate primer-based reverse transcription-polymerase chain reaction (RT-PCR) approach was used to isolate seven different intracellular PTPs and nine different receptor-type PTPs (RPTPs) from embryonic E15 mouse superior colliculus. Subsequently, the expression patterns of 11 PTPs (TC-PTP, PTP1C, PTP1D, PTP-MEG2, PTP-PEST, RPTPJ, RPTPε, RPTPRR, RPTPσ, RPTPκ and RPTPγ) were further analyzed in detail in superior colliculus from embryonic E13 to postnatal P20 stages by quantitative real-time RT-PCR, Western blotting and immunohistochemistry. Each of the 11 PTPs exhibits distinct spatiotemporal regulation of mRNAs and proteins in the developing superior colliculus suggesting their versatile roles in genesis of neuronal and glial cells and retinocollicular topographic mapping. At E13, additional double-immunohistochemical analysis revealed the expression of PTPs in collicular nestin-positive neural progenitor cells and RC-2-immunoreactive radial glia cells, indicating the potential functional importance of PTPs in neurogenesis and gliogenesis