Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum computation. In this paper we completely characterize the class of boolean functions computable by unitary two-qubit matchgate circuits with some probability of success. We show that this class precisely coincides with that of the linear threshold gates. The latter is a fundamental family which appears in several fields, such as the study of neural networks. Using the above characterization, we further show that the power of matchgate circuits is surprisingly trivial in those cases where the computation is to succeed with high probability. In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions depending on only a single bit of the input

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction

Real-time nondestructive citrus fruit quality monitoring system: development and laboratory testing

This study reports on the development and laboratory testing of the This study reports on the development and laboratory testing of the nondestructive citrus fruit quality monitoring system.  Prototype system consists of a light detection and ranging (LIDAR) and visible-near infrared spectroscopy sensors installed on an inclined conveyer for real-time fruit size and total soluble solids (TSS) measurement respectively.  Laboratory test results revealed that the developed system is applicable for instantaneous fruit size (R2 = 0.912) and TSS (R2 = 0.677, standard error of prediction = 0.48 °Brix) determination.  Future applications of such system would be in precision farming for in-field orange quality determination during the harvest and for row specific yield mapping and monitoring.    Keywords: LIDAR sensor, visible-near infrared spectroscopy, fruit size, sugar conten

Platelet volume indices: markers of carotid atherosclerosis in type 2 diabetes mellitus?

Background. Platelet volume indices (PVI) such as mean platelet volume (MPV), platelet distribution width (PDW), and platelet large cell ratio (P‑LCR) are the indicators of platelet activity and may have a role in subclinical atherosclerosis and microvascular complications in type 2 diabetes mellitus (T2DM). We evaluated PVI in diabetics for their association with carotid intima media thickness (CIMT) and micro-vascular complications. Methods. Participants — 105 T2DM patients and age, gender matched 105 controls were evaluated by history and complete blood counts (CBC) including PVI, blood sugars, HbA1c, lipid profile and microvascular complications. PVI were compared between cases and controls. Carotid Doppler was done and CIMT was correlated with PVI. Results. PVI were found significantly higher in diabetic patients compared to controls. Mean MPV in cases vs. controls was (11.09 ± 1.02 fL vs. 10.28 ± 0.96 fL, p ≤ 0.001), mean PDW (13.46 ± 1.96 fL vs. 12.85 ± 3.54 fL, p = 0.12), mean P-LCR (31.92 ± 6.23% vs. 27.94 ± 5.94%, p ≤ 0.001). CIMT showed a positive significant association with MPV, PDW and PLCR, dyslipidemia and negative with glycemic control. PVI, especially MPV was significantly elevated in those with neuropathy, nephropathy and retinopathy. Conclusion. PVI i.e. MPV, PDW, P-LCR are increased in diabetic patients. They correlate positively with CIMT, implying cardiovascular risk. PVI have a positive association with microvascular complications also. PVI as determined by simple automated CBC can be used as markers of subclinical atherosclerosis and predictor of future cardiovascular events in T2DM.

DEVELOPMENT OF A DEVICE TO MEASURE THE BLADE TIP CLEARANCE OF AN AXIAL COMPRESSOR

Axial compressors, used in gas turbines, jet engines and also small scale power plants, are rotating, airfoil based compressors in which the working fluid flows parallel to the axis of rotation. There has been continuous struggle to maximize the efficiency of these compressors. One of the many ways to achieve the same is to minimize the tip clearance i.e. to reduce the distance between the blade tip and the housing. Experiments need to be conducted to measure the changes in the tip clearance while the  compressor is operating. Conventional devices to measure this tip clearance have proven to be costly if a small scale application is under consideration. Our aim in this project is to develop a device which will measure the blade tip clearance of an axial flow compressor economically. The literature review, development of the device, its working and results will be discussed in this paper

Approximation Algorithms for Connected Maximum Cut and Related Problems

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph G[S] is connected. We present the first non-trivial \Omega(1/log n) approximation algorithm for the connected maximum cut problem in general graphs using novel techniques. We then extend our algorithm to an edge weighted case and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark contrast to the classical max-cut problem, we show that the connected maximum cut problem remains NP-hard even on unweighted, planar graphs. On the positive side, we obtain a polynomial time approximation scheme for the connected maximum cut problem on planar graphs and more generally on graphs with bounded genus.Comment: 17 pages, Conference version to appear in ESA 201

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

Fixed-parameter tractability of multicut parameterized by the size of the cutset

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most $p$ vertices. Our main result is that both problems can be solved in time $2^{O(p^3)}... n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size $p$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f(p)... n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset