Biased random satisfiability problems: From easy to hard instances

In this paper we study biased random K-SAT problems in which each logical variable is negated with probability $p$. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the typical complexity of random K-SAT problems. The exact solution of 1-SAT case is given. The critical point of K-SAT problems and results of replica method are derived in the replica symmetry framework. It is found that in this approximation $\alpha_c \propto p^{-(K-1)}$ for $p\to 0$. Solving numerically the survey propagation equations for K=3 we find that for $p<p^* \sim 0.17$ there is no replica symmetry breaking and still the SAT-UNSAT transition is discontinuous.Comment: 17 pages, 8 figure

Effects of Arbuscular Mycorrhizal Fungi and Phosphorus Supplement on Leaf P, Zn, Cu and Fe Concentrations of Tea Seedlings

Influence of arbuscular mycorrhizal fungi (AMF) (Glomus etunicatum, G. intraradices and Glomus versiforme) and external phosphorus supplement (8 and 35 mg P Kg-1 soil) on leaf P, Zn, Cu and Fe nutrition of 4-month-old tea(Camellia sinensis) was studied in an glass house pot experiment. The highest leaf P concentration (up to 59.43% increase) was found in G. versiforme inoculated seedlings grown in the zero mg P Kg-1 soil, compared to the control seedlings. Higher level of Zn, Cu, and Fe concentrations were found in plants inoculated with G. intraradices as compared to other treatments. Our results showed that inoculation with G. intraradices had greater effect on uptaking of P, Zn, Cu, and Fe by tea seedlings than inoculation with either G. etunicatum or G. versiforme

A Modal Series Representation of Genesio Chaotic System

In this paper an analytic approach is devised to represent, and study the behavior of, nonlinear dynamic chaotic Genesio system using general nonlinear modal representation. In this approach, the original nonlinear ordinary differential equations (ODEs) of model transforms to a sequence of linear time- invariant ODEs. By solving the proposed linear ODEs sequence, the exact solution of the original nonlinear problem is determined in terms of uniformly convergent series. Also an efficient algorithm with low computational complexity and high accuracy is presented to find the approximate solution. Simulation results indicate the effectiveness of the proposed method.Comment: International Journal of Instrumentation and Control Systems (IJICS) Vol.2, No.3, July 201

Simplifying Random Satisfiability Problem by Removing Frustrating Interactions

How can we remove some interactions in a constraint satisfaction problem (CSP) such that it still remains satisfiable? In this paper we study a modified survey propagation algorithm that enables us to address this question for a prototypical CSP, i.e. random K-satisfiability problem. The average number of removed interactions is controlled by a tuning parameter in the algorithm. If the original problem is satisfiable then we are able to construct satisfiable subproblems ranging from the original one to a minimal one with minimum possible number of interactions. The minimal satisfiable subproblems will provide directly the solutions of the original problem.Comment: 21 pages, 16 figure

Basal complex: a smart wing component for automatic shape morphing

Insect wings are adaptive structures that automatically respond to flight forces, surpassing even cutting-edge engineering shape-morphing systems. A widely accepted but not yet explicitly tested hypothesis is that a 3D component in the wing’s proximal region, known as basal complex, determines the quality of wing shape changes in flight. Through our study, we validate this hypothesis, demonstrating that the basal complex plays a crucial role in both the quality and quantity of wing deformations. Systematic variations of geometric parameters of the basal complex in a set of numerical models suggest that the wings have undergone adaptations to reach maximum camber under loading. Inspired by the design of the basal complex, we develop a shape-morphing mechanism that can facilitate the shape change of morphing blades for wind turbines. This research enhances our understanding of insect wing biomechanics and provides insights for the development of simplified engineering shape-morphing systems

Solution to Satisfiability problem by a complete Grover search with trapped ions

The main idea in the original Grover search (Phys. Rev. Lett. 79, 325 (1997)) is to single out a target state containing the solution to a search problem by amplifying the amplitude of the state, following the Oracle's job, i.e., a black box giving us information about the target state. We design quantum circuits to accomplish a complete Grover search involving both the Oracle's job and the amplification of the target state, which are employed to solve Satisfiability (SAT) problems. We explore how to carry out the quantum circuits by currently available ion-trap quantum computing technology.Comment: 14 pages, 6 figure

Simple models of small world networks with directed links

We investigate the effect of directed short and long range connections in a simple model of small world network. Our model is such that we can determine many quantities of interest by an exact analytical method. We calculate the function $V(T)$, defined as the number of sites affected up to time $T$ when a naive spreading process starts in the network. As opposed to shortcuts, the presence of un-favorable bonds has a negative effect on this quantity. Hence the spreading process may not be able to affect all the network. We define and calculate a quantity named the average size of accessible world in our model. The interplay of shortcuts, and un-favorable bonds on the small world properties is studied.Comment: 15 pages, 9 figures, published versio

Cycle-based Cluster Variational Method for Direct and Inverse Inference

We elaborate on the idea that loop corrections to belief propagation could be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define region in a generalized belief propagation setting. The region graph is specified in such a way as to avoid dual loops as much as possible, by discarding redundant Lagrange multipliers, in order to facilitate the convergence, while avoiding instabilities associated to minimal factor graph construction. We end up with a two-level algorithm, where a belief propagation algorithm is run alternatively at the level of each cycle and at the inter-region level. The inverse problem of finding the couplings of a Markov random field from empirical covariances can be addressed region wise. It turns out that this can be done efficiently in particular in the Ising context, where fixed point equations can be derived along with a one-parameter log likelihood function to minimize. Numerical experiments confirm the effectiveness of these considerations both for the direct and inverse MRF inference.Comment: 47 pages, 16 figure

3D imaging of colorectal cancer organoids identifies responses to Tankyrase inhibitors

Aberrant activation of the Wnt signalling pathway is required for tumour initiation and survival in the majority of colorectal cancers. The development of inhibitors of Wnt signalling has been the focus of multiple drug discovery programs targeting colorectal cancer and other malignancies associated with aberrant pathway activation. However, progression of new clinical entities targeting the Wnt pathway has been slow. One challenge lies with the limited predictive power of 2D cancer cell lines because they fail to fully recapitulate intratumoural phenotypic heterogeneity. In particular, the relationship between 2D cancer cell biology and cancer stem cell function is poorly understood. By contrast, 3D tumour organoids provide a platform in which complex cell-cell interactions can be studied. However, complex 3D models provide a challenging platform for the quantitative analysis of drug responses of therapies that have differential effects on tumour cell subpopulations. Here, we generated tumour organoids from colorectal cancer patients and tested their responses to inhibitors of Tankyrase (TNKSi) which are known to modulate Wnt signalling. Using compounds with 3 orders of magnitude difference in cellular mechanistic potency together with image-based assays, we demonstrate that morphometric analyses can capture subtle alterations in organoid responses to Wnt inhibitors that are consistent with activity against a cancer stem cell subpopulation. Overall our study highlights the value of phenotypic readouts as a quantitative method to asses drug-induced effects in a relevant preclinical model