On the Gevrey regularity for Sums of Squares of vector fields, study of some models

The micro-local Gevrey regularity of a class of "sums of squares" with real analytic coefficients is studied in detail. Some partial regularity result is also given

Error Classification and Reduction in Solid State Qubits

Quantum computers have enormous advantages over classical computers. A quantum computer can be used to calculate the factors of a number, which is sometimes impossible during one\u27s lifetime with a classical computer. Quantum information processing techniques can also be used for encryption, which makes eavesdropping impossible. Noise from the environment is a great challenge in building a reliable quantum computer. To build a reliable quantum computer, one has to protect the information content of the system from the environment. Otherwise, the information associated with the system will decay as the system interacts with the environment. The noise resulting from the system-bath interaction can be removed by using quantum error correcting codes or decoupling pulses. In addition, one could also use DFS encoding to make the information content of the system immune to the noise. In this paper, the various types of errors that could arise in a specific DFS encoding of a 3 spin qubit have been classified according to their effect on the state of the qubit. Also, the application of a specific decoupling pulse on the system, which is coupled to the environment through hyperfine Hamiltonian, has been analyzed

Archaeological and archaeometric study of the glass finds from the ancient harbour of Classe (Ravenna- Italy): new evidence

Introduction: The present study focuses on Late-Roman/Early Medieval glass found in the productive area within the ancient harbour of Classe near Ravenna, one of the most important trade centres between the 5th and 8th centuries AD of the Northern Adriatic area. Aims of the study were the identification of the main glass compositions and their contextualisation in Late-Antique groups; the identification of provenance of raw glass, and, consequently, of commercial routes; the extent, if any, of recycling glass cullet, as an alternative to the import of fresh raw glass; the identification of possible connections between archaeological typology and glass chemical composition. Results: 32 glassworking wastes and 25 drinking vessel fragments for a total amount of 57 fragments were devoted to chemical analysis in XRF and EPMA. All the analysed fragments are silica-soda lime glasses, produced with natron as a flux, and are compositionally similar to Late-Antique groups HIMT, S\ue9rie 3.2 and Levantine1. Raw glass chunks, glassworking wastes and objects of comparable compositions are identified into HIMT and S\ue9rie 3.2 groups, while the Levantine 1 group includes only objects and glassworking wastes. Systematic comparisons between Classe and Aquileia, the two most important Late-Antique archaeological sites of North-Eastern Italy, were also carried out, and the same compositional groups were identified, although S\ue9rie 3.2 in the Classe assemblage is more represented. Sr and Nd isotopic analysis confirmed that the composition of the three glasses derive from coastal sands of the Syro-Palestinian and Egyptian shore, with a slight shift in comparison to the published data. Little evidence of recycling was identified in the assemblage. Conclusions: In the 5th century, a secondary glass workshop devoted to the shaping of glass vessels starting from raw glass chunks and, possibly, glass cullet, was active in the area of the harbour. Raw glass of HIMT and S\ue9rie 3.2 was imported from the Levant and Egypt. Comparisons between Classe and Aquileia show that during the Late Antiquity these sites seem to be supplied of raw glass by the same trade routes. In addition, some connections between types and chemical compositions were highlighted

Trust model for certificate revocation in Ad hoc networks

In this paper we propose a distributed trust model for certificate revocation in Adhoc networks. The proposed model allows trust to be built over time as the number of interactions between nodes increase. Furthermore, trust in a node is defined not only in terms of its potential for maliciousness, but also in terms of the quality of the service it provides. Trust in nodes where there is little or no history of interactions is determined by recommendations from other nodes. If the nodes in the network are selfish, trust is obtained by an exchange of portfolios. Bayesian networks form the underlying basis for this model

Neural Decoder for Topological Codes using Pseudo-Inverse of Parity Check Matrix

Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then, many other researchers have applied neural networks to study a variety of problems in the context of decoding. An important development in this regard was due to Varsamopoulos et al. who proposed a two-step decoder using neural networks. Subsequent work of Maskara et al. used the same concept for decoding for various noise models. We propose a similar two-step neural decoder using inverse parity-check matrix for topological color codes. We show that it outperforms the state-of-the-art performance of non-neural decoders for independent Pauli errors noise model on a 2D hexagonal color code. Our final decoder is independent of the noise model and achieves a threshold of $10 \%$. Our result is comparable to the recent work on neural decoder for quantum error correction by Maskara et al.. It appears that our decoder has significant advantages with respect to training cost and complexity of the network for higher lengths when compared to that of Maskara et al.. Our proposed method can also be extended to arbitrary dimension and other stabilizer codes.Comment: 12 pages, 12 figures, 2 tables, submitted to the 2019 IEEE International Symposium on Information Theor

Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators

We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of squares with analytic coefficients is perturbed with a pseudodifferential operator of order strictly less than its subelliptic index it still has the Gevrey minimal regularity. We also prove a statement concerning real analytic hypoellipticity for the same type of pseudodifferential perturbations, provided the operator satisfies to some extra conditions (see Theorem 1.2 below) that ensure the analytic hypoellipticity

Targeting CXCR4 with CTCE-9908 inhibits prostate tumor metastasis

Abstract Background CXCL12/CXCR4 transactivation of epidermal growth factor family receptors in lipid raft membrane microdomains on cell surface is thought to mediate tumor growth and subsequent development of metastatic disease. CTCE-9908 is a known inhibitor of CXCR4. Herein, we tested the efficacy of CTCE-9908 in inhibiting prostate cancer cell growth, invasion, and metastasis. Methods We used a panel of in vitro assays utilizing human prostate cancer cell lines and an in vivo orthotopic prostate cancer model to assess the anti-tumoral activity of CTCE-9908. Results We demonstrated that (a) CTCE-9908 treatment resulted in no significant change in the growth of PC-3 and C4-2B cells; (b) 50 μg/ml of CTCE-9908 inhibited the invasive properties of PC-3 cells; (c) 25 mg/kg of CTCE-9908 did not alter primary tumor growth but it did significantly reduce total tumor burden in the animal including the growth of prostate and soft tissue metastases to lymph node and distant organ tissues. Histological analysis showed that CTCE-9908 treatment resulted in tumor necrosis in primary prostate tumors and no significant change in proliferation of tumor cells as measured by Ki-67 staining; (d) CTCE-9908 inhibited the tumor angiogenesis as measured by CD34 positive vessels in tumors. Conclusions These data suggest that CXCR4 inhibition by CTCE-9908 decreases the invasion potential in vitro, which then translated to a reduction of tumor spread with associated reduction in angiogenesis. Hence, CTCE-9908 may prove to be an efficacious novel agent to prevent and treat the spread of metastatic prostate cancer

PTEN loss mediated Akt activation promotes prostate tumor growth and metastasis via CXCL12/CXCR4 signaling

Abstract Introduction The chemokine CXCL12, also known as SDF-1, and its receptor, CXCR4, are overexpressed in prostate cancers and in animal models of prostate-specific PTEN deletion, but their regulation is poorly understood. Loss of the tumor suppressor PTEN (phosphatase and tensin homolog) is frequently observed in cancer, resulting in the deregulation of cell survival, growth, and proliferation. We hypothesize that loss of PTEN and subsequent activation of Akt, frequent occurrences in prostate cancer, regulate the CXCL12/CXCR4 signaling axis in tumor growth and bone metastasis. Methods Murine prostate epithelial cells from PTEN+/+, PTEN +/− , and PTEN−/− (prostate specific knockdown) mice as well as human prostate cancer cell lines C4-2B, PC3, and DU145 were used in gene expression and invasion studies with Akt inhibition. Additionally, HA-tagged Akt1 was overexpressed in DU145, and tumor growth in subcutaneous and intra-tibia bone metastasis models were analyzed. Results Loss of PTEN resulted in increased expression of CXCR4 and CXCL12 and Akt inhibition reversed expression and cellular invasion. These results suggest that loss of PTEN may play a key role in the regulation of this chemokine activity in prostate cancer. Overexpression of Akt1 in DU145 resulted in increased CXCR4 expression, as well as increased proliferation and cell cycle progression. Subcutaneous injection of these cells also resulted in increased tumor growth as compared to neo controls. Akt1 overexpression reversed the osteosclerotic phenotype associated with DU145 cells to an osteolytic phenotype and enhanced intra-osseous tumor growth. Conclusions These results suggest the basis for activation of CXCL12 signaling through CXCR4 in prostate cancer driven by the loss of PTEN and subsequent activation of Akt. Akt1-associated CXCL12/CXCR4 signaling promotes tumor growth, suggesting that Akt inhibitors may potentially be employed as anticancer agents to target expansion of PC bone metastases

(SEMI-)GLOBAL ANALYTIC HYPOELLIPTICITY FOR A CLASS OF "SUMS OF SQUARES" WHICH FAIL TO BE LOCALLY ANALYTIC HYPOELLIPTIC

The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced by P. Albano, A. Bove, and M. Mughetti, satisfying the Ho spacing diaeresis rmander condition and which fail to be either locally or microlocally analytic hypoelliptic