The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces

It is well-known that self-linking is the only Z valued Vassiliev invariant of framed knots in S^3. However for most 3-manifolds, in particular for the total spaces of S^1-bundles over an orientable surface F not S^2, the space of Z-valued order one invariants is infinite dimensional. We give an explicit formula for the order one invariant I of framed knots in orientable total spaces of S^1-bundles over an orientable not necessarily compact surface F not S^2. We show that if F is not S^2 or S^1 X S^1, then I is the universal order one invariant, i.e. it distinguishes every two framed knots that can be distinguished by order one invariants with values in an Abelian group.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-3.abs.htm

Mapped Null Hypersurfaces and Legendrian Maps

For an $(m+1)$-dimensional space-time $(X^{m+1}, g),$ define a mapped null hypersurface to be a smooth map $\nu:N^{m}\to X^{m+1}$ (that is not necessarily an immersion) such that there exists a smooth field of null lines along $\nu$ that are both tangent and $g$-orthogonal to $\nu.$ We study relations between mapped null hypersurfaces and Legendrian maps to the spherical cotangent bundle $ST^*M$ of an immersed spacelike hypersurface $\mu:M^m\to X^{m+1}.$ We show that a Legendrian map \wt \lambda: L^{m-1}\to (ST^*M)^{2m-1} defines a mapped null hypersurface in $X.$ On the other hand, the intersection of a mapped null hypersurface $\nu:N^m\to X^{m+1}$ with an immersed spacelike hypersurface $\mu':M'^m\to X^{m+1}$ defines a Legendrian map to the spherical cotangent bundle $ST^*M'.$ This map is a Legendrian immersion if $\nu$ came from a Legendrian immersion to $ST^*M$ for some immersed spacelike hypersurface $\mu:M^m\to X^{m+1}.$Comment: 13 pages, 1 figur

Toward a general theory of linking invariants

Let N_1, N_2, M be smooth manifolds with dim N_1 + dim N_2 +1 = dim M$ and let phi_i, for i=1,2, be smooth mappings of N_i to M with Im phi_1 and Im phi_2 disjoint. The classical linking number lk(phi_1,phi_2) is defined only when phi_1*[N_1] = phi_2*[N_2] = 0 in H_*(M). The affine linking invariant alk is a generalization of lk to the case where phi_1*[N_1] or phi_2*[N_2] are not zero-homologous. In arXiv:math.GT/0207219 we constructed the first examples of affine linking invariants of nonzero-homologous spheres in the spherical tangent bundle of a manifold, and showed that alk is intimately related to the causality relation of wave fronts on manifolds. In this paper we develop the general theory. The invariant alk appears to be a universal Vassiliev-Goussarov invariant of order < 2. In the case where phi_1*[N_1] and phi_2*[N_2] are 0 in homology it is a splitting of the classical linking number into a collection of independent invariants. To construct alk we introduce a new pairing mu on the bordism groups of spaces of mappings of N_1 and N_2 into M, not necessarily under the restriction dim N_1 + dim N_2 +1 = dim M. For the zero-dimensional bordism groups, mu can be related to the Hatcher-Quinn invariant. In the case N_1=N_2=S^1, it is related to the Chas-Sullivan string homology super Lie bracket, and to the Goldman Lie bracket of free loops on surfaces.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper42.abs.htm

Nuclear Medicine in Breast Cancer Diagnostics: Primary Tumor and Lymphatic Metastasis

