Tower-Complete Problems in Contraction-Free Substructural Logics

We investigate the non-elementary computational complexity of a family of substructural logics without contraction. With the aid of the technique pioneered by Lazi\'c and Schmitz (2015), we show that the deducibility problem for full Lambek calculus with exchange and weakening ($\mathbf{FL}_{\mathbf{ew}}$) is not in Elementary (i.e., the class of decision problems that can be decided in time bounded by an elementary recursive function), but is in PR (i.e., the class of decision problems that can be decided in time bounded by a primitive recursive function). More precisely, we show that this problem is complete for Tower, which is a non-elementary complexity class forming a part of the fast-growing complexity hierarchy introduced by Schmitz (2016). The same complexity result holds even for deducibility in BCK-logic, i.e., the implicational fragment of $\mathbf{FL}_{\mathbf{ew}}$. We furthermore show the Tower-completeness of the provability problem for elementary affine logic, which was proved to be decidable by Dal Lago and Martini (2004).Comment: The full version of the paper accepted to CSL 202

Tower-Complete Problems in Contraction-Free Substructural Logics

We investigate the non-elementary computational complexity of a family of substructural logics without contraction. With the aid of the technique pioneered by Lazi? and Schmitz (2015), we show that the deducibility problem for full Lambek calculus with exchange and weakening (FL_{ew}) is not in Elementary (i.e., the class of decision problems that can be decided in time bounded by an elementary recursive function), but is in PR (i.e., the class of decision problems that can be decided in time bounded by a primitive recursive function). More precisely, we show that this problem is complete for Tower, which is a non-elementary complexity class forming a part of the fast-growing complexity hierarchy introduced by Schmitz (2016). The same complexity result holds even for deducibility in BCK-logic, i.e., the implicational fragment of FL_{ew}. We furthermore show the Tower-completeness of the provability problem for elementary affine logic, which was proved to be decidable by Dal Lago and Martini (2004)

Aberrant reduction of telomere repetitive sequences in plasma cell-free DNA for early breast cancer detection.

Excessive telomere shortening is observed in breast cancer lesions when compared to adjacent non-cancerous tissues, suggesting that telomere length may represent a key biomarker for early cancer detection. Because tumor-derived, cell-free DNA (cfDNA) is often released from cancer cells and circulates in the bloodstream, we hypothesized that breast cancer development is associated with changes in the amount of telomeric cfDNA that can be detected in the plasma. To test this hypothesis, we devised a novel, highly sensitive and specific quantitative PCR (qPCR) assay, termed telomeric cfDNA qPCR, to quantify plasma telomeric cfDNA levels. Indeed, the internal reference primers of our design correctly reflected input cfDNA amount (R2 = 0.910, P = 7.82 × 10−52), implying accuracy of this assay. We found that plasma telomeric cfDNA levels decreased with age in healthy individuals (n = 42, R2 = 0.094, P = 0.048), suggesting that cfDNA is likely derived from somatic cells in which telomere length shortens with increasing age. Our results also showed a significant decrease in telomeric cfDNA level from breast cancer patients with no prior treatment (n = 47), compared to control individuals (n = 42) (P = 4.06 × 10−8). The sensitivity and specificity for the telomeric cfDNA qPCR assay was 91.49% and 76.19%, respectively. Furthermore, the telomeric cfDNA level distinguished even the Ductal Carcinoma In Situ (DCIS) group (n = 7) from the healthy group (n = 42) (P = 1.51 × 10−3). Taken together, decreasing plasma telomeric cfDNA levels could be an informative genetic biomarker for early breast cancer detection

Differential Expression of Telomere DNA in Blood content for Cancer Diagnostics

poster abstractHuman blood typically contains a very small amount of cell free DNA (cfDNA) of uncertain origin. The amount and makeup of this circulating DNA been shown to change with the presence of cancer in the body. These alterations are used currently in some countries as very rudimentary tests for specific cancers and their mutations, which is reflected in the cfDNA. Little is known about the extent of the changes as the field is very young, though very promising. Telomeres are repetitive DNA elements that function as chromosomal caps, and are essential to cancer survival. Their function in cell life limitation mandates that all cancer find a method by which to bring about telomere dysfunction, making telomere a uniquely universal cancer element. It is possible, therefore, that telomere presence in cfDNA would be altered in many cancers, providing a powerful biomarker for cancer diagnostics and prognostics. This study shows a direct link between cancer presence and an augmented telomeric DNA ration in the blood. This idea could pave the way for a powerful early warning test for difficult cancers

Josephson current in a normal-metal nanowire coupled to superconductor/ferromagnet/superconductor junction

We consider superconducting nanowire proximity coupled to superconductor / ferromagnet / superconductor junction, where the magnetization penetrates into superconducting segment in nanowire decaying as $\sim\exp[-\frac{\mid n \mid}{\xi}]$ with site index $n$ and the decay length $\xi$. We tune chemical potential and spin-orbit coupling so that topological superconducting regime hosting Majorana fermion is realized for long $\xi$. We find that when $\xi$ becomes shorter, zero energy state at the interface between superconductor and ferromagnet splits into two away from zero energy. Accordingly, the behavior of Josephson current is drastically changed due to this "zero mode-non-zero mode crossover". By tuning the model parameters, we find an almost second-harmonic current-phase relation, $\sin2\varphi$, with phase difference $\varphi$. Based on the analysis of Andreev bound state (ABS), we clarify that current-phase relation is determined by coupling of the states within the energy gap. We find that the emergence of crossing points of ABS is a key ingredient to generate $\sin2\varphi$ dependence in current-phase relation. We further study both the energy and $\varphi$ dependence of pair amplitudes in the ferromagnetic region. For long $\xi$, odd-frequency spin-triplet $s$-wave component is dominant. The magnitude of the odd-frequency pair amplitude is enhanced at the energy level of ABS.Comment: 13 pages, 17 figure