Profitable Double-Spending Attacks

Our aim in this paper is to investigate the profitability of double-spending (DS) attacks that manipulate a priori mined transaction in a blockchain. Up to date, it was understood that the requirement for successful DS attacks is to occupy a higher proportion of computing power than a target network's proportion; i.e., to occupy more than 51% proportion of computing power. On the contrary, we show that DS attacks using less than 50% proportion of computing power can also be vulnerable. Namely, DS attacks using any proportion of computing power can occur as long as the chance to making a good profit is there; i.e., revenue of an attack is greater than the cost of launching it. We have novel probability theory based derivations for calculating time finite attack probability. This can be used to size up the resource needed to calculate the revenue and the cost. The results enable us to derive sufficient and necessary conditions on the value of a target transaction which make DS attacks for any proportion of computing power profitable. They can also be used to assess the risk of one's transaction by checking whether or not the transaction value satisfies the conditions for profitable DS attacks. Two examples are provided in which we evaluate the attack resources and the conditions for profitable DS attacks given 35% proportion of computing power against Syscoin and BitcoinCash networks, and quantitatively shown how vulnerable they are.Comment: 13 pages, 1 figure. Submitted to IEEE Transactions on Information Forensics and Security. Table 1 Has been correcte

Concise Probability Distributions of Eigenvalues of Real-Valued Wishart Matrices

In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of skew symmetric matrices. In particular, we relate the multiple integrals of a determinant, which arises while finding the eigenvalue distributions, in terms of the Pfaffian of skew-symmetric matrices. Pfaffians being the square root of skew symmetric matrices are easy to compute than the conventional distributions that involve Zonal polynomials or beta integrals. We show that the plots of the derived distributions are exactly coinciding with the numerically simulated plots.Comment: Submitted to Math Journal, 7 page

Relaxation of non-order parameter field in directed Ising systems

We investigate the effect of initial conditions on the dynamic exponents of the interacting monomer-monomer model with infinitely many absorbing states in one dimension. This model exhibits a directed Ising (DI) type transition from an active phase into an absorbing phase. In case of the directed percolation universality class, it has been reported that the non-order parameter as well as the order parameter exhibits critical fluctuations, relaxing algebraically to its natural value with the same scaling exponents. We numerically confirm that this is also valid for the DI universality class. We also observe continuously varying dynamic exponents with a linear dependence on the non-order parameter initial density.Comment: 4 pages, APCTP international workshop on similarity in diversity(Seoul, Korea; Aug. 24, 2000) To appear in Journal of the Korean Physical Societ

On the Compressed Measurements over Finite Fields: Sparse or Dense Sampling

We consider compressed sampling over finite fields and investigate the number of compressed measurements needed for successful L0 recovery. Our results are obtained while the sparseness of the sensing matrices as well as the size of the finite fields are varied. One of interesting conclusions includes that unless the signal is "ultra" sparse, the sensing matrices do not have to be dense.Comment: 10 pages, 2 figures, other essential inf

Molecular orbital polarization in Na2Ti2Sb2O: microscopic route to metal-metal transition without spontaneous symmetry breaking

Ordered phases such as charge- and spin-density wave state accompany either full or partial gapping of Fermi surface (FS) leading a metal-insulator or metal-metal transition (MMT). However, there are examples of MMT without any signatures of symmetry breaking. One example is Na$_2$Ti$_2$Sb$_2$O, where a partial gapping of FS is observed but a density wave ordering has not been found. Here we propose a microscopic mechanism of such a MMT which occurs due to a momentum dependent spin-orbit coupled molecular orbital polarization. Since a molecular $d$ orbital polarization is present due to a small spin-orbit coupling of Ti, there is no spontaneous symmetry breaking involved. However, a sharp increase of polarization happens above a critical electron interaction which gaps out the $d$ orbtial FS and reduces the density of states significantly, while the rest of FS associated with Sb $p$ orbtials is almost intact across MMT. Experimental implications to test our proposal and applications to other systems are also discussed.Comment: 5 pages, 3 figure