The purpose of the study: to assess the possibility of using nuclear medicine techniques at the stages of diagnosis and treatment of breast cancer. Materials and Methods: The study included 290 patients with breast cancer and 70 patients with benign breast tumors. The study was used as a radiopharmaceutical 99mTc-MIBI, 199Tl for imaging tumors and colloid 99mTc-Aloteh for visualization sentinel lymph nodes (SLN), colloid was injected peritumoral in four points to 80 MBq one day prior to the planned operation. Results: The sensitivity of SPECT using both 99mTc-MIBI and 199Tl for breast cancer detection was shown to be rather high, being 98.5% and 98%, respectively. It should be noted that the sensitivity of SPECT in detection of small tumors (less than 1 cm in diameter) and multicentric tumors was not high irrespective of the radioisotope used (60% and 65% with 99mTc-MIBI and 65% and 59% with 199Tl, respectively). The difference in the sensitivity was found between 99mTc-MIBI and 199T for the detection of regional lymph node metastasis (91% vs 70%). SLN were detected in 31 patients. The most commonly SLN were defined in the axillary region of 96.7%. In 22 (70.9%) patients there was no metastasis SLN. The sensitivity of the method was 91.2%, specificity of 100%. Conclusion: The specificity of SPECT with 199Tl was higher than that with 99mTc-MIBI. The data obtained show that SPECT with 199Tl can be recommended for its use as an additional breast cancer detection method in cases when other imaging techniques and histological findings are not accurate enough. The clinical study of 99mTc-Aloteh, a new radiopharmaceutical agent, has shown that the studied colloid has high uptake level in SLN and can be successfully used for visualization of SLN in patients with breast cancer

Nuclear Medicine in Breast Cancer Diagnostics: Primary Tumor and Lymphatic Metastasis

The purpose of the study: to assess the possibility of using nuclear medicine techniques at the stages of diagnosis and treatment of breast cancer. Materials and Methods: The study included 290 patients with breast cancer and 70 patients with benign breast tumors. The study was used as a radiopharmaceutical 99mTc-MIBI, 199Tl for imaging tumors and colloid 99mTc-Aloteh for visualization sentinel lymph nodes (SLN), colloid was injected peritumoral in four points to 80 MBq one day prior to the planned operation. Results: The sensitivity of SPECT using both 99mTc-MIBI and 199Tl for breast cancer detection was shown to be rather high, being 98.5% and 98%, respectively. It should be noted that the sensitivity of SPECT in detection of small tumors (less than 1 cm in diameter) and multicentric tumors was not high irrespective of the radioisotope used (60% and 65% with 99mTc-MIBI and 65% and 59% with 199Tl, respectively). The difference in the sensitivity was found between 99mTc-MIBI and 199T for the detection of regional lymph node metastasis (91% vs 70%). SLN were detected in 31 patients. The most commonly SLN were defined in the axillary region of 96.7%. In 22 (70.9%) patients there was no metastasis SLN. The sensitivity of the method was 91.2%, specificity of 100%. Conclusion: The specificity of SPECT with 199Tl was higher than that with 99mTc-MIBI. The data obtained show that SPECT with 199Tl can be recommended for its use as an additional breast cancer detection method in cases when other imaging techniques and histological findings are not accurate enough. The clinical study of 99mTc-Aloteh, a new radiopharmaceutical agent, has shown that the studied colloid has high uptake level in SLN and can be successfully used for visualization of SLN in patients with breast cancer

Linking and causality in globally hyperbolic spacetimes

The linking number $lk$ is defined if link components are zero homologous. Our affine linking invariant $alk$ generalizes $lk$ to the case of linked submanifolds with arbitrary homology classes. We apply $alk$ to the study of causality in Lorentz manifolds. Let $M^m$ be a spacelike Cauchy surface in a globally hyperbolic spacetime $(X^{m+1}, g)$. The spherical cotangent bundle $ST^*M$ is identified with the space $N$ of all null geodesics in $(X,g).$ Hence the set of null geodesics passing through a point $x\in X$ gives an embedded $(m-1)$-sphere $S_x$ in $N=ST^*M$ called the sky of $x.$ Low observed that if the link $(S_x, S_y)$ is nontrivial, then $x,y\in X$ are causally related. This motivated the problem (communicated by Penrose) on the Arnold's 1998 problem list to apply link theory to the study of causality. The spheres $S_x$ are isotopic to fibers of $(ST^*M)^{2m-1}\to M^m.$ They are nonzero homologous and $lk(S_x,S_y)$ is undefined when $M$ is closed, while $alk(S_x, S_y)$ is well defined. Moreover, $alk(S_x, S_y)\in Z$ if $M$ is not an odd-dimensional rational homology sphere. We give a formula for the increment of \alk under passages through Arnold dangerous tangencies. If $(X,g)$ is such that $alk$ takes values in $\Z$ and $g$ is conformal to $g'$ having all the timelike sectional curvatures nonnegative, then $x, y\in X$ are causally related if and only if $alk(S_x,S_y)\neq 0$. We show that $x,y$ in nonrefocussing $(X, g)$ are causally unrelated iff $(S_x, S_y)$ can be deformed to a pair of $S^{m-1}$-fibers of $ST^*M\to M$ by an isotopy through skies. Low showed that if (\ss, g) is refocussing, then $M$ is compact. We show that the universal cover of $M$ is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A part of the paper (several results of sections 4,5,6,9,10) is an extension and development of our work math.GT/0207219 in the context of Lorentzian geometry. The results of sections 7,8,11,12 and Appendix B are ne

Eurasian-Scale Experimental Satellite-based Quantum Key Distribution with Detector Efficiency Mismatch Analysis

The Micius satellite is the pioneering initiative to demonstrate quantum teleportation, entanglement distribution, quantum key distribution (QKD), and quantum-secured communications experiments at the global scale. In this work, we report on the results of the 600-mm-aperture ground station design which has enabled the establishment of a quantum-secured link between the Zvenigorod and Nanshan ground stations using the Micius satellite. As a result of a quantum communications session, an overall sifted key of 2.5 Mbits and a total final key length of 310 kbits have been obtained. We present an extension of the security analysis of the realization of satellite-based QKD decoy-state protocol by taking into account the effect of the detection-efficiency mismatch for four detectors. We also simulate the QKD protocol for the satellite passage and by that validate our semi-empirical model for a realistic receiver, which is in good agreement with the experimental data. Our results pave the way to the considerations of realistic imperfection of the QKD systems, which are important in the context of their practical security.Comment: 8+2 pages, 5+2 figure

Clinical Significance of Sentinel Lymph Node Detection in Patients with Invasive Cervical Cancer

The clinical significance of determining sentinel lymph nodes (SLN) in patients with invasive cervical cancer was studied. From 2013 to 2014, 30 cervical cancer patients (T1a1NxM0-T1b1NxM0) were treated at the Gynecological Oncology Department of the Cancer Research Institute. The day before surgery, four submucosal injections of 99mTc Al2O3 at a total dose of 80 MBq were made in each quadrant around the cervical tumor. Patients were submitted to preoperative lymphoscintigraphy and intraoperative SLN detection. The feasibility of preserving the reproductive potential in patients after radical abdominal trachelectomy was assessed. The 3-year, overall, disease-free and metastasis-free survival rates were analyzed. Thirty-four SLNs were detected by single-photon emission computed tomography (SPECT) and 42 SLNs were identified by intraoperative gamma probe. The sensitivity in detecting SLNs was 100% for intraoperative SLN identification and 80% for SPECT image. The reproductive potential was preserved in 86% of patients. The 3-year overall and metastases-free survival rates were 100%. Recurrence occurred in 8.6% of cases

Development and Study of {99m}Tc-1-Thio-D-glucose for Visualization of Malignant Tumors

The preclinical studies of {99m}Tc-1-Thio-D-glucose, a new tumor-seeking agent based on technetium-99mlabeled glucose derivative, were conducted, and the feasibility of using this radiopharmaceutical for tumor visualization was studied. The preclinical studies were carried out strictly in accordance with the local legislation and were regulated by the generally accepted research standards. {99m}Tc-1-Thio-D-glucose was found to have optimal pharmacokinetic and physico-chemical properties for diagnostic imaging and was proved to belong to the low-toxic substances. The potential utility of {99m}Tc-1-thio-D-glucose for tumor imaging was studied in vitro and in vivo models. The present study demonstrated that {99m}Tc-1-Thio-D-glucose is a prospective radiopharmaceutical for cancer visualization