Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$ vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}} c_{Z,G,j}(\lambda_{Z,G,j})^m$, where $m$ denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for $N_{Z,G,j}$ for arbitrary $L_y$. We also present plots of zeros of the partition function in the $q$ plane for various values of $v$ and in the $v$ plane for various values of $q$. Explicit results for partition functions are given in the text for $L_y=2,3$ (free) and $L_y=4$ (cylindrical), and plots of partition function zeros are given for $L_y$ up to 5 (free) and $L_y=6$ (cylindrical). Plots of the internal energy and specific heat per site for infinite-length strips are also presented.Comment: 39 pages, 34 eps figures, 3 sty file

Survivability model for security and dependability analysis of a vulnerable critical system

This paper aims to analyze transient security and dependability of a vulnerable critical system, under vulnerability-related attack and two reactive defense strategies, from a severe vulnerability announcement until the vulnerability is fully removed from the system. By severe, we mean that the vulnerability-based malware could cause significant damage to the infected system in terms of security and dependability while infecting more and more new vulnerable computer systems. We propose a Markov chain-based survivability model for capturing the vulnerable critical system behaviors during the vulnerability elimination process. A high-level formalism based on Stochastic Reward Nets is applied to automatically generate and solve the survivability model. Survivability metrics are defined to quantify system attributes. The proposed model and metrics not only enable us to quantitatively assess the system survivability in terms of security risk and dependability, but also provide insights on the system investment decision. Numerical experiments are constructed to study the impact of key parameters on system security, dependability and profit

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Model-based sensitivity analysis of IaaS cloud availability

The increasing shift of various critical services towards Infrastructure-as-a-Service (IaaS) cloud data centers (CDCs) creates a need for analyzing CDCs’ availability, which is affected by various factors including repair policy and system parameters. This paper aims to apply analytical modeling and sensitivity analysis techniques to investigate the impact of these factors on the availability of a large-scale IaaS CDC, which (1) consists of active and two kinds of standby physical machines (PMs), (2) allows PM moving among active and two kinds of standby PM pools, and (3) allows active and two kinds of standby PMs to have different mean repair times. Two repair policies are considered: (P1) all pools share a repair station and (P2) each pool uses its own repair station. We develop monolithic availability models for each repair policy by using Stochastic Reward Nets and also develop the corresponding scalable two-level models in order to overcome the monolithic model''s limitations, caused by the large-scale feature of a CDC and the complicated interactions among CDC components. We also explore how to apply differential sensitivity analysis technique to conduct parametric sensitivity analysis in the case of interacting sub-models. Numerical results of monolithic models and simulation results are used to verify the approximate accuracy of interacting sub-models, which are further applied to examine the sensitivity of the large-scale CDC availability with respect to repair policy and system parameters

LSGAN-AT: enhancing malware detector robustness against adversarial examples

Adversarial Malware Example (AME)-based adversarial training can effectively enhance the robustness of Machine Learning (ML)-based malware detectors against AME. AME quality is a key factor to the robustness enhancement. Generative Adversarial Network (GAN) is a kind of AME generation method, but the existing GAN-based AME generation methods have the issues of inadequate optimization, mode collapse and training instability. In this paper, we propose a novel approach (denote as LSGAN-AT) to enhance ML-based malware detector robustness against Adversarial Examples, which includes LSGAN module and AT module. LSGAN module can generate more effective and smoother AME by utilizing brand-new network structures and Least Square (LS) loss to optimize boundary samples. AT module makes adversarial training using AME generated by LSGAN to generate ML-based Robust Malware Detector (RMD). Extensive experiment results validate the better transferability of AME in terms of attacking 6 ML detectors and the RMD transferability in terms of resisting the MalGAN black-box attack. The results also verify the performance of the generated RMD in the recognition rate of AME. © 2021, The Author(s)

Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set of possible spin values, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial $Ph(G,q,s,w)$ that counts the number of colorings of the vertices of $G$ subject to the condition that colors of adjacent vertices are different, with a weighting $w$ that favors or disfavors colors in the interval $I_s$. We derive powerful new upper and lower bounds on $Z(G,q,s,v,w)$ for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for $Z(G,q,s,v,w)$ on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur

Linear Amplifier Breakdown and Concentration Properties of a Gaussian Field Given that its L2\bm{L^2}-Norm is Large