Crystal structure and magnetism in α\alpha-RuCl3: an ab-initio study

$\alpha$-RuCl$_3$ has been proposed recently as an excellent playground for exploring Kitaev physics on a two-dimensional (2D) honeycomb lattice. However, structural clarification of the compound has not been completed, which is crucial in understanding the physics of this system. Here, using {\it ab-initio} electronic structure calculations, we study a full three dimensional (3D) structure of $\alpha$-RuCl$_3$ including the effects of spin-orbit coupling (SOC) and electronic correlations. Three major results are as follows; i) SOC suppresses dimerization of Ru atoms, which exists in other Ru compounds such as isostructural Li$_2$RuO$_3$, and making the honeycomb closer to an ideal one. ii) The nearest-neighbor Kitaev exchange interaction between the $j_{\rm eff}$=1/2 pseudospin depends strongly on the Ru-Ru distance and the Cl position, originating from the nature of the edge-sharing geometry. iii) The optimized 3D structure without electronic correlations has $P{\bar 3}1m$ space group symmetry independent of SOC, but including electronic correlation changes the optimized 3D structure to either $C2/m$ or $Cmc2_1$ within 0.1 meV per formula unit (f.u.) energy difference. The reported $P3_112$ structure is also close in energy. The interlayer spin exchange coupling is a few percent of in-plane spin exchange terms, confirming $\alpha$-RuCl$_3$ is close to a 2D system. We further suggest how to increase the Kitaev term via tensile strain, which sheds new light in realizing Kitaev spin liquid phase in this system.Comment: 10 pages, 10 figures, and 4 table

Effect of charge doping on the electronic structure, orbital polarization, and structural distortion in nickelate superlattice

Using first-principles density functional theory calculations, we investigated the effect of charge doping in a LaNiO$_3$/SrTiO$_3$ superlattice. The detailed analysis based on two different simulation methods for doping clearly shows that the electronic and structural properties change in a systematic way that the orbital polarization ({\it i.e.} relative occupation of two Ni-$e_g$ orbitals) is reduced and the Ni to apical oxygen distance enlarged as the number of doped electrons increases. Also, the rotation angles of the NiO$_6$/TiO$_6$ octahedra strongly and systematically depend on the doping so that the angle $\gamma$ gradually decreases whereas the $\alpha$ and $\beta$ increase as a function of electron doping. Further analysis shows that the electron (hole) doping can play a similar role with the compressive (tensile) strain for the octahedral rotations. Our results not only suggest a possible way to control the orbital and structural property by means of charge doping, but also provide useful information to understand the experiments under various doping situations such as oxygen vacancy.Comment: 12 pages, 12 figure

Three-photon coherence in a ladder-type atomic system

We present a theoretical study of three-photon electromagnetically induced absorption for a ladder-type three-level atomic system. A probe beam was tuned to the lower line and two counter-propagating, linearly polarized coupling beams were tuned to the upper line. The system can be modeled with a three- (or five-) level scheme when the polarization directions of the coupling beams are parallel (or perpendicular). By calculating the absorption coefficients analytically for the two schemes, we found that the corresponding absorption coefficients were identical except for different transition strengths, and that the primitive scheme embedded in those schemes was a simple four-level scheme

Mott metal-insulator transitions in pressurized layered trichalcogenides

Transition metal phosphorous trichalcogenides, $M{\rm P}X_3$ ($M$ and $X$ being transition metal and chalcogen elements respectively), have been the focus of substantial interest recently because of their possible magnetism in the two-dimensional limit. Here we investigate material properties of the compounds with $M$ = Mn and Ni employing $\textit{ab-initio}$ density functional and dynamical mean-field calculations, especially their electronic behavior under external pressure in the paramagnetic phase. Mott metal-insulator transitions (MIT) are found to be a common feature for both compounds, but their lattice structures show drastically different behaviors depending on the relevant orbital degrees of freedom, i.e. $t_{\rm 2g}$ or $e_{g}$. MnPS$_3$ undergoes an isosymmetric structural transition by forming Mn-Mn dimers due to the strong direct overlap between the neighboring $t_{\rm 2g}$ orbitals, accompanied by a significant volume collapse and a spin-state transition. In contrast, NiPS$_3$ and NiPSe$_3$, with their active $e_g$ orbital degrees of freedom, do not show a structural change at the MIT pressure or deep in the metallic phase. Hence NiPS$_3$ and NiPSe$_3$ become rare examples of materials hosting electronic bandwidth-controlled Mott MITs, thus showing promise for ultrafast resistivity switching behavior.Comment: 5 pages, 4 figure

Nearly triple nodal point topological phase in half-metallic GdN

Recent developments in topological semimetals open a way to realize relativistic dispersions in condensed matter systems. One recently studied type of topological feature is the "triple nodal point" where three bands become degenerate. In contrast to Weyl and Dirac nodes, triple nodal points, which are protected by a rotational symmetry, have nodal lines attached, so that a characterization in terms of a chirality is not possible. Previous studies of triple nodal points considered nonmagnetic systems, although an artificial Zeeman splitting was used to probe the topological nature. Here instead we treat a ferromagnetic material, half-metallic GdN, where the splitting of the triple nodal points comes from the spin-orbit coupling. The size of the splitting ranges from 15 to 150 meV depending on the magnetization orientation, enabling a transition between a Weyl-point phase and a "nearly triple nodal point" phase that exhibits very similar surface spectra and transport properties compared to a true triple-node system. The rich topological surface states, manipulable via the orientation of the magnetization, make half-metallic GdN a promising platform for future investigations and applications