APLIKASI ALGORITMA FLOYD-WARSHALL DENGAN PENDEKATAN MADM DALAM MENENTUKAN RUTE TERPENDEK PENGANGKUTAN SAMPAH

Currently, the problem of environmental hygiene caused by the accumulation of garbage becomes a serious problem for every community. In addressing this problem, an efficient waste transport process is required. This study aims to find the shortest route of garbage transportation in Gorontalo city by using Floyd Warshall Algorithm by finding the smallest weight between each point (Vertex). In this study, the weights used in the Floyd Warshall Iteration Algorithm were Alternative weights obtained by the Multi-Attribute Decision-Making approach (MADM). The criteria for determining weights in MADM use three indicators that affect the efficiency of garbage transportation, namely Distance, time, and congestion. The route used in this study is the dump truck route with 17 garbage transportation points. After obtaining the Alternate weight and iteration using Floyd Warshall algorithm obtained the shortest route with the smallest trajectory weight of 110.845.

On the extremal points of the Lambda polytopes and classical simulation of quantum computation with magic states

We investigate the $\Lambda$-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, $\Lambda_n$, for every number $n$ of qubits. We establish two properties of the family $\{\Lambda_n, n\in \mathbb{N}\}$, namely (i) Any extremal point (vertex) $A_\alpha \in \Lambda_m$ can be used to construct vertices in $\Lambda_n$, for all $n>m$. (ii) For vertices obtained through this mapping, the classical simulation of quantum computation with magic states can be efficiently reduced to the classical simulation based on the preimage $A_\alpha$. In addition, we describe a new class of vertices in $\Lambda_2$ which is outside the known classification. While the hardness of classical simulation remains an open problem for most extremal points of $\Lambda_n$, the above results extend efficient classical simulation of quantum computations beyond the presently known range.

Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories

It is known that the four-dimensional Abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg–Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg–Wilson fermions, and therefore having a simpler fermion path-integral measure, it has been argued that the mirror fermions do not decouple: in the 345 model with Dirac– and Majorana–Yukawa couplings to the XY-spin field, the two-point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the paramagnetic strong-coupling phase. We re-examine why the attempt seems to be a “Mission: Impossible” in the 345 model. We point out that the effective operators to break the fermion number symmetries (‘t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana–Yukawa couplings. We also observe that the type of Majorana–Yukawa term considered is singular in the large limit due to the nature of the chiral projection of the Ginsparg–Wilson fermions, but a slight modification without such a singularity is allowed by virtue of their very nature. We then consider a simpler four-flavor axial gauge model, the $1^4(-1)^4$ model, in which the U(1)$_A$ gauge and Spin(6)(SU(4)) global symmetries prohibit the bilinear terms but allow the quartic terms to break all the other continuous mirror fermion symmetries. We formulate the model so that it is well behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte Carlo simulations in the weak gauge-coupling limit, we show numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows regular local behavior, and we argue that all you need is to kill the continuous mirror fermion symmetries with would-be gauge anomalies non-matched, as originally claimed by Eichten and Preskill. Finally, by gauging a U(1) subgroup of the U(1)$_A$$\times$ Spin(6)(SU(4)) of the previous model, we formulate the $2 1 (-1)^3$ chiral gauge model, and argue that the induced fermion measure term satisfies the required locality property and provides a solution to the reconstruction theorem formulated by Lüscher. This gives us “A New Hope” for the mission to be accomplished.

Universal Guard Problems

Given a set [Formula: see text] of [Formula: see text] points in the plane, how many universal guards are sometimes necessary and always sufficient to guard any simple polygon with vertex set [Formula: see text]? We call this problem a Universal Guard Problem and provide a spectrum of results. We give upper and lower bounds on the number of universal guards that are always sufficient to guard all polygons having a given set of [Formula: see text] vertices, or to guard all polygons in a given set of [Formula: see text] polygons on an [Formula: see text]-point vertex set. Our upper bound proofs include algorithms to construct universal guard sets of the respective cardinalities.

PELABELAN GRACEFUL GANJIL PADA GRAF DUPLIKASI DAN SPLIT BINTANG

Graph is not an empty a finite of the objects that called point (vertex) with the couple was not that is the side (edge). The set point denoted by , while the set edge denoted by . Odd graceful labeling on graph with side is a function injective from so that induced function such that in label with so label sides would be different. A graph that have an odd graceful labeling is called odd graceful graph. The result showed that duplicate star graph for and split star graph for , for even satisfie odd graceful labeling.

Weakly coupled gravity beyond general relativity

We explore four-dimensional (4D) weakly coupled gravity beyond general relativity in an on-shell language, focusing on the graviton three-point vertex. This admits a novel structure which can be attributed to a term cubic in the Riemann tensor. We consider a generalization of the Shapiro time delay experiment that involves polarized gravitons and show that the new vertex leads to causality violation. Fixing the problem demands the inclusion of an infinite tower of massive higher spin states. Perturbative string theory provides an example of this phenomenon, the only known so far. Interestingly enough, the same argument being applied to inflation suggests that stringy signatures may be hidden in the non-Gaussianities of the primordial gravity wave spectrum.