This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions the symmetric traveling-salesman problem. The is based on general approach to heuristics that believed have wide applicability in combinatorial optimization problems. produces all problems tested, “classical” appearing literature, as well randomly generated test problems, up 110 cities. Run times grow approximately n 2 ; absolute terms, typical 100-city problem requires less than 25...

von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through commutation theorem, rendering it useful tool constructing gauge-invariant algebras. Type III algebra with its modular automorphism group is semifinite, which means that regulates divergences local quantum field theories. In this article, we find sufficient condition semifiniteness locally...

A bstract In holographic theories, the reflected entropy has been shown to be dual area of entanglement wedge cross section. We study same problem in random tensor networks demonstrating an equivalent duality. For a single we analyze important non-perturbative effects that smooth out discontinuity across Page phase transition. By summing over all such effects, obtain spectrum analytically, which agrees well with numerical studies. This motivates prescription for analytic continuation...

A bstract We study the reflected entropy S R in West Coast Model, a toy model of black hole evaporation consisting JT gravity coupled to end-of-the-world branes. demonstrate validity holographic duality relating it entanglement wedge cross section away from phase transitions. Further, we analyze important non-perturbative effects that smooth out discontinuity transition. By performing gravitational path integral, obtain spectrum analytically. The takes simple form superselection sectors,...

A bstract In ref. [1], we analyzed the reflected entropy ( S R ) in random tensor networks motivated by its proposed duality to entanglement wedge cross section EW holographic theories, $$ {S}_R=2\frac{EW}{4G} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mfrac> <mml:mi>EW</mml:mi> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>G</mml:mi> </mml:mrow> </mml:mfrac> </mml:math> . this...

The entanglement of purification <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>E</a:mi><a:mi>P</a:mi></a:msub><a:mo stretchy="false">(</a:mo><a:mi>A</a:mi><a:mo>∶</a:mo><a:mi>B</a:mi><a:mo stretchy="false">)</a:mo></a:math> is a powerful correlation measure, but it notoriously difficult to compute because involves an optimization over all possible purifications. In this paper, we prove new inequality: <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"...

A bstract We investigate the multi-partite entanglement structure of an evaporating black hole and its Hawking radiation by dividing into finer subsystems. approximate with a Haar-random state for this purpose. Using multi-entropy these configurations, we define curve , which describes how changes during evaporation. This is natural generalization Page since reduces to entropy bi-partite case. The keeps increasing in early time. It reaches maximum value at time later than time, starts...

This paper discusses the nature of problem solving by heuristic techniques. It also proposes several guidelines which have proven to be useful in construction effective algorithms solve a variety combinatorial optimization problems.

A bstract For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through network. This generalizes cut description of bipartite entanglement for these states. natural extrapolation away parameters, suggested problem, implies holographic conjecture S R = 2EW, where is entropy and EW wedge cross-section. Minimal can be formulated as programs which cannot relaxed to...

We consider the reflected entropy and associated entanglement spectrum for free fermions reduced to two intervals in 1+1 dimensions. Working directly continuum theory can be extracted from of a singular integral equation whose kernel is determined by known fermion modular evolved correlation function. find numerically analytically certain limits. For that almost touch approaches thermal density matrix. This suggests well suited task extracting physical data ground state wave

von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through commutation theorem, rendering it useful tool constructing invariant algebras. Type III algebra with its modular automorphism group is semifinite, which means that regulates divergences local quantum field theories. In this letter, we find sufficient condition semifiniteness type any locally...

This paper discusses a heuristic solution procedure for combinatorial optimization problem that originates in designing signal constellations modems. The design is to place m signals two-dimensional space minimize the average error rate under specified noise conditions, using maximum-likelihood decoding scheme. Intuitively, it amounts (roughly) spreading points as far apart possible, according distance measurement implied by function. We show how this can be reduced discrete one: Given an ℓ...

DNA is a universal language encrypted with biological instruction for life. In higher organisms, the genetic information preserved predominantly in an organized exon/intron structure. When gene expressed, exons are spliced together to form transcript protein synthesis. We have developed complexity reduction algorithm sequence analysis (CRASA) that enables direct alignment of cDNA sequences genome. This method features progressive data structure hierarchical orders facilitate fast and...

Next Generation Sequencing machines are generating millions of short DNA sequences (reads) everyday. There is a need for efficient algorithms to map these the reference genome identify SNPs or rare transcripts and fulfill dream personalized medicine. We present Fast Algorithm Sequencers (FANGS), which dynamically reduces search space by using q-gram filtering pigeon hole principle rapidly 454-Roche reads onto genome. FANGS sequential algorithm designed find all matches query sequence in...

Agent-based simulation models provide a way to investigate social phenomena that complement existing science methods. Recent advances in computing hardware such as the wide availability of multi-core CPUs and increased main memory capacities make it possible population-scale using commodity compute resources. This paper describes experiences made development an example model utilises multiple CPU cores investigation scalability resulting code. We argue resources commoditised frameworks can...

The exact closed forms of the partition functions a two-dimensional Ising model on square lattices with twisted boundary conditions are given. constructions helical tori unambiguously related to by virtue $SL(2,Z)$ transforms. numerical analyses deviations specific-heat peaks away from bulk critical temperature reveal that finite-size effect herical is independent chirality.

Millions of DNA sequences (reads) are generated by Next Generation Sequencing machines everyday. There is a need for high performance algorithms to map these the reference genome identify single nucleotide polymorphisms or rare transcripts fulfill dream personalized medicine. In this paper, we present high-throughput parallel sequence mapping program pFANGS. pFANGS designed find all matches query in tolerating large number mismatches insertions/deletions. partitions computational workload...

For general random tensor network states at large bond dimension, we prove that the integer R\'enyi reflected entropies (away from phase transitions) are determined by minimal triway cuts through network. This generalizes cut description of bipartite entanglement for these states. A natural extrapolation away parameters, suggested problem, implies holographic conjecture $S_R=2EW$, where $S_R$ is entropy and $EW$ wedge cross-section. Minimal can be formulated as programs which cannot relaxed...

We apply Plechko's Grassmann path-integral method to Ising cylinders of rectangular, triangular, and hexagonal lattices obtain the analytic solutions free energies for periodic antiperiodic boundary conditions in joined circumferences cylinders. These are used analyze scaling functions interfacial tensions isotropic anisotropic couplings. The finite-size corrections also discussed.

The distribution of partition function zeros the two-dimensional Ising model in complex temperature plane is studied within context triangular decorated lattices and their triangle-star transformations. Exact recursion relations for are deduced description evolution subject to change decoration level. In limit infinite level, essentially possess Sierpiński gasket or its transformation as inherent structure. positions shown coincide with ones transformation, distributions all appear be a...