In the context of linear amplification for systems driven by the square of a Gaussian noise, we investigate the realizations of a Gaussian field in the limit where its $L^2$-norm is large. Concentration onto the eigenspace associated with the largest eigenvalue of the covariance of the field is proved. When the covariance is trace class, the concentration is in probability for the $L^2$-norm. A stronger concentration, in mean for the sup-norm, is proved for a smaller class of Gaussian fields, and an example of a field belonging to that class is given. A possible connection with Bose-Einstein condensation is briefly discussed.Comment: REVTeX file, 11 pages, 1 added paragraph in the introduction, 2 added references, minor modifications in the text and abstract, submitted to J. Stat. Phy

Including spatial distribution in a data-driven rainfall-runoff model to improve reservoir inflow forecasting in Taiwan

Multi-step ahead inflow forecasting has a critical role to play in reservoir operation and management in Taiwan during typhoons as statutory legislation requires a minimum of 3-hours warning to be issued before any reservoir releases are made. However, the complex spatial and temporal heterogeneity of typhoon rainfall, coupled with a remote and mountainous physiographic context makes the development of real-time rainfall-runoff models that can accurately predict reservoir inflow several hours ahead of time challenging. Consequently, there is an urgent, operational requirement for models that can enhance reservoir inflow prediction at forecast horizons of more than 3-hours. In this paper we develop a novel semi-distributed, data-driven, rainfall-runoff model for the Shihmen catchment, north Taiwan. A suite of Adaptive Network-based Fuzzy Inference System solutions is created using various combinations of auto-regressive, spatially-lumped radar and point-based rain gauge predictors. Different levels of spatially-aggregated radar-derived rainfall data are used to generate 4, 8 and 12 sub-catchment input drivers. In general, the semi-distributed radar rainfall models outperform their less complex counterparts in predictions of reservoir inflow at lead-times greater than 3-hours. Performance is found to be optimal when spatial aggregation is restricted to 4 sub-catchments, with up to 30% improvements in the performance over lumped and point-based models being evident at 5-hour lead times. The potential benefits of applying semi-distributed, data-driven models in reservoir inflow modelling specifically, and hydrological modelling more generally, is thus demonstrated

Estimates of hypolimnetic oxygen deficits in ponds

Shallow tropical integrated culture ponds in the Pearl River Delta, China, have been found to stratify almost daily, with high organic loadings and dense algal growth. The dissolved oxygen (DO) concentration is super-saturated in the epilimnion and is under 2 mg/l in the hypolimnion (>1m). The compensation depth corresponds to twice the Secchi disk depth ranging from 50 to 80cm. As a result, little or no net oxygen is produced in the hypolimnion (>1m). The low DO concentration in the hypolimnion causes organic materials, such as unused organic wastes and senescent algae cells, to be incompletely oxidized, since the rate of oxygen consumption by oxidable matter in water is dependent on the dissolved oxygen concentration in water. This material becomes the source of hypolimnetic oxygen deficits (HOD) which can drive whole pond DO to a dangerously low level, should sudden destratification occur. An improved estimate of hypolimnetic oxygen deficits is introduced in this article, and the advantages of this method are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72126/1/j.1365-2109.1989.tb00341.x.pd

Stoichiometry control of magnetron sputtered Bi2_2Sr2_2Ca1−x_{1-x}Yx_xCu2_2Oy_y (0≤\lex≤\le0.5) thin film, composition spread libraries: Substrate bias and gas density factors

A magnetron sputtering method for the production of thin-film libraries with a spatially varying composition, x, in Bi2Sr2Ca1-xYxCu2Oy (0<=x<=0.5) has been developed. Two targets with a composition of Bi2Sr2YCu2O_{8.5 + \delta} and Bi_2Sr_2CaCu_2O_{8 + \delta} are co-sputtered with appropriate masks. The target masks produce a linear variation in opposite, but co-linear radial direction, and the rotation speed of the substrate table is sufficient to intimately mix the atoms. EDS/WDS composition studies of the films show a depletion of Sr and Bi that is due to oxygen anion resputtering. The depletion is most pronounced at the centre of the film (i.e. on-axis with the target) and falls off symmetrically to either side of the 75 mm substrate. At either edge of the film the stoichiometry matches the desired ratios. Using a 12 mTorr process gas of argon and oxygen in a 2:1 ratio, the strontium depletion is corrected. The bismuth depletion is eliminated by employing a rotating carbon brush apparatus which supplies a -20 V DC bias to the sample substrate. The negative substrate bias has been used successfully with an increased chamber pressure to eliminate the resputtering effect across the film. The result is a thin film composition spread library with the desired stoichiometry.Comment: 16 pages, 12 figures, 4 tables, submitted to Physica C - Superconductivity (April 15, 2005), elsart.st